Journal of Mechanical Engineering 2012 2

58 (2012) 2

http://www.sv-jme.eu

Strojniški vestnik Journal of Mechanical Engineering

Since 1955

Papers

73

Aleš Petek, Karl Kuzman: Backward Hole-Flanging Technology Using an Incremental Approach

81

Fuqing Zhao, Jizhe Wang, Junbiao Wang, Jonrinaldi Jonrinaldi: A Dynamic Rescheduling Model with Multi-Agent System and Its Solution Method

93

Suzana Uran, Riko Šafarič: Neural-Network Estimation of the Variable Plant for Adaptive Sliding-Mode Controller

102

Bohumil Taraba, Steven Duehring, Ján Španielka, Štefan Hajdu: Effect of Agitation Work on Heat Transfer during Cooling in Oil ISORAPID 277HM

107

Gorazd Krese, Matjaž Prek, Vincenc Butala: Analysis of Building Electric Energy Consumption Data Using an Improved Cooling Degree Day Method

115

Matej Volk, Marko Nagode, Matija Fajdiga: Finite Mixture Estimation Algorithm for Arbitrary Function Approximation

125

Saeed Daneshmand, Cyrus Aghanajafi: Description and Modeling of the Additive Manufacturing Technology for Aerodynamic Coefficients Measurement

Zlatko Rek, Mitja Rudolf, Iztok Zun: 134 Application of CFD Simulation in the Development of a New Generation Heating Oven

Journal of Mechanical Engineering - Strojniški vestnik

Contents

2 year 2012 volume 58 no.

Strojniški vestnik – Journal of Mechanical Engineering (SV-JME) Aim and Scope The international journal publishes original and (mini)review articles covering the concepts of materials science, mechanics, kinematics, thermodynamics, energy and environment, mechatronics and robotics, fluid mechanics, tribology, cybernetics, industrial engineering and structural analysis.

The journal follows new trends and progress proven practice in the mechanical engineering and also in the closely related sciences as are electrical, civil and process engineering, medicine, microbiology, ecology, agriculture, transport systems, aviation, and others, thus creating a unique forum for interdisciplinary or multidisciplinary dialogue.

The international conferences selected papers are welcome for publishing as a special issue of SV-JME with invited co-editor(s).

Editor in Chief Vincenc Butala University of Ljubljana Faculty of Mechanical Engineering, Slovenia Co-Editor Borut Buchmeister University of Maribor Faculty of Mechanical Engineering, Slovenia Technical Editor Pika Škraba University of Ljubljana Faculty of Mechanical Engineering, Slovenia Editorial Office University of Ljubljana (UL) Faculty of Mechanical Engineering SV-JME Aškerčeva 6, SI-1000 Ljubljana, Slovenia Phone: 386-(0)1-4771 137 Fax: 386-(0)1-2518 567 E-mail: info@sv-jme.eu http://www.sv-jme.eu Founders and Publishers University of Ljubljana (UL) Faculty of Mechanical Engineering, Slovenia University of Maribor (UM) Faculty of Mechanical Engineering, Slovenia Association of Mechanical Engineers of Slovenia Chamber of Commerce and Industry of Slovenia Metal Processing Industry Association Cover: In the middle figure presents modern manufacturing concept called the “backward incremental hole-flanging process”, which may be applied as an additional technology in multi-step forming operations and enables the formation of necks outward or inward on complex 3D products in small quantities, effectively and with minimal costs. One example of such complex product with incrementally performed symmetrical necks is shown on the cover above. The technology could be applied for symmetrical as well as for asymmetrical shapes of the necks, as shown in Figure below.

Image courtesy: Forming Laboratory, Faculty of Mechanical Engineering, University of Ljubljana, Slovenia, EMO-Orodjarna Production Company, Slovenia

ISSN 0039-2480 © 2011 Strojniški vestnik - Journal of Mechanical Engineering. All rights reserved. SV-JME is indexed / abstracted in: SCI-Expanded, Compendex, Inspec, ProQuest-CSA, SCOPUS, TEMA. The list of the remaining bases, in which SV-JME is indexed, is available on the website. The journal is subsidized by Slovenian Book Agency.

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Strojniški vestnik - Journal of Mechanical Engineering 58(2012)2 Contents

Contents Strojniški vestnik - Journal of Mechanical Engineering volume 58, (2012), number 2 Ljubljana, February 2012 ISSN 0039-2480 Published monthly

Papers Aleš Petek, Karl Kuzman: Backward Hole-Flanging Fechnology Using an Incremental Approach Fuqing Zhao, Jizhe Wang, Junbiao Wang, Jonrinaldi Jonrinaldi: A Dynamic Rescheduling Model with Multi-Agent System and Its Solution Method Suzana Uran, Riko Šafarič: Neural-Network Estimation of the Variable Plant for Adaptive SlidingMode Controller Bohumil Taraba, Steven Duehring, Ján Španielka, Štefan Hajdu: Effect of Agitation Work on Heat Transfer during Cooling in Oil ISORAPID 277HM Gorazd Krese, Matjaž Prek, Vincenc Butala: Analysis of Building Electric Energy Consumption Data Using an Improved Cooling Degree Day Method Matej Volk, Marko Nagode, Matija Fajdiga: Finite Mixture Estimation Algorithm for Arbitrary Function Approximation Saeed Daneshmand, Cyrus Aghanajafi: Description and Modeling of the Additive Manufacturing Technology for Aerodynamic Coefficients Measurement Zlatko Rek, Mitja Rudolf, Iztok Zun: Application of CFD Simulation in the Development of a New Generation Heating Oven

73 81 93 102 107 115 125 134

Strojniški vestnik - Journal of Mechanical Engineering 58(2012)2, 73-80 DOI:10.5545/sv-jme.2011.194

Paper received: 2011-09-02, paper accepted: 2011-11-10 © 2012 Journal of Mechanical Engineering. All rights reserved.

Backward Hole-Flanging Fechnology Using an Incremental Approach Petek, A. – Kuzman, K. Aleš Petek1,* – Karl Kuzman2

1 Difa

d.o.o., Slovenia; 2 University of Ljubljana, Faculty of Mechanical Engineering, Slovenia

The manufacturing of necks on the sheet metal parts using conventional hole-flanging process in small series production is sometimes too expensive or even impossible due to the complexity of the product. For these reasons, a modern manufacturing concept called the “backward incremental hole-flanging process” is proposed. It enables producing necks on the final products that can be very complex or even closed with minimal expense.

Special attention is dedicated to researching technological particularities and limitations according to industrial requirements. Due to numerous input factors having various levels of influence, empirical modelling was selected with the aim of ensuring better prediction of results. It enables predicting the impact of each particular input parameter and their iterations on the selected output variables. Results show that forming tool diameter, and horizontal and vertical step sizes have the greatest influence on the process. Moreover, the appropriate selection of process parameters results on a higher forming limit ratio and consequently, on larger necks achieved without cracks in comparison to the conventional hole-flanging process. The reason could be found in local incremental deformation of the sheet metal and a more suitable stress state.

Keywords: backward hole-flanging, incremental forming, sheet metal

0 INTRODUCTION In tool making companies working on automotive sheet metal parts, the definition of the forming procedure is one of the most important tasks, especially for producing prototypes or parts in small quantities, e.g. products for crash tests. Some parts can be very complex; therefore, their production requires the application of numerous forming steps.

In such cases, the forming tools are very large and made of various subsystems. Sometimes they consist of movable elements that are used to form a product, e.g. perpendicular to the press motion from the inner or outer sides to produce shapes like necks, as shown in Fig. 1. Usually, a conventional technology called the hole-flanging process is applied to produce necks.

Unfortunately, this technology drastically increases the complexity of the tool, tool costs and consequently product costs.

Fig. 1. The need for movable system inside the forming tool to produce necks outwards, source: EMO-Orodjarna

For these reasons, it is necessary to find a new solution in order to eliminate movable parts inside

complex forming tools, to increase technological flexibility, and reduce tool and product costs. Such an approach may be the most useful when producing necks that are very hard to do by the conventional hole-flanging process due to a lack of space inside the forming tool, and for necks on products which are almost closed (Fig. 1).

1 ANALYSIS OF EXISTING WORK The conventional hole-flanging process has been studied widely. Johnson et al. [1] investigated the influence of the materials’ plastic characteristic and performed an experimental study on the deformation of circular plates. Spur and Stoferle [2] presented how the technology for producing an initial hole influences the forming ratio, which is defined as relation between final part diameter (DFH) and initial hole diameter (DIH). They showed that the initial holes produced by drilling enable a higher limit-forming ratio in contrast to piercing, as shown in Fig. 2. The reason could be found in material hardening during the piercing process at the cut edge where the material is subjected to shear stresses. Due to this deformation, the failure on the neck periphery occurs earlier. Furthermore, they describe the hole-flanging process with a backing holder, in order to achieve higher forming ratio. In this case, the material is pressed between the punch and backing holder, where it is subjected to compression stresses. Such a condition postpones failure occurrence in the material.

Some authors dealt with their investigations of the conventional hole-flanging process in digital

*Corr. Author’s Address: Difa d.o.o., Kidričeva cesta 91, 4220 Škofja Loka, Slovenia, ales.petek@difa.si

73

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as well as in the real environment, e.g. Huang and Chien [3] and Leu [4]. They concentrate on the neck thickness distribution and the limit forming ratio. It was discovered that the deformation around the hole periphery is a combination of bending and stretching.

There are other important studies.

Fig. 2. Forming ratio (DFH/DIH) in dependence of the ratio between initial hole diameter and sheet thickness (t0) for the initial hole produced by a) drilling and b) piercing [2]

However, in recent years the global market has required inexpensive and flexible metal forming systems, which are capable of dealing with small quantity production and prototypes of different shapes. In these cases, the conventional hole-flanging process is not the most appropriate since it requires dedicated punches and dies. For these reasons, the hole-flanging process became a challenge in applying a modern technological approach called “incremental sheet metal forming”. This technology enables forming different neck shapes using only one simple forming tool irrespective of the product complexity and its deformation history. Incremental forming is a universal expression of those forming processes in which simple forming tool shapes, instead of die sets that are designed exclusively for particular product shapes, are used to form a small portion of the product consecutively until the required shape is formed. Cui and Gao [5] applied the incremental forming process to produce flanged parts using three different forming strategies. They discovered that by using optimum forming parameters parts can be obtained with even finer neck thickness and relatively longer neck heights. There are also other papers dealing with the hole-flanging process using an incremental approach, but in all cases the researcher formed necks in the forward direction. Such technology does not enable the neck formation outwards from product that are almost closed, as presented in Fig. 1. For these cases, a novel technology called the “backward incremental hole-flanging process” (BIHF) has been studied to be applied as an additional technology in multi-step 74

forming. Firstly, it is developed to produce necks that are impossible to form with forward incremental hole-flanging process and very difficult to form with classical operation due to the lack of space inside the forming tool (Fig. 1). The major differences compared to incremental sheet metal forming process (ISMF) and forward incremental hole-flanging process are in tool path kinematics, forming direction and forming tool geometry. The latter should have a high ratio between tool head diameter and rod diameter, enabling larger incremental movements in the horizontal direction and achieving higher forming ratios since the minimal initial hole diameter is limited with the forming tool rod.

Since BIHF technology is new, the main emphasis is on the studies of technological particularities and limitations according to industrial requirements. Due to a large number of process parameters influencing the results, empirical modelling was applied. It enables predicting the impact of each particular input parameter and their iterations on the selected output variables. Such analyses are indispensable, especially with newer technologies where the knowledge of the process is still not sufficiently clear. Usually, they are performed using the design of experiments and analysis of variance.

2 PROCESS DESCRIPTION Generally, hole-flanging is a process used to displace the material around a hole in a flat sheet to form symmetrical or asymmetrical necks or flanges. The BIHF process presented in this investigation is based on asymmetric single point incremental sheet metal forming. A desired shape of the neck is produced by the CNC-controlled movement of a flexible rodshaped forming tool with a smooth spherical head, which is clamped into the spindle of the forming machine. The sheet metal is fixed and positioned with the upper blank holder in which the faceplate is placed. Both are pressed onto the lower blank holder and remain fixed throughout the procedure. After the milling the required hole located in the center of the specimen, the forming tool head moves through the hole below the sheet metal and locally deforms the sheet with the upper part of the tool head. It is worth pointing out that the tool presses the sheet from the opposite direction, as is common with all variants of asymmetric incremental forming processes until now.

The tool follows the predetermined tool path and gradually forms the sheet metal in a series of incremental steps until the final neck shape is reached. In the first forming step, the forming tool

Petek, A. – Kuzman, K.

Strojniški vestnik - Journal of Mechanical Engineering 58(2012)2, 73-80

path is defined according to the size and shape of the initial hole of the specimen, which is limited with the diameter of the spherical tool head or tool rod, and the increment of the spherical path in the z direction. In additional forming steps, the tool path is defined as Dx and Dz, representing an increase of spiral path in the horizontal x- direction and the spiral step in the vertical z- direction, respectively. The steps of the BIHF process are shown in Fig. 3; h represents final neck height.

forming tool and the workpiece, a lubricant oil was used, as in severe deep drawing operations [13].

Fig. 3. BIHF process set-up

Fig. 4. Initial specimen with milled hole (left) and final test part (right), source: EMO-Orodjarna

3 EXPERIMENTAL PROCEDURE The experimental work was carried out on a CNCcontrolled milling machine (FAMUP). The basic technological parameters needed to perform the experimental test are presented in Fig. 3 (i.e. vR [rpm] – tool rotation speed, h [mm] – forming height, dRT [mm] – tool diameter, Δz [mm] – vertical step size of the spiral, Δx [mm] – horizontal step size and fRT [mm/ min] – feed rate). They were determined on the basis of preliminary research of the BIHF [6] and [7] as well as asymmetric single point incremental forming made by Petek et al. [8] to [11] and Jeswiet et al. [12].

The tool path includes the movement in 3D space, as well as the synchronized rotation along the z-axis. To avoid sheet metal positioning problems, the center hole was milled right after the clamping procedure.

Technological particularities and limitations were analysed on the simple axi-symmetrical necks presented in Fig. 4. The initial hole diameter of the specimen (DIH) was set to 28 mm and the final hole diameter (DFH) to 80 mm in all experimental tests.

Due to its frequent use in the automotive sheet metal forming industry, DC05 steel of 1.2 mm in thickness was used as specimen material. In order to avoid any undesired issues arising from friction between the

3.1 Empirical Modeling The empirical model is based on the process investigation on the adequately structural design of the forming system and the examination of the connection between the process inputs and outputs on the system level, using various statistical methods.

The performance of the empirical model depends on a large number of factors that act and interact in a complex manner. From among numerous methods of empirical modelling, regression analysis was selected.

3.2 Design of Experiment The design of the experiment is required to extract meaningful conclusions from the process responses.

Adequate experimental design requires competent process knowledge for selection factors and their levels, which could possibly significantly influence the response. Errors and inaccuracies at this stage could nullify experimental validity as suggested by Myers and Montgomery [14].

The development of the BIHF regression models is based on the central composite design (CCD) of experiments, which enables developing the secondorder response surface model in the formation of quadratic regression function. The central composite design is a two-level full factorial with nf factorial points, augmented with additional n0 centre and 2p axial points. Axial points are located at a specific distance of αDOE from the design centre in each direction in each axis. The factorial points represent a first-order model, while centre points, set to the midpoint of each range, provide information about the existence of curvature. In addition, axial points allow an estimation of the pure quadratic properties of the model.

Backward Hole-Flanging Fechnology Using an Incremental Approach

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The design of the experiments requires selecting the levels of input data, so that the regression matrix is fully determined, and that the matrix ensures the conditions of orthogonality, rotatability and symmetry.

The input process parameters were selected on the basis of preliminary tests, available literature sources and output variables chosen according to industrial requirements. In industrial practice, how the forming process is performed is often important; therefore, it is necessary to define neck height and its thinning and consequently, the limit forming ratio (LFR), since it is well known that the size of initial hole of the specimen is directly related to the fracture occurrence on the neck periphery. The knowledge of these output variables and their most influential input parameters leads to making the required product without problems. According to the above-mentioned four important input process parameters are selected: dRT [mm] – tool diameter, Δz [mm] – vertical step size of the spiral, Δx [mm] – horizontal step size and fRT [mm/min] – feed rate.

To define the influence of input process parameters on output variables, the central composite design of the experiment includes four controllable process factors (p = 4), whose levels are presented in Table 1. The convention of coding the factor levels is followed so the design points have coded levels for each factor. The region of interest, coded {‒1,1}, is the region determined by the lower and upper limits on the factor level setting combinations that are of major interest. The central composite design extends the region of interest to the region of operability, coded {‒2,2}, which is determined by the lower and upper factor level setting combinations that can be operationally achieved with acceptable safety and that will output a testable component.

In this research, 30 sets of experiments are sorted, using standard ordering, and are carried out in an accordance to experimental design matrix. Under the previously determined convention, there are 2p, eight axial points located at specific distance αDOE = 2 from the design centre in each direction on each axis defined by the coded factor levels. The applied design further includes 2p, 16 single-replicated orthogonal factorial points and is augmented by six centre points.

4 RESULTS AND EVALUATION 4.1 Design Evaluation The evaluation of the design itself is based on an advanced regression matrix analysis for the selected response surface model. In some response 76

surface designs, there can be one or more nonlinear dependencies, among the model regressors.

Such multi-collinearities can seriously affect the model coefficient estimates. Multi-collinearity is indicated by the variance inflation factor (VIF), which quantitatively expresses the variances of regression coefficients regarding to the orthogonality of the regression coefficient matrix. In case that particular regression coefficient is orthogonal regarding all the other factors in the model, the VIF is equal to 1. A VIF exceeding 10 indicates problems due to multicollinearity, as proposed by Myers and Montgomery [14]. For instance, the employed central composite design VIF values are 1 for linear and interaction regression coefficients and 1.05 for quadratic regression coefficients. From this multi-collinearity analysis, it can be concluded that the design is nearly orthogonal.

Further ascertainment is proved by the condition number, which originates in the eigenvalues of the correlation matrix. Eigenvalues near zero imply the presence of multi-collinearity. The calculated condition number of coefficient number is 1.67.

Generally, the condition number of near orthogonal design with low multi-collinearity should not exceed 100, as proposed by Myers and Montgomery [14].

Fig. 5. Standard error of the central composite design plot

Additional design evaluation criteria relates to leverage. Leverage has potential for a design point to influence the fit of the regression coefficients.

The disposition of design points is important in determining model properties. Particularly remote observations have disproportionate leverage on coefficient estimates, the predicted responses and the usual summary statistics. Leverage values are diagonal elements of the hat matrix. The average CCD leverage is 0.5, which means that the design space is not constrained. Generally, high leverage points, those

Petek, A. – Kuzman, K.

Strojniški vestnik - Journal of Mechanical Engineering 58(2012)2, 73-80

Table 1. Design factors and their levels Forming parameters Tool diameter [mm] Vertical step size [mm] Horizontal step size [mm] Feed rate [mm/min]

Symbol dRT Δz Δx fRT

-2 18 0.1 1 1200

close to 1, should be avoided as proposed by Myers and Montgomery [14].

The last considered design evaluation criterion refers to G- efficiency, which is the average prediction variance as a percentage of the maximum prediction variance. The aim of good design is G- efficiency of at least 50%, as proposed by Krajnik et al. [15]. In the applied design, the calculated G- efficiency from the design points is 85.7%, which is adequate.

In addition to numerical statistics for design evaluation, it is useful to plot the standard error over the investigated design space, which measures the estimation accuracy of mean arithmetic prediction (Fig. 5). The plot shows how the error in the predicted response varies over the design space. Because of fewer experiments outside the main experimental interest (levels ‒1 and 1), a considerable increase in design error can be noticed in the operative region, which has to be taken into account during response prediction. The shape of the plot depends only on the design points and the polynomial being fit. Fig. 5 shows circular contours and a symmetrical 3D shape indicating rotatable design. Another noticed feature is the relatively low error around the centre points.

4.2 Regression Models of the Selected Output Variables From the design evaluation, it could be established that the regression matrix is fully determined. Such design of experiments enables developing the quadratic regression models. Before that, it is necessarily to check the validity of the statistical assumptions on which the least square method basis.

The checking of the model adequacy refers to various residual diagnostics that are able to identify the eventual least square assumption violations.

The commonly used approach is to examine the residuals. For this reason, normal probability plots have been checked for all responses. Their residuals all plot approximately along a straight line; hence, the normality assumptions are satisfied.

Another graphical diagnostics is a plot of studentized residuals versus predicted responses. The residuals of all responses scatter randomly, suggesting

-1 20 0.65 1.5 2900

Factor levels 0 22 1.2 2 4600

1 24 1.75 2.5 6300

2 26 2.3 3 8000

that the variance of observations is constant for all values. The random patterns therefore indicate model adequacy.

The model fitting is the next important step and has to provide an adequate approximation to the investigated process. It uses a special decomposition algorithm on the design matrix, which is used for solving various linear algebraic equations and the least squares problems. The model fitting assessment is based on several standard statistics. The deterministic coefficient R2 of multiple determinations estimates the fraction of total variation in the data accounted by the model. For the designed experiments, it is better to employ adj-R2 statistics, which is adjusted to the number of terms in the model relative to the number of design points, and measures the amount of variation about the mean explained by the model. According to Myers and Montgomery [14], it can be expressed as:

adj − R 2 = 1 −

SSE / DFE , (1) SST / DFT

where SSE is the sum of squared errors, SST the total sum of squares, DFE the error of degree of freedom and DFT the total degree of freedom.

The determination of significant model degree and factor effects is based on the F-value and the P-value, calculated with ANOVA. These two numerical values imply a significance of a model degree and particular linear, quadratic or interaction terms. Usually, P-values smaller than 0.05 show that the particular terms of a model have a significant effect on the response.

Full regression models developed many times include some model terms that are not significant.

In these cases, model reduction is applied, which eliminates those terms in such a way that statistical hierarchy is not violated. For statistical reasons, models that contain subsets of all possible effects should preserve hierarchy. A model is hierarchal if the presence of quadratic terms and interactions requires the inclusion of all linear terms contained within those of a higher order, even if they do not appear to be significant on their own. The automatic, computer-aided model reduction follows the stepwise

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regression algorithm, which combines the forward and the backward model term elimination procedures.

In the stepwise procedure, all regressions are entered into the model at each step, according to their partial t value and are removed one at a time if their P-value is less than the specified cut-off value, usually set to 0.1. Regression surface models have been developed in the form of reduced polynomials in terms of actual factors. The first is used to predict maximal neck height at particular design points (adj-R2 = 0.96) and is expressed as:

h = 19.8 + 0.67 ⋅ d RT + 0.98 ⋅ ∆x − 4.3 ⋅ ∆z − 2 −0.02 ⋅ d RT − 0.3 ⋅ ∆x 2 + 0.79 ⋅ ∆z 2 + 0.37 ⋅ ∆x ⋅ ∆z .

between the successive tool path cycles. Since the neck height increases when using tools with smaller diameters and smaller vertical and horizontal step sizes, while a smaller pitch leads to longer forming time (up to half an hour in some cases inside DoE), there is a trade-off between production time and neck height. Therefore, it is necessary to know the requirements of the product in order to optimise production from the technological and economical points of view.

(2)

The second is used to predict average neck thickness at particular design points (adj‒R2 = 0.8) and is expressed as:

tneck = 1.9 − 0.079 ⋅ d RT − 0.047 ⋅ ∆x + 2 +0.13 ⋅ ∆z + 1.9 ⋅ d RT − 0.029 ⋅ ∆z 2 .

(3)

The regression models can be also presented using response surface plots. Fig. 6 and Fig. 7 present the three-dimensional response surface plots of the investigated response parameters plotted against the two most influential BIHF system factors, determined according to P-value (the remaining two off-axis factors were fixed to their central level) for both analysed output values. The results show that the regression model of neck thinning depends mainly on the forming tool diameter and vertical step size.

The decrease of any of those parameters influences the reduction of neck wall thickness. Of course, the thickness of the neck is not uniform. It decreases along the axial direction and reaches maximum reduction at the top of expanded hole. The thickness distribution over the neck height can be calculated approximately using simple equation:  D − 2h  th = t0 ⋅  FN  , h = 1....hmax DFN   (4)

1 hmax = ( DFN − DIH ) , 2 where th represents neck thickness at the particular neck height h, DFH is the final neck diameter, DIH is the initial hole diameter and t0 is the initial sheet metal thickness.

In contrast, the increase of forming tool diameter, vertical step size and horizontal step size influence the decrease of neck height. The reason could be found in the bigger deformation area and larger distance 78

Fig. 6. The response surface model of neck height plotted against forming tool diameter and vertical step size

Fig. 7. The response surface model of average neck thickness plotted against forming tool diameter and vertical step size

The form of the regression surface model depends on the signs and magnitudes of the model coefficients.

As could be seen, the second-order coefficients and interactions play a vital role. Finally, is worth pointing out that the general nature of the regression surface arises as a result of a fitted model, not the real experimental design matrix structure.

4.3 Determination of Limit Forming Ratio From the response surface analyses, it could be concluded that forming tool diameter, vertical step size and horizontal step size are the most influential process parameters in BIHF process from the thinning

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and neck height points of view. Indeed, appropriate selection of that process parameter would lead to determine limit forming ratio (LFR) which can be expressed as:

LFR =

df di

, (5)

where df represents final hole diameter and di the initial hole diameter of the workpiece that can be produced without failure. Necking or tearing mostly occurs due to the excessive circumferential strain, caused by tensile stresses induced in the edge of the neck. It should be mentioned that the increase of forming ratio directly influences the increase of deformation. The highest strains occur in the periphery of the expanded hole where failure usually begins.

of the initial hole leads to fractures occurring along the periphery of the expanded hole, as shown in Fig. 8. In contrast to the results of the limit forming ratio and neck height obtained by conventional hole-flanging process gained from available literature, much higher values are reached with BIHF, as was expected.

5 DISCUSSION AND CONCLUSIONS The presented new technological approach, BIHF may be applied as an additional technology in multi-step forming operations and enables the formation of necks outward on complex 3D products in small quantities, effectively and with minimal costs. The latter can be achieved due to the flexible and simple forming tool, although the time required to form one product is much longer than by conventional hole-flanging. According to the presented results, it can be concluded that the technology has three significant process parameters affecting the neck height and thickness distribution, i.e. forming tool diameter, horizontal step size and vertical step size. Moreover, due to the incremental approach and appropriate selection of the process parameters, higher limit forming ratios and neck heights can be achieved compared to conventional hole-flanging.

Fig. 8. Small failures due to exceeded limit forming ratio – initial hole was produced by milling, source: EMO-Orodjarna

However, since each particular parameter has good and bad influences on the forming results, a compromise between maximal forming neck height, neck thinning and forming time was made. Thus, the selected process parameters are tool head diameter of 24 mm with the rod diameter of 12 mm, vertical step size of 1 mm, horizontal step size of 3 mm, feed rate of 6000 mm/min and spindle rotation speed of 80 rpm.

The final hole diameter of 80 mm, initial material thickness of 1.2 mm and type of material (DC05) are kept constant in all experimental tests. Initial hole diameter was reduced progressively with the aim of finding the limit forming ratio. It should be noted that minimal initial hole diameter is limited with the diameter of forming tool rod. Nevertheless, the results show that failure occurs before minimal initial hole diameter is reached and that limit forming ration is 5.7

by BIHF process and applied parameters. In this case, a neck height of 28 mm and thickness at the top of the neck of 0.45 mm are reached. An additional reduction

Fig. 9. Asymmetrical shape produced by BIHF, source: EMO-Orodjarna

The research shows that technology could be applied effectively for symmetrical as well as for asymmetrical shapes of the necks, as shown in Fig. 9. In the latter case, many trial and error procedures were made to produce the required neck, due to the inappropriate definition of the initial hole geometry and different deformation history along the product wall. Therefore, challenges for the future are directed to defining the connection between these two variables already in the early phases of development (e.g. with the models in virtual environment proposed in [16]),

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with the aim of producing the required asymmetrical necks with minimal trial and error procedures.

6 ACKNOWLEDGEMENTS The authors are grateful to the Slovene Ministry of Higher Education, Science and Technology for their financial assistance under the ARRS project “Robust small-batch forming processes L2-1111”.

7 REFERENCES [1] Johnson, W., Chitkara, N., Minh, H. (1977).

Deformation mode and lip fracture during hole-flanging of circular plates of anisotropic materials. Journal of Engineering for Industry - Transactions of the ASME, vol. 99, 738-748, DOI:10.1115/1.3439307.

[2] Spur, G., Stoferle, T. (1985). Handbuch der Fertigungstechnik, Umformen und Zerteilen, Carl Hanser Verlag, Munchen, Wien.

[3] Huang, Y.M., Chien, K.H. (2001). The formability limitation of the hole-flanging process. Journal of Materials Processing Technology, vol. 117, 43-51, DOI:10.1016/S0924-0136(01)01060-3.

[4] Leu, D.K. (1996). Finite element simulation of holeflanging process of circular sheets of anisotropic materials. International Journal of Mechanical Sciences, vol. 38, p. 917-933, DOI:10.1016/00207403(95)00090-9.

[5] Cui, Z., Gao, L. (2010). Studies on hole-flanging process using multistage incremental forming. CIRP Journal of Manufacturing Science and Technology, vol.

2, p. 124-128, DOI:10.1016/j.cirpj.2010.02.001.

[6] Suholežnik, R. (2010). Hauling of sheet metal throat articles on small-scale production conditions.

Undergraduate thesis, University of Ljubljana, Ljubljana.

[7] Petek, A., Kuzman, K., Fijavž, R. (2011). Backward drawing of necks using incremental approach. Key Engineering Materials, p. 105-112, DOI:10.4028/ www.scientific.net/KEM.473.105.

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[8] Petek, A. (2009). The definition of stable technological window by incremental sheet metal forming. PhD Thesis, University of Ljubljana, Ljubljana.

[9] Petek, A., Kuzman, K., Suhač, B. (2009). Autonomous on-line system for fracture identification at incremental sheet forming. CIRP Annals - Manufacturing Technology, vol. 58, no. 1, p. 283-286.

[10] Petek, A., Podgornik, B., Kuzman, K., Čekada, M., Waldhauser, W., Vižintin, J. (2008). The analysis of complex tribological system of single point incremental sheet metal forming. Strojniški vestnik - Journal of Mechanical Engineering, vol. 54, no. 4, p. 266-273.

[11] Petek, A., Zaletelj, V., Kuzman, K. (2009).

Particularities of an incremental forming application in multi-layer construction elements. Strojniški vestnik - Journal of Mechanical Engineering, vol. 55, no. 7-8, p. 423-426.

[12] Jeswiet, J., Micari, F., Hirt, G., Bramley, A., Duflou, J., Allwood, J. (2005). Asymmetric single point incremental forming of sheet metal. Annals of CIRP, vol. 54, no. 2, p. 623-650, DOI:10.1016/S00078506(07)60021-3.

[13] Volk, M., Nardin, B., Dolšak, B. (2011). Application of numerical simulation in the deep-drawing process and the holding system with segments’ inserts. Strojniški vestnik - Journal of Mechanical Engineering, vol. 57, no. 9, p. 697-703.

[14] Myers, R.H., Montgomery, D.C. (2002). Response surface methodology, process and product optimization using designed experiments. John Wiley & Sons Inc., New York.

[15] Krajnik, P., Kopač, J., Sluga, A. (2005). Design of grinding factors based on response surface methodology. Journal of Materials Processing Technology, vol. 162-163, p. 629-636, DOI:10.1016/j. jmatprotec.2005.02.187.

[16] Manić, M., Miltenović, V., Stojković, M., Banić, M. (2010). Feature models in virtual product development.

Strojniški vestnik - Journal of Mechanical Engineering, vol. 56, no. 3, p. 169-178.

Petek, A. – Kuzman, K.

Strojniški vestnik - Journal of Mechanical Engineering 58(2012)2, 81-92 DOI: 10.5545/sv-jme.2011.029

Paper received: 2011-02-02, Paper accepted: 2011-11-23 ©2012 Journal of Mechanical Engineering. All rights reserved.

A Dynamic Rescheduling Model with Multi-Agent System and Its Solution Method Zhao, F. – Wang, J. – Wang, J. – Jonrinaldi, J.

Fuqing Zhao1,2,* ‒ Jizhe Wang1 ‒ Junbiao Wang2 ‒ Jonrinaldi Jonrinaldi3 1 School

of Computer and Communication, Lanzhou University of Technology, China Key Laboratory of Contemporary Design & Integrated Manufacturing Technology, Ministry of Education, Northwestern Polytechnical University, China 3 School of Engineering, Computer Science and Mathematics, University of Exeter, United Kingdom 2

Dynamic rescheduling problem is an important issue in modern manufacturing system with the feature of combinatorial computation complexity. A dynamic rescheduling model, which is based on Multi-Agent System (MAS), was proposed. The communication and negotiation mechanism between agents were addressed to support the autonomic decision for each individual agent and the multi-agent system.

Furthermore, the simulation results in dynamic scheduling accompanying with its perturbation show that the proposed model and the algorithm are effective to the dynamic scheduling problem in manufacturing system.

Keywords: MAS, agent, dynamic scheduling, Contract Net Protocol, negotiation mechanism, perturbation

0 INTRODUCTION Today’s manufacturing businesses are facing immense pressures to react rapidly and robustly to dynamic fluctuations in demand distributions across products and changing product mix. Traditional manufacturing systems and approaches to production, involving sequential stages from manufacturing systems design, construct, and setup in the preparation phase to production planning, scheduling, and control in the operational phase, can be challenging in satisfying the requirement of the variation. Efficient and practical methods for scheduling and optimization technology are the key to improve the productivity and efficiency of a manufacturing plant [1]. The traditional scheduling and optimization process, which always deals with a clear schedule and a fixed processing time, while for the actual processing problem, there are many uncertain factors, for example, changes in processing time, product demand, delivery, equipment failure, resources and production variations. The dynamic interference of these factors causes that the original dynamic scheduling can not be implemented successfully. Therefore, the rescheduling model and its solution method are of significant importance for the dynamic scheduling problem [2].

Job shop scheduling is to schedule a set of jobs on a set of machines, which is subject to the constraint that each machine can process one job at most at a given time and the fact that each job has a specified processing order through the machines.

It is not only a NP-hard problems, it also has the well-earned reputation of being one of the strong combinatorial problems in manufacturing systems.

Recently, two single-machine rescheduling problems

with linear deteriorating jobs under disruption was studied by Zhao and Tang [3]. Job shop rescheduling problem was being considered as minimizing the total completion time under a limit of the disruption from the original scheduling. However, little information has been given about the autonomic decision mechanism. A reactive scheduling framework based on domain knowledge and constraint programming was proposed by Novasand Henning [4]. An explicit object-oriented domain representation and a constraint programming (CP) approach to the model were utilized to the modeling and realizing method when unforeseen event occurs. A reactive scheduling methodology for job shop, make-to-order industries, by inserting new orders in a predetermined schedule, was introduced to iteratively update the schedules [5]. By applying local rescheduling in response to schedule disruptions was presented to reduce the size of the regarded problems by applying methods of partial rescheduling in literature [6]. Mehta [7] processed the way to absorb the random failure of the disturbance proposed by the appropriate method of inserting new orders in idle time. Kim [8] proposed a flexible production environment, which can handle processing of planning and shop scheduling with symbiotic genetic algorithm. Petrovic [9] used the fuzzy method to study the re-scheduling for the job shop problem facing uncertain disruptions. A genetic algorithm for multi-processor task with resource and timing constraints was put forward to solve the scheduling problem in the manufacturing environment with uncertain disruptions [10]. Wang [11] considered the uncertainty of the impact of events as a set of random changes in the time period for the assembly planning problem which is based on semantic

*Corr. Author’s Address: School of Computer and Communication, Lanzhou University of Technology, Lanzhou 730050, China, fzhao2000@hotmail.com

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modeling approach. Goncalves [12] proposed a hybrid genetic algorithm for the job shop scheduling problem with reactive scheduling method. Wong et al. [13] introduced multi-agent system as a platform for the dynamic shop floor scheduling problem.

With the aim of enhancing the flexibility of manufacturing systems and achieving optimization of solutions to constantly respond to increasing rates of change in demand patterns and product mixes, rescheduling approaches and production scheduling options should be taken into consideration simultaneously, and evaluated and optimized dynamically. In this way, constrains from both functions can also be fulfilled concurrently and an optimum integrated plan and schedule can then be produced. Mes et al. [14] proposed a distributed agent-based solution to real-time, dynamic transport scheduling problems, which has the advantages of less sensitive to fluctuations in demand or available vehicles than more traditional transportation planning heuristics (Local Control, Serial Scheduling) and provides a lot of flexibility by solving local problems locally. Shen et al. [15] review the research literature on manufacturing process planning, scheduling as well as their integration, particularly on agent-based approaches to the integration of the difficult problems.

A class of dynamic scheduling problems characterized by a just-in-time objective was addressed in literature [16], an on-line scheduling heuristic based on a multiagent architecture was also presented. Kemppainen [17] presented the method of the coordinating power of priority scheduling when customers request different response times and suppliers do their best to fulfill the customer expectations, especially if enforced with different pricing. Pfeiffer et al. [18] presented a simulation-based evaluation technique for the testing, validation and benchmarking of rescheduling methods.

Certain stability-oriented evaluations of periodic and hybrid rescheduling methods are described for both single- and multi-machine (job-shop) cases. Cauvin et al. [19] proposed an approach to minimize the impact of disrupting events on the manufacturing scheduling and control system, which is based on a cooperative distributed problem solving approach supported by a multi-agent system framework.

However, few attempts have been done on the universal communication and negotiation mechanism for the dynamic rescheduling problem and corresponding solution approach. We aim to construct a universal dynamic rescheduling model, which is based on Multi-Agent System (MAS), for the job shop scheduling problem in manufacturing systems.

82

This paper is organized as follows. In Section 1, the rescheduling model which is based on MAS is given. Section 2 describes the detailed functions of agent. The communication and negotiation processes and steps are introduced in Section 3. In Section 4, the proposed model and approach are validated using the popular benchmark functions. Finally, Section 5 concludes the paper with an outlook on future work.

1 MAS-BASED RESCHEDULING MODEL In dynamic shop scheduling environment, the job shop problem can be described as: in a processing unit or system, n jobs need to be processed on m machines, every job Ji (1 ≤ i ≤ n) has ni process Oij (1 ≤ i ≤ n, 1 ≤ j ≤ n) which is needed to processing. Set machine tool with a collection of M, then each process Oij can either be processed by the concentration of machine tools Mij or can be processed in one machine, where M ij ⊆ M . If Mij = M, the scheduling problem is a completely flexible scheduling problem; if M ij ⊂ M , it is a local scheduling problem with flexible strategy [20].

In scheduling operation, when one machine failure occurs, all machines need to execute the operation of rescheduling of the operation on the predetermined operation processes. As rescheduling model is the corresponding evolution process to the initial scheduling model, the initial problem modeling is as follows. min max {cis i ∈ I } ,

S.t.

sij+1 ≥ sij+1+ pij , i ∈ I, J ∈ {1, ... s−1},

(1)

(mi1 j ≠ mi2 j ) ∨ ( si1 j ≥ ci1 j ∨ si2 j ≥ ci2 j ),

(2)

i1, i2 ∈ I, i1 ≠ i2, j ∈ J,

(3)

cij = sij + pij , i ∈ I, j ∈ J,

(4)

si1 ≥ 0 , sij ≥ ∑ kj −=11 pik , i ∈ I , j ∈ {2 ,..., s} ,

(5)

mij ∈ R j = r jl ,..., r jl j j ∈ J , i ∈ I ,

{

}

(6)

where i is the workpiece number and i ∈ I = {1, ..., n}, j is the level number and j ∈ J = {1, ..., s}, rjl is the machine number, sij is the start time of initial scheduling, mij is the start machine, pij is the processing time of the workpiece.

In the above model, Eq. (1) shows that the optimization goal of the scheduling problem is minimum of total process time Cmax.

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Eq. (2) shows the operation of the timing constraints. Eq. (3) shows that if two jobs are processed on the same machine, then they can not be processed at the same time. Eq. (4) shows that once the processing for the workpiece starts, it can not be interrupted until it will be finished. Eqs. (5) and (6) show operation started with variable time window and the variable interval of processing machinery, respectively.

It is supposed that the machine r jd ld disruptions at the time interval [tb, te], the initial scheduling begins to adjust in tb, and the initial scheduling will alter to the dynamic rescheduling: ∑ ∑ wij δ1ij ∑ ∑ vij δ2ij

max f =

i∈I j∈J

∑ ∑

i∈I j∈J

wij

+

i∈I j∈J

∑ ∑ vij

,

(7)

i∈I j∈J

S.t.

(mi1 j ≠ mi2 j ) ∨ ( si1 j ≥ ci1 j ∨ si2 j ≥ ci2 j ),

i1, i2 ∈ I, i1 ≠ i2, j ∈ J,

cij = sij + pij , i ∈ I, j ∈ J,

mij ∈ R j = r j1 , ..., r jll j ∈ J , i ∈ I ,

(m'ij ≠ r jd ld ) ∨ ( s'ij ≥ te ) ,i ∈ I , j ∈ J ,

( s'ij ≥ tb ) ,i ∈ I , j ∈ J .

{

(8)

}

(9)

Eq. (7) shows that the objective of rescheduling is to maximize the time for adjustment arrangement. δ1ij is the rescheduling operation time of corresponding alternative scheduling operation workpiece oij :

δ 1ij =

{ {

max min

c'ij , cij

} − max {

s'ij , sij

pij

the the the for

} ,0} ,

where δ2ij is the dynamic rescheduling decision varible when selecting the alternative for workpiece oij :

1, m' ∈ M ij ij . δ 2ij =  other 0 ,

Eq. (8) shows the new constraints when mechanical failures occur. Eq. (9) shows the beginning of the operation of the new interval for the start time of process oij · oij means the process step j of workpiece i, wij , vij are operating weight of the workpiece and

the machine time consistency of weight, respectively. s'ij means the starting time of the operating parts in rescheduling, m'ij is the operating machine for workpiece in rescheduling.

For the rescheduling problem, the structure of the agent can be expressed as: agent = def <Id, Goal, Act, Rule, L>.

Agent Id is the identifier in multi-agent system.

Different agent has different agent Id. Goal is the objective of the agent. The goal is keeping the optimization objective of job sequence as optimum or near optimum after inserting a new job to the agent when rescheduling occurs. The goal can be expressed as: i Goali = (Cmax , J1i → J 2i ... → J nii ) , where { J1i , J 2i ...J nii } is the union of the current operating jobs and the current order queue J1i → J 2i ... → J nii for machine Mi. J1i → J 2i ... → J nii is the optimum priority sequence i is the or near optimum order of machine Mi. Cmax optimal objecive of the machine Mi or near optimal objective value.

Act is the action set of agent in the form of Act = {act1, act2, ..., actn} , which represents the operation it can be accomplished. Each agent has capabilities of communication and collaboration.

Rule represents the cooperation criterion for the communication between agent and its corresponding agent.

L is the Agent communication language. Different agents communicate with each other with L. ACL (Agent communication language) with FIPA rules and modified contract net protocol, which are used in this paper.

2 MAS BASED MODEL FOR DYNAMIC SCHEDULING SYSTEM Currently, there is a wide range of either commercial or open source agent development tools, called agent platforms, that are compliant with the FIPA specifications. For example JADE, FIPA-OS, ZEUS, GrassHopper and MAST [21], Manufacturing Agent Simulation Tool, which was developed by the Rockwell, Automation Research Center in Prague.

The initial idea was to propose and implement the agent based solution of some typical manufacturing task. The material-handling domain has been chosen, especially the task of the transportation of products between manufacturing cells using different means of transport, for instance, the conveyor belts or the AGVs (Automated Guided Vehicles). Munir Merdan et al. [22] use MAST, which has been validated with real-world hardware to strengthen the external validity of the simulation results.

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Basically, each of these agent platforms provides a user with a library of JAVA classes (since all of them are programmed in JAVA) that allow to create agents with application-specific attributes and behaviors and with the capabilities to send and receive messages following different FIPA interaction protocols.

The vital part for agent platform is the runtime environment. which provides a space for agents to live. The running environment consists of white pages services registering existing agents and their contact addresses, yellow pages services used to register and locate services offered by agents and finally the message dispatching mechanism ensuring the interagent communication within the platform as well as among agents hosted at different platforms.

tender will be distributed to Equipment Agent (EA).

According to the rules of the agreement, RA lays out a concrete processing planning, then submits it to the SA. In addition, guides the production for EA after obtaining the feedback from SA. The internal schematic for Resource Agent is shown in Fig. 2.

2.1 Function Design of Agent Traditional rescheduling is generally obtained manually and/or is computer aided in accordance with certain reallocation algorithm [23]. We use the MAS-based intelligent scheduling systems, which collaborate with each other to guarantee the intelligence of machines that utlized MAS as the software of control unit. Therefore, jobs for rescheduling in manufacturing shops can achieve the automation and optimization. The basic structure of improved contract net model consists of Management Agent (MA), Resource Agent, Supervision Agent (SA) and Workpiece Agent.

MA is the core of the scheduling system. İt is mainly responsible for evaluating and scheduling the task entered into the rescheduling system. The information of the task is composed of the host information and the degree of emergency for the concrete task. MA transmits the information to the Resource Agent for processing. Communication between MA and other Agents is shown in Fig. 1.

Fig. 2. Resource Agent internal schematic

SA is responsible for the simulation for the candidate production planning, which is returned back from the MA. Moreover, SA selects processing route and forwards it to the MA to be performed.

Furthermore, SA is responsible for the supervision of Agent equipment failure, the entering of new equipments and the arrival of other emergency tasks.

Fig. 3 shows the internal schematic of SA.

Fig. 3. Supervision Agent internal schematic

Fig. 1. Description of Management Agent

Resource Agent (RA) is responsible for receiving and processing production tasks entering into the shops. And in accordance with the current processing capacity, RA determines whether to perform the task or not. After the decomposition of tasks, the 84

EA can be considered as a manufacturing unit. Each process unit is administrated by one EA, which is responsible for the corresponding operation management, command transmission for equipment, and collection of processing information, etc. After receiving the information returned from RA, EA evaluates the corresponding equipment and decides whether to tender or not. If EA tenders for a task, it sends its bid according to the operation situation of the equipment. In addition, EA sends the capability of

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itself to RA. Internal schematic of EA is shown in Fig. 4.

request, then replies with proposed tender in given deadline. Tender request primitives for Workpiece Agent can be expressed as: (PROPOSE :Sender(Agent-identifier:name equipment@abc:1099/jade) :Receiver(Agent-identifier:name resource@abc:1099/jade) :Content”((action(bidbook(bidbook :finishtime\2010-12-01\21:30\)):cost:10:equipment (Agent-identifier:name equipment@abc:1099/jade)))” :Reply-with CFP1 :in Reply-with PROPOSE1 :Language FIPA-KQML :Ontology scheduling ontology :Protocol fipa-contract-net )

Fig. 4. Equipment Agent Internal Schematic

Afterwards, the MA sends a message to Workpiece Agent with the accepted information.

Communication primitives in the process can be expressed as: :Sender(managerAgent@abc:1099/jade) :Receiver(Equipment@abc:1099/jade) :Ontology AMS-ontology :Protocol FIPA-contract-net :Language FIFA-KQML :Content “((Issue (taskid(01),surface Type(plane),machining Type(drilling),number(8),tolerance (geometic Tol:02dimensional tol:01roughness:02), deadline(2010.12.01/21:10)))”

RA selects processing tasks in sequence from the waiting tasks to be processed. RA sends the process information as a proposition to EA. The communication primitives can be expressed as:

The proposed communication and the interaction process are implemented on the Java Agent Development Environment (JADE) platform. JADE is a multi-agent system platforms, which conforms strictly to FIPA criteria. The JADE programmer can use JAVA to exploit the system when the agent is built (Administrator Guide, Programmer Guide). Meanwhile, because JADE simplifies the communication process between agents by delivering messages which abide by FIPA criteria (FIPA), the message can also be inserted into the sequenced object to realize the standardization parameter delivery.

Furthermore, the yellow function can be directly used because of DF function provided by JADE to guarantee the register for customer system. With AMS and Sniffer tools provided by JADE, users can debug the implementation platform and easily achieve the total functioning of the system. The startup interface is shown in Figs. 5 and 6.

(CFP :Sender(Agent-identifier:name resource@abc:abc:1099/jade) :Receiver(Agent-identifier:name equipment@abc:abc:1099/jade) :Content(action issues:issuebook:taskli\task01:working procedure\01\) :task ready time”2010-12-01 21:20” :surface roughness 4:dimensional tolerance time\”60”\:deadline\”2010-12-01 21:20”\) :Reply-with CFP1 :in Reply-with PROPOSE1 :Language FIPA-KQML :Ontology scheduling ontology :Protocol fipa-contract-net )

Workpiece Agent analyzes the tender received according to the capacity of itself and status of the

Fig. 5. Startup interface of JADE platform

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2.2 The Rescheduling Process Based on Contract Net Protocol MA generates the appropriate contract according to the task order in the task allocation model. The final task allocation is determined by the bidding mechanism through the contract net protocol [24].

Fig. 7. Multi Agent Based Dynamic Scheduling Model

Fig. 6. GUI Startup interface of JADE platform

However, given the consultation efficiency and frequent dynamic scheduling in the workshop, in order to improve efficiency, a two-way consultation mechanism for global scheduling is utilized. By introducing the two-way consultation mechanism, the workshop no longer needs to accept bidding information from MA passively. It can take the initiative to inform the MA of rescheduling information for RA and EA in free time to shorten the scheduling time needed. Meanwhile, RA no longer needs to send bidding information to the workshop with broadcast mode unconditionally. In contrast, RA inspects whether there are request submitted from other agent, afterwards, invites bidding from the workshops which have submitted the bid previously. Therefore, the communication between the agent system decreases obviously, along with the improvement of negotiation by the two-way consultation mechanism. Fig. 7 shows the multi agent based dynamic scheduling model with the two-way consultation mechanism.

In multi-agent dynamic scheduling system, any agent in the agent society may be involved in more than one cluster. With on-going clustering and agents becoming involved in multiple compositions, a multidimensional cluster negotiation process is illustrated in Fig. 8. Four kinds of agents, such as scheduling agent, RA and SA, etc. are involved in the agent cluster. The interaction can be traced in the JADE platform.

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Autonomous negotiation strategy is used in the local Scheduling, which focuses primarily on the negotiation process for one single operating. When the task administration agent obtains the process needed to be perform, it selects a certain agent in the machine queues with specific status to forward notice according to the time of task obtaining.

And it authorizes it to appropriate work piece agent by negotiation. If MA obtains a task at the same time, it starts negotiation randomly. When the machine and the authorized work piece agent accomplish the task which was assigned, RA informs the MA, which is responsible for the current task, of the finished status. In addition, RA updates status of itself, and, transfers to the queues which are waiting for the tasks in the next time intervals. EA alter to idle status at the same time.

2.3 Rescheduling for Emergency Orders Due to the market fluctuating frequently, new orders arrive from time to time. Therefore, it is of significant importance to arrange new orders efficiently. İn the agent clusters, RA informs MA with conventional methods of starting negotiation mechanism. İf the new order can not be inserted to the scheduling, a certain amount of production planning is to be released by RA. However, the deadline of the order, which is released by RA, must be guaranteed. By iteratively releasing process, until emergency orders are to be rescheduled successfully. The flow chart is shown on the left in Fig. 9.

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Fig. 8. Multi-agent negotiation and interaction process based CNP (simulated result)

2.4 Failure of the Machine For the machine in breakdown, the agents system terminate its running operation immediately, and then issue a notice of repairment. Equipment Agent sends the current processing status to RA. RA records the current status, takes the processing task back and examines the alternative EA available. If there is an alternative EA, RA dispatches the process to continue the task. Whereas, if there are no altenatives available, the recalled task is to be bid and reschedule again. The flow chart is shown in middle of Fig. 9.

For other exceptions: such as the shortage of raw materials, the task can not be completed before deadline. MA is to recall the corresponding tasks in order to bring the rest rear scheduling task in production planning ahead. The unfinished task is to be scheduled until the process constraints satisfy the scheduling request. The flow chart is shown on the right of Fig. 9.

3 SCHEDULING ALGORITHMS FOR DYNAMIC RESCHEDULING MODEL The process for dynamic rescheduling, which is based on MAS, consists of multi-stage local scheduling. The local scheduling of each stage is carried out under CNP model. The basic algorithm is as follows: Step 1: MA releases initial bid price PRi after it receives scheduling information from other agents.

It can be defined as PRi = ( ti | Ta / Ba / Ma ), where ti is the deadline of answering a bid from other agents.

Ta is the time constraints to complete the task. Ba is the spatial constraints. Ma is material relationship constraints.

For an emergency order, once the original work piece delays, the total delay time should be shortened as much as possible. So, the time constraint can be expressed as:

Ta = min [ (Ts + ti ), ( Td + Tp )] ,

cik − pik + M (1 − aihk ) ≥ cih ,

(10)

S.t.

Fig. 9. Dynamic scheduling process

i = 1, 2, ..., n; h, k = 1, 2, ..., m ,

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cjk − cik + M (1 − xijk ) ≥ pjk ,

i, j = 1, 2, ..., n; k = 1, 2, ..., m ,

cik ≥ 0 ,

i, = 1, 2, ..., n; k = 1, 2, ..., m ,

xijk = 0 or 1 ,

i, j = 1, 2, ..., n; k = 1, 2, ..., m ,

where Eq. (10) indicates time constraints. Ts is the time that MA offers the initial bid. Td is the latest time that all the jobs have been accomplished. Tp is the average expectant operating time. cik is the finished time for the work piece i processed by machine k. pik is the machining time for workpiece i processed by machine k. aihk and xijk are coefficient and the decision variable, respectively.

Step 2: EA answers a bid from another agent and a bid for the tender. EA evaluates whether it can first satisfy the resource constraint or not. Then, give evaluated bid price˝ PRj = ( aj | Tc , Mc ), where aj is the wait time committed by itself. Tc is the earliest beginning time which is produced by the EA after assessment. If the EA can not satisfy Ta and Ba, or occupied by one process constraints, then EA gives up bidding. If Tc is being the idle status, then EA answers the tender to RA actively and schedules in idle time to save scheduling time.

Step 3: RA assesses the bid from EA and then authorize to the EA outperformed. MA evaluates all bids returned from all the bids with min [ (Tc + Tp ), Mc].

Select the best EA to authorize, namely, considering the earliest start time, the workpiece capacity and efficiency of the EA. Step 4: Perform the operation process. The EA which was authorized is to perform job tasks. During the process, certain failures are possible to occur.

However, if the system works well, MA calculates the total process time, and then sends the information collected by it to EA. If there are certain failure occurs, EA reports the status to SA, terminates the operation, and transfers the task needed to be rescheduled to the fault repairment negotiation process.

4 SIMULATION RESULTS AND DISCUSSION In this paper, the actual production line simulation model was used to testify the efficiency of the method which is proposed in our paper. The system is running on Intel Pentium (R) 4 CPU 2.93 GHz processor, 512 MB of memory, the operating system was Windows 2003 server, JADE version is 3.9.

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In order to testify the efficiency of the rescheduling model and the scheduling algorithms, one machine shop is utilized as a test case. The workshop we selected is composed of 5 parts, 4 processes and 8 machines. The parts and machines were mapped as resource agent and workpiece agent in MAS model as Fig. 2. The UML functional structure of Resource Agent in the model is shown as Fig. 10. The model and the communication process of SA, EA, MA and Workpiece Agent (WA) were modeled as in section 2.

Fig. 10. Resource Agent

The workshop has the capacity for planing, milling, turning, drilling and other processes. In addition, there are multi-functional machines, two different specification planers, two different specifications lathes, one milling machine and one multi-function machine in the workshop. A multifunction machine can accomplish processes for drilling, planing operations. The relationship between a process for machines is shown in Table 1 (in the table, 1 indicates that the machine can complete the process, otherwise value is 0). Process sets of the workpiece are shown in Table 2. The processing time for each process is shown in Table 3. Two cases were simulated: one case is the deadline for all parts which have no strict requirement. The other case is that all the parts ordered have tense deadline. In the experiment, for the first case, a deadline is set as the average processing cycle under FIFO scheduling rules. For the second case, the set deadline scale as 1:1.2.

The obtained results by our MAS based model and algorithm were compared with those obtained under the rules of FIFO and EDD. The performance comparison results are shown in Table 4.

In Table 1, A to H represents 8 machines. Among these machines, A and B are Planer, C is a Milling machine, D, E and G are Lathe, the others are Multifunction machine. ‘1’ means the process can be completed, and ‘0’ means it can not be completed. The processing sequence of the workpiece in the simulation model is described in detail in Table 2. In Table 3, the machine is the concrete machine equipment used for the processing sequences. ID is the number of

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the job in Table 2. The corresponding figures signify the process time in corresponding machines. The simulation results in the normal production line and emergency production line are shown in Table 4.

Fig. 13. Time delivery comparison in failure model

Fig. 11. Time delivery comparison in normal state

In Figs. 11 to 14, FIFO means first input first output. EDD means earliest due date. G-FIFO is FIFO in General status; G-EDD is EDD in General status; G-MAS means in General MAS status; E-FIFO means in Emergency FIFO status; E-MAS means in Emergency MAS status; G-F-FIFO means in General Failure FIFO status; G-F-MAS means in General Failure MAS status; E-F-FIFO means in Emergency and Failure FIFO status; E-F-MAS means in Emergency and Failure MAS status.

Fig. 12. Delay time comparison in normal state

As can be seen from Table 4, Figs. 11 and 12, the proposed consultation mechanism can reduce the weighted average delay in delivery of products.

Moreover, it can shorten product delivery time. Hence, the model and the algorithms utilized are effective to the rescheduling problem.

For the problem of equipment failure, it is assumed that there is one machine with a daily failure of 12 h and simulation time is one month.

Other test conditions are the same with previously tested cases. FIFO rules is not be used to process equipment failure, while MAS based consultation and negotiation mechanism is to reschedule the rest processes. Simulation and performance results are shown in Table 5, Figs. 13 and 14.

Under the circumstance of equipment failure, results indicate that local autonomic negotiation mechanism we utilized can alleviate the effection of equipment failure for the production line in manufacturing shops.

The case-study utilized is a real industrial problem aiming at evaluating reschedules in a large job-shop environment with MAS simulation platform. The simulation architecture presented in the previous sections constituted the stochastic evaluation environment in which absolute evaluation of static schedules was performed. The case study elaborated concerned a factory that produces mechanical products by using machining and welding resources, assembly and inspection stations and some highly specialized machines. Production is performed in a make-to-order manner where deadline is an absolute must, even regarding unpredicted orders. Since quality assurance is a key issue, tests may result in extra adjustment operations. The process for dynamic rescheduling, which is based on MAS, consists of multi-stage local scheduling. The local scheduling of each stage is carried out under the CNP model. And the Multiagent negotiation and interaction process based on CNP is in full-duplex communication manner, which is a distinct difference between our approach and the methods in [25].

Fig. 14. Average weighted delay in failure model

From Table 4, Figs. 11 and 12, in the two statuses of Normal production line and Emergency production line, the scheduling accurate delivery of MAS have advantages over those obtained under the rules of FIFO and EDD with less average weighted time.

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Table 1. Relationship between the machine and process Process P1 P2 P3 P4

A (Planer1) 1 0 0 0

B (Planer2) 1 0 0 0

C (Milling) 0 1 0 1

Machine D E (Lathe1) (Lathe2) 1 0 0 0 1 1 0 0

F (Multifunction) 1 0 0 1

G (Lathe) 1 0 1 1

H (Multifunction) 0 1 0 0

Table 2. Equipment and process Piece ID number j1 j2 j3 j4 j5

1 procedure Plane(id:1) Car (id:3) Milling (id:2) Diamond (id:4) Milling (id:2)

2 procedure Milling (id:2) Diamond (id:4) Plane (id:1) Plane (id:1) Diamond (id:4)

3 procedure Diamond (id:4) Milling (id:2) Car (id:3) Milling (id:2) Plane (id:1)

4 procedure Car (id:3) Plane (id:1) Diamond (id:4) Car (id:3) Car (id:3)

Table 3. Procedure processing time ID j1 j2 j3 j4 j5

A 3 7 2 8 3

Plane B 4 8 3 9 5

Machine Milling C G 10 8 5 6 3 5 2 7 5 3

C 6 8 3 9 6

Car D 2 6 4 11 5

Diamond E 3 7 5 12 6

F 5 6 3 7 8

H 9 4 3 7 6

Table 4. Simulation results under emergency by MAS model Production Line Status General Emergency

Scheduling rules FIFO EDD MAS FIFO MAS

A 49 46 85 0 100

B 48 54 91 0 94

C 51 55 94 0 85

Time delivery [%] D E F 57 50 50 61 65 50 88 90 84 0 0 0 89 98 89

G 50 52 93 0 92

H 51 68 80 0 94

A 21

B 18

3 55 5

3 84 7

G 50 99 0 92

H 49 94 0 94

A 41 6 35 8

B 20 8 33 6

Weighted average delay [h] C D E F G 18 16 16 20 15 1 65 5

1 59 3

8 71 10

7 65 6

H 16

9 84 8

8 74 6

Weighted average delay [h] C D E F G 15 17 19 21 19 3 3 7 6 4 24 32 29 16 31 6 11 11 8 7

H 20 5 121 8

Table 5. Simulation results under equipment failure by MAS model Production Line Status General Failure Emergency Failure

Scheduling rules FIFO MAS FIFO MAS

A 55 96 0 99

B 58 92 0 94

C 51 92 0 88

Time delivery [%] D E F 55 54 59 95 90 95 0 0 0 89 98 89

The Simulation results under equipment failure

by MAS model was shown in Table 5. In Figs. 13 and 14, it is seen that the MAS method we proposed in this paper shows a high efficiency in adjusting the jobs to 90

other machines available at the required time with the less delay and delivery time. In contrast, the adjusted rules adopted by FIFO can not be worked in the fault status.

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5 CONCLUSION Dynamic rescheduling method is widely used in the modern production plant. In this paper, the Contract Net Protocol, which is based on MAS, is introduced to the rescheduling of the workshop environment.

It is a new way of solving the communication and negotiation problem in this field. After fully considering the effection of the equipment failure and repairment in the process of production, the complex dynamic rescheduling process is to be divided into the communication and negotiation processes of multiagents. Therefore, the capability of autonomic decision for tackling the unexpected events, which occur in the production, is extended. By simulation in the actual production workshop, the model and algorithm, which are based on MAS, were identified as effective to the rescheduling problem in the manufacturing system.

It is worth pointing out that the test cases studied in this work are not very many. We will explore the efficiency of our model and approach on those problems with a larger number of decision variables in the future. The future work should also includes studies on the process specific interaction between agents in multi agent area and how to extend our model and algorithm based on MAS to solve constrained or discrete multiobjective optimization problems.

6 ACKNOWLEDGEMENT This work is financially supported by the National Natural Science Foundation of China under Grant No. 61064011. And it was also supported by Scientific research funds in Gansu Universities,Science Foundation for the Excellent Youth Scholars of Lanzhou University of Technology, Educational Commission of Gansu Province of China, Natural Science Foundation of Gansu Province, and Returned Overseas Scholars Fund under Grant No. 1114ZTC139, 1014ZCX017, 1014ZTC090, 1114ZSB091, and 1014ZSB115, respectively.

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[5] Gomes, M.C., Barbosa-Povoa, A.P., Novais, A.Q. (2010). A discrete time reactive scheduling model for new order insertion in job shop, maketo-order industries. International Journal of Production Research, vol. 48, no. 24, p. 7395-7422, DOI:10.1080/00207540903433858.

[6] Kuster, J., Jannach, D., Friedrich, G. (2010). Applying local rescheduling in response to schedule disruptions.

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[7] Mehta, S.V., Uzsoy, R.M. (1998). Predictable scheduling of a job shop subject to breakdowns. IEEE Transactions on Robotics and Automation, vol. 14, no.

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[8] Kim, Y.K., Park, K., Ko, J. (2003). A symbiotic evolutionary algorithm for the integration of process planning and job shop scheduling. Computers and Operations Research, vol. 30, no. 8, p. 1151-1171, DOI:10.1016/S0305-0548(02)00063-1.

[9] Petrovic, D., Duenas, A. (2006). A fuzzy logic based production scheduling/rescheduling in the presence of uncertain disruptions. Fuzzy Sets and Systems, vol. 157, no. 16, p. 2273-2285, DOI:10.1016/j.fss.2006.04.009.

[10] Cheng, S.C., Shiau, D.F., Huang, Y.M. (2009). Dynamic hard-real-time scheduling using genetic algorithm for multiprocessor task with resource and timing constraints. Expert System with Application, vol. 36, no. 1, p. 852-860, DOI:10.1016/j.eswa.2007.10.037.

[11] Wang, H., Xiang, D., Duan, G.H. (2009). Assembly planning based on semantic modeling appoach.

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[12] Goncalves, J.F., Mendes, J.J., Resende, M.G. (2005). A hybrid genetic algorithm for the job shop scheduling problem. European Journal of Operational Research, vol. 167, no. 1, p. 77-95, DOI:10.1016/j. ejor.2004.03.012.

[13] Wong, T.N. Leung, C.W., Mak, K.L., Fung, R.Y.K. (2006). Dynamic shop floor scheduling in multiagent manufacturing system. Expert System with Applications, vol. 31, no. 3, p. 486-494, DOI:10.1016/j. eswa.2005.09.073.

[14] Mes, M., van der Heijden, M., van Harten, A. (2007).

Comparison of agent-based scheduling to look-ahead heuristics for real-time transportation problems.

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[15] Shen, W.M. (2006). Agent-based distributed manufacturing process planning and scheduling: a state-of-the-art survey. IEEE transactions on systems,

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man, and cybernetics-part C: Applications and reviews, vol. 36, no. 4.

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[23] Jiaa, H.Z., Fuh, J.Y.H., Neea, A.Y.C., Zhang, Y.F. (2007). Integration of genetic algorithm and Gantt chart for job shop scheduling in distributed manufacturing systems. Computer and Industrial Engineering, vol.

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[24] Lim, M.K., Zhang, Z. (2003). A multi-agent based manufacturing control strategy for responsive manufacturing. Journal of Materials Processing Technology, vol. 139, no. 1-3, p. 379-38, DOI:10.1016/ S0924-0136(03)00535-1.

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Zhao, F. – Wang, J. – Wang, J. – Jonrinaldi, J.

Strojniški vestnik - Journal of Mechanical Engineering 58(2012)2, 93-101 DOI: 10.5545/sv-jme.2011.098

Paper received: 2011-05-05 , Paper accepted: 2011-11-07 ©2012 Journal of Mechanical Engineering. All rights reserved.

Neural-Network Estimation of the Variable Plant for Adaptive Sliding-Mode Controller Uran, S. – Šafarič, R. Suzana Uran ‒ Riko Šafarič*

University of Maribor, Faculty of Electrical Engineering and Computer Science, Slovenia The Lyapunov based theoretical development of a neural-network sliding-mode based estimation of highly non-linear and variable robot plant for a direct-drive robot controller is shown in the paper. Derived adaptive control law was tested for four types of robot neuralnetwork sliding-mode controllers: centralized, simplified centralized, decentralized and simplified decentralized, which were verified on a real laboratory direct-drive 3 D.O.F. PUMA like mechanism. Centralized and decentralized control approaches estimate only a part of the variable robot dynamic model (torque model due to friction, Coriolis, centripetal and centrifugal forces) and use only the part of a dynamic plant model (the so called estimated inertia matrix M). Both simplified methods do not need any plant model parameter for an accurate estimation of the direct-drive robot plant, but need some more time to learn dynamic model parameters. All four types of the neural network continuous slidingmode controllers were successfully tested for algorithm’s adaptation capability for sudden changes in the manipulator dynamics (load).

Keywords: sliding-mode adaptive controller, neural-network, robot

0 INTRODUCTION Control techniques based on soft computing methods (neural network, fuzzy logic, genetic algorithm, particle swarm algorithm, fractal theory etc. or their combinations) [1] and especially neural network control techniques have been proven to be useful to control highly nonlinear robot arm control plants for more than two decades [2] to [8]. Therefore, the neural network control methods have been used with high interest in mobile robotics [9] to [11], especially for the dynamic and kinematic control in recent years.

The research of the kinematic and dynamic neural network control of robot arm has also been evolving for two decades.

A number of publications dealing with the topic of the robot arm trajectory tracking neural network controller based on the computed torque method [12] to [15], etc. have been published. In sources [12] and [14], there was an attempt to replace the estimated model of the real mechanism (the vector h due to Coriolis forces and the inertia matrix M) with two neural networks. The disadvantage of this method is that it requires generalized learning [12] in addition to specialized learning or a time-consuming convergence of neural network learning [14] if generalized learning is not implemented. In order to speed up the convergence without generalized learning, the source [13] retained the complete compensator based on the computed torque method and added a neural network approximating an unstructured uncertainty, which would not be compensated by the computed torque method itself (friction torque) and would introduce an error into the control system if used with this method.

The disadvantage of the method described in the

source [13] is that the parameters of the inertia matrix M and vector h (torques due to Coriolis, centrifugal and centripetal forces) have to be known.

The sources [16] to [19] successfully deal with the neural network control based on an estimation of kinematics and dynamics of geared robot arms. The source [15] tried to adapt neural network controller based on the computed torque method also to high nonlinear direct drive (DD) robot arm dynamics and obtained good results in the tracking experiments, while the steady-state test and the sudden load change test had not been reported. The published paper [20] resolved the steady state problem. In order to diminish the drawbacks of all the above mentioned methods, a sliding-mode neural network controller was chosen as a robust control scheme [21], where only nominal (average) values of inertia matrix parameters were used, while the differences between actual inertia matrix parameters and nominal inertia matrix parameters torque terms due to Coriollis forces, gravitational forces and friction forces (structured uncertainties) were estimated by neural network. This was done due to the fear that the robot behaviour would be unpredictable during the first few moments of neural network learning. This method was successfully upgraded and used also for visual positioning control of robot mechanism [22] where a special four-layer neural network structure made possible to estimate the complete robot dynamics and kinematics. The next two reports [23] and [24] had shown that neural network based control approach could be effectively used also for direct driven piezo electric actuated micro robot mechanisms.

The theoretical development of a full and simplified centralized and decentralized neural-

*Corr. Author’s Address: Faculty of Electrical Engineering and Computer Science, University of Maribor, Smetanova 17, 2000 Maribor, Slovenia, riko.safaric@uni-mb.si

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network controller based on the theory of continuous sliding-mode control for DD robot arm mechanism is shown in the paper. Derived equations, based on Lyapunov theory, of the adaptive neural network controller were verified on a real laboratory directdrive 3. D.O.F PUMA like mechanism. The newly developed neural network continuous sliding-mode centralized and decentralized controllers, as full and simplified sub-methods were successfully tested for adaptation capability of the algorithm for sudden load changes in the manipulator dynamics. All the mentioned tests were made on a real laboratory 3 D.O.F. DD robot mechanisms.

The main idea presented in the paper is to give the neural network controller only a part of robot dynamic, which does not include the coupling effect between axes, so the structual and unstructual uncertainties increase. It is shown in the paper that a neural network as a part of control law is able to learn the missing part of the robot dynamics which should be included in the control law during the learning procedure. Four methods, which have more or less robot dynamic, included in the neural network control law are presented and compared.

1 SYNTESIS OF CONTINUOUS NEURAL-NETWORK SLIDING-MODE CONTROLLER A well known mathematical note of robot mechanism dynamics, Eq. (1), is transformed into an n-dimensional state-space system of equations with regard to the control value u, Eq. (2), because the Lyapunov theory for searching the control law can only be used in the following way.

T = M( θ ) ⋅  θ + h( θ, θ ) + G f ( θ ) + F( θ ) + Tn ,

(1)

where T is a torque vector, M is an inertial matrix, h is a torque vector due to centrifugal forces, centripetal forces, and Coriollis forces, F is a torque vector due to frictional forces, Gf is a torque vector due to forces of gravity, Tn is a torque vector due to unknown θ are vectors of real positions, disturbances, θ, θ and  velocity, and accelerations of the robot mechanism.

The Eq. (2) presents a non-linear state-space system as a description of Eq. (1) and it is needed for the control law development by the Lyapunov theory. x = f (x, t ) + B(x, t ) ⋅ u + d(x, t ),

(2)

x ∈ R n , u ∈ R m , B(x, t ) = B (x, t ) + ∆B(x, t ),

(3)

where:

and d is an unknown disturbance, B is an actual input matrix, B is an estimated input matrix, u is a control 94

vector, x is a state space vector of mechanism, and t stands for time. Our goal is to prove the function stability σ(x, t) = 0 (Eq. (4)) for the robot system (Eq. (2)). This means that after transient time, defined with parameters of the matrix G, the difference between the actual and the desired vector of state space variables x and will equal zero and will be stable for all disturbances. Function σ(x, t) = 0 will be stable if the Lyapunov function V > 0 and the first Lyapunov time derivative of function V < 0. The selected Lyapunov function V (Eq. (5)) is always greater than zero for whichever selected vector xr, x and matrix G. However, it is not always possible to get the negative first derivative of the Lyapunov time-dependent function V (Eq. (6)) for every xr, x and G. According to the following equation:

σ(x, t) = G(x(t) − xr(t) = σ = G(x − xr),

(4)

where xr is a vector of the desired state space variable and G is the matrix defining the control of system dynamics, we cannot prove the robot system stability (Eq. (2)). Nevertheless, we can look for suitable conditions for control law u, where the robot system will be stable. This is done in the following way.

For the simplest Lyapunov function V to determine the control law u, the following equation has been selected:

V = σT·σ / 2 .

(5)

The following is derived from the Eq. (5):

V = σ T ⋅ σ .

(6)

Owing to the fact that V is not always less than zero for all xr, x and G, the first desired Lyapunov negative time function derivative has been defined as:

V = -σ T ⋅ D ⋅ σ ,

(7)

where D is a diagonal matrix with positive diagonal elements.

If the Eq. (7) and the derivative of Lyapunov’s Eq. (6) are made equal, the result is:

σ T (Dσ + σ ) = 0.

(8)

The Eq. (8) is valid if both or at least one of multiplicators equals zero. Since the first multiplicand, the term σT, does not equal zero during the transient response, the control law can be calculated on the basis of the second multiplicand (Eq. (9)):

Uran, S. – Šafarič, R.

D ⋅ σ + σ = 0.

(9)

Strojniški vestnik - Journal of Mechanical Engineering 58(2012)2, 93-101

If Eq. (4) is differentiated and the Eq. (2) is inserted into the recently calculated derivative, we get the following result:

+ ∆Bu + d − x ). σ = G ( f + Bu r

(10)

After Eq. (10) has been inserted into the implementation condition of control law Eq. (9), the result is as follows:

u = -(GB )-1 [G (f + ∆Bu + d − x r ) + Dσ ].

(11)

Since the term (f + ΔB·u + d) is unknown and not measurable, it is, therefore, approximated with the neural network N = [o1 ... oi]T (see Fig. 1) by changing the Eq. (11) into:

u = −(GB )-1 [G (N − x r ) + Dσ ].

(12)

σ + Dσ = G (f + ∆Bu + d) − GN = G (Z − N), (14)

where we have substituted Z = (f + ΔB·u + d). To learn the weights of a neural network hidden layer the traditionally back-propagation rule [25] is used.

1.1 Centralized Control Law for Three Degrees of Freedom Mechanism In the previous section, the control law for a general robot mechanism with n-degrees of freedom has been derived; in this section, detailed equations of control law for a direct drive robot mechanism with three degrees of freedom, which is shown in Fig. 4, will be derived.

f + T , (15) T=M θ + h + G n  , and T (see Eq. (1)) are column where T, h , G f n  is the matrix of vectors of the 3×1 dimension, M

Fig. 1. Neural network

Since the term (f + ΔB·u + d) is unknown and not measurable, a classic supervised weight learning of neural network cannot be used. Therefore, a socalled on-line neural network estimator has been developed (Fig. 2), estimating a learning signal (that is the difference between the target and the output of a neural network).

The result after Eq. (4) has been differentiated is the following:

x = G -1 ⋅ σ + x r .

(13)

the 3×3 dimension, and θ = [θ1 θ1 θ1]T is the column vector of the 3×1 dimension of all three axes of the  are estimated and  , h and G robot and where M f simplificated values of real M, h and Gf (see Eq. (1)).  Only nominal or average parameters of the matrix M have been selected. This means that all 9 parameters  are constant while the robot hand is of the matrix M moving. This is, of course, only a rough simplification of how things really look like; for it is a common fact  vary according to that the parameters of matrix M individual axis movements in robot’s working space.

The previous equation can also be rewritten in the following form (see also Eq. (3)):

After Eqs. (12) and (13) have been inserted into the basic equation of mechanism dynamics (Eq. (2)), the result is as follows:

(16)

where:

Fig. 2. Neural network on-line estimator

x = f (x, t ) + B (x, t )u + d(x, t ),

x = θ1 θ 2 θ3 θ1 θ2 

T

θ3  ,  T

x = θ1 θ2 θ3 θ1 θ2 θ3  ,     θ 1 0 0   

θ2 0   0 f = − B = ,

 θ 0 0  −1 3   h + G f  M −1  M   

(17)

0 0  , (18) 0  

and where u is calculated vector of T done by control law (Eq. (19)).

Because of that the unknown variable part ΔB exists and is estimated by the neural network (see

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Eq. (14)). The dimension of vector f is 6×1 and the dimension of the matrix B is 6×3. The control law u of the 3×1 dimension is illustrated in the following equation: u = −(GB )-1 [G (N − x r ) + Dσ ] ,

(19)

where:  K p1  G= 0  0 

0 K p2 0

K v1 0 0

0 0 K p3

 d1 D =  0  0

0 d2 0

0 Kv2 0

0   0 , K v 3 

0 0  , d3 

(20)

1.2 Decentralized Control Law for Three Degrees of Freedom Mechanism T

xr = θ1r θ 2 r θ3r θ1r θ2 r θ3r  ,  

T

x r = θ1r θ2 r θ3r θ1r θ2 r θ3r  ,  

(21)

σ = G (x − xr).

(22)

Coefficients of the matrices G in D are selected in such a way that they enable the fastest convergence of neural network algorithm possible. The column vector N is of the 6×1 dimension and represents the outputs of the neural network oi with i = 1, ..., 6.

The learning procedure for all the weights of an output layer is:

∆w1j = µJ  K p1 0 0  (Dσ + σ ) g ′(net1 )o j , ∆w2j = µJ 0 K p 2 0  (Dσ + σ ) g ′(net2 )o j , ∆w3j = µJ 0 0 K p 3  (Dσ + σ ) g ′(net3 )o j , (23) ∆w4j = µJ [ K v1 0 0 ] (Dσ + σ ) g ′(net4 )o j , ∆w5j = µJ [0 K v 2 0 ] (Dσ + σ ) g ′(net5 )o j , ∆w6j = µJ [0 0 K v 3 ]( Dσ + σ ) g ′(net6 ).o j , neti = ∑ wij o j + bi ,

(24)

j

where j = 1,..., 60, i = 1, ..., 6, l = 1, ..., 9, and g’(*) is the first derivative of the sigmoid function [25].

The neural network of centralized neural network sliding mode controller (CNNSMC) consists of 9 inputs; these are: three actual positions, three actual velocities, and three differences between the desired and the actual position. All of them lie in the joint space of the robot mechanism. The scheme of CNNSMC is shown in Fig. 3.

96

Eq. (1) is simplified for the first single axis (θ1) of DD robot mechanism (Eq. (25)): T1 = J 1θ1 + h 1 + g 1 + tn1 ,

and

Fig. 3. CNNSMC control scheme

(25)

where scalars T1, h 1, g 1 and tn1 are torques needed to move the single axis. h 1 is torque due to Coriollis centripetal and centrifugal forces, g 1 is a torque due to gravitational forces and tn1 is unknown torque disturbance. J 1 is an average, constant and rough approximation of the single axis inertia parameter.

Scalars J 1, h 1, g 1 are estimated and simplificated values of real M, h and Gf (see Eq. (1)).

Eq. (25) has been transformed as follows for the first single axis: x 1 = f1 + ∆B1u1 + B 1u1 + d1 ,

(26)

 1 and where: where ∆B1 = B1 − B

T T x1 = θ1 , θ1  , x 1 = θ1 , θ1  ,

(27)

  θ 1 0  and B 1 =  -1  . f1 =  -1  −J 1 h 1 + g 1    J 1    

(28)

The dimensions of the vectors f1, B1, B 1 are 2×1.

The control law u1 is described by the following equation:

where:

u1 = −(G1B 1 ) −1 [G1 (N1 − x r1 ) + d1σ 1 ] ,

(29)

G1 = [Kp1 Kv1] .

(30)

The coefficients Kp1, Kv1 and constant d1 are selected in such a manner that the most rapid convergence of the neural network (N1 is an output of

Uran, S. – Šafarič, R.

Strojniški vestnik - Journal of Mechanical Engineering 58(2012)2, 93-101

the neural network for the first single axis) learning algorithm is made possible.

T xr1 = θ r1 , θr1 

T and x r1 = θr1 , θr1  ,

(31)

θr1 are reference joint where scalars θr1, θ r1 and  position, speed and acceleration of the single axis, respectively.

σ 1 = G1 (x1 − xr1 ) and σ1 = G1 (x 1 − x r1 ).

(32)

The column vector N1 is of the 2×1 dimension and represents the outputs of the neural network oi (i = a, b). The variable of control law u1 is a scalar.

The learning procedure for all weights of the neural network output layer is: ∆w1aj = η a1 K p1 (d1σ 1 + σ1 ) g ′(neta )o j ,

(33)

∆w1bj = ηb1 K v1 (d1σ 1 + σ1 ) g ′(netb )o j ,

neti = ∑ wij o j + bi ,

(34)

j

where j = 1, ..., 5 (a number of neurons in the hidden layer), i = 2 (indexes: a, b - the number of neurons in the output layer), l = 3 (three neural network inputs were used: an actual position, an actual velocity and a difference between desired and actual positions in the joint space) and g’(*) is the first derivative of sigmoidal function. Fig. 3 also shows the scheme of the single axis controller.

The remaining two D.O.F. single axis controllers are the same as the described one in this subsection.

Every single axis controller has the equal number of inputs and outputs of the neural network, the equal on-line estimator, the same control law etc. The difference between equations developed in current subsection and equations needed for the second and third axis is that all indexes “1” in Eqs. (25) to (34) are changed from “1” to “2” for the second axis and from “1” to “3” for the third axis. In fact, there are three equal control laws: u1, u2 and u3; the only differences between the above mentioned control laws for all three axes are different values for parameters dk, θk, Kpk, Kvk and of course different inputs θk, θ k and  where k = 1, 2, 3.

1.3 Simplified Centralized and Decentralized Control Laws Centralized and decentralized control approaches estimate a part of the variable robot dynamic model (torque model due to friction, Coriolis, centripetal and centrifugal forces) and use only the part of a dynamic

plant model – the so called estimated inertia matrix M (see Eqs. (1) to (3), (11) and (12)). If Eq. (3) is rewritten as:

B(x, t ) = C + ∆B(x, t ),

(35)

where C is a matrix, which includes the simple unity  , for CNNSMC, so Eq. diagonal matrix I instead of M (18) is changed to:

0 0 0 0 C= 0 0  −1  I

0 0  , 0  

(36)

where I is a unity diagonal matrix of 3×3 dimension.

Consequently, Eq. (19) is also changed to:

u = −(GC)−1 [G (N − x r ) + Dσ ] ,

(37)

while matrices G, D and vectors N, x r and σ are not changed in comparison to the control law of CNNSMC (see Eqs. (16) to (24)). Eq. (37) represents the control law for a simplified centralized neuralnetwork sliding-mode controller (SCNNSMC).

The equation development for the case of simplified decentralized neural-network sliding-mode controller (SDNNSMC) is similar as for the case of the SCNNSMC. Here, Eq. (28) is changed to:

0  C1 =   . 1 

(38)

Therefore, the control law for the SDNNSMC is rewritten from Eq. (29) as:

u1 = −(G1C1 ) −1 [G1 (N1 − x r1 ) + d1σ 1 ] ,

(39)

where vectors G1, x r1 , N1 and scalar variables d1 and σ1 are not changed in comparison to the control law of DNNSMC (see Eqs. (25) to (34)).

As it is seen from Eqs. (35) to (39), both simplified control laws do not need any plant model parameters for accurate estimation of the direct-drive robot mechanism dynamics.

2 APLICATION ON A REAL MECHANISM The scheme of a direct-drive three degrees of freedom mechanism is illustrated in Fig. 4, while in Fig. 5 the photo of the robot mechanism is shown. The Dynaserv’s AC-motors with maximum torque of 220, 160 and 60 Nm, and the nominal angular velocity 1 to

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2 rotations per second were used. The mechanism is made of aluminium, which is fixed on the AC-motors.

A robot wrist can be added to the top of the third axe of the robot.

Since the robot is expected to perform manipulation tasks, the complete system has been tested with all four developed controllers described in previous section to perform the following tasks: • performance of the PTP movement with the static error less than 0.1 mm, and • robustness when the top of the robot is disturbed with sudden load changes.

To satisfy the above mentioned demands, a robot controller with the sufficient computed power had to be developed. For a parallel execution of algorithms a transputer network of 8 transputers, one PowerPC, and one ordinary personal computer have been used; all have the possibility of working in parallel.

A robot computer controller is described in a source [21]. The sampling time Ts = 2 ms is the execution time of all algorithms needed for the robot computer control.

The position error of the robot tip (Eq. (40)) or a trajectory tracking error in the task space has been used to measure the quality of all four robot controller performances:

1/ 2

e = ( X di − X i ) 2 + (Ydi − Yi ) 2 + ( Z di − Z i ) 2 

, (40)

where Xdi, Ydi, Zdi are reference trajectories in the ith sampling time in the task space and Xi, Yi, Zi are the actual trajectories in the ith sampling time in the task space.

2.1 The Test of Sudden Load Changes

Fig. 4. The robot system

Fig. 5. The real lab robot mechanism

98

The position error of a robot tip in a stationary position for the centralized neural-network slidingmode controller (CNNSMC) is shown in Fig. 6, when sudden load changes occurred (approximately 80% of the maximal torque on the robot tip). The initial weights of neural network were randomly chosen between −1 and +1 learning rate η = 1e-8, d1 = 20, d2 = d3 = 30, Kp1 = Kp2 = Kp3 = 100 and Kv1 = Kv2 = Kv3 = 60.

The position error of the robot tip in stationary position for decentralized neural-network slidingmode controller (DNNSMC) is shown in Fig. 7 when the same sudden load changes occurred as in previous test. The initial weights of DNNSMC were randomly chosen between -1 and +1, learning rate η1a,b = 4e-7, η2a,b = 6e-6, η3a,b = 6e-6, d1 = 15, d2 = 23, d3 = 20, Uran, S. – Šafarič, R.

Strojniški vestnik - Journal of Mechanical Engineering 58(2012)2, 93-101

Kp1 = 115, Kp2 = 150, Kp3 = 180 and Kv1 = 25, Kv2 = 40, Kv3 = 20.

Fig. 6. Robot tip’s position error for CNNSMC during load changes in the stationary position test

Fig. 9. Position error of the robot tip for SDNNSMC during load changes in the stationary position test

The results are almost the same for the test of sudden load changes in the case of CNNSMC and DNNSMC. The difference is found in the first few seconds of Figs. 6 and 7 (PTP movement). The point to point robot tip movement is executed during this time (all three axis start in the same positions and finish in position 1 rd). It could be observed that the dynamic error is higher and the set-up time is longer in a case of DNNSMC. The sudden load changes of robot tip position for SCNNSMC and SDNNSMC are presented in Figs. 8 and 9.

2.2 Summary of Results Fig. 7. Robot tip’s position error for DNNSMC during load changes in the stationary position test

Fig. 8. Robot tip’s position error for SCNNSMC during load changes in the stationary position test

The quality of the presented DNNSMC is practically the same as for CNNSMC. The disadvantage of DNNSMC against CNNSMC is that the CNNSMC has a shorter set-up time and a smaller dynamic error during the PTP movement (see Figs. 6 and 7). The advantage of DNNSMC against CNNSMC is that DNNSMC has three completely separated control law equations with three remarkably smaller neural networks (each neural network has 5 neurons in the hidden layer, two outputs and three inputs). Therefore, a learning procedure of the neural network can be made for each axis separately which is remarkably easier than in a case of one neural network of CNNSMC with nine inputs, eighty neurons in the hidden layer and six outputs. Due to this reason the robot control computer hardware could run more axes at the same sampling time in the case of DNNSMC than in the case of CNNSMC. The average execution time for CNNSMC was 1.75 ms, while the average execution time for all three DNNSMCs was 1.05 ms.

This sampling time also includes the complete direct

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and inverse kinematics, interpolators, etc., for the robot controller.

If a comparison between both simplified (SCNNSMC and SDNNSMC) methods against “full” methods (CNNSMC and DNNSMC) is made, the next observation can be seen: both simplified methods need a remarkably greater set-up time than the other two. In case of the initial PTP movement the setup time is approximately 5 s in case of SCNNSMC against 2 s for the CNNSMC. Also, the set-up time for the transient responses to load changes is smaller in the case of “full” methods against simplified methods.

The set-up time for the transient responses to load changes is 1 s for CNNSMC, 2 s for DNNSMC and SCNNSMC and 5 s for SDNNSMC. The observation of peak values of a position error of PTP movement and during the load changes is also important for the quality comparison between the mentioned four methods (see Figs. 6 to 9). It can be seen that the best results, the smallest peak values of the position error of the robot tip for PTP movement is observed for CNNSMC (4 mm) and DNNSMC (16 mm) while the peak values of position error during load changes (disturbances) have almost the same values (4 to 5 mm) for CNNSMC and DNNSMC. The peak values of position error for PTP movement is higher for both simplified methods: SCNNSMC (32 mm) and SDNNSMC (18 mm), while an interesting effect can be observed when the position error of the robot tip during the load changes is measured.

In the case of SCNNSMC the peak position error continuously decreases from the first load change (66 mm) to next load changes and it is only 5 mm in the end of experiment, which is practically the same result as for CNNSMC and DNNSMC. This means that in the case of SCNNSM there is a longer learning period because the neural network sliding-mode estimator has to learn complete robot dynamic and not only a part as in the case of “full” methods. The worst results, which means the highest peak position error of the orbot tip was measured in the case of SDNNSMC (10 to 17 mm).

The steady-state position error of the robot tip was the smallest in the case of CNNSMC after the PTP movement and after load changes (practically zero) and almost zero in the case of DNNSMC, while in the case of SCNNSMC decreasing value of steady state position error is measured from the beginning of the experiment to the end of experiment. The worst result, the highest value of the steady-state position error is measured in the case of SDNNSMC where the steady state error is constantly between 0.5 to 1 mm.

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3 CONCLUSIONS This paper has presented the experimental development and laboratory implementation of four: centralized, decentralized, simplified centralized and simplified decentralized neural network continuous sliding-mode controllers for manipulation tasks for the real direct-drive 3 D.O.F. PUMA like robot manipulator. The neural network sliding-mode structure of the controller has been used to estimate and compensate structured (the inertia matrix) and unstructured (torques due to Coriollis forces, gravitational forces, friction forces, etc.) uncertainties of the robot manipulator. The adaptive and selfimproving capability of the neural network controllers to the unstructured effects (sudden load changes) has been shown for all four neural network controllers.

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[22] Klobučar, R., Čas, J., Šafarič, R., Brezočnik, M. (2008). Uncalibrated visual servo control with neural network. Strojniški vestnik – Journal of Mechanical Engineering, vol. 54, no. 9, p. 619-627.

[23] Čas, J., Škorc, G., Šafarič, R. (2010). Neural network position control of XY piezo actuator stage by visual feedback. Neural Computing & Applications, vol. 19, no. 7, p. 1043-1055, DOI:10.1007/s00521-010-0339-y.

[24] Čas, J., Škorc, G., Šafarič, R. (2010). Improved micropositioning of 2 DOF stage by using the neural network compensation of plant nonlinearities.

Strojniški vestnik – Journal of Mechanical Engineering, vol. 56, no. 10, p. 599-608.

[25] Cichocki, A., Unbehauen, R. (1993): Neural Netwok for Optimal Signal processing. John Wiley&Sons, Chichester.

Neural-Network Estimation of the Variable Plant for Adaptive Sliding-Mode Controller

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Strojniški vestnik - Journal of Mechanical Engineering 58(2012)2, 102-106 DOI:10.5545/sv-jme.2011.064

Paper received: 2011-03-17, paper accepted: 2011-11-23 ©2012 Journal of Mechanical Engineering. All rights reserved.

Effect of Agitation Work on Heat Transfer during Cooling in Oil ISORAPID 277HM Taraba, B. – Duehring, S. – Španielka, J. – Hajdu, Š.

Bohumil Taraba* − Steven Duehring − Ján Španielka − Štefan Hajdu Slovak University of Technology in Bratislava, Faculty of Materials Science and Technology, Institute of Production Systems and Applied Mechanics, Slovak Republic The article focuses on the issue of heat treatment. The cooling curves were obtained for Isorapid 277HM with an experimental way of temperature measuring and their statistical processing. Experimental method was consistent with the test normative ISO standard 9950 (Wolfson’s test). The cooling oil Isorapid 277HM was agitated with different agitation work and had a constant temperature of 50 °C. In the next part of this article the surface temperature depended combined heat transfers were calculated. The methodology was based on inverse heat transfer. The interpretation code was software ANSYS and ORIGIN. Keywords: quenching, cooling curve, agitated oil, heat transfer, Wolfson’s probe, ANSYS

0 INTRODUCTION Heat treatment is a multiparameters process. The selection of appropriate parameters predicts required behaviours of treated components. The kind of quenching medium, the selection of quenching medium temperature and the selection of the medium state (unagitated, agitated) are determining factors. Quenching oil Isorapid 277HM belongs to cooling oils common in use. A prediction of treated components behaviour during a cooling process is possible only in the case if the boundary conditions of the process are defined. Before the application of a cooling process numerical simulation, the heat transfer coefficient on the component surface should be defined quantitatively. The experiment, applying simulation model and numerical solution, is able to test the influence of heat treatment parameters on an immediate and final state of a component. A cooling curve is the basis for determining the combined heat transfer coefficient (HTC) as a function of temperature. The current situation presents two ways of getting the HTC cooling curve: direct and inverse approach. Direct access is represented in the publication [1]. HTC is obtained by calculating based on the classical theory of heat conduction in infinite long cylinder with small Biot’s number (Bi < 0.1) in few simple recursive computations using the “Heat Transfer Coefficient Wizard”. The comparison between measured cooling curves (derived cooling rate curve) with calculated curves is only visual.

The heat transfer coefficient inverse method is based on iterative approach loading simulation model in the form of HTC and the effect of temperature at thermocouple (TC-temperature) [2] to [4]. The inverse numerical method is implemented in the software 102

SQintegra also. This program is used as the evaluation tool of the IvfSmartQuench instrument [2].

Fig. 1. ISO probe cooling process in Isomax 166, a) vapour blanket (VP) in time 1 s, b) begin of boiling (B) in time 2.8 s, c) boiling (B) and convection (C) in time 6.3 s

Inverse-numerical-correlation method (INC) defines HTC over inverse heat transfer problem, which was proposed by the authors of this article.

The INC method is applied to the solution of direct well-posed inverse problems. Through the controlled iterative process a result which is very likely and useful for computer prediction of thermal treatment processes can be found. The main active part of this procedure is a researcher with theoretical knowledge and experiences with numerical analyses. Typical for the inverse methods is that there exist an infinite set of solutions in general. Only the right setting of statistical criteria get the result with the high degree of reality. Fig. 1 shows the cooling process of ISO probe in optically transparent quenching oil Isomax166.

Photographs in Fig. 1 show that the cooling process

*Corr. Author’s Address: Faculty of Materials Science and Technology, Slovak University of Technology, 91724 Trnava, Slovak Republic, bohumil.taraba@stuba.sk

Strojniški vestnik - Journal of Mechanical Engineering 58(2012)2, 102-106

in the three forms of heat transfers (radiation, boiling and convection) are a continuous process without step change (photo from article authors). Then, the determinate HTC must also be continuous.

The methodology and results of a cooling effect quantification of oil Isorapid 277 HM with chosen agitation work at temperature 50 °C are presented in the article.

Table 1. Thermophysical material properties of austenitic stainless steel DIN 1.4841 T [°C] 0 100 200 300 400 500 600 700 800 900

1 EXPERIMENTAL Quenching oils ISORAPID are accelerated quenching oils with very good evaporation stability and fast quenching properties. These oils have been especially designed for an application in sealed quench furnaces. They ensure rapid and homogeneous cooling of all parts during batch quenching and also rapid decay of the vapour blanket within the batch.

Their application in open quench baths reduces smoke and flame formation significantly [5].

The experimental set-up in Fig. 2 consisted of electrical resistance furnace of LM 212.10 type, cylinder-shaped experimental probe (Table 1, Fig. 3), oil Isorapid 277HM with a mass of 28 kg, portable USB-based DAQ for thermocouples NI USB 9211 for a digital record of measured temperatures, frequency converter MICROMASTER 440 (MM440), a personal computer and pneumatic manipulator for probe moving. A material of probe was austenitic stainless steel DIN 1.4841 with high temperature resistance. Thermophysical material properties were obtained from experimental measuring by NETZSCH apparatus: LFA 427, DSC 404 C Pegasus and Dilatometer 402 C. Geometrical and initial conditions of the experiment were based on the quenching test ISO 9950 [6]. Before cooling, the probe was heated to the initial temperature of 850 °C. The temperatures were measured by the standard 304SS thermocouple of K type with diameter of 1.53 mm located in the centre of the probe. Temperatures were recorded 5 times per second. A set of measurements was repeated six times for each state of oil. Each set of measured cooling curves was averaged into a core cooling curve. There were seven oil states realized, one for unagitated and six for agitated. Temperature measurement started from the moment when the centre of gravity of probe reached the oil level.

Power parameters (torque moment and input rpm) of the swirl devices were obtained from the data of frequency converter MM440.

λ [W·m-1·K-1] 13.5 15.0 16.8 18.6 20.0 21.3 23.2 24.8 25.6 27.1

ρ [kg·m-3] 7880 7854 7814 7773 7731 7689 7645 7601 7556 7511

cp [J·kg-1·K-1] 474 490 512 525 535 544 569 581 589 600

Fig. 2. Experimental setup: 1- electrical resis-tant furnace, 2- personal computer, 3 - probe with a thermocouple, 4 - NI USB 9211 converter, 5 - cooling medium and its heater, 6 - pneumatic manipulator, 7- record of cooling curve, 8- frequency inverter

2 THEORETICAL BASE OF THE TASK Transient temperature field T = T(r, z, t) of a cooled probe is described by Fourier-Kirchhoff differential equation (FKDE) of heat conduction for cylindrical coordinate system [8],

λ (T )  ∂ 2T 1 ∂T ∂ 2T  ∂T − = +   [K·s-1], (1) ρ (T )cp (T )  ∂r 2 r ∂r ∂z 2  ∂t

where λ(T) is coefficient of heat conductivity, ρ(T) density, cp(T) specific heat, r radius [m] and z is height of probe [m].

Combined heat transfer coefficient HTC(Ts) was determined as the function of the probe surface temperature Ts for constant oil temperature Tr. The

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condition of equality of heat flux is valid on the probe surface in time point ti by formula [4]:

−λ (T ) gradT

ti

= HTC (Ts ) Ts ( ti ) − Tr  . (2)

Other assumptions of thermal tasks: the probe material is isotropic and its thermophysical properties are temperature dependent, the cooling process is isobaric, the temperature field is not dependent on the angle φ, T ≠ f(φ), coolant temperature is constant throughout the process, Tr ≠ f(t). Heat generation in unit volume per unit time was not take account because in probe material there are no phase transformations in the temperature interval 50 to 850 °C. A thermal task is solved by the finite element method (FEM). The FEM solution procedure is in the form of equation:

 − P = 0 , (3) K1 ⋅ T + K 2 ⋅ T + K 3 ⋅ T

Fig. 3. Probe geometry and geometrical model with generated mesh

where K1 is heat conduction matrix, K2 matrix of boundary conditions, K3 enthalpy matrix,  time derivation of T temperature vector, T temperature and P is vector of outer loads.

Absolute value of relative error δT was obtained by formula:

δT

ti

=

TTC − Tans ⋅100 , (4) TTC

where TTC is measured temperature and Tans is temperature of numerical solution, both for time ti.

Input power into oil per 1 kg Pw was calculated from torque moment and angular velocity values at device for swirling by formula:

Pw =

2π M τ n , (5) m

where Mτ is torque moment, n rotational speed and m is mass of oil in device.

3 NUMERICAL SIMULATION Engineering-scientific program code ANSYS [7] was the interpretation program of numerical simulation.

Geometrical model of the probe was the lower half part of the cylinder, Fig. 3.

Applied elements were axisymmetric with linear base function and surface temperature behaviour option. Surface temperature behaviour allows the application of thermal load HTC(Ts) as the actual surface temperature function. The generated mesh was mapped with the length of the element edge 0.25 mm.

Calculation procedure was transient and nonlinear.

Time step was 0.01 s.

104

Fig. 4. Block diagram of iterative solution of the boundary condition - INC method

Through the solution of simulation model of thermal nonlinear and transient task in the ANSYS the temperature curve for chosen HTC-loads values was found. Then, a comparison with measurement temperature curve followed and the process was repeated. The curve fitting takes account of the temperature and cooling rate curve. Task solution by the INC method must meet the following criteria: absolute value of relative error for measured and calculated temperature in the i-time must be less

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Strojniški vestnik - Journal of Mechanical Engineering 58(2012)2, 102-106

than 1%, absolute value of relative error for cooling rates derived of measured and calculated temperature must be less than 5% and the correlation coefficient between the measured and calculated temperatures in the cooling time must be greater than 0.99. Block diagram of iterative solution of the boundary condition - INC method is showed in Fig. 4.

4 OBTAINED RESULTS Time dependences of 7 measured temperatures during probe cooling from 850 °C into unagitated and agitated oil at temperature 50 °C are shown in Fig. 5. These core cooling curves were the basis for INC method applying.

In Fig. 6 are plotted cooling rates curves (derived from core cooling curves).

There is a distinct difference between cooling in unagitated and agitated oil. The lowest value of cooling rate is for unagitated oil and with energy supplied into oil increases the cooling rate and temperature at the centre at which the maximum cooling rate. The cooling rate interval is of 103 to 114 K·s-1.

Combined heat transfer coefficient dependences of probe surface temperatures for unagitated and agitated oil are the main results of INC method and are shown in Fig. 7.

Fig. 7. HTC curves for unagitated and agitated oil ISORAPID 277HM Fig. 5. Set of measured temperatures, unagitated and agitated oil ISORAPID 277HM

Fig. 6. Cooling rates for unagitated and agitated oil ISORAPID 277HM

Forced movement of Isorapid 277HM oil alters the cooling process of probe in the vapour phase. The existence of vapour phase is shorter at higher surface temperatures and HTC reaches higher values than in the case of unagitated oil also. An important feature is knowing that the effect of agitation of oil will be reflected most in the convection heat transfer surface temperature below 317 °C. HTC varies with the size of the energy supplied into oil. HTC values are readable from Fig. 7.

Combination of experimental cooling curves and numerical simulation using INC method gives the values of absolute value of relative errors that are showed in Fig. 8.

For the purposes of clarity Fig. 8 has been selected four values of energy supplied into oil. The absolute relative error between the measured and calculated values of cooling curve was evaluated. The maximum value was 1.09% and the average error for all cases was less than 0.45%.

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5 Conclusion

Fig. 8. Absolute values of relative errors for core cooling curve fitting for chosen energy input

A definition of heat transfer from the probe into the coolant as the inverse problem of heat conduction using a suitably selected control parameters is an appropriate method to quantify the HTC under different conditions. Energy input into agitated oil in the form of work per 1 kg media allows the reproducibility of the experiment. The obtained HTC are properties of the tested oil and are also used as the boundary condition of heat transfer in the heat treatment processes. The HTC obtained for unagitated oil is used only for application to vertical surfaces. HTC data for agitated oil may be entered into the simulation models for outer surface regardless of the location of surfaces.

The results showed that the effect of oil agitation on the cooling process was reflected in the vapour phase and a significant influence of agitation in the convective heat transfer. The use of HTC for agitated oil is suitable for numerical experiments through software SYSWELD or DEFORM and of course for real experiments in the heat treatment process.

6 REFERENCES

Fig. 9. The fitting comparison for cooling rate curves for unagitated oil and agitated oil with energy input 2.59 J·s-1·kg-1

The temperature curve fitting was then very close and it was not possible to graphically represent both curves. The correlation coefficient between calculated and measured temperatures was obtained 0.9998 for all solved cases.

The test was made for a relative error between the cooling rate obtained from the measured cooling curve and the curve of the INC method also. Fig. 9 shows two selected cooling rate curves for unagitated and agitated oil with energy input 2.59 J·s-1·kg-1. For unagitated oil average absolute value of relative error was 0.23 and for energy input was the calculated error 2.02%.

106

[1] The Heat Treatment Simulation Solution from ESI GROUP (2011), from http://www.esigmbh.de/ downloads/ESI/Dokumente/Welding/old/The_Heat_ Treatment_Solution_Overview_180306.pdf, accessed on 2011-11-18.

[2] Troell, E., Kristoffersen, H., Bodin, J., Segerberg, S., Felde, I. (2007). Unique software bridges the gap between cooling curves and the result of hardening.

Carl Hanser Verlag, München, p. 110-115.

[3] Bodin, J., Segerberg, S., Lövgren, M. (2005). IVF SmartQuench to ensure the reliability of the coolant, from http://extra.ivf.se/smartquench/articles_and_lit. asp, accessed on 2011-11-18.

[4] Taraba, B., Španielka, J. (2010). Combined heat transfer coefficient calculation for cooled probe to 850 °C in quenching oil. The international conference of the Carpathian Euro-region specialists in industrial system, p. 281-286.

[5] Petrofer Hildesmein (2011), from http://www.norteks. ru/en/product/petrofer/branded_items/harden_comp/, accessed on 2011-11-18.

[6] Totten, G.E., Werster, G.M., Tensi, H.M., Liscic, B. (1997). Standards for Cooling Curve Analysis of Quenchants. Heat Treatment of Metals, vol. 4, p. 92-94 [7] Ansys Theoretical Manual (2011), from http://www. pdfqueen.com/pdf/an/ansys-10-users-manual/10/, accessed on 2011-11-18.

[8] Incropera, F.P., Dewitt, D. (1996). Fundamentals of heat and mass transfer. John Wiley & Sons, New York.

Taraba, B. – Duehring, S. – Španielka, J. – Hajdu, Š.

Strojniški vestnik - Journal of Mechanical Engineering 58(2012)2, 107-114 DOI:10.5545/sv-jme.2011.160

Paper received: 2011-08-24, paper accepted: 2011-11-18 ©2012 Journal of Mechanical Engineering. All rights reserved.

Analysis of Building Electric Energy Consumption Data Using an Improved Cooling Degree Day Method Krese, G. – Prek, M. – Butala, V. Gorazd Krese – Matjaž Prek* – Vincenc Butala

University of Ljubljana, Faculty of Mechanical Engineering, Slovenia In cases where a quick insight into the operation of an HVAC system is more important than accuracy, cooling degree days can be used for monitoring electric energy consumption dependent on meteorological conditions. Cooling degree days are calculated from differences between outdoor temperatures above the base temperature and the base temperature itself, therefore containing both climate and building information. The difficulties in applying this method are the determination of base temperature and choosing a procedure for calculating degree days, which vary depending on the resolution of the weather data used. In addition, the cooling degree method has a major flaw, i.e. it considers only a linear dependence between cooling energy consumption and sensible cooling load, thereby ignoring latent loads, which become more significant at higher outdoor temperatures.

In this article an analysis of real electric energy consumption data using the cooling degree method and an improved method derived from it that includes latent loads, as well as a comparison between them, are shown. Both methods are applied several times to metered data, each time with a different combination of a method for determining base temperature and a degree day calculation technique.

Keywords: building electric energy consumption, cooling degree day, base temperature, latent load, wet-bulb temperature

0 INTRODUCTION One of the targets of the European Union (EU) growth strategy Europe 2020 is to reduce greenhouse gas (GHG) emissions by at least 20% compared to 1990 levels, increase the share of renewable energy sources in final energy consumption to 20% and to reduce the primary energy use by 20% with projected levels by 2020 (“20-20-20” targets). Improving the energy performance of buildings is the key to achieve these goals, as buildings are responsible for 40% of EU energy consumption. Although space heating is still the dominant energy demand for buildings in most European countries, special attention should be paid to space cooling, since the energy consumption it accounts for (mostly electric energy) is growing rapidly as a consequence of global warming. For promoting energy conscious design [1] and operation simple methods are more appropriate than more complex and time-consuming computer simulations.

One of these simple methods is the cooling degree method, which allows a comparison between a building’s energy performance and past performance, as well as with other buildings in different climates.

Cooling degree days (CDD) are defined as the sum of positive differences between outdoor air temperature θo and reference temperature θb over a certain time period:

CDD = ∑ (θ o − θb ). (1)

Reference temperature, also called base temperature, represents the building’s balance point, i.e. the maximum outside temperature at which no

cooling is required to maintain the thermal comfort inside the building. The balance point temperature depends on the building’s characteristics (thermal mass, orientation, etc.), internal (people, lights, appliances and equipment) and external (through structure, fenestration, infiltration) heat gains as well as on the set indoor temperature and, is as such, specific for each building, so the base temperature should be determined for each building separately as proposed by Day et al. [2] rather than using standard published values (e.g. 15.5 °C in UK and 18.3°C in USA). Since heat gains and internal temperature vary throughout the cooling season and even during the day, the main difficulty with applying cooling degree days to building energy use lies in how to define the base temperature.

Another problem of the cooling degree day method is that it assumes that the building total cooling load consists only of sensible load components.

Huang et al. [3] suggested using enthalpy latent days (ELD) along with cooling degree days to account for the latent cooling loads. Enthalpy latent days are the summation of positive enthalpy differences between the outdoor air enthalpy ho and enthalpy at the outdoor air temperature θo and some reference absolute humidity xb:

ELD = ∑  ho ( θo , xo ) − h ( θo , xb )  . (2)

Krese et al. [4] went one step further and introduced the performance surface graph and the F-test method for determining the building’s base humidity. The performance surface is essentially a plot of building’s electric energy consumption as a

*Corr. Author’s Address: University of Ljubljana, Faculty of Mechanical Engineering, Aškerčeva 6, 1000 Ljubljana, Slovenia, matjaz.prek@fs.uni-lj.si

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function of cooling degree days and latent enthalpy days.

In this paper, different approaches for addressing the above-mentioned issues surrounding the use of cooling degree days as predictive and monitoring tools are tested on real building performance data and compared with each other.

are explained in [5] and [6], which enable to estimate monthly cooling degree days with monthly average temperature and standard deviation of daily average temperature.

1 THEORY Different ways of calculating cooling degree days and methods for determining base temperature as well as a simple way to capture latent loads with cooling degree days are described in this part of the article.

1.1 Calculation of Degree-Days From a strictly mathematical viewpoint cooling degree days are a time integral of temperature differences between a defined base temperature and outside air temperatures above it. Hence only the positive area between the outdoor temperature curve and the base temperature line is considered (Fig. 1). The calculation procedures for CDD differ in the quality of used weather data (i.e. temperature). When hourly temperature data is available CDD can be calculated simply by subtracting the base temperature θb from hourly outside air temperatures θo,i and by averaging the sum of positive hourly differences, which are called cooling degree hours (CDH) analogously to cooling degree days, over the day:

∑ (θ 24

CDD =

i =1

o ,i

− θ b ) ∀θ (

o ,i

>θb )

24

. (3)

The simplest technique for calculating cooling degree days is to calculate CDD from the mean daily temperature θ o , (Eq. (4)). This method is mathematically less accurate than the above mentioned mean cooling degree hours method (MCDH) because it considers only days with an average daily temperature higher than the base temperature. In practice this means that when calculating CDD with the same base temperature the mean daily temperature method (MDT) would produce less cooling degree days than the MCDH method for the same time period since it would leave out some days.

(

CDD = ∑ i =1 θ o ,i − θb n

)(

∀θ o ,i >θb

)

. (4)

For cases where even less detailed climate data are available, more complex calculation methods (compared to the previously described procedures) 108

Fig. 1. Principle of cooling degree-day calculation

1.2 Determination of Base Temperature Although one can determine the base temperature can be analytically determined for simple single zone constant air volume (CAV) air-conditioning systems as shown in [7], statistical methods are mostly preferred, since analytical determination for more complex systems is difficult and time-consuming. One of these methods is the energy signature method [8]. A building energy signature is a plot of building’s daily electric energy consumption Ed against mean daily temperature (Fig. 2a). The intercept of weather independent and dependent electric energy consumption represents the building’s base temperature and can be calculated with piecewise linear regression as shown in Fig. 2b. The main disadvantage of this approach is that it requires high resolution energy consumption data (i.e. daily consumption), which is not always available.

Therefore, a more practical approach for most users is to determine the base temperature via the performance line method. Performance lines are essentially bestfit straight lines through data on scatter plots of monthly electric energy consumption Em against monthly cooling degree days CDDm (Fig. 3a) and are primarily used for monitoring and analyzing energy consumption of existing buildings by means of degree days. The base temperature of a building is determined by putting a best-fit second order polynomial through data on a CDDm versus Em scatter plot and by varying the base until the polynomial best is almost equal to linear, i.e. the quadratic term’s regression becomes zero as shown in Fig. 3b. A concave upward polynomial indicates a too low base temperature,

Krese, G. – Prek, M. – Butala, V.

Strojniški vestnik - Journal of Mechanical Engineering 58(2012)2, 107-114

Fig. 2. Energy signature; a) example, b) base temperature determination

while a concave downward polynomial indicates a too high base value.

1.3 Wet-Bulb Temperature Cooling Degree Days The easiest way to include latent loads in cooling degree days is to calculate them with wet-bulb temperature θw instead of dry-bulb temperature as briefly mentioned in [9]. The wet-bulb temperature is the minimum temperature to which air can be cooled by evaporative cooling, and, as such, contains information about air temperature as well as moisture content. On the Mollier psychrometric chart points with the same wet-bulb temperature lie on fog region isotherms, which are almost parallel with the isenthalps, hence wet-bulb temperature differences are equivalent to enthalpy differences.

The main advantage of wet-bulb cooling degree days (CDDw) over enthalpy days (summations of enthalpy differences over time) is that they have the same unit (K·day) as ordinary (i.e. dry-bulb) cooling degree days and are therefore easily comparable to them. Calculation procedures and methods for base

temperature determination are simply taken over from dry-bulb cooling degree days (sections 1.1 and 1.2). Nevertheless, the physical meaning of wetbulb cooling degree days is quite different from that of cooling degree days. Whereas the CDD method presumes that moist air, regardless of state, cools down at constant absolute humidity (Fig. 4a), the CDDw method leaves open both possibilities of cooling moist air; i.e. cooling with and without dehumidification (condensation) as shown in Fig. 4b.

2 DATA The statistical analysis was carried out on energy performance data of an office building located in Ljubljana, Slovenia. It is a 13 story building with 7200 m2 of air conditioned spaces. The double glazed facade with a g-value of 0.75 (coefficient of the permeability of total solar radiation energy) has an area of 2340 m2 and internal blinds. The building is equipped with two centralised heating ventilation and air conditioning (HVAC) systems with moisture control, one for the inner and one for the exterior

Fig. 3. Performance line; a) example, b) base temperature determination Analysis of Building Electric Energy Consumption Data Using an Improved Cooling Degree Day Method

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zone. The air-conditioning system for the external zone is a 4-pipe air and water induction system, while air-conditioning for internal zone is provided by a CAV system. Cooling is provided by two water cooled vapor-compression liquid chillers each with a nominal cooling capacity of 550 kW and by an additional cooling system for the server room with a capacity of 32 kW. Building performance data was provided by a local electricity distribution company in form of 15min total electric power readings, which were hourly averaged in order to get hourly total electric energy consumption. The data were gathered for the period between February 1st, 2009 and January 31st, 2010. In addition, hourly meteorological data for the building location for the same time interval was obtained.

3 RESULTS Before calculating degree days for the selected time period we determined the building’s base (dry-bulb and wet-bulb) temperature with the methods described in section 1.2.

The energy signature method was used first.

Initially all available data (i.e. daily electric energy consumption and mean daily temperature) were used to plot the dry-bulb and wet-bulb energy signature.

Both of the resulting energy signatures indicated the existence of two energy consumption levels as shown in Fig. 5a. Since this was clearly the consequence of occupancy variation, the non-working days (weekends and holydays) were filtered out and the base temperatures were determined with piecewise linear regression from the energy signatures reploted with the filtered data (Fig. 5b). The thus obtained regression lines on the left side of base values had noticeably positive slopes, which was not in accordance with the theory of the energy signature method. By definition the left side of energy signatures is weather independent, so the regression lines should have been parallel to the temperature axis (zero slope).

A detailed analysis of hourly data revealed that the root cause of this deviation lies in the use of building overall electric energy consumption. The problem is that space cooling is not the only contributor to energy consumption, thus changes in operation of building systems and equipment whose energy consumption

Fig. 4. Cooling load assumptions; a) CDD method; b) CDDw method

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represents the base load, i.e. the non-weather related energy consumption, also influence the determination of base temperatures. In our case the reduction of night-time ventilation rate in winter resulted in considerably lower energy consumption in days in which the HVAC system operated under the winter regime compared to the days when space cooling was off and the ventilation rate was not dropped. For this reason, the building base load seemed to increase with temperature.

In order to eliminate the influence of base load variation, hours outside the working schedule (7 a.m. to 5 p.m.) were removed from the working day data.

The so filtered data was then used to plot the energy signatures for a third time and to calculate the dry-bulb and wet-bulb base temperature (Fig. 5c). All the base values obtained from the energy signature method are listed in Table 1.

Table 1. Base temperatures determined using the energy signature method Working days

Working days 7 a.m. to 5 p.m.

R2

R2

θb [°C]

14.6

0.84

16.4

0.78

θw,b [°C]

12.4

0.88

12.8

0.83

Next, the performance line method was applied.

Each base temperature was determined twice, once with degree days calculated from daily averaged hourly dry-bulb/wet-bulb temperature differences (Eq. (3)) and once with daily differences (Eq. (4)) as shown in Fig. 6. The results are listed in Table 2.

Base temperatures determined using hourly values are higher than those determined with daily values, which can be explained with the fact that hours are too small time increments to capture the thermal storage effect. In contrast, the wet-bulb base values are almost equal. The reason for this is very simple and lies in the meteorological data. The outdoor wet-bulb temperature varies little throughout the day compared to the dry-bulb temperature (Fig. 7), therefore the mean daily wet-bulb temperature differs very little from individual hourly values, i.e. the daily standard deviation of wet-bulb temperature is small.

Table 2. Base temperatures determined using the performance line method Hourly values

Daily values

θb [°C]

21.5

16.1

θw,b [°C]

12.4

12.1

In comparison with base temperatures determined via energy signature method from filtered workday data (7 a.m. to 5 p.m.), the base values obtained from performance lines using daily temperature differences (Eq. (4)) are slightly lower. The differences are due to the chosen time interval for base temperature determination from energy signatures. Because the lowest temperatures of a day occur at the filtered out hours, the mean temperatures calculated for the selected averaging period are higher than the mean daily temperatures, hence the energy signatures and with them the base temperatures are shifted forward on the temperature axis. As a result monthly dry-bulb

Fig. 5. Base temperature determination via energy signatures; a) unfiltered data, b) working days, c) working days 7 a.m. to 5 p.m.

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Fig. 6. Base temperature determination via performance lines; a) CDD calculated from hourly differences, b) CDD calculated from daily differences

and wet-bulb cooling degree days (Table 3) were calculated only for base temperatures determined via performance lines using daily values. Whereby degree days were calculated only with the calculation procedure, which was employed in determination of base values (i.e. mean daily temperature method).

To find out which cooling degree day method is more accurate, performance lines were constructed (linear regression) from monthly total electric energy consumption and each set of monthly degree day data (Fig. 8), and predictions of monthly energy consumptions were made using the performance lines equations (Table 4). The predicted monthly consumptions were then compared against actual consumptions:

Fig. 7. Daily progress of dry-bulb and wet-bulb outdoor temperature on July 23rd, 2009

Although the annual sums of dry-bulb and wetbulb cooling degree days differ marginally, the differences between degree days totals for transitional months are up to 123% (October percentage difference in relation to CDD).

112

∆E (% ) =

E p − Ea Ea

⋅100%, (5)

where ΔE is the percentage difference between actual and predicted monthly electric energy consumption, Ep is the predicted monthly energy consumption and Ea is the actual monthly energy consumption.

As seen in Fig. 9 the wet-bulb cooling degree method better predicted energy consumption for three of five months during the cooling season and for eight months overall. The dry-bulb cooling degree method had smaller prediction errors for June and August (besides for November and December), whereby the predicted values were 0.7 % for June and 0.1 % for August more accurate as the values predicted with the

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Table 3. Monthly dry-bulb and wet-bulb cooling degree days calculated to θb = 16.1 °C and θw,b = 12.1 °C Month

CDD [K·day]

CDDw [K·day]

Feb. 09 Mar. 09 Apr. 09 May 09 Jun. 09 Jul. 09 Aug. 09 Sept. 09 Oct. 09 Nov. 09 Dec. 09 Jan. 10 Σ

0 0 0 84 82 162 188 44 10 0 0 0 570

0 0 0 62 82 156 175 74 22 0 0 0 571

CDDw method. The biggest difference was between the energy consumptions predicted for September, where consumption predicted with the CDDw performance line was 5.9 % closer to the actual energy consumption. While February energy consumption was most underestimated as a consequence of that February has the least number of days, consumptions for October and November were most overrated by both performance lines. In comparison with May, the cooling degree values (dry-bulb and wet-bulb) for October were significantly lower, but the total electric energy was higher. It was similar for November, i.e. total energy consumption in November was considerably higher than in other months with zero degree days. Both of these deviations can be explained by base load modification.

4 CONCLUSSION Cooling degree days are the summation of temperature differences between the outside air and a reference

Table 4. Predicted and actual monthly total electric energy consumption Month Feb. 09 Mar. 09 Apr. 09 May 09 Jun. 09 Jul. 09 Aug. 09 Sept. 09 Oct. 09 Nov. 09 Dec. 09 Jan. 10

Ep [kWh] CDD 152977 152977 152977 180737 179896 206370 215007 167578 156167 152977 152977 152977

CDDw 151385 151385 151385 173977 181215 207874 214845 178185 159210 151385 151385 151385

Ea [kWh] 135646 151042 147405 169512 179470 207498 215859 178365 172636 160653 153638 151896

Fig. 9. Percentage differences between actual and predicted monthly electric energy consumptions

temperature over time, and can be applied to estimate future building energy consumption due to space cooling or to monitor energy performance of existing buildings. Although the cooling degree day method is superior to other simplified methods for analysing weather related energy consumption in buildings, because CDD capture both the extremity and duration

Fig. 8. Performance line; a) constructed with CDD, b) constructed with CDDw Analysis of Building Electric Energy Consumption Data Using an Improved Cooling Degree Day Method

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of outdoor temperatures, there are several issues in the application of degree days to cooling energy use in buildings. A key issue, apart from selecting a calculation procedure for degree days, is the definition of a proper base temperature, because the building’s balance point varies together with heat gains and the indoor temperature. However, the main problem lies in the definition of CDD method itself, since it neglects the influence of latent cooling loads on cooling energy, as a consequence from being derived from the heating degree day (HDD) method.

In this article an improved cooling degree method the so-called wet-bulb cooling degree method, which takes into account both the sensible and latent loads, is used to analyse electric energy consumption data from an existing building and compared against the conventional cooling degree day approach, whereby different degree day calculation techniques and statistical methods for determining base temperature are applied.

The results of the analysis are unambiguous, i.e. the CDDw method outperformed the CDD method in the majority of cases. Not only was the correlation between CDDw and electric energy consumption considerably higher (5% higher explained variance), but it was also revealed that the value of wet-bulb base temperature is less dependent on the method chosen for determination (energy signature and performance line method) and on the used degree day calculation procedure (daily averaged hourly and daily temperature differences). Nevertheless, the results obtained by any of the tested methods should be interpreted carefully when dealing with energy consumption data consisting of weather related and non-related energy consumption (i.e. total energy consumption).

In spite of the fact that the wet-bulb cooling degree approach performed well on the selected total electric energy consumption data, it will have to be additionally tested on the data obtained from other existing buildings with different types of airconditioning systems, preferably on chiller power consumption data.

5 NOMENCLATURE List of symbols: CDD E ELD h HDD t

114

Cooling degree days Total electric energy consumption Enthalpy latent days Specific enthalpy of air Heating degree days Time

[K·day] [kWh] [kJ/kg·day] [kJ/kg] [K·day] [day]

x θ

Absolute humidity of air Temperature of air

a b d m o p w

Actual Base Day Month Outdoor Predicted Wet-bulb

List of abbreviations:

[kg/kg] [°C]

6 REFERENCES [1] Košir, M., Krainer A., Dovjak M., Rudolf, P., Kristl, Ž. (2010). Alternative to the Conventional Heating and Cooling Systems in Public Buildings. Strojniški vestnik – Journal of Mechanical Engineering, vol. 56, no. 9, p. 575-583.

[2] Day, A.R., Knight, I., Dunn, G., Gaddas, R. (2003).

Improved methods for evaluating base temperature for use in building energy performance lines. Building Service Engineering Research & Technology, vol. 24, no. 4, p. 221-228, DOI:10.1191/0143624403bt073oa.

[3] Huang, Y.J., Ritschard, R., Bull, J., Chang, L. (1986).

Climatic indicators for estimating residential heating and cooling loads. Report LBL-21101. Lawrence Berkley Laboratory, Berkley.

[4] Krese, G., Prek, M., Butala, V. (2011). Incorporation of latent loads into the cooling degree days concept.

Energy and building, vol. 43, no. 7, p. 1757-1764, DOI:10.1016/j.enbuild.2011.03.042.

[5] ASHRAE (2009). Handbook – fundamentals (SI).

American Society of Heating, Refrigerating and AirConditioning Engineers, Atlanta.

[6] Hitchin, E.R. (1983).

Estimating monthly degree days.

Building Service Engineering Research & Technology, vol. 4, no. 4, p. 159, DOI:10.1177/014362448300400404.

[7] Day, A.R., Maidment, G.G., Ratcliffe, M.S. (2000).

Cooling degree-days and their applicability to building energy estimation. 20:20 Vision: CIBSE/ASHRAE Conference.

[8] Jacobsen, F.R. (1985). Energy signature and energy monitoring in building energy management systems.

Proceeding of CLIMA 2000 World Congress, vol. 3: Energy Management, p. 25-31.

[9] Guan, L. (2009). Preparation of future weather data to study the impact of climate change on buildings.

Building and Environment, vol. 44, no. 4, p. 793-800, DOI:10.1016/j.buildenv.2008.05.021.

Krese, G. – Prek, M. – Butala, V.

Strojniški vestnik - Journal of Mechanical Engineering 58(2012)2, 115-124 DOI:10.5545/sv-jme.2011.085

Paper received: 2011-04-18 , paper accepted: 2011-11-08 ©2012 Journal of Mechanical Engineering. All rights reserved.

Finite Mixture Estimation Algorithm for Arbitrary Function Approximation Volk, M. – Nagode, M. – Fajdiga, M. Matej Volk* – Marko Nagode – Matija Fajdiga University of Ljubljana, Faculty of Mechanical Engineering, Slovenia The paper considers a new prospect of the arbitrary continuous function approximation from a limited set of input data with the REBMIX algorithm, developed for the finite mixture density estimation. Since the REBMIX estimates the unknown parameters with the unique semiparametric method, it is assumed that it could be used also for the estimation of the unknown parameters in the fields that are not directly connected to density function estimation.

For the approximation of the arbitrary continuous function with the REBMIX algorithm, the required procedure is developed in the paper. The results gained by the proposed procedure and by the radial basis function network for three different datasets are compared by calculating the RMSE values between estimated and test output values. The adequacy of the proposed procedure is estimated by using both univariate and bivariate datasets. It can be concluded that with the developed procedure, the REBMIX algorithm can be applied successfully for the continuous function approximation.

Keywords: REBMIX algorithm, function approximations, finite mixtures, RBF networks, parameter estimation

0 INTRODUCTION Since the beginning of neural networks research [1], the field of neural networks has been established as an interdisciplinary subject with deep roots in neurosciences, psychology, mathematics, the physical sciences and engineering [2] to [7]. Radial Basis Function (RBF) networks emerged as a variant of artificial neural networks in the late 1980’s. However, their roots reach further back to much older pattern recognition techniques, such as potential functions, clustering, functional approximation, spline interpolation and mixture models [8]. Until now the RBF networks have been successfully applied to a large diversity of applications including interpolation [9], classification [10], speech recognition [11], image restoration [12], 3-D object modelling [13], motion estimation and moving object segmentation [14], etc. Their excellent approximation capabilities have been studied by both, Park and Sandberg and Poggio and Girosi [15] and [16]. Because of their excellent approximation properties and simple structure, RBF networks have been chosen in the research to compare the results of the arbitrary continuous function approximation.

REBMIX, which is the acronym for the Rough and Enhanced component parameter estimation that is followed by the Bayesian classification of the remaining observations for the finite MIXture estimation, is a numerical procedure that arises from an engineering viewpoint on the mixture estimation problem. The development of the REBMIX algorithm began in the late 1990’s with the work of Nagode and

Fajdiga [17]. Since then, it has evolved gradually over the years [18] to [21] and the latest improvements in modelling both univariate and multivariate finite mixtures can be found in [22] and [23] and in modelling load spectra growth in [24]. Until now it has been noted also in other research works concerning fatigue analysis [25] to [28], modelling the expected service usage [29] and [30], etc.

The paper presents an alternative perspective on the arbitrary continuous function approximation.

Although the REBMIX algorithm has been originally developed for the finite mixture estimation problems, its unique semi-parametric method for the estimation of the unknown parameters indicates that it could also be used for the parameters estimations on the fields that are not directly connected with the probability density function. Unknown number of components and their parameters are estimated on the basis of the calculated empirical densities from the observed dataset. Calculated empirical densities thus represent the desired output values for a certain region of the input space, just like the arbitrary measured data does.

The resemblance between the empirical densities and the output values of the arbitrary measured signal implies that with the proper procedure, REBMIX can be used for the approximation of the arbitrary continuous function. The next logical step forward is thus to extend the REBMIX on the field of arbitrary continuous functions approximation so that all of its properties, which proved already at the estimation of the finite mixture densities, are preserved. The adequacy of the extended REBMIX is appraised according to the results gained by the RBF network.

*Corr. Author’s Address: University of Ljubljana, Faculty of Mechanical Engineering, Aškerčeva 6, 1000 Ljubljana, Slovenia, matej.volk@fs.uni-lj.si

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The paper is structured as follows. In Section 1 the required definitions are cited. In Section 2 the results of the univariate and bivariate function estimations with the proposed procedure and RBF network are presented and compared. Finally, in Section 3 the conclusions are listed and the adequacy of the proposed procedure is discussed.

1 BASIC DEFINITIONS 1.1 Radial Basis Function Network The radial basis function (RBF) network is based on the simple intuitive idea that an arbitrary function y(x) can be approximated as the linear superposition of a set of localized basis functions ϕj(x) [3]. RBF’s are embedded in a three layer neural network shown in Fig. 1. The first layer, called the input layer is made of source nodes (sensory units) that represent the components of the input vector. The second layer, the only hidden layer in the network, consists of hidden units, which implement radial activated functions and perform a nonlinear transformation from the input space to the hidden space. The third layer, called the output layer is linear and contains units that represent a weighted sum of hidden unit outputs. Units in the output layer supply the response of the network to the activation pattern applied to the input layer and represent the components of the output vector [4].

neural networks, a general interest is not an exact interpolation since it can lead to particularly poor results when the trained network is presented with new data. Generally, a smooth approximation [31], which can be achieved by using fewer basis functions m than data points n and by minimizing a sum-ofsquares error (SSE) function, can lead to much better results [2].

When m < n, the RBF neural network corresponds to a set of functions given by [2] and [3]:

Origins of the RBF networks lie in techniques used for the exact interpolation between data points in high dimensional spaces. In applications of 116

j =0

Here wkj represents the weight of the jth basis function output which contributes to the kth network output yk and φ j (x θ j ) represents the activation of hidden unit j when the network is presented with d-dimensional input vector x, see Fig. 1. A bias for the output units is included in Eq. (1) as an extra “basis function” ϕ0 whose activation is fixed to be ϕ0 = 1. For most applications the basis functions are chosen to be Gaussian:

 x−µ j  φ j (x θ j ) = a j ⋅ exp − 2 2σ j 

2

   , (2) 

where aj controls the height of the peak, vector μj represents the center and the parameter σj represents the width of the jth basis function. Note that each basis function can have its own width parameter σj [2] and [3]. To compare the estimated values with the target values, an error function has to be used. The most commonly used form of the error function for regression problems is the SSE function [2] and [32], given by:

Fig. 1. Three layer neural network

m

yk (x m, w, Θ) = ∑ wkjφ j (x θ j ). (1)

E=

{ (

) }

2 1 n c ykq x q m, w, Θ − tkq , (3) ∑ ∑ 2 q =1 k =1

where xq denotes the qth d-dimensional input training vector and w the output layer weight vector for current basis functions parameters Θ, tkq is the kth target value in qth c-dimensional target vector tq. Bishop [2] suggests assessing the performance of the trained network using different error function from that used to train them. If the SSE function is used in the network training phase, the root-mean-square error (RMSE) function should be used in network testing.

The RMSE function is given by:

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∑ ∑{ y ( x n*

E RMS =

c

q =1 k =1

q k

n*

q

c

∑ ∑ {t q =1 k =1

)

}

* m, w, Θ − tkq * q k

}

* −t *

2

2

, (4)

where xq* denotes the qth input test vector and n* is the number of input test vectors, w and Θ denote the weight vector and the basis functions parameters of the trained network respectively and tkq * is the kth target test value in the qth c-dimensional target test vector tq*. In Eq. (4), the t* stands for the average of the target test values:

t*=

1 n* c q ∑ ∑ tk *. (5) n * c q =1 k =1

Training of the RBF networks takes place in two successive stages. First, the centers and the basis function widths are determined. In the second stage the linear output layer weights are determined. For the determination of the basis functions parameters there exists a variety of procedures [2] to [4] and [33].

Since the scope of the paper is not searching for the optimal learning procedure of the RBF networks but assessing the suitability of the REBMIX algorithm for arbitrary function approximation, only simple and fast procedures for the determination of basis functions centers and width are selected in the paper, which in spite of their simplicity assure adequate network training.

The first and simplest approach to determine the basis functions centers, denoted by C1, is to set them on the highest output values in the training dataset [3]. This approach usually results in a large number of basis functions to achieve satisfactory results. The second approach for center determination, denoted

by C2, is to select them randomly from the training dataset [3]. In this very commonly used learning technique the estimated function is much smoother and usually better approximates the training data with a fewer number of basis functions. The disadvantage of this approach is the reproduction of network training.

The widths of Gaussian basis functions are also determined by using two simple approaches. In the first approach, denoted by S1, the basis function widths are set to be equal to the average Euclidean distance between the adjacent basis function centers, which ensures that the basis functions overlap to some degree and hence give a relatively smooth approximation [2] and [3]. In the second approach, denoted by S2, the widths are no longer equal for all

basis functions, but are determined on the basis of the average Euclidean distance to the p-nearest centers [2] and [3].

The output layer weights are calculated in a way to minimize the SSE function with respect to these weights. With the insertion of Eq. (1) into Eq. (3) and the differentiation of the SEE function it is possible to rewrite the equation in matrix notation in the following form [2] and [3]:

ΦTΦWT = ΦTT, (6)

where (T) qk = tkq and (Φ ) qj = φ j (x q θ j ) . The formal solution for the weights is given by: WT = Φ†T, (7)

where the notation Φ† denotes the pseudo-inverse of Φ given by:

Φ† ≡ (ΦTΦ)-1ΦT. (8) 1.2 REBMIX Algorithm for the Finite Mixture Estimation Let x1, ..., xn be an observed d-dimensional dataset of size n of continuous vector observations xq. Each observation is assumed to follow predictive mixture density [34]:

m

f (x m, w, Θ) = ∑ w j f j (x θ j ), (9) j =1

with conditionally independent component densities:

d

f j (x θ j ) = ∏ f j ( xi θij ), (10) i =1

indexed by vector parameter θj. The objective of the analysis is the inference about the unknowns: the number m of components, component weights wj summing to 1 and component parameters θj.

Since the description of the REBMIX algorithm estimation procedure and proof of its convergence is extensive and published in [17] to [24], further details will not be presented here. For interested readers REBMIX software is available at http://CRAN.Rproject.org/package=rebmix.

1.3 Arbitrary Function Approximation with the REBMIX Algorithm There are two major differences when estimating the arbitrary function from a set of data points with REBMIX algorithm and RBF network.

Finite Mixture Estimation Algorithm for Arbitrary Function Approximation

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The first difference is related to the component weights. In the REBMIX algorithm the weights are limited with two conditions, m wj > 0 for (j = 1, ..., m) and ∑ j =1 w j = 1 , while in the RBF network approach there are no limitations concerning the weights for regression problems. In fact, output layer weights can also be negative. This property can be very useful for better estimation of the function valleys and for observations with negative output values. The observations with negative output values can be processed with the REBMIX algorithm only if they are previously properly treated so that all the observed values have positive signs.

The second major difference is related to the function estimation. When using the RBF network, the arbitrary function can be estimated directly from the set of observed data and therefore it usually does not integrate to unity. With the REBMIX algorithm, the arbitrary function can be approximated indirectly from the estimation of the finite mixture density, which integrates to unity, ∫ f (x m, w, Θ)d x = 1 .

Therefore it is necessary to properly transform the measured training dataset and postprocess estimated finite mixture density f (x m, w, Θ) in such a way that it can be compared to the observed output values.

The procedure for the preparation of the observations and postprocessing of estimated function f (x m, w, Θ) is depicted in Fig. 2 relying on the steps to follow: 1. All the data are either raised if tk min < 0 or lowered for the minimal output value:

tkq ' = tkq − tk min

the total number of vector observations used as input data for the finite mixture estimation equals n

∑t q =1

q k

'.

4. Finite mixture estimation with the REBMIX algorithm is performed.

5. The postprocessing of the estimated finite mixture density function is carried out in such a way that the continuous function, representing input-output mapping of the original dataset is gained. Estimated finite mixture density function f (x m, w, Θ) is multiplied by the volume (12) and the transformation function is gained:

yk '(x m, w, Θ) = f (x m, w, Θ)V . (13)

In the case of a univariate dataset, the volume reduces to the area under the observed data.

The estimated function yk '(x m, w, Θ) can be compared to the true one and to the function estimated by the RBF network.

q = 1,..., n, (11)

as it turned out that in such cases the REBMIX algorithm estimates the finite mixture density function much better. To improve the accuracy of the estimated function, tkq ' may be multiplied by a factor 10, 100, etc. and rounded to the nearest integer.

2. The volume under the shifted data is calculated by: d n  

V = ∑  tkq ' ∏ hiq , (12) q =1  i =1 

where hiq is the length of the hypersquare side for the qth data in the ith dimension.

3. The measured training dataset is transformed in such a way that REBMIX preprocessing methods can be used. With this purpose each d-dimensional input data vector xq is copied tkq ' times so that 118

Fig. 2. Arbitrary function estimation with REBMIX

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6. To compare the estimated values to the actual measured output ones, it is necessary to shift the estimated function yk '(x m, w, Θ) yk '(x m, w, Θ) for the minimal output value:

yk (x m, w, Θ) = yk ' (x m, w, Θ) + tk min . (14)

yk’ (x | m, w, Θ) is then raised by tk min, the trained RBF network yk (x | m, w, Θ) is subjected to the test dataset and the RMSE is calculated. The network training is stopped if RMSE ≤ RMSE lim, where the RMSElim ∈ {0.5, 0.3, 0.2, 0.1 and min} or m = n.

The correctness of the proposed procedure for the function approximation is proved by the following examples.

2 EXAMPLES 2.1 Vertical Wheel Forces Dataset The univariate dataset used in the research derives from measurements of vertical wheel forces that occur when driving the vehicle on a test track. The entire signal, measured with 250 Hz sample rate, is shown in Fig. 3. From all measured data only a section indicated with a square containing 1070 successive data is selected for further treatment due to the faster estimation process. Approximately 30% from these data are randomly selected to form the test dataset that is used only for the evaluation of the estimated functions and is not present in the training phase when the number of components, their parameters and weights are estimated. The test dataset thus consists of n* = 320 data and the remaining n = 750 data form the training dataset.

When the RBF network is applied for the estimation of the function parameters and weights, no special preparation of the training dataset is necessary. Nevertheless, all the data used in the research are lowered for tk min to reduce the estimation error especially on the edges of the observed function. For all combinations of the selected learning procedures C1-S1, C2-S1, C1-S2 and C2S2 and for each m ∈ {1,..., n} , the basis functions parameters and weights are determined. Each

Fig. 3. Measured vertical wheel forces

The results are shown in Table 1. In most cases the best learning combination turns out to be C2-S2.

It results in the smallest number of basis functions and the lowest RMSE, while C1-S1 stands for the worst learning combination possible.

On the other hand, when the REBMIX is applied, all training data are lowered by tk min and the input training data points xq are copied tq' times. Although the REBMIX allows the selection of different preprocessing, the histogram and Parzen window are only suitable. The former is chosen in the article. For the finite mixture density, the normal parametric family is chosen. To determine optimal number of components m, parameters Θ and weights w, finite mixture estimation is carried out for s ∈ {10,..., 750}.

Thus all possible arrangements of observations are captured and the optimal number of bins is obtained according to both, the information criterion and the positive relative deviation D. Estimations are carried out for all combinations of the available information criteria

Table 1. The results of function estimation for vertical wheel forces dataset with the RBF network; the - indicates that network training is stopped before the limiting RMSE value is reached RMSE limit 0.5 0.3 0.2 0.1 min equal m similar RMSE

C1-S1 m 598 636 732 13 686

C2-S1 RMSE 0.499 0.293 0.217 2.088 0.240

m 12 14 19 25 112 13 16

RMSE 0.486 0.294 0.182 0.083 0.029 0.666 0.220

m 123 524 608 691 13 598

C1-S2 p 106 3 2 3 10 2

RMSE 0.484 0.282 0.183 0.117 0.732 0.218

Finite Mixture Estimation Algorithm for Arbitrary Function Approximation

m 12 15 19 22 217 13 16

C2-S2 p 2 6 2 3 4 2 4

RMSE 0.350 0.280 0.131 0.082 0.019 0.347 0.224

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and six different D values. The estimated finite mixtures are postprocessed according to Eqs. (13) and (14) and the corresponding RMSE values are calculated. The calculated RMSE values are than used in the continuation for the performance comparison of the proposed procedure with the RBF network.

The results are shown in Table 2. The optimal number of components increases with the decrease of D and stops to increase if D < 0.0005. If D < 0.001, the optimal number of components increases rapidly while there is only a small decrease of RMSE. The mixture of 13 components is thus supposed to be the optimal one.

Table 2. The results of function estimation for vertical wheel forces dataset with the REBMIX D

m

s

0.025 0.01 0.005 0.001 0.0005 0.0001

5 7 12 13 28 28

61 75 125 151 116 116

information criterion MDL5 AIC AIC MDL2 AIC AIC

RMSE 0.522 0.428 0.329 0.240 0.211 0.211

It can be noted that the RBF network requires 16 basis functions for similar RMSE as the REBMIX (see the last row in Table 1). The corresponding functions are shown in Fig. 4. Both, the RBF network and REBMIX represent the middle section well, while larger deviations appear at the edges.

2.1 Two-Dimensional Gaussian Dataset The bivariate dataset, derived from a mixture of four Gaussian functions Bors and Pitas [33], is studied next. From a mixture of four two-dimensional (2D) Gaussian functions with the following vector parameters: θ1 = [a1 = 5, μ11 = 5, μ21 = 15, σ11 = 2, σ21 = 2], θ2 = [a2 = 5, μ12 = 5, μ22 = 15, σ12 = 5, σ22 = 2], θ3 = [a3 = 5, μ13 = 5, μ23 = 6, σ13 = 3, σ23 = 5] and θ4 = [a4 = 5, μ14 = 5, μ24 = 6, σ14 = 4, σ24 = 2] the 441 data yq are generated for x1 ∈ {0,..., 20} and x2 ∈ {0,..., 20} among which n* = 132 randomly selected data form the test dataset and the residual n = 309 data form the training dataset. In addition to the noise free bivariate dataset, the random Gaussian noise with μ = 0 and σ = 0.6 is added to yq to simulate the noisy dataset, which is usually observed in the measurements.

When the RBF network is applied, no preparation of the training dataset is carried out as tk min = 0 .

For network training each m ∈ {1,..., n} and all combinations of the selected learning procedures C1S1, C2-S1, C1-S2 and C2-S2 are used. Each trained RBF network yk (x | m, w, Θ) is subjected to the test dataset and the RMSE is calculated. The network training is stopped if RMSE ≤ RMSE lim , where RMSElim ∈ {0.5, 0.3, 0.2, 0.1 and min} or m = n.

The results are shown in Tables 3 and 4 for noise free and noisy dataset, respectively. The smallest number of basis functions and the lowest RMSE are gained when the learning combinations C2-S1 and C2-S2 are applied. The worst learning combination turned out to be the C1-S1.

Fig. 4. Comparison between measured univariate signal and both estimated functions with similar RMSE value

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Table 3. The results of function estimation for the noise free bivariate dataset with the RBF network C1-S1

RMSE limit

m 31 65 76 118 260 5 68

0.5 0.3 0.2 0.1 min equal m similar RMSE

C2-S1

RMSE 0.487 0.296 0.194 0.100 1.26E-02 0.792 0.273

m 8 14 16 20 301 5 14

RMSE 0.383 0.288 0.197 0.077 1.25E-02 0.615 0.288

m 7 16 19 35 120 5 17

C1-S2 p 1 4 4 6 20 4 4

RMSE 0.451 0.295 0.183 0.089 5.22E-04 0.738 0.273

m 8 13 19 23 120 5 13

C2-S2 p 1 2 9 3 13 2 2

RMSE 0.484 0.265 0.196 0.071 5.17E-04 0.534 0.265

m 7 14 19 26 55 5 17

C2-S2 p 2 4 6 5 4 1 4

RMSE 0.500 0.288 0.159 0.084 2.54E-02 0.585 0.255

Table 4. The results of function estimation for the noisy bivariate dataset with the RBF network C1-S1

RMSE limit

m 42 65 77 127 209 5 66

0.5 0.3 0.2 0.1 min equal m similar RMSE

C2-S1

RMSE 0.481 0.298 0.197 0.095 6.79E-02 0.810 0.265

m 11 16 16 22 50 5 19

RMSE 0.485 0.144 0.144 0.090 3.41E-02 0.590 0.261

When the REBMIX is applied, all input training data vectors xq are only copied tq' times as tk min = 0. The histogram preprocessing and the normal parametric family are used. To determine optimal number of components m, parameters Θ and weights w, finite mixture estimation is carried out for s ∈ {1,..., 30} in both dimensions so that all possible arrangements of observations are captured. The estimations are carried out for all combinations of the available information criteria and six different D values. The estimated finite mixtures are postprocessed according to (13) and (14), where yk (x | m, w, Θ) = yk' (x | m, w, Θ) and the corresponding RMSE values are calculated.

The results are shown in Tables 5 and 6. For the noise free dataset the optimal number of components is the same for all D values, whereas for the noisy dataset the optimal number of components increases by one when D ≤ 0.01.

m 9 17 24 31 97 5 17

C1-S2 p 7 4 6 6 28 4 4

RMSE 0.430 0.253 0.175 0.097 2.67E-02 0.760 0.253

With the increase of the number of components the RMSE value also increases. This means that the estimated function with a larger number of components overfits the data and consequently results in a worse estimate. The mixture of 5 components is thus supposed to be the optimal one. Unlike for the univariate dataset, where optimal s  n , for the presented bivariate datasets the optimal s > n in both dimensions. This indicates that some of the histogram bins stay empty after the observations are arranged.

Table 5. The results of function estimation for the noise free bivariate dataset with the REBMIX D

m

s

0.025 0.01 0.005 0.001 0.0005 0.0001

5 5 5 5 5 5

22 22 22 22 22 22

information criterion AIC AIC AIC AIC AIC AIC

RMSE 0.277 0.277 0.277 0.277 0.277 0.277

Fig. 5. Comparison between simulated noise free bivariate function and both estimated functions with similar RMSE value

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(see Fig. 6). The function estimated by RBF network represents the first three components very well and underestimates the fourth one.

3 CONCLUSION AND FUTURE WORK

Fig. 6. Comparison between simulated noisy bivariate function and both estimated functions with similar RMSE value

The RBF network requires 13 basis functions in the case of noise free dataset and 17 basis functions in the case of noisy dataset for similar RMSE as the REBMIX (see the last row in Tables 3 and 4). The corresponding functions are shown in Figs. 5 and 6.

Table 6. The results of function estimation for the noisy bivariate dataset with the REBMIX D

m

s

0.025 0.01 0.005 0.001 0.0005 0.0001

5 6 6 6 6 6

22 22 22 22 22 22

information criterion AIC AIC AIC AIC3 AIC3 AIC3

RMSE 0.260 0.316 0.316 0.316 0.316 0.316

In the case of the noise free dataset the function estimated by the REBMIX overestimates all four components on their peak values and slightly underestimates the simulated function in the valleys. If the analogy with the univariate function estimation is taken, it is expected that the REBMIX would estimate the underlying function even better if it was composed of a greater number of intermediate components.

On the other hand, the function estimated by the RBF network underestimates the first component considerably and the second and fourth component slightly but estimates the valley between the second and the third component well. Similar results are also obtained in the case of the noisy dataset where the function estimated by the REBMIX again overestimates the peak values of all four components and slightly underestimates the valleys between them 122

In the article continuous functions are estimated with the REBMIX algorithm for the first time. Both univariate and bivariate datasets are used to evaluate its adequacy. The estimated functions are compared to the functions estimated by the elementary RBF network.

For the applied univariate and bivariate datasets it can be concluded that the functions estimated by the REBMIX using the proposed procedure approximate the actual functions well. Hence the assumption is derived that the REBMIX can be applied for the estimation of the univariate and bivariate continuous functions if the training dataset is transformed properly and the estimated finite mixture densities are postprocessed properly. Although the procedure requires the transformation of the training data and postprocessing of the estimated function, the estimation times are still very short since all the properties of the REBMIX are preserved.

The future development of the REBMIX will be focused on its connection to the RBF networks.

Possibly, the REBMIX can be used to determine the centers of basis functions μj and widths σj in the first stage of the RBF network learning process. The determination of the final layer weights should remain unchanged. In this way the postprocessing of the estimated finite mixture density can be omitted since the estimated function would already approximate the actual observed function. The entire estimation process can also be simplified if the transformation of the training data was comprehended in the REBMIX preprocessing.

To assess the benefits of the connection between the REBMIX and the RBF neural network, further investigations are to be carried out. Future work will thus be focused on additional testing using also other parametric families and the Parzen window preprocessing. The tests will also have to be carried out for the function estimations from multivariate datasets and a larger number of data. Expectedly, by connecting these procedures the REBMIX will be used to solve other problems covered by the neural networks as well, such as classification problems, inverse problems, etc.

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[32] Šimunović, G., Šarić, T., Lujić, R. (2008). Application of neural networks in evaluation of technological time. Strojniški vestnik – Journal of Mechanical Engineering, vol. 54, no. 3, p. 179-188.

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Volk, M. – Nagode, M. – Fajdiga, M.

Strojniški vestnik - Journal of Mechanical Engineering 58(2012)2, 125-133 DOI: 10.5545/sv-jme.2010.238

Paper received: 2010-11-29, paper accepted: 2011-11-18 ©2012 Journal of Mechanical Engineering. All rights reserved.

Description and Modeling of the Additive Manufacturing Technology for Aerodynamic Coefficients Measurement Daneshmand, S. – Aghanajafi, C.

Saeed Daneshmand1,* ‒ Cyrus Aghanajafi2 1 Department

of Mechanical and Aerospace Engineering, Science and Research Branch, Islamic Azad University, Iran; 2 K. N. Toosi University of Technology, Iran

Casting, machining and additive manufacturing technologies are used in order to produce wind tunnel testing models. The models can also be analyzed by computational fluid dynamics methods. Both have their advantages and disadvantages. Since several wind tunnel models are required to accomplish aerodynamic experiments, nowadays, one of the best methods for models and airfoils manufacturing are additive manufacturing technologies. These methods are increasingly used in aerospace industry. In this research, wing and tail of a wind tunnel test model which has complicated sections, are produced by fused deposition modeling technology. In order to improve mechanical properties and surface roughness an electroplating is used on the surface of a RP model. Metal models along with fused deposition modeling models and electroplating models were tested in wind tunnels with different angels of attack. Results indicated that aerodynamic coefficients of electroplating model with a chromium coating was closer to metal model than those of AM model without electroplating.

Substituting conventionally made parts with electroplating models, saves both cost and time. These models can be used in wind tunnel tests and aerodynamic data have acceptable quality.

Keywords: additive manufacturing, wind tunnel, angels of attack, aerodynamic coefficient

0 INTRODUCTION In order to reduce the product development time and the cost of tooling, layered manufacturing techniques were developed commonly known as additive manufacturing (AM) technologies. This technology encompasses a group of manufacturing techniques, in which adding the material layer-by-layer generates the shape of the physical part. Layer manufacturing, rapid prototyping, solid free form fabrication, additive manufacturing, digital manufacturing are all the names of the processes that are capable of producing three-dimensional (3D) parts from computer aided design (CAD) data directly. The first purpose of this technology was to produce prototypes quickly in an additive manner by adding layer upon layer [1] and [2].Researchers and applicants have started to apply the new AM technologies to different areas and domains like making tools and dies which is known as rapid tooling, and manufacturing of end use products with low volume quantity, which is known as rapid manufacturing. Wind tunnel testing is an integral part of the design process in many industries. Whether an object is stationary or mobile, wind tunnels provide insight into the effects of air as it moves over or around the test model. Since the physics of flight depend on the proper flow of air to produce lift and reduce drag, wind tunnel evaluations are essential in the aerospace industry. Even in an age of advanced computer simulation, aerospace engineers still rely on the testing of physical models to verify the computer data and establish baseline aerodynamic information. In the never-ending quest for more efficient automobiles, aerodynamics plays a very important part in vehicle

design. To make the models for the wind tunnel, automotive and aerospace companies have relied on traditional manufacturing operations. They have used milling, turning and fabrication to convert metal and plastic into test models. These operations require programming, set up and operator supervision, which adds to lead time and cost. Considering the amount of material that ends up as chips on the floor, the material costs can be high. Additive manufacturing improves the lead time and cost of the test part for the wind tunnel testing. Due to the high costs of building a model, program managers often rely heavily on analytical tools, such as computational fluid dynamics (CFD), to predict how a missile system might perform.

CFD is used extensively in the aerospace field to provide designers and engineers further insight into design issues that may arise at various stages in the design process. In addition, CFD can be used to provide useful information on preexisting designs such as homebuilt aircraft. In aerospace applications, CFD can be used as the sole means of analysis, or to complement additional analysis techniques and processes. Although CFD can provide valuable data, it typically requires more time to produce final results and has limitations providing data over a full range of flight conditions. A combination of testing and CFD can be used to acquire a more complete data set.

A number of research works related to the making of wind tunnel models by additive manufacturing which can be produced, have been published in the past years. Landrum et al. [3] tested airfoil models in a subsonic wind tunnel: a conventional cast polyurethane model and two photopolymer models made by stereolithography. They reported

*Corr. Author’s Address: Depart. of Mech. and Aerospace Eng., Science and Research Branch, Islamic Azad University, Tehran, Iran, Saeed_daneshmand@yahoo.com

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comparable dimensional tolerances and fabrication times for the rapid prototyping (RP) and conventional models, with the biggest difference being in the drag coefficient for both the RP models, which was about half the value measured for the cast model. They attributed this result to the rougher surface of the RP models inhibiting the formation of laminar separation bubbles. Aghanajafi et al. [4] described the effects of layer-thickness models on aerodynamic coefficients to construct wind-tunnel-testing models produced with rapid prototyping. These models were fabricated from SOMOS NanoTool by stereolithography. Results from this study show that layer thickness does have an effect on aerodynamic characteristics. Springer et al. [5] evaluated aerodynamic characteristics of wind-tunnel models produced by rapid prototyping methods. They concluded from this study that, preliminary design studies and limited configurations could be used due to the RP material properties that allowed bending of model components under high loading conditions.

Hildebrand et al. [6] and Tyler et al. [7] described two wind tunnel models and investigated issues such as the integration of pressure taps, model sagging under load. They found that it was necessary to stiffen the plastic model to prevent excessive wing deflection.

Nadooshan et al. [8] tested a polycarbonate model made by FDM against a conventional machined steel model. The results were a generally good agreement between the metal and plastic models up to about 10 degrees of angle of attack, when the plastic model’s deflection under the higher loading produced more noticeable differences. Daneshmand et al. [9] described two wind tunnel models; these models were rocket configuration constructed using CK45 and ABSi material for wind tunnel testing. Results from this study show good agreement between the two models and increased use of RP components in wind tunnel models could reduce the time wind tunnel model fabrication. Surface roughness is an important parameter in wind tunnel testing models fabrication [10]. The purpose of this work is to demonstrate how additive manufacturing with electroplating coating can be effectively applied to fabricate test models used in aerodynamic experimental investigations.

Three models are prepared and produced at various conditions for testing in wind tunnel and determining the aerodynamics coefficients. AM models constructed using FDM with ABS-M30 as a material and FDM model with chromium coating.

AISI 1045H (CK45) was chosen as the material for the machined metal model. The roughness for each model was 16 Ra, 0.832 Ra and 0.410 µm Ra. Wind tunnel is an intermittent blow down tunnel, which 126

operates by high-pressure air flowing from storage to either vacuum or atmosphere conditions. Testing was done over the Mach range of 0.1 to 0.3. All models were tested at angle-of-attack (AOA) ranges from -2 degrees to +14 degrees at zero sideslip. Coefficients of normal force, axial force, pitching moment, and lift over drag are shown at each of these Mach numbers.

1 ADDITIVE MANUFACTURING TECHNOLOGIES AND FDM PROCESS The term additive manufacturing (AM) is used in a variety of industries to describe a process for rapidly creating a system or part representation before final release or commercialization. In other words the emphasis is on creating something quickly and that the output is a prototype or basis model from which further models and eventually the final product will be derived. AM technology certainly significantly simplifies the process of producing complex threedimensional objects directly from computer aided design data. Additive manufacturing technologies can be classified in three categories according to the initial state of the raw material used (liquid, powder, and solid). Regardless of the material state, all AM techniques use the following five main steps to produce prototypes, patterns or final parts: CAD model preparation, STL translation, slicing and production of technological program, additive manufacturing, and finally, post processing of the prototype. Performance measures of AM techniques such as dimensional accuracy, surface roughness, mechanical strength, build time, as well as material properties and post processing, define the final use of the corresponding prototype. The most common technologies used are Stereolithography (SL), Selective Laser Sintering (SLS), Fused Deposition Modeling (FDM), and 3D Printing (3DP). Each of these technologies has strengths and weaknesses with some of these technologies suitable for some application and some not [11] and [12]. Also, it is very advantageous to present a design in client presentations; consumer evaluations, bid proposals, and regulation certification.

The models produced by three dimensional printing (3DP) are not so accurate when compared to other rapid prototyping technologies [13]. Over the past few years, improvements in equipment, materials, and processes have enabled significant improvements in the accuracy of Fused Deposition Modeling technology. FDM process creates parts by extruding material through a nozzle that traverses in X and Y to create each two-dimensional layer. The use of a nozzle with a diameter of typically 0.3 mm limits

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resolution an accuracy also the need for the nozzles to physically traverse the build area limits build speed, but the process is very easy to set up and can operate in an office or factory environment. Support removal can be manual or, when water soluble supports are employed, they may simply be dissolved with the latter approach being most valuable with more complicated geometries. Fig. 1 shows a schematic of the FDM process that can produce parts in material including polycarbonate, polyphenylsulfone and, most commonly acrylonitrate butadiene styrene (ABS). The simplicity of the process should make it suitable for the development of a wide variety of thermoplastic polymers, which may open up opportunities for rapid manufacturing [14].

Fig. 1. Schematic diagram of FDM process [15]

2 CHROMIUM COATING In recent years, the AM models have found increased uses in wind tunnel. Coating AM parts with metals was shown to be a promising route for the fabrication of wind tunnel models. Electroplating deposits a thin layer of metal on the surface of a part using the FDM process. This metal coating can be both decorative and functional. The coating gives the appearance of production metal or plated parts and provides a hard, wear-resistant surface with reflective properties. The electroplated part also has improved mechanical properties. With simple finishing techniques, FDM parts are ready for electroplating with alloys such as chromium, nickel, copper, silver and gold. Combining the properties of materials with those of a metal coating, the part has strength, durability and heat resistance that is ideal for functional applications.

ABS plastic, the material that FDM models are made

from, works very well with this process. The model is chemically etched, which removes the butadiene molecules from the surface and improves bonding of the subsequent layers. Once etched, the part is then coated with a layer of palladium, which acts as an intermediate bonding agent, followed by a layer of chromium to provide the necessary conductivity. At this point, the model is placed in a tank containing a solution of the metal to be deposited and given a negative electric charge, which attracts the positively charged metal ions from the solution and becomes a solid metal again. Hard chrome electroplating gives the plastic model a very durable coating, but it can have a tendency to make the part somewhat brittle.

3 MATERIAL SELECTION Fused deposition modeling offers a unique variety of thermoplastic modeling materials for FDM systems. The mechanical properties of ABS-M30, polycarbonate (PC), PC-ABS and polyphenolsulfone (PPSF) can withstand the forces and stresses induced as the air flow strikes the modelâ&#x20AC;&#x2122;s surface. Each FDM material can be used for wind tunnel models.

Selection will be based on the strength needed to resist the wind forces in the tunnel. The material options currently include ABS, a high-impact grade of ABSi, investment casting wax, and elastomer. The use of ABS provides the impact resistance, toughness, heat stability, chemical resistance, and the ability to perform functional tests on sample parts [16].

ABS-M30 is up to 25 to 70% stronger than standard ABS and is an ideal material for conceptual modeling, functional prototyping, manufacturing tools, and enduse-parts. ABS-M30 has greater tensile, impact, and flexural strength than standard ABS. Layer bonding is significantly stronger than that of standard ABS, for a more durable part. In this research AM models were constructed using the ABS-M30 materials. ABS-M30 gives real parts that are stronger, smoother, and with better feature detail. Steel (AISI 1045H) was chosen as the material for the machined metal model. Material properties of ABS-M30 are shown in Tables 1 and 2.

Table 1. Material properties of ABS-M30 Mechanical properties Tensile strength Tensile modulus Tensile elongation Flexural stress Flexural modulus Flexural elongation

Test Method ASTM D638 D638 D638 D790 D790 D790

Description and Modeling of the Additive Manufacturing Technology for Aerodynamic Coefficients Measurement

Metric 36 MPa 2,413 MPa 4% 61 MPa 2,317 MPa 52%

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Table 2. Thermal properties of ABS-M30 Thermal properties Heat deflection Vicat softening temp.

Coefficient of thermal expansion Coefficient of thermal expansion Glass transition

Test method ASTM D648 ASTM D1525 ASTM E831 ASTM E831 DSC (SSYS)

Metric 96°C 99°C 8.82 E-05 mm/°C 8.46 E-05 mm/°C 108°C

θ Ra = α sin tan θ, 4

(1)

where Ra is the arithmetic average surface roughness, α the layer thickness and θ is the angle between the surface normal and the vertical direction [18].

4 SURFACE ROUGHNESS Additive manufacturing is a manufacturing technology that fabricates 3D physical models using a layered manufacturing process that stacks and bonds thin layers in one direction. In comparison with the previous numerically controlled (NC) manufacturing technology, AM can rapidly fabricate high level models with complex shapes without geometric restriction under more comfortable working conditions. FDM technology is fundamentally based on surface chemistry, thermal energy, and a layer manufacturing process [17]. As the AM process is performed using layered manufacturing, the surface roughness of the FDM part is excessively rough, as shown in Figs. 2 and 3. When testing at very high wind speeds, it is true that surfaces must be very smooth. However, at lower speeds, companies are using FDM models directly from the system. For those instances where parts must be finished before going into the wind tunnel, there are options. Although FDM materials are durable and somewhat abrasion resistant, and therefore somewhat resistant to sanding, there are a number of finishing techniques that are simple and fast. Once the perceived limitation of surface roughness is set aside, companies in industries that range from aerospace to architecture can leverage the strength, detail and accuracy of FDM for wind tunnel models. In doing so, they will reduce cost, time and effort. As noted previously, companies are using FDM models that go directly from the system to the wind tunnel. For many applications, surface roughness will not be an issue until tunnel speeds reach elevated levels, when the part is oriented properly. However, when surface roughness is imperative, there is a fast and efficient smoothing process. The surface roughness of the parts is not satisfactory for general engineering purposes. For this reason, surface roughness is a key issue in AM. The application of surface roughness had effect on the aerodynamic characteristics. The surface roughness for FDM model and model with electroplating coating was 16 (Ra) and 0.832 µm (Ra), which is determined by the following trigonometric equation:

128

Fig. 2. Cut surface of ABS-M30 fabricated using FDM observed under SEM

Fig. 3. Side-view of ABS-M30 fabricated using FDM observed under SEM

5 DESIGN OF TESTING MODELS Some parts of the models which had complicated sections and were very difficult to be produced by traditional methods, were manufactured by FDM method (Fig. 4). The dimensions for the scaled model of the missile are 52×8×8 cm. The model was built in several pieces and then assembled. Three models were fabricated. The first model was constructed using steel in three parts, a nose, body and tail as shown in Fig. 5.

The second model was manufactured using FDM nose and FDM tail attached to cylindrical steel as depicted in Fig. 6. As for the third model, nose and tail were produced using FDM and the roughness of the surface

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was improved by implementing a chromium coating.

This model is shown in Fig. 7. The cylindrical steel provides strength and rigidity to the plastic model and also allows larger scale models to be built. The cylindrical steel, fabricated from AISI 1045H (CK45), is a 30 cm long cylinder with a 8 cm outer diameter and a 7 cm inner diameter. The surface of the cylinder has a surface finish of a 0.410 µm (Ra).

Fig. 4. Tail model configuration

Fig. 5. Steel model configurations

Fig. 6. Steel model with tail and nose FDM

Fig. 7. Steel model with tail and nose FDM and Chromium coating

The inside forward end of the cylindrical steel was machined to a 6 cm diameter and threaded for attachment of the FDM nose. The FDM nose and tail was manufactured using a ABS-M30 and layer thickness was 0.180 mm. The FDM parts were designed with the solid geometry models that were created using CATIA software and output as a ‘stl’ file. The surface roughness for FDM model, FDM model with electroplating coating and steel model

was 16, 0.832 and 0.410 µm (Ra) that is determined by perthometer M1 from Mahr company and trigonometrically derived mentioned equation.

6 WIND TUNNEL The wind tunnel test was conducted in an openreturn low speed wind tunnel. The wind tunnel, made of Plexiglas walls, has working dimensions of 0.6×0.6×1 m, and allows a maximum velocity of 150 m/s. Test section provides a Mach number range from 0.1 to 0.5. Downstream of the test section is a hydraulically controlled pitch sector that provides the capability of testing angles-of-attack ranging from –5 to +25 degrees during each run. The wind tunnel is an intermittent blow down tunnel, which operates by high-pressure air flowing from storage to atmosphere conditions. The air then passes through the test section which contains the nozzle blocks and test region. The diffuser section has movable floor and ceiling panels, which are the primary means of controlling. A sixhole probe or a wake rake can be used to determine the wake characteristics of a test subject. Pilot probes are used to measure velocity gradients and to calculate drag through integration. Pressure ports can be used on a test subject to determine the forces on specific parts of a model or how forces are distributed across a model. Also, a boundary layer mouse can be employed to determine the boundary layer characteristics. Long force and moment data refers to the three forces (lift and drag) and three moments (roll, pitch, and yaw moment) that the wind applies to the test subject. Lift and drag forces were measured at various angles of attack (AOA) and downstream velocities, by means of a load cell and a Pitot tube. Measurements in the wind tunnel were carried out at the free-stream velocity varying from 34 to 150 m/s. The wind tunnel displays its measurements in electrical units, volts, and must be converted to forces using formulas found using derivations. Using these formulas:

ForceN = Force A =

velocity N Air On -velocity N Air Off sensitivityN

velocity A Air On - velocity A Air Off sensitivity A

velocity N Air On + .

Cross over NA

, (2) + (3)

After finding the lift and the drag, it was necessary to also find the lift and drag coefficients and the ratio between them using these equations:

Description and Modeling of the Additive Manufacturing Technology for Aerodynamic Coefficients Measurement

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Strojniški vestnik - Journal of Mechanical Engineering 58(2012)2, 125-133

FL (Lift) = FN cos (AOA) – FA sin (AOA), (4) FD (Drag) = FA cos (AOA) + FN sin (AOA), (5)

where FN is the force in the x-direction and FA is the force in the y-direction.

CL =

CD =

FL

0.5 ⋅ ρ ⋅ v 2 ⋅ S FD

0.5 ⋅ ρ ⋅ v 2 ⋅ S

, (6) , (7)

where FL is the measured lift, ρ = 1.225 kg/m3, S is the wing area, v is the air speed, and FD is the measured drag. The aerodynamic loads are presented in a non-dimensional form. In the case of the force coefficients where F is either lift, drag, or slid force the corresponding coefficient will have the form: F CF = , (8)

0.5ρ ⋅ v 2 ⋅ S thus: AF NF CA = and C N = . (9) 2 0.5ρ ⋅ v ⋅ S 0.5ρ ⋅ v 2 ⋅ S Here, CA and CN are axial force coefficient and normal force coefficient, respectively. Similarly, the non-dimensional pitching moment coefficient becomes: M

CM = , (10) q⋅S ⋅c where s is the pitching moment, q is the dynamic pressure, S is the planform area, and c is the length of the chord of the airfoil.

7 AERODYNAMIC AXIS SYSTEM AND ACCURACY

Fig. 8. Reference aerodynamic axis system

A wind tunnel test operating over Mach numbers ranging from 0.1 to 0.5 was undertaken to determine the aerodynamic characteristics of the models at 3 130

selected numbers for the precursor study. These Mach numbers were 0.1, 0.2, 0.3 and the models were tested at the angle-of-attack ranges from ‒2 to +14° at zero sideslip. The reference aerodynamic axis system and reference parameters for the precursor study are shown in Fig. 8 [19] and [20]. Coefficients of pitching moment; normal force, axial force, and lift over drag are shown at each of these Mach numbers. The data accuracy resulting from the test can be divided into source of error in model dimensions and surface roughness.

8 RESULTS Figs. 9 to 11 show the variation of the normal force coefficient via the angle of attack, for both FDM and steel testing models with respect to several typical Mach numbers. It is clear to see that the variation is almost linear and the normal force coefficient of the steel model is slightly greater than that of the FDM with chromium coating model when the angles of attack are positive. Figs. 12 to 14 show the variation of the axial force coefficient via the angle of attack changes, for both FDM and steel models with respect to several typical Mach numbers. It can be seen that the axial force coefficient of the steel model and FDM with chromium coating model is smaller than that of the FDM model for all angles of attack tested. To evaluate the aerodynamic coefficients of the models, the variation of the ratio L/D with respect to several typical angles of attack is shown in Figs. 15 to 17.

It is seen that the ratio for the steel model is slightly greater than that for the FDM with chromium coating model at the same angle of attack. Furthermore, all ratios of the FDM model are lower than of the FDM with chromium coating model at any given angle of attack. It is thereby concluded that the FDM with chromium coating model exhibits better lift capability than the FDM model in the wind tunnel test. The study showed that between Mach numbers of 0.1 to 0.3, the longitudinal aerodynamic data showed very good agreement between the steel model and FDM model with chromium coating (Figs. 9 to 20). The greatest difference in the aerodynamic data between the models at Mach numbers of 0.1 to 0.3 was in total axial force. The total axial force was slightly higher for the FDM model than the other models (Figs. 12, to 14). All the models showed good agreement in pitching moment (Figs. 18 to 20). In general, it can be said that FDM model with chromium coating longitudinal aerodynamic data showed a slight divergence at higher angles-of attack when compared to the metal model data.

Daneshmand, S. – Aghanajafi, C.

Strojniški vestnik - Journal of Mechanical Engineering 58(2012)2, 125-133

9 CONCLUSIONS Recently, new systems and processes of additive manufacturing (AM) technologies have evolved.

The suitability of the AM techniques to the required application is a question that needs to be answered.

This paper presents the development of an additive manufacturing technology based on aerodynamic analysis in the wind tunnel tests. AM methods have

been considered as a potential source of improvement for conventional wind-tunnel models. Three models are analyzed and compared in wind tunnel tests. It has been concluded from this research that, since manufacturing complicated sections and airfoils is time-consuming and costly by machining and traditional methods, and also several models may be needed in wind tunnel tests additive manufacturing methods would be used in order to decrease the 0.1

0.8

0.09

0.7

0.08 0.07

0.5

0.06

0.4

0.05 CA

CN

0.6

0.3 0.2

0.03

CK45

0.1

0.02

ABS-Chromium

CK45

0.01

ABS-M30

0

0.04

ABS-Choromium

0

-0.1

ABS-M30

-0.01 -0.02

-0.2 -4

-2

0

2

4

6

8

10

12

14

-4

16

-2

0

2

Fig. 9. Comparison of normal force coefficient at Mach 0.1

8

0.1

0.7

10

12

14

16

CK45 ABS-Chromium

0.09

0.6

ABS-M30

0.08

0.5

0.07 CA

0.4 CN

6

Fig. 12. Comparison of total axial force coefficient at Mach 0.1

0.8

0.3 0.2

ABS-Chromium

0.04

ABS-M30

0

0.06 0.05

CK45

0.1

0.03

-0.1

0.02

-0.2 -4

-2

0

2

4

6

8

10

12

14

-4

16

-2

0

2

4

6

8

10

12

14

16

AOA (Degrees)

AOA (Degrees)

Fig. 10. Comparison of normal force coefficient at Mach 0.2

Fig. 13. Comparison of total axial force coefficient at Mach 0.2

0.9

0.19

0.8

0.18

0.7

CK45 ABS-Chromium

0.17

0.6 0.5

0.16

0.4

0.15

CA

CN

4

AOA (Deegrees)

AOA (Degrees)

0.3 0.2 0.1 0

0.14

CK45

0.13

ABS-Chromium

0.12

ABS-M30

-0.1

ABS-M30

0.11

-0.2

0.1

-0.3 -4

-2

0

2

4

6

8

10

12

14

16

AOA (Degrees)

Fig. 11. Comparison of normal force coefficient at Mach 0.3

-4

-2

0

2

4

6

8

10

12

14

16

AOA (Degrees)

Fig. 14. Comparison of total axial force coefficient at Mach 0.3

Description and Modeling of the Additive Manufacturing Technology for Aerodynamic Coefficients Measurement

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StrojniĹĄki vestnik - Journal of Mechanical Engineering 58(2012)2, 125-133

cost and the time of manufacturing. Regarding the accuracy necessary in aerodynamic tests AM models or AM models with chromium coating can be utilized. Generally, the difference between aerodynamic coefficients of metal models and AM models is due to the surface roughness and generated dimension tolerance. The aerodynamic data shows some small discrepancies between the three model types. In these graphs it can be seen that AM nose

has an effect on the aerodynamic characteristics up to high speeds where the effect is less drastic than at lower Mach numbers. Using metal coating on AM models improved mechanical properties and surface roughness; accordingly aerodynamic coefficients are corrected regarding to AM models without coating and the results come closer to those of the real models or machined models. The use of AM models will provide a rapid capability in the determination

7

0.02

6

0.01

5 4

ABS-Chromium ABS-M30

-0.01

3 2

CM

L/D

CK45

0

1 0

CK45

-1

ABS-Chromium

-2

ABS-M30

-0.02 -0.03 -0.04 -0.05 -0.06

-3

-0.07

-4 -4

-2

0

2

4 6 8 AOA (Degrees)

10

12

14

-4

16

-2

0

2

4

6

8

10

12

14

16

AOA(Degrees)

Fig. 15. Comparison of lift over drag at Mach 0.1

Fig. 18. Comparison of pitching moment coefficient at Mach 0.1

6

0.01

5 ABS-Chromium

3

-0.01

2

ABS-M30

-0.02

1

CM

L/D

CK45

0

4

-0.03

0 -1

CK45

-2

ABS-Chromium

-0.04

ABS-M30

-3

-0.05

-4 -4

-2

0

2

4

6

8

10

12

14

-0.06

16

-4

-2

0

2

AOA(Degrees)

4

6

8

10

12

14

16

AOA(Degrees)

Fig. 16. Comparison of lift over drag at Mach 0.2

Fig. 19. Comparison of pitching moment coefficient at Mach 0.2

3

0.03 0.02

CK45

0.01

2

ABS-Chromium

0

ABS-M30

-0.01

1 CM

L/D

-0.02 -0.03 -0.04

0

-1

CK45

-0.05

ABS-Chromium

-0.06

ABS-M30

-0.07 -0.08 -0.09

-2 -4

-2

0

2

4

6

8

10

12

14

-4

16

Fig. 17. Comparison of lift over drag at Mach 0.3

132

-2

0

2

4

6

8

10

12

14

16

AOA(Degrees)

AOA (Degrees)

Fig. 20. Comparison of pitching moment coefficient at Mach 0.3

Daneshmand, S. â&#x20AC;&#x201C; Aghanajafi, C.

Strojniški vestnik - Journal of Mechanical Engineering 58(2012)2, 125-133

of the aerodynamic characteristics of designs over a large Mach range. The fabrication processes of the prototype were also introduced and AM models with chromium coating were chosen due to their better aerodynamic analysis in the wind tunnel tests.

10 NOMENCLATURES AOA CA CN CM L/D AM FDM RP CFD NF AF

= = = = = = = = = = =

angle-of-attack axial force coefficient normal force coefficient pitching moment coefficient lift over drag ratio additive manufacturing fused deposition modeling rapid prototyping computational fluid dynamics normal force axial force

11 REFERENCES [1] Chiu, W.K., Yu, K.M. (2008). Direct digital manufacturing of 3 dimensional functionally graded material objects. Journal of Computer-Aided Design, vol. 40, no. 12, p. 1080-1093. DOI:10.1016/j. cad.2008.10.002.

[2] Pingyu, J., Fukuda, S. (2011). Tele RP- an internet web-based solution for remote rapid prototyping service and maintenance. International Journal of Computer Integrated Manufacturing, vol. 14, no. 1, p.

83-94, DOI:10.1080/09511920150214929.

[3] Landrum, D.B., Beard, R.M., LaSarge, P.A., Sprecken, N. (1997). Evaluation of stereolithography rapid prototyping for low speed airfoil design. 35th Aerospace Sciences Meeting & Exhibit.

[4] Aghanajafi, C., Daneshmand, S., Ahmadi Nadooshan, A. (2009). Investigation of surface roughness on aerodynamics properties. Journal of Aircraft, vol. 46, no. 3, p. 981-987, DOI:10.2514/1.39702.

[5] Springer, A., Cooper, K. (1998). Evaluating aerodynamic characteristics of wind-tunnel models produced by rapid prototyping methods.

Journal of Spacecraft and rockets, vol. 35, no. 6, DOI:10.2514/2.3412.

[6] Hildebrand, R.J., Eidson, R.C., Tyler, C. (2003).

Development of a low cost, rapid prototype lambda wing-body wind tunnel model. 21st Applied Aerodynamics Conference, AIAA, paper 3813.

[7] Tyler, C., Braisted, W., Higgins, J. (2005). Evaluation of rapid prototyping technologies for use in wind tunnel model fabrication. 43rd AIAA Aerospace Sciences Meeting & Exhibit, AIAA, paper 1301.

[8] Nadooshan, A.A., Daneshmand, S., Aghanajafi, C. (2007). Application of RP technology with polycarbonate material for wind tunnel model fabrication. World Academy of Science, Engineering and Technology, vol. 32, no. 1, p. 1-6.

[9] Daneshmand, S., Adelnia, R., Aghanajafi, C. (2009).

Design and production of wind tunnel testing models with FDM technology using ABSi. Journal Manufacturing Research, vol. 4, no. 2, p. 120-136, DOI:10.1504/IJMR.2009.024533.

[10] Daneshmand, S., Dehghani, A.R., Aghanajafi, C. (2007). Investigation of surface roughness on aerodynamics properties. Journal of Aircraft, vol. 44, no. 5, p. 1630-1634, DOI:10.2514/1.28030.

[11] Masood, S.H., Song, W.Q. (2004). Development of new metal/polymer materials for rapid tooling using fused deposition modelling. Materials and Design journal, vol. 25, no. 7, p. 587-594.

[12] Jacobs, P., (1995). Stereolithography and other RP&M technologies from rapid prototyping to rapid tooling.

American society of mechanical engineering.

[13] Tomislav, G., Milan, K., Mirko, K. (2008). Geometric accuracy by 2-D printing model. Strojniški vestnik -

Journal of Mechanical Engineering, vol. 54, no.

10, p. 725-733.

[14] Hopkinson, N., Hague, R.J.M., Dickens, P.M. (2006).

Rapid manufacturing an industrial revolution for the digital age. John Wiley & Sons Ltd., England, p. 7576, 235-237.

[15] Zein, I., Hutmacher, D.W., Tan, K.C., Teoh, S.H. (2002). Fused deposition modeling of novel scaffold architectures for tissue engineering applications.

Biomaterials, vol. 23, no. 4, p. 1169-1185, DOI:10.1016/S0142-9612(01)00232-0.

[16] Noorani, R. (2006). Rapid prototyping principles and applications. John Wiley & Sons, California, p. 181182.

[17] Daekeon, A., Kweon, J.H., Soonman, K., Jungil, S., Seokhee, L. (2009). Representation of surface roughness in fused deposition modeling. Journal of Materials Processing Technology, vol. 209, no. 16, p.

5593-5600, DOI:10.1016/j.jmatprotec.2009.05.016.

[18] Camplell, R.I., Mortorelli, M., Lee, H.S. (2002).

Surface roughness visualization for rapid prototyping models. Computer Aided Design, vol. 34, no. 10, p.

717-725, DOI:10.1016/S0010-4485(01)00201-9.

[19] Springer, A. (1998). Evaluating aerodynamic characteristics of wind-tunnel models produced by rapid prototyping methods. Journal of Spacecraft and Rockets, vol. 35, no. 6, p. 755-759, DOI:10.2514/2.3412.

[20] Aghanajafi, C. (2000). Aeronomy. K. N. Toosi University of Technology Publication, Iran, p. 170-184.

Description and Modeling of the Additive Manufacturing Technology for Aerodynamic Coefficients Measurement

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Strojniški vestnik - Journal of Mechanical Engineering 58(2012)2, 134-144 DOI:10.5545/sv-jme.2011.163

Paper received: 2011-08-31, paper accepted: 2011-12-28 ©2012 Journal of Mechanical Engineering. All rights reserved.

Application of CFD Simulation in the Development of a New Generation Heating Oven Rek, Z. − Rudolf, M. − Zun, I.

Zlatko Rek1,* − Mitja Rudolf 2 − Iztok Zun1 1 University

of Ljubljana, Faculty of Mechanical Engineering, Laboratory for Fluid Dynamics and Thermodynamics, Slovenia 2 Cooking-appliance development, Gorenje d.d., Slovenia

This paper deals with the application of Computational Fluid Dynamics simulation in the development of a new generation cooking appliance in Gorenje concern. As the oven is multifunctional, radiation, conduction, natural and forced convection mechanisms of heat transfer are used. The Discrete Ordinate (DO) model is used for radiation. The density of air is described by incompressible ideal gas equation in a natural convection model. The intention was to create the best possible baking conditions for different heating systems. Several discrete models were created. The influence of geometry change and boundary conditions variations to the velocity and temperature field distribution in the oven cavity was analyzed. The results of numerical simulations are validated with measurements taken from an oven prototype. The agreement was good. After successfully passing the standard tests, the oven came into serial production and was launched on the market.

Keywords: oven, heat transfer, CFD simulation

0 INTRODUCTION Consumer society, fashion trends, new materials and demands for efficient energy use require an increasingly rapid development of new products.

This also applies to ovens, which have long been an indispensable piece of kitchen equipment.

In the past, heating ovens used solid fuel or gas, but today the main source of energy is electricity.

Electric ovens are generally combined, which means that there is a choice of three different baking methods: classic, fan and grill. In the traditional mode, the electric heaters are located on the floor and on the ceiling of the oven. Heat is transferred [1] and [2] by conduction, natural convection and radiation. In the fan mode, the air is heated by electric heaters and it circulates in the oven as a result of a fan. The main mechanism of heat transfer is forced convection. In the grill mode the electric heater on the oven ceiling is heated to such high temperatures that it glows.

Heat is transferred by radiation. Each of these heating methods is specific. In developing the new oven we tried to provide optimal conditions for all the three methods of heating.

Computational fluid dynamics [3] to [5] is very useful for predicting temperature and velocity fields in the oven. With the rapid progress of parallel computing and development of commercial codes, CFD has become an indispensable tool in the development of new products. Together with the experiment it allows for a significant reduction of time from the first design through the prototype to the finished product. Therefore, CFD is increasingly used in the food industry and in developing appliances 134

used in food preparation. This is proved by a growing number of publications in recent years.

In their study, Amanlou et al. [6] present the use of CFD for design cabinets for fruit drying. They investigated the effect of different geometries on the efficiency of the cabinet dryer. They also tried to find the best construction with regard to the uniform distribution of temperature and air flow. Comparing the experimental and CFD, data have revealed a very good correlation coefficient for drying air temperature and air velocity in the drying chamber.

Chhanwal et al. [7] use a CFD model of electric oven for baking bread, where the radiation is the dominant mechanism of heat transfer. They employed three models of radiation: discrete transfer radiation model (DTRM), surface to surface (S2S) and discrete ordinates (DO). The results were compared with the experiment. They reported a good agreement for all three models.

Boulet et al. [8] made CFD model of the bakery pilot oven. All three heat transfer mechanisms are considered and coupled with turbulent flow, for which they used k-ε realizable model whereas the S2S model simulates the radiation. The model predictions show a good qualitative agreement with the experimental measurements.

In their article Verboven et al. [9] discuss the application of CFD modeling and validation of the isothermal air flow in a forced convection oven. The governing fluid flow equations were expanded with a fan model. They used a standard and renormalization group (RNG) version of the k-ε turbulence model. The calculated speeds were validated by measurements with a hot-film velocity sensor. The calculation error was 22% of the actual velocity. The reason

*Corr. Author’s Address: University of Ljubljana, Faculty of Mechanical Engineering, Aškerčeva 6, 1000 Ljubljana, Slovenia, zlatko.rek@fs.uni-lj.si

Strojniški vestnik - Journal of Mechanical Engineering 58(2012)2, 134-144

for the relatively high error was within the limits of turbulence modeling and numerical grid density.

Therdthai et al. [10] performed a threedimensional CFD simulation of temperature profiles and flow patterns during a continuous industrial baking process. They used a moving grid approach.

Their model could predict the dynamic responses. The model was also used to investigate the oven operating conditions, which could produce optimum baking conditions. The numerical results were consistent with the actual measurements.

Williamson et al. [11] presented the development, testing and optimization of the design of a novel gasfired radiant burner for industrial tunnel ovens. CFD simulation was used to model the burner and baking chamber environment, and in particular to predict radiation heat fluxes incident on the top surface of the food. CFD model has been validated by measurements with thermocouples. The agreement was within 10%.

The simulations have indicated that the new burner is capable of delivering irradiation to a traveling conveyor more uniformly than existing radiant burner designs.

Wong et al. [12] used the 2D CFD model of the oven chamber of an industrial continuous breadbaking oven in order to better understand the process of baking. They used the sliding mesh technique to simulate the continuous movement of dough/bread during the whole traveling period. The CFD modeling was proven to be a useful approach in studying the unsteady heat transfer in the oven as well as the heating history and temperature distribution within dough/bread.

Ghani et al. [13] numerically simulated the natural convection heating of canned liquid food for axisymmetric case. They predicted transient flow patterns and temperature profiles. The density and viscosity of the fluid were dependent on temperature.

It was found that the slowest heating zone moves towards the bottom of the can. The shape and size of this area depends on the used liquid.

The optimization of new generation ovens NGKA3 was performing a numerical simulation of temperature and velocity fields. Numerical simulation of such a complex case was made on mini computational cluster Supermicro (5 nodes, 14 processors, 38 cores, 104 GB RAM) with the ANSYS Fluent software.

The numerical simulation was carried out in several steps. The solutions of transport equations enabled the study of pressure, velocity and temperature fields under steady conditions. The second step was the validation [14] of the model.

The agreement between the numerical simulation results and the measured data from the prototype was checked. After the numerical model was validated, the optimal temperature distribution in the oven cavity by changing the geometry (heaters shape, shape of the fan cover) and the boundary conditions (heater temperature, ventilation system flow rate) at the third step were looked for.

1 NUMERICAL MODEL 1.1 Governing Equations Temperature distribution and air circulation in the oven cavity are governed by conservation equations.

The system of partial differential equations is: •

•

•

•

mass conservation:  ∂ρ + ∇ ⋅ (ρv ) = 0, ∂t

(1)

momentum conservation:    ∂  ( ρv ) + ∇ ⋅ ( ρvv ) = −∇p + ∇ ⋅ τ + ρg + F , ∂t

(2)

energy conservation:

 ∂ ( ρe ) + ∇ ⋅ ( v ( ρe + p ) ) = ∇ ⋅ ( λ∇T ) + Sh , ∂t

e = h−

p v2 + , ρ 2

radiation intensity conservation:

dI ( r , s ) + ( a + σ s )I ( r , s ) = ds

4 σs

2 σT = an + I ( r , s ')Φ( s , s ')dΩ', 4π ∫ π

(3) (4)

(4)

 where v isthe velocity vector, τ is the stress tensor,  ρ g and F are the gravitational body force and external body forces respectively, e is the energy, h is the sensible enthalpy, ρ is the density, p is the pressure, T is the temperature, λ is the thermal conductivity, cp is the specific heat and Sh is the volumetric heat  source (0 in our case), I is the radiation intensity, r   is the position vector, s is the direction vector, s ' is the scattering direction vector, s is the path length, a is the absorption coefficient, n is the refractive index, σs is the scattering coefficient, σ is the Stefan-Boltzman constant.

Application of CFD Simulation in the Development of a New Generation Heating Oven

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Strojniški vestnik - Journal of Mechanical Engineering 58(2012)2, 134-144

As we were only looking for a steady state, the governing equations are simplified since all time derivatives are zero.

The Reynolds number varies between 230 (inlet) and 880 (outlet) in the case of forced convection, while the Rayleigh number is 6·108 for natural convection.

These numbers indicate [2] a transition zone between laminar and turbulent flow. We have decided to treat flow as a laminar since Reynolds averaged (RANS) turbulence models available in Fluent do not satisfy the y+ wall conditions for such a case.

The pressure variations are small enough, so the incompressible ideal gas law is used to express the relationship between air density and temperature: pop (6)

ρ= , R T Mw

Maximum temperature of the biscuit surface was compared with the measured temperature, Table 2.

Quite large differences indicate that not all models are appropriate for our simulation. The optical thickness aL is a good indicator of which model to use, where L is the length scale of the domain. In our case (L = 0.4 m) the optical thickness is <<1. This comparison proves that the P-1 and Rosseland models are not suitable for optically thin problems. Although DTRM and S2S models can be used in these kinds of problems, they do not support semi-transparent walls (glass doors). This is manifested in over-prediction of biscuit surface temperature. The only appropriate radiation model for our analysis is DO model which works across the full range of optical thicknesses, and it also allows the solution of radiation at semitransparent walls.

where pop is the operating pressure (101.325 Pa), R is the universal gas constant and Mw is the molecular weight of the air. This means that full buoyancy model was used.

The following material properties presented in Table 1 were used in the numerical model.

1.3 Influence of Biscuit Surface Emissivity

Table 1. Physical properties of the materials in use Material steel aluminum enamel glass wool glass air biscuit/HIPOR

ρ [kg/m3] 7850 2700 7870 50 2700 0.7 1075

cp [J/kgK] 465 896 481 670 840 1034 3365

λ [W/mK] 44 229 12 0.036 0.76 0.037 0.452

ε 0.8 0.9 0.94 0.6

The oven inner walls are enameled, while heaters are made from steel. The emissivities of enamel and steel are well known and were supplied by manufacturers.

On the contrary, the emissivity of biscuit is not well known. Computations with ε in the range from 0.4 to 0.8 were conducted to study the influence of biscuit wall emissivity to maximum biscuit surface temperature, Table 3.

Table 3. Maximum biscuit surface temperature at different emissivities ε

0.4

0.5

0.6

0.7

0.8

Tmax [°C]

205.3

205.2

205.1

204.9

204.8

As it can be seen, the biscuit surface emissivity has no significant effect on the surface temperature.

1.2 Choosing a Radiation Model At high temperatures, the fourth-order dependence of the radiative heat flux on temperature implies that the radiation will dominate and the radiative heat transfer should be included in the simulation. ANSYS Fluent provides five radiation models: Discrete Transfer (DTRM), P-1, Rosseland, Surface-to-Surface (S2S) and Discrete Ordinates (DO). To choose the most accurate radiation model a test simulation was done.

1.4 Discrete Models Four different geometrical models were created in GAMBIT [15] using the combination of various geometrical parameters, see Table 4: • Model 0 ― conventional heating with infrared heaters, 1 baking level and flat rear wall, see Fig. 1.

Table 2. Maximum biscuit surface temperature for different radiation models Radiation model Tmax [°C]

136

DTRM 564

P-1 380

Rosseland 241 Rek, Z. − Rudolf, M. − Zun, I.

S2S 536

DO 205

Measured 208

Strojniški vestnik - Journal of Mechanical Engineering 58(2012)2, 134-144

• • •

Model 1 ― fan-heating with hot air, 1 baking level, 0° rear wall inclination and 5 mm air inlet slot width, see Fig. 2.

Model 2 ― fan-heating with hot air, 1 baking level, 15° rear wall inclination and 15 mm air inlet slot width, see Fig. 3.

Model 3 ― fan-heating with hot air, 2 baking levels, 15° rear wall inclination and 15 mm air inlet slot width, see Fig. 4.

Table 4. Geometrical parameters Parameter heating system number of levels inclination of rear wall width of inlet slot

Value radiation 1 0° 5 mm

convection 2 15° 15 mm

of computational grids for the four models after conversion of tetrahedral cells.

Table 5. Number of tetrahedral and polyhedral cells tetrahedral polyhedral

Model 0

Model 1

Model 2

Model 3

450,818 236,065

870,576 295,820

937,746 307,246

1,096,822 447,274

The quality of polyhedral grid was checked [18] with Fluent before starting the numerical simulation.

In addition to the above parameter skewness, the criterion of aspect ratio (a measure of the stretching of the cell) and squish index (using the vector from the cell centroid to each of its faces and the corresponding face area vector) are used. Table 6 shows the parameters of cell quality for all four models. Maximum values are much lower from the recommended upper values, which means that the spatial discretization is made very well.

The mesh consistency test was not performed due to the short deadline. The choice of computational mesh size was based on experience with similar cases and available computer resources (memory and CPU time).

1.6 Boundary Conditions

Fig. 1. Conventional oven

1.5 Computational Mesh Discretization of the geometrical models was performed in the program Tgrid [16] by using tetrahedral control volumes. The grid quality parameter skewness (the difference between the shape of the cell and the shape of an equilateral cell of the equivalent area) of the automatically generated surface mesh exceeded a value of 0.85 in some cells.

The manual repair by merging of problematic cells was needed. The maximal skewness was 0.76 for all grids after mesh repair. This means that the quality of the surface mesh was very good.

The initial volume grids were generated on the basis of surface meshes. They needed additional refinement and smoothing to achieve the grid quality within the recommended limits.

For a more effective calculation (smaller number of cells, faster and more stable convergence) the tetrahedral cells were converted to polyhedral cells in Fluent [17], see Fig. 5. Table 5 shows the size

The correctness of the numerical calculation results is largely dependent on boundary conditions. If these do not correspond to the actual situation, the solution of equations does not give the expected values.

Temperature boundary conditions for oven outer walls, infrared heaters and fan cover were obtained by the measurements on the oven prototype in the Electrothermics Laboratory of Cooking Appliances department in Gorenje to approach the real situation, see Fig. 6. Thermostat was set to 200 ˚C. The measured average temperatures at the oven outer walls in the case of conventional heating are shown on Fig. 7. The influence of the heater switching with time period of 10 minutes on the top and bottom wall can be observed. After 30 minutes oscillations of temperature are minimal on the walls away from heaters. A similar scenario was observed in an oven with convection heating. Steady state conditions are established after 60 minutes of heating and they are used for temperature boundary condition at oven walls, see Table 7.

The maximum temperatures of the last three periods are used for the top and bottom wall boundary conditions.

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Fig. 2. Fan-heating oven with 1 baking level, flat rear wall and 5 mm air inlet slot width

Fig. 3. Fan-heating oven with 1 baking level, 15° rear wall inclination and 15 mm air inlet slot width

Fig. 4. Fan-heating oven with 2 baking levels, 15° rear wall inclination and 15 mm air inlet slot width

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a)

b)

Fig. 5. a) Detail of tetrahedral surface mesh; and b) polyhedral volume mesh Rek, Z. − Rudolf, M. − Zun, I.

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Table 6. Parameters of cell quality for polyhedral mesh Maximum face squish Maximum cell squish Maximum aspect ratio

Model 0 0.738 0.795 26.2

Model 1 0.751 0.816 26.6

Model 2 0.727 0.734 10.1

Model 3 0.712 0.795 12.7

Recommended 0.85 0.95 50

Fig. 6. Temperature measurement locations at oven outer wall and infrared heater

Table 7. Temperature boundary conditions at oven walls

bottom top left right front rear

Temperature [°C] Model 0 Model 1 to 3 137 105 120 110 102 108 103 105 46 88 78 100

At the perforated area (air exit from oven cavity) the pressure drop is prescribed. It is proportional to the fluid dynamic pressure: 1 ∆p = ξ ρ v 2 , 2

(7)

where the resistance coefficient [19] ξ = 11.8 depends on the ratio of the holes area and total area.  No-slip ( v = 0) boundary condition was used for momentum equation at walls.

The oven has a fan to provide hot air circulation in the case of convection heating system. The air is sucked from the oven cavity and after it is heated it travels through the slots back to the oven cavity. Due to the complexity, the fan is not modeled in details.

segment 16 segment 15 segment 14 segment 13

Fig. 7. Measured average temperatures at the oven outer walls

segment 05 segment 06 segment 07 segment 08

segment 12 segment 11 segment 10 segment 09

segment 01 segment 02 segment 03 segment 04

Fig. 8. Segments of the fan cover slots

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Fan cover slots, where hot air enters into the oven cavity, are divided into 16 segments, see Fig. 8.

Eleven different combinations of boundary conditions have been prescribed for segments, where some were closed and others open. The measured air velocity and air temperature were 0.4 m/s and 250 °C, respectively.

1.7 Numerical Simulation Four numerical simulations have been done. Only heat transfer with radiation of hot walls (infrared heater, oven cavity walls, glass door and tray with biscuit) was considered in the first case (Model 0). Forced convection was included in other simulations (Models 1, 2 and 3).

The commercial CFD code ANSYS Fluent was used for the numerical simulation. The code uses a pressure-based solver with SIMPLE [20] method for velocity-pressure coupling. The relaxation factors were 0.3 for pressure, 0.7 for velocity, and 1 for energy and radiation. The velocity and temperature fields were discretized with a second order upwind scheme, whereas the pressure field was discretized with a PRESTO! Scheme. The convergence criteria for residuals of continuity and momentum equations was 10-4 and 10-6 for energy and radiation equations.

A comparison of measured and calculated temperatures at selected points is shown in Table 8.

Peak temperature in the middle of the tray (measuring point 3) matched very well with the measurement within 1%. A slightly higher difference in temperature, up to 15%, was measured at the front region (measuring points 1 and 2), which is probably a result of inexact boundary condition for the glass doors. The deviation of temperatures at measuring points 4 and 5 was up to 10%.

Fig. 10. Biscuit surface temperature distribution Table 8. Comparison of measured and calculated temperature

2 RESULTS AND DISCUSSION

Measuring point Measured temperature [°C] Calculated temperature [°C]

2.1 Validation Validation of the numerical model was made for a conventional heating system. Fig. 9 shows the positions of five measuring probes of temperature on a tray with biscuit. The calculated temperature field on the biscuit surface is shown in Fig. 10.

1 200 170

2 199 170

3 208 205

4 205 185

5 206 185

2.2 Optimum Conditions in the Oven Cavity Several factors have an influence on the conditions inside the oven, such as: the shape and power of heaters, fan rotor rotational speed, thickness and quality of insulation, the design of oven doors, etc.

Optimum conditions can be approached through the variation of these factors. The change in the oven cavity geometry and the variation of the boundary conditions was used in this case. We varied the inclination of the back wall and the width of the air inlet slots. Boundary conditions were changed by opening or closing the segments of the air inlet slots.

The numerical simulation results for the convection heating system variants are presented below.

2.2.1 Geometry Change

Fig. 9. Positions of measuring probes

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The change in the form of oven cavity has a strong influence on the velocity field, see Fig. 11. The inlet velocity of 0.7 m/s is high because of a 5 mm slot Rek, Z. − Rudolf, M. − Zun, I.

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a)

b)

Fig. 11. Velocity distribution in the plane 10 mm above the tray for a) model 1 and b) model 2 a)

b)

Fig. 12. a) Velocity and b) temperature field in the vertical plane for variant 00 a)

b)

Fig. 13. a) Velocity and b) temperature field in the vertical plane for variant 10 Application of CFD Simulation in the Development of a New Generation Heating Oven

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a)

b)

Fig. 14. a) Velocity and b) temperature field in the horizontal plane for variant 00 a)

b)

Fig. 15. a) Velocity and b) temperature field in the horizontal plane for variant 10 a)

b)

Fig. 16. Flow optimization in forced convection;a) pathlines are shown for the initial model and b) optimal combination of fan cover slots opening

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width in the initial geometry of Model 1. The straight back wall directs hot air perpendicular to the side walls, resulting in hot air recirculation in the back corners and its rapid suction from the oven cavity due to the fan proximity.

The zone of cooler and slower air appears at the front region. Such a situation means worse baking conditions. By changing the inclination of the back wall and increasing the width of the inlet slot, the conditions are significantly improved. Due to a better flow guidance the movement of hot air is assured throughout the oven cavity.

2.2.2 Change of Boundary Conditions Figs. 12 and 13 show the velocity vectors and temperature distribution in the vertical plane in the middle of the oven for the initial Model 2 (variant 00, all segments are open) and improved conditions (variant 10, closed segments 1 to 4 and 5 to 9).

Variant 00 shows the above vortex, which causes the flow of hot air to be directed down in the middle of tray, from where the fan sucked it from the oven cavity. Therefore, the temperature field around the biscuit is non-uniform, which means poor baking at the front where there is already high heat transfer due to the glass doors (radiation, convection). Temperature is about 20 °C higher than the desired 200 °C in a great portion of the oven cavity.

Due to the top and bottom air inlet slots closure in variant 10, the vortex does not appear. Hot air flows from the glass doors along the tray towards the fan. Therefore, the air temperature in the vicinity of biscuit is constant, which results in even baking. The temperature throughout the oven cavity is only a few degrees higher than 200-°C. Figs. 14 and 15 show the velocity vectors and the temperature distribution in the horizontal plane at the middle of the oven cavity for variants 00 and 10 of the Model 2. The air circulation at the rear of the oven can be observed again in the case of initial model. This means higher temperature in that region and consequently, uneven baking.

At the variant 10, the top and the bottom air inlet slots are closed, therefore the air flow is increased at the side slots. Hot air travels along oven side walls in the direction of doors, where it turns back towards the fan on the back wall. As can be seen from the picture of isotherms, the temperature field is much more uniform as in the case of variant 00.

Fig. 16 show streamlines, where color represents temperature, and biscuit surface temperature for the

initial and the optimized variant of the fan cover slots boundary conditions.

3 CONCLUSION The velocity, pressure and temperature field in the oven cavity have been dealt with the use of CFD simulation. Natural convection, forced convection, conduction and radiation mechanisms of heat transfer were used. The comparison of five radiation models showed that only appropriate model is DO. Biscuit surface emissivity didn’t show significant effect on the surface temperature. Four different oven geometries and eleven variations of velocity boundary conditions were used.

Control of the circulating hot air velocity in the oven cavity has emerged as the decisive impact factor on the baking quality. Predictions from numerical simulations are confirmed by the positive results from the validation and the functional testing of the oven prototypes and they allowed fast optimization of the temperature field in the oven cavity.

4 REFERENCES [1] Batchelor, G.K. (2000). An Introduction to Fluid Dynamics. Cambridge University Press, Cambridge.

[2] Incropera, F.P., DeWit, D.P. (2002). Fundamentals of Heat and Mass Transfer. John Wiley & Sons, New York.

[3] Ferziger, J.H., Perić, M. (2002). Computational Methods for Fluid Dynamics. Springer-Verlag, Berlin, DOI:10.1007/978-3-642-56026-2.

[4] Shaw, C.T. (1992). Using Computational Fluid Dynamics. Prentice Hall, New Jersey.

[5] Tanehill, J.C., Anderson, D.A., Pletcher, R.H. (1997).

Computational Fluid Mechanics and Heat Transfer.

Taylor&Francis, Washington.

[6] Amanlou, Y., Zomorodian, A. (2010). Applying CFD for designing a new fruit cabinet dryer. Journal of Food Engineering, vol. 101, p. 8-15, DOI:10.1016/j. jfoodeng.2010.06.001.

[7] Chhanwal, N., Anishaparvin, A., Indrani, D., Raghavarao, K.S.M.S., Anandharamakrishnan, C. (2010). Computational fluid dynamics (CFD) modeling of an electrical heating oven for bread-baking process.

Journal of Food Engineering, vol. 100, p. 452-460, DOI:10.1016/j.jfoodeng.2010.04.030.

[8] Boulet, M., Marcos, B., Dostie, M., Moresoli, C. (2010). CFD modeling of heat transfer and flow field in a bakery pilot oven. Journal of Food Engineering, vol.

97, p. 393-402, DOI:10.1016/j.jfoodeng.2009.10.034.

[9] Verboven, P., Scheerlinck, N., De Baerdemaeker, J., Nicola, B.M. (2000). Computational fluid dynamics modelling and validation of the isothermal airflow in a forced convection oven. Journal of Food Engineering,

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vol. 43, p. 41-53, DOI:10.1016/S0260-8774(99)001338.

[10] Therdthai, N., Zhou, W., Adamczak, T. (2004). Threedimensional CFD modelling and simulation of the temperature profiles and airflow patterns during a continuous industrial baking process. Journal of Food Engineering, vol. 65, p. 599-608, DOI:10.1016/j. jfoodeng.2004.02.026.

[11] Williamson, M.E., Wilson, D.I. (2009). Development of an improved heating system for industrial tunnel baking ovens. Journal of Food Engineering, vol. 91, p.

64-71, DOI:10.1016/j.jfoodeng.2008.08.004.

[12] Wong, S., Zhou, W., Hua, J. (2007). CFD modeling of an industrial continuous bread-baking process involving U-movement. Journal of Food Engineering, vol. 78, p.

888-896, DOI:10.1016/j.jfoodeng.2005.11.033.

[13] Abdul Ghani, A.G., Farid, M.M., Chen, X.D., Richards, P. (1999). Numerical simulation of natural convection heating of canned food by computational

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fluid dynamics. Journal of Food Engineering, vol. 41, p. 55-64, DOI:10.1016/S0260-8774(99)00073-4.

[14] Roache, P.J. (1998). Verification and Validation in Computational Science and Engineering. Hermosa Publishers, New Mexico.

[15] GAMBIT Version 2.4: User’s Guide. Fluent, Inc., 2007.

[16] TGrid Version 4.0: User’s Guide (2006). Fluent, Inc. [17] FLUENT Version 6.3: User ‘s Guide (2006). Fluent Inc. [18] Special Interest Group on “Quality and Trust in Industrial CFD” (2000). Best Practice Guidelines.

European Research Community On Flow, Turbulence And Combustion (ERCOFTAC).

[19] Idelchik, I.E. (1996). Handbook of hydraulic resistance. Begell House, New York.

[20] Patankar, S.V. (1980). Numerical Heat Transfer and Fluid Flow. Hemisphere Publishing Corporation, New York.

Rek, Z. − Rudolf, M. − Zun, I.

Strojniški vestnik - Journal of Mechanical Engineering 58(2012)2 Vsebina

Vsebina Strojniški vestnik - Journal of Mechanical Engineering letnik 58, (2012), številka 2 Ljubljana, februar 2012 ISSN 0039-2480 Izhaja mesečno

Razširjeni povzetki člankov Aleš Petek, Karl Kuzman: Tehnologija protismernega vlečenja vratu z uporabo inkrementalnega pristopa Fuqing Zhao, Jizhe Wang, Junbiao Wang, Jonrinaldi Jonrinaldi: Model dinamičnega ponovnega razporejanja z večagentskim sistemom in postopek reševanja Suzana Uran, Riko Šafarič: Estimacija spremenljive proge s pomočjo nevronske mreže za adaptivni sliding-mode regulator Bohumil Taraba, Steven Duehring, Ján Španielka, Štefan Hajdu: Vpliv mešanja na prenos toplote pri hlajenju v olju ISORAPID 277HM Gorazd Krese, Matjaž Prek, Vincenc Butala: Analiza rabe električne energije stavbe z izboljšano metodo s temperaturnim presežkom Matej Volk, Marko Nagode, Matija Fajdiga: Ocenjevanje poljubnih zveznih funkcij z algoritmom za oceno mešane gostote porazdelitve verjetnosti Saeed Daneshmand, Cyrus Aghanajafi: Opis in modeliranje dodajalne izdelovalne tehnologije za meritve aerodinamičnih koeficientov Zlatko Rek, Mitja Rudolf, Iztok Zun: Razvoj pečice nove generacije s pomočjo CFD-simulacije

SI 17 SI 18 SI 19 SI 20 SI 21 SI 22 SI 23 SI 24

Osebne vesti Magistrska in diplomska dela

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Recenzenti

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Prejeto: 2011-09-02, sprejeto: 2011-11-10 © 2012 Strojniški vestnik. Vse pravice pridržane.

Tehnologija protismernega vlečenja vratu z uporabo inkrementalnega pristopa Petek, A. – Kuzman, K. Aleš Petek1,* – Karl Kuzman2

2 Univerza

1 Difa d.o.o., Slovenija, v Ljubljani, Fakulteteta za strojništvo, Slovenija

Izdelovanje vratov na pločevinastih komponentah s konvencionalno tehnologijo vlečenja vratov je v primeru prototipne oziroma maloserijske proizvodnje velikokrat stroškovno neupravičeno. Razen velikega števila preoblikovalnih stopenj in posledično velikih preoblikovalnih orodij je pri kompleksnejših izdelkih orodje sestavljeno celo iz pomičnih elementov, s katerimi je možno izdelati vratove, ki so postavljeni v različnih smereh glede na smer gibanja pehala. Kompleksnejše oblike, ki so bolj zaprte, pa je pogosto celo nemogoče izdelati.

Zato je treba poiskati rešitev, ki bi odpravila uporabo gibajočih se delov znotraj kompleksnega preoblikovalnega orodja, povečala fleksibilnost izdelave in zmanjšala proizvodne stroške. V ta namen je v članku predlagana sodobna tehnologija protismernega inkrementalnega vlečenja vratu, ki ustreza vsem prej omenjenim zahtevam.

Posebna pozornost je namenjena raziskovanju tehnoloških posebnosti in omejitev z ozirom na zahteve industrije. Tu je treba opredeliti višino in tanjšanje vratu ter posledično mejno vlečno razmerje, saj je v splošnem znano, da je premer začetne luknje neposredno povezan s porušitvijo izdelka na vrhu oboda preoblikovanega vratu.

Zaradi velikega števila vhodnih parametrov, ki imajo različne stopnje vpliva na rezultat preoblikovanja, je bila uporabljena metodologija empiričnega modeliranja s ciljem natančnejšega napovedovanja rezultatov preoblikovanja. Metoda omogoča napovedovanje vpliva posamezne vhodne vrednosti in njenih iteracij na izbrane izhodne vrednosti procesa. Takšna metoda je še posebej pomembna pri novejših tehnologijah, kjer je sam proces še dokaj slabo poznan.

Rezultati opravljenih analiz kažejo, da ima največji vpliv na izhodne vrednosti procesa premer preoblikovalnega orodja ter velikost vertikalnega in horizontalnega premika. V primeru tanjšanja pločevine ima največji vpliv premer preoblikovalnega orodja in velikost vertikalnega pomika. Zmanjšanje katerega koli od dveh omenjenih parametrov neposredno vpliva na stanjšanje stene vratu. V nasprotju s tanjšanjem pa povzroči povečanje premera preoblikovalnega orodja, vertikalnega in horizontalnega premika zmanjšanje višine vratu.

V primerjavi s konvencionalnim vlečenjem vratu lahko pravilna izbira procesnih parametrov protismernega inkrementalnega vlečenja vratu pripomore k večjemu mejnemu vlečnemu razmerju, in posledično k izdelavi višjih vratov brez porušitve. Razloge bi lahko našli v lokalnem inkrementalnem vnosu deformacij v pločevino in ugodnejšem napetostnem stanju.

Ugotovljeno je bilo, da se lahko tehnologija protismernega inkrementalnega vlečenja vratu uspešno uporablja kot dodatna tehnologija v izdelovalnih procesih tako za simetrične kot tudi za asimetrične oblike vratov. Zaradi neprimerne geometrije začetne luknje in različne zgodovine utrjevanja vzdolž stene preoblikovanca je v primeru nesimetričnih oblik potrebnih veliko iteracij ‘poskusi – popravi’, preden dobimo izdelek v skladu z zahtevami.

Zato bo treba v prihodnosti posvetiti veliko pozornosti opredelitvi povezave med omenjenima spremenljivkama že v virtualnem okolju.

Tehnologija protismernega inkrementalnega vlečenja vratu je novost na področju preoblikovanja pločevine, zato še ni intenzivnejših raziskav na tem področju. Rezultati so namenjeni tako razvojno- raziskovalnim inštitucijam kot tudi gospodarstvu, ki se vsakodnevno srečuje z izdelovalnimi tehnologijami. Slednje si lahko z uporabo takšne tehnologije v maloserijski proizvodnji pridobi konkurenčno prednost na svetovnem trgu.

Ključne besede: protismerno vlečenje vratu, inkrementalno preoblikovanje, pločevina, empirično modeliranje

*Naslov avtorja za dopisovanje: Difa d.o.o., Kidričeva cesta 91, 4220 Škofja Loka, Slovenija, ales.petek@difa.si

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Prejeto: 2011-02-02, sprejeto: 2011-11-23 © 2012 Stojniški vestnik. Vse pravice pridržane.

Model dinamičnega ponovnega razporejanja z večagentskim sistemom in postopek reševanja Zhao, F. ‒ Wang, J. ‒ Wang, J. ‒ Jonrinaldi, J. Fuqing Zhao1,2,* ‒ Jizhe Wang1 ‒ Junbiao Wang2 ‒ Jonrinaldi Jonrinaldi3 1 Šola

za računalništvo in komunikacije, Tehnična univerza Lanzhou, Kitajska za sodobno konstruiranje in integrirane izdelovalne tehnologije, Ministrstvo za šolstvo, Severozahodna politehnična univerza, Kitajska 3 Šola za tehniko, računalništvo in matematiko, Univerza Exeter, Združeno kraljestvo

2 Laboratorij

Za izboljšavo fleksibilnosti proizvodnih sistemov in optimiziranje rešitev za odzivanje na vse večje spremembe v vzorcih povpraševanja in ponudbi izdelkov je treba sočasno obravnavati, vrednotiti in optimizirati pristope k ponovnemu razporejanju in možnosti razporejanja proizvodnje. Na ta način je možno upoštevati omejitve obeh funkcij ter izdelati optimalen integrirani načrt in terminski plan.

Do sedaj je bilo le malo poskusov snovanja univerzalnega komunikacijskega in pogajalskega mehanizma za problem dinamičnega ponovnega razporejanja in ustreznega pristopa k reševanju.

Cilj je izgradnja univerzalnega modela za dinamično ponovno razporejanje na osnovi večagentskega sistema (MAS) za problem razporejanja proizvodnje in proizvodne sisteme.

V članku je predstavljena uporaba protokola Control Net na osnovi sistema MAS za ponovno razporejanje v delavniškem okolju. Po upoštevanju vseh vplivov odpovedi opreme in popravil na proizvodni proces se kompleksni proces dinamičnega ponovnega razporejanja razdeli na komunikacijske in pogajalske procese, v katerih je udeleženo več agentov. S tem je razširjena sposobnost samodejnega odločanja v primeru nepričakovanih dogodkov v proizvodnji. S simulacijo dejanske proizvodne delavnice je bila dokazana učinkovitost modela in algoritma na osnovi sistema MAS za problem ponovnega razporejanja v proizvodnem sistemu.

Uporabljen je pristop realizacije metodologije problema ponovnega razporejanja v proizvodnem sistemu, predmet članka pa je načrtovanje in razporejanje proizvodnje.

V članku je predlagan dinamičen model ponovnega razporejanja na osnovi večagentskega sistema (MAS).

Obravnavan je mehanizem komunikacije in pogajanja med agenti, ki podpira avtonomno odločanje vsakega agenta in večagentskega sistema. Rezultati simulacij dinamičnega razporejanja s perturbacijami kažejo, da predlagani model in algoritem učinkovito rešujeta problem dinamičnega razporejanja v proizvodnem sistemu.

Omeniti je treba, da obseg primerov v tem delu ni zelo velik. V prihodnje bomo raziskovali učinkovitost našega modela in pristopa pri problemih, ki vključujejo večje število odločitvenih spremenljivk. Prihodnje delo bo vključevalo tudi študij procesa specifičnih interakcij med agenti v večagentskem okolju ter razširitev našega modela in algoritma na osnovi MAS za reševanje omejenih ali diskretnih večkriterijskih optimizacijskih problemov.

Proces dinamičnega ponovnega razporejanja na osnovi sistema MAS vključuje večstopenjsko lokalno razporejanje. Lokalno razporejanje vsake stopnje se izvaja po modelu CNP. Proces večagentskega pogajanja in interakcije na osnovi modela CNP vključuje dvosmerno komunikacijo, kar je bistvena razlika med našim pristopom in metodami, ki jih najdemo v sodobni objavljeni literaturi.

Model in metode, opisane v tem članku, izboljšujejo fleksibilnost proizvodnih sistemov in zagotavljajo optimizacijo rešitev za odzivanje na vse večje spremembe vzorcev povpraševanja in ponudbe izdelkov. Sočasno so bili obravnavani, vrednoteni in dinamično optimizirani pristopi k ponovnemu razporejanju in možnosti razporejanja proizvodnje, kar predstavlja pomemben prispevek k problemu dinamičnega ponovnega razporejanja v sodobnem proizvodnem obratu.

Keywords: MAS, agent, dinamično razporejanje, protokol Contract Net, pogajalski mehanizem, perturbacije

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*Naslov avtorja za dopisovanje: Šola za računalništvo in komunikacije, Tehnična univerza Lanzhou, Lanzhou 730050, Kitajska, fzhao2000@hotmail.com

Strojniški vestnik - Journal of Mechanical Engineering 58(2012)2, SI 19

Prejeto: 2011-05-05, sprejeto: 2011-11-07 © 2012 Stojniški vestnik. Vse pravice pridržane.

Estimacija spremenljive proge s pomočjo nevronske mreže za adaptivni sliding-mode regulator Uran, S. ‒ Šafarič, R. Suzana Uran ‒ Riko Šafarič

Univerza v Mariboru, Fakulteta za elektrotehniko, računalništvo in informatiko, Slovenija

Namen prispevka je prikazati povzetek večletnih raziskav na področju razvoja adaptivnih sliding-mode regulatorjev, kjer se spremenljiva visokonelinearna regulacijska proga (neposredno gnani robotski mehanizem) estimira s pomočjo nevronskih mrež. Sam cilj raziskave pa je bil načrtovati, izdelati, praktično preizkusiti in primerjati štiri tipe regulatorjev iz družine t. i. zveznih nevronskih sliding-mode adaptivnih regulatorjev.

Opravljena je bila teoretična izpeljava enačb centraliziranega zveznega nevronskega sliding-mode regulatorja (CZNSMR), ki potrebuje za optimalno delovanje znane spremenljive parametre matrike vztrajnostnih momentov robota in eno samo veliko nevronsko mrežo, ki estimira manjkajoči del dinamike robota. Nato smo izpeljali tri enačbe vodenja decentraliziranega zveznega nevronskega sliding-mode regulatorja (DZNSMR) za vsako posamezno os, ki se od predhodnega regulatorja razlikuje po tem, da potrebuje za optimalno delovanje samo povprečne vrednosti parametrov vztrajnostnih momentov posameznih osi robota in tri majhne nevronske mreže za estimacijo dinamike sklopljenosti preostalih osi robota z enačbo zakona vodenja posamezne osi. Obe dodatno izpeljani metodi poenostavljenega centraliziranega in decentraliziranega zveznega nevronskega sliding-mode regulatorja (PCZNSMR in PDZNSMR), pa ne uporabljata nobenega znanja o dinamiki robotskega mehanizma, torej ena sama (PCZNSMR) oz. tri nevronske mreže (PDZNSMR) estimirajo celotno dinamiko robota.

Po izdelavi vseh štirih metod zakona vodenja smo posamezne metode preizkusili glede na enake motnje nenadne spremembe bremena na vrhu robota. Po primerjavi in analizi smo prišli do naslednjih rezultatov: zakon vodenja CZNSMR najhitreje odpravi tako dinamične kot statične motnje, čeprav je metoda DZNSMR povsem enakovredna pri odzivih na nenadne spremembe bremena na vrhu robota, zgolj v podrobnosti hitrosti odpravljanja dinamične motnje znanega giba robota pa se je metoda CZNSMR izkazala za malenkost hitrejšo.

Obe poenostavljeni metodi sta imeli slabše rezultate pri zgoraj omenjenih motnjah, predvsem metoda PDZNSMR je bila z ozirom na velikost dinamičnega in statičnega pogreška približno dvakrat slabša od najboljše metode CZNSMR. Čeprav je imela metoda PCZNSMR bistveno počasnejšo fazo učenja, pa je bila na koncu po nekaj ciklih motenj in s tem učenja povsem enakovredna glede statičnih in dinamičnih pogreškov pri predstavljenih motnjah. To je zanimiv praktičen rezultat, saj nam za metodo PCZNSMR ni treba vedeti ničesar o dinamiki robotskega sistema, potrebuje le nekaj deset sekund časa za učenje, ko se motnja pojavi prvič, pozneje pa je povsem enakovredna najboljši metodi CZNSMR. Sama raziskava in preizkusi so bili izvedeni na realnem robotskem mehanizmu, vendar v laboratoriju, ki je, če se izrazimo poetično, v primerjavi z realnim industrijskim okoljem dokaj sterilen (ima bistveno manj motenj). Zato bi bilo zanimivo vsaj tri od štirih obravnavanih metod preizkusiti tudi v industrijskem okolju ter analizirati hitrost učenja ter velikost dinamičnih in statičnih pogreškov.

Vse štiri opisane izpeljane različice zakona vodenja so izvirne s teoretičnega vidika, podamo pa lahko tudi že znano splošno ugotovitev, da lahko struktura, velikost in število nevronskih mrež v zakonu vodenja bistveno vplivajo na kakovost regulacijske adaptivne metode. Seveda je problem poiskati ustrezno strukturo nevronske mreže, za katero se predvideva, da bi lahko bila drugačna od uporabljenih v laboratoriju in bi ustrezala spremenjenim industrijskim pogojem uporabe takšnega regulatorja, kar je tudi izziv za nadaljnji aplikativni razvoj v industrijskih razvojnih centrih robotike.

Ključne besede: nevronska mreža, adaptivno vodenje položaja robota, sliding-mode

*Naslov avtorja za dopisovanje: Fakulteta za elektrotehniko računalništvo in informatiko, Univerza v Mariboru, Smetanova 17, 2000 Maribor, Slovenija, riko.safaric@uni-mb.si

SI 19

Strojniški vestnik - Journal of Mechanical Engineering 58(2012)2, SI 20

Prejeto: 2011-03-17, prejeto: 2011-11-23 © 2012 Stojniški vestnik. Vse pravice pridržane.

Vpliv mešanja na prenos toplote pri hlajenju v olju ISORAPID 277HM

Taraba, B. − Duehring, S. − Španielka, J. − Hajdu, Š.

Bohumil Taraba* − Steven Duehring − Ján Španielka − Štefan Hajdu Slovaška tehnična univerza v Bratislavi, Fakulteta za materiale in tehnologijo, Inštitut za proizvodne sisteme in aplikativno mehaniko, Slovaška Članek obravnava področje toplotne obdelave. Z eksperimentalno meritvijo temperature in statistično obdelavo rezultatov so bile pridobljene ohlajevalne krivulje za Isorapid 277HM, skladno s standardom ISO 9950 (Wolfsonov test). Hladilno olje Isorapid 277HM je bilo mešano z različnimi intenzivnostmi (vnosom dela) pri konstantni temperaturi 50 °C. V drugem delu članka je predstavljen izračun temperature površine v odvisnosti od kombiniranega prenosa toplote. Uporabljena je bila metodologija inverznega prenosa toplote. Za interpretacijo je bila uporabljena programska oprema ANSYS in ORIGIN. Kalilna olja ISORAPID so olja za pospešeno kaljenje z zelo dobro stabilnostjo uparjanja in omogočajo hitro kaljenje. Ta olja so zasnovana posebej za uporabo v zaprtih kalilnih pečeh ter omogočajo hitro in homogeno hlajenje vseh delov pri kaljenju v šaržah in hitro razgradnjo parne blazine v šarži. Eksperimentalni sistem je bil sestavljen iz elektrouporovne peči tipa LM 212.10, cilindričnega preizkušanca, 28 kg olja Isorapid 277HM, prenosne USB-naprave za digitalni zajem podatkov o izmerjenih temperaturah NI USB 9211, frekvenčnega pretvornika MICROMASTER 440 (MM440), osebnega računalnika in pnevmatskega manipulatorja za premikanje preizkušanca. Preizkušanec je bil izdelan iz avstenitnega nerjavnega jekla DIN 1.4841. Termofizikalne materialne lastnosti so bile izmerjene z aparati NETZSCH: LFA 427, DSC 404 C Pegasus in Dilatometer 402 C. Geometrijski in začetni pogoji preizkusa so bili izbrani po kalilnem testu ISO 9950. Preizkušanec je bil pred ohlajevanjem segret na začetno temperaturo 850 °C. Temperatura je bila merjena s standardnim termoparom 304SS tipa K in premera 1,53 mm, nameščenim na sredi preizkušanca. Temperatura je bila izmerjena petkrat na sekundo. Meritve so bile ponovljene po šestkrat za vsako stanje olja. Vsak nabor izmerjenih ohlajevalnih krivulj je bil nato povprečen v ohlajevalno krivuljo jedra. Izmerjeno je bilo sedem stanj olja, eno brez mešanja in šest z mešanjem. Meritve temperature so se začele v trenutku, ko je težišče preizkušanca doseglo gladino olja. Parametri moči (moment in številu vrtljajev) vrtinčnih naprav so bili pridobljeni iz podatkov frekvenčnega pretvornika MM440.

Za interpretacijo numerične simulacije je bil uporabljen inženirsko-znanstveni paket ANSYS. Temperaturna krivulja za izbrane koeficiente prenosa toplote je bila določena z reševanjem simulacijskega modela termičnega nelinearnega in prehodnega primera v paketu ANSYS. Temu je sledila primerjava z izmerjeno temperaturno krivuljo in ponovitev postopka. Pri postopku iskanja najboljšega prilega krivulje je bila upoštevana temperatura in krivulja hitrosti ohlajevanja. Pri reševanju naloge morajo biti izpolnjeni naslednji kriteriji: absolutna vrednost relativne napake izmerjene in izračunane temperature v času i ne sme presegati 1,0%, absolutna vrednost relativne napake hitrosti ohlajevanja za izmerjeno in izračunano temperaturo ne sme presegati 5,0%, koeficient korelacije med izmerjenimi in izračunanimi temperaturami v času hlajenja pa mora biti večji od 0,99. Ovrednotena je absolutna in relativna napaka med izmerjenimi in izračunanimi vrednostmi ohlajevalne krivulje. Največja vrednost je bila 1,09%, povprečna vrednost pa je bila v vseh primerih manjša od 0,45%. Koeficient korelacije med izračunanimi in izmerjenimi temperaturami je bil pri vseh rešenih primerih 0,9998. Prisilno gibanje olja Isorapid 277HM vpliva na proces hlajenja preizkušanca v parni fazi. Parna faza je krajša pri višjih temperaturah površine, koeficient prenosa toplote pa dosega višje vrednosti kot v primeru brez mešanja olja. Vpliv mešanja olja pri prenosu toplote s konvekcijo je največji, ko je temperatura površine nižja od 317 °C. Koeficient prenosa toplote se spreminja s količino energije, ki se dovaja olju. Uporaba koeficienta prenosa toplote pri mešanju olja je primerna tako za numerične eksperimente s paketi SYSWELD in DEFORM kakor tudi za realne eksperimente na področju toplotne obdelave.

Ključne besede: kaljenje, ohlajevalna krivulja, mešanje olja, prenos toplote, Wolfsonov preizkušanec, ANSYS

SI 20

*Naslov avtorja za dopisovanje: Slovaška tehnična univerza, Fakulteta za materiale in tehnologijo, Paulínska 16, 91724 Trnava, Slovaška, bohumil.taraba@stuba.sk

Strojniški vestnik - Journal of Mechanical Engineering 58(2012)2, SI 21

Prejeto: 2011-08-24, sprejeto: 2011-11-18 ©2011 Strojniški vestnik. Vse pravice pridržane.

Analiza rabe električne energije stavbe z izboljšano metodo s temperaturnim presežkom Krese, G. – Prek, M. – Butala, V. Gorazd Krese – Matjaž Prek* – Vincenc Butala

Univerza v Ljubljani, Fakulteta za strojništvo, Slovenija

V primerih, ko je hiter vpogled v delovanje klimatskega sistema pomembnejši od točnosti, se za spremljanje rabe električne energije v odvisnosti od meteoroloških razmer lahko uporablja temperaturni presežek (ang. Cooling Degree Days – CDD). Princip temperaturnega presežka temelji na vsoti pozitivnih temperaturnih razlik med zunanjo temperaturo in neko referenčno ali bazno temperaturo. Ker je bazna temperatura specifična za vsako stavbo, temperaturni presežek ne daje informacije le o podnebju kraja, v katerem se stavba nahaja, ampak tudi o stavbi sami. Težave pri uporabi te metode predstavljajo določitev bazne temperature in izbira postopkov za izračun temperaturnega presežka, ki se razlikujejo glede na podrobnost uporabljenih vremenskih podatkov (t.j. temperature). Glavna pomanjkljivost pristopa s temperaturnim presežkom je ta, da predpostavlja zgolj linearno odvisnost med rabo energije za hlajenje in senzibilnimi hladilnimi obremenitvami, ter s tem zanemarja vpliv latentnih obremenitev, ki so izrazitejše pri višjih zunanjih temperaturah zraka. Namen tega prispevka je predstaviti uporabo izboljšane metode s temperaturnim presežkom, ki upošteva latentne hladilne obremenitve, in primerjavo le-te s splošno veljavnim pristopom na skupni rabi električne energije obstoječe stavbe.

Za vključitev latentnih obremenitev je bil temperaturni presežek pri izboljšani metodi izračunan s temperaturo mokrega termometra zunanjega zraka, namesto z zunanjo temperaturo (temperaturo suhega termometra) kot pri ustaljeni metodi. Oba pristopa sta bila preverjena na realni stavbi, za katero so bili na razpolago 15-minutni odčitki skupne električne moči in urne vrednosti meteoroloških spremenljivk za obdobje od 1. februarja 2009 do 31. januarja 2010 (eno leto). Bazni temperaturi suhega in mokrega termometra sta bili določeni s pomočjo dveh statističnih metod ob predpostavki, da se le-ti ne spreminjata skozi obravnavano časovno obdobje. Skupno je bilo pet poskusov določitve baznih temperatur. Trije so bili s segmentno linearno regresijo iz energijskih karakteristik, dobljenih iz različno filtriranih podatkov, ter dva s polinomsko regresijo drugega reda iz obratovalnih premic: prvič z mesečnimi presežki, izračunanimi iz dnevno povprečenih urnih temperaturnih razlik, in drugič z mesečnimi presežki, izračunanimi iz dnevnih temperaturnih razlik. Na koncu je bila izvedena primerjava med mesečnimi rabami električne energije, napovedanimi z enačbami obratovalnih premic po obeh metodah, in dejanskimi mesečnimi rabami električne energije.

Rezultati analize so spodbudni. Ne samo, da je bila korelacija med rabo električne energije in temperaturnim presežkom mokrega termometra znatno višja (5% višji delež pojasnjene variance) od korelacije med rabo energije in običajnim temperaturnim presežkom (suhega termometra), ugotovljeno je bilo tudi, da je vrednost bazne temperature mokrega termometra bistveno manj odvisna od izbrane metode za njeno določitev (energijska karakteristika, obratovalna premica) in od uporabljenega postopka za izračun temperaturnega presežka (dnevne, urne temperaturne razlike) kot vrednost bazne temperature suhega termometra. Kljub temu pa bi bilo treba za boljše razumevanje pristop s temperaturnim presežkom mokrega termometra preskusiti na več stavbah, kjer bi bili na voljo podatki o dejanski rabi električne energije hladilnega agregata.

Glavna prednost predstavljenega pristopa s temperaturnim presežkom mokrega termometra je v tem, da so senzibilne in latentne hladilne obremenitve v nasprotju s pristopi, predlaganimi v drugih prispevkih, zajete z eno spremenljivko, zato ostaja težavnost na enaki ravni kot pri navadnem pristopu s temperaturnim presežkom, izračunanim z zunanjo temperaturo zraka (temperaturo suhega termometra).

Ključne besede: raba električne energije stavbe, temperaturni presežek, bazna temperatura, latentne obremenitve, temperatura mokrega termometra

*Naslov avtorja za dopisovanje: Univerza v Ljubljani, Fakulteta za strojništvo, Aškerčeva 6, 1000 Ljubljana, Slovenija, matjaz.prek@fs.uni-lj.si

SI 21

Strojniški vestnik - Journal of Mechanical Engineering 58(2012)2, SI 22

Prejeto: 2011-04-18, sprejeto: 2011-11-08 ©2011 Strojniški vestnik. Vse pravice pridržane.

Ocenjevanje poljubnih zveznih funkcij z algoritmom za oceno mešane gostote porazdelitve verjetnosti Volk, M. – Nagode, M. – Fajdiga, M.

Matej Volk* – Marko Nagode – Matija Fajdiga Univerza v Ljubljani, Fakulteta za strojništvo, Ljubljana, Slovenija

Naraščajoče zahteve po učinkovitosti izdelkov v eksploataciji in težnje po nižanju stroškov vodijo raziskovalce v razvoj novih ter izboljševanje obstoječih metod vrednotenja tako, da so že v zgodnjih fazah razvoja čim bolje upoštevani dejanski pogoji uporabe in okolja. To pomeni, da je potrebno poiskati metode, s katerimi je na podlagi kratkih časovnih zgodovin mogoče uspešno napovedovati prihodnja stanja. Kot posledica teh teženj je bil na Fakulteti za strojništvo v Ljubljani razvit algoritem za oceno končnih mešanih gostot porazdelitve verjetnosti, imenovan REBMIX. Zaradi dobrih predhodnih rezultatov, ki so bili doseženi pri ocenjevanju končnih mešanih gostot porazdelitve verjetnosti z algoritmom REBMIX, je nadaljnji razvoj le-tega usmerjen v razširitev na področje ocenjevanja poljubnih zveznih funkcij. Da bi bilo mogoče algoritem, ki je bil prvotno razvit izključno za oceno končnih mešanih funkcij gostote porazdelitve verjetnosti, uporabiti tudi za oceno poljubnih zveznih funkcij, pa je potrebno vhodne podatke ustrezno pripraviti, izhodne ocenjene vrednosti pa ustrezno dodatno obdelati. S tem namenom je v prispevku predstavljen postopek, ki omogoča uporabo algoritma REBMIX tudi za oceno poljubnih zveznih funkcij.

Pričakovati je, da bo z uporabo predlaganega postopka mogoče dobro napovedati število osnovnih funkcij, kot tudi parametre posameznih funkcij v mešanici poljubnih zveznih funkcij na podlagi omejenega števila vhodnih podatkov. Z uspešno implementacijo predlaganega postopka se odpirajo nove možnosti uporabe obstoječega algoritma tudi na področjih, kjer se v sedanjem času najpogosteje uporabljajo umetne nevronske mreže (npr.: interpolacija funkcij, klasifikacija, prepoznava govora, 3D-modeliranje objektov, ocena gibanja…).

Za ovrednotenje predlaganega postopka so v prispevku uporabljene različne izmerjene in simulirane množice podatkov, tako z eno neodvisno spremenljivko kot tudi z več neodvisnimi spremenljivkami. Glede na to, da se za oceno poljubnih mešanih funkcij običajno uporabljajo nevronske mreže z radialnimi baznimi funkcijami, so bile le-te uporabljene tudi v obravnavanih primerih za primerjavo ocenjenih izhodnih vrednosti ter ugotavljanje primernosti predlaganega postopka za tovrstne probleme. Za analizo odstopanja izhodnih vrednosti napovedanih s predlaganim postopkom oz. nevronsko mrežo z radialnimi baznimi funkcijami od testnih izhodnih vrednosti je bila izbrana funkcija napake, imenovana koren vsote srednje vrednosti napake (RMSE).

Rezultati raziskave kažejo, da je mogoče obstoječi algoritem za oceno končnih mešanih gostot porazdelitve verjetnosti z uporabo predlaganega postopka uspešno uporabiti tudi za oceno poljubnih zveznih funkcij, tako z eno kot tudi z več neodvisnimi spremenljivkami. Uspešna implementacija algoritma REBMIX na področju ocenjevanja poljubnih zveznih funkcij nakazuje smernice za njegov nadaljnji razvoj, ki se bo odvijal v smeri uporabe algoritma v kombinaciji z nevronskimi mrežami z radialnimi baznimi funkcijami, s čimer bi se njegova uporabnost razširila tudi na ostala področja, kjer se pretežno uporabljajo umetne nevronske mreže. Vsem zainteresiranim bralcem je program REBMIX na voljo na naslovu http://CRAN.R-project.org/package=rebmix.

Ključne besede: algoritem REBMIX, ocena mešanih funkcij, mešana gostota porazdelitve verjetnosti, nevronska mreža z RBF, ocena parametrov

SI 22

*Naslov avtorja za dopisovanje: Univerza v Ljubljani, Fakulteta za strojništvo, Aškerčeva 6, 1000 Ljubljana, Slovenija, matej.volk@fs.uni-lj.si

Strojniški vestnik - Journal of Mechanical Engineering 58(2012)2, SI 23

Prejeto: 2010-11-29, sprejeto: 2011-11-18 © 2012 Stojniški vestnik. Vse pravice pridržane.

Opis in modeliranje dodajalne izdelovalne tehnologije za meritve aerodinamičnih koeficientov Daneshmand, S. ‒ Aghanajafi, C. Saeed Daneshmand1 ‒ Cyrus Aghanajafi2

1 Fakulteta

za strojništvo, letalsko in vesoljsko tehnologijo, znanstveno-raziskovalni oddelek, Islamska univerza Azad, Iran 2 Tehnična univerza K.N.Toosi, Iran

Danes se za izdelavo modelov za preizkušanje v vetrovnikih uporabljajo tako obdelovalne tehnologije z odvzemanjem materiala kot dodajalne izdelovalne tehnologije. Namen tega dela je izboljšanje mehanskih lastnosti in površinske hrapavosti modelov za merjenje aerodinamičnih koeficientov v vetrovniku, izdelanih z dodajalnimi tehnologijami.

Predstavljena raziskava je bila posvečena naprednim izdelovalnim postopkom z novimi materiali, namenjenih izdelavi zahtevnih konstrukcij in aerodinamičnih profilov za preizkušanje v vetrovnikih. Rezultati so primerjani s tradicionalnimi izdelovalnimi postopki. Rezultati študije so uporabni za pomembne industrijske aplikacije pri izdelavi modelov za preizkuse v vetrovnikih, obravnavamo pa jih lahko kot inovacijo tradicionalnih metod. Verjetni uporabnik predlaganih postopkov je letalska in vesoljska industrija.

Pripravljeni in izdelani so bili trije modeli za preizkušanje in določanje aerodinamičnih koeficientov v vetrovniku. Prvi, jekleni model je bil izdelan iz treh delov: kljuna, trupa in repa. Drugi model je bil sestavljen iz valjastega jeklenega dela, na katerega sta bila pritrjena kljun in rep, izdelana po postopku FDM. Tudi pri tretjem modelu sta bila kljun in rep izdelana po postopku FDM, hrapavost površine pa je bila izboljšana s kromiranjem.

Cilindrični del zagotavlja zadostno trdnost in togost plastičnega modela, omogoča pa tudi gradnjo modelov v večjem merilu.

Preizkusi so bili opravljeni pri vrednostih Machovega števila od 0,1 do 0,3. Za vsako od teh Machovih števil so prikazani koeficienti normalne sile, aksialne sile, momenta okoli aerodinamičnega centra ter razmerje med vzgonom in uporom.

Iz rezultatov raziskave je mogoče zaključiti, da so tradicionalni postopki obdelave z odvzemanjem materiala za izdelavo zahtevnih sekcij in aerodinamičnih profilov dragi in zamudni. Ker preizkusi v vetrovnikih včasih zahtevajo tud več modelov, je stroške in čas izdelave mogoče zmanjšati z uvedbo dodajalnih izdelovalnih postopkov. Kar se tiče potrebne natančnosti in aerodinamičnih preizkusov, je smiselna uporaba modelov, izdelanih z dodajalnimi tehnologijami, tudi kromiranih. Razlike med aerodinamičnimi koeficienti kovinskih modelov in modelov, izdelanih z dodajalnimi tehnologijami, so v splošnem posledica površinske hrapavosti in dimenzijskih toleranc.

Ker je danes za izvedbo aerodinamičnih eksperimentov v vetrovniku potrebnih več modelov, so dodajalne izdelovalne tehnologije med najprimernejšimi postopki za izdelavo modelov in aerodinamičnih profilov. Uporaba modelov, izdelanih z dodajalnimi tehnologijami, omogoča hitro določanje aerodinamičnih značilnosti zasnov za velik razpon Machovih števil.

Ključne besede: dodajalna izdelava, vetrovnik, vpadni koti, aerodinamični koeficient, površinska hrapavost

*Naslov avtorja za dopisovanje: Fakulteta za strojništvo, letalsko in vesoljsko tehnologijo, Islamska univerza Azad, Tehran, Iran, Saeed_daneshmand@yahoo.com

SI 23

Strojniški vestnik - Journal of Mechanical Engineering 58(2012)2, SI 24

Prejeto: 2011-08-31, sprejeto: 2011-12-28 © 2012 Stojniški vestnik. Vse pravice pridržane.

Razvoj pečice nove generacije s pomočjo CFD-simulacije Rek, Z. − Rudolf, M. − Zun, I.

Zlatko Rek1,* − Mitja Rudolf 2 − Iztok Zun1 1 Univerza

v Ljubljani, Fakulteta za strojništvo, Laboratorij za dinamiko fluidov in termodinamiko LFDT, Slovenija 2 Razvoj kuhalnih aparatov, Gorenje d.d., Slovenija

V prispevku je prikazana uporaba računalniške dinamike tekočin (CFD) pri razvoju pečice nove generacije.

Različne zahteve narekujejo čedalje hitrejši razvoj novih izdelkov, kar velja tudi za pečice. Prenos toplote v pečici poteka s prevodom, konvekcijo in sevanjem. Pri razvoju nove pečice smo skušali zagotoviti optimalne razmere za vse tri načine ogrevanja. CFD-simulacije skupaj z eksperimentom omogočajo znatno skrajšanje časa od idejnega osnutka preko prototipa do končnega izdelka. Numerična simulacija je potekala v več korakih. Rešitev transportnih enačb je omogočala analizo tlačnega, hitrostnega in temperaturnega polja. Sledila je validacija modela, kjer smo preverili ujemanje rezultatov izračuna z meritvami na prototipu. Po validaciji smo iskali optimalno porazdelitev temperature v prostoru pečice s spremembo geometrije (oblika grelcev, oblika pokrova ventilatorja) in robnih pogojev (temperatura grelcev, pretok na ventilatorskem sistemu).

Temperaturno porazdelitev in gibanje zraka v pečici določajo ohranitveni zakoni. Reševali smo sistem parcialnih diferencialnih enačb za ohranitev mase, gibalne količine, energije in intenzitete sevanja. Narejenih je bilo več geometrijskih modelov pečice, ki so bili diskretizirani z mrežo kontrolnih volumnov. Da bi se z numerično simulacijo kar se da približali realnim razmeram, smo robne pogoje za temperaturo na zunanjih stenah pečice in za hitrost na režah pokrova ventilatorja določili z meritvami na prototipu. Ventilatorja zaradi kompleksnosti nismo modelirali. Nadomestili smo ga s predpisanim padcem tlaka, ki je sorazmeren dinamičnemu tlaku tekočine. Za reševanje enačb smo uporabili CFD-paket ANSYS Fluent. Optimalne pogoje peke smo skušali doseči s spremembo oblike prostora pečice in spreminjanjem robnih pogojev. Tako smo pri geometriji spremenili naklon zadnje stene in povečali širino vstopnih rež. Vstopne reže na pokrovu ventilatorja smo razdelili na šestnajst segmentov. Z zaprtjem oz. odprtjem določenih segmentov pa smo spreminjali robne pogoje (11 različnih kombinacij).

Validacija numeričnega modela je bila narejena za konvencionalni sistem ogrevanja. Vrednosti maksimalnih temperatur so se v srednjem delu pečice zelo dobro ujemale z izmerjenimi. Nekoliko večje odstopanje temperatur je bilo v sprednjem in zadnjem delu, kar je najbrž posledica nenatančnega predpisa robnega pogoja za steklena vrata. Sprememba oblike geometrije zelo vpliva na hitrostno polje. Pri izhodiščni geometriji je vstopna hitrost velika. Ravna stena usmeri vroč zrak pravokotno na stranice, zato se pojavi recirkulacija vročega zraka v vogalih, zaradi bližine ventilatorja pa tudi hitro odsesavanje iz prostora. V sprednjem delu nastane hladnejše območje počasnega zraka. Takšne razmere pomenijo slabše pogoje pečenja. S spremembo naklona zadnje stene in povečanjem širine vstopne reže se hitrost na vstopu zmanjša, po zaslugi usmerjanja pa je zagotovljeno gibanje vročega zraka po celotnem prostoru. Pri izhodiščnem stanju, kjer so vsi segmenti rež odprti, se pojavi vrtinec v zgornjem delu. Tok toplega zraka se zato usmeri navzdol na sredino pekača, od koder ga ventilator posesa iz prostora. Temperaturno polje v okolici peciva je neenakomerno, kar pomeni slabše pečenje na sprednjem delu.

Temperatura zraka je v precejšnjem delu prostora višja od želene. Pri izboljšani različici vrtinca ni. Temperatura zraka je zato ob pecivu konstantna, kar pomeni enakomerno pečenje po vsej površini. Tudi temperatura zraka v celotnem prostoru je le za nekaj stopinj višja od želene.

Obvladovanje hitrostnega polja krožečega vročega zraka v pečici se je izkazalo kot odločilni dejavnik vpliva na kakovost pečenja. Napovedi numeričnih simulacij potrjujejo pozitivni rezultati izvedene validacije oz. funkcionalnega preizkušanja ustrezno izdelanih prototipov pečice Simplicity v Elektrotermičnem laboratoriju KA. Najpomembnejše je dejstvo, da so dobri vmesni rezultati računalniških simulacij razvojno-raziskovalni skupini Gorenja že v zgodnji fazi preizkušanj omogočili hitrejšo in natančnejšo optimizacijo temperaturnega polja v pečici.

Ključne besede: pečica, tok tekočine, prenos toplote, prevod, konvekcija, sevanje, CFD-simulacija

SI 24

*Naslov avtorja za dopisovanje: Univerza v Ljubljani, Fakulteta za strojništvo, Aškerčeva 6, 1000 Ljubljana Slovenija, zlatko.rek@fs.uni-lj.si

Strojniški vestnik - Journal of Mechanical Engineering 58(2012)2, SI 25-26 Osebne objave

Magistrska in diplomska dela MAGISTER ZNANOSTI Na Fakulteti za strojništvo Univerze v Ljubljani je z uspehom zagovarjal svoje magistrsko delo, za pridobitev naziva magister znanosti: dne 4. januarja 2012 Erik POTOČAR z naslovom: »Vpliv plazme na zračni tok ob profilirani lopatici« (mentor: prof. dr. Branko Širok). * DIPLOMIRALI SO Na Fakulteti za strojništvo Univerze v Ljubljani so pridobili naziv univerzitetni diplomirani inženir strojništva: dne 25. januarja 2012: Janez BUDIČ z naslovom: »Razvoj obračala paketov z vertikalnim odmikom« (mentor: prof. dr.

Marko Nagode); Nejc PODMENIK z naslovom: »Primerjava različnih metod reševanja ravninskih nosilcev po teoriji III. reda« (mentor: prof. dr. Franc Kosel, somentor: doc. dr. Tomaž Videnič); Jure SEVER z naslovom: »Postavitev tehnologije izdelave orodja in kontrola geometrijske natančnosti ulitka« (mentor: doc. dr. Franci Pušavec, somentor: prof. dr. Janez Kopač); Blaž ŽABKAR z naslovom: »Zasnova, izdelava in testiranje 3-osnega CNC frezalnega stroja« (mentor: prof. dr. Janez Kopač); dne 27. januarja 2012: Tadej BORŠTNAR z naslovom: »Uporaba Greenovih funkcij za analizo nestacionarnega temperaturnega polja preprostih geometrijskih teles« (mentor: prof. dr. Iztok Golobič); Primož HOSTNIK z naslovom: »Razžveplanje dimnih plinov« (mentor: izr. prof. dr. Andrej Senegačnik); Aljoša MOHORČIČ z naslovom: »Sanacija poškodb na orodjih za delo v hladnem z varjenjem« (mentor: prof. dr. Janez Tušek); Jan ZADRAVEC z naslovom: »Vrednotenje nizkoeksergijskih tehnologij za energetsko neodvisne poslovne stavbe« (mentor: prof. dr. Sašo Medved, somentor: doc. dr. Ciril Arkar); Jordi Garcia BAYO z naslovom: »Termodinamična analiza sočasne proizvodnje električne energije in toplote s kombiniranim plinskoparnim postrojenjem« (Thermodynamic analysis of combined heat and power production based on

combined-cycle-gas-turbine power plant) (mentor: izr. prof. dr. Mihael Sekavčnik). * Na Fakulteti za strojništvo Univerze v Mariboru so pridobili naziv univerzitetni diplomirani inženir strojništva: dne 26. januarja 2012: Mihael Jan MLAKAR z naslovom: »Sprememba konstrukcijskih detajlov pregradne stene bivalnega kontejnerja ob upoštevanju vgradnih zahtev v podjetju Arcont d.d.« (mentor: izr. prof. dr. Bojan Dolšak, somentor: viš. pred. dr. Marina Novak); Dejan PLOJ z naslovom: »Vpliv geometrije kanalov na izboljšanje prenosa toplote« (mentor: red. prof. dr. Leopold Škerget, somentor: doc. dr. Jure Ravnik); Vojko VIDOVIČ z naslovom: »Določitev dopustnega Hertzovega kontaktnega tlaka na tečini ležaja v odvisnosti od dimenzij kotalnega elementa in toplotne obdelave« (mentor: red. prof. dr. Srečko Glodež, somentor: doc. dr. Tomaž Vuherer). * Na Fakulteti za strojništvo Univerze v Ljubljani so pridobili naziv diplomirani inženir strojništva: dne 11. januarja 2012: David DEBELJAK z naslovom: »Merilna naprava za preizkus tesnosti« (mentor: izr. prof. dr.

Ivan Bajsić); David GRM z naslovom: »Razvoj namenskega mlina za potrebe v živinoreji« (mentor: prof. dr. Jožef Duhovnik, somentor: izr. prof. dr. Rajko Bernik); Aleksander JANKOVIĆ z naslovom: »Konstrukcija sistema za kalibriranje oljk« (mentor: prof. dr. Jožef Duhovnik, somentor: izr. prof. dr. Rajko Bernik); Boštjan MRAK z naslovom: »Analiza toka vrednosti v oddleku stiskalnic« (mentor: prof. dr.

Marko Starbek, somentor: izr. prof. dr. Janez Kušar); dne 13. januarja 2012: Aljaž BRUMEN z naslovom: »Primerjava potniških letal Boeing B737-400 in Airbus A320 pri treh različnih vzletnih pogojih« (mentor: pred. Miha Šorn, somentor: izr. prof. dr. Tadej Kosel); Marko GORJUP z naslovom: »Struženje pastorkov z odkovanim posnetjem« (mentor: doc. dr.

Davorin Kramar, somentor: prof. dr. Janez Kopač); SI 25

Strojniški vestnik - Journal of Mechanical Engineering 58(2012)2, SI 25-26

Roland STEPAN z naslovom: »Diagnosticiranje stanja vozil« (mentor: prof. dr. Jožef Vižintin); Jurij VENE z naslovom: »Določitev primernega terena za preizkušanje brezpilotnih letal« (mentor: izr. prof. dr. Tadej Kosel); Marko ŽIGON z naslovom: »Optimizacija izdelave vzorčnih brizganih izdelkov« (mentor: izr. prof. dr. Zlatko Kampuš). * Na Fakulteti za strojništvo Univerze v Mariboru so pridobili naziv diplomirani inženir strojništva: dne 26. januarja 2012: David BEZJAK z naslovom: »Metode preprečevanja odpovedi pri vzdrževanju« (mentor: izr. prof. dr. Igor Drstvenšek); Gregor DEŽELAK z naslovom: »Načrtovanje procesa izdelave zvarjencev v podjetju Monting SK«

SI 26

(mentor: izr. prof. dr. Borut Buchmeister, somentor: doc. dr. Marjan Leber); Damijan KOLARIČ z naslovom: »Razvoj avtomatskega nanašalca emulzije za uporabo v tiskarstvu« (mentor: prof. dr. Jože Balič, somentor: asist. Simon Klančnik); Aleksander PLASKAN z naslovom: »Energetski pregled podjetja Schiedel d.o.o. Prebold« (mentor: doc. dr. Matjaž Ramšak, somentor: prof. dr. Leopold Škerget); David STOJKO z naslovom: »Ogrevanje in hlajenje poslovnih prostorov s toplotno črpalko zrakzrak« (mentor: izr. prof. dr. Jure Marn, somentor: prof. dr. Leopold Škerget); Sebastijan ŠTURM z naslovom: »Preureditev sistema tesnjenja in mazanja ležajev valjarniškega ogrodja« (mentor: doc. dr. Samo Ulaga, somentor: doc. dr. Darko Lovrec).

Strojniški vestnik - Journal of Mechanical Engineering 58(2012)2, SI 27-29 List of reviewers

List of reviewers who reviewed manuscripts in 2011 Abusoglu Aysegul, Turkey An Q.L., PR China Angseryd J., Sweden Arman Yusuf, Turkey Arshadnejad Shobeir, Iran Ataoglu Senol, Turkey Backström Theo W. von, South Africa Bajcar Tom, Slovenia Bajsić Ivan, Slovenia Bakhtiari Bahador, Canada Baldwin Jon M., USA Balestrassi P. P., Brazil Balič Jože, Slovenia Banszak Zbigniew, Poland Barbieri Renato, Brazil Barišić Branimir, Croatia Barman Swapan, India Basheer Uday M., Malaysia Basile Angelo, Italy Batista Milan, Slovenia Bauer Robert, Canada Bazaras Žilvinas, Lithuania Becker Richard, USA Belodedenko S. V., Ukraine Bergant Anton, Slovenia Bernik Rajko, Slovenia Bibb Richard, UK Bibić Dževad, BiH Biermann Kirk, Germany Birolini Alessandro, Switzerland Biswas Sandhyarani, India Bizjak Grega, Slovenia Blicher Schmidt Henrik Nikolaj, Denmark Boltežar Miha, Slovenia Borkowski Przemyslaw, Poland Brach Raymond M., USA Brekken Ted K. A., USA Brezočnik Miran, Slovenia Broek Johan, The Netherlands Bronold Franz Xaver, Germany Buchmeister Borut, Slovenia Bück Andreas, Germany

Butala Peter, Slovenia Cadogan David, USA Cao Yuan, PR China Car Zlatan, Croatia Casella Francesco, Italy Ceretti Elisabetta, Italy Chaari Fakher, Tunisia Chandrashekhara K., USA Chang Chia-Lung, Taiwan Chang Chia-Lung, Taiwan Charpentier Arnaud, USA Chien Mininghui, USA Chowdhury Sazzad Hossien, Malaysia Christoforou Eftychios G., Cyprus Chung Eun-Sung, South Korea Çomaklı Kemal, Turkey Croccolo Dario, Italy Cui Changcai, China Čep Robert, Czech Republic Čepon Gregor, Slovenia Četina Matjaž, Slovenia Čudina Mirko, Slovenia Čus Franci, Slovenia da Silva A.A.M., Spain da Silva Flavio J., Brazil Davim J. Paulo, Portugal Davis Lloyd, Australia Daxin E., PR China Dekkers Rob, United Kingdom Diaci Janez, Slovenia Dietrich Franz, Germany Dinkler Dieter, Germany Dorsch Volker, Germany Duhovnik Jožef, Slovenia Dular Matevž, Slovenia Dumas Claire, France Edl Milan, Czech Republic Ehmann Kornel F., USA El Mansori Mohamed, France Elfes Alberto, USA Emri Igor, Slovenia Essert Mario, Croatia

Evangelopoulos Nicholas, USA Fajdiga Matija, Slovenia Fang Ning, USA Farson Dave F., USA Fefer Dušan, Slovenia Ferrari Angela, Italy Ferre Manuel, Spain Ficko Mirko, Slovenia Filipič Bogdan, Slovenia Flašker Jože, Slovenia Franco Patricio, Spain Fung Rong-Fong, PR China Fuschi Paolo, Italy Gajate Agustin, Spain Gajić Zoran, USA Gallardo-Alvarado Jaime, Mexico Gao Liang, PR China García Andrés Gabriel, Argentina Gatti Gianluca, Italy Gaul Lothar, Germany Gent Michael, USA Gernaey Krist V., Denmark Ghoreishy Mir Hamid Reza, Iran Goettlich Emil, Austria Gomri Rabah, Algeria Gorjan Martin, Slovenia Gotlih Karl, Slovenia Greiner David, Spain Grigg Nigel, New Zealand Gröbl Thomas, Austria Grum Janez, Slovenia Grzes Piotr, Poland Guagliano Mario, Italy Guermah Said, Algeria Gupta Narinder Kumar, India Guzović Zvonimir, Croatia Hace Aleš, Slovenia Hackenschmidt Reinhard, Germany Hanselaer Peter, Belgium Hardell Jens, Sweden Harl Boštjan, Slovenia He Qing, PR China Helbig Ulf, Germany SI 27

Strojniški vestnik - Journal of Mechanical Engineering 58(2012)2, SI 27-29

Herakovič Niko, Slovenia Hladowski Lukasz, Poland Hlebanja Gorazd, Slovenia Hočevar Marko, Slovenia Hohe Jörg, Germany Hribernik Aleš, Slovenia Hriberšek Matjaž, Slovenia Hu Zhong, USA Isermann Rolf, Germany Ishak Anuar, Malaysia Jamwal P.K., New Zealand Jecl Renata, Slovenia Jenko Marjan, Slovenia Ji Chunqian, UK Jin Xiao Ling, PR China Johnson Eric, USA Johnston Peter R., Australia Juričić Đani, Slovenia Kamnik Roman, Slovenia Kampuš Zlatko, Slovenia Kaplunov Julius, UK Karadžić Uroš, Montenegro Katrašnik Tomaž, Slovenia Kegl Breda, Slovenia Kerkkanen Kimmo S., Finland Kesy Zbigniew, Poland Khader Iyas, Germany Khaider Bouacha, Algeria Khan M. Bilal, Pakistan Kim Sung-Min, South Korea Kim Jeong-Ho, USA Kirstein Nielsen Kaspar, Denmark Kjellander J. A. P., Sweden Klare Stefan, Germany Klemenc Jernej, Slovenia Klobčar Damjan, Slovenia Knott Andy, UK Koh Min-Sung, USA Kokalj Filip, Slovenia Komkin A. I., Russia Kopač Janez, Slovenia Korshunov Aleksander, Russia Kosel Franc, Slovenia Krainer Aleš, Slovenia Krajnik Peter, Slovenia Kramar Davorin, Slovenia Kramberger Janez, Slovenia SI 28

Krašna Simon, Slovenia Krishnaiah J., India Kruch Serge, France Kryllowicz Wladislaw, Poland Kumar Vinod, India Kurdi Ojo, Malaysia Kušar Janez, Slovenia Kuzma Karl, Slovenia Kuzmanović Siniša, Serbia Lankarani Hamid M., USA Lei Yaguo, PR China Lenart Lado, Slovenia Lewis Andrew, UK Li Shuting, Japan Li Hong, PR China Li Hui, PR China Li Liang, PR China Li Qing-Kui, China Liang Cai-Hua, PR China Liang Shin-Jye, China Lin Yan-Cherng, PR China Lin Y.C., PR China Liu Jianxiong, PR China Liu Zhongliang, PR China Liu Huibin, USA Liu Yu-Wen, Taiwan Liu R. L., PR China Liu Ruiliang, PR China Liu Kuo-Chi, Taiwan Liu Kuo-Chi, China Lovrec Darko, Slovenia Lübben Thomas, Germany Machado Alisson R., Brazil Malinowski Pawel, Poland Marcos Bernard, Canada Marinov Marin, UK Marissen Roel, The Netherlands Marklund Pär, Sweden Mavromatidis Lazaros Elias, France Maytal B.-Z., Israel Meagher Jim, USA Medved Sašo, Slovenia Mehta C.R., India Mendes Maia Nuno Manuel, Portugal Menezo Christophe, France Mežnar Dušan, Slovenia

Mirzaei Majid, Iran Modic Jurij, Slovenia Mohamed M.A.S., Egypt Mohan C. B., India Mole Nikolaj, Slovenia Morozyuk Tetyana, Germany Moser Thomas, Austria Mou Jun Min, PR China Možina Janez, Slovenia Mrvar Primož, Slovenia Muzhou Hou, PR China Nagendra Somanath, USA Nagode Marko, Slovenia Nikiforov V. N., Russia Nirmal Umar, Malaysia Nobile Enrico, Italy Nurul Amin A.K.M., Malaysia Nykänen Arne, Sweden Orbanić Henri, Slovenia Orrù Pier Francesco, Italy Ozcan Alpay, USA Palčič Iztok, Slovenia Peer Angelika, Germany Pepelnjak Tomaž, Slovenia Pevec Miha, Slovenia Piekarska W., Poland Plančak Miroslav, Serbia Polonio Vanessa Lucena, Spain Poredoš Alojz, Slovenia Potočnik Primož, Slovenia Prebil Ivan, Slovenia Precup Radu-Emil, Romania Predan Jože, Slovenia Predin Andrej, Slovenia Prek Matjaž, Slovenia Prezelj Jurij, Slovenia Pritchard Ewan, USA Provis John L., Australia Pušavec Franci, Slovenia Qiao Aike, PR China Rajar Rudolf, Slovenia Rajendran Chandrasekharan, India Ramirez Arredondo Juan M., Mexico Ramji B. R., India Ramšak Matjaž, Slovenia Randall Robert, Australia

Strojniški vestnik - Journal of Mechanical Engineering 58(2012)2, SI 27-29

Ravnik Jure, Slovenia Ravnik Jure, Slovenia Regert Tamas, Belgium Ren Zoran, Slovenia Ribeiro Marafona José Duarte, Portugal Richardson Shane, Australia Rizzetta Donald P., USA Rosa Alessandro Dalla, Denmark Rosell Joan R., Spain Rosso Mario, Italy Rowe Andrew, Canada Saaty Thomas L., USA Sadilek Marek, Czech Republic Samardžić Ivan, Croatia San Osman, Turkey Sauer Bernd, Germany Schmidt Dietrich, Germany Schreier-Alt Thomas, Germany Schuoecker Dieter, Austria Schweiker Marcel, Germany Seguy Sébastien, France Selvam Panner, USA Sheng Gang, USA Simani Silvio, Italy Sinha Sumon.K., USA Sito Stjepan, Croatia Slavič Janko, Slovenia Sluga Alojzij, Slovenia Sonthipermpoon Kawin, Thailand Starbek Marko, Slovenia Stegić Milenko, Croatia Stehlik Milan, Austria Steiger Erwin, Germany Strelnikova Elena, Ukraine Strelnikova Elena, Ukraine Stroud Ian A., Switzerland Suau-Sanchez Pere, Spain Sun Tairen, PR China

Sun Wanquan, China Sundararajan G., India Sznitman Joss, USA Širok Brane, Slovenia Škerget Leopold, Slovenia Štok Boris, Slovenia Šturm Roman, Slovenia T’Joen Chrisophe, Belgium Tamin Mohd Nasir, Malaysia Tanaka Ryutaro, Japan Tančev Ljubomir, Macedonia Tang Dewen, PR China Tarabini Marco, Italy Tavčar Jože, Slovenia Teixeira Pedro, Portugal Teodorović Dušan, Serbia Terva Juuso, Finland Thalmann Ruedi, Switzerland Theodossiades Stephanos, UK Thiriet Jean-Marc, France Tijsseling Arris S., The Netherlands Tiselj Iztok, Slovenia Toibero Marcos, Argentina Tomanik Eduardo, Brazil Totten George E., USA Tounsi Abdelouahed, Algeria Trenc Ferdinand, Slovenia Tsourveloudis Nikos C., Greece Tsuyoshi Kawanami, Japan Tuma Jiri, Czech Republic Turk Goran, Slovenia Tušek Janez, Slovenia Udiljak Toma, Croatia Ulbin Miran, Slovenia Ulewicz Robert, Poland Valentinčič Joško, Slovenia Van Gestel Nick, Belgium van Hoof Joost, The Netherlands

Vasile-Muller Carmen, France Velagić Jasmin, BiH Velázquez-Sánchez A. T., Mexico Vižintin Jožef, Slovenia Vuherer Tomaž, Slovenia Wasfy Tamer M., USA Wazwaz Abdul-Majid, USA Weckenmann Albert, Germany Wedde Horst F., Germany Willfort Reinhard, Austria Williamson Nicholas, Australia Wu Zhixue, PR China Xiang Kangtai, PR China Xu Chuang Wen, PR China Yan Shaoze, China Yao Hongliang, PR China Yu Bing-feng, PR China Yu Bingfeng, PR China Yue Z. Q., PR China Yung-chin Hsiao, Japan Zadravec Matej, Slovenia Zajc Andrej, Slovenia Zalaznik Aleš, Slovenia Zalaznik Aleš, Slovenia Zhai Haibo, USA Zhang Chun-Lu, PR China Zhang Julie Z., USA Zhang Qin-he, PR China Zhang Q. L., China Zhao Fu, USA Zimmerman William B., UK Zou Tiefang, PR China Zupan Samo, Slovenia Žavbi Roman, Slovenia Žerovnik Janez, Slovenia Žlajpah Leon, Slovenia Župerl Uroš, Slovenia

The Editorial would like to thank all the reviewers in participating in reviewing process.

We appreciate the time and effort and greatly value the assistance as a manuscript reviewer for Strojniški vestnik – Journal of Mechanical Engineering.

SI 29

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Franc Kosel, UL, Faculty of Mech. Engineering, Slovenia interdisciplinary Editorial Officeor multidisciplinary dialogue.

Thomas Lübben, University of Bremen, Germany The international conferences special issue of SV-JME with invited co-editor(s).

University of Ljubljana (UL)selected papers are welcome for publishing as a Janez Možina, UL, Faculty of Mech. Engineering, Slovenia Faculty of Mechanical Engineering Miroslav Plančak, University of Novi Sad, Serbia International Editorial Institute Board of Technology, Pasadena, USA Editor SV-JMEin Chief Brian Prasad, California Koshi School of Engineering,Tohoku Vincenc Butala Aškerčeva 6, SI-1000 Ljubljana, Slovenia BerndAdachi, Sauer, Graduate University of Kaiserlautern, GermanyUniversity, Japan Bikramjit Basu, Indian Institute of Technology, Kanpur, India University of Ljubljana Brane Širok, UL, Faculty of Mech.

Engineering, Slovenia Phone: 386-(0)1-4771 137 Anton Bergant, Litostroj Power, Slovenia Faculty of Mechanical Engineering, Slovenia Leopold Škerget, UM, Faculty of Mech. Engineering, Slovenia Fax: 386-(0)1-2518 567 Franci UM, Faculty Mech.

Engineering, GeorgeČuš, E. Totten, PortlandofState University, USASlovenia E-mail: info@sv-jme.eu Narendra B. Dahotre, University of Tennessee, USA Co-Editor Nikos C. Tsourveloudis, Technical University ofKnoxville, Crete, Greece http://www.sv-jme.eu Matija Fajdiga,University UL, Faculty Mech.Croatia Engineering, Slovenia Borut Buchmeister Toma Udiljak, of of Zagreb, Imre Felde, Bay Zoltan Inst. for Mater.Bethlehem, Sci. and Techn., University of Maribor Arkady Voloshin, Lehigh University, USA Hungary Founders and Publishers Jože Flašker, UM, Faculty of Mech.

Engineering, Slovenia Faculty of Mechanical Slovenia University of LjubljanaEngineering, (UL) Bernard Franković, Faculty of Engineering Rijeka, Croatia President of Publishing Council Faculty of Mechanical Engineering, Slovenia Janez Grum, UL, Faculty of Mech. Engineering, Slovenia Jože Duhovnik Technical Editor Imre Horvath, University of Technology, Netherlands UL, Faculty ofDelft Mechanical Engineering, Slovenia Pika Škrabaof Maribor (UM) University Julius Kaplunov, Brunel University, West London, UK University of LjubljanaEngineering, Slovenia Faculty of Mechanical Milan Print Kljajin, J.J. Strossmayer University of Osijek, Croatia Faculty of authors Mechanical Slovenia on the cover of Strojniški The of Engineering, the image published vestnik -Faculty Journal Mechanical Engineering, Janez Kopač, UL,d.o.o., of of Mech.

Engineering, Slovenia Tiskarna Present Ljubljana, Slovenia, printed in 480 copies Franc Kosel, UL, Faculty of Mech. Engineering, Slovenia Association of 1, Mechanical Engineers of Slovenia Vol. 58, No. requested the publishing of the following additional information.

Editorial Office Thomas University of Bremen, Germany GeneralLübben, information University Ljubljana (UL) Janez Možina, UL,– Faculty Engineering, Slovenia Chamber ofofCommerce and Industry of Slovenia Strojniški vestnik Journal of of Mech.

Mechanical Engineering is Cover, innerside, information on cover image Faculty of Mechanical Engineering Miroslav University Noviand Sad, Serbiais a double issue).

Metal Processing Industry Association publishedPlančak, in 11 issues per yearof(July August SV-JME Brian Prasad,prices California Institute ofonline Technology, USA Institutional include print & access:Pasadena, institutional Aškerčeva 6, SI-1000 Ljubljana, Slovenia Bernd Sauer,price University of Kaiserlautern, subscription and foreign subscriptionGermany €100,00 (the price of a Cover: Brane Faculty of Mech.

Engineering, Slovenia Phone: 386-(0)1-4771 137 single Širok, issue isUL, €10,00); general public subscription and student Above: Shematics of the first magnetic Leopold Škerget, UM, ofaMech.

Slovenia Fax: 386-(0)1-2518 567 subscription €50,00 (theFaculty price of singleEngineering, issue is €5,00).

Prices refrigerator prototype developed at the George E. Totten, Portland State University, USA E-mail: info@sv-jme.eu are exclusive of tax. Delivery is included in the price. The University of Ljubljana, Faculty of Nikos C. is Tsourveloudis, Technical University of Crete, Greece http://www.sv-jme.eu recipient responsible for paying any import duties or taxes.

Mechanical Engineering, Slovenia Toma University of Zagreb, Croatia by our distributor.

Legal Udiljak, title passes to the customer on dispatch Below: Numerical simulation results of the Arkady Voloshin, Founders and Publishers magnetic field in the NdFeB magnet assembly Single issues fromLehigh currentUniversity, and recent Bethlehem, volumes areUSA available at the University of Ljubljana (UL) current single-issue price. To order the journal, please complete President Publishing Council the form onofour website. For submissions, subscriptions and all Faculty of Mechanical Engineering, Slovenia Jože Duhovnik other information please visit: http://en.sv-jme.eu/.

UL, Faculty of Mechanical Engineering, Slovenia University of Maribor (UM) Image courtesy: Laboratory of Refrigeration and District Energy, University of Ljubljana, You can advertise on the inner and outer side of the back cover of Faculty of Mechanical Engineering, Slovenia Print Faculty of Mechanical Engineering, Slovenia the magazine. The authors of the published papers are invited to Tiskarna Knjigoveznica Radovljica, printed in for 480cover copiescontent. send photos or pictures with short explanation Association of Mechanical Engineers of Slovenia We would like to thank the reviewers who have taken part in the General information ISSN 0039-2480 peer-review process.

Chamber of Commerce and Industry of Slovenia Strojniški vestnik – Journal of Mechanical Engineering is the additional should read: Metal Processinginformation Industry Association published in 11 issues per year (July and August is a double issue). © 2011 Strojniški vestnik - Journal of Mechanical Engineering. All Strojniški vestnik Journalprint of & Mechanical Engineering is also Institutional prices -include online access: institutional rights reserved. SV-JME is indexed / abstracted in: SCI-Expanded, available on http://www.sv-jme.eu, where you access also to papers’ subscription price and foreign subscription €100,00 (the price of a Cover: Compendex, Inspec, ProQuest-CSA, SCOPUS, The list of supplements, as simulations, etc. subscription and student single issue issuch €10,00); general public Above: Shematics of theTEMA. first magnetic the remaining bases, in which SV-JME indexed, is available subscription €50,00 (the price of a single issue is €5,00). Prices refrigeratorisprototype developed at the on the website. The journal is subsidized Slovenian Book are exclusive of tax. Delivery is included in the price. The Universityby of Ljubljana, Faculty of Agency. recipient is responsible for paying any import duties or taxes.

Mechanical Engineering, Slovenia Legal title passes to the customer on dispatch by our distributor.

Below: Numerical simulation results of the Single issues from current and recent volumes are available at the magnetic field in the NdFeB magnet assembly current single-issue price. To order the journal, please complete the form on our website. For submissions, subscriptions and all Image courtesy: Laboratory of Refrigeration other information please visit: http://en.sv-jme.eu/. and District Energy and Centre for Element

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and Structure Modelling, Faculty of Mechanical Engineering, University of Ljubljana, Slovenia

ISSN 0039-2480 © 2011 Strojniški vestnik - Journal of Mechanical Engineering. All rights reserved. SV-JME is indexed / abstracted in: SCI-Expanded, Compendex, Inspec, ProQuest-CSA, SCOPUS, TEMA. The list of the remaining bases, in which SV-JME is indexed, is available on the website. The journal is subsidized by Slovenian Book Agency.

SI 30

You can advertise on the inner and outer side of the back cover of the magazine. The authors of the published papers are invited to send photos or pictures with short explanation for cover content.

We would like to thank the reviewers who have taken part in the peer-review process.

Strojniški vestnik - Journal of Mechanical Engineering is also available on http://www.sv-jme.eu, where you access also to papers’ supplements, such as simulations, etc.

Strojniški vestnik – Journal of Mechanical Engineering (SV-JME) Aim and Scope The international journal publishes original and (mini)review articles covering the concepts of materials science, mechanics, kinematics, thermodynamics, energy and environment, mechatronics and robotics, fluid mechanics, tribology, cybernetics, industrial engineering and structural analysis.

The journal follows new trends and progress proven practice in the mechanical engineering and also in the closely related sciences as are electrical, civil and process engineering, medicine, microbiology, ecology, agriculture, transport systems, aviation, and others, thus creating a unique forum for interdisciplinary or multidisciplinary dialogue.

The international conferences selected papers are welcome for publishing as a special issue of SV-JME with invited co-editor(s).

Editor in Chief Vincenc Butala University of Ljubljana Faculty of Mechanical Engineering, Slovenia Co-Editor Borut Buchmeister University of Maribor Faculty of Mechanical Engineering, Slovenia Technical Editor Pika Škraba University of Ljubljana Faculty of Mechanical Engineering, Slovenia Editorial Office University of Ljubljana (UL) Faculty of Mechanical Engineering SV-JME Aškerčeva 6, SI-1000 Ljubljana, Slovenia Phone: 386-(0)1-4771 137 Fax: 386-(0)1-2518 567 E-mail: info@sv-jme.eu http://www.sv-jme.eu Founders and Publishers University of Ljubljana (UL) Faculty of Mechanical Engineering, Slovenia University of Maribor (UM) Faculty of Mechanical Engineering, Slovenia Association of Mechanical Engineers of Slovenia Chamber of Commerce and Industry of Slovenia Metal Processing Industry Association Cover: In the middle figure presents modern manufacturing concept called the “backward incremental hole-flanging process”, which may be applied as an additional technology in multi-step forming operations and enables the formation of necks outward or inward on complex 3D products in small quantities, effectively and with minimal costs. One example of such complex product with incrementally performed symmetrical necks is shown on the cover above. The technology could be applied for symmetrical as well as for asymmetrical shapes of the necks, as shown in Figure below.

Image courtesy: Forming Laboratory, Faculty of Mechanical Engineering, University of Ljubljana, Slovenia, EMO-Orodjarna Production Company, Slovenia

ISSN 0039-2480 © 2011 Strojniški vestnik - Journal of Mechanical Engineering. All rights reserved. SV-JME is indexed / abstracted in: SCI-Expanded, Compendex, Inspec, ProQuest-CSA, SCOPUS, TEMA. The list of the remaining bases, in which SV-JME is indexed, is available on the website. The journal is subsidized by Slovenian Book Agency.

International Editorial Board Koshi Adachi, Graduate School of Engineering,Tohoku University, Japan Bikramjit Basu, Indian Institute of Technology, Kanpur, India Anton Bergant, Litostroj Power, Slovenia Franci Čuš, UM, Faculty of Mech. Engineering, Slovenia Narendra B. Dahotre, University of Tennessee, Knoxville, USA Matija Fajdiga, UL, Faculty of Mech. Engineering, Slovenia Imre Felde, Bay Zoltan Inst. for Mater. Sci. and Techn., Hungary Jože Flašker, UM, Faculty of Mech. Engineering, Slovenia Bernard Franković, Faculty of Engineering Rijeka, Croatia Janez Grum, UL, Faculty of Mech. Engineering, Slovenia Imre Horvath, Delft University of Technology, Netherlands Julius Kaplunov, Brunel University, West London, UK Milan Kljajin, J.J. Strossmayer University of Osijek, Croatia Janez Kopač, UL, Faculty of Mech. Engineering, Slovenia Franc Kosel, UL, Faculty of Mech. Engineering, Slovenia Thomas Lübben, University of Bremen, Germany Janez Možina, UL, Faculty of Mech. Engineering, Slovenia Miroslav Plančak, University of Novi Sad, Serbia Brian Prasad, California Institute of Technology, Pasadena, USA Bernd Sauer, University of Kaiserlautern, Germany Brane Širok, UL, Faculty of Mech. Engineering, Slovenia Leopold Škerget, UM, Faculty of Mech. Engineering, Slovenia George E. Totten, Portland State University, USA Nikos C. Tsourveloudis, Technical University of Crete, Greece Toma Udiljak, University of Zagreb, Croatia Arkady Voloshin, Lehigh University, Bethlehem, USA President of Publishing Council Jože Duhovnik UL, Faculty of Mechanical Engineering, Slovenia Print Tiskarna Knjigoveznica Radovljica, printed in 480 copies General information Strojniški vestnik – Journal of Mechanical Engineering is published in 11 issues per year (July and August is a double issue).

Institutional prices include print & online access: institutional subscription price and foreign subscription €100,00 (the price of a single issue is €10,00); general public subscription and student subscription €50,00 (the price of a single issue is €5,00). Prices are exclusive of tax.

Delivery is included in the price. The recipient is responsible for paying any import duties or taxes. Legal title passes to the customer on dispatch by our distributor.

Single issues from current and recent volumes are available at the current single-issue price. To order the journal, please complete the form on our website. For submissions, subscriptions and all other information please visit: http://en.sv-jme.eu/.

You can advertise on the inner and outer side of the back cover of the magazine. The authors of the published papers are invited to send photos or pictures with short explanation for cover content.

We would like to thank the reviewers who have taken part in the peerreview process.

Strojniški vestnik - Journal of Mechanical Engineering is also available on http://www.sv-jme.eu, where you access also to papers’ supplements, such as simulations, etc.

Instructions for Authors All manuscripts must be in English. Pages should be numbered sequentially. The maximum length of contributions is 10 pages. Longer contributions will only be accepted if authors provide justification in a cover letter. Short manuscripts should be less than 4 pages. For full instructions see the Authors Guideline section on the journal’s website: http://en.sv-jme.eu/.

Announcement: The authors are kindly invited to submitt the paper through our web site: http://ojs.sv-jme.eu. The Author is also able to accompany the paper with Supplementary Files in the form of Cover Letter, data sets, research instruments, source texts, etc. The Author is able to track the submission through the editorial process - as well as participate in the copyediting and proofreading of submissions accepted for publication - by logging in, and using the username and password provided.

Please provide a cover letter stating the following information about the submitted paper: 1. Paper title, list of authors and affiliations.

2. The type of your paper: original scientific paper (1.01), review scientific paper (1.02) or short scientific paper (1.03).

3. A declaration that your paper is unpublished work, not considered elsewhere for publication.

4. State the value of the paper or its practical, theoretical and scientific implications. What is new in the paper with respect to the state-of-the-art in the published papers?

5. We kindly ask you to suggest at least two reviewers for your paper and give us their names and contact information (email).

Every manuscript submitted to the SV-JME undergoes the course of the peer-review process.

THE FORMAT OF THE MANUSCRIPT The manuscript should be written in the following format: - A Title, which adequately describes the content of the manuscript.

- An Abstract should not exceed 250 words. The Abstract should state the principal objectives and the scope of the investigation, as well as the methodology employed. It should summarize the results and state the principal conclusions.

- 6 significant key words should follow the abstract to aid indexing.

- An Introduction, which should provide a review of recent literature and sufficient background information to allow the results of the article to be understood and evaluated.

- A Theory or experimental methods used.

- An Experimental section, which should provide details of the experimental set-up and the methods used for obtaining the results.

- A Results section, which should clearly and concisely present the data using figures and tables where appropriate.

- A Discussion section, which should describe the relationships and generalizations shown by the results and discuss the significance of the results making comparisons with previously published work. (It may be appropriate to combine the Results and Discussion sections into a single section to improve the clarity).

- Conclusions, which should present one or more conclusions that have been drawn from the results and subsequent discussion and do not duplicate the Abstract.

- References, which must be cited consecutively in the text using square brackets [1] and collected together in a reference list at the end of the manuscript.

Units - standard SI symbols and abbreviations should be used. Symbols for physical quantities in the text should be written in italics (e.g. v, T, n, etc.).

Symbols for units that consist of letters should be in plain text (e.g. ms-1, K, min, mm, etc.)

Abbreviations should be spelt out in full on first appearance, e.g., variable time geometry (VTG).

Meaning of symbols and units belonging to symbols should be explained in each case or quoted in a special table at the end of the manuscript before References.

Figures must be cited in a consecutive numerical order in the text and referred to in both the text and the caption as Fig. 1, Fig. 2, etc. Figures should be prepared without borders and on white grounding and should be sent separately in their original formats.

Pictures may be saved in resolution good enough for printing in any common format, e.g. BMP, GIF or JPG. However, graphs and line drawings should be prepared as vector images, e.g. CDR, AI. When labeling axes, physical quantities, e.g. t, v, m, etc. should be used whenever possible to minimize the need to label the axes in two languages.

Multi-curve graphs should have individual curves marked with a symbol. The meaning of the symbol should be explained in the figure caption.

Tables should carry separate titles and must be numbered in consecutive numerical order in the text and referred to in both the text and the caption as Table 1, Table 2, etc. In addition to the physical quantity, e.g. t (in italics), units

(normal text), should be added in square brackets. The tables should each have a heading. Tables should not duplicate data found elsewhere in the manuscript.

Acknowledgement of collaboration or preparation assistance may be included before References. Please note the source of funding for the research.

REFERENCES A reference list must be included using the following information as a guide. Only cited text references are included. Each reference is referred to in the text by a number enclosed in a square bracket (i.e., [3] or [2] to [6] for more references). No reference to the author is necessary.

References must be numbered and ordered according to where they are first mentioned in the paper, not alphabetically. All references must be complete and accurate. All non-English or. non-German titles must be translated into English with the added note (in language) at the end of reference. Examples follow.

Journal Papers: Surname 1, Initials, Surname 2, Initials (year). Title. Journal, volume, number, pages, DOI code.

[1] Hackenschmidt, R., Alber-Laukant, B., Rieg, F. (2010). Simulating nonlinear materials under centrifugal forces by using intelligent crosslinked simulations. Strojniški vestnik - Journal of Mechanical Engineering, vol. 57, no. 7-8, p. 531-538, DOI:10.5545/sv-jme.2011.013.

Journal titles should not be abbreviated. Note that journal title is set in italics.

Please add DOI code when available and link it to the web site.

Books: Surname 1, Initials, Surname 2, Initials (year). Title. Publisher, place of publication.

[2] Groover, M.P. (2007). Fundamentals of Modern Manufacturing. John Wiley & Sons, Hoboken.

Note that the title of the book is italicized.

Chapters in Books: Surname 1, Initials, Surname 2, Initials (year). Chapter title. Editor(s) of book, book title. Publisher, place of publication, pages.

[3] Carbone, G., Ceccarelli, M. (2005). Legged robotic systems. Kordić, V., Lazinica, A., Merdan, M. (Eds.), Cutting Edge Robotics. Pro literatur Verlag, Mammendorf, p. 553-576.

Proceedings Papers: Surname 1, Initials, Surname 2, Initials (year). Paper title. Proceedings title, pages.

[4] Štefanić, N., Martinčević-Mikić, S., Tošanović, N. (2009). Applied Lean System in Process Industry. MOTSP 2009 Conference Proceedings, p.

422-427.

Standards: Standard-Code (year). Title. Organisation. Place.

[5] ISO/DIS 16000-6.2:2002. Indoor Air – Part 6: Determination of Volatile Organic Compounds in Indoor and Chamber Air by Active Sampling on TENAX TA Sorbent, Thermal Desorption and Gas Chromatography using MSD/FID. International Organization for Standardization. Geneva. www pages: Surname, Initials or Company name. Title, from http://address, date of access.

[6] Rockwell Automation. Arena, from http://www.arenasimulation.com, accessed on 2009-09-07.

EXTENDED ABSTRACT By the time the paper is accepted for publishing, the authors are requested to send the extended abstract (approx. one A4 page or 3.500 to 4.000 characters). The instructions for writing the extended abstract are published on the web page http://www.sv-jme.eu/ information-for-authors/.

COPYRIGHT Authors submitting a manuscript do so on the understanding that the work has not been published before, is not being considered for publication elsewhere and has been read and approved by all authors. The submission of the manuscript by the authors means that the authors automatically agree to transfer copyright to SV-JME and when the manuscript is accepted for publication. All accepted manuscripts must be accompanied by a Copyright Transfer Agreement, which should be sent to the editor. The work should be original by the authors and not be published elsewhere in any language without the written consent of the publisher.

The proof will be sent to the author showing the final layout of the article. Proof correction must be minimal and fast. Thus it is essential that manuscripts are accurate when submitted.

Authors can track the status of their accepted articles on http://en.svjme.eu/.

PUBLICATION FEE For all articles authors will be asked to pay a publication fee prior to the article appearing in the journal. However, this fee only needs to be paid after the article has been accepted for publishing. The fee is 220.00 EUR (for articles with maximum of 10 pages), 20.00 EUR for each addition page.

Additional costs for a color page is 90.00 EUR.

58 (2012) 2

http://www.sv-jme.eu

Strojniški vestnik Journal of Mechanical Engineering

Since 1955

Papers

73

Aleš Petek, Karl Kuzman: Backward Hole-Flanging Technology Using an Incremental Approach

81

Fuqing Zhao, Jizhe Wang, Junbiao Wang, Jonrinaldi Jonrinaldi: A Dynamic Rescheduling Model with Multi-Agent System and Its Solution Method

93

Suzana Uran, Riko Šafarič: Neural-Network Estimation of the Variable Plant for Adaptive Sliding-Mode Controller

102

Bohumil Taraba, Steven Duehring, Ján Španielka, Štefan Hajdu: Effect of Agitation Work on Heat Transfer during Cooling in Oil ISORAPID 277HM

107

Gorazd Krese, Matjaž Prek, Vincenc Butala: Analysis of Building Electric Energy Consumption Data Using an Improved Cooling Degree Day Method

115

Matej Volk, Marko Nagode, Matija Fajdiga: Finite Mixture Estimation Algorithm for Arbitrary Function Approximation

125

Saeed Daneshmand, Cyrus Aghanajafi: Description and Modeling of the Additive Manufacturing Technology for Aerodynamic Coefficients Measurement

Zlatko Rek, Mitja Rudolf, Iztok Zun: 134 Application of CFD Simulation in the Development of a New Generation Heating Oven

Journal of Mechanical Engineering - Strojniški vestnik

Contents

2 year 2012 volume 58 no.