Journal of Mechanical Engineering 2011 10

57 (2011) 1 10

Platnica SV-JME 57(2011)10_01.pdf 1 4.10.2011 11:24:04

Since 1955

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Journal of Mechanical Engineering - Strojniški vestnik

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10 year 2011 volume 57 no.

Platnica SV-JME 57(2011)10_01.pdf 2 4.10.2011 11:24:04

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.

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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

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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 Coloured map of deviation between acquired geometry and CAD model Optical geometry acquisition with 3D scanner GOM ATOS II Background: Sphere measurement with co-ordinate measuring machine ZEISS UMC 850 Image courtesy: Intelligent Manufacturing Systems Laboratory, Production Engineering Institute, Faculty of Mechanical Engineering, University of Maribor

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Strojniški vestnik - Journal of Mechanical Engineering 57(2011)10 Contents

Contents Strojniški vestnik - Journal of Mechanical Engineering volume 57, (2011), number 10 Ljubljana, October 2011 ISSN 0039-2480 Published monthly Papers Bogdan Valentan, Tomaž Brajlih, Igor Drstvenšek, Jože Balič: Development of a PartComplexity Evaluation Model for Application in Additive Fabrication Technologies Gang Cheng, Wei Gu, Jing-li Yu, Ping Tang: Overall Structure Calibration of 3-UCR Parallel Manipulator Based on Quaternion Method Marin Gostimirović, Milenko Sekulić, Janez Kopač, Pavel Kovač: Optimal Control of Workpiece Thermal State in Creep-Feed Grinding Using Inverse Heat Conduction Analysis Roberto Alvarez, Rosario Domingo, Miguel Angel Sebastian: The Formation of Saw Toothed Chip in a Titanium Alloy: Influence of Constitutive Models Matjaž Dvoršek, Marko Hočevar, Brane Širok, Nikola Holeček, Božin Donevski: The Influence of Airflow Inlet Region Modifications on the Local Efficiency of Natural Draft Cooling Tower Operation Wang Jixin, Yao Mingyao, Yang Yonghai: Global Optimization of Lateral Performance for TwoPost ROPS Based on the Kriging Model and Genetic Algorithm Ivan Demšar, Matej Supej, Zmago Vidrih, Jožef Duhovnik: Development of Prosthetic Knee for Alpine Skiing Slavica Prvulovic, Dragisa Tolmac, Ljiljana Radovanovic: Application of Promethee-Gaia Methodology in the Choice of Systems for Drying Paltry-Seeds and Powder Materials Instructions for Authors

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Strojniški vestnik - Journal of Mechanical Engineering 57(2011)10, 709-718 DOI:10.5545/sv-jme.2010.057

Paper received: 09.03.2011 Paper accepted: 15.07.2011

Development of a Part-Complexity Evaluation Model for Application in Additive Fabrication Technologies Valentan, B. ‒ Brajlih, T. ‒ Drstvenšek, I. ‒ Balič, J. Bogdan Valentan* ‒ Tomaž Brajlih ‒ Igor Drstvenšek ‒ Jože Balič University of Maribor, Faculty of Mechanical Engineering, Slovenia

With the rapid development and expansion of devices for the production of both traditional (cutting) procedures and layered technologies (also known as 3D printers or rapid prototyping/manufacturing), the question arises of how to find the appropriate production technology.

The article describes the basic features of the CAD output file STL. The STL file format is a widelyused file format developed for layered technologies and, as such, a basis for analysing and developing methods when determining the complexity of a model.

For the analyses of basic STL data, and complexity determination, several real-life models are presented. Actual manufacturing procedures suitable for the manufacture of unique products or serial production are presented, with accentuation towards layered technologies.

Technological test models are analysed based on the fundamental properties of manufacturing and certain manufacturing processes are chosen using complexity estimation. The results are comparable with those choices of manufacturing procedures on the basis of experts’ estimates. Complexity evaluation is also used for post-processing time determination for several layered technologies. ©2011 Journal of Mechanical Engineering. All rights reserved.

Keywords: rapid prototyping, STL, complexity, shape, layered technology, technology selection

The development of production technologies began in the early years of human society and then expanded during the industrial revolution. Since then technologies have been refined, new versions introduced and computer support enables partial-automation. Production was optimized [1] and [2] in terms of becoming cheaper, faster and better. However, technologies are still based on old knowledge in terms of removing materials, casting or forming. In addition, technological restrictions are still present when the complexity of a product plays a key role and the selection process is necessary prior to making the product. In order to realize a project in manufacturing, people with knowledge and experience are needed and a combination of several different technologies in complex everyday products is common [3] and [4].

No serious players from the field of conventional cutting processes were interested when the origin of layered technology was first introduced in the middle of 1980’s. The technology was expensive, complex, inaccurate, slow, limited

by the dimensions and materials [5] and [6], but allowed the manufacturing of products in one piece, regardless of their complexity. In addition, technology had another advantage, which is that the time for the preparation of input parameters did not depend on the complexity of the product.

At the beginning technology acquired the names rapid prototyping or 3D printing.

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Fig. 1. Continuous growth of machine sales [7] In the field of layered technologies, constant growth [7] (Fig. 1) is still in the middle and due to, at least on paper, very promising new

*Corr. Author’s Address: University of Maribor, Faculty of Mechanical Engineering, Smetanova ulica 17, SI-2000 Maribor, Slovenia, bogdan.valentan@uni-mb.si

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revolutionary innovations, a lot of people refer to the new industrial revolution when talking about layered technologies.

1 INTRODUCING THE STL FILE FORMAT The STL data format is a polygonal (mesh) format developed for the needs of the 3D Systems’ stereolithography equipment, which is one of the layered technologies. Stereolithography (U.S. Patent called ‘’Apparatus for Production of ThreeDimensional Objects by Stereolithography’’) was patented in 1984 and in 1986 the 3D Systems Company began to manufacture devices for prototype production.

During this time, the STL file format [8] to [10] was adopted by all other layered technologies and as such became the standard format. The reason for the popularity of the STL file format is in the simplicity of model description, as the STL format describes only the external surface of the 3D model without adding any other data.

Some CAD attributes (points, lines, curves and layers) in other formats (WRML, DXF) can cause complications in non-standard formats records [11] and [12].

There are two formats of the STL file (binary and ASCII). The STL file format is supported by all modern CAD programs, although not all allow storage in both forms.

Since the STL file does not contain information about the real model size, some problems can appear such as unit change from cm to inch (SI replacement for the imperial system).

While exporting from the CAD to the STL file, part-resolution needs to be set. Export options are different in various CAD programs. The main parameters are set by the maximal allowed deviations between triangle mesh and the original CAD model, and the minimal allowed angle between two triangle edges.

When choosing model resolution, it is necessary to keep in mind that the resolution of the manufacturing device can be greater than the STL resolution, and a lack of resolution means a lower surface quality for the model produced [13] to [15] (Fig. 2). The problem is frequently set into a production line where an outside contractor cannot know the desired surface quality. By increasing the precisions of production technologies, this 710

problem shows the limitations of the STL format where, despite the most accurate resolution and large file size, a smooth surface cannot be achieved.

Fig. 2. Comparison between optimal and deficient choices for the export parameters of the STL file 2 TEST PARTS Some test parts were needed for evaluating the complexity. The limitations of the STL file were taken into consideration. For a realistic comparison, all models were designed using the same CAD software (Catia V5) with the same settings for exporting STL files (3D accuracy of 0.01 and curve precision to 0.1). All models were checked for errors and verified by the Netfabb [16] program, and appropriately placed into the positive coordinates of their own coordinate systems. Orientation is set by experience since, in normal cases, the author starts modelling in one of the basic planes.

Fig. 3. Test models for complexity evaluation

Valentan, B. ‒ Brajlih, T. ‒ Drstvenšek, I. ‒ Balič, J.

Strojniški vestnik - Journal of Mechanical Engineering 57(2011)10, 709-718

Three models of basic geometric shapes can be found among the selected test models, and all the rest are the real ‘’user’’ parts (Fig. 3). An important fact is the presumption that complexity does not depend only on the shape of the model, but also on the size. Two models are of the same shape but of different sizes.

3 BASIC PARAMETERS OF THE TEST MODELS Basic STL file parameters were used for the experiment, such as the size of the binary file, number of triangles, the part’s volume, the part’s surface (area), and the volume of the block that captures the model. All parameters can be obtained by reading the STL file. Some properties can be calculated using basic mathematical equations or by some advanced software tools that allow visualization of the model and its properties (for example Netfabb).

Table 1 shows the direction of a triangle’s normal vector that is problematic in each octant.

It is enough to look at the sign of the triangle’s vector. If a problematic vector exists, the part cannot be made by aconventional procedure without an additional fixture or the use of special tools, but in most cases manufacturing using the conventional procedure (production in one piece) is impossible.

If there is a case where octants 1 and 3, 2 and 4, 5 and 7, 6 and 8 are vectors of opposite directions (flipped through the centreline of the model and the axis passing through the junction of octants 1, 2, 3 and 4 and continuing through junction of octants 5, 6, 7 and 8) the model can be suitable for rotary machining. All test models were analyzed for the vector directions in each octant. The results are presented in Table 2.

Table 1. Triangle normals that are problematic

1 2 3 4 5 6 7 8

3.1 Determination of Octants and Problematic Sections A simple procedure for the basic manufacturing procedure determination was used due to difficulty in determining the basic form [17] to [19] – shape recognition (statistically due to the loss of data when converting into STL format). Octants of each model were determined by distributing the part’s external block into eight smaller blocks (octants) (Fig. 4).

Information about each octant, information on the overhangs and negative angles was gained from the vector’s direction, which normally constitutes a problem with conventional cutting processes during manufacture.

Fig. 4. Octant distribution through the model

X + + + +

Octant

Vector direction

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Table 2. Test part analysis and survey of problematic octants Octants Model

1 2 3 4 5 6 7 8 9 10 11 12 13

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Octants without problematic direction.

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Octants with problematic direction.

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4 COMPLEXITY DETERMINATION

4.1 Advanced Evaluation of Model Complexity

The complexity, based on our own experiences with manufacturing processes, is determined first (Fig. 5), to obtain some sort of a reference, and then these results are compare with the calculated ones. This personal classification represents a reference for finding a suitable procedure when determining the complexity [20] and [21].

The complexity of the model can be deduced from information on the number of triangles (Fig. 6) (the number of triangles is directly related to the size of the file). An increased number of triangles represents a more complex model. This comparison does not take into account the increasing complexity, while decreasing the size of the model and all models should be created with the same export parameters.

Complexity on the basis of file size or the number of triangles presents us with some basic part complexity ideas, without the model’s size being taken into consideration. For example, with models 1 and 2, and 10 and 11, the calculated complexities should not be the same, since there are significant size differences between these parts. When reducing the size of a part, its complexity increases.

For accurate complexity calculation, the proportions of the three basic parameters of the model are needed: the model’s surface, the number of the model’s triangles, and the model’s volume.

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Models classified by complexity

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model surface number of triangles . (1) model square block volume

The result of Eq. (1) is presented in the following graph (Fig. 7). It can be seen that part size plays a significant role regarding complexity determination. This relationship, taking into consideration part size is very similar to the complexity based on our own experiences.

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Fig. 5. Complexity based on expert opinion

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Fig. 7. Calculated complexity that can be compared with complexity given by experts

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Calculated complexity of the model is comparable to experientially determined complexity (Fig. 5). Three models deviate from the average (7.8 and 13) all of them have varied surfaces and are problematic for manufacturing using conventional procedures. A significant impact also occurs when reducing the scale of a model which results in an increase in the complexity (models 1 and 10 versus models 2 and 11).

Valentan, B. ‒ Brajlih, T. ‒ Drstvenšek, I. ‒ Balič, J.

Strojniški vestnik - Journal of Mechanical Engineering 57(2011)10, 709-718

5 MANUFACTURING PROCEDURES Today’s manufacturing procedures are divided into conventional (cutting operations [22]) and layered technologies. In a case of conventional procedures - a set stock of raw material is depleted until a desired shape is obtained. The material can be removed by various procedures (turning, milling, grinding, cutting, local melting ...). Due to the need of comparison milling and turning were taken into consideration.

Layered technologies (often referred to as the technology for the rapid prototyping or 3D printing) are among the modern manufacturing procedures in which the material is no longer removed, but added. Technology allows us to produce realistic models of, until then unmanufacturable forms (Fig. 8) in one piece practically overnight. Several different technologies were developed [23] and [24] besides the first presented and patented procedure – stereolithography.

time. In the end it should not be forgotten that all today’s known layered-technologies need some post-process to obtain a final part. This can be a simple cleaning procedure, the removal of support material or even infiltration with some special material, which is time-consuming and expensive.

6 SELECTING THE OPTIMAL MANUFACTURING PROCEDURE Several criteria should be taken into consideration when selecting appropriate manufacturing procedures: • the desired material, • the size of the product, • the manufacturing time and • cost of manufacture.

This paper focuses on product design, which means that at this stage some properties are ignored, such as materials, the properties of the materials, and product size, since material properties in the STL format are not given and size is not as problematic as there are different machines for producing different sizes parts.

Production is highly dependent on the complexity of the product, especially when comparing cutting processes and layered techniques.

6.1 Selection on the Basis of Vector Direction in Each Octant

Fig. 8. EOS Formiga P 100 Selective laser sintering (SLS) machine with some parts Material application layer by layer is common to all technologies [25] and [26].

Technology produces individual 2D layers and by adding 2D layers on top of each other (a 3D product is formed). Important information from the survey is that some procedures support individual layers where necessary (overhangs or the spread of the model in a Z direction), as imposed support material, which is not the same as for models. In these cases, the form of the product affects the price, as well as building

Table 3 presents the results of the selection on the basis of determining vector direction in each octant. Turning is chosen as the most affordable process when it comes to a rotary piece (models 3, 6 and 12), milling when it comes to the model without problematic vectors that define impossible tool angles and layered technology for all other models.

Layered technologies are divided into two subcategories: • Layered technologies that for support use raw modelling material. In this case, the support material can be reused and it does not represent an additional cost.

• Layered technologies that use some additional support material at the part overhangs or have support from the model material, but that material should be removed after some treatment.

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Table 3. Selecting the manufacturing procedure on an octant vector direction base Turning

Milling

LT where support is needed

LT where support is not needed

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Table 4. Selecting a manufacturing procedure on a part-complexity basis Partly

Turning

7 8 9 10 11 12 13 Procedure is appropriate.

Procedure is inappropriate.

6.2 Selection on the Basis of the Part Complexity Fig. 7 shows the complexities of the test models. Unfortunately, complexity cannot provide us with information if turning is appropriate to be the right procedure for manufacturing.

Manufacturing by turning is only possible for models 3 and 12 (Table 4), which have a relatively low ratio of fewer than 20,000 and do not stand out (Fig. 7). By imposing a limit of 20,000, models 2, 4, 5 and 11 are added to the selection, even if the manufacturing of these models in this case, is not possible.

Models, where the production with milling is impossible (7, 8 and 13) have extremely high ratio (over 120,000). Models 6 and 9 can be produced, but need an additional fixture during the manufacturing, or a complex 4 axes-production process. Models that are easy to produce have a low ratio (below 40,000). The limit for the milling process as the best possible selection was set at 100,000.

It can be seen that layered technologies are suitable for all models (from the point of manufacturing techniques, which is already a known fact), but when dividing technologies into those that need additional support material and those in which the support material is the same as the model’s material, it can be said that in the case 714

of a model with higher complexity, the production costs are higher. The limit between those two technologies was set to 50,000. Therefore, if complexity is below 50,000 any layered technology is suitable, when the complexity is beyond 50,000 layered technologies that reuse support material are more suitable.

1 2 3 4 5 6 7 8 9 10 11 12 13 Suitable.

Milling

LT where LT where support is support is needed not needed

Suitable but bigger support material consumption.

Unsuitable.

Models (1 and 10) are problematic to produce as they are resized to extremely small dimensions and can create certain problems for both processes. In the case of milling, the problem of clamping exists and in the case of layered technologies, resolution of the technology itself presents an obstacle to production.

6.3 Arrangements by Combining the Complexities of the Shapes and the Vector Direction, in Each Octant By examining the results of both selection processes (one based on the vector direction in each octant and the other on the complexity of form), it can be established that, in some instances, each selection process can favour the process by which production is impossible. By combining the two methods those procedures that are inappropriate are eliminated. The results are presented in Table 5.

Valentan, B. ‒ Brajlih, T. ‒ Drstvenšek, I. ‒ Balič, J.

Strojniški vestnik - Journal of Mechanical Engineering 57(2011)10, 709-718

Table 5. Selecting the manufacturing procedure by combining part complexity with the octant vector direction Turning

Milling

1 2 3 4 5 6 7 8 9 10 11 12 13 Suitable.

Suitable but bigger support material consumption.

Unsuitable.

Rotational Symmetry detection on an octant vector direction base

Choosing a manufacturing procedure on a part-complexity basis

Milling

7 POST-PROCESSING TIME DETERMINATION BY EVALUATION OF MODEL COMPLEXITY

LT where LT where support is support is needed not needed

STL File

Turning

parameters, that are not written in to STL file is made.

LT where support is needed

LT where support is not needed

Additional Parameters not set in STL file (material, number of peaces, etc.)

Fig. 9. Diagram presents selecting procedure In Fig. 9 first Turning is chosen if the part can be produced by turning. On the complexity base ruff decision between Milling and both layered procedures can be made, as presented.

At the end fine selection with introduction of

The time for post-processing is problematic, especially from the perspective of determining the final production costs of the model. The price consists of construction material, hardware hour costs; fixed costs, energy cost, staff cost and the cost of post-processing. So far, assessment has been individually determined solely and empirically by using peoples’ experiences. With the introduction of complexity evaluation, the post-processing time can be calculated and planned during the production time.

The time for post-processing (Fig. 10) is distinguishable between different technologies (Fig. 11), therefore, it is necessary to determine the individual impacts of complexity on time for each layered technology.

In order to do that some parts need to be built and post-processing time for those parts need to be measured. On the basis of that data function:

complexity = X , (2) post-processing time

can be derived and average value X calculated.

For all the following parts time can be calculated:

post-processing time =

complexity . (3) X

Since post-processing time is based on manual work, this function can never be exact (especially, when more than one man is working at post-processing stage), but can give us a fair estimation on the time needed for that production step.

This procedure is suitable for timedetermination in the cases when technologies that require manual removal of the support structure.

This category includes: SLS, LOM, SLA, PolyJet, FSM, LENS, DMLS, SLM and EBM. In the cases of these processes, the removal of support material takes a certain time, depending on the complexity of the product itself. In the cases of SLS, LENS, DMLS, SLM and EBM, the removal of non-solidified base material is required. In the

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case of LOM technology the removal of material surrounding the product is needed. SLA and FDM are building supports from base-material and these supports need to be broken off at the end.

PolyJet has supports from special support material that needs special water-jet treatment at the end of the process. In processes in which the support material is dissolved in liquid or the model is infiltrated with special liquids, post-processing does not depend on the complexity of design.

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Fig. 10. Time of post-processing for test models made using the LOM procedure on SOLIDO SD 300 Pro; models 1 and 10 were too small to be produced by LOM technology

Fig. 11. Waste-material removal in LOM 8 CONCLUSIONS The presented method introduces a fairly good method of fundamental decision between turning, milling and layered techniques.

Selecting an appropriate layered technology is not unambiguously determined; therefore choosing the optimal layered technology can only 716

be approximate. The reason for this lies in the sentence that is used in the marketing of layered technologies: ‘complexity for free’. The layered technologies of today have no problems with the production of highly complex forms, which is also their biggest advantage over conventional procedures. This poses a certain problem when selecting a production procedure based only on the complexity of the product.

Shape affects only a few specific technologies from layered technologies either because of expensive support material (PolyJet, SLA, SGC, MJM), or the difficulty of removing the support material from the problematic sections (LOM).

On the other hand, determining design complexity and the calculation of model resolution can mean certain selections regarding the choice of the production procedure, where less-accurate parts can be made using less-accurate technology.

The evaluation of the complexity was proven in determination of the time required for finalizing the product. This time of postprocessing was quite difficult to determine since manufacturers would prefer to skip it, even though the impact on the time of manufacture is significant. When the talk is about rapid prototyping, time is quite significant. The presented solution is suitable for the introduction into production.

This survey is a significant advancement in the direction of process selection, but for practical applications it would be necessary to include more parameters and advanced selection methods [27] to [29], so that the process can be uniquely selected.

Only after choosing basic part properties (like material properties, colour and surface quality), time of manufacture, dimensions, the number of pieces in a series and the complexity, of doe’s product come into regard.

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331-340.

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[2] Kovacic, M., Balic, J., Brezocnik, M. (2004).

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Valentan, B. ‒ Brajlih, T. ‒ Drstvenšek, I. ‒ Balič, J.

Strojniški vestnik - Journal of Mechanical Engineering 57(2011)10, 719-729 DOI:10.5545/sv-jme.2010.167

Paper received: 28.07.2010 Paper accepted: 15.07.2011

Overall Structure Calibration of 3-UCR Parallel Manipulator Based on Quaternion Method Cheng, G. ‒ Gu, W. ‒ Yu, J. ‒ Tang, P. Gang Cheng* ‒ Wei Gu ‒ Jing-li Yu ‒ Ping Tang China University of Mining and Technology, College of Mechanical and Electrical Engineering, China

In this article a simple yet effective approach for the structure calibration of a three degree-offreedom (DOF) parallel manipulator is presented. In this approach, the model of the pose error expressed by the Quaternions Parameters was established, based on complete differential-coefficient theory. This was followed by an investigation into the degree of influences represented as sensitivity percentages, of source errors on the pose accuracy with the aid of a statistical model of sensitivity coefficients. Then, the kinematic calibration model with the successive approximation algorithm was achieved. The simulation has been carried out to verify the effectiveness of the proposed algorithm and the results show that the accuracy of the calibration can be significantly improved. ©2011 Journal of Mechanical Engineering. All rights reserved.

Keywords: 3-UCR parallel manipulator, complete differential-coefficient theory, Quaternion, least squares method, sensitivity model, kinematic calibration

0 INTRODUCTION Parallel manipulators have particularly aroused interest of researchers over the past several decades for their properties of better structural rigidity, positioning accuracy, and dynamic performances [1] and [2]. Unlike serial manipulators, which suffer from the accumulation of joint errors, parallel manipulators are considered to have high accuracy [3].

However, relative investigations have shown that the parallel manipulator is not necessarily more accurate than a serial manipulator with the same manufacturing and assembling precision [4]. Accuracy remains a bottleneck for further industrial applications of parallel manipulators.

Therefore, in order to enhance the precisions of parallel manipulators, it is important to evaluate the end-effector’s accuracy in the design phase, and to calibrate the kinematic parameters after manufacturing [3]. From kinematic characteristics of lower-mobility parallel manipulators, it can be seen that complete errors compensation of the pose can not be achieved since it does not have six components in terms of both translation and orientation [5]. Therefore, the calibration method effectively reducing the pose errors of end effector is important.

Sensitivity analysis and error identification are necessary for the purpose of better kinematic

characteristics of parallel manipulators. The kinematic parameters with higher sensitivity should be found and controlled strictly. Aiming at optimizing a class of 3-DOF parallel manipulators with parallelogram struts, Huang established a statistical sensitivity model and showed quantificationally the effect of geometrical errors on the pose of end effectors [5]. Based on the sensitivity analysis, Alici optimized the dynamic equilibrium of a planar parallel manipulator [6]. Pott gave the sensitivity model by a simplified force-based method and validated the algorithm by examples of both serial and fully parallel manipulators [7].

In order to study the relations between sensitivity and geometric parameters, Binaud compared the sensitivity of five planar parallel manipulators of different architectures [8]. Therefore, estimating sensitivity of kinematic parameters and studying the priority of kinematic parameters with higher sensitivity can effectively improve the calibration of manipulators.

In the course of structure calibration, for formulating universal functions of errors between the measured and theoretical values, it is feasible to realize the static error compensation of a parallel manipulator by modifing the kinematic parameters based on the calibration model. According to the measuring instruments, calibration methods can be classified into three categories: constrained calibration method, auto-

*Corr. Author’s Address: College of Mechanical and Electrical Engineering, China University of Mining and Technology, 221008, Xuzhou, China, chg@cumt.edu.cn

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calibration or self-calibration method, external calibration method [9]. External calibration methods are based on measurements of the endeffector poses through an external device such as laser systems [10], theodolite [11], coordinate measuring machine [12] or camera systems [13]. Constrained calibration methods impose mechanical constraints on the manipulators during the calibration process through a locking device [14]. Auto-calibration or self-calibration methods rely on the measurements of the internal sensors of the manipulators. These methods have two possible approaches: the self-calibration method with redundant information [16] and [17] and the self-calibration method without redundant information [17] and [18]. Although the calibration of parallel manipulators had been study extensively and many novel methods of calibration had been presented, these studies merely focused on all kinematic parameters without sensitivity analysis. In practice, due to the impossible compensation fully of lowermobility parallel manipulator, it is critical to judge the priority of the kinematic parameters of these manipulators by their sensitivity coefficients.

This article is orginized in the following manner. In Section 1, the prototype of the parallel manipulator is described, and its corresponding error model is established based on the complete differential-coefficient matrix theory. Thereafter, the statistical model of sensitivity is studied by normalizing all error sources in the reachable workspace. In Section 2, considering the sensitivity of kinematic parameters, the calibration model and the corresponding algorithm is presented. In Section 3, the numerical simulations of sensitivity and calibration were analyzed respectively, and in the last section the paper is concluded with a number of conclusions.

0.1 Nomenclature ai Ai B 720

the fix points of the joints in the moving platform the fix points of the joints in the base the base

DO', DE

the orientation matrix of the moving platform and the the calibrated point on the end effector the third row of the orientation DO'3 matrix of the moving platform the orientation matrix consisting EW, EWS of the theoretical values and the measured values respectively the geometrical vector of the Exyz calibrated point ΔeEij the jth offset that need to be calibrated the error matrix of kinematic δER parameters δERi the ith error source in δER the error matrix of the end effector ΔESi the corresponding norm of the ΔES pose errors of the end effector the Jacobi matrix of calibration JR the Jacobi submatrix of calibration JRi the length of the equilateral LB triangle lines in the base ri (i=1,2,3) the lengths of the limbs are given as ri the length of the equilateral Lm triangle lines in the moving platform the length of the end effector LO'E which is perpendicular to the moving platform the moving platform m the absolute coordinate system O ˗ XYZ attached to the base the relative coordinate system O'˗X'Y'Z' attached to the moving platform the mapping between the pose TR errors of the end effector and the pose errors of the inputs TR6i the sixth row and the i-th column in TR the volume of workspace V xE, yE, zE the coordinates of the point E on the end effector The end point of the end effector E on the moving platform p (i=1,2,3) the components of principal vector i of rotation p referred to the body axes

Cheng, G. ‒ Gu, W. ‒ Yu, J. ‒ Tang, P.

Strojniški vestnik - Journal of Mechanical Engineering 57(2011)10, 719-729

q0, q1, q2, q3 the Unit Quaternion parameters Xq′, Yq′, Zq′ the quaternion representation of axes (X′,Y′,Z′) of m the quaternion representation of Xq, Yq, Zq axes (X,Y,Z) of B the ratio of the fix radiuses of the η base and the moving platform the vector OA , A a , O′a and OO′, i i i i OAi , Ai ai , respectively O ′ai , OO ′ the sensitivity coefficients of error τ Ri sources 1 SENSITIVITY MODEL 1.1 Quaternion Parameters In October 1843, William Rowan Hamilton formulated quaternions [18]. The quaternion parameters have several advantages over other orientation parameters as an attitude representation [19]. Quaternion is an appropriate tool for transformation of multiple orientations and control algorithms. The attitude representation based on direction-cosine matrix needs 9 parameters, and Euler angles needs 3 parameters. Compared to direction–cosine matrix, quaternion needs only 4 parameters and only has one constrained equation, while direction–cosine matrix has six constrained equations. Compared to Euler angles, quaternion does not degenerate at any point and avoids the problem of calculation singularity [18].

Quaternion can be represented as the sum of a scalar and a vector [18] and [19], composed

by Rodrigues-Hanmilton parameters (q0, qi, i = 1, 2, 3). By introducing abstract symbols k1, k2, k3 which are the imaginary unit of complex numbers and satisfying the rules k12 = k22 = k32 = k1k2k3 = −1, the analytical expression for Quaternion q is derived as below:

q = q0+q1k1+q2k2+q3k3 , (1a)

where 4 components q0, qi, (i =1, 2, 3) satisfy the constraint q02+q12+q22+q32 = 1.

The relative coordinate system O‒X′Y′Z′ on the moving platform m can coincide with the absolute coordinate system O‒XYZ by a rotation about the unit u (cosα1 cosα2 cosα3)T axis through an angle 2θu [20]. Quaternion q (q0, q1, q2, q3) corresponding to the transformation is defined by

the angle θu and the unit axis u. The orientation of m can be defined completely by the Euler parameters θu and αi, and it can also be defined completely by the Quaternion q (q0, q1, q2, q3).

The relationship between Euler parameters (θu, αi) and Rodrigues-Hamilton parameters can be expressed as follows: q0 = cosθu , q1 = sinθu · cosαi , (i=1, 2, 3). (1b) If the Quaternion Xq′= (0, X′), Yq′= (0, Y′), Zq′= (0, Z′), Xq= (0, X), Yq= (0, Y) and Zq= (0, Z), is associated respectively, with three-dimensional vectors (X′,Y′,Z′,X,Y,Z) and define the operation with the unit Quaternion q, as: X = q◦X'◦q‒1, Y = q◦Y’◦q‒1, Z = q◦Z’◦q‒1

(2)

where “◦” means Quaternion multiplication, and q-1 is the inverse Quaternion of q. Both of them satisfy q-1q = 1. Then this transformation, from Xq′ to Xq, from Yq′ to Yq, and from Zq′ to Zq, represents a rotation from O‒X′Y′Z′ to O‒XYZ. Therefore, the direction-cosine matrix based on Quaterinon parameters [21] can be written as:  2q02 + 2q12 − 1 2 ( q1q2 − q0 q3 ) 2 ( q1q3 + q0 q2 )  DO ' =  2 ( q1q2 + q0 q3 ) 2q02 + 2q22 − 1 2 ( q2 q3 − q0 q1 )  . (3)  2 ( q1q3 − q0 q2 ) 2 ( q0 q1 + q2 q3 ) 2q02 + 2q32 − 1   

1.2 System Description The symmetrical parallel manipulator consist of a fixed base, a moving platform and three identical limbs, and its topological structure is described in Fig. 1. O-XYZ is the absolute coordinate system attached to the fixed base, while O-X′Y′Z′ is the relative coordinate system attached to the moving platform. The equilateral triangle lines of the moving platform and the fixed base are denoted as Laiaj and LAiAj (i, j = 1, 2, 3; i ≠ j), respectively, while their corresponding length is denoted as Lm and LB, respectively.

Each limb connects the moving platform to the base by a universal joint (U) at ai, followed by a cylindrical joint (C) and a revolute joint (R) at Ai, where the cylindrical joint is driven by a ball screw linear actuator. The installation form of these joints provides the manipulator with 3 DOF, one translational motion along the Z-axis and two rotational motion about X-axis and

Overall Structure Calibration of 3-UCR Parallel Manipulator Based on Quaternion Method

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Y-axis, respectively. The ri (i=1, 2, 3) stands for the lengths of the three limbs. The end effector is assumed to be perpendicular to the moving platform at point O′, and its length is denoted as LO'E.

riδ e ri + δ ri e ri − δ OE − O ′aiO′δ DO′ −

(5)

−DO′δ O ′aiO′ + LO′E δ DO′3 + DO′3δ LO′E + δ OAi = 0.

T

T

Due to e ri e ri = 1 and e ri δ e ri = 0 , left T multiplied by e ri , the Eq. (5) can be simplified as

Eq. (6), where δri and δ OE equal to [δr1 δr2 δr3] and [δxE δyE δzE]T, respectively.

T e ri DO′ and DO′ O ′aiO′ equal to [TDI1 TDI2 TDI3]

and [TI1 TI2 TI3]T, respectively, where e ri denotes the corresponding unified vector of the drive limbs:

T T

T

δ ri − e ri δ OE − e ri δ DO′ O′aiO′ − e ri DO′δ O ′aiO′ +

(6) T

T

T +e ri LO′E δ DO′3 + e ri DO ′3δ LO ′E + e ri δ OAi = 0.

Ti1δxE+Ti1δxE+Ti1δxE+ +Ti1δxE+Ti1δxE+Ti1δxE = 0, i = 1, 2, 3.

.

Fig. 1. Symmetrical parallel bionic robot leg with three UCR limbs 1.3 Error Model OAiaiO'O and OO'EO in the 3-UCR parallel manipulator are considered as the closedloop kinematic chains, and the following equation can express the spatial vector of the drive limbs.

Ai ai = OE + DO′ O′aiO′ − DO′3 LO′E − OAi ,

(4)

where the vectors of O ′aiO′ and O ′EO′ with reference to the relative coordinate system can

be denoted as O ′ai and O ′EO′ , respectively. The orientation matrix of the moving platform can be denoted as DO' and DO'3 denotes the third row of it.

The vector of O ′E can be described by [0 0 LO'E]T by analyzing its spatial relation.

In the process of error transmission, the nominal numbers are different to the effective displacements of the structure parts. By complete differential calculation to the outputs of the parallel manipulator, the error effects can be fully studied, and Eq. (4) can be expressed as follows: 722

(7)

Substituting the above expressions into Eq. (6), the equation can be rearranged.

In order to solve the six output parameters, a system of six equations should be founded.

From Eq. (7), other three simultaneous equations are required. According to the kinematic model based on Quaternions parameters of the parallel manipulator conducted in previous section, three corresponding equations are obtained as follows:

xE = − yE =

Lm 2 3

2 Lm 3

q1q2 + 2q0 q2 LO′E ,

( −1 − 2q

2 1

(8)

+ 4q22 ) − 2q0 q1 LO′E , (9)

q3 = 0,

(10)

where xE and yE denote the coordinates of the point E on the end effector.

By substituting q0 = q12 + q22 + q32 into Eqs. (8), (9) and (10), the corresponding complete differential forms of the three equations can be rearranged as follows:

Ti1δ xE + Ti 2δ yE + Ti 3δ z E + +Ti 4δ q1 + Ti 5δ q2 + Ti 6δ q3 = 0, i = 4, 5, 6.

(11)

Eqs. (7) and (11) can be rearrangeed in matrix form:

Cheng, G. ‒ Gu, W. ‒ Yu, J. ‒ Tang, P.

Strojniški vestnik - Journal of Mechanical Engineering 57(2011)10, 719-729

T11 T  21 T31 T  41 T51  T61

T12 T22 T32 T42 T52 T62

T13 T23 T33 T43 T53 T63

T14 T24 T34 T44 T54 T64

T15 T16  δ xE  T17  T25 T26  δ yE  T277  T35 T36  δ z E  T37    =   = T26×23 δ E R , (12) T45 T46   δ q1  T47  T55 T56   δ q2  T57      T65 T66   δ q3  T67 

where δER denotes the error matrix of kinematic parameters, and can be expressed as follows: δ E R = [δ LO′E , δ Lm , δ r1 , δ LO′a1 x , δ LO′a1 y , δ LO′a1 z ,

δ LOA1 x , δ LOA1 y , δ LOA1 z , δ r2 , δ LO′a2 x , δ LO′a2 y , δ LO′a2 z , δ LOA2 x , δ LOA2 y , δ LOA2 z , δ r3 , δ LO′a3 x ,

(13)

δ LO′a3 y , δ LO′a3 z , δ LOA3 x , δ LOA3 y , δ LOA3 z ]1T×23 ,

where δLO'E and δLm denote the length error of the end effector and the triangle line error on the moving platform, respectively. δri represents the length errors of the drive limbs. δ LO′ai x , δ LO′ai y and δ LO′ai z denote the coordinate errors of the connectors on the m. Note that these errors are referenced to the absolute coordinate system.

Similarly, the coordinate errors of the connectors on the B are represented by δ LOAi x , δ LOAi y and δ LOAi z .

The error model of the parallel manipulator describing the relations between errors of kinematic parameters and output parameters can be obtained by the above equations.

1.4 Sensitivity Model

δES = TR δER ,

D(δES) = E(δES2) .

(15)

Rearranging the Eq. (14) gives: δ E S 2 = δ ETR TRT TRδ E R = 

23

=  ∑ δ ERiTR1i  i =1

 23   ∑ TR1iδ ERi  i =1   , (16)

∑ δ ERiTR 6i    i =1 1×6  23  ∑ TR 6iδ ERi   i =1  6×1 23

where the ith error source in δER is denoted as δERi, the element in the sixth row and ith column of TR is denoted as TR6i. Assuming that the elements in δER are independent statistically, we get:

23

6

δ E S 2 = ∑ ∑ TRji 2δ E Ri 2 .

(17)

i =1 j =1

Through the establishment of the probability model of the parallel manipulator, the effects on the pose of the end effector caused by the geometrical errors of manufacture and assembly can be studied statistically. According to the error model of the manipulator, Eq. (12) is rewritten as:

sources in the parallel manipulator, it should be assumed that all elements in δER are independent statistically and the mean of the elements equals zero. According to the error transmission matrix, the mathematical expectation of δES is zero.

Therefore, the corresponding variance of δES can be derived as follows:

(14)

where TR representing the mapping between the pose errors of the end effector and the pose errors of the inputs which denoted as δES equals to T-1T2.

In order to characterize the standard deviations of the pose errors of the end effector caused by the unified standard deviations of error

Substituting Eq. (17) into Eq. (15), the following equation is derived:

23

6

D (δ E S ) = ∑ ∑ TRji 2 E (δ E Ri 2 ).

(18)

i =1 j =1

Therefore, relations between standard deviations of δER and δES can be formulated as follows:

σ (δ E S ) =

23

6

∑ ∑T i =1 j =1

Rji

σ (δ E Ri 2 ).

2

(19)

From the above mathematical analysis, the different poses of the end effector result in

Overall Structure Calibration of 3-UCR Parallel Manipulator Based on Quaternion Method

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the change of the pose errors of outputs. In order to describe fully the standard deviations of δER and δES, the estimation standard in the whole workspace between them should be established.

Suppose that the volume of the workspace is V, it follows [22]:

τ Ri = ∫

V

6

∑T j =1

Rji

2

dv.

(20)

The above equation can describe all error sources of the parallel manipulator in its workspace, however, it cannot achieve the further sensitivity analysis under the case of specific error compensation and identification. Therefore, a novel statistical model of sensitivity coefficients, to implement the unified process on the above error sources in the workspace is presented as:

τ Ri =

τ Ri

.

23

∑τ i =1

(21)

Ri

−1 ∆E R = ( J TR J R ) J TR  ∆E S . (23)  

Implementing the Eq. (23) gives the iterative value compensating the matrix ER in the course of the kinematic calibration. The kinematic parameters can be calibrated by modifying the iterative value till the errors are less than the terminating value defined in advance. From Eq. (23), the matrix of the pose errors and the Jacobi matrix of calibration is needed to solve the iterative value. The corresponding procedures to obtain the matrices are shown as follows.

2.2 Analysis of the Pose Errors Matrix Four groups of the pose of the end effector can be synthesized as the same expression. In order to describe the pose of the end effector, formulating the orientation matrix gives: D E EW =  E xyz  , (24)  0 1 

2 STRUCTURE CALIBRATION 2.1 Calibration Model of Kinematic Parameters The mechanical structure of the parallel manipulator is assembled and the kinematic parameters can be identified by the calibration of kinematic parameters. In order to achieve the static mathematical compensation of the manipulator, it is necessary to modify the control model of kinematics according to the identified error parameters.

The pose of the end effector consists of three position parameters and three orientation parameters. In order to solve 23 kinematic parameters in δER, it is necessary to measure four groups of the pose by the testing instruments of the end effector in every calibration. According to the kinematic model and its differential form of the parallel manipulator, Eq. (22) can be obtained: T

∆E S =  ∆ETS 1 ∆ETS 2 ∆ETS 3 ∆ETS 4  = J R ∆E R , (22) where ΔESi = [ΔxE, ΔyE, ΔzE, Δq1, Δq2, Δq3]T,, i = 1, 2, 3, 4. A group of the pose error of the end effector is represented as ΔESi. JR, a matrix of 24 rows and 23 columns, denotes the Jacobi matrix of calibration. The Eq. (22) can be changed as: 724

where DE and Exyz denote the orientation matrix of the calibrated point and the geometrical vector of the calibrated point, respectively.

By calculating the orientation matrices based on the measured values and the theoretical values, the matrix of the pose errors is derived as the following equation:

∆D ∆E xyz  (25) ∆EW = EW−1 ( EWS − EW ) =  E , 1   0

where EW and EWS denote the theoretical values solved by the kinematic model and the measured values, respectively. Herein, ΔExyz equals to [ΔxE ΔyE ΔzE]T. The error of the orientation matrix ΔDE can be expressed as:

 0 ∆D E =  ∆DE 21  ∆DE 31

∆DE12 0 ∆DE 32

∆DE13  ∆DE 23  , 0 

(26)

where the expressions of elements in the matrix are the same as the above orientation matrix in the error model.

According to the relations between the elements of the error of the orientation matrix and the Quaternions parameters, the errors of the corresponding Quaternions parameters can be

Cheng, G. ‒ Gu, W. ‒ Yu, J. ‒ Tang, P.

Strojniški vestnik - Journal of Mechanical Engineering 57(2011)10, 719-729

obtained. The solutions of the matrix ΔESi can be achieved by substituting the errors of the pose and the Quaternions parameters into Eq. (22).

2.3 Analysis of Calibration Jacobi Matrix Similar to the analysis of the pose errors, the Jacobi matrix of calibration consists of four submatrices denoted as JRi. Because of the same expressions of the submatrices, the analysis of the Jacobi matrix of calibration can be simplified as the analysis of one submatrix, that is:

J Rij =

∂E S , j = 1, 2,..., 23. ∂E Rij

(27)

According to the analysis of the error sensitivity, different error sources of kinematic parameters with the same error values have a different effect on the pose error of the end effector. It is essential to redefine the offset denoted as ΔeRij in JRij based on the sensitivity coefficients of the errors for calibrating better the end effector. And the offset can be written as:

∆eRij =

∆eEij

τ Ri

,

 ∆x ∆yE ∆z E ∆q1 ∆q2 ∆q3  J Rij =  E  . (29)  ∆eRij ∆eRij ∆eRij ∆eRij ∆eRij ∆eRij  Algorithm

3.1 Sensitivity Simulation Six groups of theoretical values and error values of the parallel manipulator are defined in Table 1.

Substituting the theoretical values into the kinematic model, the corresponding positionorientations of the end effector are obtained and shown in Table 2.

According to the statistical model of sensitivity coefficients, the pose errors of the end effector caused by the errors of kinematic parameters in the whole workspace can be calculated respectively. Normalizing the results of the above process gives the sensitivity percentages of twenty-three kinematic parameter errors in Eq. (13) shown as Fig. 3.

(28)

where ΔeEij denotes the jth offset that need to be calibrated.

By the derivation of the offsets, the Jacobi matrix of calibration can be derived as:

2.4 Calibration Parameters

3 NUMERICAL SIMULATION

of

Kinematic

Measuring the practical lengths of the drive limbs and the corresponding pose of the end effector and calculating the theoretical values of the end effector, the kinematic parameters of every joint can be calibrated based on the successive approximation algorithm. The procedures of the calibration algorithm of the manipulator are shown in Fig. 2.

Fig. 2. Calibration algorithm of the kinematic parameters of the parallel manipulator From Fig. 3 it is known that the kinematic parameters with symmetrical connectors, such as A2, a2, A3 and a3, have a similar effect on the pose errors of the end effector and the result validates the sensitivity model by the structure characteristics. Comparatively, greater sensitivity percentages of the drive limbs represent that the actuator errors have more effect on the pose errors of the end effector. Due to the errors of some kinematic parameters, having the greater sensitivity percentages, it is essential to control the length errors between the origin in the absolute coordinate system and the joint connectors on the base, especially the errors along Z-axis perpendicular to the base. However, the length errors between the origin in the relative coordinate

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system and the joint connectors on the moving platform and the errors of the end effector have less sensitivity percentages. Therefore, with the promise to guarantee the whole precision of the manipulator, it is feasible to adjust the manufacture and assembly tolerance of mechanical parts by the sensitivity percentages.

The symbol η denotes the structure scales which is the ratio of the fix radiuses of the base

and the moving platform. The variation of the sensitivity percentage of the kinematic parameters with different structure scales are given in Fig. 4.

Fig. 4 shows that, with the variation of the structure scale, the sensitivity percentages of kinematic parameters have not been changed obviously in corresponding reachable workspaces.

On the other hand, it is necessary to strictly control the kinematic parameters with different structure

Table 1. Theoretical values and error values of the parallel manipulator Error value [mm]

r3

Theoretical value [mm] Six groups in the following table Six groups in the following table Six groups in the following table

LO'E

Title

Title

Theoretical value [mm]

Error value [mm]

0.02

δ LO′ai x

a1 : 0; a2 : 25 3; a3 : −25 3

0.05

0.02

δ LO′ai y

a1 : 50; a2 : ‒25; a3 : −25

0.05

0.02

δ LO′ai z

a1 : za1 ; a2 : za2 ; a3 : za3

0.05

220

0.08

LOAi x

A1 : 0; A2 : 34 3; A3 : −34 3

0.05

LB

68 3

0.08

LOAi x

A1 : 68; A2 : −34; A3 : −34

0.05

Lm

50 3

0.08

LOAi x

A1 : 0; A2 : 0; A3 : 0

0.05

r1 r2

Table 2. Theoretic values of limbs’ lengths and output parameters Group 1 2 3 4 5 6

r1 [mm] 300.042 289.905 287.356 296.341 346.459 376.653

r2 [mm] 265.307 269.18 273.15 264.903 308.792 283.193

r3 [mm] 349.770 350.913 350.147 350.822 263.091 270.914

xE [mm] yE [mm] zE [mm] 219.956 24 304.4 207.073 58.349 377 195.375 72.150 392.4 220.12 33.807 333 -116.446 -169.831 395.7 -28.924 -251.544 357.2

q0 0.714 0.823 0.843 0.758 0.847 0.794

Fig. 3. Sensitivity percentages of kinematic parameters 726

Cheng, G. ‒ Gu, W. ‒ Yu, J. ‒ Tang, P.

q1 0 -0.15 -0.20 -0.05 0.40 0.60

q2 0.7 0.55 0.50 0.65 -0.35 -0.10

q3 0 0 0 0 0 0

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Fig. 4. Sensitivity percentage of kinematic parameters with different structure scales Table 3. Poses of the end effector with four groups of limbs Group 1 2 3 4

Length of drive limbs [mm] r1 r2 r3 314.292 262.268 335.145 320.946 264.256 330.823 339.239 262.179 315.004 349.929 263.507 306.072

Pose of the end effector [mm mm mm / / /] [xE, yE, zE, q1, q2, q3] [192.582, -49.6373, 369.397, 0.154879, 0.564173, 0] [184.582, -77.5489, 323.506, 0.264831, 0.613548, 0] [137.102, -146.751, 388.413, 0.359163, 0.412386, 0] [107.704, -180.687, 394.056, 0.423459, 0.326984, 0]

scales having greater sensitivity percentages.

3.2 Calibration Simulation For validating the calibration algorithm of kinematic parameters, the iterative calculation of the given kinematic parameters by the numerical simulation is given as follows. The kinematic parameters are shown in Table 1, and the corresponding errors of these parameters are presented in ΔER: ∆E R = [−0.1, 0.1, 0.05, 0.08, −0.08, −0.08,

0.08, 0.08, −0.08, −0.05, 0.08, 0.08, −0.08,

−0.08, 0.08, −0.08, 0.05, −0.08, −0.08, 0.08, −0.08, 0.08, 0.08]1T×23 ,

where the errors of kinematic parameters ΔER correspond to Eq. (13).

Substituting four groups of the kinematic parameters into the kinematic model of the manipulator, the corresponding poses of the end effector are shown in Table 3.

Taking the lengths of the drive limbs, the poses of the end effector in Table 3 and the values of the kinematic parameters in Table 1 into the kinematic calibration program of the parallel manipulator and calculating iteratively 7 times, the modified matrix of kinematic parameters is obtained. ΔES denotes the corresponding norm of the pose errors of the end effector, it is less than the terminating value, defined as 0.01, which has no unit because of having no uniform unit in ΔES. After modifying 7 times, the values of the kinematic parameters converge gradually to the truth values which are the sums of the theoretical values and the given errors of the kinematic parameters in the numerical simulation.

The terminating time in the calibration program is decided by the absolute difference of the truth values and the modified kinematic parameters. For the purpose of representing the change of kinematic parameters, the changes of uncalibrated kinematic parameters and calibrated kinematic parameters are shown in Fig. 5.

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Fig. 5. Comparison of the uncalibrated kinematic parameters and calibrated kinematic parameters Fig. 5 shows that most errors of calibrated kinematic parameters are decreasing greatly, especially the kinematic parameters with high sensitivity percentage, and the successive approximation algorithm based on the statistical sensitivity coefficients is validated. Because of the lower-mobility parallel manipulator, the errors of kinematic parameters caused by uncontrolled degree-of-freedom cannot be compensated completely. Most errors of kinematic parameters are less than the terminating value. On the contrary, due to the equilibration effect of the least squares method, some errors of calibrated kinematic parameters, such as δ LO′a3 x and δ LOA z , 3 are increasing. In the course of calibration of kinematic parameters, the sensitivity coefficients and calibrated kinematic parameters with increasing errors have always lower sensitivity percentages partly decide the iterative value.

The significance of the sensitivity conversion is emphasized by effectively decreasing the errors of kinematic parameters with higher sensitivity percentages. From the comparison in Fig. 5, the calibration algorithm has relatively fast convergence and concrete directivity when optimizing iteratively and is effective to study the calibration questions.

4 CONCLUSIONS In this study, by the complete differentialcoefficient matrix theory, the error model of the parallel manipulator was established. Then, the statistical model of sensitivity was derived by normalizing all error sources in the reachable 728

workspace. According to the results of sensitivity simulation, the sensitivity percentages of the kinematic parameters vared slightly with the variation of the structure scales. The kinematic parameters with higher sensitivity percentages which should be controlled strictly were distinguished. In the course of manufacture and assembly, decreasing the length errors between the origin in the relative coordinate system and the joint connectors on the base is essential, especially the error decrease along Z-axis perpendicular to the base.

Based on the successive approximation algorithm, the calibration model with sensitivity conversion was established. According to the corresponding simulation, the algorithm is effective to study the calibration question by comparing the values of every kinematic error and has relatively fast convergence when optimizing iteratively. With the conversion according to analytical results of sensitivity coefficients, the operation steps have concrete directivity.

The approach of the calibration proposed in this article can be applied to structure calibration not only of less-DOF but also of sixDOF parallel manipulators. When it is applied to the six-DOF parallel manipulator, all source errors according to six limbs should be considered, and the dimensions of corresponding matrices such as △ER, TR and T2 would change accordingly, but the main analysis steps are the same as the application to the less-DOF parallel manipulators.

5 ACKNOWLEDGEMENTS This research is supported by the National Natural Science Foundation of China (Grant No. 50905180) and the youth foundation of China University of Mining and Technology (Grant No. OE090191).

6 REFERENCES [1] Hunt, K.H. (1978). Kinematic geometry of mechanisms. Clarendon Press, Oxford, New York,.

[2] Ryu, D., Song, J.B., Cho, C., Kang Kim, S.M. (2010). Development of a six DOF haptic master for teleoperation of a mobile

Cheng, G. ‒ Gu, W. ‒ Yu, J. ‒ Tang, P.

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manipulator. Mechatronics, vol. 20, p. 181191.

[3] Ropponen, T., Arai, T. (1995). Accuracy analysis of a modified Stewart platform manipulator. IEEE International Conference on Robotics and Automation, vol. 1, p. 521525.

[4] Wang, J., Masory, O. (1993). On the accuracy of a Stewart platform-Part I: The effect of manufacturing tolerances. IEEE International Conference on Robotics and Automation, vol.

1, p. 114-120.

[5] Huang, T., Li, Y., Tang, G., Li, S., Zhao, X. (2002). Error modeling, sensitivity analysis and assembly process of a class of 3-DOF parallel kinematic machines with parallelogram struts. Science in China: Series E, vol. 45, no. 5, p. 467-476.

[6] Alici, G., Shirinzadeh, B. (2006). Optimum dynamic balancing of planar parallel manipulators based on sensitivity analysis.

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1520-1532.

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A simplified force-based method for the linearization and sensitivity analysis of complex manipulation systems. Mechanism and Machine Theory, vol. 42, p. 1445-1461.

[8] Binaud, N. (2010). Sensitivity comparison of planar parallel manipulators. Mechanism and Machine Theory, vol. 45, no. 11, p. 14771490.

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Calibration and Checking the Geometrical Accuracy of a CNC Machine-Tool. Strojniški vestnik - Journal of Mechanical Engineering, vol. 52, no. 11, p. 752-762.

[11] Zhuang, H., Masory, O., Yan, J. (1995).

Kinematic calibration of a stewart platform using pose measurement obtained by a single theodolite. IEEE International Conference on Intelligent Robots and Systems, p. 329-334.

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781-787.

[14] Khalil, W., Besnard, S. (1999). Self calibration of Stewart-Gough parallel robot without extra sensors. IEEE Trans. on Robotics and Automation, vol. 15, no. 6, p. 1116-1121.

[15] Chiu, Y., Perng, M. (2004). Self-calibration of a general hexapod manipulator with enhanced precision in 5-DOF motions. Mechanism and Machine Theory, vol. 39, p. 1-23.

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Kinematics and workspace analysis of a parallel wire mechanism for measuring a robot pose. Mechanism and Machine Theory, vol. 34, p. 825-841.

[17] Chiu, Y., J., Perng, M.H. (2003). Selfcalibration of a general hexapod manipulator using cylinder constraints. International Journal of Machine Tools & Manufacture, vol. 43, p. 1051-1066.

[18] Hart, J.C., Francis, G.K., Kauffman, L.H. (1994). Visualizing quaternion rotation. ACM Transactions on Graphics, vol. 13, no. 3, p.

256-276.

[19] Senan, N.A.F., O’Reilly, O.M. (2009). On the use of quaternions and Euler–Rodrigues symmetric parameters with moments and moment potentials. International Journal of Engineering Science, vol. 47, no. 4, p. 599609.

[20] Arribas, M., Elipe, A., Palacios, M. (2006).

Quaternion and the rotation of a rigid body. Celestial Mechanics and Dynamical Astronomy, vol. 96, no. 3-4, p. 239-251.

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224-232.

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Strojniški vestnik - Journal of Mechanical Engineering 57(2011)10, 730-738 DOI:10.5545/sv-jme.2010.075

Paper received: 09.04.2010 Paper accepted: 23.06.2011

Optimal Control of Workpiece Thermal State in Creep-Feed Grinding Using Inverse Heat Conduction Analysis Gostimirović, M. – Sekulić, M – Kopač, J. – Kovač, P. Marin Gostimirović1,* – Milenko Sekulić1 – Janez Kopač2 – Pavel Kovač1 1 University of Novi Sad, Faculty of Technical Science, Serbia 2 University of Ljubljana, Faculty of Mechanical Engineering, Slovenia

Due to intensive friction between grinding particles and workpiece material, a substantial quantity of thermal energy develops during grinding. Efficient determination of real heat loading in the surface layer of the workpiece material in grinding largely depends on the reliability of basic principles of distribution of heat sources and the character of the temperature field within the cutting zone. Therefore, this paper takes a different approach towards the identification of the thermal state of the creep-feed grinding process by using the inverse problem to approximate heat conduction. Based on a temperature measured at any point within a workpiece, this experimental and analytical method allows the determination of a complete temperature field in the workpiece surface layer as well as the unknown heat flux on the wheel/ workpiece interface. In order to solve the inverse heat conduction problem, a numerical method using finite differences in implicit form was used.

When the inverse heat conduction problem is transformed into an extreme case, the optimization of heat flux leads to an allowed heat loading in the surface layer of workpiece material during grinding. Given the state function and quality criterion, the control of workpiece heat loading allows the determination of optimal creep-feed grinding conditions for particular machining conditions. ©2011 Journal of Mechanical Engineering. All rights reserved.

Keywords: creep-feed grinding, head loading, inverse problem, optimal control 0 INTRODUCTION Grinding is considered as one of the most important machining methods. In addition to the conventional fine multi-pass grinding, there has been a recent introduction of high-productivity grinding methods. These high-productivity methods use higher cutting speeds and/or larger cutting depths in order to increase the relatively low productivity which has traditionally been considered the main drawback of conventional grinding. However, the increase of grinding conditions considerably changes the grinding kinematics, i.e. the conditions in the wheel/ workpiece interface [1].

High-speed grinding is characterized by lower cutting depths and shorter time of contact between the workpiece material and grinding particles, with a more intensive friction in the cutting zone. The increased contribution of friction in the generation of the total quantity of thermal energy also increases the contact temperature.

The potential decrease of contact temperature during extremely high-speed machining can be 730

attributed to a reduced cross-section of chip and faster introduction of the next grinding particle into the wheel/worpiece interface [2]. This improves cutting conditions because of reduced friction and deformation during chip forming due to interfacing between the grinding particles and the softened material layer generated by previous grinding.

In creep-feed grinding, which is characterized by large cutting depths and small workpiece speeds, there is a longer wheel/ workpiece interface as well as a prolonged time of contact with workpiece material. At the same time, this results in the generation of more intensive heat sources in grinding particles and a prolonged time of their effect. In addition, a longer interface contributes to a better evacuation of heat from the cutting zone, which results in a decreased power of heat source per unit area [3] and [4]. Also, a small workpiece speed improves the distribution of total thermal energy within the cutting zone due to its prolonged effect. All this results in an increased total quantity of thermal energy per unit area but over a longer time period.

*Corr. Author’s Address: University of Novi Sad, Faculty of Technical Science, Trg D. Obradovica 6, 21000 Novi Sad, Serbia, maring@uns.ac.rs

Strojniški vestnik - Journal of Mechanical Engineering 57(2011)10, 730-738

Based on the previous discussion, it is evident that high-productivity grinding methods cause the development of large quantities of thermal energy within the cutting zone [5].

The generated thermal energy, located within a relatively narrow area of the cutting zone, causes high cutting temperatures in creep-feed grinding.

These increased temperatures instantaneously burst to a maximum, have short duration and exert a pronounced negative effect on wheel surface, workpiece quality and accuracy.

Since the main task of grinding is to achieve satisfactory part quality with as large productivity as possible, special attention is focused on the effect that grinding temperatures have on the change of material properties in the workpiece surface layer. If the temperatures thus generated are high enough to cause structural and phase transformations of the workpiece material, the machined surface shall suffer from a number of disadvantages. Should, in addition, dimensional errors appear as well, the overall effect can substantially diminish exploitation features of the finished part.

Efficient control of thermal phenomena in grinding, i.e. the determination of allowed heat loading on workpiece surface layer, requires knowledge of heat development and distribution in grinding, the temperature field in the cutting zone and, finally, the influence of cutting conditions on grinding temperature [6]. For that reason, identification of the thermal state in grinding based on analytical models and experimental results has been gaining popularity.

As the research so far has shown, nonstationary and non-linear technical processes involving intensive heat conduction, such as creep-feed grinding, can be successfully solved using a novel approach based on inverse problem of heat transfer [7]. The inverse problem of heat transfer allows the closest possible experimentalmodel approximation of thermal regimes for grinding.

In the case of control over the grinding thermal regime, the extreme case of the inverse problem of heat conduction [8] is practically the only way to reliably approximate the allowed heat loading on the workpiece surface layer. For a known temperature measured at a point within the workpiece surface layer, numerical methods are

used to approximate the total temperature field of the surface layer as well as the unknown heat flux density on the wheel/workpiece interface [9] and [10]. For the selected quality criteria, particular machining conditions, and a predetermined loading on the workpiece surface layer, it is possible to arrive at optimal cutting conditions in creep-feed grinding by controlling the heat flux.

1 PARAMETERS OF GRINDING HEAT SOURCE The role of mathematical theory behind thermal phenomena in grinding is to adopt the most adequate model of the workpiece, grinding wheel and their inter-relationships, Fig. 1. It can be assumed that the elementary heat source on the grinding particle is the result of friction between the grinding particle, workpiece and chip in the workpiece material shear plane. Summing up all the heat sources, i.e. grinding particles in contact with the workpiece, gives the total heat source for the entire cutting zone, qT. This total heat source, whose strength varies within a narrow range, acts continuously, shifting across the workpiece surface with constant velocity [5] and [6].

Fig. 1. Model of thermal state in creep-feed grinding The heat source in grinding is characterized by its power and length of activity. Magnitudes of these two parameters depend on the machining process, wherein cutting conditions have the predominant influence.

Heat source power in the cutting zone is the basic source parameter since it predominantly impacts the thermal state of the workpiece surface layer. An analytical definition of heat source power starts from the fact that in grinding the total

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mechanical work applied to the cutting process is transformed into thermal energy: QT = Ft ⋅ vc ⋅ te , ,

qT =

QT

∫∫ dxdy ∫ dt Ac

=

Ft ⋅ vc . (2) Ac

te

If, in Eq. (2), the wheel/workpiece interface is decomposed into Ac = lc × bc = (a × Ds)1/2 × bc, and the tangential grinding force is reduced to a unit grinding width bc, that is, we introduce the specific tangential grinding force F’t = Ft / bc, then: F ′⋅ v

qT = t c . (3) a ⋅ Ds On the other hand, the specific tangential grinding force can be expressed by a general Eq.:

Ft′ = k sm ⋅ hm , (4)

where hm = vw × a/vc is the mean cutting depth, and ksm is the mean specific cutting force.

The final form for total heat flux density as a function of the grinding conditions can be derived by substituting Eq. (4) in Eq. (3):

qT = k sm ⋅ vw

a . (5) Ds

On the other hand, the total active time interval of the heat source has a prominent influence on the heat quantity being evacuated from the cutting zone into the workpiece. The shorter active time of the heat source diminishes the heat quantity transferred via the wheel/ workpiece interface into the workpiece surface layer, while at the same time allowing a faster supply of coolant onto the freshly ground surface.

This time interval is expressed as the ratio between the interface length lc and workpiece velocity vw, that is:

732

tT =

(1)

where Ft is the tangential grinding force, vc is the cutting speed, and te is the time of contact between the grinding particles and workpiece.

The total heat quantity, Eq. (1), is transformed into heat flux density:

a ⋅ Ds vw

. (6)

2 INVERSE PROBLEM OF THE GRINDING PROCESS The process of heat transfer between solid bodies or between a system and its environment, of which heat conduction in grinding is also a part, is mostly considered from the standpoint of mutual relations between the input and output process parameters.

If the input parameters u(t) are known and the output parameters z(t) define the process state in time, then the output parameters are a function of the input parameters, i.e.:

z = f (u, t). (7)

If, for the adopted thermal model, there exist unique conditions, then the determination of the input-output relationship is the direct task of heat conduction. Conversely, the inverse heat conduction solves the problem of finding the input characteristics of the process for the known temperature field [7].

If for every unknown parameter u there is a linear, smooth operator A which allows the determination of the output parameter z, then the general case of the inverse problem is formulated by the following Eq.:

A×u = z .

(8)

2.1 Case of the Inverse Problem in Grinding In grinding, considering that the cutting depth is many times smaller than the length and width of the wheel/workpiece interface, the heat source can be treated as a strip of infinite length and constant heat distribution. Furthermore, if the dissipation of heat flow in the direction of heat source movement is disregarded, then the workpiece can be approximated with a series of adiabatic thin plates, Fig. 2.

Substitution of the real workpiece with the semi-infinite plate is completely justified, bearing in mind that the heat source in grinding is generated within a small volume of workpiece material while the heat loading of the surface workpiece layer is considered depth-wise.

Gostimirović, M. – Sekulić, M – Kopač, J. – Kovač, P.

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−λ (θ ( x, t ) )

∂θ ( x, t ) ∂x

= q (t ), (12) x=H

and unknown heat flux density:

Fig. 2. Schematic of a uni-dimensional inverse problem in grinding For such a defined thermal model of grinding, the following is the differential equation of a one-dimensional heat conduction, for x∈ (0,H) and t∈ (0,tm]:

∂θ ∂  ∂θ  = , (9) λ (θ ) ∂ t ∂ x  ∂ x  where θ = θ(x,t) is the workpiece temperature at point coordinate x at moment t, λ = λ(θ) is the heat transfer coefficient, ρc = C(θ) is the specific heat capacity (ρ - material density, c - specific heat), H is the thickness of the surface layer of workpiece material, and tm is the largest time increment.

Now the analytical form of the inverse problem of heat conduction for surface grinding can be described with Eq. (9), in conjunction with initial conditions, additional conditions and boundary conditions.

The initial temperature distribution in the workpiece for the initial moment t = 0 is:

ρ c(θ )

θ ( x, t ) t =0 = φ ( x). (10)

An additional condition is the fact that at the point x = K(0 < K < H), there is a known temperature, measured during a time interval:

θ ( x, t ) x = H = ξ (t ). (11)

Boundaries of the considered workpiece surface layer are defined by the known heat flux density:

−λ (θ ( x, t ) )

∂θ ( x, t ) ∂x

= q (t ). (13) x =0

The final solution of the inverse problem is the heat flux density on wheel/workpiece interface q(t) (part of total heat flux density [3]), and the temperature field θ = θ(x,t) throughout the elementary parts of the workpiece, D = {(x,t): x∈[0,H], t∈[0,tm]}.

Due to their complexity, differential equations, which describe the process of heat conduction in grinding, are mostly solved using numerical methods. The first step with every numerical method is the discretization of space, i.e. the approximation of a thin, isolated plate of the workpiece by a number of elementary pieces Δx, Fig. 3. When dealing with a non-stationary -heat conduction problem, the time of temperature change and heat flux is discretized by a Δt increment.

Fig. 3. The shape of a uni-dimensional mesh of heat conduction inverse problem To solve the partial differential equation shown in Eq. (9) an implicit form of the finite differences method was chosen [8]. A system of linear algebraic equations is used to calculate the unknown heat flux qn+1 on workpiece surface and the temperature field of the workpiece surface layer θhn+1 (h = 0, 1, ..., K–1, K+1, ..., H) as follows: [R]·{Θ} = {B}. (14)

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Solving the matrix system shown in Eq. (14) requires the initial task to be divided into two parts.

First, a standalone system is calculated: [R2]·{Θ2} = {B2}. (15) The matrix Eq. (15) is solved as the direct task of heat conduction within the area D2 = {(x,t): x∈[K,H], t∈[0,tm]}. The solution yields the unknown temperatures θhn+1 (K+1, ..., H).

Once vector Θ2 is determined, the problem of inverse heat conduction in the area of D1 = {(x,t): x∈[0,K], t∈[0,tm]} can be tackled by using the system:

temperatures, an iterative method of optimization is used.

J(qi) is calculated by applying the iterative optimization algorithm for particular values of functional qi(t). The procedure is repeated, decreasing the value of the functional J(qi+1) < J(qi), until its minimum is reached. The iterative gradient method procedure is considered finished for a sufficiently small functional, which means that the calculated vector components and the measured temperatures are very close.

3 EXPERIMENTATION

[R1]·{Θ1} = {B1}. (16)

3.1 Experimental Setup

From the system shown in Eq. (16), starting from the first unknown temperature θ Kn+−11 , vector Θ1 is calculated. This vector represents the unknown heat flux qn+1 and the unknown temperature θhn+1 (h = 0, ..., K–1).

The experimental work was carried out on a surface creep-feed grinding machine »Majevica« type CF 412 CNC.

2.2 Extreme Case of the Grinding Inverse Problem One of the possible ways to solve the inverse problem is to transform it into an extreme case using some method of optimization. Given the input parameters, this would allow us to determine the allowed thermal state of the process for the analytical model in hand, so as to satisfy the state and boundary functions for the given optimization criterion.

For grinding, the task of optimal heat loading control is to determine the function of the process state, θ = θ(x,t), and the control function q = q(t), so as to satisfy the analytical form of the inverse problem for the grinding process, as defined by Eqs. (9) to (13). These functions are determined under the condition that the known temperature at a particular fixed point θ (t ) = θ ( K , t ) is consistent with the temperature θ (q, K , t ) which is calculated based on control function q(t): tm 2

J (q ) = ∫ θ (q, K ,t ) −θ ( K ,t )  dt. (17) 0

In order to minimize the differences between the known and the calculated 734

Fig. 4. Measuring system of grinding process

Gostimirović, M. – Sekulić, M – Kopač, J. – Kovač, P.

Strojniški vestnik - Journal of Mechanical Engineering 57(2011)10, 730-738

The workpiece material was high-speed steel (DIN S 2-10-1-8 or B.S. BM 42) at 66 HRc hardness, with dimensions of the parts 40×20×16 mm. The test used an aluminum oxide wheel »Winterthur« type 53 A80 F15V PMF, size 400×50×127 mm. The depth of cut was a = 0.05; 0.1; 0,25; 0.5 and 1 mm, the workpiece speed was vw = 2.5; 5; 10; 25 and 50 mm/s and the wheel speed was vs = 30 m/s. A water-based coolant (emulsion 6%) was used during the grinding test with a flow rate of 175 l/min.

The temperature was measured in the workpiece surface layer using a thermocouple (type K, ø0.2 mm) built into the workpiece at a specified clearance from the wheel/workpiece interface area. Measuring, analysis and control of the temperatures and forces during the process of machining with grinding was performed with the help of a computerized measuring system, Fig. 4.

Metallographic identification of the state of the workpiece material surface layer after grinding was performed with an optic microscope.

Metallographic examination of changes in the microstructure of the workpiece surface layer show that secondary changes appeared in each case when the measured maximal grinding contact temperature was higher than the temperature of the previous remission, which is θc = 550 °C for the steel that was used in this testing, Fig. 6.

The measured microhardness indicates that the microhardness of the secondary hardened layer is a little higher than the microhardness of the basic material. The smallest measured value of microhardness is found in the secondary remission layer.

During further inspection of the workpiece material surface layer condition, not one sample was found with microcracks in it. On the other hand, burned surfaces were noticed in all samples where the measured grinding contact temperature was above the temperature of the previous remission.

3.2 Experiment Results To determine the temperature field distribution in the workpiece surface-layer, temperatures in the workpiece were measured for various distances from the measuring point to the contact surface of the workpiece and the grinding wheel. A characteristic graphic review of how creep-feed grinding temperatures change in time in the cutting zone, obtained through gradually drawing the grindstone closer to thermocouple’s hot junction, is shown in Fig. 5.

Fig. 6. Metallographic picture of workpiece material surface layer after creep-feed grinding

Fig. 5. Creep-feed grinding temperature within the workpiece material surface layer

Shown in Fig. 7 is an experimentally obtained dependence between the depth of the secondary changed surface layer of high-speed steel and the grinding conditions, for a constant specific productivity. The diagram shows the maximum measured temperature in the surface layer of workpiece material.

Optimal Control of Workpiece Thermal State in Creep-Feed Grinding Using Inverse Heat Conduction Analysis

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4 OPTIMAL CONTROL OF WORKPIECE THERMAL STATE IN GRINDING 4.1 The Results of the Inverse Problem Method In this case of verification, to calculate the workpiece heat loading by inverse heat conduction problem, the known temperature distribution at a depth of z = 1 mm was taken for the additional boundary condition, Fig. 5. Based on the experimental results, and considering the process boundary conditions and thermal/physical characteristics of grinding, the parameters of the heat source in creep-feed grinding was obtained by computation.

The total temperature field in the workpiece material surface layer was obtained by computation, Fig. 8., as well as the heat flux density in the wheel/workpiece interface, Fig. 9.

The computed distribution of heat flux density over the interface area clearly shows the direct relationship between heat source parameters, i.e. the power of the heat source and its total active time.

Fig. 9. Heat flux density over the wheel/workpiece interface 4.2 Process System for Optimal Control

Fig. 7. Secondary changes in the surface layer of HS steel as the function of creep-feed grinding conditions

Fig. 8. Computation of temperature change over time in the workpiece material surface layer 736

Optimization of creep-feed grinding conditions by the extreme case of the inverse method relies on heat source parameters. The process of optimization is the determination of the most favorable ratio between the heat source power and its active time, for the heat flux density over the interface area, Fig. 10a.

Under the condition of maximum specific machining productivity (Qw’ = vw·a = max), the process of optimization is conducted by completely searching the bounded solution space (vw, a), Fig. 10b. Thus optimal cutting depth a and workpiece velocity vw are determined. They can either be inside or on the very boundary of the search space.

Based upon the proposed model of optimization, Eqs. (9) to (13), the criterion of optimization in Eq. (17), the state functions in Eqs. (5) and (6) and boundaries, a software application was made. In order to verify the proposed model of optimal control in creep-feed grinding, testing was performed, which involved a variation of input data. Partial results are shown in Table 1.

Gostimirović, M. – Sekulić, M – Kopač, J. – Kovač, P.

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allowed ones, which were derived experimentally, shows very little differences. The differences can be explained by a large number of parameters which had to be estimated in the course of modeling the grinding process.

Fig. 10. Algorithm of optimization cutting conditions by control of heat loading in the workpiece 5 ANALYSIS OF RESULTS The computed time and depth-related change of temperature in the interface zone of the workpiece surface layer shows a high degree of conformity with the experimentally obtained results. Shown in Fig. 11 is the change of the interface temperature obtained both analytically and experimentally. A similar trend of analytically and experimentally obtained temperature changes over time is applicable to any other point within the workpiece.

High computation accuracy of the wokpiece temperature field also implies reliability of the computed heat flux density (Fig. 9).

The comparison between the computed optimal creep-feed grinding conditions with the

Fig. 11. Temperature change over time in the wheel/workpiece interface 6 CONCLUSIONS Based on this investigation, the following conclusions can be made: • The proposed analytical model of the thermal state in creep-feed grinding very well describes the real state; • Analytical inverse heat conduction problem allows approximation of the temperature field in the workpiece surface layer and heat flux density distribution in the wheel/workpiece interface; • The inverse problem was solved using the method of finite differences in implicit form;

Table 1. Optimal creep-feed grinding conditions, computed by extreme case of inverse method Coefficient of Max. heat temperature flux density conductivity qmax a [m2/s] [kW/m2] 4·10-6 6700 5550 (4+0.003·θ)·10-6 6·10-6 4300 10·10-6 4050 Machining conditions:

Elements of optimal grinding conditions vc [m/s] 30

Wheel: 58 A80 F15V Coolant: Emul. 6% Workpiece: HSS Ds = 400 mm

vw [mm/s]

a [mm]

12.14 0.207 11.04 0.171 9.53 0.128 9.46 0.126 Input parameters:

Output process parameters Q w’ [mm3/mm·s] 2.515 1.693 1.216 1.189

hm [μm]

vc/vw

0.084 0.063 0.041 0.039

2472 2717 3149 3172

ξ = θ(x,t) for z = 1 mm; θc = 550 °C; ksm = 20.34·hm-0,73 kN/mm2 λ = 21.378+0.0275·θ W/m °C; Δx = 0.5 mm; Δt = 0.25 s

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•

• •

•

For computation of the heat loading of the workpiece surface layer, it requires accurate experimentally obtained temperature distribution at a single point within the workpiece; Analytically obtained temperature field in the workpiece surface layer largely agrees with experimental results; The optimal control of heat loading in creepfeed grinding allows the parameters of heat source to be kept within limits which guarantee functional properties of the finished part; Extreme case of inverse heat conduction problem in creep-feed grinding allows reliable calculation of optimal cutting conditions.

7 REFERENCES

[1] Kopac, J., Krajnik, P. (2006). Highperformance grinding - A review. Journal of Materials Processing Technology, no 175, p.

278-284.

[2] Demetriou, M.D., Lavine, A.S. (2000).

Thermal aspects of grinding: the case of upgrinding. Journal of manufacturing science and engineering, vol. 122, p. 605611.

[3] Guo, S., Malkin, S. (1994). Analytical and experimental investigation of burnout in creep-feed grinding. Annals of the CIRP, vol. 43, p. 283-286.

738

[4] Gostimirovic, M., Kovac, P. (2008). The Thermal state of the workpiece surface layer during productivity grinding. Journal for Science, Research and Production, vol. 8, p.

55-61.

[5] Rowe, W.B. (2001). Thermal analysis of high efficiency deep grinding. Journal of Machine Tools and Manufacture, no. 41, p.

1-19.

[6] Shaw, M.C. (1994). A production engineering approach to grinding temperatures. Journal of Materials Processing Technology, vol. 44, p. 159-169.

[7] Ozisik, M.N., Orlande, R.B. (2000).

Inverse heat transfer: fundamentals and applications. Taylor & Francis, Philadelphia.

[8] Alifanov, O.M. (1994). Inverse heat transfer problems, Springer Verlag, Berlin.

[9] Gostimirovic, M., Kovac, P., Sekulic, M., Savkovic, B. (2009). Inverse task solution of heat conduction in grinding process.

10th International Conference on Flexible Technologies, p. 236-240.

[10] Kim, H.J., Kim, N.K., Kwak, J.S. (2006).

Heat flux distribution model by sequential algorithm of inverse heat transfer determining workpiece temperature in creep feed grinding. Journal of Machine Tools and Manufacture, no. 46, p. 2086-2093.

Gostimirović, M. – Sekulić, M – Kopač, J. – Kovač, P.

Strojniški vestnik - Journal of Mechanical Engineering 57(2011)10, 739-749 DOI:10.5545/sv-jme.2011.106

Paper received: 17.05.2011 Paper accepted: 05.09.2011

The Formation of Saw Toothed Chip in a Titanium Alloy: Influence of Constitutive Models Alvarez, R. – Domingo, R. – Sebastian, M.A. Roberto Alvarez1 – Rosario Domingo2,* – Miguel Angel Sebastian2 1 Universidad Nebrija, Department of Industrial Engineering, Spain 2 UNED, Department of Manufacturing Engineering, Spain

This work analyses the effect of eight constitutive models on the saw-toothed chip formation in Ti6Al4V orthogonal cutting, by means of the finite element (FE) simulation and experimental contrast, in dry and with conventional emulsion coolant, mixed with water at 7%. The models are focused in JohnsonCook equations with four different sets of constant parameters, El-Magd-Treppmann modified and three Zerilli-Armstrong models based on the behavior of different crystal structures (body-centered-cubic – BCC, hexagonal-close-packed – HCP and modified HPC model). The flow stress model of Ti6Al4V at high strain rates and temperatures has been analysed using a 2-D FE model through constitutive equations and three friction coefficients (0.4, 0.6 and 0.8). A critical comparison of outstanding process outputs as cutting force, temperature – on rake face and measurable parameters for segmented chip (the peak tooth height, the valley tooth height and the tooth width, chip compression ratio, and chip deformation) is carried out. The application of different constitutive models has proved a strong influence on the results.

Zerilli-Armstrong models, for BCC and HCP structures, have achieved the best fitting in machining with and without coolant respectively, for a friction coefficient of 0.8, getting for cutting force, temperatures, peak tooth height and chip deformation, deviation lower than 2%. The chip compression ratio has reached 4.7% and 7% for BCC and HCP respectively. Only the valley tooth height and the tooth width show some limitations. ©2011 Journal of Mechanical Engineering. All rights reserved.

Keywords: machining, orthogonal cutting, Ti6Al4V, FEM, chip morphology, constitutive models

0 INTRODUCTION Ti6Al4V has become one of the basic materials in aerospace, armour and medical device industry due to its mechanical resistance, tenacity, low density and exceptional corrosion resistance.

However, this material is difficult to machine due to its low thermal conductivity that decreases with higher temperatures, a characteristic called thermal softening. Moreover, during the process, this alloy reaches high strains, very high strain rates and temperatures close to its melting point. In addition, it is remarkable that Ti6Al4V possesses a phase transformation. Initially, an alpha phase with a Hexagonal-Close-Packed (HCP) crystal structure is presented, and it changes to a beta phase with a Body-Centered-Cubic (BCC) crystal structure, approximately at 996 ºC. The properties of the materials, the thermo-mechanical flow and the chip fracture, involved in machining processes, are essential inputs for the definition of a finite element (FE) model. The constitutive *Corr. Author’s Address: UNED University, C/ Juan del Rosal 12, Madrid, Spain, rdomingo@ind.uned.es

equation model and the set of parameters selected for the flow behavior of workpiece material could influence the saw-toothed chip morphology.

Thus, specific flow stress expressions have been proposed to approach the flow stress behavior in metal cutting. Simulations by the FE model, based on Johnson–Cook (J-C) equations, related to orthogonal cutting, focused on an analysis of influence of Ti6Al4V proprieties and found that there is a critical point – phase transformation at which the chip loses the property of continuous [1]. The chip segmentation was analyzed by means of a model based on a simple isotropic von Mises flow stress law – it is a modification of El-Magd and Treppmann constitutive model, allows an observation of the variation of thermal conductivity affecting the segmentation [2]. The development of a model based on J-C equations that takes into account the strain rate hardening, the thermal-softening phenomenon and the strainsoftening phenomenon, has found that the election of material law is primordial to the machining 739

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simulation and that at high cutting speeds it is difficult to predict the segmented chip [3]. An analysis of the cutting force, chip morphology and segmentation through the J-C’s constitutive equation with three different sets of material constants reports that a good prediction of cutting force and chip morphology can be achieved only if the material constants were identified using experimental data [4]. The influence on serrated chip formation, of three material models based on J-C equations, has been researched and it has been found that the serrated chip does not get in in its entirety and that the chip geometry in FE depends on model equation, However, it does not depend on the cutting conditions [5]. The exploration of the FE modeling use by a J-C model (although it does not report the data of constitutive equations) in a study of the chip curl, allows an observation of a reasonable agreement with a small depth of cut [6]. Also, a procedure has been defined to determine values of friction and damage coefficients to find a serrated chip [7]. A model whose constitutive equation represents the BCC structure called the Zerilli-Armstrong model in order to identify parameters for high rate metal cutting conditions has been found [8], but its adequacy to FE simulation has not been verified.

Although, the J-C model is probably the most used constitutive equation and its combination with a ductile fracture criterion has been used to simulate chip formation in machining Ti6Al4V, the equation could be considered inappropriate for the Ti6Al4V alloy, as it does not incorporate the characteristic nonlinear strength behavior shown by the material.

Thus, variations of the J-C primitive equation have been proposed. On the other hand, there are other models which have been less explored, such as the Bäker modification and specially Zerilli-Armstrong model. Moreover, the equation constitutive for HCP structure is not proved. This study focuses on eight constitutive models for the thermo-viscoplastic flow behavior of workpiece material in orthogonal cutting, with three friction coefficients and an experimental contrast, statistically verified, with and without coolant.

The introduction of dry or flooded machining is a new and important consideration since differences between the performances in dry and flooded machining have been found in an experimental 740

research focussed on biomedical applications of titanium [9]. Therefore, the contributions of this paper are the following: i) to explore the capacity of Zerilli-Armstrong models in FE simulations; ii) to integrate the Zerilli-Armstrong models, the Baker modification of El-Magd and Treppmann and a J-C model with a lower thermal softening coefficient (than others contrasted in the literature) with the fracture criterion; and iii) to find the influence of lubrication on the results and the effect of the friction coefficient in dry and flooded cutting conditions in the eight models.

1 MATERIAL MODELS AND EQUATIONS In order to express the complex flow behavior of Ti6Al4V alloy, which depends on the local strain, strain rate and temperature, a proposed 2-D orthogonal cutting FE model is used. The cutting conditions and material properties of the workpiece will be the inputs of the simulation process, while the outputs will be variables of the process as chip morphology, cutting force and temperature. The flow is studied by the models described in this Section.

1.1 Johnson and Cook Constitutive Model The J-C equation is a multiplicative phenomenological strength model, Eq. (1). Three factors describe the flow stress considering the material strain and strain rate as well as the thermal influence respectively [10]:   •  n   σ = A + B ⋅ ε · 1 + C ⋅ ln  ε•    ε   0

m    ·1 −  T − Tr   . (1)         Tm − Tr   

where σ is the equivalent flow stress [MPa], ε the •

•

equivalent plastic strain, ε and ε 0 the equivalent plastic strain rate [s-1] and the reference equivalent plastic strain [s-1], T the workpiece temperature and Tm and Tr are, respectively, the material melting and room temperatures. The coefficient A [MPa] is the yield strength; B [MPa] the hardening modulus; C the strain rate sensitivity coefficient; n the hardening coefficient; m is the thermal softening coefficient. A, B, C, n and m are constant values. Table 1 shows a different set of parameters proposed [11] to [14] and tested in this paper. The

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constants used in the models E1, E2 and E4 were identified through the Split Hopkinson Pressure Bar (SHPB) method, which was applied at a maximum strain rate of 2150 s−1 and a maximum plastic strain of 0.57. The constants for the E3 model were studied with a methodology based on analytical modelling of the orthogonal cutting process combined with metal cutting experiments [13]. It must be said that there is no information about the range of strain rate and true strain. The three first models tested [4] are used as a pattern for this work joint to the experimental verification.

1.2 Bäker Modification of El-Magd Constitutive Model El-Magd and Treppmann [15] determined a flow stress law for the alloy Ti6Al4V, which was modified by Bäker [2]. In this constitutive model (E5), the plastic behavior is described by an isotropic equation based on Von Mises flow stress law. It is given by the Eq. (2), where C is a constant and K* [MPa], n*, μ and TMT [K] are parameters calculated from experimental data through quasi-static compression tests and SHPB method (see Table 2). The appropriate range of values is strain rates between 103 and 104 s-1 for a temperature value of 400 ºC.

σ=

 * exp − T   T   MT 

  T µ  n  −  ·ε   *   TMT   K ·e

µ       

  • ε  ·1 + C ln  •  ε   o 

   (2)   

1.3 Zerilli and Armstrong BCC Constitutive Model Zerilli and Armstrong constitutive model is based on dislocation mechanics. Its development pursues to represent the behavior of BCC structure metals, which is given in Eq. (3) [16]. This structure is typical in Ti6Al4V at temperatures above 996 ºC. It presents some advantages regarding the J-C model because it better describes the strain rate hardening behavior and the thermal coupling [12]. The E6 model represents the BCC structure and the parameters for the material constants C0 [MPa], C1 [MPa], C3 [K-1], C4 [K-1], C5 [MPa] and n are taken from Meyer and Kleponis [12] research of a low

cost Ti6Al4V for strain rates up to 2,000 s-1. The strain rate and the temperature are independent of strain effects. The parameters have been selected by means of numerical simulations, choosing the values that provide the best fitting.

•

σ = C0 + C1·e( −C3 ·T + C4 ·T ·ln ε ) + C5 ·ε n . (3)

1.4 Zerilli and Armstrong HCP Constitutive Model Later on, Zerilli and Armstrong expanded the applicability of the BCC model developing a better understanding representation for metals [17] predominantly HCP structure (E7). This model is relevant in the machining because HCP is the crystal structure of Ti6Al4V until 996ºC. Its development pursues to improve the representation of the thermal softening phenomenon. Eq. (4) represents this HCP model E7. Parameters C0 [MPa], C1 [MPa] and C2 [MPa] are material constants and T is the absolute temperature. The expression under the radical is known as strain function. The recovery strain εr affects the strain ε, at which the saturation of the stress is achieved.

•

•

The parameters α0 [K-1], β0 [K-1], ε α [s-1] and ε β [s-1] are material constants [18].

The parameters have been determined in the same manner as the values for Eq. (3). σ

= C0 + C1·ε

•   ln ε − β 0 ·1− •  ln ε β

  ·T 

+ C2 ·e

•  ln ε −α 0 ·1− •   ln εα

 ·T  

· ε r ·(1 − e

−ε

εr

). (4)

Table 1. Parameters of J-C models σ in [MPa] A [MPa] B [MPa] C [-] n [-] m [-]

E1 [11] E2 [12] E3 [13] E4 [14] 782.7 896 870 862.5 498.4 656 990 331.2 0.028 0.0128 0.008 0.012 0.28 0.5 1.01 0.34 1 1 1.4 0.8

•

10-5

1

1

1

Tm [ºC]

1600

1600

1600

1600

ε o [s-1]

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Table 2. Parameters of E5 model σ in [MPa] [2] •

C [-]

εo

0.302

[s-1] 774

K* [MPa]

n* [-]

TMT [K]

μ [-]

2260

0.339

825

2

1.5 Zerilli and Armstrong HCP Modified Constitutive Model The model proposed by Zerilli and Armstrong with predominantly HCP form [17] was modified using a set of parameters obtained for a low-cost Ti6Al4V, the research focused on strain rates from 1,000 to 50,000 s-1 [18]. Eq. (5) represents the model E8. The parameters α0, β0, •

•

ε α and ε β are the material constants [12]. The meaning and units of the parameters of Eq. (5) are the same than in Eq. (4). This new model does not contain the square root that strains the function, which was eliminated due to it and provides a fair fitting in the determination of strain. Thereby, this model represents the HCP form. σ = C0 + C1ε

•   ln ε − β 0 1− •  ln ε β

  T 

+ C2 e

•  ln ε −α 0 1− •   ln εα

 T   ε

r (1 − e

−

ε εr

rake face. Thus, cutting forces and temperatures are monitored during the process. TesaVisio 300 optical measurement system allows taking data from chip geometry (the peak tooth height - hmax, the valley tooth height - hmin and the tooth width - W, indicated in Fig. 1) and from chip thickness after cutting and underformed chip thickness, parameters required to know the chip compression ratio (Rc), and the chip deformation (ε). Tests were executed with and without the coolant. Each test was repeated three times and an Analysis of Variance (ANOVA) was done to assure the measurement quality, through StatgraphicsPlus software. Thus, ANOVA analysis enables an insight into whether there are significant differences between the means of the variables in the F-test when P-values are lower than 0.05 at 95% confidence level. The experimental data, related to the turning of 4 mm, allowed carrying out a significance study. Fig. 1 exposes the length of experimental chip analysed in order to this study.

). (5)

2 EXPERIMENTAL AND SIMULATION 2-D PROCEDURE The workpieces of Ti6Al4V and inserts of tungsten carbide (WC/Co) have been used in experimental and simulated tests. Insert CNMA432 geometry is defined by a clearance angle 5º, nose radius 0.78 mm and hone radius 0.0295 mm.

The cutting conditions are the following, cutting speed (vc) 120 m/min, width of cut (d) 2.54 mm, feed rate (f) 0.35 mm/rev and tool rake angle (γ) +15º. Experimental tests have been conducted in a CNC lathe, with bars of titanium alloy, a diameter of 48 mm and turning along 4 mm, with and without coolant. The cutting fluid is a conventional emulsion coolant with water at 7%. The forces have been calculated by means of piezoelectric dynamometer, Kistler type 9257B, a multi-channel charge amplifier Kistler type 5070A and DasyLab software. The temperature is measured by an IR pyrometer Optris on the 742

Fig. 1. Experimental chips and geometric parameters The FE software DEFORMTM uses an Updated-Lagrangian implicit code to simulate the 2-D orthogonal cutting model. The model is a thermo-mechanical simulation with a plastic workpiece (5,000 elements) and a rigid tool (4,000 elements). The cutting tool is considered a rigid body because the effect of using an elastic tool is minimal on the predictions of cutting forces, temperature, and chip formation. In order to investigate the behavior of the segmentation

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process, the mesh in the shear zone must be extremely refined to simulate with sufficient accuracy, the related local deformation and the shear band formation. The shear band region concentrates very high gradients of temperature and shear velocities and they cannot be calculated using wide meshes in this zone. Remeshing algorithms based on the “interference depth” technique were employed, beginning when the tool penetrates the workpiece up to a critical value.

This value was selected after previous testing [1], to be a 20% of the smallest element edge length existing in the mesh (see Fig. 2).

∫

εR

0

σ1 d ε eq = Dcr . (6) σ eq

The friction model based on the constant shear hypothesis, derived from the Tresca law, τ = m∙τ0, has been implemented. τ is the shear stress, m the friction factor and τ0 the shear yield stress. The cutting forces, temperature and chip morphology can be well predicted with an appropriate setting of the friction coefficient, and these predictions are independent of which friction law has been defined in the simulation software, and only the coefficients used have an influence on the results [1]. The friction factor m fixes a constant relation between τ and τ0, but it has not a physical meaning. Its value conditions the frictional stress on rake face. It is ranged between 0.4 to 0.8 to evaluate different results.

The selection of the accurate value of m will be conditioned by the best results of the simulations, according to an iterative procedure conditioned by the mesh, the cutting forces and the temperature on rake face during the simulation [7].

3 EXPERIMENTAL AND SIMULATION RESULTS

Fig. 2. Mesh/Remesh refining in the shear zone The influences of the large plastic deformations and the high heat generation that take place during the metal machining process have to be considered when modelling the machining process. The modelling of friction and fracture become important issues in the prediction of the effect of tensile stress on the chip segmentation during orthogonal cutting. Cockroft-Latham fracture criterion [19] is employed to predict the effect of tensile stress on the chip segmentation process. This law is shown in Eq. (6), where εR is the fracture strain, σ1 and σeq are the maximum principal and the equivalent stresses while Dcr is a material constant known as normalized critical damage value. The crack is generated according to Dcr for the Cockroft-Latham equation [4]. In line with previous research work [3], Dcr is fixed in 0.1 in all the simulations in order to make comparisons.

To analyse the orthogonal cutting model, the predicted and experimentally measured chip morphology, cutting force and temperature were evaluated and their differences discussed.

Table 3. Results from ANOVA Analysis

hmax W hmin Rc ε Fc (dry) Fc (lubricant) T (dry) T (lubricant)

Sum of squares 375656 273598 169289 14442.1 16985.5 148331 149725 5456240 3617570

F-ratio

P-value

2.94 2.37 2.59 2.07 1.54 2.32 0.68 0.51 0.00

0.06 0.10 0.08 0.13 0.22 0.10 0.51 0.60 0.99

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3.1 Chip Morphology The predicted chip morphology is studied considering the values of the segmented chip geometry (hmax, W, hmin) defined in Fig. 1 and also taking into account Rc and ε values. The experimental and simulated data are shown in Fig. 3. Moreover, the experimental data obtained are coherent with the literature [6] using similar cutting conditions. The simulated serrated chip segments show relevant geometric similarities and reasonable dimensional attributes. Segmentation frequencies can achieve a wide range in hard machining [3], with values 5882, 2288, 5465, 5714, 2100, 3846, 4755 and 4366 Hz in each model. Fig. 4 shows the chip morphology results of the simulations using eight different constitutive models for m = 0.6. As Özel et al.

[5] showed, the chip geometry in FE depends on model equation but it is not affected by the friction coefficient; this behavior can be seen in Fig. 5.

The geometric attributes are coherent with the experimental results, except E5 model results, which present deviations higher than 60%, and a segmented chip is not very clear. The results shown using different friction coefficients are not representative (see Fig. 5). The experimental

results (hmax = 421 mm, W = 411 mm, hmin = 205 mm and chip thickness = 0.451 mm) are similar in machining with and without the coolant in order of mm. The ANOVA analysis shows that there are no relevant differences between the means of the parameters because P-values are 0.06, 0.1 and 0.08 for hmax, W and hmin, respectively. The same occurs for ε and Rc (see Table 3). E2 J-C material model and E6 show similar behavior with lower deviation than 13%. E1 and E4 J-C models and E7 and E8 also show a corresponding performance, but they have deviations next to 20% in any case (E1 and E8) and next to 30% for E4. The worst adjustment to the ratio Rc and the chip deformation is achieved by E5 model, again, while the E6 and E7 models offer very low deviations from experimental results. E5 model has a different behavior with a lower frequency of chip formation, so this material law seems to be inadequate for describing the behavior of Ti6Al4V accurately.

3.2 Cutting Forces The outcome comparison of the simulated cutting forces using the eight constitutive models and the three different friction coefficients

Fig. 3. Experimental and simulated results for serrated chip morphologies 744

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Fig. 4. Saw-toothed chips in eight models for m=0.6 with experimental results, with and without the coolant is shown in Fig. 6. The experimental data obtained are 678.5 N for dry turning and 702 N for machining with coolant. In both cases, a previous ANOVA analysis provides a P-value of 0.1 (dry) and 0.51 (flooded); this is higher than 0.05, therefore there is no relevant difference between the three measurements (see Table 3). It is clear that the cutting force is higher when the coolant is used; however the thrust force is lower in this case.

Fig. 5. Different simulation results for serrated chip morphologies

This phenomenon is common in other materials [1]. Globally, the model E4 gives lower forces than others, and the model E8 achieves higher forces, independently of the friction value, being both models, the upper and the lower bound respectively. This behavior is explained by the lower flow stress than model E4 results, which are always very low even if the friction coefficient is increased. Close to E8 model, it is the E5 model and next to E4, the E2 and E3 models, these two latter models show similar results. E1 J-C model and E6 and E7 Zerilli-Armstrong constitutive models are more successful and close to experimental data. Especially E6 and E7 even with the highest friction coefficient (m = 0.8), for dry cutting, E6 achieved a deviation of â&#x20AC;&#x201C;1.71% and with lubricant of 1.69%; besides E7 obtained a difference of 2.14% and â&#x20AC;&#x201C;1.28% for dry and with lubricant machining. Also, there is a good fitting in E1 model for m = 0.4 with deviations of 2.4% and 0.9% in machining without and with coolant respectively. Using m = 0.6 the E1 model predictions are lower than 4% and 7%, but E6 and E7 also predict on acceptable manner. The results for E5 and E8 constitutive models predicted cutting forces are always higher than others as their strain hardening effect is more observable.

As it can be seen, the friction factor has a strong influence on the results; a rise in m supposes an increase of cutting forces because the frictional stress on the rake face is higher. Its value depends on constitutive equations and their parameters and

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its election is conditioned by the experimental results.

3.3 Temperature Distribution Fig. 7 shows the differences between experimental and simulation results in temperature fields measured on the rake face. As expected, the temperatures are higher increasing the friction coefficient value m. The highest temperatures were always found in E4, E5 and E8 models, even when low friction values are used. The lowest temperatures were found in E2 and E3 models (see Fig. 4 for m = 0.6) and in addition to the highest deviation (see Fig. 7), which is probably due to stronger deformation produced, which increases the heat and causes higher temperatures.

Nevertheless, the temperature distribution pattern is similar for all the material constitutive models used. Experimental data give a temperature value of 866 ºC and 740 ºC without and with the coolant, respectively.

Fig. 6. Experimental and simulated cutting forces

Fig. 7. Experimental and simulated temperatures The ANOVA analysis gives a P-value of 0.6 (dry) and 0.99 (flooded), thus there is no significant difference between the three measurements (see Table 3). The predictions are influenced by the use of coolant. Thus, E5 746

(m = 0.6), E7 (m = 0.8) and E8 (m = 0.6) model estimations are so close to this reference value in dry machining, with deviations lower than 1% in the case of flooded machining. The best fitting is achieved with E1 (m = 0.4) and E6 (m = 0.8) models, with deviations lower than 2%.

As it occuered in the cutting forces, a rise in m supposes an increment of temperatures, although the temperature is more sensitive than the forces.

4 DISCUSSION Table 4 shows the best global adjustment and deviations found from literature. These latter comparisons are limited because some authors do not report experimental results or there are only graphic presentations of the outcomes. In this study, during the orthogonal cutting, the sawtoothed chip is achieved, which is a very important variable for the prediction of process behavior.

Thus, the integration of the FE model and fracture criterion has been favourable in all models, except E5. A possible explanation could be the thermal softening. The high temperatures provoke a lower thermal conductivity and the segmentation frequency (2,100 Hz) is not sufficient. The four J-C models have achieved good results regarding to the chip morphology; although E1 prediction is the best adjustment, and the differences between experimental and simulated hmin and Fc represent percentages lower than any other published [4]; moreover there is a very good prediction of temperatures, which is very important as FE model is a thermo-mechanical simulation (see Figs. 6 and 7), in particular in flooded machining using friction coefficient of m = 0.4. The other variables, such as hmax, W, Rc and ε achieve acceptable deviations according to other results from literature (see Table 4). In this way, the fitting of the FE model could be considered as adequate.

The Zerilli-Armstrong models provide interesting results. It is seen that E6 and E7 Zerilli-Armstrong models for BCC and HCP crystal structure have a similar behavior (approximately same forces and temperatures), while the modification of Zerilli-Armstrong (E8) is not close to that behavior and has a significant increment of cutting force and temperature. In fact, the simulated results agree with the expected behavior of the HCP structure. It was expected

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Table 4. Deviations in models with best adjustment and from literature E1

E6

E7

[3]

hmax

-18.2%

1.4%

-0.7%

3.44% (J-C Dry)

W

-6.8%

12.6%

-9.4%

2.56% (J-C Dry)

hmin

2.4%

9.2%

20.9%

16.9% (J-C Dry)

Rc

21.8%

4.7%

7%

-

ε

4%

1.4%

1.7%

-

Fc

0.9% 1.7% -1.3% -11% (m = 0.4 Coolant) (m = 0.8 Coolant) (m = 0.8 Dry) (J-C Dry)

T

-1.8% 1.2% 0.6% (m = 0.4 Coolant) (m = 0.8 Coolant) (m = 0.8 Dry)

to be harder and more difficult to machine than the BCC beta phase. However, E6 model has presented the best adjustment to chip morphology in each case (see Fig. 3). The reason could be that the high temperatures required in E8 provoke a reduction of thermal conductivity that increases the cutting forces needed to remove material during machining, although it does not affect to chip morphology. Finally, the model E6 for m = 0.8 has demonstrated the best fitting to cutting forces and temperature with coolant and E7 allows a very good approach in dry machining, with deviation of less than 2%, and good results of chip deformation (1.4% and 1.7% for E6 and E7 respectively) and chip compression ratio (4.7% and 7% for E6 and E7 respectively), as it can be appreciated in Table 4. Only W for E6 and hmin for E7 show some limitations, but not different from the deviations found in the literature (see Table 4).

The experimental verification with and without the coolant has demonstrated the influence of the lubrication on the results in cutting forces and temperature.

-

[4] E1: -9.6% E2: -13% E3: -29.1% E1: 6.4% E2: 72.6% E3: 42.1% E1: -6.5% E2: 26.1% E3: 137% E1: -9.9% E2: -13.2% E3: -29.3% E1: 7.7% E2: -7.5% E3: -8.9% -

[6] 51.7% (J-C Dry) -

10% (J-C Dry) -

5 CONCLUSIONS The application of the different constitutive models has proved a strong influence on the results. The model based on Von Mises (E5) flow stress was not capable of predicting the chip shape and forces; although the temperature is predicted for dry machining and m = 0.6. However, the other models predict the chip geometry with a reasonable accuracy, thus the integration modelfracture criterion is acceptable. The four J-C models have achieved good outcomes regarding the chip morphology, forces and temperature, but the best prediction was obtained with E1 for m = 0.4, which differs between experimental and simulated cutting forces, temperature, hmin and Fc represent percentages lower than the literature, and it has shown a adequate prediction of temperatures.

This last one is relevant for the thermo-mechanical simulations. The E4 model, with a lower thermal softening coefficient, has not improved the results.

Zerilli-Armstrong model, with BCC (E6) and HCP (E7) structures, has achieved the best fitting in flooded and dry orthogonal cutting respectively, for a friction model of m = 0.8, getting for cutting force, temperatures, peak tooth height and chip deformation, deviation lower than 2%. These

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results represent a stonger fitting than other models studied previously. The HCP modified model has not given good results mainly in the cutting forces; thereby the mathematical modificaton that affects the strain function does not seem adequate in orthogonal cutting.

The cutting force and temperature are affected by friction parameter and lubrication, but the chip morphology is not sensitive to them.

Also the models are sensitive to the friction factor, finding that the different values of m, that provide the stronger fitting, vary on function of material constitutive equations and constants values. The comparison with the literature indicates that these simulations allow obtaining, by Zerilli-Armstrong models based on the crystal structure of titanium, lower deviations respect to experimental results.

Thus, an important contribution has been the assessment of these models. Future works could focus on the exploration of Zerilli-Armstrong models, in particular to find an influence of insert geometry and power consumption during the machining process.

6 ACKNOWLEDGMENTS This work has received financial support from the MICINN (Spanish Government), by means of the project DPI2008-06771-C04-02.

The authors would like to thank the reviewers for their suggestions.

7 REFERENCES [1] Álvarez, R. (2009). Analysis of cutting simplified model, by the finite element method, in light alloys of aerospace interest. Doctoral Thesis;, UNED, Madrid. (in Spanish) [2] Bäker, M. (2003). An investigation of the chip segmentation process using finite elements.

Technische Mechanik, vol. 23, no. 1, p. 1-9.

[3] Calamaz, M., Coupard, D., Girot, F. (2008).

A new material model for 2D numerical simulation of serrated chip formation when machining titanium alloy Ti-6Al-4V. International Journal of Machine Tools and Manufacture, vol. 48, no. 3-4, p. 275-288.

[4] Umbrello, D. (2008). Finite element simulation of conventional and high speed machining of Ti6Al4V alloy. Journal of 748

Materials Processing Technology, vol. 196, p.

79-87.

[5] Özel, T., Yildiz, S., Ciurana, J. (2009).

Influence of material models on serrated chip formation in simulation of machining Ti-6Al4V titanium alloy. 12th CIRP Proceedings of Conference on Modelling of Machining Operations, p. 123-131.

[6] Li, R., Shih, A.J. (2006). Finite element modelling of 3D turning of titanium.

International Journal of Advanced Manufacturing Technology, vol. 29, no. 3-4, p. 253-261.

[7] Álvarez, R., Domingo, R., Sebastián, M., (2010). Procedure for the definition of input parameters for a three-dimensional finite element model for Ti6Al4V orthogonal cutting. Proceedings of CIRP2nd International Conference on Process Machine Interactions, p. 10.

[8] Özel, T., Karpat, Y. (2007). Identification of constitutive material model parameters for high-strain rate metal cutting conditions using evolutionary computational algorithms.

Materials and Manufacturing Processes, vol.

22, no. 5, p. 659-667.

[9] Balažic, D.M., Kopač, J. (2010). Machining of Titanium Alloy Ti-6Al-4V for biomedical applications. Strojniški vestnik - Journal of Mechanical Engineering, vol. 56, no. 3, p.

1-5.

[10] Johnson, G.R., Cook, W.H. (1983). A constitutive model and data for metals subjected to large strains, high strain rates and high temperatures. Proceedings of the 7th Symposium on Ballistics, p. 541-547.

[11] Lee, W.S., Lin, C.F. (1998). High-temperature deformation behaviour of Ti6Al4V alloy evaluated by high strain-rate compression tests. Journal of Materials Processing Technology, vol. 75, no. 1, p. 127-136.

[12] Meyer, H., Kleponis, D. (2001). Modelling the high strain rate behaviour of titanium undergoing ballistic impact and penetration.

International Journal of Impact Engineering, vol. 26, no. 1, p. 509-521.

[13] Dumitrescu, M., Elbestawi, M., El-Wardany, T. (2002). Mist coolant applications in high speed machining of advanced materials metal

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cutting and high speed machining. Kluwer Academic/Plenum Publishers, p. 329-339.

[14] Johnson, G.R. (1985). Strength and fracture characteristics of a titanium alloy (.06Al, .04V) subjected to various strains, strain rates, temperatures and pressures. NSWC TR, p. 86-144.

[15] El-Magd, E., Treppmann, C. (2001). Analysis of strain rate on flow curves for higher temperatures. Zeitschrift fur Metallkunde, vol. 92, p. 888-893. (in German) [16] Zerilli, F.J., Armstrong, R.W. (1987).

Dislocation-mechanics based constitutive relations for material dynamics calculations.

Journal of Applied Physics, vol. 61, no. 5, p.

1816-1825.

[17] Zerilli, F.J., Armstrong, R.W. (1996).

Constitutive relations for titanium and Ti-6Al4V. Proceedings of the American Physical Society Topical Group on Shock Compression of Condensed Matter Conference, vol. 370, p.

315-318.

[18] Meyer, H. (2006). A modified ZerilliArmstrong constitutive model describing the strength and localizing behaviour of Ti-6Al4V. Army Research Laboratory. Aberdeen Proving Ground, MD 21005-5069 ARLCR-0578.

[19] Cockroft, M.G., Latham, D.J. (1968).

Ductility and workability of metals. Journal of the Institute of Metals, vol. 96, no. 2, p. 3339.

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Strojniški vestnik - Journal of Mechanical Engineering 57(2011)10, 750-759 DOI:10.5545/sv-jme.2010.208

Paper received: 29.09.2010 Paper accepted: 25.07.2011

The Influence of Airflow Inlet Region Modifications on the Local Efficiency of Natural Draft Cooling Tower Operation Dvoršek, M. ‒ Hočevar, M. ‒ Širok, B. ‒ Holeček, N. ‒ Donevski, B. Matjaž Dvoršek1 ‒ Marko Hočevar2,* ‒ Brane Širok2 ‒ Nikola Holeček3 ‒ Božin Donevski4 1Termoelektrarna Šoštanj d.o.o., Slovenia 2University of Ljubljana, Faculty of Mechanical Engineering, Slovenia 3Gorenje d.d., Slovenia 4University St. Kliment Ohridski, Faculty of Technical Sciences, Macedonia

We present the influence of the cooling tower airflow inlet region modifications at the Šoštanj 4 thermal power plant on cooling tower local efficiency. Local efficiency change was estimated based on temperature fields of drift eliminators before and after the reconstruction of the cooling tower. Temperature fields were measured with thermal vision method. The local reduction of cooling tower efficiency was analyzed based on phenomenological relations of heat transfer obtained from the selected vertical segment of the cooling tower. The characteristic influence that the reconstruction had on the temperature field was detected on the circumference of the cooling tower. The efficiency reduction was the highest on the periphery of the cooling tower and in particular section it peaked at 2%, while in most part of the area it was below 0.5%. The presented measurement and analysis method enables the estimation of changes in the local efficiency of heat transfer in cooling towers. ©2011 Journal of Mechanical Engineering. All rights reserved.

Keywords: cooling tower, modifications, local efficiency

0 INTRODUCTION We present an experimental method of local efficiency measurement and analysis to evaluate adequacy of air inlet region modifications in a cooling tower. Other authors use numeric CFD simulations [1] and [2], mathematical modeling [3] or experimental methods [4] in order to estimate cooling tower performance. However, not all methods are able to locally predict efficiency.

Some thermal power plants in the past were built near residential areas, with cooling towers representing a significant source of noise. Later, measures were taken to improve this. However, such measures should not reduce the efficiency of power plants, increase emission of smoke gases or have adverse economic effects.

In thermal power systems, heat is drawn away from the cyclic process to the surroundings by the cooling water. The efficiency of cooling system operation is one of the important factors that influence the efficiency of the whole thermal power system. The amount of heat drawn away by the cooling system is greater than the amount converted to work in the steam process. The amount of drawn-away heat in recently used 750

(new and old) cooling systems varies from 1.3 to 2.5-times the amount of work gained from the system [5] which in any amount of efficiency reduction can result in a significant influence on the efficiency of the entire thermal power system and thus can have a negative impact on the environment.

The quality of heat transfer process can be described by efficiency [6]:

η=

t w, i − t w, o tw,i − twb,i

, (1)

where tw,i denotes the temperature of inlet water, tw,o is the temperature of outlet water and twb,i denotes wet-bulb temperature. Temperature twb,i represents boundary temperature and is the highest possible temperature the air flow through the cooling tower can have at present atmospheric conditions after being heated with water. A temperature difference between the temperature ta,o of the outlet air and boundary temperature twb,i [7]:

ta,o < twb,i (2) is the consequence of deviations, which in most cases are connected with anomalies in the process

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

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of heat and mass transfer inside cooling towers.

Therefore, the information on local temperatures of outlet air is of great value for diagnostics of the local efficiency of cooling towers.

However, the use of efficiency according to Eq. (1) is not appropriate if the outlet humid air is saturated or very near the saturation curve of the Mollier diagram. In the presented experiment, the humid air above the drift eliminators is constantly saturated, therefore, another definition was used as follows.

In the cooling tower, the processes of heat and mass transfer are intensive, as well as the momentum between the sprayed water droplets and humid air. Various analysis methods, which take into account the thermodynamic calculation of cooling towers, are based on Merkel’s basic equation [8] and [9]. Here, the efficiency is a function of the exponential dependence of, among others, the ratio between water- and humid air mass flows. However, because the efficiency also depends on geometry, the enthalpy efficiency of vertical segment was defined by the following relation with enthalpies for the case when the air above drift eliminators is fully saturated [10]: m da h(1+ x ),o η= = m da h(1+ x ),i + m w c pw ⋅ tw,i

(3)  m V − a  w ρ  m a L   = 1− e

b

 m  − a  w  m ≈ 1− e  a 

b

.

The efficiency can be connected with operating parameters of the process, such as local cooling water flow, local geometric anomalies with changes in the local velocity field of cooling air as a consequence, etc. In the above equation, m da is dry air mass flow, h(1+x),i is specific humid air enthalpy at inlet, h(1+x),o is specific humid air enthalpy at outlet, m w is local water mass flow, ρ is air density, cpw is specific heat of water at constant pressure, V is volume and L is the characteristic dimension of lamellate heat exchangers. Constants a , a and b must be selected by an experiment. In order to evaluate the influence of sound protection measures on the efficiency of cooling tower operation, the ratio of mass flows m w / m a has to be estimated by using temperature distribution on the drift eliminators inside the cooling tower obtained by thermal vision measurements.

Noise in a cooling tower is generated by the falling water. The emitted acoustic power is proportional to the flow rate of water, the velocity of droplets at the moment they fall into water, and water depth in the pool [11]. Most of the noise is emitted through the inlet windows around the circumference of the cooling tower, below the heat exchangers and water collecting channels.

The acoustic power emitted by a cooling tower reduces if the depth of its pool decreases [11].

In the following, we will present the applied measures for airflow inlet region modifications of the cooling tower of the Šoštanj 4 thermal power plant to reduce the above mentioned problem.

We will estimate local cooling tower efficiencies in accordance with Eq. (3). For measurements, the thermal vision method [7] for measuring the temperature field on the surface of drift eliminators was selected. In order to estimate the influence of airflow inlet region modifications on cooling tower efficiency, temperature measurements were performed prior to and after the reconstruction of the cooling tower.

1 COOLING TOWER The analyzed cooling tower is a natural draft cooling tower of a 275 MW Šoštanj 4 coal power plant. The diameter of the cooling tower at the location of lamellate heat exchangers is 80 m, while the diameter on the ground level is 90 m.

The height of the lamellate heat exchanger region is 16.3 m above the ground. The total height of the cooling tower is 92 m.

Noise generated by the Šoštanj thermal power plant at the selected location of the nearest residential houses exceeded the limit by 4 dB(A) during the night [12] to [14]. Measurements were performed in accordance with the requirements for measurements of noise in natural and living environments [12].

In order to identify the noise sources, measurements with an acoustic camera were performed [15]. The identified sources were inlet windows of the cooling tower, which are located on the periphery around the circumference of the cooling tower. Behind the inlet windows, water collecting channels are located, where falling water droplets from lamellate heat exchanger region are collected and directed into the return

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pipe. The water collecting channels are located approximately 12.5 m above the ground level.

However, as water collection channels of the cooling tower are open for inlet air entering from below, the sound is also reflected by the water surface in the pool at the ground level.

The schematics of cooling tower structure at the location of water collecting channels is shown in Fig. 1. Airflow inlet region modification was proposed to reduce the noise emission at the source as explained below.

Fig. 1. Schematics of inlet windows region of the cooling tower, modification of airflow inlet region In the given case, the selected technical solution for airflow inlet region modification was to shut the upper part of the inlet windows, as shown in Fig. 1, using perforated noise absorbing panels. Such a solution should largely eliminate direct noise propagation from inlet windows around the circumference of the cooling tower, while protection from the noise reflected from water pool surface at the ground level would be limited.

Perforated panels made of hard plastic material were used. The height of panels is 5 m, and their thickness is 7 cm. As shown in Fig. 1, panels were set on the periphery of the cooling tower around the height of channels for collecting the cooling water.

Airflow inlet region modification reduced noise level at the location of nearest residential houses [12] and [14]. The results of measurements confirm the adequacy of modifications, such that the legislatively required noise levels were achieved.

752

However, the modification of airflow inlet region has influenced the mass flow rate of cooling air and its distribution in the cooling tower, therefore changing overall and local efficiencies of cooling tower operation [7] and [10]. The influence of airflow inlet region modification on the thermal efficiency of cooling tower operation is expected above all on the periphery of the cooling tower heat exchange area.

We assume that change in local efficiency can be detected as variation of temperature distribution on the surface of drift eliminators.

Variation in temperature distribution on the surface of drift eliminators can be measured with thermal vision method [7]. To estimate the change in local efficiency according to Eq. (3), parameters of cooling tower a and b and mass flow rate ratio m w / m a must be known. Parameters a and b from Eq. (3) were measured in this particular cooling tower [10] in the selected vertical segment of the cooling tower. We assume that they are valid in the entire cooling tower. Mass flow rate ratio m w / m a has changed after the airflow inlet region modifications and the change has to be estimated using measurements of temperature of drift eliminators. The measurements of local properties of the cooling tower are required to estimate the dependency between temperature of drift eliminators and mass flow rate ratio m w / m a for the particular cooling tower. The presentation is given in section 1.1 below.

1.1 Measurements of Local Properties of Cooling Tower Measurements of local properties of the cooling tower enabled the estimation of the relationship among air/water mass flow rate ratio m w / m a and temperature of drift eliminators.

Measurements were performed on the vertical segment of cooling tower. The latter was selected in the region of the cooling tower where geometrical properties are homogeneous. The schemes of the selected segment are presented in Fig. 2. It consists of lamellate heat exchanger located at the bottom, spray element in the central part, and drift eliminators in the upper part of the segment. The following variables were measured: ta,i - temperature of inlet air, tw,i - temperature of inlet water,

Dvoršek, M. ‒ Hočevar, M. ‒ Širok, B. ‒ Holeček, N. ‒ Donevski, B.

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ta,o - temperature of outlet air, tw,o - temperature of outlet water, wa,o - humid air velocity, Vw,o - cooling water volume flow rate.

Fig. 2. Schematics of the selected cooling tower segment with location of measurement points For temperature measurements, 4-wire Pt-100 thermometers were used. The position of thermometers is presented in Fig. 2. Temperatures tw,i were measured inside the pipes in the central and two neighboring locations. Inlet air temperature ta,i was measured in a container which was open from the bottom, while water temperature at fill system outlet tw,o was measured in a container open from the top. The volume of both containers was approximately 0.5 l. The uncertainty of temperature measurement was estimated to be less than 0.25 °C. Air velocity measurements were performed using pre-calibrated vane anemometer with low friction bearings lubricated with paraffin oil. The uncertainty of velocity measurement was estimated to 0.1 m/s. Temperature signal conditioning and data acquisition were performed using Hewlett Packard HP 34970A data acquisition unit, connected to the personal computer. Measurement sampling frequency was 1 Hz, and total acquisition time was 7500 s.

Cooling water volume flow rate V was measured using volumetric method. Water volume

flow rate was measured at the outlet spray nozzle using a vessel with the volume of 30 l. Time, required to fill the vessel was measured. Care was taken that no water from neighboring spraying elements entered the vessel and that no water from measured spray element was lost. Cooling water volume flow rate was measured before the sampling of other variables was started.

Inlet air humidity was determined on the basis of dry- and wet-bulb measurements.

Humidity, as well as other ambient air parameters were observed in selected locations in 30 s intervals.

All the equipment used in experiments was pre-calibrated. The systematic measurement uncertainty met the requirements of the standard for measuring cooling tower characteristics [16].

Measurements of the local properties of the cooling tower were performed in seven measurement points in which cooling water volume flow rates Vw,o were constant at 4.2 and 4.7 l/s/m2, while other variables varied. The airflow velocity wa,o ranged from 0.95 m/s to 2.3 m/s, while mass flow rate ratio m w / m a ranged from 1.59 to 3.42. Inlet air humidity ranged from 42 to 51%, inlet air temperature ta,i ranged from 15.3 to 17.5 °C, outlet air temperature ta,o ranged from 23.1 to 33.2 °C, sprayed water temperature tw,i ranged from 25.5 to 34.0 °C, and temperature of the water at fill system outlet tw,o ranged from 17.4 to 27.4°C. 2 THERMAL VISION MEASUREMENTS OF DRIFT ELIMINATORS Thermal vision method enables to measure the temperature field of drift eliminators inside natural draft cooling towers. The measurement system is shown in Fig. 3.

Fig. 3. Schematics of the thermal vision method for temperature measurements of drift eliminators inside the cooling tower

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During the cooling tower operation, the fluid above the drift eliminators comprises air and water either in gaseous phase or in form of small droplets. Humid air and droplets generally impair the transmission of infrared electromagnetic radiation [17]. Širok et al. [7] have shown that temperature measurements inside a cooling tower using an infrared camera operating in 7.5 to 13 mm range were within a frame of measurement uncertainty with temperature measurements using precise RTD sensors up to the distance of 25 m.

2.1 Thermal Camera Temperature measurements of the surface of drift eliminators were performed by an AGEMA 570 infrared sensitive camera, which operated in far-infrared range of wavelengths between 7.5 mm and 13 mm. It had a built-in 24° lens with spatial resolution 1.3 mrad. The thermal camera applied a Focal Plane Array (FPA) detector, which consisted of a matrix with 320×240 elements/pixels. The accuracy of the camera is ±2 °C according to the manufacturer’s specifications, while the thermal sensitivity is 0.15 K. Thermal images were recorded to a PC card which was inserted in the camera.

2.2 Thermal Camera Measurement Procedure

Installation

and

The thermal camera was enclosed in a protective container (Fig. 3) which was continually purged with the compressed dry air supplied by a compressor through a hose from the outside of the cooling tower. This was necessary in order to protect the thermal camera from high relative humidity of the air (close to 100%) and condensation inside the cooling tower. The lens of the thermal camera was directed coaxially through an orifice in the protective container, while the camera lens was located 5 mm behind the orifice inside the container. The orifice was slightly larger in diameter than the camera lens, so a narrow coaxial gap was formed between the lens of the thermal camera and the wall of the orifice.

The compressed air left the protective container through this gap, thus preventing the condensed water particles from building up on the thermal camera lens. Flexible transparent foil was mounted 754

on the backside of the protective container to enable access to controls on the thermal camera.

The thermal camera, together with its protective container, was mounted on an adjustable stand as depicted in Fig. 3. The stand was located in the middle of the cooling tower. The height of the stand was 2.3 m above the surface of drift eliminators. Thermal images were acquired so that the camera and its protective container were rotated around their vertical axis in steps of approximately 22°. The temperature field of the whole surface of drift eliminators of the cooling tower was covered in 16 segments corresponding to different thermal camera rotations in the horizontal plane.

The positioning of thermal camera in the meridian plane was carried out with the aid of markers and intrinsically incorporated objects of the cooling tower, like wall structure, pathways and fences. As markers, cold objects approximately 90×180 mm in size was used.

They were placed at different positions on the drift eliminator plane of the cooling tower where access was possible; otherwise, objects that are intrinsically incorporated in the cooling tower itself were used. Positions of markers were measured by measuring tape, therefore their exact position was known. Positions of intrinsically incorporated objects were recognized based on technical drawings. Due to low temperature, markers were visible on thermal images, while intrinsically incorporated objects were visible because of different emissivity or temperature.

Four markers were used at each thermal camera position: two inner ones – close to the lower edge of camera’s field of view, and two outer ones – close to the upper edge of camera’s field of view near the circumference of the cooling tower. The same markers were used in neighboring segments of the cooling tower, whereas in segments close to the pathways markers were put as close to the pathways as possible. Markers enabled the spatial transformation from acquired thermal images to the temperature field above the drift eliminators in cooling tower coordinates.

Based on the analysis of acquired thermal images, projective transformation was used for each thermal camera position to transform temperature information to real cooling tower coordinates. Projective transformation with

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bicubic interpolation for temperature was selected as it is suitable for tilted images and because straight lines in original images are transformed to straight lines on the transformed image.

Temperatures of all 16 measured segments were then combined into a single temperature field of drift eliminators for the complete cooling tower.

The method used is based on an experimental modeling approach, which is quite common when analysing cooling towers. While the analysis of the same problem was not found in the available published literature, other authors deal with cooling tower design modifications for various reasons like guiding plates for cross-wind conditions [2] and [4].

2.3 Environmental Conditions The temperature measurements with the thermal vision method were carried out before and after the installation of sound insulation panels.

During the measurements, performed before the installation of sound insulation panels, the following average environmental conditions were recorded: inlet air temperature ta,i 22.4 °C, inlet air humidity 43%, outside air velocity 1.6 m/s, inlet water temperature tw,i 31.2 °C and outlet water temperature tw,o 24.5 °C. Measurements after the installation of sound insulation panels were performed at the following average environmental conditions: inlet air temperature ta,i 9.3 °C, inlet air humidity 81%, outside air velocity 2.9 m/s, inlet water temperature tw,i 23.0 °C and outlet water temperature tw,o 7.9 °C. 3 RESULTS AND DISCUSSION Two-dimensional temperature measurements in the plane of drift eliminators were performed using thermal camera, and for the analysis of efficiency they were used with Eq. (3), which gives local efficiency in each vertical cooling tower segment. Each measured temperature on the plane of drift eliminators is linked to the properties of cooling tower’s vertical segment by Eq. (3) through dependency presented in Fig. 4. Temperature measurements in the two-dimensional plane of drift eliminators therefore supplement the local measurement of cooling tower characteristics in the single vertical segment. By assuming that local characteristics measured in the single vertical segment of the cooling tower are valid in the entire cooling tower, the presented analysis procedure enables the analysis of local efficiency for the entire cooling tower.

Fig. 4. Mass flow rate ratio m w / m a dependence on temperature of drift eliminators ta,o Measurements in cooling tower are limited due to cooling tower size, complexity and dependence on requirements of power generation system. Usually it is not possible to vary one parameter and set all other parameters constant.

Scatter of measurements is usually large due to continuous change of most of environmental parameters. However, due to extreme large size of the system, variables change is slow and the number of measurement points low, making it difficult to evaluate the influence of environmental and other parameters. In our case it is thus impossible to show influence of environmental parameters on mass flow ratio and efficiency apart from those that were m w / m a actually measured.

3.1 Measurement Uncertainty of Temperature Measurements of Drift Eliminators Temperature of drift eliminators was measured using thermal camera as presented in sections 2.1 and 2.2. Absolute measurement uncertainty of the thermal camera is in the range of few °C, and is larger than required for measuring local efficiency change. The influence of absolute measurement uncertainty of the camera is depicted in Fig. 5, which shows the temperature

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measurements of drift eliminators before the airflow inlet region modifications. In Fig. 5, noncontinuities between 16 measured sections of the cooling tower indicate the influence of absolute measurement uncertainty.

Fig. 5. Results of temperature distribution measurements inside the cooling tower before the installation of sound absorption panels; white regions represent passages To tackle the issue of measurement uncertainty, absolute temperature measurements of drift eliminators were used only for the case of measurements before the airflow inlet region modifications. Relative measurements between the inner and outer part of cooling tower were used in the case of measurements after the airflow inlet region modifications. It was presumed that flow properties and temperatures in the middle of the cooling tower far from the position of the airflow inlet region modifications do not change. The boundary between both regions was selected at the half of the cooling tower radius. Measurements after the airflow inlet region modifications were used only to estimate the temperature change at the perimeter relative to the inner part of the cooling tower. Using this relative approach, measurement uncertainty can be estimated by the thermal sensitivity of thermal camera, which is 0.15 °C. In addition, the results in [7] indicate that the uncertainty of thermal measurement including the propagation through the saturated air in the cooling tower is below 0.4 °C.

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3.2 Estimation of Cooling Tower’s Local Properties Under the assumption that outlet cooling air temperature is the same as the temperature of the surface of drift eliminators, local efficiency in the cooling tower can be estimated according to the model represented by Eq. (3). According to Eq. (3), air and water flow rates are required for the estimation of local efficiency, but they can only be measured with difficulty and only in selected locations. Instead, the temperature of drift eliminators was used to estimate the local efficiency. The available literature only revealed the work of Kloppers [18] who experimentally evaluated the local efficiency of cooling towers based on the measurements of outlet air temperature. The measurement procedure in [18] was similar to the one presented here. The manufacturers of cooling tower equipment among others use the temperature of drift eliminators to estimate the upgrade capabilities of existing cooling towers.

The estimation of the properties of the cooling tower was performed as explained in section 1.1. Fig. 4 shows the measured relationship among air/water mass flow rate m w / m a and temperature of drift eliminators. Measurements were performed in seven measurement points. The latter were selected in a way that the operational parameters of the plant and cooling tower were constant, while it was not possible to control environmental parameters. This resulted in a large deviation of measured points from the fitted line in Fig. 5. The most important environmental parameter is inlet air humidity. Inlet air relative humidity was ranged from 42 to 51% in the case measuring the local characteristics of the cooling tower, while it was 43% while measuring the temperature of drift eliminators for the measurement of efficiency. Unfortunately, environmental variables cannot be controlled; it is only possible to postpone measurements until appropriate environmental parameters are available. However, this can only be done in a limited time interval because of the complexity of measurements.

If more measurement data were available, the fitted line could be exchanged for a more elaborate relation, taking into account other

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parameters like ambient temperature, humidity, wind speed and direction, power plant output, etc. Given the complexity of measurements and high dimensionality of the problem, the results in Fig. 4 present the cooling tower characteristics fairly well. The relation in Fig. 4 is also limited to the construction of the observed cooling tower, although it can be presumed that the general trend of the presented dependence is characteristic of all natural draft cooling towers. In this particular case, the presented relation can be used for the estimation of the influence of airflow inlet region modifications on local efficiency of the cooling tower.

3.3 Temperature of Drift Eliminators and Cooling Tower’s Local Efficiency The temperature of drift eliminators before airflow inlet region modifications is presented in Fig. 5. No spatial filtering method was used for presentation in Fig. 5. From the temperature field of drift eliminators, the local efficiency before the airflow inlet region modifications was estimated using Eq. (3) and mass flow rate ratio m w / m a in Fig. 4. The local efficiency before the installation of sound protection panels is shown in Fig. 6.

In order to estimate the difference in efficiencies from both measurements before and after the airflow inlet region modifications, we have to consider that the measurement uncertainty of the camera is high compared to expected changes in temperature distribution, and that both measurements were performed at different environmental conditions. Therefore, an approach was used which is based on the difference between the temperature in outer region and the temperature in inner region of the cooling tower as explained in section 3.1. Temperature differences in the inner and outer region of segments of both cases prior to and after modifications were then used with data from the local measurement of cooling tower properties according to the procedure presented in section 1.1.

A change in local efficiency after the installation of sound absorption panels is shown in Fig. 7.

Local efficiency after the installation of sound absorption panels decreased up to 0.02.

The changes are localized to the circumference of

the cooling tower. In addition, in some locations on the circumference, changes in efficiency were not recorded. This is not surprising, as flow and thermal properties around the circumference often differ from those in the middle of the cooling tower [3]. The current cooling tower also has lamellate heat exchangers installed high above the ground compared to it’s diameter and overall height, as can be seen in Fig. 1. Such configuration helps reducing the decrease in local efficiency. Other authors have provided mixed results for different cooling tower modifications [2] and [4], however, none of them studied the airflow inlet region modifications at the location of water collection channels.

Fig. 6. Local cooling tower efficiency before the installation of sound absorption panels; white regions represent passages

Fig. 7. Decrease of local efficiency after the installation of sound absorption panels; white regions represent passages

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The overall decrease of local efficiency of up to 0.02 can be generally estimated as small.

This is in agreement with the results presented in [19], which show that the effect of inlet height on radial non-uniformity of cooling tower properties is very small in comparison with the effect of water flow rate change. Water flow rate did not change with the airflow inlet region modifications. Also, power plant operators did not notice any decrease in overall power plant performance including inlet/outlet cooling water temperature difference from the cooling tower. Operator’s estimation was not systematically evaluated.

The presented method allows an evaluation of the cooling tower performance for the case of modifications like the airflow inlet region modifications. Temperature measurements of drift eliminators using thermal camera are fast and easy, while measurements of local properties of cooling tower require much more effort, as emphasized also in [19]. In the cooling towers, where the dependency between mass flow rate ratio m w / m a and temperature of drift eliminators is unknown, operators may only use thermal measurements of temperature eliminators to regularly check the cooling tower operation. In general, high local temperature represents the locations of lower heat transfer efficiency.

In addition to the above mentioned benefits, the following most important drawbacks of the method must be mentioned: (i) measured data represents the temperature on the surface of drift eliminators and no further information about temperature distribution inside the lamellate heat exchangers can be directly established using thermal vision method; (ii) estimation of local efficiency is limited due to the necessity to use experimentally derived constants a and b for use in Eq. (3), which is valid only for a selected cooling tower and for limited interval of operational and environmental parameters; (iii) use of experimentally derived relationship between mass flow ratio m w / m a and temperature of drift eliminators according to Fig. 5, which is also valid for the selected cooling tower and for the limited interval of operational and environmental parameters, which usually do not match environmental parameters during measurements either before or after modifications. Among 758

environmental parameters, inlet air humidity was estimated as the most important one.

Verification of the local efficiency decrease cannot be measured using any other method known to us except local measurement of all variables from Eq. (3), which is difficult, time consuming and therefore not feasible. We see measurements in accordance with [16] or numerical modeling [1] and [19] as one of the possible comparisons.

4 CONCLUSIONS Temperature measurements of drift eliminators were performed before and after the installation of sound protection panels. Based on these results, changes in local efficiencies were estimated. Results show a slight decrease of local efficiency at the circumference of the cooling tower, while in general decrease is small.

Verification of the estimated changes of local efficiency can also be determined using measurements performed in accordance with [14].

5 REFERENCES [1] Al-Waked, R., Behnia, M. (2006). CFD simulation of wet cooling towers. Applied Thermal Engineering, vol. 26, no. 4, p. 382395.

[2] Al-Waked, R., Behnia, M. (2007). Enhancing performance of wet cooling towers. Energy Conversion and Management, vol. 48, p.

2638-2648.

[3] Williamson, N., Armfield, S., Behnia, M. (2008). Numerical simulation of flow in a natural draft wet cooling tower – The effect of radial thermofluid fields. Applied Thermal Engineering, vol. 28, no. 2-3, p.178-189.

[4] Wang, K., Sun, F. Z., Zhao, Y. B., Gao, M., Ruan, L. (2010). Experimental research of the guiding channels effect on the thermal performance of wet cooling towers subjected to crosswinds – Air guiding effect on cooling tower. Applied Thermal Engineering, vol.

30, no. 5, p. 533-538.

[5] El-Wakil, M.M. (1985). Powerplant Technology, McGraw-Hill, New York.

[6] Ibrahim, G.A., Nabhan, M.B.W., Anabtawi, M.Z. (1995). An investigation into a falling film type cooling tower. International

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Journal of Refrigeration, vol. 18, no. 8, p.

557-564.

[7] Širok, B., Hočevar, M., Bajcar, T., Blagojević, B., Dvoršek, M., Novak, M. (2006). Thermovision Method for Diagnostics of Local Characteristics of Natural Draft Cooling Towers.

Instrumentation Science & Technology, vol.

34, no. 3, p. 289-304.

[8] Hampe, E. (1975), Kühltürme, VEB Verlag für Bauwessen, Berlin.

[9] Heyns, J.A., Kröger, D.G. (2010).

Experimental investigation into the thermal-flow performance characteristics of an evaporative cooler. Applied Thermal Engineering, vol. 30, no. 5, p. 492-498.

[10] Širok, B., Blagojević, B., Novak, M., Hočevar, M., Jere, F. (2003). Energy and mass transfer phenomena in natural draft cooling towers. Heat transfer engineering, vol. 24, no. 3, p. 66-75.

[11] Presnov, G.V., Zroichikov, N.A., Galas, I.V., Patakin, A.A., Moskvin, A.G., Lisitsa, V.I., Morozova, E.A. (2006). An efficient method for suppressing noise from the cooling tower at OAO Mosenergo’s TETs-23 cogeneration station. Thermal Engineering, vol. 53, no.

11, p. 910-912.

[12] Decree on noise in the natural and living environment (1995). Official Gazette of the Republic of Slovenia, vol. 45, p. 3530-3535. (in Slovene)

[13] Deželak, F. (2005). Report on measurements and expert opinion - noise in the natural and living environment. Technology report LFIZ 05123, ZVD, Ljubljana. (in Slovene) [14] Deželak, F. (2006). Report on measurements of noise in environment - noise in the natural and living environment. Technology report LFIZ-20060172-FD/M, ZVD, Ljubljana. (in Slovene) [15] Deželak, F. (2006). Results of recording with acoustic camera. Technology report LFIZ-20060132-FD/M, ZVD, Ljubljana (in Slovene).

[16] DIN (VDI Code of practice) 1947 (1989).

Thermal performance acceptance testing of water cooling towers. Deutsches Institut Für Normung E.V., Berlin.

[17] Gayo, E., de Frutos, J. (1997). Interference filters as an enhancement tool for infrared thermography in humidity studies of building elements. Infrared Physics & Technology, vol. 38, no. 4, p. 251-258.

[18] Kloppers, J.C. (2003). A critical evaluation and refinement of the performance prediction of wet-cooling towers. PhD thesis, University of Stellenbosch, Stellenbosch.

[19] Hawlader, N.A., Liu, B.M. (2002).

Numerical study of the thermal–hydraulic performance of evaporative natural draft cooling towers. Applied Thermal Engineering, vol. 22, no. 1, p. 41-59.

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Strojniški vestnik - Journal of Mechanical Engineering 57(2011)10, 760-767 DOI:10.5545/sv-jme.2010.246

Paper received: 06.12.2010 Paper accepted: 15.07.2011

Global Optimization of Lateral Performance for Two-Post ROPS Based on the Kriging Model and Genetic Algorithm Jixin, W. ‒ Mingyao, Y. ‒ Yonghai, Y. Wang Jixin* ‒ Yao Mingyao ‒ Yang Yonghai Jilin University, College of Mechanical Science and Engineering, China

To improve their energy-absorption capacity, the current study provides a global optimization design method for two-post rollover protective structures (ROPS) that utilizes the Latin hypercube method to determine sample point values, the Kriging model as an alternative to traditional second-order polynomial response surfaces for constructing global approximations, and the genetic algorithm to yield optimized results. Through optimization, a satisfactory variation tendency of object function in the lateral loading analysis is obtained, and the load-carrying capability, deformation, and energy absorption are found to match each other well. The matching rationality between energy absorption and lateral loadcarrying capability effectively improves the energy-absorption capacity of the ROPS. ©2011 Journal of Mechanical Engineering. All rights reserved.

Keywords: engineering vehicle, rollover protective structure (ROPS), global optimization, Kriging, genetic algorithm, energy absorption 0 INTRODUCTION Earthmoving machinery is susceptible to rollovers because of poor working conditions and complicated roads where stability is decreased [1] and [2]. Rollover casualties of earthmoving machinery have been identified as a serious problem. To reduce rollover fatalities, rollover protective structures (ROPS) were developed [3] to [5]. ROPS, together with operator restraint systems (seatbelts), keep the operator within a protected area and provide a survival zone during lateral rollover accidents. This survival zone, however, is not enough for major accidents, and a considerable amount of the rollover kinetic energy must be absorbed through the permanent plastic deformation of ROPS components, so that the rollover kinetic energy absorbed by the driver is at a minimum.

Traditional design methods for ROPS, such as empirical design and qualitative-analogical design, usually go through a repetitive process of design–test–revise design–retest, leading to substantial wastage of manpower and material resources. Furthermore, a significant disadvantage of the traditional method is that it is not valid for an effective analysis of the lateral energy absorption of ROPS because it often increases the lateral force to values much larger than the International Organization for Standardization (ISO) minimum 760

standard even when the lateral energy absorption meets ISO requirements (Sketch map shown in Fig. 1).

Fig. 1. Sketch map of performance curves of typical lateral energy absorption and load carrying If the energy-absorption coefficient is deficient, cracking failures may occur at the connection between the beam and the post (shown in Fig. 2), which may result in the collapse of the whole ROPS [6]. When the ROPS cracks, the lateral energy is not absorbed by the permanent plastic deformation, especially the plastic hinge rotation, of the ROPS components.

To solve this energy-absorption problem, reduce the failure rate during laboratory tests, and shorten the design period, the current work

*Corr. Author’s Address: College of Mechanical Science and Engineering, Jilin University, Changchun, China, jxwang@jlu.edu.cn

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provides a global optimization method for ROPS design. Here, the values of the sample points are selected using the Latin hypercube method, the response surface is established using the Kriging model, and the sample points are optimized through genetic algorithm (GA).

• • •

orthogonal experimental design, uniform test, latin hypercube.

In the present study, the Latin hypercube method is used to determine the sample points because it can control the location of sample points, thus avoiding superposing within a small neighborhood [7]. If n sample points are carried out, m random variables are divided into n short equiprobable intervals, and the whole sample space is divided into equiprobable n×m intervals.

For each variable, n sample points separately fall in each short interval − equiprobably located in the whole randomly dispersed space.

Using the Latin hypercube sampling method, an approximation response surface with preferable overall performance is obtained.

1.2 Calculation of ROPS Response

Fig. 2. Cracking failure of weld in two-post ROPS connection 1 ESTABLISHMENT OF KRIGING MODEL Many factors can affect the weight and performance of ROPS, such as the height, width, and length of the cab; the height, length, and thickness of the post and the beam; and the dimensions and thickness of the stiffeners. Because the correlation between the above-mentioned design variables and ROPS performance cannot be explicitly expressed, each design proposal should be processed through nonlinear finite element analysis, along with a large deformation study, which is time-consuming. To save computational expenses, the paper uses the Kriging model to construct the response surface to represent the approximate relation between the design variables and ROPS performance.

1.1 Selection of Sample Points Before constructing the Kriging model, a certain amount of given information is obtained through tests. The selection of sample points is a key step during the tests. Several choice methods used to determine the sample points are the following:

A finite element model (FEM) of the ROPS using ANSYS software [ANSYS Parametric Design Language (APDL)] is created. The response of the ROPS is obtained using material and geometric nonlinear analysis for each sample point.

1.3 The Kriging Model Generally, a second-order polynomial response surface model and a Kriging model are used to improve the efficiency of optimization design. Based on Refs. [8] to [12], the construction of a second-order polynomial response surface model becomes relatively more simple with less computation. However, it does not have ideal prediction accuracy when high-grade nonlinear problems are encountered.

Simpson et al. [13] have shown that the Kriging model has features of unbiased estimation for sample points and super nonlinearapproximation ability. Therefore, the Kriging model is a relatively ideal model for the nonlinear optimization of ROPS. The Kriging model consists of a parametric model and a non-parametric random process [10].

Suppose that the actual relationship between system response values and independent variables could be expressed as follows:

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y(x) = f(x)+z(x) ,

(1)

where y(x) is the unknown function of interest, f(x) is the deterministic part generally expressed as a polynomial, and z(x) is the random field and the realization of a stochastic process. The f(x) in Eq. (1) is similar to a polynomial response surface and can provide a “global” model of the design space. In many cases, f(x) is taken as a constant.

Meanwhile, f(x) globally approximates the design space, and z(x) creates “localized” deviations.

Therefore, the Kriging model can well interpolate the sample points. The mean, variance, and covariance matrices of z(x) are given in Eqs. (2) to (4): E[z(x)] = 0 ,

(2)

Var[z(x)] = σ2 ,

(3)

Cov[z(xi), z(xj),] = σ2 R[R(xi, xj)] ,

(4)

where R is the correlation matrix and R(xi, xj) is the space-related equation between any two sample points xi and xj in ns sample points that play a decisive role in the accuracy of simulation. The relevant equation that yields the best calculation results is the Gaussian correlation equation [14].

The form of the Gaussian correlation function is as follows:

nv

R( xi , x j ) = exp(−∑ θ k xk − xk i

j δk

),

(5)

k =1

where nv is the known number of design variables and xki and xkj are the kth constituent of the sample points xi and xj. Parameters θk and δk stand for the related parameter and smoothness parameter, respectively, which ensure sufficient flexibility in the calculation of relevant equations. R(xi,xj) is entirely continuous but non-differentiable when θk = 1 and infinitely differentiable when δk = 2.

Linear combinations of known response values of samples are usually used to estimate the response of any given sample. Through derivation, the predicted value of the model is:

∧

∧

∧

y = β + r T ( x) R −1 ( y − f β ).

(6)

where y = [y1, y1,..., yn]T is the response value ∧ and y is the estimation value; f is the post vector when f(x) takes a constant value; and rT(x) is the correlation vector of length ns between an untried x and the sampled data points {x1, x1,..., xn}, as shown in Eq. (7): 762

rT = [R(x,x1), R(x,x2), ..., R(x,xn)]T

(7)

∧

by:

β is an estimator that can be calculated ∧

β = ( f T R −1 f ) −1 f T R −1 y.

(8)

∧ 2

∧

The variance σ can be determined by β and y by the following:

∧

∧

( y − f β )T R −1 ( y − f β ) σ = . ns ∧ 2

(9)

θk, which is the unbiased estimator of the Kriging model, can be calculated by Eq. (10). ∧

max Φ (θ k ) = −

[n ln(σ 2 ) + ln R ]

θk > 0

2

.

(10)

Therefore, the model parameters for the Kriging model construction that must be identified include f(x), r(x), and θ [8], [15] and [16]. In summary, the Kriging model construction problem is converted into a non-linear unconstrained optimization problem.

2 GENETIC ALGORITHM OPTIMIZATION 2.1 Genetic Algorithm (GA) In the current study, the objective function is the minimum difference between the force from the lateral load-carrying capability test and the force from the minimum lateral energy-absorption test. The constraint function is the performance index of ROPS. GA is an adaptive random-search algorithm, with features of concurrency and global convergence. GA directly takes the fitness function as search information and encodes all solutions in the solution space when solving optimization problems. During the optimization process, by combining (genetic variation and mating) chromosomes (coding of individual solutions), new solutions are continuously generated. According to the fitness function, some combinations of chromosomes are selected to be continued in the new solutions until the optimal solution is finally achieved.

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2.2 Optimization A flow chart of optimization for two-post ROPS based on the Kriging model and GA is shown in Fig. 3.

1. After the initial number of sample points is determined, specific values of the initial sample points are selected using the Latin hypercube method.

2. According to the selected points, the FEMs of ROPS, along with large elastic-plastic deformation properties, are created in finite element software. The responses, such as load carrying, deformation, and energy-absorption capability, are obtained through nonlinear materials and geometric nonlinear analyses.

3. An approximate response surface is established using Design and Analysis of Computer Experiments software, which is a MATLAB toolbox for converting Kriging approximations to computer models [18] to [22].

4. Optimal results are obtained using the GA optimization program based on the Kriging model.

5. After GA optimization, optimal results of GA are substituted into FEM for the verification of ROPS performance. The obtained points are checked in a regular sequence to determine whether or not the conditions satisfy the constraints and meet the accuracy requirements. If there is a sample point that meets both requirements, it is considered the optimization result. Otherwise, all the sample points will be added into the FEM of ROPS to update the Kriging model. This process is carried out repeatedly from Steps 3 to 5 until the final optimal results are obtained.

3 APPLICATION A two-post ROPS was taken as an example.

Its FEM is shown in Fig. 4.

Fig. 3. Flow chart of GA optimization for two-post ROPS based on the Kriging model Global Optimization of Lateral Performance for Two-Post ROPS Based on the Kriging Model and Genetic Algorithm

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and the force from the minimum lateral energyabsorption test is taken as an object function.

min ΔF = ΔF(x1, x2, x3, x4, x5) ,

(12)

where ΔF is the difference value between the two forces. As shown in Eq. (11), x1, x2, x3, x4, x5 are the design variables.

3.1.3. Constraint Conditions

Fig. 4. FEM and boundary conditions of two-post ROPS 3.1 Mathematical Model of Optimization 3.1.1 Design Variable The height and width of the ROPS are held constant; the structural parameters of the bracket, frame, top components of Falling object protective structures (FOPS), and the parameters of the ribs of ROPS are considered constant.

The design variables that have a considerable influence on the lateral load-carrying capacity and energy-absorption capacity of ROPS are the sectional dimensions of the beams and posts. In order to easily weld the joint of the post and beam, the width of the post is taken as the width of the beam.

Therefore, the independent design variables are shown as follows.

x = [x1, x2, x3, x4, x5] ,

(11)

where x1 and x2 are the width and the height of the bridging beam sections, respectively; x3 is the height of the post section; x4 is the wall thickness of the bridging beam section; and x5 is the wall thickness of the post section.

(1) Boundary constraints of design variables.

According to the section size of the available profile of steel and design space constraints on ROPS, the values of design variables are as follows: 80 ≤ x1 ≤ 190,  60 ≤ x2 ≤ 160,

60 ≤ x3 ≤ 120, 6 ≤ x ≤ 12, 4  6 ≤ x5 ≤ 16.

(2) Deformation constraint. The deflection limitation volume (DLV) is fixed based on the Seat Index Point of a seat. The allowable maximum lateral deformat ion can be calculated according to the space between ROPS and DLV. For this two-post ROPS, the maximum lateral displacement DL is 300 mm, so DL ≤ 300 mm.

(3) Load-carrying capability constraint. Based on [5], the lateral load carrying FL is 150 kN, so FL ≤ 150 kN. (4) Energy-absorption constraint. The larger the energy absorbed by ROPS, the better its performance is for protecting the operator.

[5] shows that the lowest lateral energy absorption EL of this ROPS is 33,000 J, so EL≥ 33,000 J. 3.1.4 Mathematical Model of ROPS Optimization

3.1.2 Object Function

According to the above design variables, object function, and constraint conditions, a mathematical model is set up as follows:

The minimum difference between the force from the lateral load-carrying capability test

min f = ΔF(x1, x2, x3, x4, x5) ,

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80 ≤ x1 ≤ 190, 60 ≤ x ≤ 160, 2  60 ≤ x3 ≤ 120,  6 ≤ x4 ≤ 12, s.t.  6 ≤ x5 ≤ 16,  DL − 300 ≤ 0,  150 − FL ≤ 0, 33000 − E ≤ 0.  L

3.2 Optimization Establishment of the Kriging model requires few sample points; based on the results of pre-calculation, 30 initial sample points are determined. Based on the upper and lower limits of the design variables, the specific values of these initial sample points are determined by the Latin hypercube method. These values are inputted into APDL to create the FEM of ROPS. The response values of ROPS performance, such as load carrying, deformation, and energy absorption, are obtained by large elastic-plastic deformation simulations.

As the polynomial function f(x) is not of decisive importance in the accuracy of the simulation, let f(x) = 1 (linear regression model) for convenience of calculation. In contrast,

the correlation equation R(xi,xj) is of decisive importance in the accuracy of the simulation, so the Gaussian correlation equation is selected.

An optimization program is written in MATLAB based on the Kriging model and the GA. During optimization, the initial population Psize is 200, the crossover probability PC is 0.7, the mutation probability Pm is 0.01, and the terminal generation T is 120.

3.3 Optimization Results The tendency of each design variable changes with the terminal generations, as shown in Fig. 5. The tendency of the object function also changes along with the terminal generations, which is shown in Fig. 6.

Considering that the Kriging model approximately represents the true response surface, the points that meet the limiting conditions during optimization may not be able to exactly meet the limiting conditions in the true model. As shown in Fig. 3, the primary results of the GA optimization are substituted into the FEM of ROPS, and the ROPS performance is again analyzed to check that the optimization results meet the desired constraints and accuracy.

The results are optimized and rounded.

According to the specifications of the available standard profile of steel, the final optimal solution

Fig. 5. Variations of design variables change with the Generations Global Optimization of Lateral Performance for Two-Post ROPS Based on the Kriging Model and Genetic Algorithm

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for this two-post ROPS is x(1) = 150, x(2) = 110, x(3) = 120, x(4) = 8, and x(5) = 6. In addition, the lateral load carried is 154 kN, and the energyabsorption value is 34,500 J. The relationship between lateral displacement and lateral force is shown in Fig. 7.

Fig. 6. Variation of the object function changes with the Generations

force from the minimum lateral energy-absorption test as an object function, and the performance index of ROPS as constraint conditions. The number of initial sample points was fixed, and the specific values of sample points were determined through the Latin hypercube method within the limits of the design variables. Large plastic deformation FEM was established in APDL, and the responses (load carrying, deformation, and energy absorption) in the initial design points were obtained by simulation. Finally, the Kriging model was established, and the GA was applied to optimization. The results of the global optimization of this two-post ROPS show that the ROPS performance, which is closely related to the sectional dimensions of the beams and posts of ROPS, was improved using global optimization based on the Kriging model and GA. As the lateral force met the standard minimum lateral force requirement, lateral displacement obviously increased along with the increasing lateral force so that the lateral energy was significantly absorbed by ROPS through the permanent plastic deformation of components, particularly through the plastic hinge rotation of ROPS beam components.

5 ACKNOWLEDGEMENT The work described in this paper is supported by the National Natural Science Foundation of China (No. 50805065). The authors would like to thank the individuals who contributed to the project, especially Zhang Lihui.

6 REFERENCES

Fig. 7. Relationship between lateral displacement and lateral force 4 SUMMARY This current work provided a global optimization method for a typical earthmoving machinery ROPS. The optimization method took the minimum difference between the force from the lateral load-carrying capability test and the 766

[1] Clark, B.J., Thambiratnam, D.P., Perera, N.J. (2006). Analytical and experimental investigation of the behavior of a rollover protective structure. The Structural Engineer, vol. 84, no. 1, p. 29-34.

[2] Thambiratnam, D.P., Clark, B.J., Perera, N.J. (2009). Performance of a roll over protective structure for a bulldozer. Journal of Engineering Mechanics, vol. 135, no. 1, p.

31-40.

[3] Yamagata, K., Tsumura, D. (2007).

Introducing a simulation of a cab protecting operator during rolling over of a hydraulic

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excavator. Komatsu Tech Rep, vol. 52, no. 2, p. 2-7.

[4] Karliński, J., Rusiński, E., Smolnicki, T. (2008). Protective structures for construction and mining machine operators. Automation in Construction, vol. 17, no. 3, p. 232-244.

[5] ISO3471 (2008). Earth-moving machinery Roll-over protective structures Laboratory tests and performance requirements.

Geneva, International Organization for Standardization, Geneva.

[6] Wang, J.X., Yang, X., Yu, X.J. (2009).

Nonlinear finite element analysis and test of lateral loading for two-post ROPS. Applied Mechanics and Materials, vol. 16-19, p. 866870.

[7] Fang, K.T. (2004). Method of uniform design and its application. Mathematical Statistics and Management, vol. 23, no. 3, p. 69-80. (in Chinese) [8] Wang, J.X. (2006). Design method and experimental study on the rollover protective structures for engineering vehicles. Ph.D. dissertation, Jilin University, Jilin.

[9] Kleijnen, J.P.C. (2005). An overview of the design and analysis of simulation experiments for sensitivity analysis. European Journal of Operational Research, vol. 164, no. 2, p. 287300.

[10] Martin, J., Simpson, T. (2005). Use of Kriging models to approximate deterministic computer models. AIAA Journal, vol. 43, no.

4, p. 853-863.

[11] Simpson, T.W., Korte, J.J., Mauery, T.M. Mistree, F. (2001). Kriging models for global approximation in simulation-based multidisciplinary design optimization. AIAA Journal, vol. 39, no. 12, p. 2233-2241.

[12] You, H.L., Jia, X.Z., Dong, P. (2005).

Constructing circuit metamodel using Kriging interpolation integrated with Latin hypercube sampling experiment. Journal of System Simulation, vol. 17, no. 11, p. 2752-2755.

[13] Simpson, T.W., Poplinski, J.D., Koch, P.N., Allen, J.K. (2001). Metamodels for

computer-based engineering design: Survey and recommendations. Engineering with Computers, vol. 17, no. 2, p. 129-150.

[14] Giunta, A.A., Watson, L.T. (1998). A Comparison of approximation modeling techniques: polynomial versus interpolating models. AIAA-1998-4758, Proceedings of the 7th AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary analysis and optimization, St. Louis, Missouri, vol. 2, p. 392-440.

[15] Zhang, Q. (2005). Structural reliability analysis and optimization based on Kriging technique. Ph.D. dissertation, Dalian University of Technology, Dalian.

[16] Simpson, T.W., Manery, T.M., Korte, J.J., Mistree, F. (1998). Comparison of response surface and Kriging models for multidisciplinary design optimization. AIAA Journal, vol. 4758, no. 7, p. 381.

[17] Zbigniew, M., Fagel, D.B. (2004). How to solve it: modern heuristics. Springer, Berlin, New York.

[18] Lophaven, S., Nielsen, H., Søndergaard, J. (2002). DACE: A Matlab Kriging toolbox (Documentation), from http://www2.imm.dtu. dk/~hbn/dace/, retrieved on 2008-08-02.

[19] Sasena, M.J. (2002). Flexibility and efficiency enhancements for constrained global design optimization with Kriging approximations.

Ph.D. dissertation, University of Michigan, Michigan.

[20] Schonlau, M., Welch, W.J. (1997). Computer experiments and global optimization.

University of Waterloo, Waterloo.

[21] Chu, D.Z. (2004). The globec Kriging software package - easykrig3, from ftp:// globec.whoi.edu/pub/software/kriging/easy_ krig/v3.0.1/, retrieved on 2008-08-02.

[22] Lophaven, S., Nielsen, H., Søndergaard, J. (2002). DACE: A matlab Kriging Toolbox (Software), from http://www2.imm.dtu. dk/~hbn/dace/, retrieved on 2008-08-02.

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Strojniški vestnik - Journal of Mechanical Engineering 57(2011)10, 768-777 DOI:10.5545/sv-jme.2011.017

Paper received: 18.01.2011 Paper accepted: 28.07.2011

Development of Prosthetic Knee for Alpine Skiing Demšar, I. ‒ Supej, M. ‒ Vidrih, Z. ‒ Duhovnik, J. Ivan Demšar1,* ‒ Matej Supej2 ‒ Zmago Vidrih3 ‒ Jožef Duhovnik1 1 University of Ljubljana, Faculty of Mechanical Engineering, Slovenia 2 University of Ljubljana, Faculty of Sport, Slovenia 3 ART-LEG d.o.o., Slovenia

Above-knee amputation significantly reduces the amputee’s mobility and physical condition that can be built up through training or other sports activities. Alpine skiing is one of them. This paper deals with an above-knee prosthesis, which provides better kinematics of the leg structure. Imitating the kinematics of the human body, we looked for the kinematics of a system that comes closest to imitating natural movement and replace the missing limb to the highest possible degree. Based on the analysis of human leg kinematics and entire human mass system dynamics, a prototype for a special multi-axis prosthetic knee was developed. Measurements of leg movement during skiing were performed, which served as a basis for the concept. The concept was verified by kinematics, dynamics and strength analysis, and a complete geometric model was made. The concept was then verified on a working prototype, tested on a ski slope. ©2011 Journal of Mechanical Engineering. All rights reserved.

Keywords: alpine skiing, above-knee amputation, prosthesis kinematics, skiing dynamics, research, development, testing, product adoption 0 INTRODUCTION The number of lower limb amputations has been significantly increasing in recent years [1].

Accidents result in an increase of amputations among young people who attempt to integrate into everyday life as much as possible. In order to be able to perform basic life functions, such as walking, there are many aids available; from simple and low-cost ones to more sophisticated ones, allowing broader application and comfort, but of a much higher price-bracket [2].

As soon as the threshold of basic and vital functions is crossed, it becomes apparent that in the area of aids for other activities, sporting ones in particular, there is a lot of room for new products [3]. Given the fact that we have been working with an above-the-knee amputee, who was an active skier before the injury and who can therefore provide direct testing of equipment, we decided to focus primarily on the area of alpine skiing.

The so-called three-track skiing is the most frequently used ski method by above–the-knee amputees [4] and [5]. Together with a normal ski on the sound leg, special poles (outriggers) with a flip-up ski attached to the bottom are used to provide aid in balancing. An example is shown in Fig. 1.

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Fig. 1. Three-track skiing – skiing on the sound leg with the assistance of two specially designed poles In addition to three-track skiing for abovethe-knee amputees, a few varieties of above knee prostheses have been developed in recent years for regular, two-track skiing [6] and [7]. Fig. 2 shows an example of an above-knee prosthesis, incorporating the XT9 prosthetic knee, produced by the US company Symbiotech [8].

Practical use of the particular prosthesis, shown in Fig. 2 revealed that it fails to provide the optimum movements, required for quality alpine skiing. Tests showed that in combination with an ordinary ski boot this prosthesis does not allow

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

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enough forward movement of the knee, which moves the gravity centre of the body backwards.

This results in the skier losing dynamic balance and control of the skis (Fig. 3).

Fig. 2. Above-knee prosthesis for alpine skiing with the XT9 prosthetic knee

Fig. 3. Kinematics of above-knee prosthesis for alpine skiing with the XT9 prosthetic knee The paper presents the development of a prosthetic knee as the key element of an aboveknee prosthesis for alpine skiing. In doing so, we will use the problems observed above as a basis and try to eliminate them. The prosthetic knee is of particular importance for skiing and the kinematics of human structure because skiing and sports activities in general require the dynamics of the human body as the key element of motor skills [9].

The prosthetic knee is connected upwards to the body via the prosthesis socket and stump.

Downwards, the prosthetic knee is connected via the tubular adapter to the prosthetic foot and further down to the ski boot [10]. Each of the elements has its own function, forming a unit together with the others. An above-knee prosthesis in an assembly is shown in Fig. 4.

In developing a new prosthetic knee, the theory of design and development process based

on the idea that technical systems should come closest to imitating natural processes and should have a minimum effect on the environment [11] and [12], was followed. To achieve maximum quality of the defined natural process that the structure of the human body deals with in skiing, first typical human skiing motion was recorded.

To facilitate data acquisition, a purpose-built test area, shown in Fig. 5 was built, where the kinematics of the whole human structure was measured, particularly the leg part during the skiing process of an able-bodied individual. The measurement results were used as the basis for a special multi-axis prosthetic knee concept.

Fig. 4. Above-knee prosthesis assembly; 1 – prosthesis socket, 2 – prosthetic knee, 3 – tubular adapter, 4 – prosthetic foot A mechanism was designed on the basis of the analysis of the skier’s motion, which was then compared to the measurement results. Varying the locations of the prosthetic knee’s kinematic system axes, the kinematics of a sound knee in skiing were approximated.

Having researched and recorded behaviour during skiing, it was concluded that in addition to kinematics, dynamics. Ordinary above-knee walking prostheses have the basic function of knee contracture in the swing phase, followed by system stabilisation at landing [13] and [14]. Contrary to this, in the knee-contracture phase skiing requires adequate force upon the ski and surface in order to be able to perform the function of guiding the ski.

Due to this additional function required for skiing, it is necessary to equip the knee prosthesis system with an energy accumulation system, so that some force returns to the surface – the ski in this case – during the knee contracture phase [15].

On the basis of the recorded states of real skiing motions, a geometric knee-prosthesis

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model was made. Defining mechanism fulcrums, we tried to improve it in such a way as to come closest to natural movement. This was followed by building a virtual model of the prosthetic knee, which then required verification of its strength suitability. The virtual model was strength tested at maximum loads, specified on the basis of the kinetic analysis of the mechanism.

For higher quality reasons, a prototype was built and tested on a ski slope.

1 LEG KINEMATICS MEASUREMENT IN SKIING According to the method [16], the development of each new product first requires recognising the natural process, which the new product should provide in the form of a technical system. To this end, a special test area was arranged which in the first place provided forces exerted by the skier on the surface, which is basically a simulation of increased forces when making a turn [17]. Together with the measurement of forces, the kinematics of human structure in the leg area was also measured. It allowed us to recognise the key condition of the kinematics of the structure in connection with forces acting on the structure of the human body.

Fig. 5. Test area concept; 1-skier, 2-extra loads transfer system, 3-tensiometric plate, 4-weights, 5-data capturing system from the side, 6-data capturing system from behind Four measurements of human body kinematics were executed at different extra loads, depending on the skier’s body weight (BW).

A – no extra load, B – extra load 1/3 BW, C – extra load 2/3 BW, D – extra load 1 BW.

1.1 Test Area and Performance of Measurements For some loads on the lower (leg) part of human structure, a test area provides fully contactless optical tracking of skier motion in space. The test area concept is shown in Fig. 5.

Skis are attached to an AMTI tensiometric plate, which measures loads on the surface. Other forces that appear during skiing were simulated by means of a rope system, attached from the skier’s lower body to vertically guided weights.

Data were captured by a system, based on a 2-D image capturing of control points movement on two planes (Fig. 6). Control points positions were captured using two high speed cameras CASIO EXILIM F-1, positioned at an angle of 90° relative to each other. Using image analysis of each camera and space calibration, the location of control points in space was determined. The test track enabled tracking the size and direction of the extra load, which significantly affected the quality of the executed measurements.

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Fig. 6. Location of control points for the kinematic analysis of skier’s leg; 1.1–boot-ankle left, 1.2–boot-upper left, 1.3–lower leg left, 1.4– knee left, 1.5-thigh left, 1.6–pelvis left, 2.1- bootcentre rear, 2.2–boot–upper rear, 2.3–lower leg rear, 2.4–thigh rear, 2.5–pelvis rear Capturing data from two orthogonal directions – from the side (Fig. 6, 1.1. to 1.6) and

Demšar, I. ‒ Supej, M. ‒ Vidrih, Z. ‒ Duhovnik, J.

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from behind (Fig. 6, 2.1 to 2.5), a description of leg kinematics in space was achieved. Fig. 7 shows the range of measurements and the choice of coordinate system. Measurement results for each direction are presented below.

of individual control points, representing human structure in individual planes.

Fig. 10 shows comparison between measurement results at different extra loads. For better transparency reasons, each measurement is presented by a single cycle, simulating one turn.

The results clearly show that knee movement increases with increasing extra loads. The reason for this is in the stiffness of the ski boot, which restricts forward movement (displacement) of the foot.

Fig. 7. Space calibration and setting up a coordinate system

Fig. 9. Measurement result for the kinematics with no extra load – y-z plane 2 MULTI-AXIS MECHANISM CONCEPT AND KINEMATIC ANALYSIS

Fig. 8. Measurement result for the kinematics with no extra load – x-z plane 1.2 Measurement Results of the Kinematics of Human Structure Coordinates of individual points were determined by means of space calibration and image analysis. Figs. 8 and 9 show the movement

Developing the prosthetic knee concept, the principle of making a simple and low-cost prosthesis, which would at the same time closely imitate natural movement, was followed. The solution was found in a multi-axis prosthetic knee which would, independently of the ski boot, provide the kinematics similar to that in the sound leg. The prosthetic knee concept is shown in Fig. 11. It consists of a lower plate, to which a tubular adapter is attached, followed by a prosthetic foot.

The prosthesis socket is attached to the upper plate.

The plates are connected by arms that provide the necessary movement in the horizontal and vertical directions relative to the turn (contracture) of the

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Fig. 10. Comparison between measurement results at different extra loads;a) x-z plane, b) y-z plane A – no extra load, B – extra load 1/3BW, C – extra load 2/3BW, D – extra load 1BW

Fig. 11. Multi-axis prosthetic knee concept: 1-lower plate, 2-upper plate, 3-front arm, 4-rear arm, 5-shock absorber, Δφ-knee turn (contracture), Δx-horizontal movement, Δ z-vertical movement; A, B, C, D and E – mechanism axes 772

knee. The dynamics of the mechanism is provided by a corresponding pneumatic shock absorber and coil spring system.

A kinematic analysis of the mechanism was carried out for the presented multi-axis prosthetic knee. Trajectories of individual axes were calculated by means of which the movement of the upper part of the prosthetic knee, relative to the lower one, was determined. Fig. 12 shows movements of the pivot points of the upper part.

Point (axis) C represents the control point for the comparison between the kinematics of a sound knee and a prosthetic one.

Fig. 13 shows a comparison between the measurement results of the control point movement on the knee (control point 1.4 in Fig. 6) at different loads, and the results of the kinematic analysis of the prosthetic knee concept (C in Figs.

11 and 12). Fig. 13a shows a comparison between movements in the horizontal (x) direction, and

Demšar, I. ‒ Supej, M. ‒ Vidrih, Z. ‒ Duhovnik, J.

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Fig. 13b in the vertical direction (z), relative to the angle of knee turn (contracture).

3 VIRTUAL PROSTHETIC KNEE MODEL AND STRENGTH ANALYSIS

Fig. 12. Results of kinematic analysis of the mechanism

Judging by the kinematic analysis results (Fig. 12) and comparing measurement results (Fig. 13) the selected concept is deemed suitable.

The next step in the development of the prosthetic knee was building a virtual model and performing the strength test.

One of the structure’s key elements is also the combination of a pneumatic shock absorber and a coil spring, which provides suitable stiffness of the knee assembly and thus load transfer from the skier onto the surface. To this end, we tested several combinations of pneumatic shock absorbers and coil springs. The choice of the most suitable combination mostly depends on the user’s psychophysical and morphological characteristics, skiing technique and skills. The structure is designed in such a way that it allows simple changes of combinations and fine tuning, depending on the user’s requirements and preferences.

The strength analysis of prosthetic knee’s virtual model structure was performed for the

Fig. 13. Comparison between measurements and simulation of control point movement on the knee, depending on knee contracture: a) horizontal direction (x) movement, b) vertical direction (z) movement; A, B, C and D curves - control point 1.4 measurement (Fig. 5) at different loads, curve E – control point C simulation (Fig. 10) on the prosthetic knee concept Development of Prosthetic Knee for Alpine Skiing

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strongest pneumatic shock absorber (F = 2,200 N) and coil spring (81 N/mm constant) combination.

Using the kinetic analysis of the selected mechanism, forces in specific points of the mechanism were determined. These forces served as a basis for the strength analysis of particular critical elements of the structure.

Fig. 14. Virtual model of prosthetic knee: 1-lower part, 2-upper part, 3-connecting rod front, 4-connecting rod rear, 5-shock absorber, 6 coil spring

Fig. 15 shows a kinetic model of the prosthetic knee. Points A, B, C, D and E represent the mechanism axes. Point G represents the external force point of application, located at the far lower part of the prosthesis socket. Force FE represents the joint force of the coil and the shock absorber. Force FG represents the external force, required for knee contracture. The size of forces FC in FD was calculated by means of balance equations.

Analysis results and sizes of forces as a function of knee contracture angle are shown in Fig. 16.

Strength calculation of prosthetic knee elements in Fig. 14 was performed by means of the finite elements method (SolidWorks 2010).

Individual elements were checked separately, taking account of the largest forces that appear at contracture.

The material of choice was aluminium alloy AlMg4,5Mn (EN AW-5083).

• elastic modulus: 71 000 N/mm2, • poisson number: 0.33, • cone module: 2 640 N/mm2 • material density: 2 660 kg/m3, • tensile strength: 275 - 350 N/mm2, • yield strength: 125 – 190 N/mm2.

Strength analysis showed appropriateness of the structure. Figs. 17 and 18 show the tension condition of prosthetic knee rods as the most stressed elements of the structure when they are under maximum load.

Table 1. Loads on the front connecting rod Turn Δφ 50.23°

Fig. 15. Prosthetic knee model for kinetic analysis: A, B, C, D and E represent mechanism axes, G – external force point of application, FG – external force, FE – joint force of coil and shock absorber, FC and FD – forces in connecting rods 774

Point B FD/2 2,019 N

Point D FD/2 2,019 N

Table 2. Loads on the rear connecting rod Turn Δφ 81.11°

Demšar, I. ‒ Supej, M. ‒ Vidrih, Z. ‒ Duhovnik, J.

Point A FC/2 2,387 N

Point C FC/2 2,387 N

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Fig. 18. Tension distribution in the rear connecting rod

Fig. 16. Results of kinetic analysis of prosthetic knee for a selected combination of coil and pneumatic shock absorber, FC, FD, FE and FG â&#x20AC;&#x201C; forces in individual points of mechanism

Fig. 19. Art-Leg Sport Knee prosthetic knee prototype

Fig. 17. Tension distribution in the front connecting rod 4 PROTOTYPE BUILDING AND TESTING The next phase in the development of the prosthetic knee for alpine skiing was building a prototype and its testing in real-life conditions.

On the basis of the virtual model, two prosthetic knee prototypes, called Art-Leg Sport Knee, were built, as shown in Fig. 19.

Fig. 20. Above-knee prosthesis assembly for alpine skiing

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The whole assembly of the above-knee prosthesis for alpine skiing is shown in Fig. 20.

Together with the prosthetic knee, which is at the core of the prosthesis, existing, i.e. standard prosthetic elements, were used for building the prosthesis (socket, foot, adapters, fixing elements etc.).

adaptation was required for right turns, where the prosthesis is on the inner ski and more contracture in the knee joint is required. In this case, less resistance in the knee contracture phase would be required, which would also lead to smaller load on the inner ski and thus better ski control in right turns. The knee itself allows it (Fig. 16).

However, the feeling is unusual when resistance at knee contracture from a certain angle onwards weakens, which takes some getting used to.

Fig. 21. Skiing with the above-knee prosthesis (Kitzsteinhorn, October 2010) The prosthesis was tested using different skiing techniques and speeds. In cooperation with alpine skiing instructors, we observed the prosthesis response, particularly that of the prosthetic knee, to the situations that arise. We also observed the quality of turning and ski control throughout the turn. The vital information on the suitability of the prosthesis, particularly the prosthetic knee, was provided by the skier (user) according to his feelings and advanced skiing skills.

6 RESULTS The test results confirmed the suitability of the selected concept of the multi-axis mechanism that simultaneously provides knee flexion-extension and translation, which enables maintaining optimum position of the centre of gravity throughout the turn (Fig. 22).

The selected combination of a shock absorber and a spring coil, which together with mounting geometry provided variable resistance at different contracture angles, proved to be a good solution. In left turns, where the prosthesis was on the outer side, it provided suitable resistance and consequently load transfer to the outer ski, which reduced knee contracture. A little more effort and 776

Fig. 22. Above-knee prosthesis with prosthetic knee Art-Leg Sport Knee After two-day testing on a ski slope (cold, snow, real physical stress) we also checked visually and by means of geometry the suitability of the prosthetic knee structure from the viewpoint of wear and other defects (ventilation, deformation, etc.). There were no visible traces of use, which confirms strength appropriateness of the structure and the correctness of choice and accuracy of strength control.

7 CONCLUSION Judging by the results of prosthesis (prosthetic knee) testing on a ski slope we conclude that with proper knowledge, a correct approach and carefully selected working methods it is possible to significantly improve patient care with special aids after leg amputation.

Although the prosthetic knee does not allow lateral knee flexing (abduction/adduction), which is not significant in skiing anyway, the prosthesis allows skiing with the carving technique, as well as turning with skidding, which

Demšar, I. ‒ Supej, M. ‒ Vidrih, Z. ‒ Duhovnik, J.

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makes it suitable for the entire range of skiers. It is necessary to adjust the prosthetic knee according to the skier’s psychophysical abilities and his or her skiing skills.

The prosthetic knee can also be used for other activities, such as snowboarding, wakeboarding, skateboarding, water skiing, surfing, skating, rollerblading, etc. Owing to its structure, it keeps the body in the optimum position during sports activity. When the user squats, its centre of gravity does not move backwards, but does exactly the opposite - prosthetic knee shrinks and moves forward, keeping the user in its optimal position.

8 ACKNOWLEDGEMENTS We would like to express our gratitude to Zvone Petek (Art-leg d.o.o.) as the user of the prosthesis for his advice and experience during the construction phase, and particularly for testing the prosthesis, and results, in view of his great skiing skills and experiences.

We would also like to thank ski instructor Blaž Lešnik, (University of Ljubljana, Faculty of Sport) and Vid Baruca of the Ski Instructors and Coaches Club (ZUTS) for his professional assistance and assessment during the testing of the above-knee prosthesis.

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[2] Burger, H. (2009). The future of amputee rehabilitation, prosthetic and orthotics.

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[5] Jessen, J. Adaptive Skiing, from http:// nwskiers.org, accessed on 2010-12-27.

[6] Mannino, G. Two-track skiing not just for BK’s anymore, from http://www.dsusa.org, accessed on 2010-12-27.

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[8] Symbiotechs, A specially designed prosthetic knee engineered for extreme athletic use, from http://xt-9.com/ accessed on 2010-1228.

[9] Winter, A.D. (2009). Biomechanics and Motor Control of Human Movement, 4th ed., John Wiley & Sons, Hoboken.

[10] Edelstein, J.E. (2007). Amputations and Prostheses. Cameron, M., Monroe, L. (eds.), Physical Rehabilitation: Evidence-Based Examination, Evaluation, and Intervention.

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[12] VDI 2221 (1987). Systematic approach to the design of technical systems and products.

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[13] Zarrugh, M.Y., Radcliffe, C.W. (1976) Simulation of swing phase dynamics in aboveknee prostheses. Journal of Biomechanics, vol. 9, no. 5, p. 283-292.

[14] Berry, D. (2006). Microprocessor prosthetic knees. Physical Medicine and Rehabilitation Clinics of North America, vol. 17, no. 1, p.

91-113.

[15] Kugovnik, O., Supej, M., Nemec, B. (2003).

Biomechanics of alpine skiing. University of Ljubljana, Faculty of sport, Ljubljana.

[16] Duhovnik, J., Balić, S. (2004). Detail functionality analysis using the design golden loop. Proceedings of the 4th International Seminar and Workshop, University of Zielona Gora, p. 29-36.

[17] Müller, E., Schwameder, H., Raschner, C., Lindinger, S., Kornexl, E. (2001). Science and Skiing II. Verlag Dr. Kovač, Hamburg.

Development of Prosthetic Knee for Alpine Skiing

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Strojniški vestnik - Journal of Mechanical Engineering 57(2011)10, 778-784 DOI:10.5545/sv-jme.2008.068

Paper received: 14.06.2008 Paper accepted: 02.08.2011

Application of Promethee-Gaia Methodology in the Choice of Systems for Drying Paltry-Seeds and Powder Materials Prvulovic, S. − Tolmac, D. − Radovanovic, L. Slavica Prvulovic − Dragisa Tolmac* − Ljiljana Radovanovic University of Novi Sad, Technical Faculty ''Mihajlo Pupin'', Serbia

This work deals with the application of Promethee-Gaia methodology and the choice of three systems for drying paltry-seeds and powder materials pneumatic driers, spiral driers and rotation driers with a drum with regard to five different criteria. The analysis is based on the Promethee I method, the Promethee II method and the Promethee-Gaia method, which withal shows a complex figure of the relation between alternatives and criteria in the Gaia plane. In this work the application of Decision Lab program is shown, which was the basis in analysing results and ranking alternatives.

The paper analyzes three different systems for drying. When choosing the system of drying the comparative analysis of five influential parameters, such as: the coefficient of heat transfer, price, drying energy, thermal usefulness, specific use of energy. Based on the analysis, the application of a pneumatic dryer is the cheapest, given the significant savings in cost, ie. investment cost and energy efficient. Next in order of the spiral dryer, and third in the rotation with a drum dryer, in terms of benefits administration. © 2011 Journal of Mechanical Engineering. All rights reserved.

Keywords: method Promethee-Gaia, multi-criteria, systems for drying, Decision Lab program 0 INTRODUCTION An analysis of decision problems shows philosophy which manage a sistematical and formal introduction to a desicion problem and offers practical approach to the problem.

This is a way which uses its own set of logical methodologis and specification of a procedure which enables a sistematical analysis of a complex decision problem.

In the decision-making process atributes demonstrate characteristics of alternatives which we believe are relevant in our case. Alternatives are known beforehand, but atributes are always chosen and formulated alone.

The choice of attributes represents a considerable stage in the process of multi-criteria decision where the way is defined in terms of how the realization of appointment aims bare going to be followed. Due to this the schedule should be: • complete and • disconnect.

The ideal case in the choice between complicated alternatives is the choice between the dominating option, i.e. the apropos option which meets all the criteria and better in one atribute than in the another. But in practise this is not often the case. A well paid job means little free time. In 778

other words, aims which we want to achieve are problematic so they cannot be realized at the same time.

Many methods of choice (which are suggested in literature principally in operation of exploration) can be placed into related groups which enable the ranking of offer alternatives or a choice between the best alternatives [1].

In the recent years several decision aid methods or decision support systems have been proposed to help in the selection of the best compromise alternatives. In this paper based on a short example, an overview of the PrometheeGaia methodology for treating multi-criteria problems [2] is given. This methodology is known not just as one of the most efficient ones but also one of the easiest in the field.

A particularly user-friendly software, called the Decision Lab has been developed in collaboration with a Canadian company Visual Decision to assist all kinds of decision-makers.

Software Decision Lab [3], as a support at decision making was developed in cooperation with company Visual Decision, and is available to be used by individuals.

The Promethee-Gaia methodology is better than other methods of multiple criteria, as it, firstly, it provides a complete ranking

*Corr. Author’s Address: University of Novi Sad, Technical Faculty »Mihajlo Pupin«, Djure Djakovic bb, 23000 Zrenjanin, Serbia, dragisat@gmail.com

Strojniški vestnik - Journal of Mechanical Engineering 57(2011)10, 778-784

of alternatives, from best to worst. At some other methods this is not the case, for example, the method of Elektra. Also, a clear graphical representation of alternatives and their values can be seen here and the decision maker does not have to go into the text part, which usually seems annoying. What distinguishes this particular methodology is the Gaia-plan alternatives and the criteria, which clearly show the best alternative, and the alternative for which criterion is the best.

1 THE PROMETHEE METHOD The PROMETHEE method is a multicriteria decision-making method developed

by Brans [3] and [4]. It is a ranking method quite simple in conception and application compared to other methods for multi-criteria analysis. It is well adapted to problems where a finite number of alternative actions are to be ranked considering several, sometimes conflicting, criteria [5] and [6].

The PROMETHEE method is appropriate to treat the multi-criteria problem of the following type: max{f1(a), ... , fn(a)|a \A}, (1) where A is a finite set of possible alternatives, and fj are n criteria to be maximized. For each alternative, fj(a) is an evaluation of this alternative. When we compare two alternatives a, b \ A, we must be able to express the result of these comparisons in terms of preference. We, therefore, consider a preference function P. Let

P(a, b) = F(d) = F[f (a) − f (b)], (2)

0 ≤ P(a,b) ≤ 1, (3)

be the preference function associated to the criteria, where F(d) is a monotonically increasing function of the observed deviation (d) between f(a) and f(b). In order to facilitate the selection of specific preference function, six basic types of this preference function are proposed to the decision maker, in each case no more than two parameters (thresholds q, p or s) have to be fixed [5] and [7].

Indifference threshold q: the largest deviation to consider as negligible on that criterion. It is a small value with respect to the scale of measurement.

Preference threshold p: the smallest deviation to consider as decisive in the preference

of one alternative over another. It is a large value with respect to the scale of measurement.

Gaussian threshold s: it is only used with the Gaussian preference function. It is usually fixed as an intermediate value between an indifference and a preference threshold.

Promethee permits the computation of the following quantities for alternatives a and b: a and b are alternatives from the first set of alternatives A. Then is:

π ( a, b) =

k

∑ P ( a, b) w , j

(4)

j

j =1

•

•

π (b, a ) =

k

∑ P (b, a)w , (5) j

j

j =1

positive course):

course

Φ + (a) =

of

preferential

(output

1 π (a, x), (6) n − 1 x∈A

∑

negative course of preferential (input course): 1 Φ − (a) = π ( x, a ), (7) n − 1 x∈A

∑

where wj are weights associated with criteria.

For each alternative a, belonging to the set A of alternatives, π(a,b) is an overall preference index of a over b. The leaving flow Φ+(a) is the measure of the outranking character of a (how a dominates all the other alternatives of A).

Symmetrically, the entering flow Φ−(a) gives the outranked character of a (how a is dominated by all the other alternatives of A). Φ(a) represents a value function, whereby a higher value reflects a higher attractiveness of alternative a. Φ(a) is called the net flow of alternative a [8]. All the alternatives can be completely ranked (Promethee II) by net flow.

The geometrical analysis for interactive aid (Gaia) plane displays graphically the relative position of the alternatives in terms of contributions to the various criteria [8] and [9].

1.1 The Promethee & Gaia Analysis The purpose of this paper is not to explain in details the Promethee methodology. See for instance Brans [3] and [8]. Only the results

Application of Promethee-Gaia Methodology in the Choice of Systems for Drying Paltry-Seeds and Powder Materials

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Strojniški vestnik - Journal of Mechanical Engineering 57(2011)10, 778-784

provided by the Decision Lab software on the above-mentioned example [10].

Promethee requests additional information.

For each criterion a specific preference function must be defined. This function is used to compute the degree of preference associated to the best action in case of pair wise comparisons [11] and [12]. Six possible shapes of preference functions are available in the software (Table 2). These are described for instance in Brans [8]. In this example, the shapes 5 (linear), 3 (V-shape), 2 (U-shape), 6 (Gaussian) and 1 (usual) have been respectively associated to the five criteria.

Promethee & Gaia calculate positive and negative preference flows for each alternative [8]. The positive flow expresses how much an alternative is dominating (power) the other ones, and the negative flow how much it is a dominated (weakness) by the other ones. Based on these flows, the Promethee I, partial ranking is obtained, Fig. 1.

1.2 The Decision Lab 2000 Software The Decision Lab 2000 software is an up-to-date implementation of the Promethee & Gaia methods [13] and [14]. It includes many practical developments, such as the treatment of missing values, the definition of categories of actions or criteria, as well as a powerful group decision extensions through the definition of multiple scenarios [4], [15] and [16]. The Canadian company Visual Decision develops decision Lab. It works under Windows 95, 98, NT or 2000 on PC compatible microcomputers will be commented on. A demo version as well as full versions (Executive or Developer – including programming capabilities) is available from Visual Decision (http://www.visualdecision.com).

2 APPLICATION OF THE PROMETHEE METHOD IN THE CHOICE OF THE SYSTEM FOR DRYING CORN STARCH, RESULTS AND DISCUSSION In this work a choice has been made of the most effective driers between the three which are offered and pointed with ai on the base of five criterium pointed with fj.

Offered alternatives ai: a1 – pneumatic dryer, a2 – spiral dryer, a3 – rotation dryer with a drum.

Offered characteristic (criterion) (fj): f1 – coefficient of heat transfer[W/m2K], f2 – price [€], f3 – drying energy [kW], f4 – termic useful degree [%], f5 – specific use of energy [kJ/kg].

For each of the criteria responsive weights T(0.15 0.15 0.20 0.25 0.25) are offered. In Table 1, systems for drying which are ranked on the base of offered criteria, are shown. Such dryer systems are introduced in literature [17] and [18] and [19] and [20].

Definition type, parameters and weight coefficient: The person who makes a decision resolves problems, defines types of general criteria, parametres and weight useful criteria apropos each criterion is given an analogous function of preferention [1].

In this case, the person who makes a decision is decided next, Table 2.

Determinate input (Ф+) , output (Ф˗) and a clean course of preferention .

Table 1. System characteristics for drying corn starch

Pneumatic dryer Spiral dryer Rotation dryer with a drum Weight coefficient 780

Coefficient of heat transfer [W/m2K] max 295 308

Price [€]

Drying energy [kW] max 2215 1850

Termic useful degree [%] max 66 52

Specific use of energy [kJ/kg] min 3710 3056

min 673500 555000

195

753000

2510

54

4150

0.15

0.15

0.20

0.25

0.25

Prvulovic, S. − Tolmac, D. − Radovanovic, L.

Strojniški vestnik - Journal of Mechanical Engineering 57(2011)10, 778-784

Table 2. Award function of preferention, responsive parametres and weights Type m n t

f1 III 2.5 0.15

f2 V 0.2 0.5 0.15

f3 I 0.20

f4 IV 1.0 2.0 0.25

f5 I 0.25

To determine the input course action the Eq (8) [4] is used: +

Φ (a) =

∑ IP(a, x) or Φ

+

(a) =

∑ IP(a, x) x∈ A

x∈ A

i −1

. (8)

To determine the output course action the expression is used: IP ( x, a ) −

Φ (a) =

∑ IP( x, a) or Φ

−

x∈ A

(a) =

∑ x∈ A

i −1

. (9)

The obtained results are shown in Table 3, according to [8] and [10].

Table 3. Input, output and clean course of preferention Pneumatic dryer Rotation dryer with a drum

Ф+ 0.6250

Ф0.3750

Ф 0.2500

0.2625

0.6750

-0.4125

Ranking action on the base of the weight clean course. On the other hand, the Promethean II provides a complete ranking, Fig. 2. It is based on the balance of the two preference flows. The information looks more reliable but some part of it gets lost in the process. Both Promethean I and II help the decision-maker to finalize the selection of the best compromise. A clear view of the outranking relations between the alternatives is obtained.

It is clear the Promethee I and II rankings are influenced by the weights allocated to the criteria. A special feature of the software, called The Walking Weights, Fig. 3, allows to modify the weights and to observe the resulting modifications of the Promethee II ranking. For the following weight distribution [21] to [23] it can be easily observed that pneumatic driers still dominates the other ones. It is a position, as the best compromise, which seems to be very stable. On the other hand, the ranking of the last five actions is now completely opposite. Such a sensitivity analysis tool is particularly valuable when the decisionmaker has no predetermined weights in mind.

The information relative to a decision problem including k criteria can be represented in a k-dimensional space. The GAIA plane is obtained by projection of this information on a plane such that as few information as possible get lost. Points and criteria represent alternatives. The conflicting character of the criteria appears clearly, in Fig.

Fig. 1. Promethee I ranking

Fig. 2. Promethee II ranking Application of Promethee-Gaia Methodology in the Choice of Systems for Drying Paltry-Seeds and Powder Materials

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Strojniški vestnik - Journal of Mechanical Engineering 57(2011)10, 778-784

Fig. 3. Walking Weight – option which is used to make sensible score analysis

Fig. 4. GAIA plane for afford decide problem (activity plane dryer)

Fig. 5. GAIA plane for afford deciding problem (criterion plane dryer) 4, and the criteria expressing similar preferences of the data point to the same direction, while conflicting criteria point in opposite directions.

782

In addition to the representation of the alternatives and criteria, the projection of the weight vector in the GAIA plane which corresponds to another axis (π, the Promethee

Prvulovic, S. − Tolmac, D. − Radovanovic, L.

Strojniški vestnik - Journal of Mechanical Engineering 57(2011)10, 778-784

decision axis) that shows the direction of the compromise resulting from the weights allocated to the criteria. The decision-maker is invited to consider the alternatives located in that direction.

When the weights are modified, the positions of the alternatives and the criteria remain the same, and only the decision axis π is changing [8].

The software allows using the weights vector as a decision stick to orientate the decision.

The movements of the stick corresponding to modifications of the weights are directly displayed in the 3D-view window of the GAIA screen, Figs. 4 and 5. When the decision-maker is not able or does not want to allocate precise weights to the criteria, it is possible to specify intervals of possible values rather than one fixed value for each weight. In this case, the Promethee VI procedure can be used to indicate whether the problem is soft or hard. It is soft when the decision axis π always remains in the same general direction for the weight distributions that are compatible with the intervals. It is hard when the opposite direction is possible depending on the actual values of the weights. In case of a difficult problem, the decision-maker should concentrate on more precise values of the weights.

This feature is currently not implemented in the Decision Lab. With regard to the Gaia plane, a conclusion can be made that the best alternative is the pneumatic drier, having the π vector in its plane. It is best regarding the thermal exploitation level criteria. The rotation dryer is the best regarding heat energy criteria, whereas the spiral dryer is the best regarding criteria of heat transfer, price and specific energy consumption, whose vectors overlap.

3 CONCLUSION It can be concluded that in this work a multi-criteria analysis of three systems for drying has been done, on the base of five criteria which were helped with Promethee, and with the application of responsive software [8], which enabled easy work, a faster finishing date and enabled faster choice appropriate drying. The final result was achieved in a few steps and it began from the base jig with her alternatives and criteria and finished with a definitive choice, apropos ranking. Based on ranking, a definitive choice between the best drying, apropos the best solution

at all the criteria is the choice of pneumatic dryers and which can be clearly seen in the Figs. 1 to 5, where it is shown that alternative a1 (pneumatic dryers) has dominated above alternatives a2 (spiral dryers) and a3 (rotation dryers with a drum).

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Strojniški vestnik - Journal of Mechanical Engineering 57(2011)10 Vsebina

Vsebina Strojniški vestnik - Journal of Mechanical Engineering letnik 57, (2011), številka 10 Ljubljana, oktober 2011 ISSN 0039-2480 Izhaja mesečno

Povzetki člankov Bogdan Valentan, Tomaž Brajlih, Igor Drstvenšek, Jože Balič: Razvoj modela za oceno zahtevnosti oblike izdelka in uporaba v slojevitih tehnologijah Gang Cheng, Wei Gu, Jing-li Yu, Ping Tang: Umerjanje celotne strukture paralelnega manipulatorja 3-UCR z metodo kvaternionov Marin Gostimirović, Milenko Sekulić, Janez Kopač, Pavel Kovač: Optimalno krmiljenje toplotnega stanja obdelovanca pri globokem brušenju z analizo inverznega prevoda toplote Roberto Alvarez, Rosario Domingo, Miguel Angel Sebastian: Formiranje nazobčanega odrezka pri rezanju titanove zlitine: vpliv konstitutivnih modelov Matjaž Dvoršek, Marko Hočevar, Brane Širok, Nikola Holeček, Božin Donevski: Vpliv sprememb na vstopnem delu na lokalni izkoristek hladilnega stolpa na naravni vlek Wang Jixin, Yao Mingyao, Yang Yonghai: Globalna optimizacija bočne zmogljivosti dvostebrne varnostne konstrukcije pri prevrnitvi s pomočjo Krigingovega in genetskega algoritma Ivan Demšar, Matej Supej, Zmago Vidrih, Jožef Duhovnik: Razvoj proteznega kolena za alpsko smučanje Slavica Prvulovic, Dragisa Tolmac, Ljiljana Radovanovic: Uporaba metodologije PrometheeGaia pri izbiri sistemov za sušenje majhnih semen in praškastih materialov

SI 141 SI 142 SI 143 SI 144 SI 145 SI 146 SI 147 SI 148

Navodila avtorjem

SI 149

Osebne vesti Doktorske disertacije in diplome

SI 151

Strojniški vestnik - Journal of Mechanical Engineering 57(2011)10, SI 141

Prejeto: 09.03.2011 Sprejeto: 15.07.2011

Razvoj modela za oceno zahtevnosti oblike izdelka in uporaba v slojevitih tehnologijah Valentan, B. ‒ Brajlih, T. ‒ Drstvenšek, I. ‒ Balič, J. Bogdan Valentan* ‒ Tomaž Brajlih ‒ Igor Drstvenšek ‒ Jože Balič Univerza v Mariboru, Fakulteta za strojništvo, Slovenija

Klasičnim odrezovalnim postopkom so se v zadnjih letih pridružili tako imenovani dodajalni postopki (slojevite tehnologije ali po domače 3D-tiskalniki). Če smo še pred leti vsaj okvirno vedeli kateri postopek izbrati za kateri izdelek, pa danes, ob upoštevanju vedno širše palete slojevitih tehnologij, temu ni več tako in le redki posamezniki še zmorejo slediti razvoju na tem izredno živahnem in hitro rastočem področju. Predstavljen je način določanja kompleksnosti izdelka na osnovi 3D-modela in uporaba izračuna pri izbiri izdelovalnega postopka ter določanju časa poobdelave pri določenih slojevitih tehnologijah. Članek opisuje osnovne značilnosti formata STL kot izhodne CAD-datoteke, ki predstavlja osnovo za analizo in razvoj postopkov določanja kompleksnosti oblike samega modela. Predstavljenih je več modelov iz realnega okolja, na katerih je izvedena analiza vhodnih podatkov in postopek določanja kompleksnosti oblike. Predstavljeni so aktualni izdelovalni postopki, primerni tako za izdelavo unikatnih izdelkov kot tudi za serijsko izdelavo, s posebnim poudarkom na slojevitih tehnologijah. Na osnovi temeljnih lastnosti izdelovalnih tehnologij so analizirani testni modeli in s pomočjo ocene kompleksnosti določeni primerni postopki izdelave oziroma čas, potreben za poobdelavo posameznega izdelka, izdelanega po postopkih slojevitih tehnologij.

Rezultati so primerljivi z izkustveno določitvijo izdelovalnega postopka na osnovi ocene strokovnjakov, tako da je ob manjših dodelavah metoda tudi praktično uporabna. Sistem dokaj natančno izloči modele, ki jih je moč izdelati po postopku struženja, prav tako je ustrezno določena meja za uporabo rezkalnega stroja. Pri slojevitih tehnologijah enoznačno izbiro omejuje dejstvo, da te tehnologije v večini primerov omogočajo izdelavo izdelkov ne glede na njihovo kompleksnost. Izbira se je tako omejila na dve skupini, in sicer slojevite tehnologije, pri katerih je potreben dodaten podporni material, in slojevite tehnologije, pri katerih podporni material ni potreben, oziroma ga je mogoče reciklirati.

Pri izbiri izdelovalnega postopka bi, ob upoštevanju določenih dodatnih omejitev posameznih slojevitih tehnologij, bila mogoča natančnejša izbira glede na kriterije, kot so čas izdelave, proizvodni stroški, material idr., vendar bi to zahtevalo aktualno bazo podatkov o samih postopkih. Sam način izračuna je bil izbran zaradi razmeroma preprostega izračuna in dokaj natančnega določanja kompleksnosti.

Uporaba kompleksnosti za določanje izdelovalnega postopka pred tem ni bila raziskana.

S problemom določanja časa poobdelave se danes srečujemo pri praktično vseh slojevitih tehnologijah, ta dejavnik pa bistveno vpliva tako na celoten čas izdelave kot tudi na ceno izdelka.

Predstavljena rešitev omogoča izračun časa poobdelave na uporabniku razumljiv način in ob upoštevanju individualnih vplivov specifične naprave s preprosto primerjalno metodo glede na čas poobdelave testnih modelov. © 2010 Strojniški vestnik. Vse pravice pridržane.

Ključne besede: hitra izdelava, STL, zahtevnost, oblika, slojevite tehnologije, izbira tehnologije

*Naslov avtorja za dopisovanje: Univerza v Mariboru, Fakulteta za strojništvo, Smetanova ulica 17, SI-2000 Maribor, Slovenija, bogdan.valentan@uni-mb.si

SI 141

Strojniški vestnik - Journal of Mechanical Engineering 57(2011)10, SI 142

Prejeto: 28.07.2010 Sprejeto: 15.07.2011

Umerjanje celotne strukture paralelnega manipulatorja 3-UCR z metodo kvaternionov

Cheng, G. ‒ Gu, W. ‒ Yu, J. ‒ Tang, P. Gang Cheng* ‒ Wei Gu ‒ Jing-li Yu ‒ Ping Tang Kitajska univerza za rudarstvo in tehnologijo, Fakulteta za strojništvo in elektrotehniko, LR Kitajska Popolna kompenzacija napak pozicioniranja manj mobilnih paralelnih manipulatorjev ni mogoča.

Metode umerjanja iz literature, ki se osredotočajo samo na kinematične parametre in ne vključujejo analize občutljivosti, niso uporabne za kompetentno obravnavo umerjanja celotne strukture paralelnih manipulatorjev 3-UCR. V članku je zato predlagan enostaven in učinkovit pristop k umerjanju konstrukcije.

V študiji je vzpostavljen model napak vzporednega manipulatorja na podlagi matrične teorije diferenčnih koeficientov. Nato je izpeljan statistični model občutljivosti z normalizacijo vseh virov napak v dosegljivem delovnem prostoru. Ob upoštevanju občutljivosti kinematičnih parametrov je predstavljen model umerjanja. Nato je predlagan algoritem umerjanja na osnovi metode najmanjših kvadratov. Sledi analiza numeričnih simulacij občutljivosti in umerjanja.

Pristop k problemu: umerjanje celotne konstrukcije na podlagi analize občutljivosti.

Obseg problema: umerjanje konstrukcije paralelnih manipulatorjev.

(1) Odstotki občutljivosti kinematičnih parametrov so nekoliko odvisni od sprememb razmerij konstrukcije.

(2) Določeni so kinematični parametri z višjimi odstotki občutljivosti, ki jih je treba nadzorovati bolj strogo.

(3) Nujno je zmanjšanje napake dolžine med izhodiščem relativnega koordinatnega sistema in spoji zglobov na podnožju, zlasti zmanjšanje napake po osi Z pravokotno glede na podnožje.

(4) Algoritem umerjanja na osnovi metode najmanjših kvadratov je učinkovito sredstvo za obravnavo vprašanja umerjanja in konvergira razmeroma hitro. Koraki izvajanja so dobro usmerjeni.

(5) Vključitev kvaternionov v metodo umerjanja prinaša dobre rezultate.

Omejitve: (1) Zaradi eksperimentalnih omejitev smo za preverjanje predlagane metode umerjanja namesto praktičnih eksperimentov izbrali metodo simulacije.

(2) Uporaba predlagane metode umerjanja pri paralelnih manipulatorjih s šestimi prostostnimi stopnjami in pri nesimetričnih manipulatorjih z manj prostostnimi stopnjami še ni bila dobro preučena. Pri takšnih aplikacijah lahko nastopijo določene težave.

(3) Zaradi vpliva izenačevanja metode najmanjših kvadratov v algoritmu umerjanja se nekatere napake umerjenih kinematičnih parametrov povečujejo.

Predlogi za prihodnje raziskave: (1) Poglobljene študije uporabe predlagane metode umerjanja; (2) Izboljšanje algoritma umerjanja za odpravo pomanjkljivosti metode najmanjših kvadratov.

V članku je predstavljena metoda na podlagi analize občutljivosti s kvaternioni za umerjanje celotne konstrukcije paralelnih manipulatorjev. Algoritem umerjanja konvergira razmeroma hitro, njegovi koraki izvajanja pa so dobro usmerjeni. Z vrednotenjem prioritete kinematičnih parametrov po koeficientih občutljivosti je mogoče določiti tiste parametre, ki jih je treba strogo nadzorovati, in tiste, kjer to ni potrebno. Pri praktični proizvodnji in montaži je s smiselno razvrstitvijo in nadzorom reda velikosti vsake napake mogoče zanesljivo zagotavljati natančnost manipulatorjev ter zmanjšati težave pri proizvodnji in montaži. Še bolj pomembna pa je uvedba kvaternionov v to metodo umerjanja, z njo se namreč zmanjša obseg računanja, poveča natančnost izračunov, algoritem pa je globalno nesingularen. Dosedanje splošne metode umerjanje iz literature teh nalog ne izpolnjujejo dobro. © 2010 Strojniški vestnik. Vse pravice pridržane.

Ključne besede: paralelni manipulator 3-UCR, teorija diferenčnih koeficientov, kvaternion, metoda najmanjših kvadratov, model občutljivosti, kinematično umerjanje SI 142

*Naslov avtorja za dopisovanje: Kitajska univerza za rudarstvo in tehnologijo, Fakulteta za strojništvo in elektrotehniko, 221008, Xuzhou, LR Kitajska, chg@cumt.edu.cn

Strojniški vestnik - Journal of Mechanical Engineering 57(2011)10, SI 143

Prejeto: 09.04.2010 Sprejeto: 23.06.2011

Optimalno krmiljenje toplotnega stanja obdelovanca pri globokem brušenju z analizo inverznega prevoda toplote Gostimirović, M. – Sekulić, M – Kopač, J. – Kovač, P. Marin Gostimirović1,* – Milenko Sekulić1 – Janez Kopač2 – Pavel Kovač1 1 Univerza v Novem Sadu, Fakulteta tehniških znanosti, Srbija 2 Univerza v Ljubljani, Fakulteta za strojništvo, Slovenija

Brušenje je eden najpomembnejših obdelovalnih procesov. Razen konvencionalnega finega brušenja v več prehodih se v zadnjem času vse bolj uveljavljajo tudi postopki globokega brušenja. Za globoko brušenje so značilne večje globine rezanja in manjše hitrosti obdelovanca, stik med kolutom in obdelovancem je daljši, prav tako pa je daljši tudi čas stika med orodjem in obdelovancem. Posledica tega je nastajanje večjih količin toplotne energije na enoto površine v daljšem obdobju.

Toplotna energija, ki pri globokem brušenju nastaja v razmeroma ozkem delu področja rezanja, povzroča visoke rezalne temperature. Če so temperature dovolj visoke, da v materialu obdelovanca nastopijo strukturne in fazne spremembe, ima obdelana površina vrsto slabosti, v končni fazi pa se lahko tudi občutno zmanjšajo funkcijske zmogljivosti končnega izdelka. Problem toplotnih pojavov pri globokem brušenju in pojavi v površinskem sloju materiala obdelovanca si zato zaslužijo posebno pozornost.

Učinkovito določanje dejanske toplotne obremenitve površinskega sloja materiala obdelovanca pri globokem brušenju je v veliki meri odvisno od zanesljivosti osnovnega modela porazdelitve toplotnih virov in od značilnosti temperaturnega polja v področju rezanja. V tem delu je bil zato uporabljen drugačen pristop k identifikaciji toplotnega stanja procesa globokega brušenja z uporabo metode inverznega prevoda toplote. Ta eksperimentalna in analitična metoda omogoča ugotavljanje celotnega temperaturnega polja v površinskem sloju materiala obdelovanca in neznanega toplotnega toka na stiku med kolutom in obdelovancem na osnovi temperature, izmerjene v katerikoli točki obdelovanca.

Metoda inverznega prevoda toplote je bila doslej na področju brušenja uporabljana pretežno za identifikacijo procesov z aproksimacijo gostote toplotnega toka ali temperaturnega polja v področju rezanja. V tem članku je bila uporabljena za optimalno krmiljenje toplotnega stanja obdelovanca pri globokem brušenju. Po transformaciji problema inverznega prevoda toplote v ekstremalno obliko lahko z optimizacijo toplotnega toka pridobimo dovoljeno toplotno obremenitev površinskega sloja materiala obdelovanca. Ob dani funkciji stanj in kriterijih kakovosti omogoča krmiljenje toplotne obremenitve obdelovanca določitev optimalnih pogojev globokega brušenja za želene pogoje obdelave.

Problem inverznega prevoda toplote je bil rešen z numerično metodo končnih razlik v implicitni obliki. Koncept te metode je zelo podoben fizikalnemu procesu, kjer se temperatura ali toplotni tok v vsaki opazovani točki v naslednjem časovnem koraku izračunavata iz izmenjave toplote s sosednjimi točkami.

Kot metoda optimizacije za določitev optimalnega krmiljenja nad prej definiranim problemom inverznega prevoda toplote v ekstremalni obliki je bila izbrana iterativna metoda iskanja. Iterativni postopek se konča, ko sta si izračunana in izmerjena temperatura zelo blizu oziroma sta skoraj identični.

V članku je predstavljen drugačen pristop k toplotni energiji pri globokem brušenju. Članek predstavlja analitične in eksperimentalne raziskave dovoljenih toplotnih obremenitev v površinskem sloju materiala obdelovanca med globokim brušenjem. Rezultati študije so uporabni v industriji. Raziskave, opravljene v sklopu tega dela, so ključnega pomena za optimalno krmiljenje pogojev pri globokem brušenju. Eno od možnih področij uporabe so proizvodni sistemi za izdelke z natančno geometrijo iz materialov, ki se težko obdelujejo. ©2011 Strojniški vestnik. Vse pravice pridržane.

Ključne besede: globoko brušenje, toplotna energija, temperatura, toplotni tok, problem inverznega prevoda toplote, optimalno krmiljenje

*Naslov avtorja za dopisovanje: Univerza v Novem Sadu, Fakulteta tehniških znanosti, Trg D. Obradovica 6, 21000 Novi Sad, Srbija, maring@uns.ac.rs

SI 143

Strojniški vestnik - Journal of Mechanical Engineering 57(2011)10, SI 144

Prejeto: 17.05.2011 Sprejeto: 05.09.2011

Formiranje nazobčanega odrezka pri rezanju titanove zlitine: vpliv konstitutivnih modelov Alvarez, R. – Domingo, R. – Sebastian, M.A. Roberto Alvarez1 – Rosario Domingo2,* – Miguel Angel Sebastian2 1Univerza Nebrija, Oddelek za industrijski inženiring, Španija 2UNED, Oddelek za proizvodno strojništvo, Španija

Članek obravnava ortogonalno rezanje zlitine Ti6Al4V, natančneje: i) možnosti uporabe ZerilliArmstrongovih modelov pri simulacijah po metodi končnih elementov; ii) integracijo Zerilli-Armstrongovih modelov, Bakerjeve modifikacije El-Magdovega in Treppmannovega modela ter Johnson-Cookovega (J-C) modela z nižjim koeficientom toplotnega mehčanja s kriterijem loma; in iii) raziskavo vpliva mazanja na rezultate in vpliv koeficienta trenja pri suhem in mokrem rezanju za osem modelov.

V tem prispevku je analiziran vpliv osmih konstitutivnih modelov na formiranje nazobčanega odrezka pri ortogonalnem rezanju zlitine Ti6Al4V v okviru simulacije po metodi MKE in primerjava z eksperimentalnimi rezultati, in sicer za suho odrezavanje in za obdelavo ob prisotnosti običajne 7-odstotne vodne emulzije hladilno-rezalne tekočine. Modeli vključujejo enačbe J-C s štirimi različnimi nabori konstantnih parametrov, El-Magdov in Treppmannov modificirani model in tri Zerilli-Armstrongove modele na osnovi obnašanja različnih kristalnih struktur (telesno centrirana kocka BCC, heksagonalni gosti zlog HCP in modificirani model HCP).

Model napetosti tečenja pri Ti6Al4V je bil analiziran s pomočjo dvodimenzionalnega modela MKE ob upoštevanju konstitutivnih enačb in treh koeficientov trenja (m = 0,4; 0,6 in 0,8). Opravljena je bila primerjava izhodov procesa kot so rezalna sila, temperatura na cepilni ploskvi in merljivi parametri segmentiranega odrezka (višina vrhov in dolin zob, širina zoba, stopnja stiskanja odrezka in deformacije odrezka).

Pri ortogonalnem rezanju nastane nazobčan odrezek, zato je bila pri vseh modelih smiselna integracija modela MKE in kriterija loma, razen pri modificiranem El-Magdovem in Treppmannovem modelu, morda zaradi nižje toplotne prevodnosti pri visokih temperaturah. Štirje modeli J-C dajejo dobre rezultate glede morfologije odrezka, čeprav je najbolje prilagojen model z nižjo mejo plastičnosti.

Zerilli-Armstrongovi modeli za strukturi BCC in HCP se obnašata podobno, medtem ko je pri modifikaciji Zerilli-Armstrongovega modela opaziti občutno povečanje rezalne sile in temperature zaradi strukture HCP, obdelava pa je težavnejša kot pri strukturi BCC. Model za strukturo BCC se je izkazal kot najbolje prilagojen za morfologijo odrezka pri vrednosti m = 0,8 z najboljšim ujemanjem sil in temperature pri uporabi hladilne tekočine. Model strukture HCP je lahko dober pristop za suho obdelavo, z odstopanji manjšimi od 2 % in dobrimi rezultati za deformacijo odrezkov (1,4 in 1,7 % za BCC in HCP) in stopnjo stiskanja odrezkov (4,7 in 7 % za BCC in HCP).

Modeli napovedujejo geometrijo odrezkov z dobro natančnostjo, z izjemo modificiranega ElMagdovega in Treppmannovega modela, zato je integracija kriterija loma sprejemljiva. Štirje modeli J-C dajejo dobre rezultate, model z nižjim koeficientom toplotnega mehčanja pa rezultatov ni izboljšal.

Zerilli-Armstrongovi modeli s strukturo BCC in HCP izkazujejo najboljše ujemanje pri suhem in mokrem ortogonalnem rezanju. Modificirani model HCP ni dal dobrih rezultatov, zato matematična modifikacija, ki vpliva na funkcijo deformacij, ni primerna za ortogonalno rezanje. Trenje in mazanje vplivata na rezalno silo in na temperaturo, medtem ko morfologija odrezkov nanju ni občutljiva. Modeli so občutljivi tudi na faktor trenja, rezultati pa so odvisni od konstitutivnih enačb materiala in od vrednosti konstant.

Primerjave z literaturo kažejo, da simulacije z uporabo Zerilli-Armstrongovih modelov omogočajo manjša odstopanja glede na eksperimentalne rezultate. ©2011 Strojniški vestnik. Vse pravice pridržane.

Ključne besede: obdelava, ortogonalno rezanje, Ti6Al4V, MKE, morfologija odrezkov, konstitutivni modeli

SI 144

*Naslov avtorja za dopisovanje: UNED, Oddelek za proizvodno strojništvo, C/ Juan del Rosal 12, Madrid, Španija, rdomingo@ind.uned.es

Strojniški vestnik - Journal of Mechanical Engineering 57(2011)10, SI 145

Prejeto: 29.09.2010 Sprejeto: 25.07.2011

Vpliv sprememb na vstopnem delu na lokalni izkoristek hladilnega stolpa na naravni vlek Dvoršek, M. ‒ Hočevar, M. ‒ Širok, B. ‒ Holeček, N. ‒ Donevski, B. Matjaž Dvoršek1 ‒ Marko Hočevar2,* ‒ Brane Širok2 ‒ Nikola Holeček3 ‒ Božin Donevski4 1Termoelektrarna Šoštanj d.o.o., Slovenija 2Univerza v Ljubljani, Fakulteta za strojništvo, Slovenija 3Gorenje d.d., Slovenija 4Univerza St. Kliment Ohridski, Fakulteta za tehnične vede, Makedonija

V prispevku je predstavljen vpliv izvedenih sprememb hladilnega stolpa na lokalni izkoristek hladilnega stolpa na naravni vlek Termoelektrarne Šoštanj 4. Lokalni izkoristek je bil ocenjen na podlagi sprememb temperatur na izstopu iz eliminatorjev kapljic pred in po rekonstrukciji. Pred modifikacijami je ponoči hrup na izbranih lokacijah presegal dovoljeno mejo za 4 dB(A). Za določitev virov hrupa so bile izvedene meritve z akustično kamero, pri čemer je bilo ugotovljeno, da so najpomembnejši vir hrupa vstopne odprtine na obodu hladilnega stolpa na višini lovilnikov kapljic. Zaradi prekomernega hrupa hladilnega stolpa so bile na mestu največjega vira hrupa odprtine na obodu hladilnega stolpa zaprte s perforiranimi ploščami za absorpcijo hrupa. Zaradi izvedenih protihrupnih ukrepov se je zmanjšala prosta površina na vstopu hladnega zraka v hladilni stolp. Namen dela je bil ugotoviti, ali se je posledično spremenil tudi lokalni izkoristek hladilnega stolpa.

Izkoristek stolpa je določen z enačbo, ki temelji na osnovni Merklovi enačbi za izkoristek hladilnega stolpa. Ker lokalni izkoristek vsebuje tudi vpliv geometrije elementov stolpa, smo izkoristek posameznega vertikalnega segmenta stolpa definirali z eksponentno enačbo z entalpijami za primer, ko je zrak na izstopu popolnoma nasičen. Temperature eliminatorjev kapljic smo merili s termalno kamero, ki je bila nameščena v stolpu. Lokalno zmanjšanje izkoristka na podlagi meritev smo analizirali s pomočjo fenomenoloških zvez prestopa toplote, ki smo jo izmerili na izbranem vertikalnem segmentu hladilnega stolpa.

Značilno zmanjšanje lokalnega izkoristka smo zaznali na obodu hladilnega stolpa. Največje zmanjšanje lokalnega izkoristka je znašalo 2%, povprečno zmanjšanje na obodu hladilnega stolpa je znašalo 0,5%, na večini mest po površini stolpa pa zmanjšanje izkoristka ni bilo izmerjeno. To ni presenetljivo, saj se termodinamske in aerodinamske lastnosti v hladilnem stolpu na obodu pogosto razlikujejo od lastnosti v sredini stolpa. Preizkušani hladilni stolp ima toplotne izmenjevalnike z ozirom na premer stolpa nameščene visoko nad tlemi, kar pomaga k majhni razliki v lokalnem izkoristku.

Lokalne meritve v hladilnem stolpu so težavne in omejene z velikostjo in kompleksnostjo hladilnega stolpa ter odvisnostjo od okoljskih parametrov in zahtev dispečerja električne energije. Običajno ni mogoče spreminjati posameznega parametra in ohraniti vse ostale parametre konstantne. Razen tega so spremembe merjenih spremenljivk zaradi velikosti sistema počasne. Razpršenost merilnih rezultatov je zato velika, število merilnih točk pa majhno.

V prispevku predstavljamo eksperimentalen postopek za določanje lokalnega izkoristka.

Druge metode za določanje izkoristka temeljijo na CFD simulacijah, matematičnem modeliranju ali eksperimentalnih metodah, vendar izkoristka ne morejo določati lokalno. ©2011 Strojniški vestnik. Vse pravice pridržane.

Ključne besede: hladilni stolp, modifikacija, lokalni izkoristek, temperatura, termalna kamera, meritve

*Naslov avtorja za dopisovanje: Univerza v Ljubljani, Fakulteta za strojništvo, Aškerčeva 6, 1000 Ljubljana, Slovenija, marko.hocevar@fs.uni-lj.si

SI 145

Strojniški vestnik - Journal of Mechanical Engineering 57(2011)10, SI 146

Prejeto: 06.12.2010 Sprejeto: 15.07.2011

Globalna optimizacija bočne zmogljivosti dvostebrne varnostne konstrukcije pri prevrnitvi s pomočjo Krigingovega in genetskega algoritma Jixin, W. ‒ Mingyao, Y. ‒ Yonghai, Y. Wang Jixin* ‒ Yao Mingyao ‒ Yang Yonghai Jilin University, College of Mechanical Science and Engineering, China

Namen študije je priprava razvojne metode za globalno optimizacijo varnostnih konstrukcij pri prevrnitvi (ROPS), ki izboljšuje sposobnost absorpcije energije, zmanjšuje poškodbe operaterja v primeru prevrnitve gradbenega stroja, zmanjšuje stopnjo odpovedi pri laboratorijskih preizkusih in skrajšuje čas konstrukcije.

V članku je predstavljena metoda globalne optimizacije konstrukcije ROPS na osnovi Krigingovega modela in genetskega algoritma. Za določitev vzorčnih točk je uporabljena metoda latinske hiperkocke, uporabljena pa sta tudi Krigingov model namesto tradicionalnih polinomskih odzivnih površin drugega reda za globalne aproksimacije ter genetski algoritem za optimizacijo rezultatov. Dvostebrna varnostna konstrukcija pri prevrnitvi je primer uporabe globalne optimizacijske metode pri gradbeni mehanizaciji. Članek obravnava optimizacijo varnostne konstrukcije pri prevrnitvi gradbene mehanizacije za povečanje bočne absorpcije energije in zmanjšanje stopnje odpovedi pri laboratorijskih preizkusih.

Postopek, prikazan v tem članku, omogoča razvoj optimalne konstrukcije ROPS. Odzivi v začetnih konstrukcijskih točkah se pridobijo s simulacijo velikih plastičnih deformacij po MKE. Za zmanjšanje računskega dela se določi Krigingova odzivna površina, za iskanje globalne rešitve pa se uporabi genetski algoritem.

Z optimizacijo konstrukcije ROPS se očitno izboljša razmerje med bočno silo in bočnimi deformacijami konstrukcije ROPS. Bočna sila konstrukcije ROPS izpolnjuje zahtevo po standardni minimalni bočni sili, zato so se bočne deformacije konstrukcije ROPS z večanjem bočne sile večale.

Varnostna konstrukcija ROPS lahko torej absorbira pomemben del bočne energije s trajnimi plastičnimi deformacijami komponent, zlasti nosilnih komponent konstrukcije ROPS. Na ta način je mogoče zmanjšati poškodbe operaterja pri različnih nesrečah s prevračanjem.

V delu je predstavljena nadomestna Krigingova metoda optimizacije za tipično varnostno konstrukcijo pri prevrnitvi gradbenega stroja. Z optimizacijo je bila dosežena zadovoljiva variabilnost pri analizi bočnih obremenitev; nosilnost, deformacije in absorpcija energije pa se dobro ujemajo. Povezava med absorpcijo energije in bočno nosilnostjo lahko učinkovito izboljša sposobnost absorpcije energije, tako da lahko operater preživi morebitno prevrnitev z manj poškodbami. ©2011 Strojniški vestnik. Vse pravice pridržane.

Key words: razvoj vozil, zaščitna konstrukcija pri prevrnitvi (ROPS), globalna optimizacija, Kriging, genetski algoritem, absorpcija energije

SI 146

*Naslov avtorja za dopisovanje: Univerza Jilin, Fakulteta za tehniške vede in strojništvo, Changchun, LR Kitajska, jxwang@jlu.edu.cn

Strojniški vestnik - Journal of Mechanical Engineering 57(2011)10, SI 147

Prejeto: 18.01.2011 Sprejeto: 28.07.2011

Razvoj proteznega kolena za alpsko smučanje Demšar, I. ‒ Supej, M. ‒ Vidrih, Z. ‒ Duhovnik, J. Ivan Demšar1,* ‒ Matej Supej2 ‒ Zmago Vidrih3 ‒ Jožef Duhovnik1 1 Univerza v Ljubljani, Fakulteta za strojništvo, Slovenija 2 Univerza v Ljubljani, Fakulteta za šport, Slovenija 3 ART-LEG d.o.o., Slovenija

Prispevek predstavlja razvoj posebnega proteznega kolena za alpsko smučanje, namenjenega osebam z nadkolensko amputacijo. S preizkušanjem proteznih kolen, ki so dosegljiva na trgu, smo ugotovili, da le-ta ne zagotavljajo ustrezne kinematike nožne strukture, ki je pogoj za kakovostno alpsko smučanje.

Cilj raziskave je razvoj in izdelava novega proteznega kolena, ki bo čim bolje posnemalo naravno gibanje in v največji možni meri nadomeščalo manjkajoči ud.

Pri razvoju proteznega kolena smo sledili teoriji razvojno-konstrukcijskega procesa, ki je osnovana na teoriji, da moramo razvijati take tehnične sisteme, ki v največji meri posnemajo naravne procese. Metoda temelji na analizi naravnega procesa in na razvojno-konstrukcijskem procesu, podprtem s kinematično, kinetično in trdnostno analizo virtualnega modela. V ta namen smo razvili in izdelali namensko preizkuševališče, ki omogoča simulacijo obremenitev smučarja in merjenje obremenitev podlage ter sočasno zajemanje kinematike človekove strukture v področju nog. Sledila je analiza meritev in izdelava koncepta večosnega proteznega kolena. Analitično smo preverili kinematiko koncepta in jo primerjali z meritvami. Naslednji korak je bila izdelava virtualnega modela proteznega kolena in trdnostna kontrola ključnih elementov. Kontrola trdnosti je bila izvedena s pomočjo metode končnih elementov (FEM analiza). Največje obremenitve na posameznih elementih konstrukcije smo določili s pomočjo kinetične analize mehanizma za izbrano kombinacijo pnevmatskega amortizerja in vzmeti, ki zagotavlja ustrezno togost kolenskega sklopa in s tem prenos obremenitev iz smučarja na podlago. Naslednja faza v razvoju proteznega kolena za alpsko smučanje je bila izdelava prototipa in njegovo preizkušanje v realnih razmerah.

Primerjava rezultatov meritev kinematike noge in kinematične analize proteznega kolena je potrdila ustreznost izbranega koncepta večosnega mehanizma. Pri preizkušanju prototipa v realnih razmerah na smučišču je bilo ugotovljeno, da tovrstno protezno koleno, ki razen rotacije izvaja še translacijo v vzdolžni in vertikalni smeri, ohranja optimalno lego težišča telesa, s tem pa bistveno pripomore k nadzoru nad smučmi in večji kakovosti alpskega smučanja.

Delo je bilo osredotočeno predvsem na zagotavljanje ustrezne kinematike proteznega kolena oz. celotne proteze. V nadaljevanju sledi analiza obremenitev podlage pri različnih načinih smučanja.

Na osnovi teh podatkov bomo skušali določiti togost proteznega kolena, ki bo ustrezala določenemu uporabniku. Pri tem je treba upoštevati njegove karakteristike, psihofizične sposobnosti in smučarsko znanje.

Pri testiranju se je izkazalo, da je razen kinematike ključna tudi togost kolenskega sklopa. Le-ta mora biti prilagojena posameznemu uporabniku in načinu smučanja. Težava je v tem, da so obremenitve v zunanjem in notranjem zavoju različne, kar zahteva tudi drugačno togost proteznega kolena.

V prispevku je prikazan primer razvoja novega izdelka na način, ki se na področju protetike še ni uveljavil in temelji na meritvah, predhodnih analizah in hitri izdelavi prototipa. Namenjen je vsem, ki se ukvarjajo z razvojem novih izdelkov oz. pripomočkov. ©2011 Strojniški vestnik. Vse pravice pridržane.

Ključne besede: alpsko smučanje, nadkolenska amputacija, kinematika proteze, dinamika pri smučanju, raziskave, razvoj, preizkušanje, osvajanje izdelka

*Naslov avtorja za dopisovanje: Univerza v Ljubljani, Fakulteta za strojništvo, Aškerčeva 6, 1000 Ljubljana, Slovenija, ivan.demsar@lecad.fs.uni-lj.si

SI 147

Strojniški vestnik - Journal of Mechanical Engineering 57(2011)10, SI 148

Prejeto: 14.06.2008 Sprejeto: 02.08.2011

Uporaba metodologije Promethee-Gaia pri izbiri sistemov za sušenje majhnih semen in praškastih materialov Prvulovic, S. − Tolmac, D. − Radovanovic, L. Slavica Prvulovic − Dragisa Tolmac* − Ljiljana Radovanovic Univerza v Novem Sadu, Tehnična fakulteta ‘’Mihajlo Pupin’’, Srbija

V članku so analizirani trije različni sušilni sistemi. Pri izbiri sušilnega sistema je uporabljena primerjalna analiza petih vplivnih dejavnikov: koeficienta prenosa toplote, cene, energije za sušenje, toplotnega izkoristka in specifične porabe energije. Analiza kaže, da je najcenejša uporaba pnevmatskega sušilnika, ki prinaša občutne prihranke (z ozirom na strošek naložbe in prihranek energije). Po koristih mu sledita spiralni sušilnik in rotacijski bobnasti sušilnik.

V članku je predstavljena uporaba metodologije Promethee-Gaia in izbira med tremi sistemi za sušenje majhnih semen in praškastih materialov – pnevmatskim sušilnikom, spiralnim sušilnikom in bobnastim rotacijskim sušilnikom – po petih različnih kriterijih. Analiza je bila opravljena po metodah Promethee I, Promethee II in Promethee-Gaia, pri čemer prikazuje tudi kompleksna razmerja med alternativami in kriteriji v ravnini Gaia. V delu je prikazana uporaba programa Decision Lab, ki je osnova za analizo rezultatov in razvrščanje alternativ.

Do končnih rezultatov smo prišli v nekaj korakih, začenši z osnovnim vzorcem alternativ in kriterijev, končali pa smo z definitivno izbiro glede na razvrstitev. Na osnovi razvrstitve je bila opravljena končna izbira najbolje rešitve sušenja po vseh kriterijih, pri čemer ima alternativa a1 (pnevmatski sušilnik) prednost pred alternativama a2 (spiralni sušilniki) in a3 (rotacijski sušilnik z bobnom).

Metodologija PROMETHEE-GAIA je enostavna metodologija, ki omogoča razvrščanje med več alternativami od najboljše do najslabše. Prednost te metode pred drugimi metodami večkriterijskega izbiranja so razen analitične vrednosti rezultatov tudi grafikoni rezultatov raziskave, ki dajejo bolj jasno sliko za izbiro najboljše alternative. Grafična predstavitev rezultatov je možnost, ki daje tej metodologiji prednost pred drugimi metodami večkriterijske izbire. Metodo je mogoče uporabiti pri vsakem sprejemanju odločitev po različnih kriterijih, kjer je na voljo več alternativ.

Pri izbiranju sušilnega sistema so razen tega uporabne tudi druge metode večkriterijske izbire, kot so ELECTRE, AHP in TOPSIS, ki dajejo primerljive rezultate za končno izbiro. Te metode pa niso tako celovite kot metoda PROMETHEE-GAIA, saj nekatere od njih dajejo samo analitične rezultate, nekatere pa ne omogočajo razvrščanja in dajejo samo najboljšo alternativo. Metodologija PROMETHEE-GAIA se od drugih metod razlikuje po analitičnih vrednostih za vsako alternativo, popolnem razvrščanju alternativ, predstavitvi rezultatov v obliki preglednic in grafičnem prikazu rezultatov. Metodologija PROMETHEEGAIA bo uporabljena tudi pri nadaljnjih raziskavah, saj ima le malo omejitev in daje zanesljive rezultate.

V članku je predstavljena večkriterijska analiza treh sistemov za sušenje s petimi kriteriji in metodo Promethee, ob podpori odzivne programske opreme, ki omogoča enostavno delo in hitrejšo izbiro ustreznega sušilnega sistema. ©2011 Strojniški vestnik. Vse pravice pridržane.

Ključne besede: metoda Promethee-Gaia, večkriterijska izbira, sušilni sistemi, program Decision Lab

SI 148

*Naslov avtorja za dopisovanje: Univerza v Novem Sadu, Tehnična fakulteta “Mihajlo Pupin” Djure Djakovic bb, 23000 Zrenjanin, Srbija, dragisat@gmail.com

Strojniški vestnik - Journal of Mechanical Engineering 57(2011)10, SI 149-150 Navodila avtojem

Navodila avtorjem Članke pošljite na naslov: Strojniški vestnik Journal of Mechanical Engineering Aškerčeva 6, 1000 Ljubljana, Slovenija Tel.: 00386 1 4771 137 Faks: 00386 1 2518 567 E-mail: info@sv-jme.eu strojniski.vestnik@fs.uni-lj.si Članki morajo biti napisani v angleškem jeziku. Strani morajo biti zaporedno označene.

Prispevki so lahko dolgi največ 10 strani. Daljši članki so lahko v objavo sprejeti iz posebnih razlogov, katere morate navesti v spremnem dopisu.

Kratki članki naj ne bodo daljši od štirih strani.

Navodila so v celoti na voljo v rubriki “Informacija za avtorje” na spletni strani revije: http://en.sv-jme.eu/ Prosimo vas, da članku priložite spremno pismo, ki naj vsebuje: 1. naslov članka, seznam avtorjev ter podatke avtorjev; 2. opredelitev članka v eno izmed tipologij; izvirni znanstveni (1.01), pregledni znanstveni (1.02) ali kratki znanstveni članek (1.03); 3. izjavo, da članek ni objavljen oziroma poslan v presojo za objavo drugam; 4. zaželeno je, da avtorji v spremnem pismu opredelijo ključni doprinos članka; 5. predlog dveh potencialnih recenzentov, ter kontaktne podatke recenzentov. Navedete lahko tudi razloge, zaradi katerih ne želite, da bi določen recenzent recenziral vaš članek.

OBLIKA ČLANKA Članek naj bo napisan v naslednji obliki: Naslov, ki primerno opisuje vsebino članka.

Povzetek, ki naj bo skrajšana oblika članka in naj ne presega 250 besed. Povzetek mora vsebovati osnove, jedro in cilje raziskave, uporabljeno metodologijo dela, povzetek rezultatov in osnovne sklepe.

- Uvod, v katerem naj bo pregled novejšega stanja in zadostne informacije za razumevanje ter pregled rezultatov dela, predstavljenih v članku.

- Teorija.

- -

-

Eksperimentalni del, ki naj vsebuje podatke o postavitvi preskusa in metode, uporabljene pri pridobitvi rezultatov.

- Rezultati, ki naj bodo jasno prikazani, po potrebi v obliki slik in preglednic.

- Razprava, v kateri naj bodo prikazane povezave in posplošitve, uporabljene za pridobitev rezultatov. Prikazana naj bo tudi pomembnost rezultatov in primerjava s poprej objavljenimi deli. (Zaradi narave posameznih raziskav so lahko rezultati in razprava, za jasnost in preprostejše bralčevo razumevanje, združeni v eno poglavje.)

- Sklepi, v katerih naj bo prikazan en ali več sklepov, ki izhajajo iz rezultatov in razprave.

- Literatura, ki mora biti v besedilu oštevilčena zaporedno in označena z oglatimi oklepaji [1] ter na koncu članka zbrana v seznamu literature.

Enote - uporabljajte standardne SI simbole in okrajšave. Simboli za fizične veličine naj bodo v ležečem tisku (npr. v, T, n itd.). Simboli za enote, ki vsebujejo črke, naj bodo v navadnem tisku (npr. ms1, K, min, mm itd.)

Okrajšave naj bodo, ko se prvič pojavijo v besedilu, izpisane v celoti, npr. časovno spremenljiva geometrija (ČSG).

Pomen simbolov in pripadajočih enot mora biti vedno razložen ali naveden v posebni tabeli na koncu članka pred referencami.

Slike morajo biti zaporedno oštevilčene in označene, v besedilu in podnaslovu, kot sl. 1, sl. 2 itn. Posnete naj bodo v ločljivosti, primerni za tisk, v kateremkoli od razširjenih formatov, npr. BMP, JPG, GIF. Diagrami in risbe morajo biti pripravljeni v vektorskem formatu, npr. CDR, AI. Vse slike morajo biti pripravljene v črnobeli tehniki, brez obrob okoli slik in na beli podlagi.

Ločeno pošljite vse slike v izvirni obliki Pri označevanju osi v diagramih, kadar je le mogoče, uporabite označbe veličin (npr. t, v, m itn.). V diagramih z več krivuljami, mora biti vsaka krivulja označena. Pomen oznake mora biti pojasnjen v podnapisu slike.

Tabele naj imajo svoj naslov in naj bodo zaporedno oštevilčene in tudi v besedilu poimenovane kot Tabela 1, Tabela 2 itd.. Poleg fizikalne veličine, npr t (v ležečem tisku), mora biti v oglatih oklepajih navedena tudi enota. V tabelah naj se ne podvajajo podatki, ki se nahajajo v besedilu.

SI 149

Strojniški vestnik - Journal of Mechanical Engineering 57(2011)10, SI 149-150

Potrditev sodelovanja ali pomoči pri pripravi članka je lahko navedena pred referencami. Navedite vir finančne podpore za raziskavo.

REFERENCE Seznam referenc MORA biti vključen v članek, oblikovan pa mora biti v skladu s sledečimi navodili. Navedene reference morajo biti citirane v besedilu. Vsaka navedena referenca je v besedilu oštevilčena s številko v oglatem oklepaju (npr. [3] ali [2] do [6] za več referenc). Sklicevanje na avtorja ni potrebno.

Reference morajo biti oštevilčene in razvrščene glede na to, kdaj se prvič pojavijo v članku in ne po abecednem vrstnem redu. Reference morajo biti popolne in točne. Vse neangleške oz. nenemške naslove je potrebno prevesti v angleški jezik z dodano opombo (in Slovene) na koncu Navajamo primere: Članki iz revij: Priimek 1, začetnica imena, priimek 2, začetnica imena (leto). Naslov. Ime revije, letnik, številka, strani, DOI oznaka.

[1] Hackenschmidt, R., Alber-Laukant, B., Rieg, F. (2010). Simulating nonlinear materials under centrifugal forces by using intelligent cross-linked simulations. Strojniški vestnik - Journal of Mechanical Engineering, vol.

57, no. 7-8, p. 531-538, DOI:10.5545/svjme.2011.013.

Ime revije ne sme biti okrajšano. Ime revije je zapisano v ležečem tisku.

Knjige: Priimek 1, začetnica imena, priimek 2, začetnica imena (leto). Naslov. Izdajatelj, kraj izdaje [2] Groover, M. P. (2007). Fundamentals of Modern Manufacturing. John Wiley & Sons, Hoboken.

Ime knjige je zapisano v ležečem tisku.

Poglavja iz knjig: Priimek 1, začetnica imena, priimek 2, začetnica imena (leto). Naslov poglavja. Urednik(i) knjige, naslov knjige. Izdajatelj, kraj izdaje, strani.

[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. Članki s konferenc: Priimek 1, začetnica imena, priimek 2, začetnica imena (leto). Naslov. Naziv konference, strani.

[4] Štefanić, N., Martinčević-Mikić, S., Tošanović, N. (2009). Applied Lean System in Process

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Industry. MOTSP 2009 Conference Proceedings, p. 422-427.

Standardi: Standard (leto). Naslov. Ustanova. Kraj.

[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.

Spletne strani: Priimek, Začetnice imena podjetja. Naslov, z naslova http://naslov, datum dostopa.

[6] Rockwell Automation. Arena, from http://www. arenasimulation.com, accessed on 2009-09-27.

RAZŠIRJENI POVZETEK Ko je članek sprejet v objavo, avtorji pošljejo razširjeni povzetek na eni strani A4 (približno 3.000 - 3.500 znakov). Navodila za pripravo razširjenega povzetka so objavljeni na spletni strani http://sl.svjme.eu/informacije-za-avtorje/.

AVTORSKE PRAVICE Avtorji v uredništvo predložijo članek ob predpostavki, da članek prej ni bil nikjer objavljen, ni v postopku sprejema v objavo drugje in je bil prebran in potrjen s strani vseh avtorjev. Predložitev članka pomeni, da se avtorji avtomatično strinjajo s prenosom avtorskih pravic SV-JME, ko je članek sprejet v objavo. Vsem sprejetim člankom mora biti priloženo soglasje za prenos avtorskih pravic, katerega avtorji pošljejo uredniku. Članek mora biti izvirno delo avtorjev in brez pisnega dovoljenja izdajatelja ne sme biti v katerem koli jeziku objavljeno drugje.

Avtorju bo v potrditev poslana zadnja verzija članka. Morebitni popravki morajo biti minimalni in poslani v kratkem času. Zato je pomembno, da so članki že ob predložitvi napisani natančno.

Avtorji lahko stanje svojih sprejetih člankov spremljajo na http://en.sv-jme.eu/.

PLAČILO OBJAVE Domači avtorji vseh sprejetih prispevkov morajo za objavo plačati prispevek, le v primeru, da članek presega dovoljenih 10 strani oziroma za objavo barvnih strani v članku, in sicer za vsako dodatno stran 20 EUR ter dodatni strošek za barvni tisk, ki znaša 90,00 EUR na stran.

Strojniški vestnik - Journal of Mechanical Engineering 57(2011)10, SI 151-160 Osebne objave

Doktorske disertacije in diplome DOKTORSKE DISERTACIJE Na Fakulteti za strojništvo Univerze v Ljubljani sta z uspehom obranila svojo doktorsko disertacijo: dne 27. septembra 2011 Mitja MAZEJ z naslovom: »Lokalno prezračevanje za kontrolo navzkrižne okužbe v prostorih« (mentor: prof.dr.

Vincenc Butala, somentor: izr. prof. dr. Arsen K. Melikov); Navzkrižna okužba preko prostorskega zraka v zaprtih prostorih predstavlja v razvitem svetu enega izmed najpomembnejših faktorjev pri zagotavljanju ustreznega bivanjskega okolja.

Tveganje pred navzkrižno okužbo v zaprtih prostorih je namreč v razvitem svetu postalo del vsakdana, saj večina ljudi živi, dela in opravlja velik del svojih vsakodnevnih aktivnosti v zaprtih in največkrat gosto zasedenih notranjih okoljih, v katerih je nehote izpostavljena različnim primesem in patogenom v zraku. V večini primerov njihov vir predstavljajo okuženi ali bolni ljudje, ki s svojimi dihalnimi aktivnostmi kot so dihanje, govorjenje, kašljanje ali kihanje sproščajo patogene kapljice različnih velikosti, katerih nehlapni ostanki se lahko daljši čas zadržujejo v prostorskem zraku, preden se iz njega odstranijo bodisi z odlaganjem na različnih površinah zaradi gravitacijskih sil bodisi z izmenjavo zraka s prezračevanjem.

Pravilno zasnovano in učinkovito prezračevanje, ki omogoča nadzor nad zračnimi tokovi v prostorih, ima tako ključno vlogo pri kontroli navzkrižne okužbe in zaščiti uporabnikov. Kljub temu večina obstoječih prezračevalnih sistemov ni zasnovana tako, da bi preprečevala širjenje patogenov preko zraka, saj princip redčenja onesnaženega zraka z dovajanjem velikih količin svežega zraka s konvencionalnimi prezračevalnimi sistemi zaradi lokacije vira patogenov (ljudi v prostoru) ni učinkovit. V določenih primerih lahko prezračevalni sistem prenos patogenov celo poveča. Razmeroma malo razpoložljivega znanja na tem interdisciplinarnem področju dodatno omejuje razvoj učinkovitejših rešitev kontrole pred navzkrižno okužbo v zahtevnejših primerih direktne izpostavljenosti pred izdihanimi patogenimi kapljicami, kot je npr. v primeru kašlja. Zaradi tega je poglavitni cilj doktorskega dela usmerjen v razvoj in optimizacijo napredne lokalne prezračevalne metode, ki omogoča

učinkovito kontrolo navzkrižne okužbe in zaščito izpostavljene osebe tako v primeru dolgotrajne izpostavljenosti patogenom, generiranih v primeru dihanja ali govorjenja, kot tudi v primeru direktne kratkotrajne izpostavljenosti patogenom, generiranih pri kašlju.

V doktorski disertaciji je podrobno analiziran problem navzkrižne okužbe zaradi širjenja izdihanih patogenih kapljic preko prostorskega zraka med dvema osebama, ki sedita druga nasproti druge v prostoru z mešalnim prezračevanjem, brez in z uporabo na novo razvite napredne lokalne prezračevalne metode, ki temelji na principu zračne zavese.

V prvem delu disertacije je podrobno predstavljen razvoj in optimizacija delovanja sistema zračne zavese na osnovi opravljene eksperimentalne analize v primeru dolgotrajne izpostavljenosti patogenom v izdihanem zraku.

Eksperimentalna analiza z uporabo toplotnih manekenov je pokazala, da je z uporabo zračne zavese mogoče pomembno zmanjšati izpostavljenost in s tem verjetnost za prenos okužbe preko prostorskega zraka. Pri tem se je s stališča učinkovitosti delovanja sistema kot pomemben izkazal vpliv različnih parametrov (stopnja izmenjave zraka s prezračevalnim sistemom, zasnova in geometrija difuzorja za generiranje zračne zavese, dovedena količina zraka skozi sistem zračne zavese, oddaljenost zračne zavese od vira okužbe itd.), hkrati pa smo potrdili, da je za optimalno učinkovitost principa ključno ravnotežje med efektom indukcije izdihanega zraka s curkom zračne zavese in jakostjo mešanja evakuiranega izdihanega zraka s prostorskim zrakom v ozadju. Efekt mešanja izdihanega zraka s prostorskim zrakom namreč zmanjšuje evakuacijo patogenov iz dihalne cone ter povečuje njihov delež v ozadju, s tem pa tudi učinkovitost principa. S tega stališča je pomembna tudi oddaljenost vira okužbe od curka zračne zavese, saj je v primeru prevelike oddaljenosti razpršenost patogenov ustrezno večja. Sistem zračne zavese se je v kombinaciji z mešalnim prezračevanjem hkrati izkazal tudi za bolj energetsko učinkovito strategijo kontrole navzkrižne okužbe, saj je bilo pri optimalnem delovanju zmanjšanje verjetnosti za okužbo z virusom influence enakovredno kot v primeru povečanja količine svežega zraka s prezračevanjem za vsaj 1,4 menjave/h.

SI 151

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V drugem delu disertacije je analiziran potencial zračne zavese s stališča zaščite v primeru direktne izpostavljenosti izkašljanemu zraku. Opravljene eksperimentalne in numerične analize so potrdile, da sistem zračne zavese pri dovodu 16 L/s zraka zagotavlja popolno zaščito pred povprečno močnim kašljem, medtem ko je v primeru najmočnejšega analiziranega kašlja izpostavljenost pred patogeni zmanjšana za kar 87% z ozirom na referenčno izpostavljenost.

Ugotovljeno je bilo, da v vseh simuliranih primerih ustrezno močan curek zračne zavese zagotavlja učinkovito zaščito tudi pred večjimi patogenimi kapljicami, z velikostjo nad 12 µm.

Te ugotovitve so zelo vzpodbudne upoštevaje preprostost same metode in dejstvo, da v analiziranem primeru izpostavljenosti samo s konvencionalnim prezračevanjem prostora ni mogoče doseči učinkovite zaščite pred navzkrižno okužbo tudi pri najšibkejšem analiziranem kašlju.

Princip zaščite na osnovi zračne zavese se je izkazal za zelo primernega v primeru direktne izpostavljenosti pred izdihanim in izkašljanim zrakom, saj uporaba prostorskega zraka kot ovire na eni strani zagotavlja učinkovito evakuacijo izdihanega zraka iz dihalne cone, hkrati pa ima velik potencial za zmanjšanje jakosti impulza curka izkašljanega zraka in posledično vpliva na njegovo preusmeritev stran od dihalne cone izpostavljene osebe. Inovativni princip zaščite je poleg tega dosežen brez vidnih in motečih posegov v prostor tako s stališča funkcije kot tudi toplotnega ugodja, kar je v skladu z moderno filozofijo zasnove interjerja, ki temelji na odprtih prostorih. Pričakovati je, da bodo pridobljena znanstvena spoznanja pomembno vplivala na nadaljnje raziskave na področju navzkrižne okužbe preko prostorskega zraka z uporabo naprednih prezračevalnih metod ter na prihodnji razvoj prezračevalnih sistemov v notranjih okoljih, kjer je direktna izpostavljenost med osebami odvisna od lokacije v prostoru; dne 28. septembra 2011 Matej PLETERSKI z naslovom: »Lasersko reparaturno navarjanje orodij za delo v hladnem« (mentor: prof. dr. Janez Tušek); V raziskavi je predstavljena študija vpliva parametrov pri laserskem navarjanju orodnega jekla za delo v hladnem z veliko vsebnostjo C in Cr, AISI D2 (Mat. No.: 1.2397) z namenom določitve parametrov in oblike laserskega bliska, ki bi zagotavljali navare brez napak. Z metodologijo površin odziva so bili razviti matematični SI 152

modeli za napovedovanje geometrijskih lastnosti pretaljenih površin in navarov. Pretaljene površine in navari so bili detajlno analizirani tudi z vidika makro in mikrostruktur, XRD analizami in meritvami trdot. V zadnjem delu je bila opravljena študija vpliva temperature predgrevanja in podhlajanja na lastnosti navarov. Z vidika praktične evaluacije kakovosti navarov pa so bili opravljeni še drsni obrabni testi navarjenih površin. Razviti matematični modeli se dobro ujemajo z rezultati eksperimentov. Določeno je bilo tudi območje parametrov in oblika laserskega bliska, ki zagotavlja pretaljevanje in navarjanje brez razpok. Rezultati analiz kažejo na visok delež zaostalega avstenita v navarih, ki pa kljub nizki trdoti zagotavlja veliko stopnjo deformacijske utrditve in s tem odlične obrabne lastnosti pri nižjih silah obremenjevanja. * Na Fakulteti za strojništvo Univerze v Maribor je z uspehom obranila svojo doktorsko disertacijo: dne 27. septembra 2011 Nina NOVAK z naslovom: »Integracija naprednih tehnologij čiščenja obarvanih odpadnih vod iz tekstilne industrije« (mentor: prof. dr. Alenka Majcen le Marechal); V doktorski disertaciji predstavljamo študijo določitve stroškovno optimalnih obratovalnih pogojev za razbarvanje in čiščenje vodne raztopine barvila C. I. Reactive Blue 268 z naprednimi procesi čiščenja. Najprej predstavljamo rezultate laboratorijskih eksperimentov in matematične modele procesov UV/H2O2 in Fe2+/H2O2. Rezultati kažejo, da lahko z uporabo metodologije odzivnih površin razvijemo ustrezna matematična modela, ki statistično zadostno opišeta odvisnost merjenih odzivov od izbranih (vplivnih) obratovalnih parametrov. Nato prikazujemo študijo optimiranja energijsko intenzivnega procesa UV/H2O2. Kot vplivne parametre smo upoštevali koncentracijo barvila, koncentracijo vodikovega peroksida, pH, čas obdelave in temperaturo. Stroške elektrike, stroške vodikovega peroksida in stroške vode za uravnavanje koncentracije barvila smo upoštevali kot relevantne obratovalne stroške. Čeprav so minimalni stroški čiščenja ocenjeni na visokih 17 €/m3, dobljeni rezultati jasno kažejo, da moramo, če želimo zagotoviti obratovalno in ekonomsko učinkovitost, proces optimirati z obeh vidikov

Strojniški vestnik - Journal of Mechanical Engineering 57(2011)10, SI 151-160

hkrati. Ekonomsko učinkovitost lahko dodatno izboljšamo z integracijo naprednih procesov čiščenja. Kot alternative v integriranem sistemu smo upoštevali proces UV/H2O2, proces Fe2+/ H2O2 in membransko filtracijo. Procesno shemo integriranega procesa in vrednosti obratovalnih parametrov, pri katerih sistem obratuje pri minimalnih stroških, smo določili s pristopom, ki temelji na matematičnem programiranju.

Iz rezultatov je razvidno, da lahko z ustrezno integracijo izbranih procesov znatno znižamo povprečne stroške čiščenja. V primerjavi s procesom UV/H2O2 so ocenjeni povprečni stroški čiščenja integriranega proces približno 75% nižji (2,4 €/m3).

DIPLOMIRALI SO Na Fakulteti za strojništvo Univerze v Ljubljani so pridobili naziv univerzitetni diplomirani inženir strojništva: dne 29. septembra 2011: Mario ĐURIĆ z naslovom: »Analiza deformacij pozicionirne enote laserskega mikroobdelovalnega sistema« (mentor: prof. dr. Janez Diaci); Rok FELDIN z naslovom: »Optimiranje tlačne posode za utekočinjen zemeljski plin v kriogenih pogojih« (mentor: prof. dr. Franc Kosel, somentor: doc.dr. Tomaž Videnič); David PIŠLAR z naslovom: »Konkurenčnost mikro trigeneracijskih sistemov na lesno biomaso« (mentor: prof. dr. Vincenc Butala, somentor: doc.dr. Uroš Stritih); dne 30. septembra 2011: Matej BIČEK z naslovom: »Določitev obdelovalnosti ležajnega jekla 100Cr6 s kriogenim odrezavanjem« (mentor: prof. dr. Janez Kopač, somentor: doc.dr. Franci Pušavec); David DERŽIČ z naslovom: »Preizkuševališče za testiranje železniških zavornih diskov« (mentor: prof. dr. Miha Boltežar); Nejc KOSEDNAR z naslovom: »Geometrijske značilnosti obdelave z abrazivnim vodnim curkom« (mentor: prof. dr. Mihael Junkar); Aleš TUREL z naslovom: »Načrtovanje vibracijskega preizkusa elektronskega krmilnika hibridnega plovila« (mentor: prof. dr. Miha Boltežar); Janez VRABEC z naslovom: »Postavitev in merjenje natančnosti visokohitrostnega

obdelovalnega stroja SODICK MC 430-L« (mentor: prof. dr. Janez Kopač, somentor: doc. dr.

Franci Pušavec). * Na Fakulteti za strojništvo Univerze v Mariboru so pridobili naziv univerzitetni diplomirani inženir strojništva: dne 15. septembra 2011: Mihael HUMAR z naslovom: »Simulacija motorja v realnem času - delovni tok in nastavitev hil modela motorja« (mentor: prof. dr. Breda Kegl, somentor: asist. dr. Zoran Žunič); dne 22. septembra 2011: Marko BUDLER z naslovom: »Fotovoltaični materiali« (mentor: prof. dr. Ivan Anžel, mentor: doc.dr. Zdenka Ženko); Boštjan HRAŠAR z naslovom: »Pomen razvojnega laboratorija za razvoj pralnih in sušilnih aparatov v podjetju Gorenje d.d.« (mentor: doc. dr. Leber Marjan, mentor: prof.dr.

Anton Hauc); Marko PLUT z naslovom: »Ekološki in ekonomski vidiki izrabe lesne biomase z uplinjanjem za soproizvodnjo toplote in električne energije« (mentor: prof. dr. Aleš Hribernik, mentor: prof.dr. Anton Hauc); Vito STRAŠEK z naslovom: »Optimizacija oskrbe s sestavnimi deli v podjetju ADK d.o.o.« (mentor: izr. prof. dr. Borut Buchmeister, mentor: prof. dr. Majda Bastič); Primož ROBNIK z naslovom: »Investicijski elaborat za nakup tehnološko inovativne sušilnice za termično obdelavo lesa« (mentor: doc. dr. Iztok Palčič, mentor: doc. dr.

Zdenka Ženko); dne 23. septembra 2011: Gregor STREHAR z naslovom: »Razvoj potisnega čevlja in določitev mejne nosilnosti« (mentor: doc. dr. Jožef Predan, somentor: prof. dr.

Nenad Gubeljak); dne 28. septembra 2011: Matic VAUKAN z naslovom: »Oblikovanje procesa ravnanja s kovinskimi odpadki v podjetju Vaukan d.o.o.« (mentor: prof. dr. Andrej Polajnar, somentor: doc. dr. Karin Širec); dne 29. septembra 2011: Aljaž KLASINC z naslovom: »Razvoj daljinsko vodene ključavnice dvokolesa« (mentor: izr. prof. dr. Bojan Dolšak, mentor: viš. pred. dr.

Marina Novak); SI 153

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Jan JURJEC z naslovom: »Analiza energetske učinkovitosti v podjetju TUS KO-SI d.d.« (mentor: prof. dr. Aleš Hribernik, mentor: prof.dr. Anton Hauc); Sebastijan JURKOŠEK z naslovom: »Optimizacija proizvodnje in sistem nabave v podjetju EMO ETT« (mentor: doc. dr. Iztok Palčič, mentor: prof.dr. Anton Hauc); Sandi KAČIČNIK z naslovom: »Projekt vzpostavitve centra za izvedbo simulacij pri razvoju novega izdelka« (mentor: doc. dr. Iztok Palčič, mentor: prof. dr. Anton Hauc); Peter KIRBIŠ z naslovom: »Karakterizacija neoksidiranega dela notranje oksidirane baker aluminijeve zlitine preoblikovane po Ecap postopku in preučitev postopka z vidika difuzije inovacij« (mentor: prof. dr. Ivan Anžel, mentor: doc. dr. Zdenka Ženko); Aleš KREL z naslovom: »Inovativne obdelave z vodnim curkom« (mentor: izr. prof. dr. Miran Brezočnik, somentor: doc. dr. Zdenka Ženko); Amadej LIPIČ z naslovom: »Upravljanje vhodnih zalog materiala v podjetju Transpak d.o.o.« (mentor: doc. dr. Iztok Palčič, mentor: prof. dr. Vojko Potočan); Nejc SATLER z naslovom: »Obdelava odpadnih tehnoloških emulzij in mulja v podjetju Gkn Driveline Slovenija« (mentor: prof. dr. Niko Samec, mentor: doc. dr. Zdenka Ženko); Matej ZATLER z naslovom: »Analiza in izboljšava konstrukcije nadstreška za vozila« (mentor: doc. dr. Boštjan Harl, mentor: doc. dr.

Zdenka Ženko); Tadej PLANTEV z naslovom: »Konstruiranje sistema za generiranje pare in njenega dovoda v pečniški prostor« (mentor: izr. prof. dr. Bojan Dolšak, somentor: izr. prof. dr.

Jurij Avsec); Miha VEČKO z naslovom: »Sodobno načrtovanje daljinskega ogrevanja v manjših mestih« (mentor: prof. dr. Niko Samec, somentor: asist. dr. Filip Kokalj); Tomaž VERLAK z naslovom: »Konstruiranje in preračun ključa z ragljo« (mentor: doc. dr. Aleš Belšak, somentor: izr. prof. dr. Miran Ulbin); dne 30. septembra 2011: Jure POTEKO z naslovom: »Avtomatizacija namenskega stroja za gumarsko industrijo« (mentor: doc. dr. Darko Lovrec, somentor: prof. dr. Riko Šafarič). * SI 154

Na Fakulteti za strojništvo Univerze v Mariboru so pridobili naziv diplomirani inženir strojništva (UN): dne 13. septembra 2011: Nejc BOŽIČ z naslovom: »Uporaba karbonskih kompozitov pri gradnji tricikla« (mentor: izr. prof. dr. Stanislav Pehan, somentor: prof. dr. Breda Kegl); Matej FÜRST z naslovom: »Koncipiranje in zasnova stirlingovega motorja, ki bo izrabljal potencial dimnih plinov iz peči« (mentor: izr. prof. dr. Stanislav Pehan); Jernej KREVS z naslovom: »Izboljšava mehanizma za vpetje naslona za glavo na avtomobilski sedež« (mentor: izr. prof. dr.

Stanislav Pehan). dne 15. septembra 2011: Tadej NOVAK z naslovom: »Programiranje in analiza ravninskega končnega elementa za dinamiko konstrukcij« (mentor: izr. prof. dr. Marko Kegl, somentor: prof. dr. Matjaž Hriberšek); Lio PAVLIČ z naslovom: »Vpliv geometrije valjčka na napetostno polje pri velikih aksialnih ležajih« (mentor: prof. dr. Srečko Glodež); Matej ULČNIK z naslovom: »Zasnova vležajenja kotne glave horizontalnega vrtalnorezkalnega stroja« (mentor: prof. dr. Srečko Glodež). dne 22. septembra 2011: Matej GRM z naslovom: »Računalniško podprto konstruiranje valjčnega transporterja z dvojnim odvzemom« (mentor: izr. prof. dr. Miran Ulbin, somentor: doc. dr. Tone Lerher); Nejc LAZAR z naslovom: »Postavitev proizvodnje sivega stiropora na novi lokaciji« (mentor: izr. prof. dr. Borut Buchmeister, somentor: doc. dr. Iztok Palčič); Klemen MEVC z naslovom: »Prilagajanje oblike izdelka tehnologiji brizganja plastike« (mentor: izr. prof. dr. Igor Drstvenšek, somentor: asist. mag. Tomaž Brajlih).

Bogdan PLAZOVNIK z naslovom: »Računalniško podprto načrtovanje in vodenje proizvodnje v podjetju Metal Ravne« (mentor: izr. prof. dr. Borut Buchmeister); David ŠEKORANJA z naslovom: »Optimizacija oblike ohišja reduktorja za tehnološki postopek litja« (mentor: izr. prof. dr.

Igor Drstvenšek, somentor: asist. mag. Tomaž Brajlih);

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Marko TEMENT z naslovom: »Primerjava meritev učinkovitosti toplotne črpalke po standardih SIST-EN 255-3:2001 in FPR-EN 16147« (mentor: prof. dr. Aleš Hribernik, somentor: doc. dr. Matjaž Ramšak); dne 23. septembra 2011: David BELOVIČ z naslovom: »Večkanalne meritve s programom Labview« (mentor: doc. dr.

Aleš Belšak, somentor: prof. dr. Aleš Hribernik); dne 28. septembra 2011: Jure JEŽ z naslovom: »Robotska prijemala« (mentor: izr. prof. dr. Miran Brezočnik, somentor: prof. dr. Jože Balič); Gašper KLANČNIK z naslovom: »Računalniško podprto programiranje CNC strojev« (mentor: prof. dr. Jože Balič, somentor: doc. dr. Mirko Ficko).

Metod PEČOLER z naslovom: »Programiranje izdelave avtomobilskega distančnika na CNC stroju« (mentor: prof. dr. Jože Balič).

Denis VALENTAN z naslovom: »Računalniško podprto merjenje prizmatičnih obdelovancev na trikoordinatni merilni napravi« (mentor: izr. prof. dr. Bojan Ačko, somentor: izr. prof. dr. Borut Buchmeister).

Franci VRANETIČ z naslovom: »Uporaba inteligentnih sistemov pri montaži« (mentor: izr. prof. dr. Brezočnik Miran, somentor: prof. dr. Jože Balič). dne 29. septembra 2011: Matej CENTRIH z naslovom: »Izdelava vzmeti D3,2 ETB2-6 3S s postopki preoblikovanja« (mentor: izr. prof. dr. Ivan Pahole, somentor: prof. dr. Zoran Ren).

Matjaž GAJŠEK z naslovom: »Numerična simulacija krožne in parabolične izvedbe sončnega kolektorja« (mentor: doc. dr. Matjaž Ramšak, somentor: prof. dr. Aleš Hribernik).

Matija GLINŠEK z naslovom: »Izračun toplotne obremenitve hiše po DIN in ISO standardu« (mentor: doc. dr. Matjaž Ramšak).

Jernej HRIBERNIK z naslovom: »Snovanje preoblikovalnih orodij za upogibanje pločevine« (mentor: izr. prof. dr. Ivan Pahole).

Tomaž KASTELIC z naslovom: »Konstruiranje mehanizma za utrujanje sedeža Sitty« (mentor: doc. dr. Matej Vesenjak, somentor: doc. dr. Boštjan Harl).

Luka PRŠINA z naslovom: »Oblikovanje delovnega mesta konvencionalne stružnice z upoštevanjem antropometrije« (mentor: doc. dr.

Nataša Vujica Herzog, somentor: doc. dr. Simona Jevšnik).

Borut SRČNIK z naslovom: »Konstruiranje zgibnih dvoriščnih vrat« (mentor: izr. prof. dr.

Gotlih Karl).

Marko ŠLAMBERGER z naslovom: »Ogrevanje hiše podprto z izkoriščanjem energije sonca« (mentor: prof. dr. Aleš Hribernik, somentor: doc. dr. Matjaž Ramšak).

Iztok ŠOSTER z naslovom: »Analiza pogonov malih vetrnih elektrarn« (mentor: prof. dr. Srečko Glodež, somentor: doc. dr. Janez Kramberger).

Nejc ŠTROVS z naslovom: »Rekonstrukcija vgradnega stikala sv z možnostjo montaže daljinskega sprožnika« (mentor: doc. dr.

Matej Vesenjak, somentor: izr. prof. dr. Marko Kegl).

Simon URBAS z naslovom: »Določitev procesnih značilnosti aeracijskega mešala« (mentor: prof. dr. Matjaž Hriberšek, somentor: prof. dr. Leopold Škerget).

Edis VEHABOVIĆ z naslovom: »Izkoriščanje toplotnega potenciala izpušnih plinov s stirlingovim motorjem« (mentor: izr. prof. dr. Stanislav Pehan, somentor: prof. dr.

Breda Kegl). dne 30. septembra 2011: Boštjan FERK z naslovom: »Ultrazvočno varjenje« (mentor: izr. prof. dr. Miran Brezočnik).

Damjan STRAMEC z naslovom: »Nadzor stanja tekočin na obdelovalnih strojih« (mentor: doc. dr. Darko Lovrec, somentor: asist. Vito Tič).

Samoel URAN z naslovom: »Zasnova univerzalne dvižne mize« (mentor: doc. dr. Darko Lovrec).

Sebastjan ZADRAVEC z naslovom: »Uporaba sodobnih tehnologij pri izdelavi traktorskih prikolic« (mentor: izr. prof. dr. Miran Brezočnik, somentor: izr. prof. dr. Ivan Pahole).

Gašper ZDOVC z naslovom: »Montaža z roboti v elektronski industriji« (mentor: izr. prof. dr. Miran Brezočnik, somentor: asist. Simon Brezovnik). * Na Fakulteti za strojništvo Univerze v Mariboru so pridobili naziv univerzitetni diplomirani gospodarski inženir: dne 22. septembra 2011: Janže ARLIČ z naslovom: »Trend uporabe metod inovacijskega managementa pri razvoju SI 155

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izdelkov v slovenskih podjetjih« (mentor: izr. doc. dr. Marjan Leber, somentor: prof. dr. Majda Bastič); Mitja BERAS z naslovom: »Vpliv regulacijske opreme na energetsko učinkovitost zgradb« (mentor: prof. dr. Niko Samec, somentor: doc. dr. Aleksandra Pisnik Korda); Jure NAGLIČ z naslovom: »Optimizacija proizvodnega modula v podjetju Šumer d.o.o.« (mentor: doc. dr. Iztok Palčič, somentor: prof. dr.

Vojko Potočan). * Na Fakulteti za strojništvo Univerze v Mariboru so pridobili naziv diplomirani inženir mehatronike (UN): dne 15. septembra 2011: Vid ČREŠNIK z naslovom: »Elektronski sistem za vodenje izmeničnih motorjev pretvorniško vezje« (mentor: izr. prof. dr. Karl Gotlih, somentor: prof. dr. Miro Milanovič); Miljenko ŠARIĆ z naslovom: »Merjenje rezalnih sil med procesom VH obdelave« (mentor: doc. dr. Uroš Župerl, somentor: izr. prof. dr. Aleš Hace); Benjamin ŠKAFAR z naslovom: »Glasovno upravljanje sistema za nadzor rezalnih sil« (mentor: doc. dr. Uroš Župerl, somentor: izr. prof. dr. Aleš Hace); dne 29. septembra 2011: Mitja FILIPIČ z naslovom: »TObčutljivost kriterijev gibljivosti robotov v okolici singularnih točk« (mentor: izr. prof. dr. Gotlih Karl, somentor: prof.dr. Riko Šafarič); Primož FIŠER z naslovom: »Dvosmerni DC/DC pretvornik« (mentor: izr. prof. dr. Karl Gotlih, somentor: doc.dr. Andreja Rojko); Matej JUHART z naslovom: »FPGA krmilnik za BLAC motor pralnega stroja« (mentor: izr. prof. dr. Karl Gotlih, somentor: izr. prof. dr. Aleš Hace); Aleš KAPUN z naslovom: »Litij-polimerna akumulatorska baterija za električno vozilo« (mentor: izr. prof. dr. Karl Gotlih, somentor: doc. dr. Andreja Rojko); Ivan KELEMINA z naslovom: »Vodenje 3 osnega mehanizma s krmilnikom Compactrio« (mentor: izr. prof. dr. Karl Gotlih, somentor: doc. dr. Darko Hercog); Rok KOVŠE z naslovom: »Vodenje CNC rezkalnega stroja z uporabo G kode« (mentor: SI 156

doc. dr. Mirko Ficko, somentor: doc.dr. Darko Hercog); Aljaž KRAMBERGER z naslovom: »Vodenje sklopa hibridnega pogona« (mentor: izr. prof. dr. Karl Gotlih, somentor: doc.dr. Andreja Rojko); Benjamin MEGLIČ z naslovom: »Računalniško vodeni 3 osni mehanizem« (mentor: doc. dr. Mirko Ficko, somentor: doc.dr.

Darko Hercog); Tom PEINKIHER z naslovom: »Načrtovanje in izvedba vodenja robotskega stereo vida« (mentor: izr. prof. dr. Karl Gotlih, somentor: prof. dr. Riko Šafarič); Darko PODRŽAJ z naslovom: »Elektronski sistem za vodenje izmeničnih motorjev - programska oprema za mikrokrmilnik TMS320F28335« (mentor: izr. prof. dr. Karl Gotlih, somentor: doc. dr. Miran Rodič); * Na Fakulteti za strojništvo Univerze v Ljubljani so pridobili naziv diplomirani inženir strojništva: dne 14. septembra 2011: Janez DOLENEC z naslovom: »Zasnova orodja za brizganje pokrova« (mentor: prof. dr.

Jožef Duhovnik); Simeon GLOGOVŠEK z naslovom: »Razvoj skladovnika paketov« (mentor: prof. dr.

Marko Nagode); David LANGUS z naslovom: »Razvoj diagonalne pnevmatike za motorno kolo« (mentor: doc. dr. Jernej Klemenc, somentor: prof. dr. Matija Fajdiga); Andraž TRAMPUŠ z naslovom: »Programi Evropske Unije in Slovenije na področju zmanjševanja emisij toplogrednih plinov iz industrijskih kurilnih naprav« (mentor: izr. prof. dr. Andrej Senegačnik); Luka BOVHA z naslovom: »Vpliv geometrije valovnega jadralca na tokovno polje in aerodinamične lastnosti pri Machovih številih od 2,5 do 4,5« (mentor: izr. prof. dr. Tadej Kosel); Marko FRANK z naslovom: »Izdelava brezpilotnega letala EDA-X« (mentor: izr. prof. dr. Tadej Kosel); Atina LAZIĆ z naslovom: »Letalska frazeologija« (mentor: pred. mag. Alenka Helena Kukovec); Matej OGOREVC z naslovom: »Analiza trajektorije leta pri izvajanju standardne odletne

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procedure MODRO 1D pri največjih dovoljenih vzletnih masah letalnikov (MTOM)« (mentor: pred. mag. Andrej Grebenšek, somentor: izr. prof. dr. Tadej Kosel); Matic Vrečko z naslovom: »Analiza izboljšave pogojev instrumentalnega vodenja zrakoplovov na Letališče Portorož« (mentor: pred.

Miha Šorn, somentor: izr. prof. dr. Tadej Kosel); dne 16. septembra 2011: Vilijem ČIBEJ z naslovom: »Uporovno varjenje diod na usmernik« (mentor: prof. dr.

Janez Diaci, somentor: izr. prof. dr. Ivan Polajnar); Matic OMAN z naslovom: »Primerjava izračunov letne rabe energije za stanovanjsko stavbo« (mentor: prof. dr. Vincenc Butala, somentor: doc. dr. Uroš Stritih).

Miha PELKO z naslovom: »Zasnova novega sesalnika za prah na ejektorskem principu« (mentor: prof. dr. Mirko Čudina); Tomaž PETERLIN z naslovom: »Lasersko površinsko pretaljevanje toplotno utrjevalne aluminijeve zlitine« (mentor: izr. prof. dr. Roman Šturm, somentor: prof. dr. Janez Grum); Gašper POTOČNIK z naslovom: »Energijska analiza stavb in vgrajenih klimatskih sistemov s programskim orodjem ArchiMAID« (mentor: prof. dr. Vincenc Butala, somentor: doc. dr. Uroš Stritih); Jure COLARIČ z naslovom: »Izdelava vzorcev zvarnih spojev z umetnimi napakami za šolske namene« (mentor: prof. dr. Janez Tušek, somentor: doc. dr. Andrej Lešnjak); Marko LUŽAN z naslovom: »Lasersko reparaturno varjenje orodij z manjšimi poškodbami« (mentor: prof. dr. Janez Tušek); Jernej MALIK z naslovom: »Priprava tehnologije varjenja zgorevalnega cilindra tunelske peči« (mentor: prof. dr. Janez Tušek); Primož PAHOR z naslovom: »Hlajenje bakrenih terminalov med uporovnim varjenjem« (mentor: prof. dr. Janez Tušek); Boštjan SKUBE z naslovom: »Analiza energetske učinkovitosti struženja« (mentor: prof. dr. Janez Kopač, somentor: doc. dr. Franci Pušavec); Borut TEPINA z naslovom: »Obdelava in racionalnost novega profila koles pri železniških vozilih« (mentor: prof. dr. Janez Kopač, somentor: viš. pred. dr. Jože Jurkovič); dne 20. septembra 2011: Bine KRPIČ z naslovom: »Spajkanje aluminijeve in jeklene pocinkane pločevine po

postopku CMT« (mentor: prof. dr. Janez Tušek, somentor: doc. dr. Damjan Klobčar); Dušan OBREZA z naslovom: »Optimizacija porabe filtrirane vode - vračanje dekantata v proizvodnjo titanovega dioksida« (mentor: doc. dr. Andrej Bombač); Miha RAJER z naslovom: »Atestirano varilsko osebje« (mentor: prof. dr. Janez Tušek); dne 21. septembra 2011: Andi LEGAT z naslovom: »Verifikacija obratovalnih režimov inštaliranih turbinskih agregatov na HE Moste po prenovi« (mentor: prof. dr. Branko Širok); Tom SODJA z naslovom: »Vrtljiva ploščad za lahka motorna letala« (mentor: doc. dr. Boris Jerman); Silvo ŠNEBERGER z naslovom: »Večnamenska prikolica« (mentor: izr. prof. dr.

Roman Žavbi); * Na Fakulteti za strojništvo Univerze v Mariboru so pridobili naziv diplomirani inženir strojništva: dne 12. septembra 2011: Josip PEJIĆ z naslovom: »Optimizacija procesa izdelave senzorja za avtomobilsko industrijo« (mentor: izr. prof. dr. Borut Buchmeister, somentor: doc. dr. Marjan Leber); Rene ČERVEK z naslovom: »Dimenzioniranje stebra vetrne elektrarne« (mentor: doc. dr. Janez Kramberger); Janez JELEN z naslovom: »Optimiranje toplotne črpalke zrak-voda z zunanjim toplotnim prenosnikom« (mentor: prof. dr. Milan Marčič, somentor: izr. prof. dr. Jurij Avsec); Gregor ČREŠNIK z naslovom: »Vpliv bioetanola na karakteristike procesa vbrizgavanja« (mentor: prof. dr. Breda Kegl); Žan ŠINKOVEC z naslovom: »Konstruiranje naprave za mletje pet embalaže« (mentor: doc. dr. Janez Kramberger, somentor: izr. prof. dr. Ivan Pahole); Mitja OZMEC z naslovom: »Linija za avtomatsko izdelavo žlebnih kljuk« (mentor: prof. dr. Iztok Potrč, somentor: doc. dr. Tone Lerher); dne 22. septembra 2011: Zvonko FRANC z naslovom: »Posodobitev krmilja na stroju za izdelavo jeder PGM20« (mentor: doc. dr. Uroš Župerl); SI 157

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Krešimir GORIŠEK z naslovom: »Snovanje baterijske kosilnice na nitko« (mentor: izr. prof. dr. Stanislav Pehan); Denis KAVAŠ z naslovom: »Uvajanje avtomatskega merjenja skupne učinkovitosti opreme v proizvodni proces« (mentor: izr. prof. dr.

Igor Drstvenšek, somentor: doc. dr. Samo Ulaga); Matej KUŠER z naslovom: »Energetska analiza delovanja med toplotno črpalko, ploščatim in vakuumskim solarnim sprejemnikom« (mentor: izr. prof. dr. Jurij Avsec, somentor: prof. dr. Milan Marčič); Mihael MIHELJAK z naslovom: »Konstruiranje diskaste kosilnice« (mentor: doc. dr. Samo Ulaga, somentor: doc. dr. Aleš Belšak); dne 23. septembra 2011: Davor HVALA z naslovom: »Avtomatizacija strege injekcijskih stiskalnic za brizganje gume« (mentor: doc. dr. Aleš Belšak, somentor: izr. prof. dr. Miran Ulbin); dne 28. septembra 2011: Kristjan ARBEITER z naslovom: »Izboljšave kakovosti odkovka z optimiranjem gravure utopa« (mentor: izr. prof. dr. Bojan Ačko, somentor: izr. prof. dr. Borut Buchmeister); Boštjan VARGAZON z naslovom: »Uvajanje CNC rezkalnega stroja in pripadajoče opreme v proizvodnjo« (mentor: izr. prof. dr. Ivan Pahole, somentor: prof. dr. Jože Balič); dne 29. septembra 2011: Dejan ČUČEK z naslovom: »Konstruiranje gondole male vetrne turbine« (mentor: doc. dr.

Janez Kramberger, somentor: prof. dr. Srečko Glodež); Andraž JUG z naslovom: »Delni energetski pregled podjetja hankel slovenija, ki zajema pitno, toplo, dravsko vodo ter paro, plin in ogrevanje«

SI 158

(mentor: prof. dr. Niko Samec, somentor: asist. dr.

Filip Kokalj); Uroš JUSTINEK z naslovom: »Fotovoltaična elektrarna na strehi enodružinske hiše - donosna naložba ali modern trend« (mentor: doc. dr. Marjan Leber, somentor: doc. dr. Iztok Palčič); Simon NOVAK z naslovom: »Konstruiranje vpenjalnega sistema za obdelavo aluminijastih adapterjev« (mentor: izr. prof. dr.

Bojan Dolšak, somentor: viš. pred. dr. Marina Novak); Primož PIRC z naslovom: »Temelji načrtovanja opreme vhoda in izhoda v avtomatiziranem skladišču« (mentor: prof. dr.

Iztok Potrč, somentor: doc. dr. Tone Lerher); Predrag RADONJIĆ z naslovom: »Kogeneracijski sistem na lesno biomaso« (mentor: prof. dr. Milan Marčič, somentor: doc. dr. Matjaž Ramšak); Rudi TOLAR z naslovom: »Tehnološka zasnova namenskega vrtalnega stroja« (mentor: izr. prof. dr. Ivan Pahole); Mitja TURK z naslovom: »Delni energetski pregled podjetja henkel slovenija, ki zajema komprimiran zrak, električno energijo in klime« (mentor: prof. dr. Niko Samec, somentor: asist. dr. Filip Kokalj); Leopold GAJŠEK z naslovom: »Pregled programov za simulacijo brizganja plastike in preoblikovanja pločevine« (mentor: izr. prof. dr. Miran Brezočnik, somentor: doc. dr. Mirko Ficko); Eric HERŽENJAK z naslovom: »Sodobna računalniška tehnologija za CAD/CAM« (mentor: izr. prof. dr. Miran Brezočnik, somentor: doc. dr.

Mirko Ficko).

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Prof. dr. Viljem Kralj – osemdesetletnik

Dne 31.7.2011 je prof. Viljem Kralj dopolnil 80 let. Rodil se je v Dugem Ratu pri Splitu, kot prvi od petih otrok, materi Zlati in očetu Rudolfu. Oče je v tem obdobju sodeloval kot strokovnjak pri izgradnji francoske tovarne karbida L`Air Liquide, delniške družbe La Dalmatien.

Kasneje se je družina Kraljevih preselila v Novi Sad, kjer je obiskoval osnovno šolo. V začetku druge svetovne vojne, so se naselili v Mariboru.

Tu je obiskoval Klasično gimnazijo ter maturiral na Srednji hidrometeorološki šoli v Beogradu.

Po dveletni zaposlitvi na Hidrometeorološkem zavodu SR Slovenije je nadaljeval s študijem na Naravoslovno matematični fakulteti. V začetku leta 1957 diplomiral na Tehniški fakulteti iz elektrotehnike, na področju šibkega toka.

Prva inženirska zaposlitev je bila v tovarni Telekomunikacije v Ljubljani. V Zavodu za varjenje se je aktivno vključil v strokovno delo za potrebe intenzivno razvijajoče kovinsko predelovalne industrije. Že takrat pa je sodeloval tudi pri znanstveno raziskovalnem delu Zavoda in pri predavanjih za praktično delo na področju varilstva za varjenje po različnih postopkih talilnega varjenja pa tudi tehnikom in inženirjem, ki so želeli pridobiti poglobljeno znanje s področja varilstva.

Njegove zgodnje pedagoško delo je bilo usmerjeno tudi na predavanja izven Zavoda za varjenje. Na srednji tehniški šoli v Ljubljani, oddelek varjenja je predaval in pripravil učni program za predmet Avtomatika in elektronika.

Na strokovni šoli Jurija Vege v Ljubljani je predaval predmet »Vakumska tehnika«. Nekatera predavanja je profesor Kralj pripravil v obliki učbenikov, kot so: Novejši varilni postopki, Varjenje v zaščiti CO2, Kontrole brez porušitve, Točkovno uporovno varjenje, Stroji in naprave za uporovno točkovno varjenje. V zelo pregledni obliki je predstavil celotno varjenje v novejšem Krautovem strojniškem priročniku.

Leta 1961 je bil poslan na varilsko specializacijo, ki je potekala v Parizu, v okviru organizacije Astef (Association pourl'organisation des stages en France) in Asmic (Association pour l'organisation des missions de cooperation technique).

Na Zavodu za varilstvo je postal vodja raziskovalnega oddelka, kjer so z večjo skupino raziskovalcev delali na področju razvoja varilnih strojev in naprav za številna podjetja. Pod njegovim vodstvom so bile razvite naprave za obločno varjenje v zaščitni atmosferi nevtralnih plinov: VARTIG in MIGVAR. Razvil je napravi za varjenje v nevtralnih zaščitnih plinih TIGVAR in MIGVAR, razvil s sodelavci namizno izvedbo stroja za plamensko rezanje z ročnim, magnetnim ali fotoelektronskim vodenjem, vodil in sodeloval pri razvoju stroja za sočelno obžigalno varjenje in naprav za plazemsko rezanje in varjenje, vodil in sodeloval pri prenosu transformatorjev in strojev za uporovno točkovno varjenje tipa Furlan v proizvodnjo v tovarni Varstoj iz Lendave, razvijal in prenašal različne stroje in naprave za varjenje v druge tovarne (Avtomontaža Ljubljana, Iskra Kranj). Leta 1969 je uspešno zaključil podiplomski magistrski študij iz področja avtomatike na Fakulteti za elektrotehniko. Uvodne raziskave v magistrski nalogi so dobila polno potrditev v doktorski nalogi z naslovom: »Raziskave gibov roke človeka elektrovarilca pri ročnem obločnem varjenju z metodami biokibernetike« pod mentorstvom akad. prof. Alojza Vodovnika in akad. prof. Ludvika Gyergyeka, letu 1973. V doktorskem delu je prof. Kralj na biokibernetski osnovi z merjenjem parametrov gibanja varilčeve roke proučeval proces obločnega varjenja s paličasto elektrodo. Nov postopek popisa procesa ročnega obločnega varjenja na osnovi biokibernetike je bil zelo odmeven v svetovnih znanstvenih in strokovnih krogih. Zato ni čudno, da je kasneje na Letni skupščini Mednarodnega SI 159

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instituta za varjenje – IIW, bil prav ta pristop sprejet v redni raziskovalni program Komisije IIb. Aktivno je sodeloval v več delovnih komisijah, najpomembnejše rezultate svojega znanstvenega dela pa je predstavljal v Študijski skupini 212 za fiziko varjenja. Kot eden vidnejših ekspertov v tej skupini, je tudi sodeloval pri pripravi knjige »Physics of Welding«, ki je bila izdana leta 1984 in 1986, pri založbi Pergamon Press. Leta 1982 je bil tudi med organizatorji in eden od predsednikov javnega posvetovanja z naslovom »Welding and Allied Processes«. Ob tej priliki je za goste organiziral tudi oglede najpomembnejših laboratorijev v RS, ki so bili dejavni na področju varjenja in avtomatizacije ter raziskav materialov.

Prof. Kralj je predstavljal svoje raziskovalno razvojne rezultate še na številnih drugih simpozijih in v strokovnih revijah, zlasti v domači reviji »Varilna tehnika«. V letu 1973 so v strokovnem glasilu takratnega vsesovjetskega instituta za znanost in tehniko in akademije za znanost objavili njegov prispevek z naslovom »Ekonomske primerjave plazemskega rezanja z različnimi plini in plinskimi mešanicami«.

Njegovo znanstveno raziskovalno delo na Fakulteti za strojništvo je bilo usmerjeno predvsem na temeljne raziskave. Na osnovi njegovih znanstvenih dosežkov je bil prof. Kralj v letu 1975 na Fakulteti za strojništvo habilitiran za docenta, v letu 1979 v izrednega ter 1984 v rednega profesorja na področju »Varjenja«.

Izjemno hitra gospodarska rast in številna povpraševanja po inženirskih kadrih z znanjem s področja varilstva so narekovala prilagoditev takratnega našega višješolskega programa. V tem obdobju je bila v smeri Proizvodno strojništvo sprejeta nova tako imenovana Varilska usmeritev.

Prof. Kralj je z znanjem elektrotehnike in strojništva uspešno pripravil vsebino predavanj in vaj za nove varilske predmete: Varilni stroji in naprave, Oprema za varilne procese in varstvo pri delu ter skupaj s prof. Prosencem tudi vsebine za predmet Fizikalno-kemične osnove varjenja.

Pri naslednji prenovi študijskega programa v letu 1985 pa sta prof. Prosenc in prof. Kralj izdelala in končno tudi predlagala nov predmetnik za varilsko usmeritev na univerzitetnem študiju. Tako je bil v letu 1985 na Fakulteti za strojništvo prvič izvajana Varilska usmeritev v okviru Proizvodnega strojništva na univerzitetnem študiju. V okviru podiplomskega študija pa sta skupaj s profesorjem Roethelom pripravila nov podiplomski predmet z naslovom Posebni načini obdelave, kjer je prof.

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Kralj med drugim obravnaval posebne načine toplotnega varjenja in rezanja. Prof. Kralj je predaval tudi v Mariboru na Visoki tehniški šoli oz. kasneje na Fakulteti za strojništvo v Mariboru.

Njegov prispevek na pedagoškem področju v veliki meri kaže preko 300 mentorstev diplomantom, najprej na višješolskem študiju in nato tudi na visoko strokovnem študiju ter končno tudi na univerzitetnem študiju. Med kolegi in študenti je bil vedno zelo priljubljen predvsem zaradi njegove pripravljenosti za sodelovanje in pomoč, kot tudi zaradi njegovega strokovnega znanja.

Prof. Kralj je bil tudi na družbenem področju zelo aktiven kot član in predsednik Sveta Zavoda za varilstvo, član njegovega upravnega odbora, član Odbora za razvoj in raziskave ter tudi član Znanstvenega sveta Zavoda, kasneje Instituta za varilstvo. Na Fakulteti za strojništvo je bil član in nato tudi predsednik Odbora za vzgojno in izobraževalno delo in predsednik Odbora za znanstveno raziskovalno delo ter Odbora za koordinacijo v samoupravni interesni skupnosti RS. V obdobju od leta 1990 pa do njegove upokojitve 1996 je bil Predstojnik Katedre za tehnologijo materialov in tudi vodja Laboratorija za varjenje. Eno mandatno obdobje (1991-93) je bil tudi prodekan za znanstveno raziskovalno delo.

Za svoje delo na področju Varilstva je prejel več priznanj s strani delovnih organizacij, s katerimi je izjemno uspešno sodeloval, t.j. ISKRA Avtomatika in VARSTROJ. Od leta 1976 je častni član Društva za varilno tehniko Slovenije. Za zasluge na razvoju Varilne tehnike v slovenskem prostoru je dobil priznanje od Slovenskega društva za varilno tehniko ter od mednarodnih varilnih organizacij.

V 65. letu starosti, to je v letu 1996, ko je izpolnjeval vse pogoje, se je upokojil a ohranil stike tako s Fakulteto za strojništvo ter Institutom za varilstvo. Na fakulteti je neposredno po upokojitvi krajše obdobje sodeloval kot mentor pri diplomskih nalogah in magistrskem delu. Na Institutu za varilstvo pa neprekinjeno sodeluje ko predavatelj na tečajih specialističnega programa za Evro varilnega inženirja in tehnologa.

Ob visokem življenjskem jubileju mu prijatelji in nekdanji sodelavci želimo predvsem zdravja ter vedrino in optimizem, ki jo je vedno pripravljen predajati svoji okolici. prof. dr. Janez Grum prof. dr. Viktor Prosenc

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Platnica SV-JME 57(2011)10_01.pdf 1 4.10.2011 11:24:04

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Journal of Mechanical Engineering - Strojniški vestnik

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10 year 2011 volume 57 no.