Journal of Mechanical Engineering / Strojniški vestnik 10-2010

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10 year 2010 volume 56 no.

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

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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 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: Compair2 air conditioner unit with an inbuilt recuperation system and a complete automatic system. The units feature flows from 1000 to 10.000 m3/h.

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Strojniški vestnik - Journal of Mechanical Engineering 56(2010)10 Contents

Contents Strojniški vestnik - Journal of Mechanical Engineering volume 56, (2010), number 10 Ljubljana, October 2010 ISSN 0039-2480 Published monthly

Papers Jure Čas, Gregor Škorc, Riko Šafarič: Improved Micropositioning of 2 DOF Stage by Using the Neural Network Compensation of Plant Nonlinearities Mahmoud Shariati, Mehdi Sedighi, Jafar Saemi, Hamid Reza Allahbakhsh: A Numerical and Experimental Study on Buckling of Cylindrical Panels Subjected to Compressive Axial Load Andreas Gleiter, Christian Spießberger, Gerd Busse: Lockin Thermography with Optical or Ultrasound Excitation George Bourkas, Emilios Sideridis, Christos Younis, Ioannis N. Prassianakis, Victor Kitopoulos: Strength and Fracture Strain of Resin/filler Systems Using Two Models (1) of Perfect and (2) of Low Adhesion Quality Tadeja Primožič Merkač, Bojan Ačko: Thread Gauge Calibration for Industrial Applications Cuneyt Fetvaci: Generation Simulation of Involute Spur Gears Machined By Pinion-Type Shaper Cutters Milosav Ognjanovic, Fathi Agemi: Gear Vibrations in Supercritical Mesh-Frequency Range Caused by Teeth Impacts Slobodan Morača, Miodrag Hadžistević, Igor Drstvenšek, Nikola Radaković: Application of Group Technology in Complex Cluster Type Organizational Systems Instructions for Authors

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Strojniški vestnik - Journal of Mechanical Engineering 56(2010)10, 599-608 UDC 004.032.26:681.5

Paper received: 07.12.2009 Paper accepted: 01.10.2010

Improved Micropositioning of 2 DOF Stage by Using the Neural Network Compensation of Plant Nonlinearities 1

Jure Čas1,* - Gregor Škorc2 - Riko Šafarič1 University of Maribor, Faculty of Electrical Engineering and Computer Science, Slovenia 2 RESISTEC UPR d.o.o. & Co.k.d., Slovenia

This paper describes the system for micropositioning of a 2 DOF mechanism with piezoelectric actuators (PEAs) called a piezo actuated stage (PAS). The PAS is fabricated by a photo structuring process from photosensitive glass and PEAs are built-on to meet the request for its precise movement.

The PAS is designed as a general 2 DOF stage. It can be used for different micropositioning or microassembling tasks according to the selected end-effector. The other components of the closed-loop control system for micropositioning of PAS are the high voltage drivers, the incremental position sensors and the control processing unit. Due to the nonlinear behaviour of the system for micropositioning, the precise position control of PAS with traditional PI controller is aggravated. Concerning the plant nonlinearities, the feedforward neural networks (NN) are used as a tool for their compensation. After the training procedure with the back-propagation (BPG) algorithm, the trained NN inverse model of plant nonlinearities is used as a feedforward part of the proposed controller. The experiment results have shown that the NN compensation improves the control performance of traditional PI controller. ©2010 Journal of Mechanical Engineering. All rights reserved.

Keywords: piezo actuated stage, position control, hysteresis, feedforward neural networks 0 INTRODUCTION Micropositioning is advanced technology, which is used in many research laboratories and companies, especially for the microscopy and advanced electronics manufacturing. The micropositioning systems are also employed in every day devices such as hard discs, camcorders, cars, etc. The usability of these devices depends on their precise movement, usually with submicron resolution. A micropositioning stage generally refers to a system which can automatically move an end-effector in its workspace with submicron resolution. For micropositioning stages it is desirable that they have high resolution, large workspace and compact size.

The applications with micropositioning stages have already been reported [1].

There are several different materials and actuation principles for the actuation of micropositioning stages. Due to their nano-metre resolution, high stiffness, big driving force, and fast response PEAs are recognized as fundamental elements for managing extremely small displacements [2]. PEAs are compact and rugged. They exhibit high stability and are practically immune to electromagnetic

interference. However, the existence of nonlinear multi-path hysteresis in piezoelectric material aggravates the position control of PEAs in high precision applications. When compared with the maximal displacement of PEAs, the maximum hysteretic error is typically between 15 to 20%.

The hysteresis makes it difficult to control the displacement in a case of varying target position because the voltage needed for the desired displacement, is not constant but varies with each actuation and also depends on the history of the motion. Understanding hysteresis behaviour is a fundamental step when designing the position controller for PAS. Control techniques to reduce the hysteresis effect in PEAs can be divided into four categories, i.e. electric charge control, feedforward (open-loop) position control, feedback (close-loop) position control and combination of feedforward and feedback position control. The electric charge control exploits the fact that the relationship between the position of PEAs and the induced charge has less hysteresis than that between position and applied voltage, as shown in [3] and [4]. However, this approach requires specialized equipment to measure and amplify the induced charge. The feedforward (open-loop) and feedback (closed-

*

Corr. Author's Address: University of Maribor, Faculty of Electrical Engineering and Computer Science, Smetanova ulica 17, 2000 Maribor, Slovenia, jure.cas@uni-mb.si

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Strojniški vestnik - Journal of Mechanical Engineering 56(2010)10, 599-608

loop) controllers, which are utilized with highvoltage drivers, are mainly studied with the systems with PEAs. The feedforward controllers are known for their many advantages. The instability problem, which is presented in feedback controllers, is avoided with the feedforward controllers.

Furthermore, the accurate and usually expensive position sensors are not needed. Instead of measuring the actual submicron displacement, the feedforward controllers are based on different hysteresis models, which can be approximated, for example, by the polynomial approximation [5], least-mean-square (LMS) algorithm approximation [6] etc. Among the proposed hysteresis models, the Preisach model [7] is by far the most well known and widely used. The subclass of the Preisach model is PrandtlIshlinskii model [8], which is less complex.

Furthermore, the inverse of Prandtl-Ishlinskii model can be computed analytically, thus making it more attractive for real-time applications.

However, the feedforward controllers, which are designed for hysteresis compensation, are generally not appropriate for systems with changing load and environment parameters, i.e. changing plant model. Additionally, the creep of PEAs, which can be described as a slow variation of displacement under constant voltage, aggravates the usability of open-loop controllers.

The feedforward controllers are known for their many advantages, but with regard to the described restrictions, they are usually employed for positional control of systems with the PEAs. The PI controller [9] is a proven control technique, which is, owing to its simplicity and reliability, utilized with the majority of the control applications. The parameters of PI controller are usually tuned to match the overshoot and rise-time criteria. According to the hysteresis nonlinearity, the tuning of these parameters is not a trivial problem for the systems with PEAs. Furthermore, the constant parameters of a PI controller cannot assure the optimal performance of the controller over the whole workspace.

In order to make a good use of feedforward control (hysteresis compensation) and feedback control, the authors have also proposed the combinations of both techniques.

The inverse hysteresis model (e.g. Preisach model) can be employed in parallel with the

600

close-loop PI controller [10]. The inverse hysteresis model can also be modelled with the neural networks as in [11]. As a result of this research, authors propose the cerebellar model articulation neural network controller, which can be used for compensation of nonlinearities of the piezo-actuated plant.

The proposed control approach, which is described here, is conceptually similar to that presented in [11], but with other important differences. Instead of cerebellar model articulation neural networks, the feedforward NN are used for the hysteresis compensation. The NN training by the back-propagation algorithm is similar to that described in [12]. The proposed training is executed before the control process as a sort of controller calibration. The NN model is used in combination with the linear PI controller.

It is proven by experiments that NN compensation of plant nonlinearities improves the control performance of linear PI controller.

Section 1 describes the PAS and other components of the closed-loop control system for micropositioning, i.e. the experimental set-up.

Section 2 describes the nonlinear characteristic of the controlled plant. Section 3 describes the short theory of the NN and the training configuration.

Section 4 describes the control results of PI controller and PI controller combined with NN hysteresis compensation. The control experiments prove the usability of the proposed control scheme. Section 5 gives some final conclusions.

1 SYSTEM FOR MICROPOSITIONING The PAS consists of a parallel glass mechanism (PGM) and two PEAs. The PGM is similar to a parallelogram. It is designed to transmit the displacement of PEAs on the tip displacement of the PAS, where the end-effector can be mounted. Due to its mechanical construction with dual flexure hinges, the motions are limited with only the actuated DOF, i.e. the axes of PAS are not coupled. The PEA A actuates the X DOF and PEA B actuates the Y DOF on the workspace (Fig. 1).

The PGM [13] is made of a photosensitive glass with a thickness of 1 mm. The photo structuring process, with partial process steps UV-lithography, thermal treatment, and etching, forms the basis for producing micro-structured glass components. The process is based on

Čas, J. - Škorc, G. - Šafarič, R.

Strojniški vestnik - Journal of Mechanical Engineering 56(2010)10, 599-608

different etching rates of exposed and nonexposed glass.

other hypothetical use of PAS can be utilized by using the micro-gripper, which is also made of a photo-sensitive glass. The micro-gripper is actuated with PEAs. The whole system can be used as a tool for handling micro-sized objects. It is described in greater detail in [14].

Precise micropositioning of PAS is a complicated task due to the plant nonlinearities.

In order to guarantee the precise micropositioning of PAS, the voltage drivers, incremental position encoders and appropriate control processing unit are developed as components of a close-loop control system. Fig. 2 shows the close-loop control system and the data flow between the components. The host computer is used as a user interface for programming the control processing unit and for the user interaction with the PAS.

Fig. 1. Operating principle of PAS (ground plan view) Two PEAs with dimensions 27 by 3 mm, with a thickness of 0.2 mm are joined to the PGM. The driving voltages for the PEAs must be inside the maximal driving voltage interval, i.e. from -100 to 100 V. According to the maximum driving voltages, the theoretical displacement of unloaded PEA is ±3.3 μm. However, the maximum displacement of the PEAs is not reached when they are joined to the PGM, because PGM generates a reactive/opposite force similar to the spring force. When the maximum voltage of ±100 V is applied, the maximal theoretical displacement of PEA is ±1.1 μm only.

By the transmission rule, the displacement of the PEAs is multiplied by a transmission ratio of PGM. The theoretical tip displacement over one DOF is approximately ±15 μm. Accordingly, the theoretical workspace of PAS is equal to square with 30 μm long sides as described in [12].

The PAS is designed as a general purpose micropositioning device. Its practical usage depends on the type of the end-effector on the tip.

The PAS can be mounted on the mechanical stage of a microscope as the specimen holder in order to guarantee an effective microscopy of the specimen. The approximate positioning of PAS with specimen can be provided with the fine adjustment knob of the microscope, while the precise positioning of the specimen can be provided by PAS. The specimen positioning can be referenced by using the graphical user interface running on the desktop computer. The

Fig. 2. The close-loop control system with PAS The Compact Vision System (CVS) from the National Instruments is used as a control processing unit [15]. Voltage drivers are developed based on the operational amplifiers from the Apex Microtechnology [16], and the position measuring is established based on the incremental encoders from NANOS Instruments GmbH [17].

Developed voltage drivers have two parts, i.e. signal electronics and power electronics parts.

The signal electronics part is designed to filter the reference pulse width modulated (PWM) signal to the corresponding voltage within ±10 V. The

Improved Micropositioning of 2 DOF Stage by Using the Neural Network Compensation of Plant Nonlinearities

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power electronic part is designed to amplify the voltage within ±10 V to driving voltage by differential pairing of operational amplifiers. Two operational amplifiers with part number PA-78 from Apex Microtechnology are configured in a bridge circuit [18]. In this configuration, the operational amplifiers supply an output-voltage swing twice that of a single operational amplifier.

The system for measuring the actual position of PAS with submicron resolution is based on the linear incremental encoders. The linear encoder works on a magnetic principle with a resolution of 0.061 μm. Two magnetic scales are fixed on the PAS perpendicularly, while two belonging encoder sensors are fixed on the base.

The vertical distance between the magnetic scales and the encoder sensors is less than 0.1 mm. The magnetic scale moves under the encoder sensor without any mechanical contact. Each pair of sensor and magnetic scale is used to measure one DOF. The photo of PAS with incremental encoders is shown in Fig. 3.

unit. The communication with the host computer is established through the Ethernet port with the TCP/IP server-client communication protocol.

The user can manipulate with the PAS through the user interface application which runs on the host computer. The actual user interface application is adopted to measure the control performance with the proposed controllers. The user interface can be simply adopted for other micropositioning or micromachining applications like the microscopy image acquiring.

2 DESCRIPTION OF NONLINEAR PLANT The PWM duty cycle-displacement characteristic of the PAS is mainly affected by the highly nonlinear hysteresis effect of piezoelectric material. The developed close-loop control system was used for measuring the nonlinear positioning behaviour of PAS. Fig. 4 shows 6 successive point-to-point (PTP) movements, i.e. the movement trajectories for X DOF with respect to the PWM duty cycle.

Fig. 3. PEA with linear incremental encoders The CVS is equipped with 15 digital input lines and with 14 digital output lines. Two PWM output signals with frequency 100 kHz are generated for two voltage drivers. On the other hand, two pairs of encoder signals are used to sample the position of PAS. The maximal sampling frequency of input signals equals 100 kHz. According to this, the maximum detected speed of PAS in one direction is 6.1 mms-1.

In order to make the system for micropositioning robust and autonomous, the CVS is configured as a stand-alone processing

602

Fig. 4. Graph of PWM duty cycle vs. displacement (X DOF) The above experiment shows that the PAS displacement mainly depends on the PWM duty cycle (driving value) and on the history of motion. In order to describe and evaluate the history of motion, the definition of extreme points, i.e. position turning values, is introduced.

The turning values are classified into two categories, i.e. as upper turning values ( X TU or

Čas, J. - Škorc, G. - Šafarič, R.

Strojniški vestnik - Journal of Mechanical Engineering 56(2010)10, 599-608

YTU ) and lower turning values ( X TL or YTL ).

Turning values indirectly describe the level of saturation of PEAs, which depends on the strength of the applied electrical field. Physically it is presented as friction between the moving crystals in the piezo material structure.

The hysteresis effect renders impossible to precisely set the desired position of PAS without using an appropriate position controller. This is also proved with the experiment (Fig. 4), by which it is clearly seen that the actual position of 15 μm, is achieved with different driving values of PWM duty cycle, i.e. 0.79, 0.55 and 0.65.

The simple linear feedforward controller (LFFC) is used in the following experiments as a part of NN training configuration which is described in the section below (Fig. 6). At the beginning of the LFFC design, the size of the PAS workspace is defined with four boundary pairs, i.e. the lower and the upper boundary of workspace for X DOF and the lower and the upper boundary of workspace for Y DOF. For each of these four boundary pairs, the corresponding driving value (PWM duty cycle) is measured. Accordingly, four boundary pairs are

 





16 μm). In the second case (the movement from 16 to 2 μm), the actual position is equal to 13.8 μm. However, the LFFC is primarily not designed for accurate position control of the PAS, but it is used to train the proposed NN with BPG algorithm. After the training, the NN are used to generate the appropriate output to minimize the position error of PAS. According to this, the PWM duty cycles for driving PAS are defined as follows: PWM X  LFFC X  NN X

,

(3)

PWM Y  LFFC Y  NN Y

,

(4)

X

Y

where PWM and PWM are the driving X values, LFFC and LFFC Y are the outputs from the LFFC and NN X and NN Y are the outputs from the NN for both DOF. Based on NN inputs, the trained NN are capable to generate the appropriate driving values ( NN X and NN Y ). In other words, the NN are capable of estimating and compensating the nonlinear behaviour of PAS.



X X X X X X defined as Pmin bmin , dvmin , Pmax bmax , dvmax , Y Pmin



Y Y bmin , dvmin

and

Y Pmax



Y Y bmax , dvmax

 , where

b is a boundary and dv is a driving value. The boundary pairs are used as the parameters of LFFC, which is defined as: X LFFC X  dvmin 

Y LFFC Y  dvmin 

X X dvmax  dvmin X X bmax  bmin Y Y dvmax  dvmin Y Y bmax  bmin

 X ref

,

(1)

 Yref

.

(2)

Eqs. (1) and (2) define the LFFC output as a straight line through two points (boundary pairs). The LFFC cannot guarantee the appropriate position control for most reference positions on the workspace (Fig. 5).

When the reference position is selected at 10 μm, for example, the LFFC output (driving value) is equal to 0.59. Considering the first ‘1’ and the second trajectory ‘2’ on the graph, the required driving values to reach this reference position are equal to 0.75 and 0.48, separately.

When the LFFC is used, the actual position in the first case equals 6.4 μm (the movement from 2 to

Fig. 5. The output of LFFC with nonlinear characteristic of PAS 3 NN TRAINING OF INVERSE MODEL OF PLANT NONLINEARITIES Any function can be arbitrarily closely approximated by NN that has enough neurons, at least one hidden layer, and an appropriate set of weights [19]. The general modelling capability of NN is a very attractive property for nonlinear approximation problems. Our approach is to

Improved Micropositioning of 2 DOF Stage by Using the Neural Network Compensation of Plant Nonlinearities

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Strojniški vestnik - Journal of Mechanical Engineering 56(2010)10, 599-608

globally linearize the behaviour of the PAS, by training the NN to compensate the hysteresis.

In regards to the observations from the previous section, the plant nonlinearities are mainly dependent on two values, i.e. the reference position value and turning value. Therefore, the input layer of the NN must be defined as: NN In 

where

n X REF



n n X REF , YREF , X Tn , YTn

and

n YREF



T

,

(5)

are normalized reference

X Tn

and YTn are normalized position values and turning values of PAS. According to the experiments with the PAS, the accuracy and the speed of the inverse nonlinearities estimation is more effective with 2 NN (Fig. 7). Due to its special mechanical construction with parallel movement, the axes of PAS are not coupled.

Therefore, the estimation of inverse nonlinearities with two NN is possible. In order to use two NN, Eq. (5) is modified to Eqs. (6) and (7), which describe the NN input layer:

  Y

, .

n NN In  X REF , X Tn

NN In

n n REF , YT

T

(6)

T



 netJ  j 

,

(8)

2

netJ ( j ) 

  w J ij  NNIn i  ; j  1  n ,

(9)

i 1

where w J ij is the matrix of weights in the hidden layer and n is the number of nodes in the hidden layer. The activation function of the node in the output layer (SO) is the linear function, which is defined as: SO  netL  l    0.1  netL  l  , (10) n

netL(l ) 

  wL jl  SH  netJ  j   ,

(11)

j 1

where w L jl is the matrix of weights in the output layer and r is the number of nodes in the output layer, and it is equal to 1.

604

Δw Lp jl    SO  netL  l    e  S H  netJ  j   ,

(12)

where Δw Lp jl is the matrix of weight’s variations of the output layer and  is the learning rate value. The error (e) is a measurement of how far away a particular solution (output of NN) is from a desired solution. Furthermore, the variations of the weights in the hidden layer are defined as: Δw p    S  netJ  j    NN  H

J ij

In i

n



  e  SO  netL l    wL jl ,

(13)

j 1

Δw Jp ij

where

is the matrix of the weight’s

variations of the hidden layer. At the end of each iteration step (p) the weight matrixes are updated as:

(7)

According to [19], two equal NN with three layers of neurons are proposed. The activation function of nodes in the hidden layer (SH) is a widely used sigmoid function, which is defined as: S H  netJ  j    1/ 1  e

For an estimation of the inverse nonlinearities of the controlled object (PAS), the BPG [20] is used as a training algorithm of NN. The BPG algorithm is summarized as:

w Lp jl1  Δw Lp jl  w Lp jl ,

(14)

w Jpij1  Δw Jpij  w Jpij .

(15)

The updated weight matrixes are used in the following iteration step (p+1).

The BPG is a supervised training algorithm of NN. In the supervised training, the actual output of NN is compared with the target output, which is provided by the external teacher (supervisor). Depending on those two values, the error is defined and back-propagated in order to decrease it in every iteration step of the training process.

However, in our application we use a gradually different procedure of training with BPG algorithm. The error is not defined as the difference between the target output and the actual output of NN, but it is measured on-line, based on the step response of LFFC (Fig. 6).

According to the proposed training configuration, the errors are defined as: n n (16) e X  X REF  X ACT for 1st NN and n n e Y  YREF  YACT for 2nd NN.

Čas, J. - Škorc, G. - Šafarič, R.

(17)

Strojniški vestnik - Journal of Mechanical Engineering 56(2010)10, 599-608

Fig. 7. Measurement of SSE

Fig. 6. The NN training configuration The errors are defined as the difference between the reference position value and the actual position value of the PAS for each DOF. The NN training is executed by using the train data set, which consists of randomly distributed train data pairs defined as



n n T X X REF , X TV







n n and TY YREF , YTV . During

the training, train data pairs are randomly selected from the train data set and the BPG is repeated on the selected train data pair. After a 100 repetitions of the BPG training algorithm, the new train data pair is selected and the BPG training procedure is repeated.

The learning ability of NN is measured with the sum square error (SSE), which is defined by the following equation: SSE X 

500

   X

n REF

n  X ACT

n REF

n  YACT

i 1

SSE Y 

500

  Y i 1





2

2

 , 

 , 

(18)

(19)

where i is the number of measurement. Due to the maximum number of measurements (500), it is evident that the SSE is summed-up for every five successive train data pairs from the train data set.

Fig. 7 shows three different measurements of SSE. The lower two lines show the measurements of SSEX and SSEY separately. The upper line shows the measurement of SSE1NN when only one NN with 4 inputs and 2 outputs is used for the estimation of plant nonlinearities. According to SSE measurements, we decided to use two NN for hysteresis compensation (each for one DOF).

According to the SSE measurements, the NN are unable to completely approximate the inverse nonlinearities of PAS. The SSE values are more than zero after 60 seconds of the approximation process, and they do not decrease significantly after this time period. However, at SSE decreased to some minimal value, we manually stop the learning and save the trained weights of NN into a folder on a disc.

4 FEEDBACK POSITION CONTROL Since LFFC, combined with the NN compensation, is not able to completely remove the control error of PAS, the LFFC is replaced with a feedback PI controller. A PI and PID controller, respectively, are robust control techniques widely used in the industrial applications. PID controller involves three separate parts, i.e. the proportional part (P) determines the reaction to the current error, the integral part (I) determines the reaction based on the sum of recent errors, and the derivative part (D) determines the reaction based on the rate at which the error has been changing.

In the proposed control application, the derivative gain value is eliminated because it does not have a significant influence on control performance. The optimal proportional gain value (KP) and the integral time value (Ti) must be determined to assure the optimal control performance of the selected PI controller.

The Ziegler-Nichols closed loop tuning method [9] is a proven heuristic method for online tuning of P, PI and PID controllers.

However, by involving the constant parameters (KP and Ti), the control performance of linear PI

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controller cannot be equal (optimal) over the whole workspace of PAS. In order to avoid this restriction, the PI controller is combined with the NN compensation of plant nonlinearities (Fig. 8).

significant for micropositioning micropositioning device.

with

any

Fig. 8. Feedback control scheme By using the Ziegler-Nichols tuning method, the approximate parameters of the PI controller were first calculated. Furthermore, the parameters of the PI controller and the PI controller with NN compensation were manually tuned on-line by using the step responses with reference positions 5 and 10 μm.

Fig. 10. PTP response of the controlled system with PI controller and PI controller with NN compensation (Y DOF) The PTP responses with PI controller at 1.5 and at 2.5 seconds are almost ideal, but the PTP responses at 0.5 seconds and at 1.0 seconds exhibit large overshoots (Fig. 9). When PI controller is used, the overshoot is also obtained in the Fig. 10.

When the PI controller with NN compensation is used, the PTP response of the controlled system is equal (without overshoot) for all reference positions on the workspace.

Therefore, the NN compensation of plant nonlinearities improves the step response of the controlled system with PI controller.

Fig. 9. PTP response of the controlled system with PI controller and PI controller with NN compensation (X DOF) The following experiments show the PTP responses of the controlled system with PI controller and PTP responses of PI controller with NN compensation for arbitrary reference positions on the workspace for X DOF (Fig. 9) and for Y DOF (Fig. 10). The aim of experiments is to provide the PTP responses without an overshoot over the whole workspace, as this is 606

Fig. 11. TT with PI controller and with PI controller with NN compensation (X DOF)

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Figs. 11 and 12 show the trajectory tracking (TT) errors of the system with the PI controller and the PI controller with NN compensation. The reference position is described as a circular movement with a radius of 7.5 μm and circular frequency 2 Hz.

hysteresis model with the mathematical functions is complicated to model thus, the NN are used.

The experiments in section 4 show the control results of the linear PI and PI controller with the NN hysteresis compensation. It is evident that the additional NN compensation of plant nonlinearities improves the control performance of linear PI controller.

6 REFERENCES [1]

[2]

[3] Fig. 12. TT with PI controller and with PI controller with NN compensation (Y DOF) The experiments show that maximum error decreases by 20 % when NN compensation is included into the control scheme.

The presented results show that the proposed NN compensation of hysteresis improves the control performance of the traditional PI controller. The experiments have shown that the control performance of linear PI controller is more stable over the whole workspace of PAS.

[4]

[5]

[6]

5 CONCLUSION The first part of the presented research focuses on the development of the system for close-loop micropositioning. The presented observations may provide readers with some useful information when designing their own micropositioning systems. Furthermore, the development of an appropriate position controller of PAS is described. The experiments in section 2 clearly show that PAS displacement is a nonlinear function of driving values (PWM duty cycle) and position turning values. The proposed method focuses on the development of the inverse model of hysteresis, which is used as a feedforward part of the proposed controller. However, the inverse

[7]

[8]

[9]

Yang, R., Jouaneh, Z., Schweizer R. (1996).

Design and characterization of a low-profile micropositioning stage.

Precision Engineering, vol. 18, p. 20-29.

Yao, O., Dong, J., Ferreira, P. (2007).

Design, analysis, fabrication and testing of a parallel-kinematic micropositioning XY stage. International Journal of Machine Tools and Manufacture, vol. 47, no. 6, p.

946-961.

Comstock, R.H. (1981). Charge control of piezoelectric actuators to reduce hysteresis effects, U.S. Patent num.: 4,263,527.

Ronkanen, P., Kallio, P., Koivo, H. (2002).

Current Control of Piezoelectric Actuators with Power Loss Compensation. IEEE/RSJ International Conference on Intelligent Robots and System, Lousanne.

Chonan, S., Jiang, Z., Yamamoto, T. (1996).

Nonlinear hysteresis compensation of piezoelectric ceramic actuators. Journal of Intelligent Material Systems and Structures, vol. 7, no. 2, p. 150-156.

Ru, C-H., Sun, L., Kong, M. (2005).

Adaptive inverse control for piezoelectric actuator based on hysteresis model. Proc. of 4th Int. Conf. on Machine Learning and Cybernetics, Guangzhou.

Weibel, F., Michellod, Y., Mullhaupt, P., Gillet, D. (2008). Real-time compensation of hysteresis in a piezoelectric-stack actuator tracking a stochastic reference.

American Control Conference, Washington.

Krejci, P., Kuhnen, K. (2001). Inverse control of systems with hysteresis and creep. IEE Proceedings - Control Theory Applications, vol. 148, no. 3, p. 185-192.

Zigler, J.G., Nichols, N.B. (1942). Optimum settings for automatic controllers. American Society of Mechanical Engineer, p. 759-768.

Improved Micropositioning of 2 DOF Stage by Using the Neural Network Compensation of Plant Nonlinearities

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[10]

[11]

[12]

[13]

[14]

608

Ge, P., Jouaneh, M. (1996). Tracking control of a piezoceramic actuator. IEEE Transactions on Control Systems Technology, vol. 4, no. 3, p. 209-216.

Ku, S.-S., Pinsopon, U., Cetinkunt, S., Nakajima, S. (2000). Design, fabrication, and real-time neural network control of a three-degrees-of-freedom nanopositioner.

IEEE/ASME Transactions on Mechatronics, vol. 5, no. 3, p. 273-280. Čas, J., Škorc, G., Šafarič, R. Neural network position control of XY piezo actuator stage by visual feedback. Neural Computing and Applications, vol. 19, no. 7, p. 1043-1055.

Keoschkerjan, R., Qiao, F., Wurmus, H. (2000). Piezoelectric XY-Micropositioner made of photosensitive glass to form one micro-handling unit. Proceedings of 7th International Conference on New Actuators, Bremen.

Keoschkerjan, R., Wurmus, H. (2002). A novel microgripper with parallel movement of gripping arms. Proceedings of 8th

[15] [16] [17] [18] [19]

[20]

International Conference on New Actuators, Bremen.

NI CVS-1450 Series User Manual. From http://www.graftek.com/pdf/Brochures/Nation alInstruments/cvsmanual.pdf Power Operational Amplifiers (PA-78). From http://www.cirrus.com/en/pubs/proDatasheet/ PA78U_B.pdf Linear Encoders. From http://www.nanosinstruments.de/nanosweb/media/pdf/Encoder _engl_v4.pdf PA78 Design Ideas.

From http://www.cirrus.com/en/pubs/appNote/AN _PA78_Design_Ideas.pdf Hornik, K., Stinchombe, M., White H. (1989). Multilayer feedforward networks are universal approximator. Neural Networks, vol. 2, p. 359-366.

Hecht-Nielsen, R. (1989). Theory of backpropagation neural network. Proc. of Int. Joint Conf. on Neural Networks, Washinghton DC.

Čas, J. - Škorc, G. - Šafarič, R.

Strojniški vestnik - Journal of Mechanical Engineering 56(2010)10, 609-618 UDC 669.14:539.4

Paper received: 19.03.2010 Paper accepted: 15.07.2010

A Numerical and Experimental Study on Buckling of Cylindrical Panels Subjected to Compressive Axial Load Mahmoud Shariati - Mehdi Sedighi* - Jafar Saemi –Hamid Reza Allahbakhsh Shahroud University of Technology, Iran In this paper, the effects of the length, sector angle and different boundary conditions on the buckling load and post buckling behavior of CK20 cylindrical panels have been investigated using experimental and numerical methods. The experimental tests have been performed using the INSTRON 8802 servo hydraulic machine and for numerical analysis. Abaqus finite element package has been used.

The numerical results are in good agreement with the experimental tests. ©2010 Journal of Mechanical Engineering. All rights reserved.

Keywords: cylindrical panels, elastic and plastic behavior, buckling analysis, CK20 steel 1 INTRODUCTION Shell structures have been widely used in pipelines, aerospace and marine structures, large dams, shell roofs, liquid-retaining structures and cooling towers [1]. Buckling is one of the main failure considerations when designing these structures [2]. At first, researchers focused on the determination of the buckling load in the linear elastic zone, but experimental studies [3] and [4] showed that the buckling capacity of thin cylindrical shells is much lower than the amount determined in the classic theories [5]. Thin cylindrical panels are used in different structures.

When the stress distribution in this structure is compressive, the structure will collapse usually before yielding or the buckling phenomena determines its loading capacity due to the large value of radius to thickness ratio. This subject is usually studied using the numerical methods based on the finite element (FE) and analytical methods in elastic region. The exact solution for isotropic and anisotropic panels has been presented by Timoshenko [6] and Lekhnitskii [7].

El-Raheb [8] investigated the stability of simply supported panels subjected to uniform external pressure. Magnucki et al. [9] solved the Donnell's equation for the buckling of panels with three edges simply supported and one edge free subjected the axial load using the Galerkin method. Patel et al. [10] discussed on static and dynamic stability of panels with edge harmonic loading. Buermann et al. [11] presented a semianalytical model for the post-buckling analysis of stiffened cylindrical panels using trigonometric Fourier series as approximated solutions for displacements. Lanzi et al. [12] performed a

multi-objective optimization procedure based on Genetic Algorithms for the design of composite stiffened panels capable of operation in postbuckling. The results without considering any kind of imperfection, are closed and in good agreement with the tests in terms of buckling and post-buckling stiffness, as well as in terms of collapse loads. Jiang et al. [13] studied the buckling of panels subjected to compressive stress using the differential quardrature element method. Keweon [14] and [15] carried out numerical and experimental studies for the postbuckling of axially loaded cylindrical panel with curved edges clamped and with straight edges simply supported. Bisagni et al. [16] presented an analytical formulation for the study of linearized local skin buckling load and nonlinear post-buckling behavior of isotropic and composite stiffened panels subjected to axial compression. The results are compared with the FE analysis.

In this paper, numerical and experimental studies have been performed on cylindrical panels for determining the bulking load and investigating the post-bulking behavior of the panels. For a numerical analysis Abaqus FE package has been used to study the effects of the length, sector angle, thickness and different boundary conditions and the experimental tests have been applied on the panels using a servo-hydraulic machine. The experimental results are in good agreement with the experimental one.

1 PANELS GEOMETRY Fig. 1 shows the schematic of a cylindrical panel. The mechanical properties of steel panels

*

Corr. Author's Address: Shahroud University of Technology, Shahrood, I.R. IRAN, msedighi47@gmail.com

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have been determined using the tensile test. The steel grade is CK20. For this purpose, some standard test specimens have been prepared from the original tubes according to ASTM E8 standard [10] and the tensile test was performed using the INSTRON 8802 tensile test machine.

Fig. 2 shows the stress-strain diagram for the material of a specimen. The Poisson's ratio was assumed to be 0.33. The geometrical and mechanical properties of panels have been listed in Table 1.

2 BOUNDARY CONDITIONS For applying boundary conditions on the edges of the cylindrical panel, two rigid plates that were attached to the ends of the cylindrical panel were used. In order to analyze the buckling subject to axial load similar to what was done in the experiments; a 15 mm displacement was applied centrally to the center of the upper plate, which resulted in a distributed, compressive load on both edges of the cylindrical panel.

Additionally, all degrees of freedom in the lower plate and all degrees of freedom in the upper plate, except in the direction of longitudinal axis, were constrained. In the section on experimental results, it will be shown that the fulcrum used in these tests has an edge that is 18.1 mm high (Fig. 3). For this reason, in numerical simulations, the edges of the shell are constrained to this elevation except in the direction of cylinder axis.

Fig. 1. Schematic of a cylindrical panel

Stress [MPa]

500

a

400 300 200

3 NUMERICAL ANALYSIS

100 0 0

0.02

0.04 0.06 Strain [mm/mm]

0.08

Fig. 2. Stress-strain diagram Table 1. Mechanical and geometrical properties of cylindrical panels Diameter D = 42 mm Thickness T = 2 mm Θ = 90°, 120°, 180°, 355°, Sector angle Complete Length L = 100, 150, 250 mm Yield stress σy = 340 [MPa] Elasticity E = 192 [GPa] modulus

610

b

Fig. 3. Fixtures for experimental test: a) simply support, b) clamped

The numerical analysis has been performed with Abaqus FE package. For this analysis, the nonlinear element S8R5, which is an eight-node element with six degrees of freedom per node, suitable for analysis of thin shells, and the linear element S4R, which is a four-node element were used [18]. Part of a meshed specimen is shown in Fig. 4. Both linear and nonlinear elements were used for the analysis of the shells, and the results were compared.

The boundary conditions have been considered clamped or simple at arc edges and free at straight edges. Eigenvalue analysis overestimates the value of buckling load, because in this analysis the plastic properties of a material do not play any role in the analyses procedure.

For buckling analysis, an eigenvalue analysis

Shariati, M. – Sedighi, M. – Saemi, J. –Allahbakhshy, H.R.

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4 EXPERIMENTAL ANALYSIS Some specimens with characteristics listed in Table 1 were prepared and the compression test was applied using a servo-hydraulic machine on panels. At first, for investigating the reliability of system for repeating the tests, three similar panels with L = 100 mm and , θ = 120○ were tested. Fig. 6 shows the load–displacement diagrams for these panels. It is clear that the results are the same and the machine is reliable so the tests can be repeated.

30

Load [kN]

should be done initially for all specimens to find the mode shapes and corresponding eigenvalues.

Primary modes have smaller eigenvalues and buckling usually occurs in these mode shapes. For the eigenvalues analysis the ‘‘Buckle’’ step was used in software. Three initial mode shapes and corresponding displacements of all specimens were obtained. The effects of these mode shapes must be considered in nonlinear buckling analysis (Static Riks step). Otherwise, the software would choose the buckling mode in an arbitrary manner, resulting in unrealistic results in nonlinear analyses. For ‘‘Buckle’’ step, the subspace solver method of the software was used. It is noteworthy that due to the presence of contact constraints between rigid plates and the shell, the Lanczos solver method cannot be used for these specimens [18]. In Fig. 5, two primary mode shapes are shown for the specimen L100-θ90°. After completion of the Buckle analysis, a nonlinear analysis was performed to plot the load– displacement curve. The maximum value in this curve is the buckling load.

20

10

Test 1 Test 2 Test 3

0 0

1

2 Displacement [mm]

3

4

Fig. 6. Load-displacement diagrams for three similar panels with L = 100 mm, θ = 120○

Fig. 4. Mesh pattern for a cylindrical panel

Fig. 7. Experimental test setup Fig. 5. Buckling mode shape for specimen L = 100 mm, θ = 90○: a) first mode, b) second mode, c) third mode This step is called ‘‘Static Riks’’ and uses the arc length method for post-buckling analysis.

In this analysis, nonlinearity of both material properties and geometry is taken into consideration.

For different boundary conditions, the axial load was applied on the panels and the loadaxial displacement diagrams of panels were drawn. In all the tests, the straight edges were free and the arc edges were clamped or simply supported. To produce the clamped and simple boundary conditions, some appropriated fixtures were designed. Fig. 7 shows the test setup.

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5 DISCUSSION OF RESULTS Fig. 8 shows the numerical and experimental load-displacement diagrams for panels with different lengths. The peak values in diagrams stand for the buckling load. Figs. 9 and 10 show the load-displacement diagrams for θ = 90°, 180°.

Fig. 9. Load-displacement diagrams for different lengths (θ = 90°, simply supported): a) numerical analysis, b) experimental test

Fig. 8. Load-displacement diagrams for different lengths (θ = 120°, simply supported): a) numerical analysis, b) experimental test It can be seen that by increasing the length of the panel, the buckling load slightly decreases.

These variations are more for shorter lengths. For longer lengths, the load-displacement diagram for the smallest sector angle i.e. θ = 90° (Fig. 9) tends to Euler’s buckling mode. Fig. 11 shows that by increasing the sector angle, the buckling load increases. When there is a narrow cut (θ = 355°), the buckling load decreases noticeably. The variations of the buckling load in terms of the sector angle are shown in Fig. 12. Its variation is nearly linear and it changes very large for a cylinder. Fig. 13 shows the deformed shape of a panel with a narrow cut.

612

Fig. 10. Load-displacement diagram for different lengths (θ = 180°, simply supported): a) numerical analysis, b) experimental test

Shariati, M. – Sedighi, M. – Saemi, J. –Allahbakhshy, H.R.

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Fig. 11. Buckling load in terms of the length for different sector angles: a) numerical analysis, b) experimental test The load-displacement diagrams and the first buckling modes for different panels are shown in Table 2. The buckling modes are similar and there is a good agreement between the loaddisplacement diagrams in most cases.

Most differences between the diagrams return to the post buckling region and the values for FE results are greater than the test values. This may be due to the approximated definition of the plastic part of the stress-strain diagram and no consideration of the specimens defects in FE model. The FE stress analysis shows that in some cases, the Von-Mises stresses in panels are larger than the yield stress or the panel is not elastic at the buckling load. Fig. 14 shows the Von-Mises stresses of a panel under buckling load.

Fig. 12. Buckling load in terms of the sector angle for different lengths (simply supported): a) numerical analysis, b) experimental test

Fig. 13. Deformed shaped of panel (θ = 355°, L = 150 mm, simply supported): a) experimental, b) numerical

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Table 2. Numerical and experimental load-displacement diagrams and buckling modes for different lengths and sector angles Numerical mode Experimental mode Load–displacement diagrams

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6 EFFECTS OF BOUNDARY CONDITIONS To investigate the effects of different boundary conditions, some tests were performed on the panels with clamped and simple supports.

Table 3 shows the load-displacement diagrams for clamped and simply supported boundary conditions. The results show that in all tests, the clamped boundary conditions can increase the buckling load capacity of the panels. This is because the clamped boundaries can restrict the degrees-of-freedom. The Euler buckling mode has been seen for L = 250 mm and θ = 120° in numerical and experimental results. The values of buckling loads for these boundary conditions are listed in Table 4.

After comparing the curves in Fig. 15, it can be said that in comparison to nonlinear elements, linear elements, have a better prediction power for the post-buckling behavior of mild steel alloy cylindrical shells with elliptical cutouts. In the prebuckling phase, both elements produce similar results.

It can be seen that the slope of load vs. end shortening curves is higher in numerical results than in experimental results before the buckling.

This discrepancy is the result of the presence of internal defects in the material which reduces the stiffness of the specimens in the experimental method, while the materials are assumed to be ideal in the numerical analyses.

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Fig. 14. Von-Mises stress (Pa) distribution in panel due to different loads (simply supported): a) applied load is in elastic region, b and c) applied loads are in post-buckling region 7 CONCLUSIONS

Fig. 15. Comparison of the experimental and numerical result

616

The experimental tests and numerical analysis which were performed on the panels showed that: 1. Increasing the length will slightly decrease the buckling load. This effect is more important for shorter panels.

2. By increasing the sector angle, the buckling load will increase nearly linearly and for a perfect cylinder, it changes more.

3. The existence of a longitudinal narrow slot will decrease the buckling load noticeably.

4. The clamped boundary conditions will increase the capacity of the panel to undergo the load or the buckling load will increase.

Shariati, M. – Sedighi, M. – Saemi, J. –Allahbakhshy, H.R.

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5.

6.

In most of the analysis, there are good agreements between the numerical and experimental results.

The results show that the curves from linear elements predict the post-buckling region

better than nonlinear elements, while the nonlinear elements are a better indicator of the buckling load.

Table 3. Load-displacement diagrams for clamped and simply supported boundary conditions Numerical Experimental

Table 4. Buckling load [kN] for different boundary conditions L = 100 mm L = 150 mm   120  Numerical Experimental Numerical Experimental simply supported 28.23 26.75 27.29 25.55 clamped 32.02 29.56 30.76 26.04 8 ACKNOWLEDGEMENT The authors thank the Manager of the “Mechanical Properties Laboratory” of Shahrood University of Technology for supporting the tests.

L = 250 mm Numerical Experimental

26.37 27.21

24.34 25.58

9 REFERENCES [1] [2]

Farshad, M. (1992). Design and analysis of shell structures, Kluwer, Dordrecht.

Budiansky, B., Hutchinson, J.W. (1972).

Buckling of circular cylindrical shells under axial compression. Contributions to the

Numerical and Experimental Study on Buckling of Cylindrical Panels Subjected to Compressive Axial Load

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[3]

[4]

[5] [6] [7] [8] [9]

[10]

[11]

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theory of aircraft structures. Delft University Press, p. 239-260.

Arbocz, J., Hol, J.M.A.M. (1991). Collapse of axially compressed cylindrical shells with random imperfections. AIAA J., vol.

29, p. 2247-2256.

Jullien, J.F., Limam, A. (1998). Effect of openings on the buckling of cylindrical shells subjected to axial compression. Thin Wall Struct, vol. 31, p. 187-202.

Farshad, M. (1994). Stability of structures.

Elsevier, Amsterdam.

Timoshenko, S.P., Gere, J.M. (1961).

Theory of elastic stability. McGraw-Hill, NewYork.

Lekhnitskii, S.G. (1968). Anisotropic plates. Gordon and Breach, NewYork.

El-Raheb, M. (2006). Response of a thin cylindrical panel with constrained edges. Int J. Solids Structures, vol. 43, p. 7571-7592.

Magnucki, K., Mackiewicz, M. (2006).

Elastic buckling of an axially compressed cylindrical panel with three edges simply supported and one edge free. Thin-Walled Structures, vol. 44, p. 387-392.

Patel, S.N., Datta, P.K., Sheikh, A.H. (2006). Buckling and dynamic instability analysis of stiffened shell panels. ThinWalled Structustures, vol. 44, p. 321-333.

Buermann, P., Rolfes, R., Tessmer, J., Schagerl, M. (2006). A semi-analytical model for local post-buckling analysis of

[12]

[13]

[14]

[15]

[16]

[17] [18]

stringer- and frame-stiffened cylindrical panels. Thin-Walled Structures, vol. 44, p.

102-114.

Lanzi, L., Giavotto, V. (2006). Postbuckling optimization of composite stiffened panels: Computations and experiments. Composite Structures, vol. 73, no. 2, p. 208-220.

Jiang, L., Wang, Y., Wang, X. (2008).

Buckling analysis of stiffened circular cylindrical panels using differential quadrature element method. Thin-Walled Structures, vol. 46, p. 390-398.

Bisagni, C., Vescovini, R. (2009).

Analytical formulation for local buckling and post-buckling analysis of stiffened laminated panels. Thin-Walled Structures, vol. 47, p. 318-334.

Kweon, J.H., Hong, C.S. (1994). An improved arc-length method for postbuckling analysis of composite cylindrical panels. Computers Structs, vol.

53, no. 3, p. 541-549.

Kweon, J.H. (1998). Post-failure analysis of composite cylindrical panels under compression. J. Reinforced Plastics Composites, vol. 17, no. 18, p. 1665-1681.

ASTM A370-05, Standard test methods and definitions for mechanical testing of steel products.

ABAQUS 6.4 PR11 user’s manual.

Shariati, M. – Sedighi, M. – Saemi, J. –Allahbakhshy, H.R.

Strojniški vestnik - Journal of Mechanical Engineering 56(2010)10, 619-624 UDC 544.344.016.2

Paper received: 22.08.2009 Paper accepted: 04.03.2010

Lockin Thermography with Optical or Ultrasound Excitation Andreas Gleiter - Christian Spießberger - Gerd Busse* University of Stuttgart, Institute of Polymer-Technology, Germany Thermography is a well established non-destructive testing (NDT) technique providing images of temperature distributions. If the temperature field on a sample surface is modulated by periodical injection of heat either from outside or inside the sample, the time dependence of the temperature field provides information on thermal features hidden underneath the surface. Using the Fourier-transform, this information is finally compressed into a phase and an amplitude image. Phase images are more robust than amplitude images, because surface features and reflections are effectively suppressed.

With excitation by ultrasound, the heating mechanism is local conversion of elastic energy into heat which occurs preferably due to local friction losses caused e.g. by the relative motion of boundaries in a crack. As intact material and boundaries are suppressed in such an image, it displays defects selectively. The techniques and their applications are illustrated by examples that were obtained on various industry-relevant components. ©2010 Journal of Mechanical Engineering. All rights reserved.

Keywords: optical lockin-thermography, ultrasound lockin-thermography, defect-selective imaging

0 INTRODUCTION Lockin-Thermography is an NDT method with a broad field of applications. It can be used for quality assurance during production processes or for maintenance purposes. Many types of defects are detectable, e.g. bonding seems and rivets, or delaminations of layered materials, connection of inner structure elements or inclusions of impurities.

Maintenance of aerospace structures is a challenge for NDT which requires methods that respond with a high probability of detection (POD) to such high-specific-strength materials and their defects. Conventional NDT like x-ray inspection or ultrasound cannot always satisfy those needs. Some defects are caused by imperfect manufacturing processes, others occur due to in-use damage. Therefore, fast and robust methods for industrial environments and in-field measurements are needed. Lockin-Thermography with phase evaluation complies with those requirements.

0.1 Optically Activated Lockin-Thermography Heat deposition can be done by a pulse (e.g. flash lamps) or by modulation (e.g. halogen lamps, laser). The simplest way of evaluation is to record a temperature image sequence after a pulse and to evaluate just the image of highest contrast.

The disadvantage of this transient method is a

poor signal-to-noise (S/N) ratio and the fact that images are highly affected by reflections and surface features. The lockin-technique solves these problems. Lockin-Thermography with optical excitation is sensitive to thermal boundaries within the sample as the thermal wave propagates into the sample and is reflected back to the surface. An infrared camera records an infrared image sequence of the surface over several excitation periods (Fig. 1).

A Fourier transformation at the frequency of amplitude modulation (“lockin frequency”) analyses this thermography image sequence at each pixel and compresses the information into an amplitude and a phase image. Some early lockinthermography approaches are given in [1] to [3].

The Fourier transformation is equivalent to a narrow band filtering with a corresponding improvement in S/N ratio. Artefacts caused by inhomogeneities of infrared emission coefficient or of power deposition are reduced. Another advantage of Lockin-Thermography is the adjustable depth range given by the thermal diffusion length.

The thermal diffusion length depends on material parameters like thermal conductivity or specific heat capacity but also on the lockin frequency. The depth range can therefore be increased by decreasing the lockin frequency.

The disadvantage of optically activated thermography is that not only defects are visible in the results but also all other thermal features

*

Corr. Author's Address: Gerd Busse, Institute for Polymer Technology, NDE Group (IKT-ZfP), University of Stuttgart, Pfaffenwaldring 32, D-70569 Stuttgart, Germany, gerd.busse@ikt.uni-stuttgart.de

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within the thermal depth range. This reduces the probability of defect detection (POD) in samples with complicated thermal structures like CFRP stringer panels.

superposed temperature pattern hiding defects. In addition to the amplitude modulation, ultrasound frequency modulation can solve this problem [8].

The frequencies causing the standing wave pattern are reduced and a more homogeneous phase image with an improved signal-to-noise ratio is achieved. Another version is burst phase ultrasound thermography which is basically multi-frequency ULT [9] and [10].

It should be mentioned that there are further methods of activating a specimen. For electric conductive materials, eddy current could be used [11] to [14].

Fig. 1. Schematical setup of optically activated Lockin-Thermography

0.2 Ultrasound Activated LockinThermography (ULT) Heat can also be generated at damaged areas directly by ultrasound excitation. The elastic energy is converted into heat in areas of stress concentration and defects like cracks or delaminations [4] and [5]. These heat sources can be detected by an infrared camera even in the presence of complicated intact features.

Ultrasound activated thermography (“ultrasound attenuation mapping”) is a defect selective “dark field” NDT-technique as only defects produce a signal.

The operation principle of ultrasound activated Lockin-Thermography (ULT) is shown in Fig. 2. The elastic excitation waves are amplitude modulated at the lockin frequency which is typically in the range of 0.01 to 1.0 Hz [6] and [7]. This results in periodical heat generation so that the defects are pulsating at the modulation (lockin) frequency and thereby emitting thermal waves.

Ultrasound activated thermography with a fixed carrier frequency close to a resonance frequency of the sample can lead to a strong standing wave pattern which might appear as a

620

Fig. 2. Schematical setup of ultrasound activated Lockin-Thermography

1 APPLICATIONS For thermography measurements it is advantageous to deal with specimen surfaces of high infrared emissivity. Therefore, especially carbon fibre reinforced plastics (CFRP) are suited for thermographic testing methods.

1.1 Maintenance of CFRP Rims In addition to being used in aviation industry, light weight constructions are used in racing cars. The following example is a CFRP rim. Different layer thickness and metal inserts can be investigated. This measurement shows an intact rim (see Fig. 3). At very low lockinfrequencies (here 0.03 Hz) the kernel made of foam becomes visible. Higher lockin-frequencies

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Fig. 3. Phase images at 0.03 and 0.2 Hz; specimen from “Rennteam Uni-Stuttgart” [15]

may reveal near-surface delaminations. Here (at 0.2 Hz) no defect was detected.

1.2 Testing of Turbine Blades

non-destructively with optically excited LockinThermography. OLT is well-suited for this task because the method provides information about heat flow through the walls of the turbine blades which is exactly the property essential for the cooling process. Fig. 4 shows different types of cooling channels within a turbine blade measured with OLT at a lockin frequency of 1 Hz. 1.3 Detection of Stringer Delaminations with OLT

Fig. 4. Cooling channels of a turbine blade, imaged with optically excited LockinThermography (lockin frequency 1 Hz) Modern turbine blades have complexshaped cooling channels, which can be imaged

Stringers are used to improve the stiffness of large CFRP structures like fuselage panels of airplanes. This is why stringer disbonds together with excessive loading could cause a loss of structural integrity. Therefore, a fast and reliable detection of such defects in an early stage is needed.

A stringer reinforced CFRP panel was tested during a cyclic compression test (performed at DLR Braunschweig [16]). One result is shown in Fig. 5. Starting with an intact specimen the stringer delaminations grow slowly after each cycling test. The image was obtained when the panel was mechanically loaded.

Therefore, a high contrast in the OLT measurement is achieved, because the delaminated stringers have lost thermal contact with the skin layer.

Another example is an ultra light aircraft (type: Fascination). The skin of the wing is made

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of glas fibre reinforced plasics (GRFP). OLT was used to monitor the bonding quality of the connection between wing beam and GRFPsurface. Note that the straight lines and the arrows are drawn on the surface.

1.4 Detection of Loose Rivets with ULT Loose rivets, cracks, corrosion, and fatigue are critical defects in aerospace structures. For these kind of problems, ultrasound excited Lockin-Thermography can be a solution. An example is shown in Fig. 7 where a panel made for demonstration purposes is imaged using Lockin-Thermography with access only to the outer surface. With optical excitation the whole hidden structure is imaged regardless of the riveting quality. With ultrasound generation, however, loose rivets cause heating by friction, so they appear selectively as bright areas [17].

1.5 Crack Detection with ULT Another example for applying ULT is shown in Fig. 8. The ULT amplitude image reveals cracks (bright spots) in a defect gearwheel.

Fig. 5. Growing stringer delaminations in cyclic compression testing; phase image of the loaded panel at 0.1 Hz

a)

b)

Fig. 6. Hidden bonded area of an aircraft wing: a) tolerable bonding area, b) poor bonding (phase images at lockin-frequency 0.05 Hz)

a)

b)

Fig. 7. Riveted fuselage panel of A340: a) inspected with OLT, b) ULT [17]

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a)

b)

Fig. 8. a) ULT amplitude image at 0.2 Hz reveals the cracks in a gearwheel, b) photo of the specimen

2 CONCLUSIONS New materials like CFRP and complex structures are a challenge for modern NDT. In many cases these requirements can be met by Lockin-Thermography methods. The excitation can be adapted to the specific application so that defects can be detected in a fast and reliable way.

Using the lock-in method, the signal to noise ratio is enhanced substantially. OLT phase images as well as ULT amplitude images are homogeneous and artefacts like stationary infrared reflections are suppressed effectively. Therefore, the results obtained with these methods are suitable for automated defect evaluation. It should be emphasized that OLT and ULT complement each other since they are based on different physical mechanisms.

[5]

[6]

[7]

[8]

3 REFERENCES [9] [1]

[2]

[3]

[4]

Nordal, P.-E., Kanstad, S.O. (1979).

Photothermal Radiometry. Physica Scripta, vol. 20, p. 659-662.

Busse, G. (1979). Optoacoustic phase angle measurement for probing a metal. Appl.

Phys. Lett., vol. 35, p. 759-760.

Kuo, P. K., Feng, Z. J., Ahmed, T., Favro, L.D., Thomas, R.L., Hartikainen, J. (1988).

Parallel thermal wave imaging using a vector lockin video technique in Photoacoustic and Photothermal Phenomena. Hess, P., Pelzl, J. (eds.), Springer-Verlag, Heidelberg, p. 415-418.

Mignogna, R.B., Green, R.E., Duke, J., Henneke, E.G., Reifsnider, K.L. (1981).

[10]

[11]

[12]

Thermographic investigations of high-power ultrasonic heating in materials. Ultrasonics, vol. 7, p. 159-163.

Staerk, F. (1982).

Temperature measurements on cyclically loaded materials. Werkstofftechnik. Verlag Chemie GmbH, Weinheim, vol. 13, p. 333-338.

Patent DE 42 03 272 C2 (1992). Methods for phase-sensitive imaging of effect-modulated objects. IKP-ZfP. (in German) Rantala, J., Wu, D., Busse, G. (1996).

Amplitude modulated lockin vibrothermography for NDE of polymers and composites. Research in Nondestructive Evaluation, vol. 7, p. 215-218.

Zweschper, T., Dillenz, A., Riegert, G., Scherling, D., Busse, G. (2003). Ultrasound excited thermography using frequency modulated elastic waves. Insight, vol. 45, no.

3, p. 178-182.

Dillenz, A., Zweschper, T., Busse, G. (2000). Elastic wave burst thermography for NDE of subsurface features. Insight, vol. 42 no. 12, p. 815-817.

Gleiter, A., Riegert, G., Zweschper, T., Busse, G. (2006). Advanced ultrasound activated Lockin-Thermography for defect selective depth resolved imaging. Proc.

Thermosense, XXVIII, vol. 6205, SPIE, Bellingham.

Bamberg, J., Erbeck, G., Zenzinger, G. (1999). EddyTherm: An imaging Technique for Crack-detection of metallic components.

ZfP-Zeitung, vol. 68, p. 60-62. (in German) Oswald-Tranta, B. (2004). Thermoinductive investigations of magnetic materials for

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[13] [14]

[15] [16]

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surface cracks. QIRT Journal, vol. I, no. 1, p.

33-46.

Riegert, G., Zweschper, T., Busse, G. (2004). QIRT Journal, vol. I, no. 1, p. 21-31.

Riegert, G., Gleiter, A., Busse, G. (2006).

Potential and Limitations of Eddy Current Lockin-Thermography. Proc. Thermosense XXVIII, vol. 6205, SPIE, Bellingham. http://www.rennteam-stuttgart.de/ R. Degenhardt, A. Kling, W. Hillger, H.C. Goetting, R. Zimmermann, K. Rohwer, A. Gleiter (2007). Experiments on Buckling and

[17]

Postbuckling of Thin-Walled CFRP Structures using Advanced Measurement Systems. International Journal of Structural Stability and Dynamics, vol. 7, no. 2, p. 337358.

Riegert, G., Zweschper, T., Dillenz, A., Busse, G. (2002). Inspection of rivets and cracks in metal using thermography methods.

Quantitative Infrared Thermography, Lodart S.A.: Akademickie Centrum Graficzno, vol. 6, p. 293-298.

Gleiter, A. – Spießberger, C. – Busse, G.

Strojniški vestnik - Journal of Mechanical Engineering 56(2010)10, 625-636 UDC 539.61

Paper received: 20.08.2009 Paper accepted: 19.07.2010

Strength and Fracture Strain of Resin/filler Systems Using Two Models (1) of Perfect and (2) of Low Adhesion Quality George Bourkas, Emilios Sideridis, Christos Younis, Ioannis N. Prassianakis*, Victor Kitopoulos Faculty of Applied Mathematical and Physical Sciences, Department of Mechanics, Laboratory of Testing and Materials, National Technical University of Athens – Zografou Campus, Greece The tensile strength and the fracture strain of particulate composites have been evaluated for the case that adhesion exists between the matrix and filler. Two models, each of three components on the basis of cube-within-cube formation, have been used as representative volume elements. By comparing the derived theoretical results of the strength with experimental data for treated and untreated particles in resin/filler systems, the first model can be characterised as corresponding to perfect adhesion quality between the matrix and filler, while the second one to low adhesion quality. The strength predicted by the first model is close to that of treated particles corresponding to high strength. This model corresponds to an upper bound of the strength in cube-within-cube models. The strength predicted by the second model is close to that of untreated particles corresponding to low strength, but this model does not correspond to a lower bound of strength. The systems used for comparison were resin/glass, resin/iron and resin/SiC particulate composites. For the case that adhesion exists between the matrix and filler, the strengths and fracture strains predicted by the present models are in agreement to those provided by an existing evaluation method in the literature. ©2010 Journal of Mechanical Engineering. All rights reserved.

Keywords: resin/filler systems, microstructure, fracture strain, perfect adhesion quality, low adhesion quality 0 INTRODUCTION As pointed out by Nielsen [1], when there is no adhesion between matrix and filler, the tensile strength of particulate composites depends on the tensile strength of the matrix, the filler volume fraction and the stress concentration factor. When adhesion between the matrix and filler exists, the tensile strength depends on the fracture deformation and the elastic modulus of the composite. Consequently, in this latter case the tensile strength results from a complex interplay between the properties of the individual constituent phases; the resin, the filler and the interface [2].

In general, when adhesion exists between the matrix and filler, the mechanical properties of the composite are affected by a number of parameters; the size, the shape, the aspect ratio (ratio of the length to the side of the base), the distribution of the reinforcing particles, the interaction between the inclusions and the agglomerations of fillers. In the case of nonspherical inclusions the orientations of the

fillers with respect to the applied stress are also essential [2]. Some significant parameters also play an important role upon the tensile strength; the quality of adhesion between the matrix and filler, air bubbles in the matrix, the stress concentration factor, the plastic behavior of the matrix near the filler and the crack pinning effect (that is when the crack propagation is embedded by a group of particles) [2] and [3].

In [4] and [5], tensile experiments in particulate composites prepared by treated and untreated particles, have shown that the adhesion quality between the matrix and filler considerably affects the strength behavior of the composites.

The kind of adhesion also affects the values of the stress intensity factor [3] and [6].

In this study the tensile strength and the fracture strain of particulate composites are evaluated using two cube-within-cube models, each one consisting of three components. One of these models [7] gives a constant strength of the composite, independent of the filler content, which is equal to the strength of the matrix. Thus, this model is characterized as corresponding to

* Corr. Author's Address: Faculty of Applied Mathematical and Physical Sciences, Depart. of Mechanics, 625 National Tech. University of Athens – Zografou Campus, GR – 15773, Athens, Greece, prasian@central.ntua.gr

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perfect adhesion quality between the matrix and filler. In the other model [8] the strength decreases as the filler content increases up to 20%, attains a minimum and then increases steadily with a slow rate. A comparison to experimental results [4] and [5] shows that this model corresponds to low adhesion quality between the matrix and filler. The strength and fracture strain predicted by the above models are in agreement with the theory of Nielsen [1] for the case when adhesion exists between the matrix and filler. The theoretical results derived by the presented models are compared to the values of the strength predicted by existing equations in the literature and to experimental results in resin/glass particulate composites. A comparison of the theoretical values of strength and fracture strain is also made with experimental results in resin/iron and resin/SiC particulate composites.

5) Both the matrix and the inclusion are prepared from perfectly homogeneous, elastic and isotropic materials of known mechanical properties.

6) The matrix is brittle and the stress-strain linearity is maintained up to the failure of the composite.

7) There is no transverse variation of the strains in the components which are connected in parallel and have the same length in the load direction.

8) The stresses do not vary in the direction of the applied load in the components which are connected in a series and have the same cross sections.

1 THEORETICAL CONSIDERATIONS The theoretical analysis is based on the following assumptions: 1) The particles are perfectly cubic.

2) The matrix volume distribution of each filler is also cubic.

3) The volume fraction of the particles is sufficiently low, so that there is no interaction between the stress fields around the neighboring particles.

4) The particles are uniformly distributed in the matrix, so that homogeneity can be assumed.

Fig. 1. A schematic representation of the cubewithin-cube model

Fig. 2. The two cube-within-cube models each consisting of three components, a) Paul’s model [7], b) Ishai-Cohen’s model [8]

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As shown in Fig. 1 the filler volume fraction is given by:

uf  a

3

c

3

2

.

(1)

The components (1) and (2) of the model presented in Fig. 2a, called model 1, are connected in parallel and the resulting element is connected in a series with a component (3).

When an external force acts in the direction shown in Fig. 2a the stress equilibrium and strain compatibility equations are:

3 c , 2

(2) 2

 c   1u f 3   2 (1  u f 3 ) ,

(3)

1   2 ,

(4)

1

1

 c   1u f 3   3 (1  u f 3 ) ,

(5)

where the indexes 1, 2 and 3 correspond to the components (1), (2), (3) and the composite respectively. The constitutive equations are:

 1   1E f ,

(6)

 2   2Em ,

(7)

 3   3E m ,

(8)

 c   cEc ,

(9)

where the indexes correspond to the matrix and the filler respectively.

Combining Eqs. (2) to (9) one obtains:

1   3   c   2 .

(10)

Assuming that failure in the component (3) corresponds to failure of the whole composite, the strength of the whole composite is given by:

 cu   mu ,

(11)

where the index denotes strength.

Eqs. (2) to (9) give:    1 1  ,  cu   mu 1  u f 3 1  (12) 2   (m  1)u 3  1  f    where the index u denotes fracture deformation and m 

Ef

Em

(3). When a load acts in the direction shown in Fig. 2b the governing stress-strain equations are:

.

On the other hand, in the model presented in Fig. 2b, called model 2, the components (1) and (2) are connected in a series and the resulting element is connected in parallel with component

2

 c   1u f 3   3 (1  u f 3 ) ,

(13)

1   2 ,

(14)

3  c ,

(15)

1

1

 c   1u f 3   2 (1  u f 3 ) .

(16)

The constitutive relations are given by Eqs. (6) to (9). Combining Eqs. (6) to (9) with Eqs. (13) to (16) it follows that:

1   2   c   3 .

(17)

Assuming that failure of the composite coincides with failure of the component (2), Eqs. (6) to (9) and (13) to (16) give 1 m  1   cu   mu 1  (u f 3  u f ) (18) m   and  m  1 13  ,  cu   mu 1  uf  (19) m   E where m  f E . m Alternatively, in both models (1) and (2) strength can also be given by the relation:

 cu   cu E c ,

(20)

where the elastic modulus derived by model (1) is given [7] by:   1  (m  1) u 2 3 f ,  Ec  E m  (21) 2 3  1  ( m  1) (u  u )  f f   while the elastic modulus derived by model (2) is given [8] by:     uf .

E c  E m 1  (22) 1 m   u f 3   m 1   To take into account the effect of the matrix volume distribution of each filler on the values of the fracture constants, the models 3 and 4 are introduced, shown in Figs. 3a and 3b, respectively.

Following a similar procedure to that presented for models 1 and 2, model 3 gives:

 cu   mu ,

Strength and Fracture Strain of Resin/Filler Systems Using Two Models (1) of Perfect and (2) of Low Adhesion Quality

(23)

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a) b) Fig. 3. The two cube-within-prisma parametric models consisting of three components (models 3 and 4 respectively)

 cu

  u 2 3 m - 1   1  f     mu 1  u f 3  2   3   u f n m  1  1 

(24)

and     uf .

E c  E m 1  (25) 2 1    1 uf3 n uf   m 1   Similarly for Model 4 the following is obtained: 1 m  1 ,   cu   mu 1   u f 3 n 1  u f  (26)  m   

 cu   mu

 u 13 (m  1)  f   1   mn  

(27)

and     uf .

E c  E m 1  (28) 1 m   3  u n   f m 1   Using Eqs. (23) to (28) the effect of inhomogeneous distribution of the fillers into the volume of the matrix can be estimated.

2 MATERIALS AND EXPERIMENTAL WORK The first material used in the present work was derived from a basic diglycidyl ether of bisphenol-A resin epoxy matrix with an epoxy

628

equivalent of 185 to 192 m mol/kg, a molecular mass between 370 and 384 and a viscosity of 15 Ns/m2 at 25°C. A curing agent, 8 p.h.r. by weight triethylenetetramine was employed. This material was filled with iron particles of average radius 75 µm. The elastic moduli of the matrix and filler were 3.50 and 210 GPa respectively, their Poisson ratio were 0.35 and 0.29 respectively and the densities were 7800 and 1190 kg/m3 , respectively. The volume fraction was 0, 0.05, 0.1, 0.15, 0.2, 0.25, 0.3, and 0.4.

The second material consisted of an epoxy resin with a viscosity of 10 to 12 Ns/m2 at 25 °C and an epoxy equivalent of 5340 to 5500 m mol/kg and density of 1160 kg/m3. The used hardener was Epilink 177 with an equivalent of ~95 and viscosity between 0.25 and 0.70 Ns/m2 at 25 °C. The rate of mixture with the resin was 50 p.h.r. Also, a plasticizer D.O.P. at a rate of 35 p.h.r. was employed.

A filler SiC particles of an average radius of 46 µm was used. The elastic modulus, the Poisson ratio and the density of the filler were 400 GPa, 0.2 and 3170 kg/m3 , respectively. The elastic modulus and the Poisson ratio of the system matrix-hardener-plasticizer were determined from the experiments as 2.20 and 0.39 GPa, respectively. The volume fraction of this material was 0, 0.05, 0.1, 0.2 and 0.3.

In order to measure ultimate stress, fracture strain and the Elastic modulus of the materials, tensile experiments were carried out with an Instron-type testing machine at room

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temperature. Specimens were tested at a rate of extension of 0.2 mm/sec. The specimens were of dog-bone type with dimensions at a measuring area of 50·10-3×20·10-3×9·10-3 m3 and of total length 150·10-3 m. In order to obtain the stressstrain diagrams for each material, strain gauges (KYOWA type, gauge factor k = 1.99) were located on each specimen to measure the strain.

(33) and (34) (Appendix 1) are also shown. The experimental results come from [4] and [5] of Spanoudakis and Young for the following cases: 1. treated particles with an improvement of the adhesion quality between matrix and filler, 2. untreated particles, and 3. treated particles with a result in a way that there is no adhesion between matrix and filler.

3 RESULTS AND DISCUSSION

Fig. 4. Ratio  cu /  mu (strength of the composite over strength of the matrix) as a function of the volume fraction filler uf 4.5 µm particles:  treated with A187;  untreated;  DC 1107 treated (after Spanoudakis and Young), (a) Nikolais and Narkis, Eq. (34), (b) B. Nielsen, Eq. (33), (c) model 2; (d) model 1 In Figs. 4 and 5 the tensile strength in resin/glass particulate composites versus the filler content is plotted. The strength predicted by Eqs. (18) and (11) corresponds to the curves (c) and (d), respectively. In the same figures the theoretical values of the strength derived by Eqs.

Fig. 5. Ratio  cu /  mu as a function of the volume fraction filler uf 62 µm particles;  treated with A187,  untreated;  DC 1107 treated (after Spanoudakis and Young); (a) Nikolais and Narkis, Eq. (34); (b) B. Nielsen, Eq. (33); (c) model 2; (d) model 1 From Figs. 4 and 5 it is observed that the straight line which corresponds to model 1, curve (d), is close to the experimental results of treated glass particles with an improved adhesion between matrix and filler. The observed discrepancies are owed to the fact that the adhesion in the specimens is not perfect and due to too many parameters which affect the strength and which are referred to in the Introduction. For

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the above reasons Model 1 is characterized as corresponding to perfect adhesion quality between the matrix and filler.

From the above Figs. 4 and 5 it is also observed that the strength derived by Model 2 is close to the experimental curve corresponding to the lower values of untreated particles. Thus, Model 2 corresponds to low adhesion quality between matrix and filler. This model does not consist of a lower bound of the strength because there can be models with the same geometry of the components but with different dimensions that give lower values of the strength. In the case of Model 2 failure of the component (2) causes failure of the whole composite in which the local stress concentration factor is given by: 

m(1  u f 3 )  u f 3

 

m

 3'  k  mu

1

1

  mu

2 uf3     mu .

2 1  u f 3 

(29) The first term in the brackets is the stress in component (3), when failure takes place in component (2). The second term in the brackets is the stress in component (2) which is now transferred to component (3). The above procedure is based on the assumption that the stresses can be transferred to the inclusion through component (2).

From the above expression the values of the stress concentration factor k, for different

values of the filler volume fraction uf in resin/iron particulate composites are given in Table 1.

Table 1. Stress concentration factor k versus filler volume fraction uf uf

0.05

0.10

0.15

0.20

0.25

k

1.26

1.21

1.13

1.05

0.94

The above values of k determine if failure of component (2) causes failure of the whole composite.

In Figs. 6 to 9 the ratio of the strength of the composite to the strength of the matrix is plotted, versus the filler volume fraction in resin/iron composites (Figs. 6 to 8) and in resin/SiC particulate composites (Fig. 9). In the same figures the theoretical results derived from Eqs. (33) and (34) (Appendix 1) and by the models 1 and 2 are also presented. Especially in Figs. 7 and 8, the theoretical curves derived by models 3 and 4 for different values of n, are also depicted. In Figs. 6 to 8 the behavior of the strength can be divided into three ranges. In the first range, of low values of the filler content, it seems that fracture occurs at a finite number of individual inclusions, so that the strength can be related to the quality of the adhesion between the matrix and filler, while the crack pinning effect is not predominant. In the second range it seems that fracture occurs at a finite number of

Fig. 6. Ratio  cu /  mu as a function of the volume fraction uf in resin/iron particulate composites

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Fig. 7. Ratio  cu /  mu as a function of the volume fraction uf in resin/iron particulate composites individual inclusions, and a combination of the quality of the adhesion between the matrix and filler with the crack pinning effect are predominant. In the third range it seems that fracture occurs in agglomerations-clusters. In Figs. 6 and 7 one can observe that inside the second range, the average value of the strength derived by the Models 1 and 2, approximates the experimental results. It seems that the quality of the adhesion between the matrix and filler corresponds to a mean value between the values

of the adhesion qualities which are provided by the Models 1 and 2. This second region is characterized by an equilibrated-constant value of the strength given by the experimental results, which can be interpreted by the presence of adhesion and the crack pinning effect (crack arrest). It can be observed that this equilibratedconstant value of the strength results from Eqs. (11) and (18) and not from Eqs. (33) and (34).

Fig. 8. Ratio  cu /  mu as a function of the volume fraction uf in resin/iron particulate composites

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Fig. 9. Ratio  cu /  mu as a function of the volume fraction uf in resin/SiC particulate composites The values of the experimental points in Fig. 8 are lower compared to the values of the experimental points in Figs. 6 and 7. This can be interpreted with the remark that probably there is an inhomogeneous distribution of the filler in the

Fig. 10. Ratio  cu /  mu as a function of the volume fraction uf in resin/iron particulate composites

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volume of the matrix and the strength can be evaluated using Model 4 with n<1. Actually, Model 4 seems that corresponds to a single quality of the adhesion between matrix and filler, but it gives different values of the strength, depending on n. Thus one can say that this model can be characterized as an idealized model corresponding to different low and intermediate qualities of the adhesion. The local stress concentration factors of Model 4 are given in Appendix 2.

The experimental results shown in Fig. 9 can be interpreted considering an “optimal” combination of the quality of the adhesion between the filler and matrix, and the crack pinning effect since there can be a competing effect between a high adhesion quality and a low effect of the crack arrest, or between an intermediate adhesion quality and a high effect of the crack arrest [13]. It can be seen that in this case the experimental results are close to the theoretical results provided by Models 1 and 3.

From the experimental results shown in Fig. 9 it can be concluded that agglomerations do not exist in the specimens.

Fig. 11. Ratio  cu /  mu as a function of the volume fraction uf in resin/iron particulate composites

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It can be noticed that the theoretical results of the stresses furnished by Eqs. (33) and (34) correspond to the case that when there is no adhesion between the matrix and filler, which implies that stresses are not transferred to the inclusion. The deviation of these theoretical results from those predicted by the presented models can be explained by the fact that in the presented models there is adhesion between the matrix and filler and thus stresses are transferred to the inclusion. This can explain clearly why in the presented models the strength is not a decreasing function of uf as in the case of Eqs. (33) and (34).

In Figs. 10 to 12 the ratio of the fracture strain of the composite to the fracture strain of the matrix is plotted, versus the filler volume fracture in resin/iron composites (Figs. 10 and 11) and in resin/SiC particulate composites (Fig. 12). In the same figures the theoretical results given by Eqs. (A3) and (A4) (Appendix 1) as well as those given by the used models are also presented.

figures it can be verified that the above theoretical results are very close. This can be explained by taking into account the fact that in all those equations it was assumed that there is adhesion between the matrix and filler. In [1] Nielsen mentions that in the case of no adhesion, the fracture strain takes higher values than those provided by Eq. (35). In Figs. 10 and 11 it can be seen that the experimental results are approximated closer by the theoretical results provided by Model (1) than by the results of the other models. The high values of strength in Fig. (10) can be explained by the homogeneous distribution of the filler in the volume of the matrix (Model (4), n>1) and probably by viscoelastic and plastic phenomena taking place in the matrix. As can be easily verified from Eqs. (24) and (27), the fracture strain in Models 3 and 4 is a decreasing function of n (the same holds in the case of strength). In Fig. 12 the theoretical results given by Eqs. (12), (19) and (35) coincide.

This is due to the high value of m  E f / Em . It is remarkable to notice that although Models 1 and 2 correspond to different adhesion qualities as far as the strength is concerned, however both models give almost the same values for the fracture strain. This can be explained by taking into account that the values of the elastic moduli, provided by each of the above models, are different.

The presented procedure for the evaluation of the strength and the fracture strain in both models is in agreement with Nielsen’s theory in which the strength is given by  cu   cu E c , (30) where

Fig. 12. Ratio  cu /  mu as a function of the volume fraction uf in resin/SiC particulate composites In Figs. 10 to 12 the ratio of the fracture strain of the composite to the fracture strain of the matrix is plotted, versus the filler volume fracture in resin/iron composites (Figs. 10 and 11) and in resin/SiC particulate composites (Fig. 12). In the same figures the theoretical results given by Eqs. (35) and (36) (Appendix 1) as well as those given by the used models are also presented. From these

 cu

is given by Eq. (35) (Appendix 1).

Thus, since the predicted strains by the presented models are close to the strains provided by Eqs. (35), (11) and (18), as well as Eqs. (30) and (35) give the same values of the strength respectively.

4 MICROFAILURE EFFECTS In Fig. 9 the curve of the ultimate stress behavior versus the variation of the volume fraction for Epoxy-matrix-SiC particles is shown.

By comparison with Figs. 6 to 8 referring to the case of Fe-particles, an overall shift of the first curve to higher values can be deduced, a fact which means an increasing microcrack-pinningarrest effect on the critical crack propagation in

Strength and Fracture Strain of Resin/Filler Systems Using Two Models (1) of Perfect and (2) of Low Adhesion Quality

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the given composite. In [13] a detailed explanation of such effects by means of an elastic-small scale yielding microfracture-fracture toughness modeling approach, is presented. In [13] it was shown that similar ultimate stress behavior as observed in the above figures, can be explained by taking into consideration the degree of inhomogeneity expressed by some structural parameters such as the particle (inclusion) size as well as the interinclusion spacing. In the light of the mentioned reference it can be argued that the above observed shift may be also attributed to the difference of the SiC particle average size of ~75 µm compared to Fe-particle size of ~150 µm.

Furthermore, from the well-known relation for the fracture toughness K c   f  a 0 taken as a constant material parameter, it is easy to deduce that an increase (decrease) of the defect (inclusion/particle) size a0, can lead to a decrease in the fracture stress σf. Therefore, for the same volume fraction and adhesion strength, the reduced particle size of SiC can also lead to a relative increase in the fracture (ultimate) stress of the composite and in this way to the observed shift to higher values compared to Fe-particle composite. At the same time the mechanism of microcrack-pinning and/or arrest can play a competing role. This means that for the same volume fraction and adhesion strength, the probability for a microcrack to become pinned and/or arrested around a particle is higher for a composite with finer dispersed particles (SiC), where the effective interinclusion spacing is smaller compared to Fe-composite, where the effective interinclusion spacing is greater.

The constant k of Eq. (31) can be determined by this method.

An alternative way to estimate the strength of particulate composites is to use Eqs. (30) and (35) in which the value of the elastic modulus can be measured using ultrasounds.

This study presents two models for the evaluation of the strength which can be used for a comparison to the strength evaluated by ultrasonic measurements.

5 CONCLUSIONS 1.

2.

3.

4.

4 STRENGTH AND ULTRASOUNDS It is known that the strength is related with the hardness predicted by Brinel’s method. The existing relation is:   k  BHN 30 , (31) where BHN is Brinel’s hardness and k is a constant of the material. The index 30 corresponds to the relation: P   30  2 , (32) D where P is the applied load on the specimen and D is the diameter of the penetrator.

It is also known that the hardness can be obtained by means of ultrasonic measurements.

634

5.

6.

The strength evaluated by Model 1 is independent of the filler volume fraction and equal to the strength of the matrix. This value of strength compared to experimental results is found to be close to the strength of treated particles and gives an upper bound of the strength of particulate composites predicted by cube-within-cube models. The model is characterized as corresponding to perfect adhesion quality.

Comparing the strength obtained by Model 2 to experimental results, it is found to be close to the lower values of the strength of untreated particles. Thus, the model is characterized as corresponding to low adhesion quality. The strength derived by Model 2 does not give a lower bound of the strength of particulate composites.

The strength predicted by the presented procedure is in agreement to the strength predicted by Nielsen’s theory when there is adhesion between matrix and filler.

In Model 2, when an initial failure takes place in the matrix, a local stress concentration factor is assumed by means of which the failure in the whole composite is considered.

Although Models 1 and 2 correspond to different adhesion qualities as far as the strength is concerned, however they provide almost the same values of the fracture strain.

When there are not agglomerations, the adhesion quality and the crack pinning effect seem to be predominant in the fracture behavior of the composite. As it arises from Models 3 and 4 and the experimental results, inhomogeneities in the composite influence the values of the strength and the fracture strain.

Bourkas, G. – Sideridis, E. – Younis, C. – Prassianakis, I.N. – Kitopoulos, V.

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6 APPENDIX 1 Equations of the strength used for comparison: 1) Nielsen’s equation (no adhesion) [1] 2

 cu   mu (1  u f 3 )  k ,

As it turns out, the values of the concentration factor, when n < 1, are not too high, if one considers that at a circular hole in an infinite plate the concentration factor is n = 3 [14].

(33)

7 REFERENCES

where k is a stress concentration factor.

[1] 2) Nikolais and Narkis equation (no adhesion) [10] and [11] 2

 cu   mu (1  1,21 u f 3 ) .

(34)

[2]

3) Nielsen’s equation for fracture strain [1] 1

 cu   mu (1  u f 3 ) .

(35) [3]

4) Smith’s equation for fracture strain [12] 1

 cu   mu (1  1.106 u f 3 ) .

(36)

[4]

APPENDIX 2 Values of the Local Stress Concentration Factor in Model 4: 1) In the case of Model 4 failure of the component (2) causes failure of the whole composite in which the local concentration factor K is given by: 1 1 2  m( n  u f 3 )  u f 3 uf3     mn  3  K  mu   mu 2 1  mn 3  n u f   (37) 2) In Model 2 the values of the concentration factor K in epoxy/iron composites are given in the following Table 2, for different values of n and uf.

[5]

[6]

[7]

Nielsen, L.E. (1966). Simple theory of stress-strain properties of filled polymers.

Journal of Applied Polymer Science, vol. 10, p. 97-103.

Ahmed, S., Jones, F.R. (1990). A review of particulate reinforcement theories for polymer composites. Journal of Materials Science, vol. 25, no. 12, p. 4933-4942.

Moloney, A.C., Kausch, H.H., Kaiser, T., Beer, H.R. (1987). Review. Parameters determining the strength and toughness of particulate filled epoxide resins. Journal of Materials Science, vol. 22, p. 381-393.

Spanoudakis, J., Young R.J. (1984). Crack propagation in a glass particle-filled epoxy resin, Part1: Effect of particle volume fraction and size, Journal of Materials Science, vol. 19, p. 473-486.

Spanoudakis, J., Young, R.J. (1984). Crack propagation in a glass particle-filled epoxy resin, Part2: Effect of particle-matrix adhesion, Journal of Materials Science, vol.

19, p. 487-496.

Kinloch, A.J., Maxwell, D.L., Young, R.J. (1985). The fracture of hybrid-particulate composites. Journal of Materials Science, vol. 20, p. 4169-4184.

Paul, B. (1960). Prediction of elastic constants of multiphase materials.

Transactions of the Metallurgical Society of AIME, vol. 218, p. 36-41.

Table 2. The values of the concentration factor K n 1.3 1.2 1.1 0.9 0.8 0.7

0.05 1.07 1.12 1.18 1.35 1.50 1.70

0.10 0.964 1.03 1.12 1.36 1.57 1.90

uf 0.15

0.20

0.25

0.93 1.07 1.31 1.57 2.00

0.93 1.23 1.52 2.03

1.13 1.45 2.00

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[8]

[9] [10]

[11]

636

Ishai, O., Cohen, L.J. (1967). Elastic properties of filled and porous epoxy composites. International Journal of Mechanical Sciences, vol. 9, no. 8, p. 539546.

Prassianakis, I.N., Kourkoulis, S.K. (1999).

Experimental Strength of Materials Symmetria Editions, Athens.

Nikolais, L., Mashelkar, R.A. (1976). The strength of polymer composites containing spherical fillers. Journal of Applied Polymer Science, vol. 20, p. 561-563.

Narkis, J. (1975). Crazing in glassy polymers: studies on polymer-glass bead composites, Polymer Engineering and Science, vol. 15, no. 4, p. 316-320.

[12]

[13]

[14]

Smith, T.L. (1961). Volume changes and dewetting in glass bead-polyvinyl chloride elastometric composites under large deformations. Rubber Chemistry and Technology, vol. 34, p. 125-140.

Kytopoulos, V. Sideridis, N.E., Bourkas, G. (2003). A study of some thermomechanical and fractural properties of particle reinforced polymer composites and SEM-aided microfailure approach of certain fracture parameters, Journal of Reinforced Plastics and Composites. vol. 22, no. 17, p. 15471587.

Andrianopoulos Kyriazi N.E., Liakopoulos, K. (1988). Experimental Strength of Materials. Simeon Editions, Athens.

Bourkas, G. – Sideridis, E. – Younis, C. – Prassianakis, I.N. – Kitopoulos, V.

Strojniški vestnik - Journal of Mechanical Engineering 56(2010)10, 637-643 UDC 621.7.08:621.99

Paper received: 23.02.2010 Paper accepted: 30.06.2010

Thread Gauge Calibration for Industrial Applications Tadeja Primožič Merkač1,* - Bojan Ačko2 1 KAKO, d.o.o., Kotlje, Slovenia 2 Faculty of Mechanical Engineering, University of Maribor, Slovenia There are two most commonly used methods for calibration of thread rings, with different measuring uncertainty. The method of mechanical sensing with two balls is mostly used on one-axial measuring machines and on coordinate measuring machines. However, the method of calculating the core diameter of the thread ring combined with the technique of adaptation (in accordance with the method of the smallest squares) is used on the profile scanner.

The required tolerances, which are very narrow for adjustable and laboratory thread ring, so the measuring uncertainty may be too high when using the method of mechanical sensing with two balls, and the low quality of some control rings, are the decisive factors for choosing an appropriate method in the industry. This also depends on the laboratory’s capability of executing a specific method.

The measurements of the core diameter of thread rings, which are the main topic of this article, were included into an international inter-comparison in which the main subject was the same thread ring as the one mentioned in this article. © 2010 Journal of Mechanical Engineering. All rights reserved.

Keywords: thread ring gauge, calibration, pitch diameter, measurement uncertainty, dimensional measurements 0 INTRODUCTION Calibration of thread gauges has always been the domain of metrologists, who calibrate length. If determining inner measurements of smooth hollow objects is a much more difficult task than determining the diameter of cylinder (plug gauges etc.), then this claim is more valid for determining measurements of inner threads. In numerous cases, people used to help themselves by pouring liquid metal, sulphur or paraffin wax or other appropriate mixtures in the nut, and then unscrew the core from the nut and measure it.

Later on, more precise calibration types were developed, where the thread ring did not require cutting, but different devices to check the diameter of the thread. They used different calibers for threads and also devices, which resemble today’s universal length device. Berndt already describes calibration in his book Gewinde [1], which is very similar to today’s calibration on 1-D measuring machine.

There are a few methods how to calibrate thread plug gauges also used in industry, but only classical methods, such as the two balls method, are used for calibration of thread ring gauges.

Those classical methods have been well known since the 19th century and are executed by means

of universal measuring machines [1], and in the last two decades even by means of coordinate measuring machines while more modern methods, used in some laboratories in Europe, deal with scanning the profile and mathematical processing of the received data. These methods are executed on optical as well as on mechanical scanning machines.

In the past years, a lot of comparison studies of thread gauges calibrations were made by dimensional laboratories in Europe. There were no great deviations in measurements of thread plug calibrations, but many in measurements of thread ring gauge calibrations.

The obtained results were different, which means that the calibration results obtained from different machines of individual laboratories did not match.

By comparing calibrations of the thread ring gauge performed with different methods and by changing the influences of an individual method as well as statistical processing of the gained results, the impact of the influences on the uncertainty of the calibration of the thread ring pitch diameter could be reduced. The most common influence is form deviation, and there is an influence of the mechanics of the measuring machine as well as mechanical probing by means

*

Corr. Authors' Address: KAKO, d.o.o., Kotlje 36, SI-2394 Kotlje, Slovenia, tadeja.primozic@ka-ko.si

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of the machine, which are considered to be less controllable. The guidance for accreditation of the procedure and the calculation of the measuring uncertainty of all calibration types is the Euramet document EURAMET/cg-10/v.01 [2].

1 THREAD RING CALIBRATIONS 1.1 Definition of Thread Ring If a point travels in a circle and at the same time performs a vertical move up or down, which is proportional to the individual rotation angle, then this point describes a thread. The easiest way of obtaining such a thread is to wind up a rectangular triangle around a round cylinder (with a diameter d), while the baseline of the triangle should be equal to the circumference of the cylinder (d·π) – in this way its hypotenuse represents the screws line.

The cylinder, which is equipped with a thread, represents the bolt; however, should the inner side of the cylinder be equipped with a thread, then it represents a ring.

1.2 Thread Ring Calibration Categories As mentioned above, two different methods to calibrate thread rings were used. The first method is a classical two balls method and the second is mechanical scanning of the profile with mathematical processing of the received data. In [2], several categories of thread ring calibration are introduced. These categories are:  measurement of the diameter,  measurement of diameter and pitch,  measurement of the 2D axial profile.

In this article both methods of calibration and three different categories are compared.

1.2.1 Measurement of the Diameter The pitch diameter D2 of a thread is calculated from the measured value ΔL, for which the rake and the measurement force must be corrected, and from the assumed nominal values of the pitch and the angle of the thread.

1.2.2 Measurement of Diameter and Pitch The pitch diameter D2 of a thread is calculated from the measured value ΔL and the measured pitch P, for which the rake and the measurement force must be corrected, and from the assumed nominal values of the distance and the angle of the thread.

1.2.3 Measurement of the 2D Axial Profile The measurement of the whole profile allows a much more precise characterization of the thread as if measuring only its certain points, because the profile of the thread ring is scanned and the desired parameters are mathematically calculated.

1.2.4 Implementation of Each Category

Fig. 1. The main parameters of thread ring The main parameters of a thread ring are: the maximum diameter (D), the minimum diameter (D1), the pitch (P), the flank angles (β, γ), thread angle (α), where α = β + γ, the lead angle (ψ), the pitch diameter (D2).

638

The compared categories of thread ring calibration are implemented on:  1-D measuring machine [3] (category 1.2.1, Fig. 2),  coordinate measuring machine (CMM) [4] (category 1.2.2, Fig. 3),  profile scanner [5] and [6] (category 1.2.3, Fig. 4),

Primožič Merkač, T. – Ačko, B.

Strojniški vestnik - Journal of Mechanical Engineering 56(2010)10, 637-643

which have one common calibration category; the measurement of medium thread diameter (category 1.2.1), therefore this research is limited to a comparison of results solely in this category as in Slovenia this category of calibration of thread rings meets a big part of the industry.

the number of parameters, for which we assume to have nominal values.

Fig. 4. Profile scanner Fig. 2. 1-D measuring machine

2.1 Mathematical Model of the Measurement Bias (calibration result) is calculated by the expression according to [7]:  P  1 D2  L  C  d D   1  cot( / 2) (1)  sin( / 2)  2 

dD   1  a2  B tan 2   cos  cot  4  3 dD 2 2 2

and a2 is short expression for 2

9 F 2  (1  v12 ) (1  v22 )  ,   a2   8  E1 E2  3

Fig. 3. Calibration of thread ring gauge on CMM 2 UNCERTAINTY OF PITCH DIAMETER CALIBRATION Due to a wide range of thread ring types we decided to analyse the measurement uncertainty of metrical thread rings.

The measurement uncertainty of the pitch diameter calibration of the thread ring on a used measuring machine (which determines D2, or which parameters of the thread ring can be determined with this machine and how accurately they can be determined, which is of even higher significance) and also depends on the number of the measured parameters of the thread ring and on

(2)

where: ∆L the average of the displacements between three positions C stylus constant dD diameter of the probing element α thread angle P pitch Ψ lead angle w0 indentation of ball-on-flat contact νi Poisson-coefficient (0.28 for steel; 0.25 for ruby) F measuring force (perpendicular to the flat) Ei elasticity modulus (2·1011 N/m2 for steel; 4·1011 N/m2 for ruby) Δb accounts for imperfections of the calibrated thread gauge, such as form deviations, and further instrument or procedure dependent

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contributions, which have not been taken into account so far.

For the contribution of thread angle uncertainty the P in the mathematical model (1) is replaced with P  2d 0 cos

, 2

(3)

where d0 is the best size diameter of the probing element according to [8].

Table 1. The coefficients value for the first degree estimates to measurement uncertainty D ci  2 xi xi

L

1

C

1 1

dD

sin

2.2 Standard Uncertainty The standard uncertainty of pitch thread calibration is calculated [9] out of 1

N N , 1      cij2  ci2  cijj2  u 2 ( xi )u 2 ( x j )  1 1 2

where coefficients are:  3 D2  2 D2 , D , cijj  ci  2 , cij  xi xix 2j xix j and xi are the input estimates.

(4)

1

1   1 tan 2   cos  cot  6a2 3 4 2 2 2 dD

2

P

N

uc2 ( D2 )   ci2 u 2 ( xi ) 



α/2

 2d 0 cos

 2

 d D cos

2

2 dD

(6)

xi

D cP  2 ; c  D2 ; cB  D2 . P  / 2  (B )    

2 The next step is to calculate the partial derivatives cj, ci and cij from Eq. (1), to obtain the sensitivity coefficients [10]. For the purpose of clarity, we shall use the tabular view. In Tables 1 and 2 the values of coefficients which were defined in Eq. (5) are shown.

The main emphasis of the research is on the influence on the uncertainty due to the theoretical angle and the thread step since the thread angle is not measured (nor the step for the first calibration) when calibrating the pitch diameter of a thread ring. Instead, the theoretical step and angle values are used.

640



 2

 1))

2

 2 D2 xix j

xj= L C

dD

P

α/2

δB

L

•

•

•

•

•

•

C

•

•

•

•

•

•

dD

•

•

•

•

A

•

P

•

•

•

•

+ higher degree estimates.

The coefficients of first degree estimates obtained from Eq. (5) are: D2 ; c  D2 ; c  D2 ; cL  (7) C C d D d D D2 L

(2  tan 2  (sin 2

Table 2. The coefficients value for the second degree estimates; the • indicates that the value is 0

2

 c 2p u 2 ( P)  c2 / 2 u 2 ( )  u 2 (B) 2

2

2

1

cij 

u ( D2 )  u (L)  u (C )  c u (d D ) 2

2



2 sin 2

For our case Eq. (4) is: 2



δB (5)

ctg

1

1 α/2

•

•

A

δB

•

•

•

2 sin 2 •

2 sin 2





•

2

B

•

•

•

2

In order to determine the realistic standard uncertainty of the thread step and the thread angle, certain measurements were performed.

Dental acrylic material was used in order to make casts (negatives) of some thread rings whose angles were then measured on a measuring microscope.

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Table 3. The coefficients value for the third degree estimates; the • indicates that the value is 0

cijj 

xi xjj= L

 3 D2 xix 2j

C

dD

P

α/2

δB

L

•

•

•

•

•

•

C

•

•

•

•

•

•

dD

•

•

•

•

C

•

P

•

•

•

•



cos sin

3

 2



•

2

α/2

•

•

•

•

D

•

δB

•

•

•

•

•

•

From 50 measurements of metrical thread rings, which differed in diameter and step, a standard measurement deviation was calculated.

In order to confirm the assumption that in Slovenia there are a lot of thread etalons which are not at all appropriate despite their appropriate D2 (errors from calibrations are within tolerance limits), we also performed some angle measurements on thread bolts that we received from the industry.

The angle measurements were performed by means of measuring knives on a measuring microscope. The obtained results in means of angle deviations matched the results, which have been performed on thread rings. The alternative thread angle measurement of industrial thread rings was executed on a profile scanner to calculate the pitch diameter with an adjustment technique and deviated from the measurements executed on the microscope for maximum 0.2°.

2.3 Influence of Nominal Value Parameters

Where: A

cos

  (2  tan 2  (sin 2  1)) 2 2 , 2  2 sin 2

    sin 4 tan 2   sin 2 tg 2  2 2 2   2sin 3 2  2  2  2  2 cos tg  )  4d 0 cos 2 4 cos 2 2 2,  3  2sin 2

B

d D (2 sin 2

C

   tan 2  cos 4 2 2, 3  2sin 2

2  tan 2   2 cos 2

  (2  4 cos 2 ) 2 2  D  2sin 4 2    d D cos ( sin 2 tan 2   sin 4 tan 2  2 2 2   4  2sin 2  2  2  10sin  12 cos  6 cos 2 tan 2  ) 2 2 2 .   2sin 4 2 2d 0 cos

When determining standard step uncertainty the data of the last thread ring step calibration was considered. The calibrations were executed on the CMM with a two-ball stylus for mechanical probing and the profile scanner to calculate the pitch diameter with an adjustment technique.

The contributions to the final measuring uncertainty of thread angle and thread pitch uncertainty (by considering nominal values instead of measured values) and the final measuring uncertainty of calibrations (determinated by research and assumed by [2]) are presented in Table 1.

3 CONCLUSION The executed measurements performed on casts, whose deviations reached max. 2° and with a standard deviation of measurement deviations 0.5° or 30' showed that the estimation about the standard deviation anticipated in [2] was overly optimistic. It needs to be said that the thread rings, which provided the largest differences in angle measurements were all manufactured in the same manufacturing works.

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Table 4. Contributions of thread angle and thread pitch uncertainty and the final measuring uncertainty of calibrations Calibration implemented on 1-D measuring CMM machine machine Assumed by [2] 1 1 u(a/2) Determinated 0.29 0.43 First degree estimates Assumed by [2] 0 0 u(P) Determinated 0.8 0.34 Assumed by [2] 1 1 u(dD)·u(a/2) Second Determinated 4.1 4.46 degree Assumed by [2] 0 0 estimates u(P)·u(a/2) Determinated 4.4 3.44 Assumed by [2] 1.2 1,2 Combined standard uncertainty -6 in µm, L in m: Determinated 6.4 µm + 2 · 10 · L 5.9 µm + 2 · 10-6 · L Lower quality of thread rings would not be of great importance if mutual uncertainties and contributions from the first measuring uncertainty degree would have been considered. In addition, the guidance claims the fact that the values are independent from each other. This is true, however D2 is calculated out of a nonlinear function and for that very reason we checked to what extent the links of the second degree influence the measuring uncertainty of the measurement.

By knowing that the values are not independent and low quality of thread rings contributes to the final measuring uncertainty, the actual angle value of the thread should not be used in the calculation of the final value D2.

The magical boarder of measuring uncertainty for calibrating the pitch diameter of a thread ring of 3 µm is set because of very narrow tolerance limits (9 µm) in [11] for calibration of the pitch diameter of thread rings, which can be achieved with great difficulty when performing calibrations and considering the theoretical thread angle values. The introduced research leads us to re-verification of the measuring uncertainty of the mentioned procedures or at least these have to be chosen very carefully, depending on the demands of direction accuracy. According to [12] and [13] the expanded measuring uncertainty of thread ring pitch diameter calibration on the 1D-length measuring machine with a two-ball stylus for mechanical probing and CMM with a two-ball stylus for mechanical probing is greater than 10 642

µm, therefore these two types of calibration are suitable for calibration of industrial thread rings.

Since the quality of laboratorial and adjustable thread rings is much better than that of control thread rings it is therefore possible to calibrate the later on this kind of machines, however a much greater number of measurements would be needed in order to assure a correct result or value.

Further research should be aimed at finding new principles [14] for determining the pitch diameter.

4 REFERENCES [1] Berndt, G. (1925). Die Gewinde, ihre Entwicklung, ihre Messung und Ihre Toleranzen, Springer Verlag. (in German) [2] Calibration Guide EURAMET/cg-10/v.01 (2007). Determination of Pitch Diameter of Parallel Thread Gauges by Mechanical Probing.

[3] Modic, M. (2001). Measurement procedure QNCL107 Screw ring gauges – T probe, Sistemska tehnika.

[4] Ačko, B. (2004). Uncertainty of thread gauge calibration by using a coordinate measuring machine. Strojarstvo, vol. 10, no.

1/3, p. 5-10.

[5] Galestin, R. (2006). Advanced 2D scanning: the solution for the calibration of thread ring and thread plug gauges, www.iacinstruments.com

Primožič Merkač, T. – Ačko, B.

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[6] Galestin, R. (2001). Measurement of geometric parameters of internal and external screw thread and similar grooves – G01B 5/20. World intellectual property organization.

[7] DKD Richtlinie: DKD-R 4-3 Blatt 4.9 (2003). Kalibrieren von Messmitteln für geometrische Messgrößen - Kalibrieren von zylindrischen Gewinde-Einstellringen, Gewinde-Lehrringen. (in German) [8] Evaluation of Measurement data - Guide to the expression of uncertainty in measurement (2008) JCGM. [9] ISO Guide to the expression of uncertainty in measurement (1995). International organization for standardization, Geneva.

[10] Gusel, A., Ačko, B., Mudronja, V. (2009).

Measurement uncertainty in calibration of

[11] [12] [13]

[14]

measurement surface plates flatness.

Strojniški vestnik – Journal of Mechanical Engineering, vol. 55, no. 5, p. 286-292.

DIN Tachenbuch 45; DIN13 Gewinde (2000). DIN Deutsches Institut für Normung e.V., Beuth Verlag, Berlin (in German) EA document EA-4/02 (1999). Expressions of the uncertainty of measurements in calibration. European Accreditation, Paris.

Ačko, B. (2003). A universal model for evaluating measuring uncertainty in calibration. Int. j. simul. model., vol. 2, no.

4, p. 121-129.

Kostanjevec, T., Polajnar, A., Sarjas, A. (2008). Product development through multicriteria analysis. Strojniški vestnik – Journal of Mechanical Engineering, vol. 54, no. 11, p. 739-750.

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StrojniĹĄki vestnik - Journal of Mechanical Engineering 56(2010)10, 644-652 UDC 621.833.1:004.94

Paper received: 07.04.2010 Paper accepted: 04.08.2010

Generation Simulation of Involute Spur Gears Machined by Pinion-Type Shaper Cutters Cuneyt Fetvaci* University of Istanbul, Department of Mechanical Engineering, Turkey A pinion-type shaper cutter is considered as the generating tool for the generation of the gear, and a mathematical model of spur gears with asymmetric involute teeth is given according to the gearing theory. The equations of the profile of the cutter, the principle of coordinate transformation, the theory of differential geometry, and the theory of gearing are applied for describing generating and generated surfaces. Trochoidal envelope traced by cutter during the generating process is also investigated.

Trochoidal curves of the cutter depends on the type of tip rounding. Computer graphs of involute spur gears are presented based on the given model. In addition, generation simulation is illustrated. The simulated motion path of the cutter can be used to determine chip geometry for further analysis. The results of this research should be helpful in the design and manufacture of spur gears. Š2010 Journal of Mechanical Engineering. All rights reserved.

Keywords: asymmetric involute teeth, gear design, gear shaper, generation simulation, spur gears, trochoidal fillet 0 INTRODUCTION Involute gears are widely used because of their advantages, such as, simple geometry, ease of manufacture, and constant gear ratio even if the centre distance changes. As modern applications demand higher power density gears, accurate numerical tools to predict gear stress are required. Computer simulations performed during the design process reduce the cost and time required to simulate many possible transmission designs. A mathematical model which defines all generating and generated tooth surfaces is the basis for accurate numerical tools and tooth contact analysis. Therefore, a good knowledge of the gear geometry is required [1] and [2].

In practice, cylindrical gears are produced by generation cutting using rack- and pinion-type cutters. In the generation cutting process, gear teeth are generated as a result of relative motion between the gear blank and the cutter. Gear shaping with pinionâ&#x20AC;&#x201C;type cutter is a versatile and accurate means of manufacturing spur and helical gears and internal gears. Equations that determine the gear tooth profile manufactured by generating-type cutters have been studied by various authors [3] to [10]. Chang and Tsay proposed a complete mathematical model of involute-shaped shaper cutters [7]. Chen and Tsay developed the mathematical models of helical gear sets with small numbers of teeth *

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manufactured by modified rack- and pinion-type cutters [8]. Yang proposed the mathematical models of asymmetric helical external gears generated by rack-type cutters and internal gears generated by shaper cutters [9] and [10].

Asymmetric involute teeth have been studied as a promising design alternative to the standard involute for increasing the load carrying capacity of gear mechanisms [9] to [11].

The gear tooth profile can be split into three distinct regions, each generated by a different part of the cutter. The first part of the gear profile, the involute edge, is cut by the involute flank of the cutter. It is the rounded edge of the cutter which cuts the second section, the trochoidal root fillet. The final portion, the bottomland is generated by the topland of the cutter. The shape of the fillet depends upon the form of generating tool and the method used to produce this gear. In gears machined by generation a tooth fillet arises as an envelope of successive rolling locations of the tool tip. The tip of the tooth of the pinion-shaped cutter is rounded to give a larger radius of fillet or to produce a full-rounded-root form to reduce the stress concentration at the root section of the tooth on critical and heavily loaded gear drives.

Procedures for computing a form of root fillet of spur or helical gear produced by different generation methods are available in literature [3] to [10] and [12]. In addition, the machining

Corr. Author's Address: University of Istanbul, Department of Mechanical Engineering, Avcilar Kampusu, TR-34320, Istanbul, Turkey, fetvacic@istanbul.edu.tr

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parameters of the generating cutter have been given for rack-type and pinion-type cutters with two round edges or single round edge [12].

Alipiev [13] investigated geometric varieties of the rounded corner of rack-type cutter tooth for generating symmetric and asymmetric involute gear teeth profiles. Su and Houser studied the application of trochoids to find exact fillet shapes generated by rack-type cutters [14]. Fetvaci and Imrak [15] have adapted the equations of trochoids given by Su and Houser to Yang’s mathematical model for spur gears with asymmetric involute teeth. In addition, simulated motion path of the generating cutter has been illustrated.

The aim of this paper is to present a method for computerized tooth profile generation of symmetric and asymmetric involute gears manufactured by pinion-type shapers. A mathematical model available in literature [7] is adopted for generating cutter surfaces. Different coordinate systems and transformations are used for generated external tooth surfaces. In addition to mathematical models of tool and generated gear, trochoidal paths traced by the tool tip are investigated. The following Section 1 provides mathematical models of the shaper cutter surfaces based on Litvin’s vector approach and Chang and Tsay’s application [6] and [7]. The mathematical

models: the locus of the cutter surfaces, the equation of meshing and the generated gear tooth surface are given in Section 2. Trochoidal envelope of the rounded tip of the generating cutter is studied in Section 3. Based on the mathematical models given in Sections 1 to 3, a computer simulation of the generating process is presented in Section 4. The relative positions of the cutter with respect to the gear during the generation process are also illustrated. The effects of tool settings on generated surfaces are shown.

Finally, a conclusive summary of this study is given in Section 5.

1 MATHEMATICAL MODEL OF THE GEAR CUTTER The mathematical model of the gear cutter is adopted from [7] to asymmetric gearing.

Contrary to symmetric gearing, left and right sides of the cutter have different pressure angles.

A shaper cutter of asymmetric involute teeth that composes six curves is depicted in Fig. 1.

Regions 1 and 6 of the cutter are involute-shaped curves, regions 2 and 5 are circular arcs with centers at E and F, and regions 3 and 4 are straight lines. For simplicity, only the parameters of the left side regions are indicated in Fig. 1.

Fig. 1. Geometry of the shaper cutter with asymmetric involute teeth (adapted from [7])

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Coordinate systems S s ( X s , Ys ) and S c ( X c , Yc ) represent the reference and the shaper cutter coordinate systems, respectively.

According to the relationship between coordinate systems Ss and Sc, the position vector of region i can be transformed from coordinate systems Ss to Sc by applying the following coordinate transformation [6] and [7] :  x   sin  Rci       y  cos i c i c

 cos   x   , sin    y  i s i s

(1)

where    / 2 N s  tan    determines half the tooth width of the shaper on the base circle, N s is the number of shaper cutter teeth and  is the pressure angle of the cutter at the pitch point, as depicted in Fig. 1. Supercript i represents regions 1 to 6.

As shown in Fig. 1, the regions 1 and 6 of the shaper cutter are used to generate the opposite sides of the working tooth surfaces of involute spur gears.  is the curve variable of the left side cutter surface which determines the location of points on the involute region and 0     m . The position vector of region 1 is represented in the coordinate system Ss as follows [7] :  x1  r sin   rb cos   R1s   s1    b (2) ,  y s  rb cos   rb sin   where is the radius of base circle. Substituting Eq. (2) into Eq. (1) yields the position vector of region 1 represented in coordinate system as follows [7]:  r cos(   )  rb sin(   )  Rc1   b (3) .  rb sin(   )  rb cos(   ) Regions 2 and 5 of the shaper cutter generate different sides of the fillet surfaces of spur gears. As indicated in Fig. 1, parameter  of the cutter surface determines the location of points on the fillet region and it is limited by 0     / 2  tan 1 ( m  (  f / rb )) . The position

vector of region 2 is represented in the coordinate system Ss as follows [7]:

rb sin  m  rb m cos  m   rb cos  m  rb m sin  2 Rs  ,   f cos  m   f cos(   m )    f sin  m   f sin(   m ) 

where  f

is the radius of tip fillet of the

generating cutter, and  m is the maximum extension angle of the involute curve at point A. The position vector of region 2 can be represented in coordinate system Sc as follows [7]:  rb cos( m   )  rb m sin( m   )   r sin( m   )  rb m cos( m   ) .

Rs2   b   f sin( m   )   f sin(   m   )     f cos( m   )   f cos(   m   

(5)

As depicted in Fig. 1, the regions 3 and 4 are used to generate the bottomland of the machined gear.  is a linear parameter on the cutter topland and its range is  m     / 2    tan      / 2 N s . Based on the cutter geometry, equation of region 3, represented in coordinate system Ss, can be expressed as [7]:  x 3   r sin   Rs3   s3    a ,  y s  ra cos 

(6)

where ra  rb2  (rb  m   f ) 2   f is the radius of the tip circle of the cutter 1 and    / 2  tan ( m  (  f / rb )) . Substituting Eq. (6) into Eq. (1) yields the position vector of region 3 represented in coordinate system Sc as follows [7]:  x   r sin(   )  Rc   c    a .  yc   ra cos(   )

(7)

Based on the differential geometry, the unit normal vectors of the above mentioned shaper cutter surface represented in coordinate system Sc are [6] and [7] : nc 

646

(4)

Fetvaci, C.

dRci  kc dl j dRci  kc dl j

,

(8)

Strojniški vestnik - Journal of Mechanical Engineering 56(2010)10, 644-652

Fig. 2. Kinematic relationship between the shaper cutter and the generated gear where k c is the unit vector of the Z c -axis.

Parameter l j represents  ,  and  , respectively. By substituting Eq. (3) in Eq. (8), the unit normal vector of region 1 can be obtained as follows [7]: n    sin(   )  nci      (9) . n   cos(   ) By substituting Eq. (5) in Eq. (8), the unit normal vector of region 2 can be obtained as follows [7]: i xc i yc

n i    sin(   m   )  nci   ixc    (10) . n yc   cos(   m   ) By substituting Eq. (7) in Eq. (8), the unit normal vector of region 3 can be obtained as follows [7] : n i   cos(   ) nci   ixc    (11) . n yc   sin(   )  The equations for the right side of the cutter are similar to those of the left provided that the parameters are calculated according to the corresponding pressure angle, and all equations corresponding to Xc coordinate are assigned an appropriate sign.

2 GENERATED GEAR TOOTH SURFACES Fig. 2 illustrates the relationship between shaper cutter and generated gear of the gear generation mechanism. The right-handed

coordinate systems are considered. The coordinate system S f ( X f , Y f ) is the reference coordinate system, the coordinate system S g ( X g , Y g ) denotes the gear blank coordinate

system, and the coordinate system Sc ( X c , Yc ) represents the shaper cutter coordinate system.

On the basis of the gear theory, the cutter rotates through an angle  c while the gear blank rotates through an angle  g . Based on the above idea, the coordinate transformation matrix from Sc to Sg can be represented as [6]  cos( c   g ) sin( c   g )  (rc  rg ) cos  g  cos( c   g ) (rc  rg ) sin  g  c g )   0 0 1

M    sin( gc

.

(12)

The relationship between the angles  g and  c is g  ( N c / N g ) c where Nc is the number of the teeth of the cutter and Ng denotes the number of the teeth of the generated gear.

Point I is the instantaneous center of rotation and rc and rg are the standard pitch radii of the shaper cutter and the gear, respectively.

According to the theory of gearing [6], the mathematical model of the generated gear tooth surface is a combination of the meshing equation and the locus of the rack cutter surfaces. The locus of the shaper cutter surface, expressed in coordinate system Sg, can be determined as follows [6]: R ig  M gc R ic , (i  1,...,6) .

(13)

 

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Fig. 3. Gear cutter tip geometry When two gear surfaces are meshing, both meshing surfaces should remain in tangency throughout the contact under ideal contact conditions. Conjugate tooth profiles have a common surface normal vector at the contact point which intersects the instantaneous axis of rotation (pitch point I) for a parallel axis gear pair. Therefore, the equation of meshing can be represented using the coordinate system S c ( X c , Yc , Z c ) as follows [6] :

X c  xci Yc  yci  , i i ncx ncy

(14)

where X c  rc cos  c and Yc  rc sin  c are coordinates of the pitch point I represented in coordinate system Sc; x ci and y ci are the surface coordinates of the shaper cutter; symbols n cxi and n cyi symbolize the components of the common

unit normal represented in coordinate system Sc. In Eqs. (13) and (14), supercript i represents regions 1 through 6 of the corresponding shaper cutter surfaces.

The mathematical model of the generated gear tooth surfaces is a combination of the meshing equation and the locus of the rack cutter surfaces according to the gearing theory. Hence, the mathematical model of the gear tooth surfaces

648

can be obtained by simultaneously considering Eqs. (13) and (14).

3 EPITROCHOIDAL PATH OF THE GENERATING CUTTER The tooth fillet resulting from gear generation is in fact a trochoid which is created by the tool tip in its rolling movement [2]. An epitrochoid curve determines the shape of the fillet of the generated external gear tooth as a result of the generation process by pinion-type shaper cutters. An epitrochoid is a curve traced by a point attached to a circle of radius r rolling around the outside of a fixed circle of radius R, where the point is a distance d from the center of the exterior circle. According to the analytical mechanics of gears, the rolling circle is the pitch circle of the generating shaper cutter, the fixed circle is the pitch circle of the machined gear and the distance d is measured from the origin of the cutter to the center of its rounded corner at the tip (point E).

During the generating process of spur gear tooth presented in this paper, the center of the rounded corner at the tip traces out a trochoid. An equidistant curve with a distance of  f defines the gear tooth root fillet. As depicted in Figs. (1) and (3), the rounded edge of the cutter is a circular arc and its center is located at point E. To

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ensure the tangents of the involute curve and circular arc at point A are the same and continuous, point E should be on the line PA . It is first necessary to find the coordinates of points A and E [5].

The maximum involute extension angle at point A, denoted as  m , can be evaluated from the following equation when the radius of tip circle rB is given. rb tan  m  (rB   f ) 2  rb2   f

.

(15)

According to involute geometry, the polar coordinates of point A (rA ,  A ) are given by , rA  rb / cos  m .

(16)   A   / 2 N s  inv  inv m The rectangular coordinates of point E can then be expressed in terms of x E and y E ,

 x E  rA cos  A   f sin( m   A )   y E  rA sin  A   f cos( m   A ) .  1  E  tan ( y E / x E )

(17)

 x E cos(c   g )  x  T   x E sin(c   g ) ,     yT   y E sin(c   g )  (rc  rg ) cos  g    y E cos(c   g )  (rc  rg ) sin  g 

(18)

where ( x E , y E ) is the coordinate of point E ,  c and g are the rolling parameters, rc and rg are the pitch circle radius of the shaper and the machined gear, respectively.

The envelope of the path of a series of circles with their geometric centers on the primary trochoidal path determine the actual form of spur gear tooth fillet. This new path is called the secondary trochoid which is the paralel curve of the primary trochoid. As a result, the coordinate of the corresponding point F on the secondary trochoid can be expressed as:  f yT   x F  xT  2 2 xT  yT  , (19)   f xT  y F  yT  2 2  xT  yT  where  f denotes the tip rounding radius of the shaper cutter, xT  dxT /d c and y T  dy T /d c .

4 COMPUTER IMPLEMENTATIONS

Fig. 4. Primary and secondary trochoids of the cutter with rounded tip corners Fig. 4 displays a general point on the primary trochoid which is the envelope of the center of round tip. Applying the homogeneous coordinate transformation matrix given in Eq. (12), the equation of the primary trochoid (epitrochoid curve) can be written as follows:

A computer program has also been developed to compute coordinates of the gear tooth profile generated by different shaper cutters with partially round and full round tip. The computer graphs of generating cutter and generated gear can be obtained. Furthermore, considering appropriate limits of the rolling parameter, the simulated motion path of the cutting tool during the generation process can also be visualized. The effect of tool parameters on the generated tooth profile can be investigated before it is manufactured. Illustrative examples investigating the effect of tool tip radius follow: Cutters with rounded tip corners are widely used in manufacturing. The centers of the roundings are not on the center line of the tooth.

In asymmetric involute gearing, the left and the right sides of cutter are designed with different pressure angles. In this case, the left and right secondary trochoids are the offset curves of their corresponding primary ones with distances ρf and ρf2, respectively. The radius of the tip fillet

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surface at left side of the cutter is ρf. Similarly, the radius of the tip fillet surface at the right side is ρf2. Fig. 5 displays the shaper with asymmetric involute teeth, trochoidal paths of the centers of left and right rounded corners and the generated profile.

trochoidal paths of the centers of the left- and right sides of tip fillet. The centers of the rounded tip are at the center line of the cutter tooth. For visual clarity, only the corresponding halves (of secondary trochoids) that contribute to final formation of the generated tooth shape are shown.

Fig. 5. Trochoids of the cutter with rounded tip corners Fig. 7. Trochoids of the asymmetric cutter with a full radius tip

Fig. 6. Trochoids of the symmetric cutter with a full radius tip In symmetric involute gearing, the location of the center of the tool’s fully-rounded tip is on the center line of the tool tooth. The trochoid of the center of the rounding, the secondary trochoid, the generating and generated surfaces are shown in Fig. 6.

Fig. 7 displays the asymmetric involuteshaped shaper cutter with a full rounded tip and

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Fig. 8. Generation simulation of gear blank Fig. 8 displays the work gear and simulated motion path of the generating cutter.

Each gear gap is produced through successive penetrations of the tool teeth into the workpiece, in the individual generating positions. This simulation can be used to determine the chip geometry.

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5 CONCLUSIONS

6 ACKNOWLEDGEMENTS

In this paper, computerized tooth profile generation of involute gears manufactured by pinion-type cutters is studied based on the Litvin’s vector method. The asymmetric involute teeth are adopted to Chang and Tsay’s application. The developed computer program provides an investigation of the effect of tool parameters on the generated tool profile before manufacture. Trochoidal paths traced by the generating tool tip are investigated. It has been noticed that geometric varieties of the rounded corner of the pinion-type cutter determine the position of trochoidal paths relative to the center line of the tooth space of the generated gear. The relative position of the cutter to the workpiece has been illustrated. The simulation of shaper cutting action can be used to determine the chip geometry for further analysis about tool wear and tool life.

The optimisation of the generating shaping process to increase productivity and cost efficiency, enhance gear quality is beyond the scope of this paper. However, related studies [16] and [17] should be mentioned here for further studies. Bouzakis et al. developed methods describing the chip geometry and predicting the tool life and cutting forces for manufacturing cylindrical gears by generating cutters. It has been found that chip formation and chip flow have a varying influence on wear behavior depending on the width of land at the tip of shaper cutter tooth.

As a result it has been stated that while designing the geometry of the cutter the chip formation should be considered to improve the productivity [16]. Recently, Pedersen has introduced a shape optimization method based on rack-cutter tooth geometrical parameterization for improving bending stresses in spur gears with asymmetric teeth [17]. As a result, the two new standard rack cutters that can reduce the bending stress rather significantly, have been introduced [17]. In the present paper, shaper cutters with rounded tips are studied. The methods proposed for optimisitions [16] and [17] can be applied to symmetric and asymmetric involute spur gears manufactured by the shaper cutters with rounded tips for further investigations.

This work was supported by Scientific Research Projects Coordination Unit of Istanbul University. Project number YADOP-4577.

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[10]

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Kawalec, A., Wiktor, J. (2004). Tooth-root stress calculation of internal spur gears.

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218, no. 9, p. 1153-1166.

Buckingham, E. (1988).

Analytical Mechanics of Gears, McGraw-Hill, New York.

Salamoun, C., Suchy, M. (1973).

Computation of helical or spur gear fillets.

Mechanism and Machine Theory, vol. 8, p.

305-323.

Colbourne, J.R. (1987). The Geometry of Involute Gears, Springer-Verlag, New Jersey.

Litvin, F.L. (1994). Gear Geometry and Applied Theory. Prentice Hall, New Jersey.

Chang, S.-L., Tsay, C.-B. (1998).

Computerized tooth profile generation and undercut analysis of noncircular gears manufactured with shaper cutters. Journal of Mechanical Design, vol. 120, p. 92-99.

Chen, C.-F., Tsay, C.-B. (2005). Tooth profile design for the manufacture of helical gear sets with small numbers of teeth.

International Journal of Machine Tools and Manufacture, vol. 45, p. 1531-1541.

Yang, S.-C. (2005). Mathematical model of a helical gear with asymmetric involute teeth and its analysis. International Journal of Advanced Manufacturing Technology, vol. 26, p. 448-456.

Yang, S.-C. (2006). Study on an internal gear with asymmetric involute teeth.

Mechanism and Machine Theory, vol. 42, no. 8, p. 977-994.

Kapelevich, A. L., Shekhtman, Y.V. (2009).

Tooth fillet profile optimization for gears

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with symmetric and asymmetric teeth. Gear Technology, vol. 26, no. 7, p. 73-79.

Lin, T., Ou, H., Li, R. (2007). A finite element method for 3-D static and dynamic contact/impact analysis of gear drives.

Computer Methods in Applied Mechanics and Engineering, vol. 196, p. 1716-1728.

Alipiev, O. (2009). Geometric synthesis of symmetric and asymmetric involute meshing using the method of realized General Machine Design potential.

Conference, Ruse â&#x20AC;&#x201C; Bulgaria, p. 43-50.

Su, X., Houser, D.R. (2000). Characteristics of trochoids and their application to determining gear teeth fillet shapes.

Mechanism and Machine Theory, vol. 35, p.

291-304.

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[17]

Fetvaci, C.

Fetvaci, C., Imrak, C. (2008). Mathematical model of a spur gear with asymmetric involute teeth and its cutting simulation.

Mechanics Based Design of Structures and Machines, vol. 36, p. 34-46.

Bouzakis, K.-D., Lili, E., Michailidis, N., Friderik, O. (2008). Manufacturing of cylindrical gears by generating cutting processes: A critical synthesis of analysis methods. CIRP Annals - Manufacturing Technology, vol. 57, p. 676-696.

Pedersen, N.L. (2010). Improving bending stress in spur gears using asymmetric gears and shape optimization. Mechanism and Machine Theory, in press.

Strojniški vestnik - Journal of Mechanical Engineering 56(2010)10, 653-662 UDC 534.1:621.83

Paper received: 18.11.2008 Paper accepted: 23.06.2010

Gear Vibrations in Supercritical Mesh-Frequency Range Caused by Teeth Impacts 1

Milosav Ognjanovic1,* - Fathi Agemi2 University of Belgrade, Faculty of Mechanical Engineering, Serbia 2 Research and Development Centre, Libya

After gear teeth impact, natural free vibrations arise, attenuating in a short period of time. Teeth impacts repeat with the frequency of teeth entering the mesh, vibrations become restorable, and restore with teeth mesh frequency. In the range of sub-critical teeth mesh frequency range these natural free vibrations are covered by forced vibrations caused by the fluctuation of teeth deformations. In the supercritical mesh frequency range, restorable free vibrations dominate in the frequency spectrum of gear system vibrations. These restorable free vibrations effectuate the increase of total vibration level with the speed of rotation increase. Also, in this frequency range the modal structure (natural frequency) of the gear system is not stable and effectuates super-critical resonances arising. Gear vibration measurements and frequency analysis (FFT-Analysis) are performed in very high speeds of gear rotations as high as 40,000 rpm. A mathematical model for experimental results synthesis is established. For this purpose, the theory of singular systems is used. Gear teeth mesh is treated as a singular system, with a continual process of load transmission with singularities caused by teeth impacts. Damping coefficients and energy attenuation is determined using the developed mathematical model. ©2010 Journal of Mechanical Engineering. All rights reserved.

Keywords: gears, vibration, singular system, frequency spectrum 0 INTRODUCTION Gear vibrations have been the subject of studies for a long time. Research was oriented, both theoretically and experimentally, toward identifying the teeth mesh process or toward analysing gear drive system behaviour. Different models were used, starting from a single-degree model for teeth mesh analysis to complex multidegree models for identification of effects in a complete gear transmission system. Excitation arises from the teeth mesh. Basically, during the process of gear meshing two excitation processes are performed: fluctuation of gear teeth deformation and teeth impacting. Both of them enable the inclusion of the influence of teeth transmission errors, teeth stiffness non-linearity, friction forces, etc. Calculations of gear vibrations are predominantly performed in the form of forced vibrations caused by the fluctuation of gear teeth deformation. Compared with experimental results, this approach produces satisfactory results in sub-critical and in resonant mesh frequency range. However, in super-critical mesh frequency range (extremely high rotation speeds) the difference between the calculated and measured vibrations is significant. In this frequency range, the calculated level of vibrations

decreases with increase of rotation speed, however, measured gear vibration level slightly increases (Fig.1).

In the Gear research centre, TU Munich (FZG) managed very intensive investigations of gear vibrations 40 years ago. This research was analytical and experimental [1] and [2]. Knabel [2] performed detailed calculations of forced vibration caused by fluctuation of teeth deformations. Calculations were carried out using the model of three-degree freedom of meshed gear pair and analogy calculation system (computer). In Fig. 1, line 2 presents one of these results. The same vibrations were measured (line 1 in Fig. 1), and the difference between the obtained vibration levels in the supercritical teeth mesh-frequency range is evident. In [1] and [2] the basic line 3 (Fig. 1) is defined, which presents basic and general increase of gear vibrations.

Using the results of the FZG, the gear calculation procedure was standardized [3]. Internal dynamic forces are involved in calculations by dynamic factor Kv (Fig. 2). In supercritical teeth meshfrequency range is defined as independent of the teeth mesh-frequency, however, with the value close to maximal values in sub-critical range if teeth mesh frequency f is not higher than natural fn more than 2.5 times.

* Corr. Author's Address: Milosav Ognjanovic, Faculty of Mechanical Engineering, Kraljice Marije 16, 11120 Belgrade, Serbia, mognjanovic@mas.bg.ac.rs

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Further research was performed mainly in sub-critical and critical gear rotation speeds.

Vibrations in those calculations are excited by time function of fluctuation of teeth in mesh deformation [4] and [5]. This function is suitable for inclusion of transmission errors and their effects analysis [6], inclusion of sliding friction effects [7] and [8], dynamic loads calculations [6] and [9]. All of these and similar calculations or analyses were processed in sub-critical and critical teeth mesh frequency ranges. Supercritical teeth mesh frequency range was not processed in the mentioned analysis. Research in the field of gear vibration was also performed in respect of non-linearity [10] and [11], and it was found that the effects of non-linearity are not significant. In some research works on gears, analyses of balance of vibration energy [12] and [13] were also performed. Calculations of gear vibrations using a discrete systems approach in some of the research works were coupled with FEM calculations of elastic systems [13] and [14].

In order to define the nature of gear vibrations in supercritical teeth mesh frequencies and to define a mathematical model, so as to make a synthesis of the measured results, a new approach to gear vibrations treatment is taken.

Gear vibrations are defined as restorable free (natural) vibrations caused by teeth impact at the moment of contact start (addendum impact).

Every impact disturbs natural free damped vibrations which are restored with a new teeth impact. The theory of singular systems is used to develop a mathematical model.

increase. Using the model presented in Fig. 1, vibrations were calculated and are presented by Fig. 1, line 2. Excitation was performed by the function of stiffness fluctuation in the gear teeth mesh. In the supercritical mesh-frequency range, the calculated level of vibration decreased to minimal values. This is a phenomenon which needs a new approach to the process of description and modelling.

1 PROBLEM FORMULATION

For practical use and load capacity calculation of gear drives, dynamic factor Kv is defined and standardized by ISO 6336. For this purpose, measured dynamic forces and vibrations were used, and values of Kv were defined separately for sub-critical, critical and supercritical teeth mesh-frequency range (Fig. 2).

The levels of dynamic forces for a practical use are approximated by interrupted lines. Resonant teeth mesh-frequency is defined based on middle gear teeth stiffness and equivalent mass of connected gears and other rotating masses. In the supercritical teeth mesh-frequency range, the level of dynamic forces is approximated by a horizontal line, i.e. the value of Kv is independent of teeth mesh-frequency increase (if f < 2.5 fn).

However, it is important that the level of Kv in this

1.1 Comparing Measured and Calculated Gear Vibrations The measured results of vibration for one gear pair in a very wide teeth mesh-frequency range [2] show fluctuations, which can be explained by comparing them to those calculated (Fig. 1). Measurements were carried out to 20,000 rpm and the main resonance was at 5000 rpm (Fig. 1, line 1). The range of other 15,000 rpm was supercritical, where the level of vibration was approximately between 50g and 100g (g - earth acceleration). After the main resonance acceleration decreased to the level of 40g, it then slightly increased with the speed of rotation

654

Fig. 1. Comparing measured and calculated gear vibration level [2]

Fig. 2. Dynamic factor Kv [3] and approximation of gear dynamic forces and vibration

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range is significant, and it is necessary to investigate this phenomenon.

where = 200. The concentrated masses is:

mt 1 mt 2 , Fc  v c c' me ; me 

1.2 Addendum Gear Teeth Impact

mt 1  mt 2

There are a few kinds of teeth impacts during gear meshing. Much stronger than others is addendum impact, especially in spur gears without teeth flank corrections.

Teeth deformations are proportional to teeth load and teeth stiffness. Deformations replace the first point of contact from the right position A, to position A’ which is ahead of point A. Contact of teeth pair starts with intensive addendum impact (Fig. 3a). Collision speed vc is proportional to teeth deformation, speed of rotation n and gear design parameters. By analyzing teeth geometry, deformations and speeds, collision speed at the first point of teeth contact is defined as:  1   cos '   . vc  rb11 1   1  cos  w   u

force

of (4)

where c’ is teeth stiffness at the moment of collision and me equivalent mass. a)

(1)

Angular speed 1  2n1 , n1 - revolution per minute (rpm) of pinion, transmission ratio u  z 2 z1 , teeth number of connected gears are z1 and z2, and other parameters are presented in Fig. 3a. In Fig. 3b relative collision speed vc/n for the chosen parameters for spur gear pair is presented (z1 = z2 = 25, module m = 5 mm, offset factors x1=x2=0). For the other spur gear pairs with the radius of basic circle of pinion rb1 in mm, using ratio (vc/n) from diagram in Fig. 3b, collision speed is v  1 r vc   c  1   b1 n1 .  n   u  117.5

collision

(2)

Collision speed vc is defined in the direction of teeth contact line. For a further application of this speed, it is necessary to transform the model of rotating masses into a harmonic oscillator. Inertia moments of rotating masses (of gears and all others connected to them) J1 and J2 should be transformed in concentrated masses in the teeth contact line direction, J J mt1  12 ; mt 2  22 .

(3) rb1 rb 2 The radii of the basic circle of gear pair are rb1  mz1 2 cos  and rb 2  mz 2 2 cos ,

b) Fig. 3. Teeth collision: a) addendum collision, b) relative speed of addendum collision for chosen gear parameters 1.3 Testing Rig for Vibrations in Supercritical Mesh Frequency Range For the purpose of gear vibration in the supercritical teeth mesh-frequency range, a specific testing rig is designed and realised (Fig. 4). In order to perform the extreme high speed of rotation, the masses of rotating components are of relatively small dimensions, with specific type of lubrication and sealing. The speed of rotation can vary from zero to 40,000 rpm measured at the shaft of pinion z1. The torque which applies load in gear teeth is made by middle coupling using the principle of back-to-back system. The application of torque takes place before the rotation and vibration measurement. For the experiments presented in this work, the torque in the coupling (gear z2 = 47) was T2 = 30 Nm, and

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in the pinion z1 = 32 it was T1 = 20.4 Nm. The speed of rotation n = n1 in rpm was measured in the shaft of the pinion z1 = 32 and teeth meshfrequency was calculated f = nz1/60. The accelerometer for vibration measurement is fixed by the screw on the left gear housing. The position of the accelerometer is presented in Fig. 4b. The direction of the main accelerometer sensitivity is covered with gear contact line direction. The dynamic forces from the teeth mesh area are transmitted to the housing walls through bearings. Vibrations in the teeth contact area and in the housing walls differ in intensity but the structure of vibration spectrums is very similar. This relation is provided by a specific design of housing which eliminates additional natural frequencies with significant effects. The difference in the vibration level is proportional to vibration transmissibility factor between the teeth mesh area and the position point of the accelerometer.

by elasticity of gear teeth in mesh. Before measuring the vibrations with a high speed of rotation, measurements with very slow speed of rotation were done. The aim of those measurements was to detect vibrations caused by separated teeth impacts. The results of these measurements are presented in Fig. 6. After the impact, gears vibrate with natural frequency fn.

This vibration was measured in a tangent direction in the gears. After a short time, the vibration is damped. The next impact excites a new damped vibration, again and again. Small speed of rotation produces vibration, as presented in Fig. 6.

The measured results presented in Fig.6 show that gear vibrations contain restorable free component. Teeth collisions repeat with teeth mesh frequency f and restore a new cycle of free damped vibrations. This effect in the gear vibration analysis first used by Umezawa and thereafter Cai, reference [4], is referred to as the Umezawaâ&#x20AC;&#x2122;s effect. Using this effect and doing calculations, Cai [4] obtained an increase in vibrations in the supercritical teeth mesh frequency range, however, the range was very small. If the gears are damaged [16] these effects become dominant in the frequency spectrum.

a)

b) Fig. 4. Back-to-back test rig: a) gears centre distance surface, b) right side view (centre distance a = 85 mm, z1 = 32, z2 = 47, m = 2 mm, b = 8.5 mm) Measurement and spectrum analysis were performed using software for this purpose for real time and FFT analysis. Prior to measurement, the modal testing of back-to-back system was performed. The system was excited by the impact in the gear flank. One of those results is presented in Fig. 5. The three natural frequencies were detected, fn1 and fn2 caused by corresponding shafts and shaft supports elasticity and fn caused 656

Fig. 5. Natural frequencies of testing rig

Fig. 6. Restorable free damped vibration after every teeth impact

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2 ANALYSES OF EXPERIMENTAL RESULTS Using installation, as presented in Fig. 4, the measurement was performed in the range as high as 40,000 rpm of pinion z1 = 32. The main objective was to obtain similar results presented in Fig. 1 [2] and identify the phenomenon which increases vibration level in the supercritical meshfrequency range. In addition, an objective was to identify “supercritical resonances” (Fig. 2) and the phenomenon which creates fluctuation of vibration level in this teeth mesh-frequency range. One of the measured results is presented in Fig. 7. At the teeth mesh-frequency f = fn = 5200 Hz (Fig. 5) the main resonance increased vibration level to 168g. There is a small difference between the natural frequencies fn1 = 4800 Hz and fn = 5200 Hz and it is possible to conclude that both of them were affected at a very high level of resonant vibration. After resonance, the level of vibration was decreased to 40g and then fluctuated to 60g for 20,000 rpm. In the range of up to this speed, something was changed in the tested system. The level of vibrations decreased to 20g for 28,000 rpm and then fluctuated between 20g and 45g. These results are not identical with those presented in Fig. 1, because the testing rigs are not the same, but the phenomenon is similar.

Fig. 7. Total level of gear vibration measured using installation presented in Fig. 4 For the purpose of identifying the structure of gear vibrations, a spectral analysis was carried out. Using software for Furrier transformation, the spectrums of frequencies and amplitudes of component time functions were obtained. In the range of sub-critical area frequency, the

spectrums consist of time functions with teeth mesh-frequencies f and their higher harmonics 2f, 3f, etc. and with natural frequencies fn1, fn2 and fn.

The value of amplitudes of free vibrations increases when mesh frequency gets close to some of naturals. In Fig. 8a one of those spectrums is presented for the speed of rotation n1 = 4050 rpm. In full resonance, teeth meshfrequency became equal to the main natural one f = fn = 5200 Hz. It was for the speed of rotation n1 = 9750 rpm. In frequency spectrum (Fig. 8b) only very high amplitudes dominate with resonant frequency of 5200 Hz. After resonance, a further increase of the speed of rotation revealed one specific phenomenon. In frequency spectrum, vibration with teeth mesh-frequencies f increasingly decreases until it disappears, as indicated by the interrupted line in Fig. 7. The total level of vibration in this area is the result of natural vibrations with natural frequencies (Fig. 8c).

Within the range of speed of rotation n1=10,000 to 20,000 rpm (Fig. 7), frequency spectrums are similar to the spectrum in Fig. 8c, i.e. vibrations within this range are natural (free) vibrations with frequency fn. With an increase in the speed of rotation, the intensity of the teeth impact also increases and the level of natural vibrations increases. In the frequency spectrum in Fig. 8c, the vibration amplitude increases with the increase of the speed of rotation. It should be noted that in the f > fn range the situation is opposite to that in Fig. 6. The time of impact repetition is shorter than the period of natural free vibrations 1/f < 1/fn.

Within the range of the pinion speed of rotation n1 = 20,000 to 40,000 rpm (Fig. 7) the level of vibrations was first decreased and then, for higher speeds, was increased again. Frequency analyses reveal one additional phenomenon. In the frequency spectrum (Fig. 8d) the amplitude with frequency f disappears completely and all natural frequencies become active. The spectrum becomes crowded with the already detected fn1, fn2, fn and of many new ones. The amplitudes for these frequencies are relatively small but when combined, using corresponding phase positions, they create a total level of vibrations, which corresponds to the level in Fig. 7. Also, it is noticeable that teeth impact energy is distributed to all of these natural vibrations, and this can be the reason why they have small amplitudes.

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Additionally, the modal structure of the tested system at these high speeds of rotation is changed. This phenomenon of modal structure instability at a very high speed of rotation has been identified in other experiments unrelated to gear testing.

again and, with one of them or a few of them, the level of vibrations increases. In Fig. 1 this occured for 19,000 rpm, and in Fig. 2 for f/fn = 2, and is marked as supercritical resonance. The possible explanation of supercritical resonances can be found in model instability and in the concentration of all modal frequencies (shapes) in a small group or in one group only.

3 ANALYTIC MODELLING OF MEASURED RESULTS

a) [Hz]

b) [Hz]

c) [Hz]

d) [Hz]

Fig. 8. Frequency spectrums of gear vibrations presented in Fig.7 Modal instability and only free vibrations in the range of very high speeds of rotation can explain the fluctuation of vibration level in this range of speeds. When many natural frequencies occur, the level of vibrations decreases. For higher speeds these natural frequencies disappear 658

The gear teeth meshing process presents by itself a singular process [15] which contains two processes: continual and transient one. The continual process is a continual increase of the free vibration level ( x a by frequency fn) with increase of teeth mesh frequency f. The transient process is the gear response also with a natural frequency fn after teeth impact, especially in resonance areas.

Collision force (Eq. 4) increases proportionally to the speed of rotation. For a gear pair with a certain tooth load (Fig. 3b), using Eqs. (2) and (4), this force can be presented in direct relation with teeth mesh frequency f and constant K, nz f  1; Fc  K f ; 60 (5) 60 v  1 r K  cme  c  1   b1 .  n   u  117.5 z1

The impact force increases proportionally to the speed of rotation (teeth mesh frequency f).

This force makes deformation in teeth contact direction xc and produces deformation work F x K xc W c c  f .

(6) 2 2 Displacement xc (deformation) is independent of the force Fc and of the speed of rotation. This deformation depends on the gear load, i.e. consists of teeth deflection and teeth contact deformations. There is a difference between teeth deformations at the moment of teeth impact xmax and before impact xmin (xc = xmax - xmin) with amplitude x0 = xc/2 and frequency f.

Deformation work W absorbs elastic system and part of it returns in the form of vibration. These are damped free vibrations with natural frequency fn. The potential energy of these vibrations is:

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Ep 

c xa 2

;

xa  Ax0 f .

(7)

2 Displacement xa presents gear vibration after impact (Fig. 6). This response is much weaker compared to teeth impact. The ratio between the vibration energy and disturbance energy is marked by a constant A and by product Af. The units for the constant A are seconds and product Af is a dimensionless parameter which defines the ratio between amplitude of impact displacement x0 and amplitude of free vibrations with frequency fn. This product (Af)2 shows how much energy is produced by vibrations compared to deformation work absorbed by impact elastic deformations.

3.1 Continuous Process

Impact energy increases continually with teeth mesh frequency f increase. Potential energy Ep is a part of impact energy which also increases continually. Potential energy is released in the form of natural free vibration, such as vibrations presented in Fig. 6. Kinetic energy of gear vibrations is Ek  me x a 2 / 2 . The transformation of potentional into kinetic energy is defined by Lagrange's equations. For a certain mesh frequency f, these equations for natural free vibrations are as follows: E p 1 Ek   0 ; me xa  c xa  0 .

(8) dt xa xa This vibration between the two impacts (Fig. 6) is with damping, i.e. with dissipation of vibration energy. The part of Eq. (8) which can present this effect is removed due to the fact that with impact repetition by frequency f, the free natural vibration with frequency fn 

 c

me

 2

is

restored.

Those

are

restorable free vibrations. In the supercritical mesh frequency range (f > fn) this kind of dissipation is not effective. The damping effect in the system response is included in the transient part of this model. Using Eqs. (7) and (8), the first part of acceleration level in direction of contact line is: c x xa  A  0 f .

(9) me

This is the first (algebraic) part of a singular solution (Fig. 9). Therefore, with the increase in mesh frequency f acceleration increases, and this in turn is proportional to the increase in the absorbed disturbance energy.

3.2 Transient Process

Teeth collision presented in Fig. 3a generates collision force Fc which is repeated with mesh frequency f. This force produces two kinds of teeth deformations (displacements). The total displacement is x = xa + xb. The first xa is already included in the continuous process and this part corresponds to the force and torque which meshed gears transmit (corresponds to gear pair load). The second part xb is additional displacement which is the result of inertia after the teeth impact and corresponds to the gear pair sensitivity.

Gear pair can be presented by an equivalent single mass model with the mass me (Eqs. 3 and 4) supported by mean teeth in mesh stiffness c with damping with coefficient b. The action of force Fc in this model produces the additional transmitted force: FT  bxb  c xb , (10) where xb is the additional displacement caused by teeth impact. Since forces bxb and c xb are 90o out of phase, the magnitude of the additional transmitted force is: FT  b 2 xb 2  c 2 xb 2

.

(11)

The ratio of the additional transmitted force FT  me xb to the applied Fca  me xa can be expressed in terms of a transmission function, i.e. transmissibility: x FT  b   T sin 2ft    ,  Fca xa

T 

1  f

  tan 1

1  2f f n 2 2

1 f

fn

  2f

2 2

2  f f n 

2

fn 

2

,

f n 2  4 2 f 2 f n 2

(12)

.

The function T is well known as a transmission function for a single degree model excited by acceleration. These relations were

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obtained in the form of response ratio, where   0...1 is a dimensionless damping parameter.

At the moment of impact (t = 0), the responded force is FT  Fca T sin  and the responded part of vibrations for the single degree mathematical model is: xb  xa T sin  .

(13) This is the response at the moment of impact after which vibrations continue with natural frequency fn. This is the transient part of vibration which together with the continuous one produces the total gear vibration level. The maximal response of the system, i.e. T is for full resonance when f = fn, and = /2.

3.3 Total Level of Vibration

By summing the results of continual and transient process the total level of vibrations is:  x   xa   xb   xa 1   T sin    A

c x0 me

f 1   T sin   .

(14)

Fig. 9. Relation between measured and calculated level of gear vibrations Using the presented mathematical model and corresponding software, the curve of the total level of gear vibration was calculated (Fig. 9).

Calculations were carried out using software developed for equation (14) and parameters of the tested gear pair. The damping parameters A and  were adapted to the measured level of vibrations.

These parameters offer the opportunity to analyse the relation between the energy of the gear teeth impact and the energy dissipated inside the 660

machine parts. For this purpose, vibrations measured to 20,000 rpm were used, i.e. in the speed range before vibration level starts to fluctuate in a wider range (Fig. 7).

The presented model gives the opportunity to compare the measured and calculated results and to check the hypothesis about the nature of gear vibration as well as to analyze the gear vibration phenomenon. In addition, the model provides the possibility of analyzing impact energy balance of accounts, i.e. energy distribution within the system, and of damping coefficient calculations. For this purpose, vibrations of the testing rig (Fig. 4) were calculated and analyzed. The parameters of the presented testing rig are as follows: inertia moments of rotating masses are J1 = 5.351·10-4 kgm2 and J2 = 16.117·10-4 kgm2 which include mass inertia of the corresponding shaft with both gears and other parts in the shaft. Basic radii of the tested gears are rb1 = 0.0323 m and rb2 = 0.0475 m (module m = 2 mm and teeth numbers z1 = 32, z2 = 47), transformed masses mt1 = 0.5351 kg, mt2 = 0.714 kg and equivalent mass of the system me = 0.2978 kg. The gears are connected by stiff shafts and one shaft with both gears was treated like one rotating mass. Mean stiffness of the teeth in mesh for both gear pairs, including the shaft effect is c= 3.14·108 N/m. Back-toback system (Fig. 4) was loaded by the torque of 30Nm at the gear z2, i.e. with the normal force in the flanks of each gear pair Fn = 631 N. This force makes deformations of gear teeth in mesh with amplitude x0 = 0.674935·10-6 m. Using Eqs. (9), (13) and (14), and the measured result of gear vibrations, the following gear parameters were calculated: response constant A = 5.92848·10-5 seconds, and product Af presents vibration response caused by gear teeth impact. In resonant conditions vibration response is increased by (1+T) = (1+6.5) = 7.5 times. Dimensionless damping coefficient is = 0.078 and damping coefficient in gear mesh b = 1.61·10-5 Ns/m.

4 CALCULATED AND MEASURED RESULTS ANALYSIS By the measurement of the gear vibration in the super-critical mesh frequency range, the phenomenon of gear vibration increase is a proof.

Also, in this range natural free vibrations only are identified. After every teeth impact, gears vibrate

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Strojniški vestnik - Journal of Mechanical Engineering 56(2010)10, 653-662

with natural frequencies and these are restorable free vibrations. With teeth mesh frequency the absorbed disturbance power and the level of natural vibrations are increased. By measured vibration analysis, the nature of gear vibrations in the super-critical mesh frequency range is identified. An additional phenomenon in the form of supercritical resonance is recognised.

Following the nature of gear vibrations, a specific mathematical model is established, using the singular system theory. The model of restorable free vibrations consists of two parts; a continuous and transient one. Both of them present the gear vibrations as natural free vibrations with natural frequencies fni . The teeth mesh frequency f is the parameter which corresponds to disturbance energy absorption by repeatable impacts. The teeth impact force is, in this way, included in both parts of the mathematical model. The results of the continuous part of the mathematical model follow the increasing trend of total vibrations.

The results of the transient part follow variations of the total level of gear vibrations caused by resonances.

The main objective of specific mathematical modelling i.e. a synthesis of the measured vibrations is to present the vibrations by following the nature of experimental results.

The next objective is to identify the relation between the absorbed disturbance energy and the realised energy by natural free vibration (vibration power). For this purpose, it was necessary to identify damping parameters which include the inside energy dissipation and the outside energy dissipation in contact (elastic deformations, frictions, etc.). Using identified parameters for a calculation of gear vibrations, the calculated results are equal to those measured.

The line of the calculated results (Fig. 9) follows the main resonance but not the other smaller resonances. By the presented mathematical model, it is possible to satisfy secondary resonances and cover the measured results much better.

vibrations caused by teeth impact. After every impact the free vibrations with natural frequency are restored. The level of these vibrations increases with an increase in teeth mesh frequency f which increases teeth impact intensity.

A mathematical model is developed to simulate excitation process caused by teeth impacts and to synthesize the measured results of gear vibrations. According to the singular systems theory, gear meshing is presented in the form of a continual and transient process. The continual process is presented by a continual part of the model using algebraic equation. The transient process which includes resonances, is presented by transfer function of the single mass model of the tested gear system.

Using the measured results and the developed mathematical model, a few key facts are analyzed. Restorable free vibrations are proportional to teeth impact intensity and increase with enlargement of the teeth mesh frequency. In the resonant range the system response additionally magnifies free vibration level with natural frequency. The quantity of the impact disturbance energy which is released by gear vibration is defined by the value of constant A. Damping of gear free vibrations is presented by dimensionless coefficient . Numerical values of both of these parameters are calculated.

The presented approach explains gear vibrations in the supercritical teeth mesh frequency range and this explanation is based on the modal structure of the mechanical system. In this frequency range the structure is not stable.

For some teeth mesh frequencies those main natural frequencies separate into a number of new ones, while for others they unify. When natural frequencies separate, the level of free vibrations decreases and for the unified it increases. This explains the phenomenon called “supercritical resonance”.

5 CONCLUSIONS

This work is a contribution to the Ministry of Science and Technological Development of Serbia funded projects TR 14052 and TR 14033.

By measurement, frequency analysis, mathematical modelling and calculation, the main hypothesis about gear vibrations nature has been confirmed. In the range of supercritical teeth mesh frequency (f > fn), those are restorable free

6 AKNOWLEDGEMENT

Gear Vibrations in Supercritical Mesh-Frequency Range Caused by Teeth Impacts

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Winter, H., Gerber, H., Muller, R. (1989).

Investigations on the excitation of vibration and noise at spur and helical gears.

Proceedings of the Power Transmission and Gears, Chicago, vol. 2, p. 765-772.

Knabel, W. (1977). Noise and vibration of gear transmissions. Doctoral dissertation, Technical University of München. (in German) Höhn, B.R. (2002) Modern gear calculation.

Proceedings of the International conference on gears, München, vol.1, p. 23-43.

Cai, Y. (1995). Simulation on the rotational vibration of helical gears in consideration of the tooth separation phenomenon (A new stiffness function of helical involute tooth pair. ASME -Journal of Mechanical Design, vol. 117, p. 460-468.

Huang, K.J., Liu, T.S. (2000). Dynamic analysis of a spur gear by the dynamic stiffness method. Journal of Sound and Vibration, vol. 234, p. 311-329.

Tamminana, V.K., Kahraman, A., Vijayakar, S. (2007). A study of the relationship between the dynamic forces and the dynamic transmission error of spur gear pairs. ASME Journal of Mechanical Design, vol. 129, p.

75-84.

Vaishia, M., Singh, R. (2003). Strategies for modelling friction in gear dynamics. ASME Journal of Mechanical Design, vol. 125, p.

383-393.

He, S., Gunda, R., Singh, R. (2007).

Inclusion of sliding friction in contact dynamics model for helical gears. ASME Journal of Mechanical Design, vol. 129, p.

48-57.

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Verdmar, L., Andersson, A. (2003). A method to determine dynamic loads on spur gear teeth and on bearings. Journal of Sound and Vibration. vol. 267, p. 1065-1084.

Parker, R.G., Vijayakar, S.M., Imajo, T.B. (2000). Non-linear dynamic response of a spur gear pair: modelling and experimental comparisons. Journal of Sound and Vibration, vol. 237, p. 435-455.

Vaishya, M., Singh, R. (2001). Sliding friction-inducted non-linearity and parametric effects in gear dynamics. Journal of Sound and Vibration, vol. 248, p. 671694.

Dimitrijevic, D., Nikolic-Stanojevic, V. (2007). Eigenfrequency analysis of spur gear pair with moving eccentric masses on the body of one of the gears. FME Transactuions, vol. 35, no. 3, p. 157-163.

Pavic, G. (2005). The role of damping on energy and power in vibrating systems.

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Sabot, J. (1999). Integrated vibroacoustic approach to compute and reduce gear transmissions noise. Proceedings of the International conference on Power transmission. Pairs, p. 2039-2050.

Debeljkovic, D., Owens, D. (1985). On practical stability of singular systems.

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Belšak, A., Flašker, J. (2008). Vibration analysis to determine the condition of gear units. Strojniški vestnik - Journal of Mechanical Engineering, vol. 54, no. 1, p.

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Strojniški vestnik - Journal of Mechanical Engineering 56(2010)10, 663-675 UDC 005.72: 005.74

Paper received: 17.03.2009 Paper accepted: 25.01.2010

Application of Group Technology in Complex Cluster Type Organizational Systems Slobodan Morača1,* - Miodrag Hadžistević1 - Igor Drstvenšek2 - Nikola Radaković 1 1 University of Novi Sad, Faculty of Technical Sciences, Serbia 2 University of Maribor, Faculty of Mechanical Engineering, Slovenia The aim of this research was to contribute to the development of structural design procedures of complex - cluster type organizational systems. Industrial clusters can help companies to improve their own market positions, effectiveness, productivity and product quality. Organization of the production process in a company is an extremely complex process itself, and when it is transferred to the cluster level, the result is a complex task which is difficult to solve. For that purpose, this paper analyses the conditions and possibilities that would enable those structures to adapt to changes in the surroundings flexibility and management adequacy of production and organizational structures - by lowering the degree of complexity.

For the time being, no simple models which would enable an increase of process effectiveness in complex organizational units like clusters have been developed. One of the possible solutions which would decrease the complexity of flows and increase process effectiveness within an industrial cluster is the application of Group approach. ©2010 Journal of Mechanical Engineering. All rights reserved.

Keywords: industrial clusters, group technology, planning, work cells, complexity, flexibility 0 INTRODUCTION Modern concepts of increasing the effectiveness of production are based on the processes of automation, the application of modern materials and IT technology. They significantly reduce production costs, increase productivity and reduce the need for labour.

However, despite the revolutionary application of modern technology, the end of the 20th century and the beginning of the 21st century is further characterized by increased mobility of investments and recession, which is visible in the most developed countries, where the modern technology is most applied. All that has resulted in a constant decrease of production, which directly caused a decrease of employment rate, an increase of company debt and reduced possibilities of investments in new development projects.

In a competitive environment success of an organization is a function of industry attractiveness, its relative position in the industry, and the activities (strategy) it undertakes to remain ahead of others ([1] and [2]). Mintzberg explained that strategy is an evolutionary and organic process which is unpredictable; [3] explained that core competence gives an

organization competitive capability and remains central to its strategy planning process. Small and medium organizations encounter different kinds of problems such as resource limitations (especially human and financial resources), and market information [4], they face competition within and between large organizations [5].

Analyses have showed that the reasons for these problems are not only the inability of companies or their production or service systems.

Changes occur apart from how a company is capable to independently decrease its production costs or to increase the range of products.

Changes often depend on other economic and non-economic entities, geo-political factors and changes on the global market.

Investments in development are limited, so companies mainly have to find their development paths on their own, as well as their positions on the global market. One of the important development strategies which also provides competitive development, especially of Small and Medium-sized Enterprises (SMEs) and Regions, is to associate and develop complex organizational structures – clusters and business networks. Large enterprises merge and become even larger, and the best example is automotive industry. Small companies can survive on the

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Corr. Author's Address: University of Novi Sad, Faculty of Technical Sciences, Trg Dositeja Obradovica 6, Novi Sad, Serbia, moraca@uns.ac.rs

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market only if they associate with each other into systems which simulate a large enterprise, but maintain their flexibility.

Although this form of associating provides a lot of advantages, which will be mentioned in the Chapter 1, there are also many problems in functioning of complex systems. One of these problems is how to organize and manage such complex systems and establish effective production process? In chapters 2 and 3, we will describe a group approach as a possible solution.

1 CLUSTER AS A FORM FOR COMPANIES TO ASSOCIATE Companies are constantly asked to improve performances in order to get the chance to maintain or to improve their own market positions and financial situation. Clusters have the possibility to develop their own specific mixture of competitive advantages which is created on the basis of locally-developed knowledge as a result of mutual relations, cultural heritage and local characteristics. This is evident in the focus on clusters as an important concept in understanding growth and in thinking about development policy [6].

The idea of localized economies of scale in geographic agglomerations has a long history in economics, going back to Adam Smith’s early observations of labour specialization and to [7] explanations of why companies continue to localize in the same areas. Clusters arise in the presence of Marshallian externalities, which signify that companies benefit from the production and innovation activities of neighbouring companies in the same and related industries. There is abundant evidence that such externalities exist and lead to industry-level agglomeration [8].

Development of clusters is an effective way to improve business operations and bring it to a higher level. Modern business is based on fast response, quality, flexibility, innovation, connections and building the critical mass of capital and production / service potential. This relatively new style of doing business requires a team approach on the local level - cluster approach.

Clusters represent complex organizational systems that are flexible and can quickly be adjusted to oscillatory changes at the sale and purchase markets, generate employment,

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help the diversification of economic activities and make a significant contribution to exports and trade. Clusters also play an important role in innovation and businesses where there is a need for application of modern technology. Thanks to their innovative flexibility, many of them become more productive and efficient than some large international corporations. In this process, emphasis should be put on creating a friendly business environment where the transformation of society towards a market economy shall take its place.

Cluster differs from other forms of associations within its geographical boundaries, involvement and utilization of funds, ways of exchange of products and partially finished products, information management - knowledge chains, and the importance of how they are connected. Clusters can be best understood and used as regional systems. According to Porter [9] they represent, "Geographic concentrations of mutually connected companies, specialized suppliers, service providers, companies from similar industries and institutions tied to them (i.e. universities, standardization agencies, trade unions), who compete, but also cooperate".

This paper focuses on the establishment of organizational and managerial mechanisms within a cluster, which will enable an increase of production processes' effectiveness to the level of a cluster as a whole. That is why one of more important segments is to determine the levels of specialization in companies – participants in a cluster, and what desirable levels of specialization for more effective business are in case of specialization or in other words, economic diversity. Research shows that traditional production sectors are inclined to do better business when densely concentrated in one geographical area. Contrary to this, newer, hightech and service sectors are more comfortable with economic diversity environment.

General opinion is that specialization means lack of economic diversity and vice versa.

If that is the case, then improving industrial clusters bears a risk of creating highly specialized local economies. If local economies are specialized in only one industrial sector or a couple of them, then they are indeed much more sensitive to cyclic falls in those sectors. However, other opinions suggest that specialization and diversification do not necessarily exclude each

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other. Malizia and Feser [10] define economic diversity as "existence of multiple specializations". This means that is possible for local economies to be highly specialized in certain sectors and, at the same time, to have sound combination of economic activities. So we come to the concept of flexible specialization, which represents the possibility of companies to do what they do best, and cluster has the obligation to provide optimal utilization of capacities.

The establishment of organizational and managerial structures in complex organizational systems like cluster represents a big challenge because of diversity of clusters and characteristics of member companies. One of the possible models whose application shall enable the optimal use of the potentials of clusters is Group approach which is described in more details in Chapter 2.

2 THE GROUP APPROACH IN DESIGNING MATERIAL FLOWS

process, which originated at the beginning of 20th century. It emerged as a single machine concept that was created to reduce setup times [12].

Group approach in the design flows of material in the production system based on the idea of group technology which, since the work of Mitrofanov [13], never stopped being up-to-date in scientific and expert circles.

This concept was further extended by collecting machine parts with similar requirements, completely processing them within a machine group or cell [14]. The ideas for Group approach came from the fact that there is similarity in objects which enter the production process of any company and that in real conditions there is a limited number of forms of these objects. In the core of Group technology set up by Mitrofanov is a unification of objects with similar characteristics into families.

Based on ideas of Group technology of Mitrofanov, as well as the results of the research made by Burbidge [11], the new approach in production was developed: Group approach to design of effective industrial structures.

The concept of Group Technology [11] is based on the simplification and standardization

Fig. 1. Working Unit (WU) â&#x20AC;&#x201C; the basic changes in approaches for production structures designing a)Individual Approach to Flows Designing; b) Group Approach to Flows Designing [15]

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of the program are made. At the same time, each part of the production program consists of previously shaped operational groups of mutually very similar objects.

Apart from work places for production, as shown in Fig. 2, other resources join the composition of a working unit (technological preparation, operational preparation, distribution of materials and tools, process QA, operational maintenance), which gives independent (autonomous) unit – a part of production process which is fully capable to produce one separate component of production program. This approach in designing material flows in a production system provides a range of advantages, including the following most important ones:  significant simplification of material flows – with shorter transport paths,  simplified production management (each working unit is managed independently),  production related problems, management, quality control, maintenance, etc, are located in much smaller parts of the production processes – work units.

Using this approach, based on a classification of objects within the production process, groups of geometrically and technologically similar objects are created – operational groups (families), which represent the basis for Group approach in the planning of production technology. However, matters have been taken further here, by merging individual operational groups which have mutually similar technologies (using the same work places) into larger groups. By assigning all the necessary work places into a created large group, we create a so called working unit (production cell, work cell), capable for the production of all objects.

Working Unit has all the characteristics of Production Cell but besides its executive (production) independence it has to have an organizational and controlling independence too, which means its total responsibility for quantity, quality, and delivery terms of similar working objects, and also for organizing and managing of processes [15]. The final result is, as shown in Fig. 1 that the entire production program is divided in parts of the program - a group of objects, and the whole production system into independent operating units in which some parts

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Presented Group approach in designing material flows has been applied in a large number of companies and described in details in [16] and [17], and the process of clustering and the formation of business units has been supported by a computer program system APOPS-08 [18].

The major advantages of Group technology have been reported in literature as reduction in setup time, reduction in throughput time, reduction in work-in-process inventories, and reduction in material handling costs, better quality and production control, increment in flexibility, etc., [19], [20] and [21].

3 ADVANTAGES OF THE APPLICATION OF GROUP APPROACH IN CLUSTER ORGANIZATIONS Productivity and productivity growth determine prosperity. Innovation is a key driver of productivity growth. Clustering supports both productivity and innovation. Porter's Diamond theory provides a useful concept that can help businesses, government and other institutions to explore improvements in the productivity environment. Various models and solutions have been extensively studied in literature. These models can be divided into the following categories:  Integration of production planning at the level of industrial clusters.  Integration of production planning at the level of companies within the industrial cluster.  Integration of production planning and distribution on the spot of procurement of raw materials, transport and distribution of semi or finished products to customers.

The aim of this paper is to present the application of the Group approach as a model of optimization of planning and programming production processes in complex organizational structures like clusters. The application of group technology in cluster produces savings and benefits in almost every area of the business:  It combines tasks, equipment, gages, tooling and schedules into larger groups of similar elements for similar solutions.  Purchasing can group similar parts and achieve quantity discounts. For non-standard purchased parts, grouping helps suppliers achieve savings and reduce price.

 Accounting in industrial cluster is simpler in a group technology - costs are collected by cell and family rather than individual part.

Cluster production program can be diversified and composed of all products which are made by the member companies. Disparity in regional economic development is strongly influenced by the proportion of trade, local industries, resources and mix of organizations present in the cluster [22]. Participating companies can enter a cluster with only one part of their production program, and produce or distribute other products on their own, or in cooperation with companies which are not in their cluster. It is necessary to define basic products which are offered by a cluster, and adjustments of organizational and managerial cluster structures is done in regard to these products. Production program is further divided into structures and sub- structures, where individual requests towards cluster companies are defined for processing and assembling. Possibilities for process control and the shortening of production cycle depend on organization of a cluster.

Organization of the production process in a company is extremely complex process itself, and when we transfer it to the cluster level, we get a complex task which is difficult to solve. For the time being, there are no simple models developed which would enable an increase of process effectiveness in a complex organizational units like clusters. In that regard, this paper makes a pioneering attempt. One of the possible solutions which would decrease the complexity of flows and increase process effectiveness within a cluster is application of Group approach.

By applying a Group approach in complex cluster type organizational systems, the role of work units from the Fig. 2 is replaced by cluster member companies, as shown in Fig. 3.

Previously, we stated that one of the significant characteristics of clusters is flexible specialization of companies for processing and assembling of structures and sub- structures from cluster production program. It enables the processing of structures and sub- structures with minimum costs and minimum time required.

In accordance with the Group approach the parts for processing are grouped according to two criteria: similarity of parts and potential of production system.

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Fig. 3. Production realization within a cluster in accordance with the Group approach Application of the Group Technology on complex Cluster type organizational systems represents a new approach in creating effective production systems. Given approach is based on concepts of flexible specialization and Working Units with extended flexibility. Flexible specialization, as one of the basic advantages of Clusters, provides companies in Cluster to work on what they do best, for what they have trained labor force or technical-technological capacities, and still to have enough volume of work.

Companies, Cluster members, considered from the aspect of flexible specialization represent Working Units of extended flexibility.

Having in mind that Companies participating in a Cluster can choose which part of the Cluster production program or production capacity they will be part of, then the same applies for branches of the Companies as well.

Application of the Group Technology covers many issues. On the basis of the Analyses of the methods applied in designing technological procedures and designing the organization of

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work processes in Clusters on the territories of Serbia, Croatia, Slovenia and Italy, there have been determined the basic processes of Application of Group Approach on the level of an Industrial Cluster:  Harmonizing a common Cluster production program.  Classification of objects of work: o Adjusting the Systems of Classifications of objects of work according to the increase of performances of technicaltechnological systems of Work Units with extended flexibility, o Defining the Systems of Classifications of companies participating in Clusters and companies cooperating with a Cluster from the aspect of performances of technical-technological systems, organizational and managerial structures, o Defining correlations between the above mentioned Systems of Classifications.

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Adjusting organizational and managerial structures of Clusters and member companies which will provide both, a more efficient information flow amongst the companies in a Cluster and an increased quality in controlling working processes.

3.1 Harmonizing a Production Programe

Common

3.2 Classification of Objects of Work Production program of a Cluster can comprise a huge number of different elements assembles, subassemblies or parts (Fig. 4a).

These elements can differ in regard to shape, material, technical-technological specifics etc.

Also, these elements are an integral part of different products which can be produced in different companies. For each of the individual elements produced in a Cluster, it is necessary to define the technological procedure starting from geometrical and technological characteristics of an element which, in case of a huge number of elements, requires a considerable waste of time.

The Group approach has in its basis the procedure of grouping of objects according to their similarities. In order, from non-homogenous group of elements (Fig. 4a), to make a homogenous group of elements (Fig. 4b), it is necessary to have the existence of Unique System for Classification which is applied on the level of the whole Cluster. When the homogenous groups of elements are generated, then designing technological procedure for a Group is carried out.

Cluster

Companies in a Cluster have to harmonize which products, assembles, subassemblies and parts are important on the Cluster level from the aspect of requests coming from the environment and from the aspect of companies participating in producing them. In that way, two basic goals are accomplished: directing activities towards fulfilling customer demands and creating the synergy effect amongst the companies participating in the production. Research carried out in the period 2007 to 2009 by the Center for Competitiveness and Cluster Development both individually and also participating in GIFIP1, and UNIDO projects supporting development of the Cluster AC Serbia, demonstrate that without the existence of the above mentioned elements it is very difficult to accomplish effective functioning of Clusters.

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Finally designing individual technological procedures including utilizing the defined technological procedure for a Group as the starting point.

It is essential that due to similarities of elements in a Group, there are existing technological procedures covering the whole Group which reduces the waste of time in regard to individually defined technologies.

Modification of an application of the Group approach in a Cluster also lies in the fact that the process of designing a Group technology is placed on the Cluster level - which significantly relieves resources of participating companies and decreasing the costs.

In practice, a series of more or less similar systems of classification have been developed.

All developed systems provide gradual classification in terms of identifying classes, families and groups - types of parts with similar characteristics and specific measurement areas.

Defining operational groups at the clusters level brings certain limitations in the implementation of classification systems. Classification system KSIIS-08* developed for the needs of the industrial systems of geometrically shaped products, basically includes characteristics related to design operational groups in a relatively simple way. The structure of the system is schematically shown in Fig. 5.

Depending on the combination of technical-technological systems of companies, it is later chosen which company will process which group of selected parts including specific operations.

General characteristics of the above mentioned Classification system are the following:  classification label has 14 areas - features (1 to 14),  each feature has 10 fields (0 to 9),  each field has a specific meaning.

Classification System KS-IIS-08*, shown in Fig. 5, represents the modification of the System which has been developed and utilized at the Faculty of Technical Sciences in many projects related to Application of Group Approaches for individual companies. Having in mind that homogenous groups of elements are created in regard to Working Units with extended flexibility – the degree of decomposition of Classification System is being kept on a lower level of details which simplifies the process of classification. It is also important to classify companies, or branches of companies, from the following aspects: type of industry, technicaltechnological potential, the degree of automation and organizational and managerial structures.

In order to reach the optimal choice of companies, in other words, the effective distribution of homogenous groups of objects of work amongst the companies, the following matrix shown in Fig. 6 is used. On its basis a comparison is done, comparing companies’ capabilities and technological requirements of a group of elements. In that way, the problem of participating companies having similar technicaltechnological potentials is being solved.

Fig. 5. Structure of the Classification system 670

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Fig. 6. Uses a matrix of part numbers and machine numbers to group families The result of the above mentioned activities is demonstrated with decrease of system complexity (Fig. 7), creation of simplified and more effective information flows and creation of the basis for development of effective and efficient organizational and managerial structure of a Cluster. In Fig. 7, the expected result of the Application of Group Technology on the Cluster level is shown. Companies in the Cluster are marked with the characters of Alphabet, and flows of material and information are shown with the lines. Each group of products has its flow, which is defined on the Cluster level which enables easier control and consideration of possible critical points and possibilities for improvement. On the other hand, each innovation implies small changes in the layout of such arranged processing structures of Clusters.

The process of Adjusting organizational and managerial structures of Clusters and member companies is the next phase which shall provide utilization of established processing structures of Clusters.

4 PROGRAMMING AND PLANNING OF PRODUCTION IN CLUSTER In order to achieve balanced utilizations of capacities, companies would have to submit their

production plans and engagement of their systems in advance, e.g. by utilizing IT technologies, and on the basis of these plans to make detailed termplans at the cluster level. Any change of termplan is recorded and must be available to all participating enterprises.

Many intersections in the system, diversity of procedures mutually connected with connections of different degrees of strength, courses and directions and a lot of feedback connections, hamper the process of managing to the great extent. Directed control procedures, in the case of artificial (man-made) systems, have basically mandatory character which provides designed system operations. However, in the case of natural systems, management procedures based on the homeostasis self-regulating principle, have a natural character and maintain a managed variable on the necessary level in the significantly narrower boundaries of tolerance fields and in significantly longer duration period.

Special environmental requirements, disorders in the work processes, delivery delays, organizational deficiencies and other similar influences condition the need for further settings of operational plans at the time of their performance. Since the above mentioned phenomena are constant in time, the need for settings of operational plans is constant in time

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too. Only a full harmonization of working elements of the operational plans execution system - working processes – provides anticipated effects. Here is an illustration of what this concept means: We suppose that firms M, N, U are cooperating in the cluster. Firm M supplies (row materials and components) from firms N and U, and firm U supplies from firm N. If we want to apply a group approach, it is considered

that every firm has developed a management production system and that at the beginning of making an operating plan for the next period has a correct time schedule for all the processes in a firm. Plan of processes can be illustrated through matrix (firm M) or through Gantt chart (firms N and U). See Fig. 8. Deviations of the results of given phenomena leads also to deviations of designed effects.

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Group flows h

Fig. 7. Simplified network of flows at the cluster level The basic problems which condition the need for planning in the most of the production system are reduced to the following elements:  maintenance of delivery deadlines,  control of the level of unfinished production,

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 minimization of waiting lines,  optimization of the sequence of inputs of orders in the working process,  harmonization of the work load (capacity),

Morača, S. - Hadžistević, M. - Drstvenšek, I. - Radaković, N.

Strojniški vestnik - Journal of Mechanical Engineering 56(2010)10, 663-675

 elimination (minimization) of the time in the state of cancellation by providing integrated system support,  maintenance of a balanced relationship between the continuity of flow in the system and the cost of supplies (materials, participants, energy, money).

From the above mentioned, it is clear that data processing and information design about the system status in a specific cross-section, must be done continuously and in real-time in order to have the working process adjusted before entering the next cross-section of the system when needed.

In this sense, there is no use to plan the status for the next day on the basis of the data from the previous week. Information about the status of the cross-section "i" must be the basis for planning the cross-section "i +1". The process must be carried out in real-time – therefore, at the end of

the operation that generates the status "i" it is necessary to design the status "i +1".

Knowing that with the hierarchy access there is practically no feedback connection between the system programming and system planning, the decisions made by system programming - operating plan (part of the production program stipulating the structure and the quantity that will be produced in the upcoming, accurately specified period of time) is not affecting decisions made in the planning stage, but is limiting them. Therefore, it becomes difficult to carry out the production plan taking into account the precise program for hierarchy systems.

It is necessary to make the integration of programming and planning systems for the sake of global optimization of processes in order to have industrial clusters functioning as one entity.

Production plan of Firm M N

Production plan of Firm N

V 4 5 6 7 8 9 10 11 12 13 14 15 16 C P S N P U S C P

17

S N P U S

18 19

C

10r

Q

x

U

N P U S

C P

S N P

9

x 1,3 1

xxx

xxx xx x

xx x 10

14

M

20 21 22 23 24 25 26 27 28 29

P S

x x x 7 7 5

x x x

3,5

x xx xx x

x

7

3,5

xx xx x

xx x

x x

xx x

x x x

1

xx x

S

x xx xx x

x

1.4

Group flows 2

Production plan of Firm U Fig. 8. Integration of production plans

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Strojniški vestnik - Journal of Mechanical Engineering 56(2010)10, 663-675

The model of simultaneous planning and programming for more periods was suggested by Birewar and Grossmann [23], where programming decisions are built on the level of planning. It has been shown that planned profit increases significantly when planning and programming decisions are optimized simultaneously. The bad side of this approach is that the model of planning and monitoring is restricted to the specific category of simple problems because it requires an extremely large number of binary variables needed to solve the problems of integrated planning and programming.

simultaneously because each company is assigned a task to develop a part of a product for which it is specialized. Thus, the development of shorter duration and an increased number of different combinations available for utilization is achieved.

6 REFERENCES [1] [2] [3]

5 CONCLUSIONS Group technology adoption helps small organizations to acquire process competence and better process control.

Investment in measurement and testing equipment leads to long term advantages. They can manufacture high precision products and get price advantage on these value added products as they grow through forward integration [24]. With this approach, a number of structural elements and a variety of relations between them are the basic parameters which define the complexity degree of organizational structure and simultaneously determine the complexity of cluster information flows. Therefore, the complexity degree of organizational structure determined upon those parameters enables a comparison of the designed structure variants using the quality defined as control adequacy. With process expertise they can also develop many new products and cater for the international market [25].

The system defined in this way enables high-performance production, and provides optimal use of capacities and great flexibility of the entire system. Such systems enable the production in small series with very low costs.

Since there is a large number of small and medium-sized enterprises, any changes in processing, shaping or any changes of material are solved within a few enterprises either by replacement or purchase of a small number of machines or by including some companies with the required technology in the cluster. By doing so, a very fast reaction to any disorder or any changes is achieved. This means that the development processes are carried out

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International Journal of Production Economics, vol. 76, no. 1, p. 27-38.

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Birewar, D.B., Grossman, I.E. (1990).

Simultaneous Synthesis, Sizing, and Scheduling of Multiproduct Batch Plants.

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Swann, P., Prevezer, M. (1996). A comparison of the dynamics of industrial clustering in computing and biotechnology.

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Porter, M. (1998). Clusters versus industrial policy. On Competition, HBS Press.

Swamidass, P.M., Newell, W.T. (1987).

Manufacturing strategy, environmental uncertainty and performance: a path analytic model. Management Science, vol. 33, p. 509524.

Boynton, A.C., Victor, B. (1991). Beyond Flexibility: Building and Managing the Dynamically Stable Organization. California Management Review, vol. 34, no. 1, p. 5366.

Broekhuizen, T.L.J., Alsem, K.J. (2002).

Success Factors for Mass Customization: A Conceptual Model. Journal of MarketFocused Management, vol. 5, no. 4, p. 309330.

Hauser, D.P., de Weck, O.L. (2007).

Flexibility in component manufacturing systems: evaluation framework and case study. Journal of Intelligent Manufacturing, vol. 18, no. 3, p. 421-432.

Zelenovic, D., Cosic, I., Maksimovic, R. (1998). Design and Reenginering of Production Systems: Yugoslavian (IISE) Approaches. vol. 16 in: Group Technology and Cellular Manufacturing - State-of-theArt Synthesis of Research and Practice, Kluwer Academic Publishers, Massachusetts, p. 517-537.

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Strojniški vestnik - Journal of Mechanical Engineering 56(2010)10, 676-677 Instructions for Authors

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Pro literatur Verlag, Mammendorf, p. 553-576.

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Strojniški vestnik - Journal of Mechanical Engineering 56(2010)10 Vsebina

Vsebina Strojniški vestnik - Journal of Mechanical Engineering letnik 56, (2010), številka 10 Ljubljana, oktober 2010 ISSN 0039-2480 Izhaja mesečno

Povzetki člankov Jure Čas, Gregor Škorc, Riko Šafarič: Napredno mikropozicioniranje 2 DOF mizice z uporabo nevronskih mrež za kompenzacijo nelinearnosti proge Mahmoud Shariati, Mehdi Sedighi, Jafar Saemi, Hamid Reza Allahbakhsh: Numerična in eksperimentalna analiza uklona cilindričnih panelov, izpostavljenih tlačnim aksialnim obremenitvam Andreas Gleiter, Christian Spießberger, Gerd Busse: Zaprta termografija z optičnim ali ultrazvočnim vzbujanjem George Bourkas, Emilios Sideridis, Christos Younis, Ioannis N. Prassianakis*, Victor Kitopoulos: Trdnost in deformacije pri porušitvi po modelu (1) popolne in (2) nizke kakovosti adhezije za sistem smola/polnilo Tadeja Primožič Merkač, Bojan Ačko: Kalibracija navojnih obročev za uporabo v industriji Cuneyt Fetvaci: Simulacija izdelave evolventnih čelnih zobnikov z rezalnimi zobniki Milosav Ognjanović, Fathi Agemi: Vibracije zobnikov v nadkritičnem frekvenčnem območju vprijema zaradi udarcev zobnikov Slobodan Morača, Miodrag Hadžistević, Igor Drstvenšek, Nikola Radaković: Uporaba skupinske tehnologije v sestavljenih sistemih grozdov

SI 129 SI 130 SI 131 SI 132 SI 133 SI 134 SI 135 SI 136

Navodila avtorjem

SI 137

Osebne vesti Življenje in delo prof. dr. Jožeta Puharja Jubilej ob 70-letnici prof. dr. Alojza Križmana Doktorati, magisteriji, specializacija in diplome

SI 139 SI 140 SI 141

Strojniški vestnik - Journal of Mechanical Engineering 56(2010)10, SI 129 UDK 004.032.26:681.5

Prejeto: 07.12.2009 Sprejeto: 01.10.2010

Napredno mikropozicioniranje 2 DOF mizice z uporabo nevronskih mrež za kompenzacijo nelinearnosti proge 1

Jure Čas1,* - Gregor Škorc2 - Riko Šafarič1 Univerza v Mariboru, Fakulteta za elektrotehniko, računalništvo in informatiko, Slovenija 2 RESISTEC UPR d.o.o. & Co. k.d., Slovenija

Članek opisuje sistem za mikropozicioniranje 2 DOF mehanizma s piezoelektričnimi aktuatorji (PEA), ki ga imenujemo tudi piezo-aktuirana mizica (PAM). PAM je izdelana s procesom fotostrukturiranja iz fotosenzitivnega stekla. Vgrajeni piezoelektrični aktuatorji zagotavljajo njeno natančno gibanje. PAM je splošno namenska 2 DOF mizica, ki se v odvisnosti od izbranega končnega efektorja lahko uporabi za različne namene pri mikropozicioniranju in mikro-manipulaciji. Zaprto-zančni sistem za mikro-pozicioniranje oziroma položajno vodenje poleg same PAM vsebuje še druge komponente kot so visokonapetostni ojačevalniki, inkrementalni položajni senzorji in kontrolno-procesno enota. Zaradi nelinearnosti proge položajno vodenje PAM z uporabo klasičnega PI regulatorja ne daje zadovoljivih rezultatov. Upoštevajoč nelinearnosti proge se za njihovo kompenzacijo pri položajnem vodenju uporabljajo usmerjene nevronske mreže. Po končanem postopku učenja nevronskih mrež z algoritmom vzvratnega razširjanja, se tako naučeni inverzni model proge uporabi kot komponenta (pred-krmilnik) predlagane metode položajnega vodenja. Glede na eksperimentalne rezultate je očitno, da kompenzacija nelinearnosti proge z nevronskimi mrežami v kombinaciji s PI regulatorjem izboljša rezultate položajnega vodenja PAM v primerjavi s tradicionalnim PI regulatorjem. ©2010 Strojniški vestnik. Vse pravice pridržane.

Ključne besede: piezoelektrični mehanizem, položajno vodenje, histereze, usmerjene nevronske mreže

Slika 1. Princip delovanja PAM (tlorisni pogled)

*

Naslov odgovornega avtorja: Univerza v Mariboru, Fakulteta za elektrotehniko, računalništvo in informatiko, Smetanova ulica 17, 2000 Maribor, Slovenija, jure.cas@uni-mb.si

SI 129

Strojniški vestnik - Journal of Mechanical Engineering 56(2010)10, SI 130 UDK 669.14:539.4

Paper received: 19.03.2010 Paper accepted: 15.07.2010

Numerična in eksperimentalna analiza uklona cilindričnih panelov, izpostavljenih tlačnim aksialnim obremenitvam Mahmoud Shariati - Mehdi Sedighi* - Jafar Saemi –Hamid Reza Allahbakhsh Tehnična univerza Shahrood, Iran V članku je predstavljena eksperimentalna in numerična raziskava vpliva dolžine, kota delnega kroga in raznih robnih pogojev na uklonsko obremenitev in obnašanje po uklonu za valjaste panele iz jekla CK20. Eksperimentalni preizkusi so bili opravljeni s servohidravličnim strojem INSTRON 8802, numerična analiza pa je bila izvedena s paketom Abaqus za analize po metodi končnih elementov.

Numerični rezultati se dobro ujemajo z rezultati eksperimentalnih preizkusov. ©2010. Strojniški vestnik. Vse pravice pridržane.

Ključne besede: cilindrični paneli, elastično in plastično obnašanje, analiza uklona, jeklo CK20

Slika 13. Oblika deformiranega panela (θ = 355°, L = 150 mm, enostavna podpora): a) eksperimentalno določena, b) numerično določena

SI 130

Naslov odgovornega avtorja: Shahroud university of technology, Shahrood, I.R. IRAN, msedighi47@gmail.com

Strojniški vestnik - Journal of Mechanical Engineering 56(2010)10, SI 131 UDK 544.344.016.2

Prejeto: 22.08.2009 Sprejeto: 04.03.2010

Zaprta termografija z optičnim ali ultrazvočnim vzbujanjem Andreas Gleiter - Christian Spießberger - Gerd Busse* Univerza v Stuttgartu, Inštitut za tehnologijo polimerov, Nemčija Termografija je uveljavljena metoda za neporušne preiskave, ki daje posnetke temperaturne porazdelitve. Modulacija temperaturnega polja na površini preizkušanca s periodičnim dovodom toplote od zunaj ali od znotraj omogoča ugotavljanje časovne odvisnosti temperaturnega polja, ki daje informacije o termičnih značilnostih, skritih pod površino. S Fourierjevo transformacijo lahko te informacije strnemo v fazni in amplitudni posnetek. Fazni posnetki so robustnejši od amplitudnih posnetkov, saj učinkovito pridušijo tako značilnosti na površini kot odboje.

Pri vzbujanju z ultrazvokom je mehanizem segrevanja lokalna pretvorba elastične energije v toploto, do katere pride zaradi lokalnih tornih izgub, npr. pri relativnem gibanju ploskev ob razpoki.

Nedotaknjen material in meje so pri takem posnetku pridušene in napake so selektivno izpostavljene.

Tehnike in aplikacije so predstavljene na primeru različnih komponent iz industrije. ©2010 Strojniški vestnik. Vse pravice pridržane.

Ključne besede: optična zaprta termografija, ultrazvočna zaprta termografija, selektivno slikanje napak

a)

b)

Slika 8. a) ULT amplitudni posnetek pri 0,2 Hz razkrije razpoke v zobniku; b) fotografija preizkušanca

*Naslov avtorja za dopisovanje: Univerza v Stuttgartu, Inštitut za tehnologijo polimerov, Pfaffenwaldring 32, D-70569 Stuttgart, Nemčija, gerd.busse@ikt.uni-stuttgart.de

SI 131

Strojniški vestnik - Journal of Mechanical Engineering 56(2010)10, SI 132 UDK 539.61

Prejeto: 20.08.2009 Sprejeto: 19.07.2010

Trdnost in deformacije pri porušitvi po modelu (1) popolne in (2) nizke kakovosti adhezije za sistem smola/polnilo George Bourkas, Emilios Sideridis, Christos Younis, Ioannis N. Prassianakis*, Victor Kitopoulos Fakulteta za uporabno matematiko in fiziko Oddelek za mehaniko, Laboratorij za preizkušanje in materiale, Nacionalna tehniška univerza v Atenah – kampus Zografou, Grčija Za primer adhezije med vezivom in polnilom je bila ovrednotena natezna trdnost in deformacije pri porušitvi kompozitnih materialov z delci. Za reprezentančna prostorninska elementa sta bila uporabljena dva modela, vsak sestavljen iz treh komponent na osnovi sestava kocka-v-kocki. Na podlagi primerjave izpeljanih teoretičnih rezultatov za trdnost ter eksperimentalnih podatkov za obdelane in neobdelane delce v sistemih smola/polnilo je prvi model mogoče okarakterizirati za primer popolne kakovosti adhezije med vezivom in polnilom, drugi model pa za primer nizke kakovosti adhezije. Trdnost, ki jo napoveduje prvi model, je podobna trdnosti obdelanih delcev, ki ustrezajo visoki trdnosti. Ta model ustreza zgornji meji trdnosti pri modelih kocka-v-kocki. Trdnost, ki jo napoveduje drugi model, je blizu trdnosti neobdelanih delcev, ki ustrezajo nizki trdnosti, vendar ta model ne ustreza spodnji meji trdnosti.

Za primerjavo so bili uporabljeni sistemi kompozitnih materialov z delci sestave smola/steklo, smola/železo in smola/SiC. V primeru, da obstaja adhezija med vezivom in polnilom, se trdnost in deformacije pri porušitvi, ki jih napovedujejo modeli, ujemajo z vrednostmi, ki jih najdemo v literaturi za obstoječe metode vrednotenja. ©2010 Strojniški vestnik. Vse pravice pridržane.

Ključne besede: sistemi smola/polnilo, mikrostruktura, deformacije pri porušitvi, popolna kakovost adhezije, nizka kakovost adhezije

Slika 2: Dva modela kocke-v-kocki, sestavljena iz treh komponent (a) Paulov model [7], (b) Ishai-Cohenov model [8]

132

*Naslov odgovornega avtorja: Nacionalna tehniška univerza v Atenah – kampus Zografou, Fakulteta za uporabno matematiko in fiziko, Oddelek za mehaniko, Atene, Grčija, GR – 15773, prasian@central.ntua.gr

Strojniški vestnik - Journal of Mechanical Engineering 56 (2010)10, SI 133 UDK 621.7.08:621.99

Prejeto: 23.02.2010 Sprejeto: 30.06.2010

Kalibracija navojnih obročev za uporabo v industriji Tadeja Primožič Merkač1,* - Bojan Ačko2 1 KAKO, d.o.o., Slovenija 2 Fakulteta za strojništvo, Univerza v Mariboru, Slovenija Za kalibracijo navojnih obročev sta najpogosteje uporabljeni dve metodi, katerih merilna negotovost je dokaj različna. Metoda mehanskega tipanja z dvema kroglicama se večinoma uporablja na enoosnih merilnih strojih ter koordinatnih merilnih napravah. Metoda izračunavanja srednjega premera navojnega obroča s tehniko prilagajanja (po metodi najmanjših kvadratov) pa se uporablja na profilnem skenerju.

Zahtevane tolerance, ki so za nastavitvene in laboratorijske navojne obroče zelo ozke (tako da je lahko pri metodi mehanskega tipanja z dvema kroglicama merilna negotovost previsoka) in pa slaba kvaliteta nekaterih kontrolnih obročev v industriji narekujeta izbiro metode, ki pa je veliki meri odvisna tudi od zmožnosti laboratorija za izvedbe določene metode.

Meritve srednjega premera navojnega obroča, ki so rdeča nit tega članka so bile vključene v mednarodno interkomaparacijo, katere predmet je bil isti navojni obroč, kot je omenjen v tem članku. © 2010 Strojniški vestnik. Vse pravice pridržane.

Ključne bedede: navojni obroč, kalibracija, korak navoja, merilna negotovost, dimenzijske meritve

Slika 3. Kalibracija navojnega obroča na koordinatnem merilnem stroju

*

Naslov odgovornega avtorja: KAKO, d.o.o., Kotlje 36, 2394 Kotlje, Slovenija, tadeja.primozic@ka-ko.si

SI 133

Strojniški vestnik - Journal of Mechanical Engineering 56(2010)10, SI 134 UDK 621.833.1:004.94

Prejeto: 07.04.2010 Sprejeto: 04.08.2010

Simulacija izdelave evolventnih čelnih zobnikov z rezalnimi zobniki Cuneyt Fetvaci * Univerza v Istanbulu, Oddelek za strojništvo, Turčija V članku je obravnavan rezalni zobnik v obliki pastorka kot orodje za izdelavo zobnikov. V skladu s teorijo zobnikov je podan matematični model čelnih zobnikov z asimetričnimi evolventnimi zobmi.

Delovne in ustvarjene površine so opisane na podlagi enačb profila rezalnega zobnika, principa transformacije koordinat, teorije diferencialne gemoetrije in teorije zobnikov. Obravnavana je tudi ovojnica trohoide, ki jo rezalni zobnik opiše med postopkom obdelave. Trohoide rezalnega zobnika so odvisne od vrste zaokrožitve konice. Na osnovi danega modela so bili izdelani računalniški grafikoni evolventnih čelnih zobnikov, prikazana pa je tudi simulacija izdelave. Simulacija poti gibanja rezalnega zobnika omogoča določitev geometrije odrezkov za nadaljnjo analizo. Rezultati te raziskave bodo uporabni pri konstruiranju in izdelavi čelnih zobnikov. ©2010 Strojniški vestnik. Vse pravice pridržane.

Ključne besede: asimetrično evolventno ozobje, konstruiranje zobnikov, rezalni zobnik, simulacija izdelave, čelni zobniki, zaokrožitev trohoide

rezalni zobnik

izdelani zobnik

Slika 2. Kinematična zveza med rezalnim in izdelanim zobnikom

SI 134

*Naslov odgovornega avtorja: Univerza v Istanbulu, Oddelek za strojništvo, Avcilar Kampusu TR-34320, Istanbul, Turčija, fetvacic@istanbul.edu.tr

Strojniški vestnik - Journal of Mechanical Engineering 56(2010)10, SI 135 UDK 534.1:621.83

Prejeto: 18.11.2008 Sprejeto: 23.06.2010

Vibracije zobnikov v nadkritičnem frekvenčnem območju vprijema zaradi udarcev zobnikov 1

Milosav Ognjanović1,* - Fathi Agemi2 Univerza v Beogradu, Fakulteta za strojništvo, Srbija 2 Razvojno-raziskovalni center, Libija

Ob udarcih zob prihaja do naravnih prostih vibracij, ki v kratkem času izzvenijo. Udarci zob se ponavljajo s frekvenco zob, ki pridejo v vprijem, zato se tudi vibracije obnavljajo s frekvenco vprijema zob. V podkritičnem frekvenčnem območju vprijema zob so te naravne proste vibracije krite z vsiljenimi vibracijami, ki jih povzročajo fluktuacije deformacij zob. V nadkritičnem frekvenčnem območju vprijema pa v frekvenčnem spektru vibracij sistema ozobja prevladujejo obnovljive proste vibracije. Te obnovljive proste vibracije so vzrok za povečanje celotne ravni vibracij ob povečevanju vrtilne hitrosti. Modalna struktura (naravna frekvenca) sistema zobnikov v tem frekvenčnem območju ni stabilna in vpliva na pojav nadkritičnih resonanc. Opravljene so bile meritve vibracij zobnikov in frekvenčna analiza (analiza FFT) pri zelo visokih vrtilnih hitrostih zobnikov do 40.000 vrt./min. Določen je bil matematični model za sintezo rezultatov eksperimenta. V ta namen je bila uporabljena teorija singularnih sistemov. Vprijemanje zobnikov je obravnavano kot singularen sistem s kontinuiranim procesom prenosa obremenitve in singularnostmi, ki jih povzročajo udarci zob. S pomočjo razvitega matematičnega modela so bili določeni koeficienti dušenja in slabljenje energije. ©2010 Strojniški vestnik. Vse pravice pridržane Ključne besede: zobniki, vibracije, singularni sistem, frekvenčni spekter

vrt./min.

Slika 1. Primerjava izmerjene in izračunane ravni vibracij zobnikov [2]

*Naslov odgovornega avtorja: Univerza v Beogradu, Fakulteta za strojništvo, Kraljice Marije 16, 11120 Beograd, Srbija, mognjanovic@mas.bg.ac.rs

SI 135

Strojniški vestnik - Journal of Mechanical Engineering 56(2010)10, SI 136 UDK 005.72: 005.74

Prejeto: 17.03.2009 Sprejeto: 25.01.2010

Uporaba skupinske tehnologije v sestavljenih sistemih grozdov Slobodan Morača1,* - Miodrag Hadžistević1 - Igor Drstvenšek2 - Nikola Radaković 1 1 Univerza v Novem Sadu, Fakulteta za tehniske vede, Srbija 2 Univerza v Mariboru, Fakulteta za strojnistvo, Slovenija Cilj te raziskave je prispevek k prizadevanjem za razvoj postopkov strukturiranega načrtovanja kompleksnih grozdnih organizacijskih sistemov. Industrijski grozdi pomagajo podjetjem k boljšemu položaju na trgu, večji učinkovitosti, produktivnosti in boljši kakovosti izdelkov. Organizacija proizvodnje je zelo zapleten proces že v samem podjetju, če pa nalogo prestavimo na nivo grozda, dobimo še bolj zapleten in težko rešljiv problem. V ta namen v prispevku analiziramo pogoje in možnosti, ki bi omogočale takšnim strukturam prilagajanje spremembam v okolju – s prilagodljivostjo in ustreznim vodenjem proizvodnih in organizacijskih struktur – z zmanjšanjem stopnje kompleksnosti.

Trenutno ni na voljo razvitih preprostih modelov, ki bi omogočali povečanje učinkovitosti procesov v kompleksnih organizacijski sistemih, kot so industrijski grozdi. Ena izmed možnosti za zmanjšanje kompleksnosti pretokov in povečanje učinkovitosti procesov v industrijskem grozdu je uporaba skupinskega pristopa. © 2010 Strojniški vestnik. Vse pravice pridržane.

Ključne besede: Industrijski grozdi, skupinska tehnologija, načrtovanje, delovne celice, kompleksnost, prilagodljivost

Izvršilni odbor

Revizijski odbor

Pisarna grozda Podjetje B

Podjetje A

Podjetje E Podjetje C

Podjetje H

Podjetje F

Podjetje D

Podjetje G

Plastični izdelki PROIZVODNI

Izdajatelj orodij

Vstop materiala

Rotacijski izdelki Ozobljeni izdelki

Preddelavec Načrtovalec

Prizmatični izdelki

Pločevinasti izdelki

Podjetje – član grozda Izhod izdelkov Nadzor kakvosti

Operativno vzdrževanje

PROGRAM

Slika 5. Proizvodnja v grozdu, v skladu s skupinskim pristopom *

SI 136

Naslov odgovornega avtorja: Univerza v Novem Sadu, Fakulteta za tehniške vede, Trg Dositeja Obradovica 6, Novi Sad, Srbija, moraca@uns.ac.rs

Strojniški vestnik - Journal of Mechanical Engineering 56(2010)10, SI 137-138 Navodila avtorjem

Navodila avtorjem Navodila so v celoti na voljo v rubriki "Informacija za avtorje" na spletni strani revije: http://en.sv-jme.eu/ Članke pošljite na naslov: Univerza v Ljubljani Fakulteta za strojništvo SV-JME 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.

V spremnem dopisu navedite podatke o predhodnem ali hkratnem predlaganju članka v objavo drugje. Prosimo, da članku določite tudi tipologijo – opredelite ga lahko kot izvirni, pregledni ali kratki članek. Navedite vse potrebne kontaktne podatke (poštni naslov in email) in predlagajte vsaj dva potencialna recenzenta.

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. ms-1, 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.

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]

SI 137

Strojniški vestnik - Journal of Mechanical Engineering 56(2010)10, SI 137-138

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. Navajamo primere: Članki iz revij: Priimek 1, začetnica imena, priimek 2, začetnica imena (leto). Naslov. Ime revije, letnik, številka, strani.

[1] Zadnik, Ž., Karakašič, M., Kljajin, M., Duhovnik, J. (2009).

Function and Functionality in the Conceptual Design Process. Strojniški vestnik – Journal of Mechanical Engineering, vol. 55, no. 7-8, p.

455-471.

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 revije 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. (Editors), 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 Industry. MOTSP 2009 Conference Proceedings, p. 422-427.

Standardi: Standard (leto). Naslov. Ustanova. Kraj.

SI 138

[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.

Rockwell Automation.

Arena, from http://www.arenasimulation.com, accessed on 200909-27.

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 Avtorji vseh sprejetih prispevkov morajo za objavo plačati prispevek v višini 180,00 EUR (za članek dolžine do 6 strani) ali 220,00 EUR (za članek dolžine do 10 strani) ter 20,00 EUR za vsako dodatno stran. Dodatni strošek za barvni tisk znaša 90,00 EUR na stran.

Strojniški vestnik - Journal of Mechanical Engineering 56(2010)10, SI 139-145 Osebne vesti

Življenje in delo prof. dr. Jožeta Puharja

Po hudi in dolgotrajni bolezni je 22. septembra 2010 zaključil svojo življenjsko pot prof. dr. Jože Puhar.

Prištevamo ga med soustvarjalce slovenske avtomobilske industrije, ki je nastala po drugi svetovni vojni iz nekdanje okupatorjeve tovarne letalskih motorjev v Mariboru ter soustvarjalec slovenskih industrijsko tehnoloških obdelovalnih procesov in slovenske tehnične besede.

Rojen je bil leta 1926 v Majšperku. Nižjo klasično gimnazijo je končal z odliko v Mariboru zaradi okupacije šele leta 1946, med vojno pa je bil zaposlen kot vajenec kovinarske stroke v nemški tovarni letalskih motorjev, predhodnici TAM-a. V tem času se je izučil za rezkarja, mojstrski izpit za orodjarja in izpit za strojnega tehnika pa je opravil leta 1951.

Leta 1951 je postal konstruktor vpenjalnih naprav in merilih orodij, znanje tega zahtevnega tehničnega področja je s študijem neprekinjeno dopolnjeval ter zato postal vodja tega oddelka. Prof. dr. Puhar je imel prirojen čut za točnost pri delu in natančnost meritev, to pa je osnova, brez katere ni uspešne industrijske proizvodnje.

Na obeh področjih, pri vpenjanju obdelovancev in tehnologiji merjena izdelkov, je bil prof. dr. Puhar izjemno uspešen. Znal je usposobiti krog sodelavcev, zato ga smemo prištevati med soustvarjalce uspešne TAM-ove industrijske proizvodnje motorjev in kamionov.

Pomembna prelomnica v razvoju TAM-a je bila leta 1957 sklenjena licenčna pogodba z zahodno nemško družbo Klöckner-Humbolt-Deutz za proizvodnjo tovornjakov.

Takrat so v TAM-u začeli osvajati 30% delež domačih delov avtomobila, med drugim tudi zahtevne zobniške menjalnike. Po ustanovitvi Instituta za motorje in motorna vozila TAM je leta 1962 prof. dr. Puhar postal projektant zobniških prenosnikov. Na osnovi poznavanja teoretičnih osnov, tehnologije izdelave, meritev in zahtevnih toleranc ter vztrajnim in trdim delom je to nalogo izvršil zelo uspešno. Trud je bil poplačan še z osvojitvijo zahtevne proizvodnje menjalnikov v tovarni TAM. Nemci tega niso pričakovali ter so šele na osnovi dokazov začeli verjeti v sposobnost TAM-ovih delavcev.

Iz pridobljenega znanja in izkušenj je dr. Puhar v Strojniškem vestniku objavil več člankov iz teorije in

tehnologije izdelave zobnikov, neprecenljiv je njegov terminološki prispevek s področja zobnikov, ki ga je objavil v knjigi »Evolventne zobniške dvojice«.

Kot vodja oddelka je občutil pomanjkanje kakovostnih delavcev, zato se je s svojim znanjem vključil v pedagoško delo. Od 1953 do 1963 je na Mojstrski šoli ter na TSŠ v Mariboru honorarno poučeval strojniške predmete: risanje, strojne elemente, teorijo odrezovanja in odrezovalne stroje; je avtor tudi skript za risanje in za strojne elemente.

Prof. dr. Puhar je bil v 60-tih letih prejšnjega stoletja poznan širši strokovni javnosti, kot vrhunski strokovnjak, zato ga je profesor Kraut leta 1966 povabil, da je na Fakulteti za strojništvo Univerze v Ljubljani prevzel vodstvo Inštituta za strojništvo. Leta 1977 je bil izvoljen za profesorja višje šole za področja obdelovalne tehnike, teorije odrezovanja in tehnoloških meritev ter leta 1982 za izrednega profesorja. Pedagoško delo je nadgradil z učbeniki: »Tehnologija odrezovanja I in II«, »Mehanska tehnologija« in »Tehnološke meritve I in II«. Pomembno področje njegove aktivnosti je bilo delovanje v uredništvu Strojniškega vestnika. Bil je 12 let pomočnik glavnega urednika SV prof. dr. h. c. Bojana Krauta, v letih od 1985 do 1993 pa je bil glavni in odgovorni urednik, ko mi je bilo delo zaupano v razmeroma težkih okoliščinah. Sledilo je obsežno delo novih, popravljenih in dopolnjenih slovenskih izdaj Krautovega Strojniškega priročnika. Tako je izšla leta 1994 enajsta, 1997 dvanajsta, 2001 trinajsta in leta 2003 štirinajsta izdaja. Strojniški priročnik obsega približno 700 strani, vsebuje bistvena strojniška poglavja ter predstavlja za vse strojnike od srednješolcev do akademikov priročnik, v katerem so zbrani podatki za vsakodnevno rabo. To dokazujejo številne in pogosto razprodane izdaje; je pa priročnik tudi uporaben, če se komu izneveri spomin.

Prof. dr. Puhar je leta 1983 postal član Tehniške terminološke komisije za slovenski jezik Inštituta Frana Ramovša pri Slovenski akademiji znanosti in umetnosti.

Kot na področju tehnike, tako tudi na področju strojništva terminologija sledi razvoju. Prof. dr. Puhar je imel smisel za oblikovanje izvirnih slovenskih tehničnih terminov, tako, da se je z izgovorjeno ali pisano besedo izrazilo tisto, kar termin dejansko pomeni. Sodeloval je pri številnih znanstvenih srečanjih in je pogosto objavljal prispevke v javnih glasilih o problemih oblikovanja novih tehničnih izrazov. Ko je bolezen ustavila njegovo delo, je v terminološki komisiji ostala za njim velika praznina.

Prof. dr. Jože Puhar spada med pomembne slovenske tehnologe in med tiste strojne inženirje, ki so veliko prispevali k razvoju slovenske strojne industrije.

Njegovo pedagoško delo je temeljilo na znanju in praktičnih izkušnjah, kar je lastnost dobrega in uspešnega visokošolskega profesorja.

V spominu nam bo ostal kot zaveden Slovenec, predan strojništvu in lepi slovenski besedi.

Osebne vesti

Prof. dr. Jože Hlebanja

SI 139

Strojniški vestnik - Journal of Mechanical Engineering 56(2010)10, SI 139-145 Osebne vesti

Jubilej ob 70-letnici prof. dr. Alojza Križmana

V letošnjem letu je 24. maja svoj 70. življenjski jubilej praznoval red. prof. dr. Alojz Križman, častni član Društva livarjev Slovenije, kakor tudi glavni in odgovorni urednik Livarskega vestnika, ki ga izdaja Društvo livarjev Slovenije in predsednik programskega odbora vsakoletnega mednarodnega Livarskega posvetovanja.

Rojen je bil v Križevcih pri Ljutomeru.

Osnovno šolo in klasično gimnazijo je obiskoval v Mariboru. Leta 1965 je diplomiral na Fakulteti za naravoslovje in tehnologijo Univerze v Ljubljani z diplomskim delom: Strukturne in mehanske lastnosti kontinuirano ulitih palic iz bakrovih zlitin. Kot strokovnjak s področja materialov in strojništva se je leta 1964 zaposlil v gospodarstvu v podjetju Mariborska livarna Maribor sprva kot razvojni inženir, nato pa kot vodja razvoja tehnologije. V podjetju je deloval na področju razvoja tehnologije in investicijske izgradnje in kot vodja razvoja tehnologije veliko prispeval k takratnemu hitremu vzponu MLM. Že od leta 1968 naprej je deloval tudi honorarno na takratni Višji tehniški šoli kot asistent za področje gradiva. Na osnovi uspešnih industrijskih projektov in izvedenih del mu je bil na Univerzi v Leobenu (Avstrija) dovoljen neposreden doktorski študij. Leta 1980 je na tej univerzi doktoriral z delom "Die Fertigung von Rohrluppen im horizontalen Strangguß für die Herstellung von Kondensatorrohren aus Cu-Zn-Legierungen".

Na Univerzi v Mariboru se je redno zaposlil leta 1976. Deloval je kot profesor in raziskovalec, pri čemer njegovo znanstveno in strokovno delo obsega področje neželeznih kovinskih gradiv in livarstva. V naziv rednega profesorja za predmetno

SI 140

področje Gradiva in predmet Industrijski inženiring je bil habilitiran leta 1989. Od leta 1979 do 1983 je bil predstojnik VTO Strojništvo, od leta 1983 do 1987 dekan Tehniške fakultete Maribor in od leta 1987 do 1993 rektor Univerze v Mariboru. Od leta 1979 je bil predstojnik Laboratorija za raziskavo materialov in od 1980 predstojnik Katedre za materiale. Ustanovil je Inštitut za tehnologijo materialov, katerega predstojnik je bil 10 let. Ob koncu rednega delovanja na univerzi je ustanovil še Univerzitetni center za elektronsko mikroskopijo.

Univerza v Mariboru mu je leta 1991 podelila najvišje priznanje za delo: Zlato plaketo univerze in leta 2000 naziv Častni senator Univerze v Mariboru.

Tudi Mesto Maribor mu je za prispevek k uveljavitvi Maribora na področju univerzitetnega izobraževanja in znanosti leta 1992 podelilo najvišje priznanje mesta: Zlati grb mesta Maribor.

Leta 1988 je postal član Odbora za varstvo človekovih pravic. Bil je med ustanovitelji Slovenske demokratske zveze, ustanovitelj in predsednik Liste za Maribor in predsednik stranke Zveza neodvisnih Slovenije. Na prvih županskih volitvah v samostojni Sloveniji je leta 1994 postal župan Univerzitetnega mesta Maribor, od leta 1998 do leta 2006 pa je deloval kot član mestnega sveta.

Od leta 2002 do 2007 je bil član Državnega sveta Republike Slovenije. Od leta 1994 naprej je predsednik najstarejšega slovenskega športnega društva, MŠD Branik in od leta 2006 naprej častni predsednik Zveze mariborskih športnih društev Branik. Je vodja projekta izgradnje največjega urbanega športnega centra v Sloveniji, Športnega parka Ljudski vrt v Mariboru. 0d leta 2009 je predsednik Športne zveze Maribor. Alojz Križman je dobitnik številnih javnih priznanj, med njimi državne nagrade sklada Borisa Kidriča za raziskovalne dosežke.

Njegova bibliografija obsega 654 enot, od tega 74 izvirnih znanstvenih člankov, 96 objavljenih strokovno-znanstvenih prispevkov na konferencah, 22 idejno/izvedbenih projektov – projektna dokumentacija, 2 patenta, 4 mentorstva pri doktorskih disertacijah, 3 mentorstva pri magistrskih delih, 38 mentorstev pri diplomskih delih, 2 komentorstva pri doktorskih disertacijah, 8 komentorstev pri magistrskih delih, 35 komentorstev pri diplomskih delih idr. Prof.dr. Križman ima 103 normiranih citatov.

Osebne vesti

Fakulteta za strojništvo Univerze v Mariboru

Strojniški vestnik - Journal of Mechanical Engineering 56(2010)10, SI 139-145 Osebne vesti

Doktorati, magisterij in diplome DOKTORATI

SPECIALISTIČNO DELO

Na Fakulteti za strojništvo Univerze v Ljubljani je z uspehom obranil svojo doktorsko disertacijo: dne 20. septembra 2010 Mihael DEBEVEC z naslovom: "Modeliranje strege orodij pri obdelavi v digitalnem okolju" (mentor: doc. dr. Niko Herakovič, somentor: prof. dr.

Marko Starbek); Proizvodni proces spremljajo tudi izgube, ki se kažejo predvsem v povezavi s proizvodnimi časi obdelav, strege in montaže, za kar je povečini vzrok nerazpoložljivost sredstev. Zato je dandanes v majhnih in večjih podjetjih nujno stalno izboljševanje proizvodnega procesa vnaprej, torej še pred dejansko izvedbo v praksi in sicer z vnaprejšnjim odkrivanjem ter odpravljanjem napak in motenj, ki lahko povzročijo zastoje v proizvodnem procesu.

Orodja za optimizacijo, ki so razpoložljiva na trgu, imajo ponavadi previsoko ceno, da bi jih manjša podjetja s posamičnim obsegom proizvodnje in visokotehnološkimi izdelki lahko vključila v svoje proizvodne procese. Zato smo v okviru doktorske naloge razvili nov koncept, ki bi ob uporabi standardnega simulacijskega orodja omogočal vnaprejšnje preverjanje proizvodnega plana. Bistveno vodilo je cenovna dostopnost uporabljenih orodij za majhna in srednje velika podjetja ter upoštevanje prisotnosti proizvodnih sredstev za vsako operacijo. Nerazpoložljivost sredstev je namreč najpogostejši vzrok za zastoje v proizvodnem procesu. Novi koncept, ki je predstavljen v doktorski nalogi, upošteva prisotnost vseh zahtevanih sredstev za uspešno izvedbo posamezne operacije. Na podlagi tega koncepta smo v standardnem simulacijskem orodju vzpostavili virtualno tovarno, ki omogoča izvajanje virtualnega proizvodnega procesa.

Model virtualne tovarne smo oblikovali tako, da se le-ta na podlagi terminskega plana oblikuje za vsako posamezno operacijo. Po uspešno opravljeni verifikaciji, ki dokazuje primerljivost rezultatov virtualne tovarne z rezultati realne proizvodnje in zato njeno uporabnost v praksi, smo na različnih primerih prikazali možnosti optimizacije, ki jih je z uporabo virtualne tovarne mogoče izvajati.

Na Fakulteti za strojništvo Univerze v Ljubljani je z uspehom zagovarjal svoje specialistično delo: dne 27. septembra 2010 Simon KROTEC z naslovom: »Numerično modeliranje vstopnega trakta SAXO turbine« (mentor: prof. dr. Brane Širok). * Na Fakulteti za strojništvo Univerze v Mariboru je z uspehom zagovarjal svoje specialistično delo: dne 30. septembra 2010 Milan SKERBIŠ z naslovom: "Posodobitev montažnega sistema za sestavo relejev" (mentor: izr. prof. dr. Miran Brezočnik).

DIPLOMIRALI SO Na Fakulteti za strojništvo Univerze v Ljubljani so pridobili naziv univerzitetni diplomirani inženir strojništva: dne 29. septembra 2010: Jaka Kokot z naslovom: »Analiza toka vrednosti - korak v vitki proizvodnji« (mentor: prof. dr. Marko Starbek, somentor: doc. dr. Janez Kušar); Rok Lacko z naslovom: »Testni laboratorij za sočasno proizvodnjo toplote in električne energije z gorivnimi celicami« (mentor: izr. prof. dr. Mihael Sekavčnik); Sandi Matjašič z naslovom: »Fino planiranje layouta podjetja ter delovnih mest z uporabo Schmigallove metode« (mentor: doc. dr.

Janez Kušar, somentor: prof. dr. Marko Starbek); Peter Zakšek z naslovom: »Koncentrirani solarni stirlingov sistem z uporabo toplotne cevi« (mentor: prof. dr. Iztok Golobič); Tadej Dobrun z naslovom: »Razvoj naprave za geometrijsko kontrolo ulitkov« (mentor: prof. dr. Alojzij Sluga); Jaka Kuzmanić z naslovom: »Aerodinamske karakteristike melaminskih odprtoceličnih struktur« (mentor: prof. dr. Branko Širok, somentor: prof. dr. Janez Diaci); Aljoša Počkaj z naslovom: »Brezdotična kontrola mer pedala sklopke« (mentor: prof. dr.

Janez Diaci);

Osebne vesti

SI 141

Strojniški vestnik - Journal of Mechanical Engineering 56(2010)10, SI 138-145

Uroš Vrbajnščak z naslovom: »Mehatronski sklop za premikanje filtrirnega traku v etalometru« (mentor: prof. dr. Janez Diaci); dne 4. oktobra 2010: Dejan Grubar z naslovom: »Kvalitativna analiza konstrukcijskih rešitev sponke čelade« (mentor: prof. dr. Boris Štok, somentor: doc. dr.

Nikolaj Mole); Jernej Habe z naslovom: »Razvoj in krmiljenje robota SCARA z dvema prostostnima stopnjama« (mentor: doc. dr. Niko Herakovič); Matija Nemanič z naslovom: »Zasnova merilnega protokola in analiza rezultatov merjenja sile trenja krmilnega bata pnevmatičnega potnega ventila« (mentor: doc. dr.

Niko Herakovič); * Na Fakulteti za strojništvo Univerze v Mariboru so pridobili naziv univerzitetni diplomirani inženir strojništva: dne 1. septembra 2010: Primož Kocutar z naslovom: »Klasičen Couettov tok z viskozno disipacijo in spremenljivimi lastnostmi tekočine« (mentor: prof. dr. Leopold Škerget, somentor: doc. dr. Jure Ravnik); Rok Kopun z naslovom: »Numerični izračun toka v vstopnem delu Peltonove turbine« (mentor: prof. dr. Leopold Škerget); dne 8. septembra 2010: Marko Hrelja z naslovom: »Uporaba robotov za obdelave z odvzemanjem materiala« (mentor: izr. prof. dr. Miran Brezočnik, somentor: prof. dr. Franci Čuš); dne 16. septembra 2010: Sašo Berić z naslovom: »Numerična analiza vplivnih faktorjev emisijskih modelov v dizelskem motorju« (mentor: prof. dr. Matjaž Hriberšek, somentorica: prof. dr. Breda Kegl ); Bojan Hebar z naslovom: »Konstrukcija delovne ploščadi« (mentor: prof. dr. Iztok Potrč, somentor: doc. dr. Janez Kramberger); Matjaž Oštir z naslovom: »Vodenje nelinearnega mehanizma z metodami mehkega računanja« (mentor: izr. prof. dr. Karl Gotlih); Uroš Jeke z naslovom: »Analiza vpliva tokovnih razmer na zmanjševanje koncentracije plinov v laboratorijskem digestoriju« (mentor: prof. dr. Matjaž Hriberšek);

SI 142

Tomaž Kocijančič z naslovom: »Upravljanje vhodnih zalog materiala v podjetju Impol FT d.o.o.« (mentor: prof. dr. Vojko Potočan); Darko Milanović z naslovom: »Zagotavljanje kakovosti in sistem zagotavljanja sledljivosti v proizvodnem procesu« (mentor: izr. prof. dr. Bojan Ačko); Uroš Pešaković z naslovom: »Parametrično modeliranje in numerična analiza orodja za izsekovanje rondelic« (mentor: doc. dr.

Miran Ulbin, somentor: izr. prof. dr. Ivan Pahole); Iztok Stopeinig z naslovom: »Konstrukcijska in tehnološka preureditev skladiščenja aluminijastih kolutov« (mentor: prof. dr. Iztok Potrč, somentor: doc. dr. Miran Ulbin); dne 20. septembra 2010: Marjan Bukšek z naslovom: »Določitev vrtilnega mehanizma mobilnega žerjava« (mentor: prof. dr. Iztok Potrč, somentor: doc. dr.

Tone Lerher); Matjaž Bukšek z naslovom: »Določitev nagibnega mehanizma mobilnega žerjava« (mentor: prof. dr. Iztok Potrč, somentor: doc. dr.

Tone Lerher); Jani Dobaj z naslovom: »Analiza skladiščnega poslovanja Distribucijskega centra Tobačna, d.d. (mentor: prof. dr. Iztok Potrč, somentor: doc. dr. Tone Lerher); Jure Štrekelj z naslovom: »Načrtovanje linijske montaže v podjetju Arcont, d.d.« (mentor: prof. dr. Iztok Potrč, somentor: doc. dr. Tone Lerher); Niko Vrečič z naslovom: »Preračun dvižnega mehanizma mobilnega žerjava« (mentor: prof. dr. Iztok Potrč, somentor: doc. dr.

Tone Lerher); dne 23. septembra 2010: Maja Berložnik z naslovom: »Načrtovanje tehnološkega procesa izdelave avtomata za avtomatske klešče v podjetju Serpa d.o.o.« (mentor: izr. prof. dr. Borut Buchmeister, somentor: doc. dr. Iztok Palčič); Klemen Gajšek z naslovom: »Računalniško programiranje in modeliranje delovnega stroja« (mentor: prof. dr. Jože Balič, somentor: doc. dr. Marjan Leber); David Javornik z naslovom: »Analiza procesa vodenja proizvodnje v Gorenju, d.d., Kuhalni aparati« (mentor: izr. prof. dr. Borut Buchmeister, somentor: doc. dr. Iztok Palčič);

Osebne vesti

Strojniški vestnik - Journal of Mechanical Engineering 56(2010)10, SI 138-145

Mitja Matjaž z naslovom: »Programiranje CNC strojev« (mentor: prof. dr. Jože Balič); Marta Pliberšek z naslovom: »Fizikalno modeliranje Wanklovega motorja« (mentor: izr. prof. dr. Bojan Dolšak, somentorica: Urška Sancin); Danijel Pogorevc z naslovom: »Optimizacija razvrščanja nalogov v proizvodnji po naročilu« (mentor: izr. prof. dr. Borut Buchmeister, somentor: doc. dr. Iztok Palčič); Nika Sajko z naslovom: »Uporaba tehnoloških simulacij v CAD/CAM procesih« (mentor: prof. dr. Jože Balič, somentor: doc. dr.

Mirko Ficko); Andrej Turičnik z naslovom: »Programiranje izdelave orodij na CNC strojih« (mentor: prof. dr. Jože Balič); David Verdel z naslovom: »Zagon proizvodnje vakuumsko-izolacijskih panelov v podjetju Turna d.o.o.« (mentorja: prof. dr. Duško Uršič, izr. prof. dr. Borut Buchmeister); Martin Werdonig z naslovom: »Zasnova in preračun pogona sledilnika sonca z velikim aksialnim krogličnim ležajem« (mentor: prof. dr.

Srečko Glodež, somentor: doc. dr. Janez Kramberger); dne 30. septembra 2010: Lea Barton z naslovom: »Fizikalno modeliranje elektrarne na valovanje« (mentor: izr. prof. dr. Bojan Dolšak, somentorica: Urška Sancin); Nejc Cvörnjek z naslovom: »Inovativen pristop za izboljšanje proizvodnega procesa s pomočjo evolucijskih metod« (mentor: izr. prof. dr. Miran Brezočnik); Primož Černič z naslovom: »Sodobno računalniško podprto programiranje CNC strojev v orodjarstvu« (mentor: prof. dr. Jože Balič); Matej Čontala z naslovom: »Simulacija prezračevanja bazena z računalniško dinamiko tekočin« (mentor: doc. dr. Matjaž Ramšak, somentor: prof. dr. Matjaž Hriberšek); Jernej Ferjanc z naslovom: »Optimiranje energetskih instalacij v Splošni bolnišnici Celje« (mentor: prof. dr. Andrej Predin); Matej Golavšek z naslovom: »Prehod na uporabo umetnih mas kot strateška odločitev podjetja« (mentor: izr. prof. dr. Borut Buchmeister); Tomaž Hodnik z naslovom: »Merilne naprave in postopki za merjenje oblikovnih odstopanj« (mentor: izr. prof. dr. Bojan Ačko);

Nejc Kamnik z naslovom: »Izdelava orodja za brizganje umetnih mas za izdelek sifon« (mentor: prof. dr. Duško Uršič); Rok Karažinec z naslovom: »Izdelava individualizirane drobne notranje opreme in dodatkov z inoviranjem dodajalnih tehnologij« (mentor: izr. prof. dr. Igor Drstvenšek); Marko Kavzar z naslovom: »Pregled inovativnih nekonvecionalnih izdelovalnih postopkov v proizvodnji« (mentor: izr. prof. dr.

Miran Brezočnik); Nika Kopše z naslovom: »Inovativnost v procesu razvoja izdelkov« (mentor: doc. dr.

Marjan Leber); Primož Krajnc z naslovom: »Montaža z roboti« (mentor: izr. prof. dr. Miran Brezočnik, somentor: Simon Brezovnik); Matic Kreča z naslovom: »Primerjava sotočnega in protitočnega načina delovanja uplinjevalne naprave« (mentor: prof. dr. Niko Samec); Emilija Mateja Lakičević z naslovom: »Vrednostna analiza kot integralni del razvoja izdelka Invisimax« (mentor: doc. dr. Iztok Palčič); Goran Lušo z naslovom: »Postavitev sončne elektrarne v podjetju Unior Zreče d.d.« (mentor: izr. prof. dr. Aleš Hribernik); Andrej Orel z naslovom: »Priprava energetske izkaznice stavbe« (mentor: izr. prof. dr. Aleš Hribernik, somentor: doc. dr. Matjaž Ramšak); Matej Ozim z naslovom: »Poslovni načrt postavitve bioplinarne na območju ormoške občine« (mentor: prof. dr. Niko Samec); Mario Pešić z naslovom: »Konstruiranje paketa pravokotnih torzijskih vzmeti« (mentor: prof. dr. Nenad Gubeljak, somentor: doc. dr.

Jožef Predan); Rok Pišek z naslovom: »Projekt avtomatizacije ekstrudirne linije PVC-ja z vstavitvijo magnetnih trakov« (mentor: izr. prof. dr. Borut Buchmeister); Boštjan Pišotek z naslovom: »Pregled gorivno celičnih energetskih sistemov in primer 20MW-GC postroja« (mentor: prof. dr. Andrej Predin); Jure Planinc z naslovom: »Preoblikovanje pločevine iz jekla s povišano trdnostjo« (mentor: izr. prof. dr. Ivan Pahole, somentor: doc. dr.

Mirko Ficko);

Osebne vesti

SI 143

Strojniški vestnik - Journal of Mechanical Engineering 56(2010)10, SI 138-145

Robi Pogorevc z naslovom: »Optimizacija konstrukcije nosilca bobna pralnega stroja s pomočjo računalniških simulacij« (mentor: prof. dr. Zoran Ren, somentor: izr. prof. dr. Marko Kegl); Simon Studenčnik z naslovom: »Individualno prilagojena "ergo" pisarna« (mentor: prof. dr. Andrej Polajnar, somentor: izr. prof. dr. Vojmir Pogačar); Gregor Umek z naslovom: »Sistemi računalniško podprtega načrtovanja in vodenja proizvodnje« (mentor: izr. prof. dr. Borut Buchmeister, somentor: doc. dr. Iztok Palčič); * Na Fakulteti za strojništvo Univerze v Ljubljani so pridobili naziv diplomirani inženir strojništva: dne 2. septembra 2010: Sandi Kojić z naslovom: »Predpisi o letenju v zračnem prostoru severnega Atlantika« (mentor: viš. pred. mag. Aleksander Čičerov, somentor: doc. dr. Tadej Kosel); Tomaž Majdič z naslovom: »Program "CRM" za usposabljanje pilotov helikopterja« (mentor: pred. mag. Primož Škufca, somentor: doc. dr. Tadej Kosel); Dane Resnik z naslovom: »Trdnostni preračun okvirne plošče tlačnega orodja z MKE« (mentor: prof. dr. Boris Štokk, somentor: doc. dr.

Nikolaj Mole); Gašper Sedej z naslovom: »Uvedba vitke proizvodnje z uporabo analize toka vrednosti« (mentor: doc. dr. Janez Kušar, somentor: prof. dr.

Marko Starbek); Gregor Zupančič z naslovom: »Razvoj namenske gradbene žage« (mentor: prof. dr.

Marko Nagode); dne 7. septembra 2010: Sani Ćejvanović z naslovom: »Konstrukcija naprave za sprotno spremljanje stanja olja« (mentor: prof. dr. Jožef Vižintin); Aleš Jevnik z naslovom: »Orbitalno varjenje cevi iz nerjavnega jekla« (mentor: prof. dr. Janez Tušek); Igor Merhar z naslovom: »Projektno vodenje osvajanja izdelka« (mentor: doc. dr.

Janez Kušar, somentor: prof. dr. Marko Starbek); Anton Smrekar z naslovom: »Analiza naprave za učenje obločnega varjenja« (mentor: prof. dr. Janez Tušek);

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dne 8. septembra 2010: Uroš Braz z naslovom: »Varjenje z gnetenjem aluminijevih zlitin za litje s čistim aluminijem« (mentor: prof. dr. Janez Tušek, somentor: doc. dr. Damjan Klobčar); Igor Frlic z naslovom: »Vpliv vlage na izdelke iz termoplastov« (mentor: izr. prof. dr.

Ivan Bajsić); Matej Kleva z naslovom: »Razvoj daljinsko vodene snemalne naprave« (mentor: prof. dr. Marko Nagode); Janez Sternad z naslovom: »Razvoj preizkuševališča za testiranje učinkov termičnega utrujanja« (mentor: izr. prof. dr. Ivan Bajsić); Peter Žugelj z naslovom: »Lasersko točkovno varjenje bakra z nerjavnim jeklom« (mentor: prof. dr. Janez Tušek); dne 9. septembra 2010: Rok Bajec z naslovom: »Kontrola nosilnosti brezstrojničnega električnega osebnega dvigala« (mentor: doc. dr. Jernej Klemenc, somentor: prof. dr. Matija Fajdiga); Miha Benčan z naslovom: »Samopostavljiv stolpni žerjav« (mentor: doc. dr.

Boris Jerman); Primož Grkman z naslovom: »Določitev upora različnim aerodinamičnim oblikam« (mentor: doc. dr. Tadej Kosel); Blaž Strmec z naslovom: »Mikro soproizvodni sistemi za dvig energijske učinkovitosti stavb« (mentor: prof. dr. Vincenc Butala); Gregor Šömen z naslovom: »Tehničnoekonomska analiza ogrevanja stanovanjskega objekta s toplotno črpalko« (mentor: prof. dr.

Alojz Poredoš); dne 10. septembra 2010: Jernej Faganel z naslovom: »Preoblikovalne lastnosti toplotno utrjenih jekel« (mentor: izr. prof. dr. Zlatko Kampuš, somentor: doc. dr. Tomaž Pepelnjak); Gregor Humar z naslovom: »Varjenje z gnetenjem aluminija za preoblikovanje« (mentor: prof. dr. Janez Tušek, somentor: doc. dr. Damjan Klobčar); Jure Janežič z naslovom: »Izdelava orodja za preoblikovanje pločevine z uporabo postopka« (mentor: prof. dr. Janez Kopač); Tomaž Pegam z naslovom: »Montaža in balansiranje rotorjev elektromotorjev« (mentor: prof. dr. Janez Kopač, somentor: doc. dr. Peter Krajnik);

Osebne vesti

Strojniški vestnik - Journal of Mechanical Engineering 56(2010)10, SI 138-145

* Na Fakulteti za strojništvo Univerze v Mariboru so pridobili naziv diplomirani inženir strojništva: dne 16. septembra 2010: Miha Cvörnjek z naslovom: »Trdnostna analiza sklopa bagerskih rok« (mentor: doc. dr.

Janez Kramberger); Marko Mešiček z naslovom: »Manipulator steklenih polizdelkov« (mentor: prof. dr. Iztok Potrč, somentor: doc. dr. Tone Lerher); Aleš Vršič z naslovom: »Optimiranje proizvodnje s pomočjo 5s metode« (mentor: doc. dr. Samo Ulaga, somentor: izr. prof. dr. Igor Drstvenšek); dne 23. septembra 2010: Edita Kac z naslovom: »Uporaba nevronskih mrež v proizvodnem okolju« (mentor: prof. dr. Jože Balič); Karl Mlakar z naslovom: »Konstruiranje in izdelava orodij za ekstruzijo Al profilov« (mentor: prof. dr. Jože Balič, somentor: doc. dr.

Mirko Ficko); dne 30. septembra 2010: Jure Braniselj z naslovom: »Numerična analiza pršilnega stolpa razžvepljevalnika dimnih plinov« (mentor: prof. dr. Matjaž Hriberšek); Uroš Cvelbar z naslovom: »Eksperimentalna in numerična analiza toplotnih razmer v ogrevani terminalski učilnici« (mentor: prof. dr. Matjaž Hriberšek, somentor: doc. dr.

Matjaž Ramšak);

Simon Černec z naslovom: »Večnamenska naprava z vpenjalno pripravo za 6D lasersko označevanje« (mentor: prof. dr. Franci Čuš); Primož Dobnik z naslovom: »Odpravljanje težav namenskih potnih ventilov« (mentor: doc. dr. Darko Lovrec, somentor: doc. dr. Samo Ulaga); Damjan Gaberc z naslovom: »Nadzor, upravljanje in vzdrževanje tehniškega sistema zunanje okrasne fontane z vodnimi efekti« (mentor: doc. dr. Samo Ulaga); Jože Habjanič z naslovom: »Vzdrževanje prezračevalnih naprav« (mentor: prof. dr. Boris Aberšek); Denis Kovačič z naslovom: »Zasnova sodobne polnilne linije za plastenke« (mentor: izr. prof. dr. Miran Brezočnik, somentor: prof. dr.

Jože Balič); Danijel Meglič z naslovom: »Optimiranje proizvodnje v podjetju Almont d.o.o.« (mentor: izr. prof. dr. Borut Buchmeister, somentor: doc. dr. Nataša Vujica Herzog); Denis Nemeš z naslovom: »Hlajenje letalskega motorja z uporabo računalniške dinamike tekočin« (mentor: doc. dr. Matjaž Ramšak); Aleksander Pavlič z naslovom: »Postavitev montažne linije polgredi s standardom ISO TS 16949« (mentor: prof. dr.

Andrej Polajnar, somentor: doc. dr. Nataša Vujica Herzog).

Osebne vesti

SI 145