A study on the bearingless switched reluctance rotation motor with improved motor performance

Journal of Mechanical Science and Technology 27 (5) (2013) 1407~1414 www.springerlink.com/content/1738-494x DOI 10.1007/s12206-013-0321-6 A study on the bearingless switched reluctance rotation motor with improved motor performance Jaeyoon Wang, Sangjo Kim and Naksoo Kim * Department of Mechanical Engineering, Sogang University, Seoul, 121-742, Korea (Manuscript Received October 22, 2011; Revised November 3, 2012; Accepted December 26, 2012) ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- Abstract Optimum product design can be realized through applying reasonable design of experiment (DOE) using state of the art computer simulations. The bearingless motor is a product combing the conventional electromotor with the active magnetic bearing (AMB) which rotates without a contact area. Therefore, it does not yield friction and there is no energy loss. The bearingless motor has a simple structure which enables high speed and precise positional controls. This study proposes an AMB with a new structure, which offers more stabilized rotations by enhancing flows of magnetic flux density. Also, this study provides optimum design of a bearingless motor which maximizes the torques, a general indicator of motor performances given conditions. For the purpose of designing a bearingless motor, proper design parameters have been selected. Design of experiment has been constructed using orthogonal arrays. Also, using the response surface method, an objective function which depicts the performance of a motor is obtained. The objective function which evaluates the performance of the motor has been optimized, and a bearingless rotation motor with the improved performance has been designed. By comparing the performance of the actual motor produced from the optimum design, the reliability is validated. Keywords: Design of experiment; Electromagnetic analysis; Bearingless switched reluctance rotation motor; Optimum design ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- 1. Introduction The recent development trend in machine tools and industrial machinery is focusing on high speed and compactness for the enhanced outputs and productivities. In this paper, the bearingless switched reluctance motor is introduced. Conventional switched reluctance motors with mechanical bearings have generated significant interest among researchers and industrial engineers. For particular environments and applications, the switched reluctance motor can have superior performance because of its inherent features such as being failsafe, robustness, low cost and possible operation at high temperature or in intense temperature variation [1]. A bearingless motor is a device that combines the function of motor and the active magnetic bearing (AMB). It is also called self-bearing motor. As a bearingless rotation motor performs rotations without mechanical contacts with the rotors during the rotations, there are no wear losses due to the friction. Also, it is possible to realize speed of 100-10000 rpm. The bearingless rotation motor can operate in extreme conditions such as vacuum condition or extremely low temperature conditions. Furthermore, high precision controls can be maintained such as in * Corresponding author. Tel.: +82 2 705 8635, Fax.: +82 2 712 0799 E-mail address: nskim@sogang.ac.kr Recommended by Associate Editor Sung Hoon Ahn KSME & Springer 2013 active control of rotation rate, automatic balancing, and vibration control. Consequently, it is highly promising in the future application of semi-conductor manufacturing process, machine tools and other high tech industries such as aerospace industry [2]. The bearingless rotation motor is a magnetic structure that is composed of a rotor and a stator. It achieves both rotational force and levitation force enabling rotations in the magnetically levitated state and enables to increase a torque and a levitation force. Therefore, a bearingless rotation motor can be made in a small size for high-speed operation [3]. Alasuvanto et al. (1990) undertook theoretical torque analysis based on electromagnetic force using the finite element method for an equivalent magnetic circuit network [4]. Seo et al. (2007) also showed that the optimum design of the cored linear motor is able to be performed by the experimental design using finite element analysis [5]. Kim et al. (2011) examined the effect of the number of poles from BLDC motors [6]. Many researchers have studied the robust design of bearingless rotation motors using the Taguchi method to optimize the torque of the motor [7-9]. Motor efficiency is also regarded as an optimization objective in many papers [10-13]. Multi-objective optimum designs focusing on the motor efficiency and weight are also presented [11, 12]. The motor torque and torque ripples are used as objective functions in some design optimizations

1408 J. Wang et al. / Journal of Mechanical Science and Technology 27 (5) (2013) 1407~1414 [14, 15]. The improvement of motor torque-speed characteristics is also aimed [16, 17]. By the advent of relatively expensive high energy permanent magnet materials and an ongoing penetration of interior permanent magnet (IPM) motors in medium and high power applications, the volume of permanent magnet used in a motor plays the main role in deciding the motor initial cost. Recently, permanent magnet volume and torque ripples are taken into account in a design optimization [18]. In this paper, we take into account motor torque maximization in fixed motor volume. This study proposes an AMB with a new structure which provides more stabilized rotations through enhancing the flows of magnetic flux density. Also, with torque, which is an indicator for the performance of a motor being set as the objective function, we have employed optimization algorithm for numerical analysis of the optimization. The design of an AMB with the proposed structure enables more stabilized rotations of the motor. The optimum design provides the design methodology for a bearingless rotation motor with the maximum performance. 2. Theoretical background 2.1 Bearingless switched reluctance motor Bearing is an important element for high speed spindle machine tools or storage devices. Conventional bearings suffer the problems of wear and short lifetime due to the contact between bearing and rotor. There exist several types of noncontact bearings such as hydrodynamic, air, and magnetic types. The non-contact bearings can reduce or eliminate the problems of friction, vibration, and acoustic noise. Among them, the AMB is the most promising one due to the advantages of high load capacity, large stiffness, and no lubrication. A bearingless motor is a device that combines the function of motor and AMB. It is also called self-bearing motor. To this aim, the system must be able to produce not only the translational force, but also the rotational torque. In order to generate the rotational torque, the original 3-pole AMB design must be modified so that it can become a bearingless motor. The translation and rotational forces are generated by two independent sets of coils and/or permanent magnets. According to the way the torque is generated, bearingless motors are in general classified into 3 types: permanent magnetic type, induction type, and switched reluctance type. Permanent magnetic type bearingless motors usually contain permanent magnet in its rotor. Similar to permanent magnetic motor, the torque is generated by Lorentz force. In addition, there always exist several additional windings on the stator to provide reluctance forces for rotor levitation. The main advantage is that the torque and levitation force can be controlled independently. Induction type bearingless motor has the advantages of lowcost, no permanent magnet, easy design, and larger radial suspension force. However, energy losses are considerably large because of slip. Also, the rotational flux and levitation flux are strongly coupled and hence complicated vector control is necessary. Reluctance type bearingless motor is similar to the switched reluctance motor [19-23]. The motoring torque is usually produced by the non-uniform magnetic reluctance and the magnetic flux must pass through the path with the least reluctance, so the salient pole on rotor will be engaged and rotate. For reluctance type self-bearing motor, it adds additional windings on stator to provide radial suspension force. Both the motoring torque and levitation force are produced by reluctance force, and they can be reinforced simultaneously. There are many advantages for this type. First, it has the characteristic of failsafe and can be easily broken in case of emergency. Second, it is low-cost because of no coils or permanent magnet on the rotor and it is easy to be manufactured. Third, both translational and rotational torques can be enhanced simultaneously since they are both reluctance force. Fourth, temperature effect is insignificant compared to the permanent magnetic type. The main disadvantage is that the coupling between the rotational flux and levitation flux is very serious and it is difficult for analysis. Also, the effect of cogging force cannot be neglected. To further improve the motor performance, a reluctance type bearingless motor is considered in this study. 2.2 Design of experiment Design of experiment means a plan of experiment numbers, including the method of setting up an experiment about a problem, method of data collection and method of obtaining the most information by using the minimum number of experiments based on statistical data analysis [24]. Therefore, using design of experiment requires the selection of parameters about a problem, selection of an experimental method, decision on the experiment order and selection of the optimum analysis method for the data obtained from the an experiment. In the case of a design that has many parameters, predictable interactions of two parameters are detected, and information on two or more interactions is sacrificed. As a result, a table is made for a design of experiment with a small number of experiments. The table is called as the Table of orthogonal arrays. In a general design, there are many parameters to be considered. The table of orthogonal array excludes information about an interaction of higher degree between parameters. So we can make a design of experiment with a small number. In the table of orthogonal array, many parameters can be included without an expansion of the experiment and can be used to easily calculate the effect of parameters from experiment data. 2.3 Response surface method The response surface method (RSM) is mainly used to obtain an explicit function from experimental data. Recently it has been used to represent a relationship between design vari-

J. Wang et al. / Journal of Mechanical Science and Technology 27 (5) (2013) 1407~1414 1409 Table 1. Target of the bearingless wafer rotation motor. Fig. 1. Structure of the bearingless wafer rotation system. Parameters characters Values Outer radius of the rotor (mm) 180 Rotor weight (kg) 2.7 Rated speed (rpm) 240 Rated output power (W) 18 Rated voltage (V) 17 Acceleration time (s) 3 Deceleration time (s) 3 ables and response function from a mathematical equation, assumes a coefficient of equation with the least square method from measured data, and makes useful response surface model as the explicit function [25]. In this study, a second-order regression model such as that given by Eq. (1) is used to calculate a response surface nd nd nd (1) y= β + β x+ β x x o i i ij i j i= 1 i= 1 j i (a) where x i denotes the design variables; n d, the number of design variables; and β i, β ij, the unknown coefficients. Eq. (2) is used to calculate the coefficients of RSM that minimize the square summation of the residuals using least square method. T ( ) -1 T β= X X X Y (2) where X denotes the design matrix comprising experimental points and Y denotes the response vector. (b) 3. Numerical study 3.1 Design requirements The bearingless rotation system is illustrated in Fig. 1. The radial bearing actuator has an outside diameter of 360 mm, an overall length of 78 mm, a tooth length of 6 mm, and a radial air gap of 2 mm at rest. At a rated speed of 240 rpm, the radial air gap increases to 1 mm. In this bearing, the bias field is established with neodymium-iron-boron (NdFeB) permanent magnets located in the end of the stator. The stator is fabricated from 508 mm STS420 and includes coil slots to reduce rotating losses. As depicted in Fig. 2(a), the bearingless rotation motor is composed of three parts. A role in the electromotor part is controlling a rotation. The rotor is rotated as according to the electric current of the coil where each slots are wound as shown in Fig. 2(b). One tooth of the electromagnet has three slots and each slot is bound with coils of 80 turns. The electric current with 120 degree of phase difference to U, V and W enters into 3.5 A. In Fig. 2(c) the first levitation core is controlling the movement of rotational axis due to the absence of the spindle and the second core is for raising the rotor. The permanent magnet, which is placed on top of and bottom (c) Fig. 2. (a) 3D schematic; (b) electromotor part; (c) cross section of the bearingless rotation motor. of the AMB, serve the role of reinforcing the deficient magnetic flows. In this study, the designed bearingless rotation motor has to reach a rated speed of 240 rpm within acceleration time of 3 seconds. The weight and the outer radius of the rotor are 2.7 kg and 180 mm, respectively. Also, a rated voltage determined is 17 V and input electric currents of 3.5 A should pass through coils. These design requirements of a bearingless wafer rotation system is listed in Table 1.

1410 J. Wang et al. / Journal of Mechanical Science and Technology 27 (5) (2013) 1407~1414 (a) (a) (b) Fig. 3. Schematic of the bearingless rotation system: (a) the conventional model; (b) the proposed one. 3.2 Design of the bearingless rotation drive In a typical magnetic bearing application, there were two permanent magnets placed on the top of the axial levitation core and the bottom of the radial levitation core, respectively as shown in Fig. 3(a). The magnetic forces, which are applied by sets of electromagnets, must be adjusted to ensure that the rotor is accurately positioned. However, such layout induces the saturation of magnetic flux between the permanent magnet and the levitation core. When the saturation occurs, the magnetic flux can enter into the levitation cores, causing the difficulties in controlling the rotor to the axis direction. This control problem is complicated due to the inherent nonlinearities associated with the electromechanical dynamics. In this study, a new structure of the magnetic bearing which is capable of reducing the saturation of the magnetic flux is proposed. The newly designed magnetic bearing has added a magnetic plate on the levitation core as shown in Fig. 3(b). As according to the proposed structure, by adding the magnetic plate on the levitation core, the back electromotive force is much more generated and the magnetic flux shifts behind the stator as shown in Fig. 4. Thus, the saturation occurs partially at the radial and the axial levitation core nearby the permanent magnet. With the increased air gap, the magnetic resistance in air gap is also increased. The magnetic resistance in air gap hinders the flow of the magnetic flux density. Therefore, the magnetic flux will be induced to flow to the direction of less magnetic resistance. Consequently, the saturation of the magnetic flux in the levitation core is reduced and enables the control of the axial direction because the magnetic flow is constrained from entering behind the magnetic plate. In the reluctance type of bearingless motor, these magnetic poles have equal attractive force. Thus, a vector sum of the radial forces is zero. However, one pole is stronger than the other poles, the net attractive force is strong. The unbalanced airgap flux density distribution results in radial magnetic force acting on the rotor. In this case, the rotor is moved on the right-hand direction. In the bearingless motor, rotor radial force is generated by an unbalanced magnetic field. In other words, the rotor radial force is generated by the difference of radial forces between the magnetic poles. The attractive force is an inherently unstable force as it is stronger if the rotor moves in the force direction. Torque is generated by magnetic attraction between rotor and stator poles. In this process a significant amount of attractive radial force is generated because the switched reluctance motor has salient poles and a short airgap length between these poles in order to effectively produce a reluctance torque. 3.3 FE Modeling (b) Fig. 4. Magnetic flux line: various material of plate: (a) air; (b) steel. In this paper, Maxwell, an electromagnetic analysis program, has been used to perform the 2D magnetostatic field analyses of the bearingless rotation motor. FE model is composed of rotor, stator and permanent magnet. There are 24 slots at the rotator and 18 slots at the stator. 50 turns of coil is wound on the slots at the stator. The bearingless rotation system is comprised of the newly designed AMB to enhance the control of the radial and the axial direction and the electromotor. The magneto-static analysis is performed using the scalar potential method of Maxwell. Flux by the permanent magnet is made in the opposite direction at grooves of rotor. In the simulation with the electromagnet, the electric current of 5A is charged. The gap between rotor and stator is fixed to meet the load capacity of 0.4 T because it is assumed that the value of load capacity is needed to levitate the radial levitation part without the external force about the direction of x and y axis in this study. Table 2 lists materials properties and Table 3 summarize dimensional information in each part of the bearingless rotation motor.

J. Wang et al. / Journal of Mechanical Science and Technology 27 (5) (2013) 1407~1414 1411 Table 2. Material properties for FE analyses. Table 4. Effect of stator and rotor embrace. Material property Values used for FEA Initial Case 1 Case 2 Motor core Rotor core Stator core S18 STS420 STS420 Design variables Stator embrace, x 1 0.30 0.30 0.40 Rotor embrace, x 2 0.35 0.50 0.35 number of turns, x 3 80 80 80 Permanent magnet Magnetic plate Coil NdFeB Steel Copper Simulation results Output torque (Nm) 0.75 0.55 0.45 Output power (W) 18.1 13.7 11.5 Input current (A) 3.5 2.8 2.6 Table 3. Dimensions for FE analyses. Dimension Values used for FEA Inner diameter (mm) 362 Stator Outer diameter (mm) 508 Tooth length (mm) 6 Inner diameter (mm) 322 Rotor Outer diameter (mm) 358 Tooth length (mm) 6 Permanent Height (mm) 4.5 magnet Length (mm) 18 Fig. 6. Definition of the rotor embrace. Fig. 5. Magnetic flux density of bearingless rotation system (No electric current, only permanent magnet effect). 3.4 Effect of the permanent magnet In general, if the thickness of permanent magnet is larger, the larger torque can be produced. However, the radial attractive force will become smaller. In the bearingless rotation system, to examine effects of permanent magnet only, the magnetic flux density should be measured as shown in Fig. 5. In each part, we calculated the magnetic flux density in air gap between rotor and stator. The magnetic flux density at motor part, the radial, and the axial levitation core are 0.09, 0.22, and 0.31 T, respectively. In motor part, because the torque generated by permanent magnets is not enough to drive a motor, it is necessary to set up a rated electrical current in motor coils. 4. Design procedures 4.1 Determination of design variables In this paper, in order to determine design variables in the reluctance type bearingless motor which affect the torque, the following three design variables, stator embrace, rotor embrace and number of turns, have been determined. As shown in Fig. 6, the ratio between the tooth (b) and the pitch (a) in a rotor and stator has been defined as rotor embrace (x 1 ) and stator embrace (x 2 ), respectively. According to Maxwell force equation given by Eq. (4), the rotating force of a motor is proportional to the airgap area and the squared value of the magnetic flux density. As these design variables are change, the area of the core and the airgap is changed. As a result, the magnetic flux density is changed. Also, according to Kirchoff s law, the magnetic flux density is proportional to the number of coils and to the intensity of the electric current so the number of coils (x 3 ) also affects the magnetic flux density. 4.2 Effect of each design variable 4.2.1 Rotor and stator embrace Before considering the optimum design, a value of the output torque, the output power and the input current are obtained by increasing the value of a rotor embrace. Results show the output torque, the output power and the input current are decreased as the value of the rotor embrace increase. As depicted in Table 4, increased width of the rotor would reduce the output torque. This is also obvious in the case of a stator. The output torque, the output power and the input current according to changes of the design variable were summarized in Table 4. 4.2.2 Number of turns per coil At a rated speed of 240 rpm, a stator embrace, a rotor embrace and a number of turns per coil is set 0.3, 0.35 and 40, respectively. In order to know the effect of a number of turns per coils, we calculate analytical results of the output torque, the input electric current and the output power. As summarized in Table 5, the output torque value and the output power value are greater than the initial model. However, in this instance, a high voltage current of 14.3 A is passing through the

1412 J. Wang et al. / Journal of Mechanical Science and Technology 27 (5) (2013) 1407~1414 Table 5. Effect of number of turns. Design variables Simulation results coil. In this paper, it is necessary to design the bearingless rotation motor considering a number of turns per coil which the input electric current with less than 5 A pass thorough. When a number of turns per coil set 60 turns, the input electric current passed through coils is 6.1 A, so this value is constrained for the lowest limit. 4.3 Design of experiment As according to the determined design variables, 3-level design of experiment is constructed. Initial values and the level of design variables are listed in Table 6. The table of orthogonal array has been constructed to evaluate the effects in the interaction between design variables. An electromagnetic field simulation result based on the table of orthogonal array listed in Table 7. 4.4 Optimization of the cost function Initial Case 1 Case 2 Stator embrace, x 1 0.30 0.30 0.30 Rotor embrace, x 2 0.35 0.35 0.35 number of turns, x 3 80 40 60 Output torque (Nm) 0.75 2.9 1.3 Table 6. Level of design variables. Output power (W) 18.1 73.3 32.0 Input current (A) 3.5 14.3 6.1 Design variables Initial Level 0 Level 1 Level 2 Stator embrace, x 1 0.30 0.15 0.30 0.45 Rotor embrace, x 2 0.35 0.20 0.35 0.50 Number of turns, x 3 80 60 80 100 Table 7. Table of orthogonal arrays - optimization of the torque. Exp. Level of design variables No. x 1 x 2 x 3 Input current (A) Output torque (Nm) 1 0 0 0 13.2 2.12 2 0 1 1 6.3 1.16 3 0 2 2 3.2 0.61 4 1 0 1 4.7 0.86 5 1 1 0 6.6 1.34 6 1 2 2 1.9 0.37 7 2 0 1 2.9 0.42 8 2 1 2 1.5 0.25 9 2 2 0 3.5 0.54 To obtain the objective function that is comprised of the determined design variables, the response surface method is used. As for the minimization of the objective function, BFGS Table 8. Simulation with optimum values. method which is an optimization technique which directly updates on Hessian Matrix, and the result is described in Eq. (3). x= 0.27, x = 0.45, x = 90.411. (3) 1 2 3 Between the finite element analysis results derived from the obtained optimized value and the results obtained by substituting to the objective function, there are approximately 3% of errors as shown in Table 8. Consequently, it can be concluded that the optimization through the optimization process has been performed efficiently. Using the initially configured values and the values of variables obtained through the optimization, the motor torque is calculated. The initial model s stator embrace, rotator embrace and the number of coils wound were 0.3, 0.35 and 80 respectively. The calculated results of the initial model and the optimized model s torque are listed in Table 9. Results show that the 227% of the motor torque has been improved. 5. Results and discussion Cost function Simulation Error (%) Torque (Nm) 0.53 0.513 3.3 Table 9. Improvements of the optimized model. Initial Optimized Improvement (%) Stator embrace 0.3 0.27 - Rotor embrace 0.35 0.45 - number of turns 80 90.4 - Input current (A) 1.93 1.93 - Torque (Nm) 0.16 0.51 227 In this paper, we have designed an AMB which has a nonmagnetic plate on the levitation core in order to allow the enhanced control of the radius direction and the axial direction. Based on this study, in the given conditions, electromotor which has the maximized output torque using the various optimization design methodologies such as design of experimental and response surface method is designed. With given conditions, we have evaluated the effects of variables to the performance of the motor. Also, along with values determined from the optimum design, we have produced the bearingless rotation motor as shown in Fig. 7. The output angular velocity for different time is obtained through a performance test. As shown in Fig. 8, the bearingless rotation motor reaches a rated speed of 240 rpm in 4 seconds. Table 10 show measurement and computation values. As analytical results agree with measurement results, the superiority of theoretical design methodologies was demonstrated. In the bearingless rotation motor, the control of the motor is accomplished by controlling the output torque. However,

J. Wang et al. / Journal of Mechanical Science and Technology 27 (5) (2013) 1407~1414 1413 Table 10. Comparison of the optimized model and experiment values. Optimized model Experiment Stator embrace 0.27 0.3 Rotor embrace 0.45 0.4 number of turns 90.41 92 Input current (A) 1.93 1 Output torque (Nm) 0.51 0.42 (a) (b) Fig. 7. Bearingless rotation motor system: (a) without wafer; (b) with wafer. Angular velocity (rpm) 300 250 200 150 100 50 0 0 2 4 6 8 10 Time (sec) m = 3.1kg Fig. 8. Acceleration performance of developed motor system. when the bearingless rotation system is driven, the torque ripple is occurred due to characteristics of the motor itself. This torque ripple becomes a cause of a speed fluctuation so additional studies to minimize torque ripple are necessary. Also, besides the minimization of the torque ripple, when a precise speed control is required, the motor speed is controlled with performance. 6. Conclusions This study proposes an AMB with a new structure which can provide stabilized control of the rotor s movement by reducing the saturation of magnetic flux density. With the application of such design in the radial and axial levitation part, the saturation of permanent magnets is reduced during the rotation of the motor, enabling enhanced flows of magnetic flux. Consequently, it is considered that controlling of axial direction and the radial direction can be more readily achieved with smaller amount of the forces exerted. Also, we have performed the optimum design of an electromotor which can achieve the maximum torque at the rated speed. For the effective design, we have determined proper design variables which can affect the rotational force of the motor. Also the objective function has been derived with the design of experiment (DOE) and response surface method (RSM). Consequently, the optimum design variables which can determine the shape of the motor at a specific volume. The motor analyzed using the optimum design variables has demonstrated approximately 227% performance enhancement. Using the minimum simulation using the computer-based finite element analysis and design of experiment, the optimum design of the bearingless rotation motor has been constructed. It is considered that the proposed design metrology can be readily and sufficiently applied in to the designing process of other parts as well. In a rapid thermal processing system to keep a vacuum state, a wafer rotation system using ball bearing have been used but at present a wafer rotation system using magnetic levitation technique was required on account of problems about bearing wear, dust by friction, increase defective products. Design and analysis techniques using this research apply for the present semiconductor manufacturing process and another magnetic levitation system like to turbo pump or chemical pump in future. Acknowledgment This work supported by Sogang University Research Program with a grant no. 201010042. References [1] A. Chiba, T. Fukao, O. Ichikawa, M. Oshima, M. Takemoto and D. G. Dorrell, Magnetic bearings and bearingless drives, First Ed. Newnes, London, UK (2005). [2] M. Oshima, A. Chiba, T. Fukao and M. A. Rahman, Characteristics of a permanent magnet type bearingless motor, IEEE Transactions on Industry Applications, 32 (1994)

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Fukao, A method of determining the advanced angle of square-wave currents in a bearingless switched reluctance motor, IEEE Transactions on Industry Applications, 37 (6) (2001) 1702-1709. [23] M. Takemoto, H. Suzuki, A. Chiba, T. Fukao and M. A. Rahman, Improved analysis of a bearingless switched reluctance motor, IEEE Transactions on Industry Applications, 37 (1) (2001) 26-34. [24] J. M. Lim, S. Han, S. Jeon, D. Woo and G. J. Park, Analysis and design considerations of energy absorbing steering system using orthogonal arrays, Transactions of the Korean Society of Automotive Engineers, 7 (1999) 144-155. [25] B. D. Youn and K. K. Choi, A new response surface methodology for reliability based design optimization, Computers and Structures, 82 (2004) 241-256. Jaeyoon Wang received her B.S. and M.S. degree from the department of Mechanical Engineering, Sogang University, Seoul, Korea in 2010 and 2012, respectively. Her research interests are in area of sheet metal forming and computer aided process analysis. Naksoo Kim is currently a professor at the department of mechanical engineering, Sogang University. He received his B.S. and M.S. degree from the department of Mechanical Design, Seoul National University in 1982 and 1984, respectively. He then went on to receive his Ph.D. degree from U.C. Berkeley. Dr. Kim had worked for the ERC/NSM at the Ohio State University as a senior researcher and Hongik University as an assistant professor. Dr. Kim s research interests are in the area of metal forming plasticity, computer aided process analysis, and optimal design.