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Application of Taguchi Experiment Design for  Decrease of Cogging Torque in Permanent  Magnet motors
Application of Taguchi Experiment Design for  Decrease of Cogging Torque in Permanent  Magnet motors
Application of Taguchi Experiment Design for  Decrease of Cogging Torque in Permanent  Magnet motors
Application of Taguchi Experiment Design for  Decrease of Cogging Torque in Permanent  Magnet motors
Application of Taguchi Experiment Design for  Decrease of Cogging Torque in Permanent  Magnet motors
Application of Taguchi Experiment Design for  Decrease of Cogging Torque in Permanent  Magnet motors
Application of Taguchi Experiment Design for  Decrease of Cogging Torque in Permanent  Magnet motors
Application of Taguchi Experiment Design for  Decrease of Cogging Torque in Permanent  Magnet motors
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Application of Taguchi Experiment Design for Decrease of Cogging Torque in Permanent Magnet motors

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GENICHI TAGUCHI developed statistical methods for quality improvement of engineering products, …

GENICHI TAGUCHI developed statistical methods for quality improvement of engineering products,
marketing, etc. This method is called Taguchi method that more recently applied to engineering and
applied science. The Taguchi experiment design method for optimal design to mitigate cogging torque of a
surface permanent magnet (SPM) motor is used in this article. In this paper, an efficient algorithm to the
solutions for shape of PM is proposed and applied to optimize the shape of PMs in a surface-mounted PM
motor to reduce the cogging torque. Finally, Simulation results are presented that indicates the reduction
of magnitude of cogging torque.

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  • 1. International Journal on Computational Sciences & Applications (IJCSA) Vol.3, No.2, April 2013DOI:10.5121/ijcsa.2013.3204 31Application of Taguchi Experiment Design forDecrease of Cogging Torque in PermanentMagnet motorsA.Noori Shirazi1, B. Yousefi2, S. Asghar Gholamian3*and S. Rashidaee31Department of Engineering, Islamic Azad University-Nour Branch,Nour , Iran.abdoreza.noori@gmail.com2Department of Engineering, Islamic Azad University-Nour Branch,Nour , Iran.borzoyou@yahoo.com3Babol University of Technology, Faculty of Electrical andComputer Engineering, Babol, Iran*Corresponding author: S. Asghar GholamianABSTRACT:GENICHI TAGUCHI developed statistical methods for quality improvement of engineering products,marketing, etc. This method is called Taguchi method that more recently applied to engineering andapplied science. The Taguchi experiment design method for optimal design to mitigate cogging torque of asurface permanent magnet (SPM) motor is used in this article. In this paper, an efficient algorithm to thesolutions for shape of PM is proposed and applied to optimize the shape of PMs in a surface-mounted PMmotor to reduce the cogging torque. Finally, Simulation results are presented that indicates the reductionof magnitude of cogging torque.KEYWORD:TAGUCHI METHOD, PM MOTOR, PERMANENT MAGNET POLELIST OF SYMBOLSPM Permanent MagnetFEA finite element analysisMMF magnetomotive forceSPM Surface-mounted permanent magnetA the ratio of magnet pole arc to pole pitchB the distance from motor centreC the slot opening heightD the slot opening widthE the air gap lengthDOE design of experimentsANOM analysis of meansANOVAanalysis of variancef converter frequencyp machine pole pairs
  • 2. International Journal on Computational Sciences &1. INTRODUCTIONRecently, because of high reliability, high efficiency and improvement of the torque density,surface permanent magnet motors (SPM) are used in industrial applications.However, cogging torque problem is one of the maintype of motors. The interaction of the stator teeth with magnets produced cogging torque thatcauses the increasing the noise, vibration and ultimately reduces efficiency of SPM motor.The stator slots shape and permanent magnet pole configuration in SPM motors is the main causeof cogging torque production. Manytorque in SPM motors. Some of these techniques are to modify the permanent magnet polesconfiguration [8]-[11] and some of the other methods are to modify the shape of stator teeth[13].Surface permanent magnet motor with four poles, due to reduced consumption of copper and easymanufacturing process, now widely used in air conditioning compressotechniques, such as genetic algorithm [15], [16], rosenbrocks method [18], [19] and [17] is usedfor improvement of cogging torque in SPM motors. But, the Taguchi method has been provenuseful in applied science especially in engiThe Taguchi method does not require using additional programmingelement method analysis (FEM). Hence, effects ofbe investigated in this method [20].2. SURFACE PM MOTORSurface-mounted permanent magnet (SPM) motors are widely used in industry.problem in SPM motors is the cogging torque and it affects the performance, produces noise andresults in mechanical vibration, thereforetorque in SPM motors.In this paper, the 2D view of SPM motor shown in Figure1 and the main parameters are shown inTable1. This kind of stator and rotor configurationforce or flux density under the PM rotorand rotor, which will increase the ripple and noisetorque) with variations in stator and PM shapes hasanalysis (FEM), in this paper.International Journal on Computational Sciences & Applications (IJCSA) Vol.3, No.2, April 2013Recently, because of high reliability, high efficiency and improvement of the torque density,surface permanent magnet motors (SPM) are used in industrial applications. [1]-[4].However, cogging torque problem is one of the main restrictions in usage development in thisThe interaction of the stator teeth with magnets produced cogging torque thatcauses the increasing the noise, vibration and ultimately reduces efficiency of SPM motor.permanent magnet pole configuration in SPM motors is the main causeMany methods have been proposed to reduction ofSome of these techniques are to modify the permanent magnet polessome of the other methods are to modify the shape of stator teethSurface permanent magnet motor with four poles, due to reduced consumption of copper and easymanufacturing process, now widely used in air conditioning compressors [5]. Some optimizationtechniques, such as genetic algorithm [15], [16], rosenbrocks method [18], [19] and [17] is usedfor improvement of cogging torque in SPM motors. But, the Taguchi method has been provenuseful in applied science especially in engineering process to improve best quality.does not require using additional programming algorithms aside from finite). Hence, effects of many factors on cogging torque[20].OTOR MODELmounted permanent magnet (SPM) motors are widely used in industry. An importantcogging torque and it affects the performance, produces noise andtherefore it is necessary and important to reduction ofof SPM motor shown in Figure1 and the main parameters are shown inand rotor configuration cannot produce symmetrical magnetomotivePM rotor poles, and harmonics exist in the air gap between stator, which will increase the ripple and noise in torque. Calculation of The torque (coggingstator and PM shapes has been computed using finite elementFigure1. SPM motorApplications (IJCSA) Vol.3, No.2, April 201332Recently, because of high reliability, high efficiency and improvement of the torque density,restrictions in usage development in thisThe interaction of the stator teeth with magnets produced cogging torque thatcauses the increasing the noise, vibration and ultimately reduces efficiency of SPM motor.permanent magnet pole configuration in SPM motors is the main causetion of a coggingSome of these techniques are to modify the permanent magnet polessome of the other methods are to modify the shape of stator teeth [12],Surface permanent magnet motor with four poles, due to reduced consumption of copper and easySome optimizationtechniques, such as genetic algorithm [15], [16], rosenbrocks method [18], [19] and [17] is usedfor improvement of cogging torque in SPM motors. But, the Taguchi method has been provenaside from finitereduction canAn importantcogging torque and it affects the performance, produces noise andecessary and important to reduction of the coggingof SPM motor shown in Figure1 and the main parameters are shown intrical magnetomotivebetween statorCalculation of The torque (coggingbeen computed using finite element method
  • 3. International Journal on Computational Sciences & Applications (IJCSA) Vol.3, No.2, April 201333Table1. Main parameters of the SPM motor30 HpRated power120 mmStator outer diameter60 mmStator inner diameter70 mmLamination length1.7 mmPM thickness0.5 mmAir gap lengthDW360-50Stator and rotor core materialNdFeB 30SHPM material2. DESIGN OF EXPERIMENTExperimental design or design of experiments (DOE) is the design of any information wherevariation is present, whether under the full control or not. DOE often used in evaluating appliedphysic, engineering and material science.The Taguchi method extremely reduced the number of experiments by using orthogonal arraytables. This array is selected the special features among the total number of experiments [6],[7].In this paper, the design factors and their respective levels are given in Table2.Where,A is the ratio of PM Pole arc to pole pitchB is the distance from motor centre used as the centre of circle for PM (mm)C is the slot opening height (mm)D is the slot opening width (mm)E is the air gap length (mm)Table2. Design FactorsLevel 4Level 3Level 2Level 1Factors0.90.860.820.78A0.450.30.150B [mm]1.110.90.8C [mm]21.91.81.7D [mm]0.60.50.40.3E [mm]The orthogonal array L-16 selected for the matrix experiments based on standard Taguchi isshown in table 3. As shown in Table3, there are 16 experiments required to determine theoptimum combination of the levels of these factors.If there are 5 variable each at 4 levels, full factorial approach needs 4 5or 1024 experiments. To2D FEM analysis is conducted to obtain the average values of torque and cogging torque for eachcase.Table4 shows the results of simulation results.
  • 4. International Journal on Computational Sciences & Applications (IJCSA) Vol.3, No.2, April 201334Table3. L-16 Orthogonal ArrayEDCBAExperiment1111112222123333134444144321253412262143271234282431391342310421331131243123241413413241414234152314416Table4. Motor Simulation ResultsTavg(N.m)Tc (N.m)Experiment4.07470.796213.98300.731923.88270.674733.77780.622443.73310.657553.79760.725963.87230.658373.94540.725983.94860.835294.02420.8336103.72970.5350113.79850.5203124.02200.6698133.91330.5225144.14480.8063154.03040.6443163. ANALYSIS OF SIMULATION RESULTSAfter obtaining all the simulation results from the matrix experiment and, ANOM (analysis ofmeans) and ANOVA (analysis of variance) are carried out to estimation of the four designparameters and determination of the relative importance of each design variable [21].The means of all simulation results can be calculated by Equation1.1 6111 6iim T== ∑(1)
  • 5. International Journal on Computational Sciences & Applications (IJCSA) Vol.3, No.2, April 201335Table5 tabulates the results.Table5. Analysis of MeansTavg(N.m)Tc(N.m)3.91740.6850m3.1. Average EffectThe average torque of variable A at level 3 is calculated by Equation2.31( ) ( (9) (10) (11) (12))4avg avg avg avg avgmA T T T T T= + + +(2)As shown in table3, the factor A is set to in experiments 9, 10, 11, 12 at level 3. Similar way canbe used for computing of Average torque of all variables.Table 6 shows the results. A plot of main factors effects is illustrated in Figure2 It is seen that thefactor-level combination (A4, B1, C4, D2, and E1) contributes to maximization of averagetorque.Table6. Average torque for all levels of all factorsEiDiCiBiAii4.04733.91473.90813.94963.929613.95863.92003.91483.9293.837123.87523.91763.923.90743.875333.7803.91723.92413.88804.02764Figure2. Main factor effects on average torqueThe peak to peak value of cogging torque for all levels of factors is shown in Table7. Main factoreffect on the peak to peak value of cogging torque is shown in Figure33.753.783.813.843.873.93.933.963.994.024.05A1 A2 A3 A4 B1 B2 B3 B4 C1 C2 C3 C4 D1 D2 D3 D4 E1 E2 E3 E4Tavg(N.m)setting of factors
  • 6. International Journal on Computational Sciences & Applications (IJCSA) Vol.3, No.2, April 201336Table7. Peak to peak value of cogging torque for all levels of all factorsEiDiCiBiAii0.19530.15900.17240.18740.179410.18130.16940.17280.17890.180320.16710.17920.17570.17040.174730.15440.19050.17710.16140.16364Figure3. Main factor effects on peak to peak value of cogging torque3.2. Analysis Of Variance (ANOVA)To conduct Analysis Of Variance is calculated the sum of squares. It is measure of the deviationof simulation data from the mean value of the data. The sum of squares (SSFA) due to variousfactors can be calculated as:4214 ( )iAiSSFA m m== −∑(3)SSFB, SSFC, SSFD and SSFE can be obtained in the same way. Table8 is shown the data of themachine among the initial, Taguchi parameter designs and simulation results.It can be seen that average torque increases from the initial design of 3.8276 Nm to Taguchiparameter design of 4.1118 Nm, and to simulation result of 4.10 Nm. The cogging torque valuedecreases from 0.7315 Nm to 0.6390 Nm in Taguchi parameter design, and to 0.6400 Nm insimulation result.Table 8. Comparison ResultsTc (N.m)Tavg. (N.m)0.73153.8276Initial0.63904.1118Taguchi results0.6404.10Simulation results0.150.1540.1580.1620.1660.170.1740.1780.1820.1860.190.1940.198A1 A2 A3 A4 B1 B2 B3 B4 C1 C2 C3 C4 D1 D2 D3 D4 E1 E2 E3 E4Tc(N.m)setting of factors
  • 7. International Journal on Computational Sciences & Applications (IJCSA) Vol.3, No.2, April 2013374. CONCLUSIONThe Taguchi method applied to design optimization of SPM motor for the reduction of coggingtorque value. The peak to peak value of cogging torque decreases before and after optimizationby Taguchi method.The peak to peak value of cogging torque decreases from 0.7315 Nm to 0.6390 Nm in Taguchiparameter design, and to 0.6400 Nm in simulation result.Proposed method for solving this problem is significantly reduced the peak to peak value ofcogging torque of SPM motor.REFERENCES[1] S. RASHIDAEE and S. Asghar GHOLAMIAN;"REDUCTION OF COGGING TORQUE IN IPMMOTORS BY USING THE TAGUCHI AND FINITE ELEMENT METHOD", International Journalof Computer Science & Engineering Survey (IJCSES) Vol.2, No.2, 2011.[2] S. Asghar Gholamian, S. Rashidaee;"Cogging Torque Reduction in Surface Permanent MagnetMotors Using Taguchi Experiment Design and Finite Element Method", I.J. Intelligent Systems andApplications, 2012, 11, 33-39.[3] K. Ogasawara, T. Murata, J. Tamura, and T. Tsuchiya, “High performance control of permanentmagnet synchronous motor based on magnetic energy model by sliding mode control,” in 2005 Eur.Conf. Power Electronics and Applications, Sept. 2005, p. 10.[4] B. Stumberger, G. Stumberger,M. Jesenik, V. Gorican, A. Hamler, and M. Trleps, “Power capabilityand flux-weakening performance of interior permanent magnet synchronous motor with multiple fluxbarriers,” in Proc. 12th Biennial IEEE Conf. Electromagnetic Field Computation, 2006, p. 419.[5] P. Zheng, J. Zhao, J. Han, J. Wang, Z. Yao, and R. Liu, “Optimization of the Magnetic Pole Shape ofa Permanent-Magnet Synchronous Motor”, in IEEE Trans. Magn.,vol. 43, no. 6, June 2007.[6] C. Hwang, P. Li, F. C. Chuang, C. T. Liu, and K. H. Huang, “Optimization for Reduction ofTorque Ripple in an Axial Flux Permanent Magnet Machine”, in IEEE Trans. Magn.,vol. 45, No. 3,march 2009.[7] S. I. Kim, J. Y. Lee, Y. K. Kim, J. P. Hong, Y. Hur and Y. H. Jung, “Optimization for Reduction ofTorque Ripple in Interior Permanent Magnet Motor by Using the Taguchi Method”, in IEEE Trans.Magn.,vol. 41, no. 5, may 2005.[8] Y. Y. ang, X. Wang, R. Zhang, T. Ding, and R. Tang, “The optimization of pole arc coefficient toreduce cogging torque in surface-mounted permanent magnet motors”, in IEEE Trans. Magn., vol. 42,no. 4, April 2006.[9] . H. Kang, Y. D. Son, G. T. Kim, and J. Hur, “A novel cogging torque reduction method forinterior-type permanent-magnet motor”, in IEEE Trans on Industry applications., vol. 45, No. 1,Jan/Feb 2009.[10] K. Y. Hwang, S. B. Rhee, B. Y. Yang, B. Kwon, “Rotor pole design in spoke-type brushless dcmotor by response surface method”, in IEEE Trans. Magn., vol. 43, no. 4, April 2007.[11] R. Islam, I. Husain, A. Fardoun, and K. McLaughlin, “Permanent - magnet synchronous motormagnet designs with skewing for torque ripple and cogging torque reduction”, in IEEE Trans onIndustry applications., vol. 45, no. 1, Jan/Feb 2009.[12] S. W. Youn, J. J. Lee, H. S. Yoon, and C. S. Koh, “A new cogging-free permanent-magnet linearmotor”, in IEEE Trans. Magn., vol. 44, no. 7, July 2008.[13] S. W. Youn, J. J. Lee, H. S. Yoon, and C. S. Koh, “Robust design of a spindle motor: a casestudy”, in reliability engineering and system safety 75 (2002) 313-319.[14] N. Bianchi and S. Bolognani, “Design optimisation of electric motors by genetic algorithms,” IEEProc.—Electr. Power Appl., vol. 145, no. 5, pp. 475–483, Sep. 1998.[15] M. Lukaniszyn, M. JagieLa, and R. Wrobel, “Optimization of permanent magnet shape for minimumcogging torque using a genetic algorithm,” IEEE Trans. Magn., vol. 40, no. 2, pp.1228–1231, Mar.2004.
  • 8. International Journal on Computational Sciences & Applications (IJCSA) Vol.3, No.2, April 201338[16] J. T. Li, Z. J. Liu, M. A. Jabbar, and X. K. Gao, “Design optimization for cogging torqueminimization using response surface methodology,” IEEE Trans. Magn., vol. 40, no. 2, pp. 1176–1179, Mar. 2004.[17] T. Ohnishi and N. Takahashi, “Optimal design of efficient IPM motor using finite element method,”IEEE Trans. Magn., vol. 36, no. 5, pp. 3537–3539, Sep. 2000.[18] N. Takahashi, Optimal Design Using Finite Element Method for Magnetic Field Analysis. Tokyo,Japan: Morikita, 2001.[19] R. K. Roy, Design of Experiments Using the Taguchi Approach. NewYork: Wiley, 2001.[20] M. S. Phadke, Quality Engineering Using Robust Design. Englewood Cliffs,NJ : Prentice-Hall, 1989.

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