Title: Optimal design of permanent magnet linear synchronous motors based on Taguchi method
Abstract: IET Electric Power ApplicationsVolume 11, Issue 1 p. 41-48 Research ArticlesFree Access Optimal design of permanent magnet linear synchronous motors based on Taguchi method Juncai Song, Juncai Song Department of Electrical Engineering, Anhui University, Hefei, 230601 People's Republic of ChinaSearch for more papers by this authorFei Dong, Fei Dong Department of Electrical Engineering, Anhui University, Hefei, 230601 People's Republic of ChinaSearch for more papers by this authorJiwen Zhao, Corresponding Author Jiwen Zhao [email protected] Department of Electrical Engineering, Anhui University, Hefei, 230601 People's Republic of ChinaSearch for more papers by this authorSiliang Lu, Siliang Lu Department of Electrical Engineering, Anhui University, Hefei, 230601 People's Republic of ChinaSearch for more papers by this authorShaokun Dou, Shaokun Dou Department of Electrical Engineering, Anhui University, Hefei, 230601 People's Republic of ChinaSearch for more papers by this authorHui Wang, Hui Wang Department of Electrical Engineering, Anhui University, Hefei, 230601 People's Republic of ChinaSearch for more papers by this author Juncai Song, Juncai Song Department of Electrical Engineering, Anhui University, Hefei, 230601 People's Republic of ChinaSearch for more papers by this authorFei Dong, Fei Dong Department of Electrical Engineering, Anhui University, Hefei, 230601 People's Republic of ChinaSearch for more papers by this authorJiwen Zhao, Corresponding Author Jiwen Zhao [email protected] Department of Electrical Engineering, Anhui University, Hefei, 230601 People's Republic of ChinaSearch for more papers by this authorSiliang Lu, Siliang Lu Department of Electrical Engineering, Anhui University, Hefei, 230601 People's Republic of ChinaSearch for more papers by this authorShaokun Dou, Shaokun Dou Department of Electrical Engineering, Anhui University, Hefei, 230601 People's Republic of ChinaSearch for more papers by this authorHui Wang, Hui Wang Department of Electrical Engineering, Anhui University, Hefei, 230601 People's Republic of ChinaSearch for more papers by this author First published: 01 January 2017 https://doi.org/10.1049/iet-epa.2016.0164Citations: 54AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Abstract This study focuses on optimisation design of permanent magnet linear synchronous motors that are applied in laser engraving machines with no cutting force. Traditional analytical optimisation method based on magnetic field with particle swarm optimisation algorithm was introduced to obtain the best combination of motor structure parameters. By contrast, the novel optimisation design method – Taguchi method based on orthogonal array was proposed to optimise the thrust and thrust ripple. After the design of experiments using finite-element analysis, the relative importance of each design parameter was estimated in detail. Experimental results of prototype can certify the superiority and validity of Taguchi optimisation method. 1 Introduction Permanent magnet linear synchronous motors (PMLSM) are widely used in ultraprecise fields (such as laser engraving machines and 3D printers) because of their evident advantages – high acceleration, excellent accuracy, and direct drive [1]. When the laser engraving machine works, the three-dimensional movers in rectilinear motion are driven by three motors, which can satisfy the high-level demands more effectively than conventional solutions by routing motors and ball screws. Compared with other types of motors, PMLSM can provide better synchronicity, higher accuracy, and faster speed. This paper presents a PMLSM with double secondary applied in laser engraving machines. The speed and accuracy of PMLSM can be influenced by motor thrust and thrust ripple. The thrust ripple can be caused by many factors, when the PMLSM is driven by sinusoidal currents, the main influencing factors can be summarised as end effect and magnetic saturation, these factors are due to structure parameters, control method, and load gathered together non-linearly, and the dominant one is variable owing to structure parameters [2, 3]. This paper attempt to model a novel PMLSM with high speed and high accuracy by optimising the motor structure parameters as air gap, polar pitch, length of permanent magnet, and width of permanent magnet. These thrust promotion and thrust ripple suppression methods can be achieved by design optimisation methods. Traditional analytical optimisation method is commonly used in motor design optimisation. This method can be surmised as analysis to deduce the objective function of the motor operation performance, then an intelligent algorithm is used to search the extremum of objective function [4, 5]. For instance, Siadatan et al. [6] proposed an analytical method to optimise a novel three-phase seven-layer switched reluctance motor, with the total torque per volume as a key indicator. Hasanien et al. [7] used particle swarm optimisation (PSO) to improve the analytical thrust of the motor. Li et al. [8] introduced the multiple population genetic algorithm to optimise the air-cored PMLSM with overlapping windings. The aforementioned analytical method where the constraints and independent variables are given analytically with an equivalent magnetic circuit. However, the major shortcoming of this technique would be a reduction in accuracy due to essential assumptions and the objective functions. Another method known as finite-element analysis (FEA) method is more accuracy, but it is low efficiency, much simulated calculation need to conduct. Compared with the aforementioned methods, Taguchi optimisation method [9-11] with 3D-finite element method (FEM) of electromagnetic field analysis does not need to use complicated algorithms and additional programming, and it also allows many settings of necessary structure parameters in design optimisation simultaneously. This method based on FEA has admirable accuracy compared with analytical method, after the minimal FEM analysis and weight influence analysis of different factors, the best combination of structure parameters can be obtained, its efficiency. Omekanda [12] used the Taguichi method to optimise the torque for a switched reluctance motor, Hwang et al. [13] proposed Taguchi method to optimise the surface-mounted permanent magnet motor. This study introduces the Taguchi method to PMSLM design optimisation to maximise the thrust and minimise the thrust ripple. The prototype of the PMLSM is manufactured according to the best combination of structural parameters, measurements of the motor can prove the superiority of the Taguchi optimisation method. 2 Initial PMLSM design The initial design model of the PMLSM is shown in Fig. 1. The main mechanical structure of this PMSLM was made of back-iron, coils and magnets. This PMSLM has a primary and double secondary, the machine design structure is the 'U'-model structure. Fig. 1Open in figure viewerPowerPoint PMLSM with double secondary According to requirements of laser cutting machines, namely, thrust should be up to 45 N, thrust ripple should under 1.5% and the highest speed should be up to 1.0 M/S. This three-phase, seven-pole, six-slot, and double-secondary PMLSM was selected for the initial PMLSM, which is constituted by 56 permanent magnets and six coils. The motor design implies the consideration of eight structure parameters comprising the geometrical dimensions presented in Fig. 2. Beyond the magnet width (w), magnet height (h), air gap between magnets and coils (δ), pole pitch (τ), distance between adjacent coils (d), coil width (l), coil length (hj), and thickness of stator (hi), the material of permanent magnet and the type of material used for the back iron should also be considered. The permanent magnets were made of Ndfe material with a remanence (Br) of 1.23 T, and the stator was constituted by M20 steel silicon. Magnet length, magnet width (w), distance between adjacent coils (d), coil width (l), and coil length (hj) were fixed at 40, 15, 14, 8 and 40 mm. Turns per coil was 200 as the other parameters were regarded as fixed and known. Four main undetermined factors of structure parameters are shown in Table 1 [8], h will influence the volume of magnets which result the magnetic field intensity, δ will influence the magnetic field distribution, τ will affect the end effect of PMSLM, d will influence the driving force of coils part. Table 1. Four main structure variables of motor design No. Factor Description 1 h height of magnets 2 δ air gap 3 τ pole pitch 4 d distance between two coils Fig. 2Open in figure viewerPowerPoint Semi-analytical model of PMLSM 3 Traditional analytical optimisation method 3.1 Thrust analysis The flow diagram of the traditional analytical optimisation method is shown in Fig. 3. Fig. 3Open in figure viewerPowerPoint Flow diagram of analytical optimisation method Thrust characteristics of the PMLSM is similar to the torque of rotary motors; they represent an important indicator to measure the motor performance [14]. High thrust can guarantee high acceleration and high speed which can result in significant moving quality and high load capability. The general objective of PMLSM design optimisation is to obtain a high thrust per volume [15]; furthermore, low thrust ripple can be the key to improve location precision and operation accuracy, it is highly important to reduce the thrust ripple of PMLSM; many scholars have investigated reducing the thrust ripple, which includes cogging force [16-22]; dominant thrust ripple reducing methods can be summarised into two types: software and structural methods. This paper adopted the latter method. Thrust is determined by many factors that are non-linear and extremely complex; several researchers have examined the subject of field calculations by semi-analytical modelling [23] to improve the accuracy and speed of analysis. A semi-analytical model of the PMLSM shown in Fig. 2 is presented for magnetic field calculation, which is generated by the permanent magnets; in this analytical model, we analyse the thrust on the basis of the following assumptions [7]: Variations along the z-axis do not exist. The permanent magnets are linearly demagnetised and permanently magnetised. The permeability of back-iron is infinite and the copper lines of coil are homogeneous. Magnetic vector potential distribution and magnetic flux density distribution are shown in Fig. 4. Fig. 4Open in figure viewerPowerPoint Magnetic vector and flux lines of PMLSM The permanent magnets can be replaced by the equivalent magnetising current distribution, and the magnetisation of permanent magnets can be expressed by Fourier series as follows (1)where Br, μ0, τ, and w are residual magnetisation, free space permeability, pole pitch, and magnet width, respectively, and mk is spatial frequency as follows (2)The Maxwell equations lead to the following Laplace and Poisson equations (3)where A1 is the magnetic vector potential of air gap and coils, and A2 is the magnetic vector potential, Ax1 and Ax2 are the vector potential of region 1, 2 along x- axis direction, Ay1 and Ay2 are the vector potential of region 1, 2 along y-axis direction. Boundary conditions are as follows (4)The flux density of air gap produced by the permanent magnets is as follows (5)where Mk is the coefficient given by (6)Electromotive thrust of each phase produced by flux density generated by permanent magnets is calculated as follows (7)S is the area of equivalent coils, L is the effective length of coils, and J is the current density. The different J of phases A, B, and C are as follows (8)where Nw, I, θ0, ω, and P are the number of wires in each phase, current effective value, initial phase angle, angular speed, and number of motor pole pairs, respectively. Thrust FA produced by phase A is calculated as follows (9)Hk is the coefficient given as follows (10)Therefore, electromagnetic thrust produced by three phases can be calculated as follows (11)Thrust ripple rate η can be expressed as follows (12)where k is the sampling point of time and is the average thrust. 3.2 PSO and evaluation According to our design model of the PMLSM, the design factor bounds followed the principles of PMLSM design and can be expressed as follows (13)PSO is an evolutionary calculation method introduced by Kennedy and Eberhart [24], which was stimulated by the social dynamics of fish schooling and bird flocking. PSO adopts the 'population' of particles that go through the problem hyperspace in the given velocities. At each iteration, according to the historical best position of the particle itself and the neighbourhood best position, the velocities of the individual particle are self-adapted to the appropriate value. According to the fitness function defined by users, both the particle best and the neighbourhood best can be gained. The movement of each particle naturally evolves to an optimal or close to optimal solution. The word 'swarm' comes from the irregular movements of the particles in the problem space [10]. In this study, PSO is applied to optimise the motor structure parameters to maximise the motor thrust and minimise the thrust ripple; after (11) and (12) are optimised, the 'optimal' of the motor thrust can reach 43.28 N through 250 evaluation iterations, and the 'optimal' of motor thrust ripple can be reduced to 2.27% after 200 evaluation iterations. The calculation of iteration results are shown in Fig. 5. Fig. 5Open in figure viewerPowerPoint Optimisation results obtained by PSO The comparison of results based on the initial model and PSO optimisation is shown in Table 2, the performance of the motor, which is optimised by analytical optimisation method and PSO, is better than that of the initial model. However, because of the veracity of the objective functions, the essential assumptions, and the local optimum of the algorithm, this method based on the equivalent magnetic circuit has a weakness in that accuracy is decreased and the optimum of results are approximate extremum. Table 2. Comparison results obtained by initial model and traditional analytical optimisation Variables Initial design PSO A: h, mm 2 3.43 B: δ, mm 1.8 1.93 C: τ, mm 18 18.8 D: d, mm 4 4.1 F: thrust, N 27.25 43.28 η: thrust ripple rate, % 6.46 2.27 4 Taguchi optimisation method Taguchi optimisation proposes a comprehensive framework for design optimisation of the PMLSM as shown in Fig. 6. Fig. 6Open in figure viewerPowerPoint Framework of Taguchi optimisation method Compared with the traditional analytical model, the FEM model can be more accurate, the FEM model is used for the thrust and thrust ripple calculation for each value of the structure parameters by conducting several 'numerical experiments' [25]. In the FEA software, a finite-element parametric model of a PMLSM shown in Fig. 7 was built, all the performances of the motor in the matrix experiments were analytically demonstrated [26]. Fig. 7Open in figure viewerPowerPoint Meshed cross section of PMLSM using finite elements 4.1 Establishment of orthogonal array Design of experiments (DOE) [27, 28] is a widely used approach to investigate a process or a system. A chain of organised experiments are designed in which several changes are proposed to the input variables of the process or the system. Influences of those changes on the outputs can be obtained online. In the PMLSM optimisation design, DOE can be used to explore the effects of various structure parameters on motor thrust and thrust ripple [29]. The method proposed in this paper is one of DOE, which is commonly known as Taguchi optimisation method; this method is one of those that use orthogonal array to screen the experimental conditions and means [30], the advantage of this method is that it uses the least experimental data based on the number of factors and levels in factor parameter space to achieve the best combination of parameter design and optimal results. Four undetermined factors exist, namely, h, δ, τ, and d, and each factor has three levels [31]. Corresponding to the main factor of the motor design shown in Table 3, a Taguchi orthogonal array L9 is established for numerical experiments. Nine combinations of structure parameters are the representations of multitudinous sample data. The traditional motor design method needs to calculate every time as each factor level changes, and it needs to calculate at least 34 = 81 times for experimental analysis, whereas the orthogonal array established by the Taguchi method using FEA software only needs to calculate for nine times. The calculation time is reduced by 89% because of the orthogonal array, and the analysis process becomes more efficient as uncertain factors increase [32]. The calculation results of array L9 are shown in Table 4. Table 3. Levels of main factor variables Factor variables, mm Level 1 Level 2 Level 3 A: h 2 3 4 B: δ 1.8 2.0 2.2 C: τ 18 19 20 D: d 4 5 6 Table 4. Experimental arrays and results of FEA No. Levels of each factor Performances A B C D F, N η, % 1 2 1.8 18 4 27.25 12.46 2 2 2.0 19 5 34.14 0.79 3 2 2.2 20 6 34.10 2.27 4 3 1.8 19 5 41.79 0.54 5 3 2.0 20 4 41.51 2.34 6 3 2.2 18 6 30.16 10.97 7 4 1.8 20 5 46.10 2.13 8 4 2.0 18 6 33.08 8.16 9 4 2.2 19 4 43.33 0.89 4.2 Analysis of mean value To analyse the influences on motor performances produced by different factors at different levels, Taguchi optimisation method uses the statistical mean made by orthogonal arrays and analysis results of FEM, as shown in Table 4. The average values are calculated as follows (14)The average F is 36.83 N and average η is 4.51% as shown in Table 5. Table 5. Average values of each performance Performances F(N) η, % average values 36.83 4.51 The average value of F under factor C (τ) at level 3 is calculated as (15). All the analysis results are shown in Table 6 and in Figs. 8 and 9. (15) Table 6. Average values of performance under each level of factor variable index Variables Level of each factor F, N η, % A 1 31.83 5.17 2 37.82 4.62 3 40.84 3.73 B 1 38.38 5.04 2 36.24 3.76 3 35.86 4.71 C 1 30.16 10.53 2 39.75 0.74 3 40.57 2.24 D 1 37.36 5.23 2 40.68 1.15 3 32.45 7.13 Fig. 8Open in figure viewerPowerPoint Main factor effects on motor thrust Fig. 9Open in figure viewerPowerPoint Main factor effects on motor thrust ripple 4.3 Proportions of influences produced by each factor's different levels on motor performance To analyse the proportions of influences on motor performances that are produced by each factor's different levels, analysis of variance that provides a measure of confidence is conducted, the sum of squares (SS) is a measure of the deviation of the experimental data from the average value of data; SS generated by various factors and different levels can be calculated as (16). All the results of SS and proportion are reported in Table 7. (16)x different factors: A, B, C, D, i levels of factors: 1, 2, 3, P motor performances: thrust: F (N), thrust ripple rate: η(%), average values of performances under x factor at i level as shown in Table 6, average values of performance as shown in Table 5. Table 7. Proportion of influences produced by various factors on motor performance Various factors F η SS Proportion, % SS Proportion, % A 126 28.58 3.17 1.39 B 11.07 2.5 2.65 1.15 C 201.01 45.59 166.82 72.94 D 102.86 23.33 56.08 24.52 total 440.94 100 228.72 100 A is the key factor of permanent magnets that can influence the magnetic vector potential and flux density distributions, B is crucial to the magnetic saturation that acts on the coils, C has a close relationship with the traveling wave magnetic field that is the dominant to the speed of a mover, and D has a large effect on coils, thereby influencing the active area result in the different current density. As shown in Table 7, F is sensitive to A, C, and D; C is the most sensitive factor; B has a relatively weak effect on F; η is sensitive to C and D; C is the most sensitive factor; and A has a relatively weak effect on η. Table 6 and Fig. 10 show that the best combination of factors for maximum motor thrust is determined to be (A3, B1, C3, and D2). Table 6 and Fig. 11 also show that the best combination of various factors for minimum motor thrust ripple is determined to be (A3, B2, C2, and D2). However, no elements are obviously selected to constitute the combination of the optimum design for maximum motor thrust and minimum motor thrust ripple at the same time. To achieve this goal, according to Tables 6 and 7, we can determine the effect proportion generated by each factor's different levels on motor performances. Finally, the best combination of factors for maximum motor thrust and minimum thrust ripple is selected to be (A3, B1, C2, and D2) [33-35]. Fig. 10Open in figure viewerPowerPoint Test platform for PMLSM (➊ Motor framework ➋ Coils ➌ Dynamometer ➍ Data collection device ➎ Prototype of test PMSLM ➏ Accompany motor ➐ Screw) Fig. 11Open in figure viewerPowerPoint Comparison of results 5 Experiment verification The prototype of the PMLSM was manufactured to validate the performances of optimised, test platform for the PMLSM was shown in Fig. 10, the motor was driven at 1.0 M/S by DSP controller as the dynamometer was adopted to measure the thrust curve [36]. Table 8 compares the structure parameters and output performances of the PMLSM between the initial model, traditional analytical optimisation method, Taguchi optimisation method and test. Table 8. Comparison of results gained by four approaches Initial PSO Taguchi Test A, mm 2 3.43 4 4 B, mm 1.8 1.93 1.8 1.8 C, mm 18 18.8 19 19 D, mm 4 4.1 5 5 F, N 27.25 43.28 46.71 46.62 η, % 6.46 2.27 0.41 0.46 The differences in motor thrust and thrust ripple produced by four different design approaches are shown in Fig. 11. From the initial to Taguchi, the promotion results are obvious. From PSO to Taguchi design, because of the veracity of the objective functions, the essential assumptions, and the local optimum of the algorithm, analytical method based on the equivalent magnetic circuit has a weakness that accuracy is decreased, and the optimum of results are approximate extremum. Owing to the increase in magnet volume, the thrust has a modest increase of 7.93%, thrust ripple has a significant reduction of 81.94% due to the more appropriate pole pitch, air gap and distance between two coils. The thrust curve of the Taguchi optimisation method is more stable because of the lowest thrust ripple. The results of the PMLSM measurement under the practical experimental condition are approximately the same. Thus, the results can prove the validity of the Taguchi optimisation method. 6 Conclusion A double secondary PMLSM applied in laser engraving machine with no cutting force was presented in this paper. Taguchi optimisation method was introduced to the motor design optimisation for thrust maximisation and thrust ripple minimisation after the comparative analytical formulas of thrust and thrust ripple based on the magnetic field analysis. After the accurate analysis of DOE and FEM, the different significances orders of magnet height (h), air gap between magnets and coils (δ), pole pitch (τ), distance between adjacent coils (d) are analysed and the proportions of influences produced by each factor's different levels on motor performances can be gained. The measurement of prototype shows that this optimisation method is more effective and believable to obtain the best combination of design parameters, which can result in the highest thrust and lowest thrust ripple. Compared with the traditional analytical method with PSO, due to the essential electromagnetic assumptions, and the local optimum of the algorithm, this method has a weakness that accuracy is decreased, the thrust of Taguchi method is promoted by 7.71% and thrust ripple is reduced by 79.7%. This novel optimisation method can obtain better optimisation results with high efficiency. 7 Discussion These parameters' variation will affect many performances of PMSLM [6], such as electromagnetic field distribution, no-load induced electromotive force, harmonic distortion rate, efficiency, thrust and thrust ripple. However, according to the performances requirements of laser machines which mainly influenced by thrust and thrust ripple. In this study, we mainly focus on these two performance indicators. Optimisation results of this study can also promote other performance such as the reduction of harmonic distortion rate and the no-load induced electromotive force waveform sine distortion rate. In the future work, we will study technology of high speed laser interference to test the repetition position accuracy which can promote the PMSLM more comprehensively. 8 Acknowledgment This work was supported by the National Natural Science Foundation of China under grant nos. 51277002 and 51577001 and 51637001. 9 References 1Cai, J.J., Lu, Q., Huang, X., et al: 'Thrust ripple of a permanent magnet LSM with step skewed magnets', IEEE Trans. Magn., 2012, 48, (11), pp. 4666– 4669 (doi: https://doi.org/10.1109/TMAG.2012.2198437) 2Zhu, Y.W., Lee, S.G., Chung, K.S., et al: 'Investigation of auxiliary poles design criteria on reduction of end effect of detent force for PMLSM', IEEE Trans. Magn., 2009, 45, (6), pp. 2863– 2866 (doi: https://doi.org/10.1109/TMAG.2009.2018778) 3Inoue, M., Sato, K.: 'An approach to a suitable stator length for minimizing the detent force of permanent magnet linear synchronous motors', IEEE Trans. Magn., 2000, 36, (4), pp. 1890– 1893 (doi: https://doi.org/10.1109/20.877814) 4Wang, M., Li, L., Pan, D.: 'Detent force compensation for PMLSM systems based on structural design and control method combination', IEEE Trans. Ind. Electron., 2015, 62, (11), pp. 6845– 6854 (doi: https://doi.org/10.1109/TIE.2015.2443096) 5Herisanu, N., Marinca, V., Gh, M.: 'An analytical approach to non-linear dynamical model of a permanent magnet synchronous generator', Wind Energy, 2014, 18, (9), pp. 1657– 1670 (doi: https://doi.org/10.1002/we.1785) 6Siadatan, A., Afjei, E., Torkaman, H.: 'Analytical design and fem verification of a novel three-phase seven layers switched reluctance motor', Prog. Electromagn. Res., 2013, 140, (11), pp. 131– 146 (doi: https://doi.org/10.2528/PIER13040705) 7Hasanien, H.M.: 'Particle swarm design optimization of transverse flux linear motor for weight reduction and improvement of thrust force', IEEE Trans. Ind. Electron., 2011, 58, (9), pp. 4048– 4056 (doi: https://doi.org/10.1109/TIE.2010.2100338) 8Li, L., Tang, Y., Pan, D.: 'Design optimization of air-cored PMLSM with overlapping windings by multiple population genetic algorithm', IEEE Trans. Magn., 2014, 50, (11), pp. 1– 5 9Ashabani, M., Mohamed, A.R.I., Milimonfared, J.: 'Optimum design of tubular permanent-magnet motors for thrust characteristics improvement by combined Taguchi–neural network approach', IEEE Trans. Magn., 2011, 46, (12), pp. 4092– 4100 (doi: https://doi.org/10.1109/TMAG.2010.2067450) 10Lee, S., Kim, K., Cho, S., et al: 'Optimal design of interior permanent magnet synchronous motor considering the manufacturing tolerances using Taguchi robust design', IET Electr. Power Appl., 2014, 8, pp. 23– 28 (doi: https://doi.org/10.1049/iet-epa.2013.0109) 11Hong, Y., Lin, F., Yu, T.: 'Taguchi method-based probabilistic load flow studies considering uncertain renewables and loads', IET Renew. Power Gener., 2015, 10, (2), pp. 221– 227 (doi: https://doi.org/10.1049/iet-rpg.2015.0196) 12Omekanda, A.M.: 'Robust torque and torque-per-inertia optimization of a switched reluctance motor using the Taguchi methods', IEEE Trans. Ind. Appl., 2005, 42, (2), pp. 473– 478 (doi: https://doi.org/10.1109/TIA.2006.870031) 13Hwang, C.C., Lyu, L.Y., Liu, C.T., et al: 'Optimal design of an SPM motor using genetic algorithms and Taguchi method', IEEE Trans. Magn., 2008, 44, pp. 4325– 4328 (doi: https://doi.org/10.1109/TMAG.2008.2001526) 14Tavana, N.R., Shoulaie, A., Dinavahi, V.: 'Analytical modeling and design optimization of linear synchronous motor with stair-step-shaped magnetic poles for electromagnetic launch applications', IEEE Trans. Plasma Sci., 2012, 40, (2), pp. 519– 527 (doi: https://doi.org/10.1109/TPS.2011.2178616) 15Yoshimura, T., Kim, H.J., Watada, M., et al: 'Analysis of the reduction of detent force in a permanent magnet linear synchronous motor', IEEE Trans. Magn., 1995, 31, (6), pp. 3728– 3730 (doi: https://doi.org/10.1109/20.489752) 16Bianchi, N., Bolognani, S., Cappello, A.D.F.: 'Reduction of cogging force in PM linear motors by pole-shifting', IET Electr. Power Appl., 2005, 152, (3), pp. 703– 709 (doi: https://doi.org/10.1049/ip-epa:20045082) 17Youn, S.W., Lee, J.J., Yoon, H.S., et al: 'A new cogging-free permanent-magnet linear motor', IEEE Trans. Magn., 2008, 44, (7), pp. 1785– 1790 (doi: https://doi.org/10.1109/TMAG.2008.918921) 18Lim, J., Jung, H.K.: ' Cogging force reduction in permanent magnet linear motor using phase set shift'. Int. Conf. on Electrical Machines and Systems, 2008, pp. 1– 4 19Lim, K.C., Woo, J.K., Kang, G.H., et al: 'Detent force minimization techniques in permanent magnet linear synchronous motors', IEEE Trans. Magn., 2002, 38, (2), pp. 1157– 1160 (doi: https://doi.org/10.1109/20.996296) 20Lee, H.W., Park, C.B., Ju, L.: 'Improvement of thrust force properties of linear synchronous motor for an ultra-high-speed tube train', IEEE Trans. Magn., 2011, 47, (11), pp. 4629– 4634 (doi: https://doi.org/10.1109/TMAG.2011.2158584) 21Meessen, K.J., Gysen, B.L.J., Paulides, J.J.H., et al: 'Halbach permanent magnet shape selection for slotless tubular actuators', IEEE Trans. Magn., 2008, 44, (11), pp. 4305– 4308 (doi: https://doi.org/10.1109/TMAG.2008.2001536) 22Liu, Z., Zhao, W., Ji, J., et al: 'A novel double-stator tubular vernier permanent-magnet motor with high thrust density and low cogging force', IEEE Trans. Magn., 2015, 51, (7), pp. 1– 1 23Li, L., Pan, D., Huang, X.: 'Analysis and optimization of ironless permanent-magnet linear motor for improving thrust', IEEE Trans. Plasma Sci., 2013, 41, (41), pp. 1188– 1192 (doi: https://doi.org/10.1109/TPS.2013.2245425) 24Eberhart, R., Kennedy, J.: ' A new optimizer using particle swarm theory', Proc. Int. Conf. Micro Machine and Human Science (MHS), ( Washington, USA, October 1995) pp. 39– 43 25Lin, F.J., Chou, P.H., Hung, Y.C., et al: 'Field-programmable gate array-based functional link radial basis function network control for permanent magnet linear synchronous motor servo drive system', IET Electr. Power Appl., 2010, 4, (5), pp. 357– 372 (doi: https://doi.org/10.1049/iet-epa.2009.0104) 26Kazerooni, M., Hamidifar, S., Kar, N.C.: 'Analytical modelling and parametric sensitivity analysis for the PMSM steady-state performance prediction', IET Electr. Power Appl., 2013, 7, (7), pp. 586– 596 (doi: https://doi.org/10.1049/iet-epa.2011.0281) 27Cheng, H., Chen, H., Yang, Z.: 'Design indicators and structure optimisation of switched reluctance machine for electric vehicles', IET Electr. Power Appl., 2015, 9, (4), pp. 319– 331 (doi: https://doi.org/10.1049/iet-epa.2014.0291) 28Tavakoli, A., Sohrabi, M., Choi, C.J., et al: 'Effects of pertinent operating parameters on the size of iron nanoparticles synthesised by chemical vapour condensation method applying experimental design procedure', IET Micro Nano, 2010, 5, (2), pp. 135– 139 (doi: https://doi.org/10.1049/mnl.2009.0109) 29Tsili, M.A., Amoiralis, E.I., Kladas, A.G., et al: 'Optimal design of multi-winding transformer using combined FEM, taguchi and stochastic-deterministic approach', IET Electr. Power Appl., 2012, 6, pp. 437– 454 (doi: https://doi.org/10.1049/iet-epa.2011.0310) 30Kim, S.A., Zhu, Y.W., Lee, S.G., et al: 'Electromagnetic normal force characteristics of a permanent magnet linear synchronous motor with double primary side', IEEE Trans. Magn., 2014, 50, (1), pp. 1– 4 31Zhang, Y., Yang, Z., Yu, M., et al: 'Analysis and design of double-sided air core linear servo motor with trapezoidal permanent magnets', IEEE Trans. Magn., 2011, 47, (10), pp. 3236– 3239 (doi: https://doi.org/10.1109/TMAG.2011.2156398) 32Ma, C., Qu, L.: 'Multiobjective optimization of switched reluctance motors based on design of experiments and particle swarm optimization', IEEE Trans. Energy Convers., 2015, 30, (3), pp. 1– 10 (doi: https://doi.org/10.1109/TEC.2015.2411677) 33Hasanien, H.M., Abd-Rabou, A.S., Sakr, S.M.: 'Design optimization of transverse flux linear motor for weight reduction and performance improvement using response surface methodology and genetic algorithms', IEEE Trans. Energy Convers., 2010, 25, (3), pp. 598– 605 (doi: https://doi.org/10.1109/TEC.2010.2050591) 34Kim, Y.S., Park, I.H.: 'Topology optimization of rotor in synchronous reluctance motor using level set method and shape design sensitivity', IEEE Trans. Appl. Supercond., 2010, 20, (3), pp. 1093– 1096 (doi: https://doi.org/10.1109/TASC.2010.2040725) 35Sarikhani, A., Mohammed, O.A.: 'HIL-based finite-element design optimization process for the computational prototyping of electric motor drives', IEEE Trans. Energy Convers., 2012, 27, pp. 737– 746 (doi: https://doi.org/10.1109/TEC.2012.2200897) 36Dhariwal, R., Leonard, M., Desmulliez, M.P.Y., et al: 'Microengineered dynamometer for microfan thrust measurement', Electron. Lett., 2006, 42, (24), pp. 1394– 1395 (doi: https://doi.org/10.1049/el:20062596) Citing Literature Volume11, Issue1January 2017Pages 41-48 FiguresReferencesRelatedInformation
Publication Year: 2017
Publication Date: 2017-01-01
Language: en
Type: article
Indexed In: ['crossref']
Access and Citation
Cited By Count: 65
AI Researcher Chatbot
Get quick answers to your questions about the article from our AI researcher chatbot