基于有限元模型的SR电机振动分析
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摘要
开关磁阻电机(Switched Reluctance Motor简称:SR电机)是双凸极的结构形式,磁路的高度非线性使得其精确模型很难建立;且由于SR电机由脉冲供电,电机气隙小,有显著变化的径向磁吸力,使壳体结构发生压缩形变而振动,引起SR电机较大的振动和噪声,限制了其应用范围。本文基于虚位移原理得出径向力数值解,并进一步研究了径向力所引起的振动响应,对SR电机振动和噪声的研究有重要的实际意义。
基于有限元原理,本文利用ANSYS软件对SR电机二维电磁场进行分析和计算,并应用虚位移法求解非线性径向力,得出样机径向力与转子位置角和定子相电流的非线性关系曲线,在二维电磁场计算结果的基础上,利用Matlab/Simulink仿真软件建立仿真模型,实行电流斩波控制(CCC)进行动态仿真,仿真结果与理论分析一致,验证了有限元模型的准确性和仿真模型的有效性。从振动系统的运动方程出发,导出了从激振力到振动加速度的传递函数,结合由磁场有限元计算得到的径向力非线性模型进行振动仿真,对径向力及振动加速度波形进行频谱分析,从而可找到它们主要的谐波分量,避免与SR电机定子的固有频率接近而引起共振是降低SR电机振动和噪声的必要条件。
The double saliency of the stator and the rotor poles of switched reluctance motor(SRM), as well as the highly saturated nature of the flux density induces the accurate model of SRM is difficult to be constructed. SRM is excited by the pulse and the gap of the motor is small. The remarkable variational radial force during the motor running makes the shelly structure distortion, which induces the serious vibration and acoustic noise of SRM. This paper obtains the exact numeric results of radial force and studies the vibration response caused by the radial force. The results are very helpful to the reseach of vibration and acoustic noise of SRM.
In this dissertattion, 2D electromagnetic field of SRM is analysed and calculated by using ANSYS based on the finite element formulation. The non-linear static radial forces at different rotor positions and different phase current excitations are obtained according to the principle of virtual-work. The Matlab/Simulink software is employed to build the simulation model based on the results calculated by the finite element and the dynamic system simulation is done under Chopped Current Control (CCC). The results of simulation are corresponding with theoretical analysis, which validate the effective of the finite element model and simulatiton model.From motion equations, the transfer function from exciting force to the vibrative acceleration is derived. Vibration simulation is completed combining the non-linear model of the radial force obtained by the finite element calculation. The main harmonics components of radial force waveform are derived by the spectrum analysis. It is the primary condition of reducing vibration and acoustic noise to avoid the matching of main harmonics of the radial force with the natural frequencies of SRM.
基于有限元原理,本文利用ANSYS软件对SR电机二维电磁场进行分析和计算,并应用虚位移法求解非线性径向力,得出样机径向力与转子位置角和定子相电流的非线性关系曲线,在二维电磁场计算结果的基础上,利用Matlab/Simulink仿真软件建立仿真模型,实行电流斩波控制(CCC)进行动态仿真,仿真结果与理论分析一致,验证了有限元模型的准确性和仿真模型的有效性。从振动系统的运动方程出发,导出了从激振力到振动加速度的传递函数,结合由磁场有限元计算得到的径向力非线性模型进行振动仿真,对径向力及振动加速度波形进行频谱分析,从而可找到它们主要的谐波分量,避免与SR电机定子的固有频率接近而引起共振是降低SR电机振动和噪声的必要条件。
The double saliency of the stator and the rotor poles of switched reluctance motor(SRM), as well as the highly saturated nature of the flux density induces the accurate model of SRM is difficult to be constructed. SRM is excited by the pulse and the gap of the motor is small. The remarkable variational radial force during the motor running makes the shelly structure distortion, which induces the serious vibration and acoustic noise of SRM. This paper obtains the exact numeric results of radial force and studies the vibration response caused by the radial force. The results are very helpful to the reseach of vibration and acoustic noise of SRM.
In this dissertattion, 2D electromagnetic field of SRM is analysed and calculated by using ANSYS based on the finite element formulation. The non-linear static radial forces at different rotor positions and different phase current excitations are obtained according to the principle of virtual-work. The Matlab/Simulink software is employed to build the simulation model based on the results calculated by the finite element and the dynamic system simulation is done under Chopped Current Control (CCC). The results of simulation are corresponding with theoretical analysis, which validate the effective of the finite element model and simulatiton model.From motion equations, the transfer function from exciting force to the vibrative acceleration is derived. Vibration simulation is completed combining the non-linear model of the radial force obtained by the finite element calculation. The main harmonics components of radial force waveform are derived by the spectrum analysis. It is the primary condition of reducing vibration and acoustic noise to avoid the matching of main harmonics of the radial force with the natural frequencies of SRM.
引文
[1]吴建华.开关磁阻电机设计与应用[M].北京:机械工业出版社,2000
[2]刘迪吉.开关磁阻电机发展与应用[J].微电机,2006(7),17~20
[3]李俊卿,李和明.开关磁阻电机发展综述[J].华北电力大学学报,2002,29(1):1~5
[4]刘迪吉等.开关磁阻调速电动机[M].北京:机械工业出版社.1994
[5]王宏华.开关型磁阻电动机调速控制技术[M].北京:机械工业出版社,1995
[6] Cameron D E et al. The Origin of Acoustic Noise in Variable-Reluctance Motors[J]. Proc. IEEE. IAS Annual Meeting, 1989: 108~115
[7] Cameron D E et al. The Origin and Reduction of Acoustic Noise in Doubly Salient Variable-reluctance Motors, IEEE. Trans. on IA, 1992, 28(6): 1250~1255
[8] Wu C Y et al. Analysis and Reduction of Vibration and Acoustic Noise in the Switched Reluctance Drive. IEEE. Trans. on IA, 1995, 31(1): 91~98
[9] S.P.Verrna, R.S.Girgis,“Method for accurate determination resonant frequencies and vibration behavior of stators of electrical machines”, Proceedings of lEE, Part B, 1981, 128(1): 1-11
[10] W.Cai, P.Pillay and A.Omekanda, An analytical model to predict the modal frequencies of switched reluctance motors, IEEE IEMDC, Boston, MA, June 2001, pp.203~207
[11]吴建华等.开关磁阻电机定子固有频率的计算[J].中国电机工程报,1997,17(5):326-329
[12]王宏华等.开关磁阻调速电机定子振动抑制[J].电工技术学报, 1998,13(3):9~12
[13] Yifan Tang,“Characterization, numerical analysis, and design of switched reluctance motors”, IEEE Transactions on Industry Applications, 1997, 33(6): 1544~1522
[14] A.M.Michaelides, C.Pollock,“Modeling and Design of Switched Reluctance Motors with Two Phases Simutaneously Excited”, IEE Proc.-Electr. Power Appl., 1996, 143(5): 361~370
[15] R.S.Colby, F.Mottier, T.J.E.Miller,“Vibration modes and acoustic noise in a 4-phase switched reluctance motor”, IEEE Trans. On Industry Applications, 1996, 32(6): 1357~1364
[16] P.Pillay, W.Cai,“Investigation into vibration in switched reluctance motor”, IEEE Transactions on Industry Applications, 1999, 35(3): 589~596
[17] S.A.Long, Z.Q.Zhu, D.Howe,“Vibration Behavior of Stators of Switched Reluctance Motors”, IEE Proceedings: Electric Power Aplications, 2001, 148(3): 257~264
[18] M.Besbes, C.Picod, F.Camus, M.Gabsi,“Influence of Stator Geometry upon Vibratory Behavior and Electromagnetic Performances of Switched Reluctance Motors”, IEEE Proceedings: Electric Power Applications, 1998, 145(5): 462~467
[19] W.Cai, P.Pillay and K.Reichert,“Accurate Computation of Electromagnetic Forces in Switched Reluctance Motors”, Proceedings of the 5th International Conference on ElectricalMachines & Systems, Aug 2001, Shenyang, China
[20] R.S.Girgis, S.P.Verma,“Experimental verification of resonant frequencies and vibration behavior of stators of electrical machines, partⅠ- models, experimental procedure an apparatus”, proceedings of IEE, Part B, 1981, 128(1): 12~21
[21] S.P.Verma, R.S.Girgis,“Experimental verification of resonant frequencies and vibration behavior of stators of electrical machines, partⅡ- experimental investigations and results”, Proceedings of IEE, Part B, 1981, 128(1): 22~32
[22] W.Cai, P.Pillay, Z.Tang,“Impact of Stator Windings and End Bells on Resonant Frequencies and Mode Shapes of Switched Reluctance Motors”, IEEE Transactions on Industry Applications, 2002, 38(4): 1027~1036
[23] Zhangjun Tang,“Vibration Analysis and Reduction in Switched Reluctance Motors”[D], Ph.D. thesis, Clarkson University, 2002
[24]纪志成,薛花.基于MATLAB的开关磁阻电机控制系统仿真建模研究[J].系统仿真学报,2005,17(4):1015~1021
[25]陈新,郑洪涛,蒋静坪.基于MATLAB的开关磁阻电动机非线性动态模型仿真[J].电气传动,2002(6):52~56
[26]全星慧,开关磁阻电机磁场有限元分析及稳态特性研究[D],大庆石油学院,2005
[27]汤蕴璆.电机内的电磁场.北京:科学出版社,1998
[28]金建铭.电磁场有限元方法[M].陕西:西安电子科技大学出版社,2004
[29]张榴晨,徐松.有限元法在电磁计算中的应用[M].北京:中国铁道出版社,1996
[30]詹琼华等.四极四相开关磁阻电机电磁场的有限元分析[J].华中理工大学学报,1998, 17(1):1~8
[31] Omekanda A M, Renglet M,“Calculation of the electromagnetic parameters of a switched reluctance motor using an improved FEM BIEM- application to different models for the torque calculation”, IEEE Trans. on Ind. Applic, 1997, 33(4): 914~918
[32]林鹤云,周鹗,黄建中,蒋全.开关磁阻电机磁场有限元分析与铁耗计算[J].电工技术学报, 1996,11(1):24~29
[33]陈隆昌,毛立志.用有限元法分析和计算开关磁阻电机的特性[J].中小型电机,1994,21(1):8~12
[34]阎照文,工程电磁分析技术与实例祥解[M].北京:中国水利水电出版社,2006
[35]王国强,使用工程数值模拟技术及其在ANSYS上的实践[M].西安:西北工业大学出版社, 2001
[36] F.Soares, P.J.Costa Branco,“Simulation of a 6/4 Switched Reluctance Motor Based on Matlab/Simulink Environment”[J]. IEEE Trans. on Aerospace and Electronic Systems, 2001, 37(3): 989~1009
[37]杨燕,杨松,王振民.ANSYS软件在开关磁阻电机电磁分析中的应用[J].煤炭科学技术, 2001,29(4):20~22
[38]王忠建.开关磁阻电机振动的有限元分析与控制研究[D].江苏:河海大学,2002
[39]严加根,刘闯,姚国飞等.开关磁阻电机矩角特性的研究与应用[J].电工技术学报,2005,20(9):29~33
[40]谭国俊,蒯松岩,何凤有.电压斩波控制的开关磁阻电机非线性仿真分析[J].系统仿真学报,2006,18(2):478~481
[41]谢德馨,姚缨英,白保东,李锦彪.三维涡流场的有限元分析[M].北京:机械工业出版社,2000
[42]阎秀恪,谢德馨,高彰燮,于存湛.电磁力有限元分析中麦克斯韦应力法的积分路径选取的研究[J].电工技术学报
[43] Kabashima T.,Kawahara A.,Goto T.,“Force calculation using magnetizing currents”. Megnetics, IEEE Transactions on Magnetics, 1988, 24(1): 451~454
[44] Akihisa Kameari,“Local force calculation in 3D FEM with edge elements”, International J.applied electromagnetics in materials, 1993(3): 231~240
[45]王蔷,李国定,龚克.电磁场理论基础[M].北京:清华大学出版社,2001
[46]姚俊,马松辉.Simulink建模与仿真[M].陕西:西安电子科技大学出版社,2007
[47]孙亮.MATLAB语言与控制系统仿真[M].北京:北京工业大学出版社,2001
[48]吴建华.基于物理模型开关磁阻电机定子模态和固有频率的研究[J].中国电机工程学报.2004,24(8):109~114
[49] Zhangjun Tang, Pillay, P., Omekanda, A.M..“Vibration prediction in switched reluctance motors with transfer function identification from shaker and force hammer tests”[J]. IEEE Transactions on Industry Applications, 2003, 39(4): 978~985
[2]刘迪吉.开关磁阻电机发展与应用[J].微电机,2006(7),17~20
[3]李俊卿,李和明.开关磁阻电机发展综述[J].华北电力大学学报,2002,29(1):1~5
[4]刘迪吉等.开关磁阻调速电动机[M].北京:机械工业出版社.1994
[5]王宏华.开关型磁阻电动机调速控制技术[M].北京:机械工业出版社,1995
[6] Cameron D E et al. The Origin of Acoustic Noise in Variable-Reluctance Motors[J]. Proc. IEEE. IAS Annual Meeting, 1989: 108~115
[7] Cameron D E et al. The Origin and Reduction of Acoustic Noise in Doubly Salient Variable-reluctance Motors, IEEE. Trans. on IA, 1992, 28(6): 1250~1255
[8] Wu C Y et al. Analysis and Reduction of Vibration and Acoustic Noise in the Switched Reluctance Drive. IEEE. Trans. on IA, 1995, 31(1): 91~98
[9] S.P.Verrna, R.S.Girgis,“Method for accurate determination resonant frequencies and vibration behavior of stators of electrical machines”, Proceedings of lEE, Part B, 1981, 128(1): 1-11
[10] W.Cai, P.Pillay and A.Omekanda, An analytical model to predict the modal frequencies of switched reluctance motors, IEEE IEMDC, Boston, MA, June 2001, pp.203~207
[11]吴建华等.开关磁阻电机定子固有频率的计算[J].中国电机工程报,1997,17(5):326-329
[12]王宏华等.开关磁阻调速电机定子振动抑制[J].电工技术学报, 1998,13(3):9~12
[13] Yifan Tang,“Characterization, numerical analysis, and design of switched reluctance motors”, IEEE Transactions on Industry Applications, 1997, 33(6): 1544~1522
[14] A.M.Michaelides, C.Pollock,“Modeling and Design of Switched Reluctance Motors with Two Phases Simutaneously Excited”, IEE Proc.-Electr. Power Appl., 1996, 143(5): 361~370
[15] R.S.Colby, F.Mottier, T.J.E.Miller,“Vibration modes and acoustic noise in a 4-phase switched reluctance motor”, IEEE Trans. On Industry Applications, 1996, 32(6): 1357~1364
[16] P.Pillay, W.Cai,“Investigation into vibration in switched reluctance motor”, IEEE Transactions on Industry Applications, 1999, 35(3): 589~596
[17] S.A.Long, Z.Q.Zhu, D.Howe,“Vibration Behavior of Stators of Switched Reluctance Motors”, IEE Proceedings: Electric Power Aplications, 2001, 148(3): 257~264
[18] M.Besbes, C.Picod, F.Camus, M.Gabsi,“Influence of Stator Geometry upon Vibratory Behavior and Electromagnetic Performances of Switched Reluctance Motors”, IEEE Proceedings: Electric Power Applications, 1998, 145(5): 462~467
[19] W.Cai, P.Pillay and K.Reichert,“Accurate Computation of Electromagnetic Forces in Switched Reluctance Motors”, Proceedings of the 5th International Conference on ElectricalMachines & Systems, Aug 2001, Shenyang, China
[20] R.S.Girgis, S.P.Verma,“Experimental verification of resonant frequencies and vibration behavior of stators of electrical machines, partⅠ- models, experimental procedure an apparatus”, proceedings of IEE, Part B, 1981, 128(1): 12~21
[21] S.P.Verma, R.S.Girgis,“Experimental verification of resonant frequencies and vibration behavior of stators of electrical machines, partⅡ- experimental investigations and results”, Proceedings of IEE, Part B, 1981, 128(1): 22~32
[22] W.Cai, P.Pillay, Z.Tang,“Impact of Stator Windings and End Bells on Resonant Frequencies and Mode Shapes of Switched Reluctance Motors”, IEEE Transactions on Industry Applications, 2002, 38(4): 1027~1036
[23] Zhangjun Tang,“Vibration Analysis and Reduction in Switched Reluctance Motors”[D], Ph.D. thesis, Clarkson University, 2002
[24]纪志成,薛花.基于MATLAB的开关磁阻电机控制系统仿真建模研究[J].系统仿真学报,2005,17(4):1015~1021
[25]陈新,郑洪涛,蒋静坪.基于MATLAB的开关磁阻电动机非线性动态模型仿真[J].电气传动,2002(6):52~56
[26]全星慧,开关磁阻电机磁场有限元分析及稳态特性研究[D],大庆石油学院,2005
[27]汤蕴璆.电机内的电磁场.北京:科学出版社,1998
[28]金建铭.电磁场有限元方法[M].陕西:西安电子科技大学出版社,2004
[29]张榴晨,徐松.有限元法在电磁计算中的应用[M].北京:中国铁道出版社,1996
[30]詹琼华等.四极四相开关磁阻电机电磁场的有限元分析[J].华中理工大学学报,1998, 17(1):1~8
[31] Omekanda A M, Renglet M,“Calculation of the electromagnetic parameters of a switched reluctance motor using an improved FEM BIEM- application to different models for the torque calculation”, IEEE Trans. on Ind. Applic, 1997, 33(4): 914~918
[32]林鹤云,周鹗,黄建中,蒋全.开关磁阻电机磁场有限元分析与铁耗计算[J].电工技术学报, 1996,11(1):24~29
[33]陈隆昌,毛立志.用有限元法分析和计算开关磁阻电机的特性[J].中小型电机,1994,21(1):8~12
[34]阎照文,工程电磁分析技术与实例祥解[M].北京:中国水利水电出版社,2006
[35]王国强,使用工程数值模拟技术及其在ANSYS上的实践[M].西安:西北工业大学出版社, 2001
[36] F.Soares, P.J.Costa Branco,“Simulation of a 6/4 Switched Reluctance Motor Based on Matlab/Simulink Environment”[J]. IEEE Trans. on Aerospace and Electronic Systems, 2001, 37(3): 989~1009
[37]杨燕,杨松,王振民.ANSYS软件在开关磁阻电机电磁分析中的应用[J].煤炭科学技术, 2001,29(4):20~22
[38]王忠建.开关磁阻电机振动的有限元分析与控制研究[D].江苏:河海大学,2002
[39]严加根,刘闯,姚国飞等.开关磁阻电机矩角特性的研究与应用[J].电工技术学报,2005,20(9):29~33
[40]谭国俊,蒯松岩,何凤有.电压斩波控制的开关磁阻电机非线性仿真分析[J].系统仿真学报,2006,18(2):478~481
[41]谢德馨,姚缨英,白保东,李锦彪.三维涡流场的有限元分析[M].北京:机械工业出版社,2000
[42]阎秀恪,谢德馨,高彰燮,于存湛.电磁力有限元分析中麦克斯韦应力法的积分路径选取的研究[J].电工技术学报
[43] Kabashima T.,Kawahara A.,Goto T.,“Force calculation using magnetizing currents”. Megnetics, IEEE Transactions on Magnetics, 1988, 24(1): 451~454
[44] Akihisa Kameari,“Local force calculation in 3D FEM with edge elements”, International J.applied electromagnetics in materials, 1993(3): 231~240
[45]王蔷,李国定,龚克.电磁场理论基础[M].北京:清华大学出版社,2001
[46]姚俊,马松辉.Simulink建模与仿真[M].陕西:西安电子科技大学出版社,2007
[47]孙亮.MATLAB语言与控制系统仿真[M].北京:北京工业大学出版社,2001
[48]吴建华.基于物理模型开关磁阻电机定子模态和固有频率的研究[J].中国电机工程学报.2004,24(8):109~114
[49] Zhangjun Tang, Pillay, P., Omekanda, A.M..“Vibration prediction in switched reluctance motors with transfer function identification from shaker and force hammer tests”[J]. IEEE Transactions on Industry Applications, 2003, 39(4): 978~985