笼型感应电动机断条故障的有限元计算与分析
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摘要
笼型感应电动机是各种生产过程中应用最为广泛的能量转换装置,保证它们在生产过程中安全可靠的运行具有重要意义。转子断条故障是这类电机的一种较难避免而又不易被检测到的常见故障。因此,了解笼型感应电机转子断条故障机理对防止感应电机运行中出现事故,保障安全生产具有重要意义。
本文首先根据电磁场理论建立Y802-2型三相笼型感应电动机二维电磁场的数学模型,并对其进行了有限元离散以及泛函分析,推导出总体方程;在基本假设和边界条件基础上,给出笼型感应电动机二维电磁场的求解区域,然后应用有限元并结合内外双收敛方法,对样机稳态运行进行数值计算,得出电机在转子完好、一根导条断裂、连续两根导条断裂、间隔一根两根导条断裂、间隔两根两根导条断裂及连续四根导条断裂六种情况下的磁场分布和导条所受电磁力的变化情况。为了考虑转子斜槽对电机特性的影响,应用多截面有限元法求解在上述各种故障情况下的转子导条电流。其次,利用时步有限元理论,建立了求解域内的场路耦合时步有限元方程,对样机的上述故障情况下的起动过程进行了仿真分析,并对多种断条故障下的定子电流进行了快速傅立叶分析,确定出其边频分量,得出一些有益的结论。最后对样机在转子完好、一根导条断裂、连续两根导条断裂这三种情况进行了实验,与计算结果相符,为电机故障诊断提供了理论依据。
Squirrel-cage induction motors are used most widely in the process of energy conversion in industry. It is important to keep them in reliable and safe operation. The fault of broken bars is an ordinary fault which can not be easily avoided and is difficult to examine. Therefore, it plays an important part in preventing accidents and insuring safe operation to study the influence of broken bars on the motor’s operation.
Firstly, according to electromagnetic field theory, the 2-dimensional (2-D) mathematical model of a three phase squirrel-cage Y802-2 induction motor is developed. Then general equations can be deduced from finite element discrete and functional analysis. The motor’s 2D solving region of electromagnetic field is given based on the boundary conditions and assumption conditions of the squirrel-cage induction motor. Through finite element mothod (FEM) and inner–outer convergence method, magnetic field distributions and magnetic forces of bars can be calculated in following rotor conditions: health rotor, one single broken bar, two adjacent broken bars, two broken bars with one good interval, two broken bars with two good interval and four adjacent broken bars. In order to consider the influence of skewed slots on the motor’s performances, the multi-slice EFM is used to calculate currents of bars with the above mentioned conditions. Secondly, according to the time-step finite element method, the equations of time-step FEM coupling field and circuit in the solving region were established, and the starting performances of squirrel-cage induction motor with rated load are simulated and analyzed. In addition, the A phase stator current is analyzed using FFT, some valuable conclusions are obtained by comparing the side frequency component. In the procedure of finishing this paper, some experiments are done under conditions such as health rotor, one bar broken and two adjacent bars broken. Theoretical approach and experimental results confirm the validity of the proposed method and offer theoretical support for diagnosing broken bars technology.
本文首先根据电磁场理论建立Y802-2型三相笼型感应电动机二维电磁场的数学模型,并对其进行了有限元离散以及泛函分析,推导出总体方程;在基本假设和边界条件基础上,给出笼型感应电动机二维电磁场的求解区域,然后应用有限元并结合内外双收敛方法,对样机稳态运行进行数值计算,得出电机在转子完好、一根导条断裂、连续两根导条断裂、间隔一根两根导条断裂、间隔两根两根导条断裂及连续四根导条断裂六种情况下的磁场分布和导条所受电磁力的变化情况。为了考虑转子斜槽对电机特性的影响,应用多截面有限元法求解在上述各种故障情况下的转子导条电流。其次,利用时步有限元理论,建立了求解域内的场路耦合时步有限元方程,对样机的上述故障情况下的起动过程进行了仿真分析,并对多种断条故障下的定子电流进行了快速傅立叶分析,确定出其边频分量,得出一些有益的结论。最后对样机在转子完好、一根导条断裂、连续两根导条断裂这三种情况进行了实验,与计算结果相符,为电机故障诊断提供了理论依据。
Squirrel-cage induction motors are used most widely in the process of energy conversion in industry. It is important to keep them in reliable and safe operation. The fault of broken bars is an ordinary fault which can not be easily avoided and is difficult to examine. Therefore, it plays an important part in preventing accidents and insuring safe operation to study the influence of broken bars on the motor’s operation.
Firstly, according to electromagnetic field theory, the 2-dimensional (2-D) mathematical model of a three phase squirrel-cage Y802-2 induction motor is developed. Then general equations can be deduced from finite element discrete and functional analysis. The motor’s 2D solving region of electromagnetic field is given based on the boundary conditions and assumption conditions of the squirrel-cage induction motor. Through finite element mothod (FEM) and inner–outer convergence method, magnetic field distributions and magnetic forces of bars can be calculated in following rotor conditions: health rotor, one single broken bar, two adjacent broken bars, two broken bars with one good interval, two broken bars with two good interval and four adjacent broken bars. In order to consider the influence of skewed slots on the motor’s performances, the multi-slice EFM is used to calculate currents of bars with the above mentioned conditions. Secondly, according to the time-step finite element method, the equations of time-step FEM coupling field and circuit in the solving region were established, and the starting performances of squirrel-cage induction motor with rated load are simulated and analyzed. In addition, the A phase stator current is analyzed using FFT, some valuable conclusions are obtained by comparing the side frequency component. In the procedure of finishing this paper, some experiments are done under conditions such as health rotor, one bar broken and two adjacent bars broken. Theoretical approach and experimental results confirm the validity of the proposed method and offer theoretical support for diagnosing broken bars technology.
引文
1 徐伯强. 异步电动机绕组故障分析及其检测方法研究. 华北电力大学博士学位论文, 2005:1~2, 17~19
2 M. Jufer and M. A. Abdul. Influence D’une Rupture de Barre ou D’un Anneau Sur les Charactristiques externs d’un Motor Asynchrony a Cage. Bull SEV/LSE(Switzerland), Vol.69, No.17,Sept.1978
3 B. G. Gaydon, C. Hargis, K. Kamash. The Detection of Rotor Faults in Induction Motor. IEE Conference on Electrical Machines-Design and Applications. London (UK), 1982:216~220
4 M. E. Steele, R. A. Ashen and L. G. Knighe. An Electrical Method of Monitoring motor. Proc. of Int Conf on Electrical Machines. IEE London, Conference Publn 312, July,1982:231~235
5 S. Williamson, A. C. Smith. Speedy State Analysis of 3-phase Cage Motors. in Proc. Inst. Elec. Eng. Nol. 129 No.3, 1982:93~100
6 A. J. Marques Cardoso, S. M. A. Cruz, J. F. S. Carvalho. Rotor Cage Fault Diagnosis in Three-phase Induction Motor. by Park’s Vector Approach. Proceedings of the 1995 IEEE IAS Annual Meeting. San Diego(USA), 642~646
7 S. M. A. Cruz, A. J. Marques Cardoso. Rotor Cage Fault Diagnosis in Three-phase Induction Motor by Extended Park’s Vector Approach. Electric Machines and Power Systems. 2000,28:289~299
8 窦玉琴, 付立军等. 微机在线检测鼠笼异步电动机转子的故障. 电工电能新技术. 1993,(1):13~18
9 王凤昌, 李面换. 异步电机故障的电流检测和诊断. 哈尔滨工业大学学报. 1994,26(6):88~93
10 时献江, 周馨, 屈梁生. 设备故障诊断的电机电流法. 哈尔滨电工学院学报. 1992,15(1):57~61
11 周东华. 三相感应电动机的在线故障检测与诊断问题的研究. 控制理论与应用. 1995,12(1):58~63
12 马宏忠, 胡虔生, 黄允凯等. 感应电机转子断条根数影响分析. 河北大学学报. 2003,9(5):573~576
13 马宏忠, 王惠庆, 胡虔生等. 感应电机转子断条位置影响分析. 河北大学学报. 2003,11(6):690~693
14 刘振兴, 尹项根, 张哲. 鼠笼式异步电动机转子故障在线检测与诊断方法.电力自动化设备. 2004,1(1):30~33
15 孙李玲, 李和明. 基于多回路数学模型的异步电动机内部故障瞬变过程. 电力系统自动化. 2004,(12):35~40
16 高景德, 王样布. 交流电机的多回路理论. 清华大学学报. 1987,27(1):1~8
17 C. E. Kim, Y. B. Jung, S. B. Yoon. The Fault Diagnosis of Rotor Bars in Squirrel Cage Induction Motors by Time-stepping Finite Element Method. IEEE Transactions on Magnetics. 1997,33(2):2131~2134
18 R. Fiser, S. Ferkolj. Simulation of Steady-state and Dynamic Performance of Induction Motor for Diagnostic Purpose. Proceedings of the 1997 International Electric Machines and Drives Conference. Milwaukee(USA), WB3-10.1~10.3
19 R. Fiser, S. Ferkolj. Calculation of Magnetic Field Asymmetry of Induction Motor with Rotor Faults. Proceedings of the 1998 IEEE Mediterranean Electrotechnical Conference. Tel Aviv (Israel), 1998,2:1175~1179
20 J. F. Waston, N. C. Paterson, D. G. Dorrell. The Use of Finite Element Methods to Improve Techniques for the early Detection of Faults in 3-phase Induction Motors, IEEE Transactions on Energy Conversion. 1999,14(3):655~660
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25 V. Ostovic. Three Dimensional Eddy Current Computation in Conductors of Electric Machines. IEEE Industry Applications Society. 2001,(2):737~744
26 D. Albertz, G. Henneberger. Calculation of 3D Eddy Current Fields Using both Electric and Magnetic Vector Potential in Conducting Regions. IEEETransactions on Magnetics. 1998,34(5):2644~2647
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28 D. Zhou, C. B. Rajanathan, A. T. Sapeluk. Finite-Element-Aided Design Optimization of a Shaded-Pole Induction Motor for Maximum Starting Torque. IEEE Transactions on Magnetics. 2000,36(5):3551~3554
29 S. J. Salon. Finite Element Analysis of Electric Machinery. IEEE Computer Applications in Power. 1990:29~32
30 朱东起, 许德伟, 姜新建. 磁场定向异步电机的磁饱和影响及转矩优化分析. 清华大学学报(自然科学版). 2001,41(9):1~4
31 梁得亮, 陈世坤. 用时步有限元法分析实心转子异步电机的瞬态特性. 中小型电机. 1995,22(5):3~6
32 严登俊, 刘瑞芳, 胡敏强等. 鼠笼异步电机起动性能的时步有限元计算. 电机与控制学报. 2003,7(3):177~181 190
33 S. L. HO, W. N. Fu. Inclusion of Current in a Network-field Coupled Time-Stepping Finite-element Model of Skewed-rotor Induction Motors. IEEE Trans. On Magnetics. 1999,35(5):4218~4225
34 E. Vassent, G. Meunier, J. C. Sbonnadiere. Simulation of Induction Machine Operation Using Complex Magnet-dynamic Finite Elements. IEEE Transactions on Magnetics. 1989,25(4):12~14
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36 梁得亮, 陈世坤. 用时步有限元法分析实心转子异步电机的瞬态特性. 中小型电机. 19957,22(5):3~6
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46 S. Williamson. Induction Motor Modeling using Finite Elements. Inter. Conf. On Electrical Machines. Paris, 1994:5~8
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49 B. Boualem, F. Piriou. Modeling of Induction Motor Accounting for Skewed Slots Effects. International Conference on Electrical Machine. Pairs, France, Sept, 1994:699~704
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51 江建中, 傅为农. 斜槽异步电机的多截面有限元法分析. 电工技术学报. 1997:11~16
52 傅为农, 江建中. 异步电机高频杂耗的自适应时步法有限元计算. 电工技术学报. 1996,(6):1~6
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58 B. G. Gaydon, C. Hargis, K. Kamash. The Detection of Rotor Faults in Induction Motors. IEE Conference on Electrical Machines-Design and Applications. London(UK), 1982:216~220
59 F. Filippetti, G. Franceschini, C. Tassoni. AI Techniques in Induction Machines Diagnosis including the Speed Ripple Effect. IEEE Transactions on Industry Application. 1998,34(1):98~108
60 郑方, 徐明星等. 信号处理原理. 清华大学出版社, 2002:49~50, 219~220
2 M. Jufer and M. A. Abdul. Influence D’une Rupture de Barre ou D’un Anneau Sur les Charactristiques externs d’un Motor Asynchrony a Cage. Bull SEV/LSE(Switzerland), Vol.69, No.17,Sept.1978
3 B. G. Gaydon, C. Hargis, K. Kamash. The Detection of Rotor Faults in Induction Motor. IEE Conference on Electrical Machines-Design and Applications. London (UK), 1982:216~220
4 M. E. Steele, R. A. Ashen and L. G. Knighe. An Electrical Method of Monitoring motor. Proc. of Int Conf on Electrical Machines. IEE London, Conference Publn 312, July,1982:231~235
5 S. Williamson, A. C. Smith. Speedy State Analysis of 3-phase Cage Motors. in Proc. Inst. Elec. Eng. Nol. 129 No.3, 1982:93~100
6 A. J. Marques Cardoso, S. M. A. Cruz, J. F. S. Carvalho. Rotor Cage Fault Diagnosis in Three-phase Induction Motor. by Park’s Vector Approach. Proceedings of the 1995 IEEE IAS Annual Meeting. San Diego(USA), 642~646
7 S. M. A. Cruz, A. J. Marques Cardoso. Rotor Cage Fault Diagnosis in Three-phase Induction Motor by Extended Park’s Vector Approach. Electric Machines and Power Systems. 2000,28:289~299
8 窦玉琴, 付立军等. 微机在线检测鼠笼异步电动机转子的故障. 电工电能新技术. 1993,(1):13~18
9 王凤昌, 李面换. 异步电机故障的电流检测和诊断. 哈尔滨工业大学学报. 1994,26(6):88~93
10 时献江, 周馨, 屈梁生. 设备故障诊断的电机电流法. 哈尔滨电工学院学报. 1992,15(1):57~61
11 周东华. 三相感应电动机的在线故障检测与诊断问题的研究. 控制理论与应用. 1995,12(1):58~63
12 马宏忠, 胡虔生, 黄允凯等. 感应电机转子断条根数影响分析. 河北大学学报. 2003,9(5):573~576
13 马宏忠, 王惠庆, 胡虔生等. 感应电机转子断条位置影响分析. 河北大学学报. 2003,11(6):690~693
14 刘振兴, 尹项根, 张哲. 鼠笼式异步电动机转子故障在线检测与诊断方法.电力自动化设备. 2004,1(1):30~33
15 孙李玲, 李和明. 基于多回路数学模型的异步电动机内部故障瞬变过程. 电力系统自动化. 2004,(12):35~40
16 高景德, 王样布. 交流电机的多回路理论. 清华大学学报. 1987,27(1):1~8
17 C. E. Kim, Y. B. Jung, S. B. Yoon. The Fault Diagnosis of Rotor Bars in Squirrel Cage Induction Motors by Time-stepping Finite Element Method. IEEE Transactions on Magnetics. 1997,33(2):2131~2134
18 R. Fiser, S. Ferkolj. Simulation of Steady-state and Dynamic Performance of Induction Motor for Diagnostic Purpose. Proceedings of the 1997 International Electric Machines and Drives Conference. Milwaukee(USA), WB3-10.1~10.3
19 R. Fiser, S. Ferkolj. Calculation of Magnetic Field Asymmetry of Induction Motor with Rotor Faults. Proceedings of the 1998 IEEE Mediterranean Electrotechnical Conference. Tel Aviv (Israel), 1998,2:1175~1179
20 J. F. Waston, N. C. Paterson, D. G. Dorrell. The Use of Finite Element Methods to Improve Techniques for the early Detection of Faults in 3-phase Induction Motors, IEEE Transactions on Energy Conversion. 1999,14(3):655~660
21 汤蕴璆. 电机内的电磁场(第二版). 科学出版社, 1998:1~14 274~279 341
22 陈丕章 , 严烈通 , 姚若萍 . 电机电磁场理论与计算 . 科学出版社 , 1986:106~107
23 章名涛, 肖如鸿. 电机电磁场. 机械工业出版社, 1988:426~442
24 F. N. Isaac, A. A. Arkadan, A. E. Antably. Magnetic Field and Core Loss Evaluation of ALA-Rotor Synchronous Reluctance Machines Taking into Account Material Anisotropy. IEEE Transactions on Magnetics. 1998,34(5):3507~3514
25 V. Ostovic. Three Dimensional Eddy Current Computation in Conductors of Electric Machines. IEEE Industry Applications Society. 2001,(2):737~744
26 D. Albertz, G. Henneberger. Calculation of 3D Eddy Current Fields Using both Electric and Magnetic Vector Potential in Conducting Regions. IEEETransactions on Magnetics. 1998,34(5):2644~2647
27 李开成, 马志云. 一种精确计算异步电机电感参数的通用方法. 电工技术学报. 1996,11(1):21~23
28 D. Zhou, C. B. Rajanathan, A. T. Sapeluk. Finite-Element-Aided Design Optimization of a Shaded-Pole Induction Motor for Maximum Starting Torque. IEEE Transactions on Magnetics. 2000,36(5):3551~3554
29 S. J. Salon. Finite Element Analysis of Electric Machinery. IEEE Computer Applications in Power. 1990:29~32
30 朱东起, 许德伟, 姜新建. 磁场定向异步电机的磁饱和影响及转矩优化分析. 清华大学学报(自然科学版). 2001,41(9):1~4
31 梁得亮, 陈世坤. 用时步有限元法分析实心转子异步电机的瞬态特性. 中小型电机. 1995,22(5):3~6
32 严登俊, 刘瑞芳, 胡敏强等. 鼠笼异步电机起动性能的时步有限元计算. 电机与控制学报. 2003,7(3):177~181 190
33 S. L. HO, W. N. Fu. Inclusion of Current in a Network-field Coupled Time-Stepping Finite-element Model of Skewed-rotor Induction Motors. IEEE Trans. On Magnetics. 1999,35(5):4218~4225
34 E. Vassent, G. Meunier, J. C. Sbonnadiere. Simulation of Induction Machine Operation Using Complex Magnet-dynamic Finite Elements. IEEE Transactions on Magnetics. 1989,25(4):12~14
35 梁艳萍, 周封. 用时步有限元法计算汽轮发电机直轴瞬态参数.电机与控制学报, 1998,2(2):69~74
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