Abstract:When using finite element method (FEM) to solve transient electromagnetic-thermal indirect coupling, the response time of temperature field is longer than the electromagnetic field. And if a unified computing time step was used in solving, extras solving number occur in thermal field calculations which increase the total computation time. To solve the electromagnetic-thermal coupling problem, an adaptive coupling time step method is proposed in this paper. First, the coupling time is predicted by exponential smoothing forecast. And then between the two coupling time nodes, the best discrete time steps of thermal and electromagnetic field are calculated by predictor-corrector method and the response eigenvalue method. Compared with the traditional unified time step coupling method, electromagnetic and thermal field are using the best discrete time steps. The extra calculation number of temperature field is avoided. Finally, the proposed method is employed to calculate a conducting copper ring’s temperature within 1% under an AC excitation as an example. The results show that the calculation time is 26.6% less. Thus, the effectiveness of the proposed method is verified.
张宇娇, 汪振亮, 徐彬昭, 黄雄峰, 智李. 瞬态电磁-温度场耦合计算中自适应时间步长研究[J]. 电工技术学报, 2018, 33(19): 4468-4475.
Zhang Yujiao, Wang Zhenliang, Xu Binzhao, Huang Xiongfeng, Zhi Li. Research on the Adaptive Time Step in Transient Calculation of Coupled Electromagnetic and Thermal Fields. Transactions of China Electrotechnical Society, 2018, 33(19): 4468-4475.
[1] 纽春萍, 陈德桂, 刘颖异, 等. 交流接触器温度场仿真及影响因素的分析[J]. 电工技术学报, 2007, 22(5): 71-77.Niu Chunping, Chen Degui, Liu Yingyi, et al. Temperature field simulation of AC contactor and analysis of its influence factors[J]. Transactions of China Electrotechnical Society, 2007, 22(5): 71-77. [2] 梁盼望, 李震彪, 何整杰, 等. 反复短时工作制下密封电磁继电器瞬态热分析仿真[J]. 电工技术学报, 2011, 26(1): 57-62.Liang Panwang, Li Zhenbiao, He Zhengjie, et al. Transient thermal analysis of sealed electro- mechanical relay in repeated short-term operation system[J]. Transactions of China Electrotechnical Society, 2011, 26(1): 57-62. [3] 谢颖, 王泽, 单雪婷, 等. 基于多场量的笼型感应电机三维瞬态磁热固耦合计算分析[J]. 中国电机工程学报, 2016, 36(11): 3076-3084. Xie Ying, Wang Ze, Shan Xueting, et al. The calculations and analysis of 3D transient magnetic-thermal-solid coupling for squirrel-cage induction motors based on multi fields[J]. Proceedings of the CSEE, 2016, 36(11): 3076-3084. [4] 陈益广, 郑军, 魏娟, 等. 舵机用永磁同步电机的设计与温度场分析[J]. 电工技术学报, 2015, 30(14): 94-99.Chen Yiguang, Zheng Jun, Wei Juan, et al. Design of PMSM for actuator and its temperature field analysis[J]. Transactions of China Electrotechnical Society, 2015, 30(14): 94-99. [5] 林抒毅, 许志红. 交流电磁阀三维温度特性仿真分析[J]. 中国电机工程学报, 2012, 32(36): 156-164.Lin Shuyi, Xu Zhihong. Simulation and analysis on the three-dimensional temperature field of AC solenoid valves[J]. Proceedings of the CSEE, 2012, 32(36): 156-164. [6] 姜志鹏, 周辉, 宋俊燕, 等. 干式空心电抗器温度场计算与试验分析[J]. 电工技术学报, 2017, 32(3): 218-224.Jiang Zhipeng, Zhou Hui, Song Junyan, et al. Temperature field calculation and experimental analysis of dry-type air-core reactor[J]. Transactions of China Electrotechnical Society, 2017, 32(3): 218-224. [7] 李伟力, 李金阳, 李丹. 变截面转子通风沟对全空冷水轮发电机转子温度场和流体场的影响[J]. 电工技术学报, 2017, 32(增刊2): 42-49.Li Weili, Li Jinyang, Li Dan. Influence of variable section rotor ventilation ducts on temperature and fluid fields of a full air-cooled large hydro-generator rotor[J]. Transactions of China Electrotechnical Society, 2017, 32(S2): 42-49. [8] 崔行磊, 周学, 张勇, 等. 基于彩色摄像和光谱分析联合测温方法的电弧温度场分布测量[J]. 电工技术学报, 2017, 32(15): 128-135.Cui Xinglei, Zhou Xue, Zhang Yong, et al. Measurement of static arc temperature distribution based on colorful photographing and spectroscopy analysis[J]. Transactions of China Electrotechnical Society, 2017, 32(15): 128-135. [9] 王晓远, 高鹏. 等效热网络法和有限元法在轮毂电机温度场计算中的应用[J]. 电工技术学报, 2016, 31(16): 26-33.Wang Xiaoyuan, Gao Peng. Application of equivalent thermal network method and finite element method in temperature calculation of in-wheel motor[J]. Transactions of China Electrotechnical Society, 2016, 31(16): 26-33. [10] 张宇娇, 秦威南, 刘东圆, 等. 面向电磁装置磁-热耦合分析的异型网格映射方法[J]. 电工技术学报, 2016, 31(13): 141-148.Zhang Yujiao, Qin Weinan, Liu Dongyuan, et al. Non-matching meshes mapping method in coupled magnetic and thermal analysis of electromagnetic devices[J]. Transactions of China Electrotechnical Society, 2016, 31(13): 141-148. [11] 朱高嘉, 朱英浩, 朱建国, 等. 永磁电机温度场的改进有限公式迭代算法[J]. 电工技术学报, 2017, 32(16): 136-144.Zhu Gaojia, Zhu Yinghao, Zhu Jianguo, et al. A modified thermal rewind model of permanent magnet motors based on finite formulation method[J]. Transactions of China Electrotechnical Society, 2017, 32(16): 136-144. [12] Ibrahimbegovic A, Niekamp R, Kassiotis C, et al.Code-coupling strategy for efficient development of computer software in multiscale and multiphysics nonlinear evolution problems in computational mechanics[J]. Advances in Engineering Software, 2014, 72(4): 8-17. [13] Combescure A, Anthony G.A numerical scheme to couple subdomains with different time-steps for predominantly linear transient analysis[J]. Computer Methods in Applied Mechanics and Enginerring, 2002, 191(11): 1129-1157. [14] Kassiotis C.Nonlinear fluid-structure interaction problem, part I: implicit partitioned algorithm, nonlinear stability proof and validation examples[J]. Computational Mechanics, 2011, 47(3): 305-323. [15] Rabello A A, Silva E J, Saldanha R, et al.Adaptive time-stepping analysis of nonlinear microwave heating problems[J]. IEEE Transactions on Magnetics, 2005, 41(5): 1584-1587. [16] Fu W N.Elimination of nonphysical solutions and implementation of adaptive step size algorithm in time-stepping finite-element method for magnetic field-circuit-motion coupled problems[J]. IEEE Transactions on Magnetics, 2010, 46(1): 29-38. [17] 赵振, 张树有. 自适应时间步长顺序耦合法及其在瞬态场耦合问题分析中的应用[J]. 计算机集成制造系统, 2011, 17(7): 1404-1414.Zhao Zhen, Zhang Shuyou. Self-adaptive step sequential-interaction method and its application in transient-fields coupling problems[J]. Computer Integrated Manufacturing Systems, 2011, 17(7): 1404-1414. [18] 王勖成. 有限单元法[M]. 北京: 清华大学出版社, 2012. [19] 潘超, 何雯婷, 郝文波, 等. 一种变压器时域场路耦合计算的自适应算法[J]. 电工技术学报, 2014, 29(12): 113-119. Pan Chao, He Wenting, Hao Wenbo, et al. A self-adaptive algorithm of time-domain magnetic field and electric circuit coupled computation for transformer[J]. Transactions of China Electrotechnical Society, 2014, 29(12): 113-119. [20] Hughes T J R. Analysis of transient algorithms with particular reference to stability behavior[C]// Computational Methods for Transient Analysis, Computational Methods in Mechanics Series, North- Holland, Amsterdam, 1983: 67-155. [21] 司守奎. 数学建模算法与应用[M]. 北京: 国防工业出版社, 2011. [22] Biro O, Preis K.On the use of the magnetic vector potential in the finite element analysis of three-dimensional eddy currents[J]. IEEE Transactions on Magnetics, 1989, 25(4): 3145-3159.