含换相转矩波动的小型伺服驱动系统机电耦合模型及动态特性分析

doi:10.3901/JME.2025.08.374

摘要/Abstract

摘要： 小型伺服驱动系统是小型无人机、服务机器人、智能医护等精密智能装备的核心部件，其动态特性直接影响整机运动精度、灵敏度和振动噪声。针对以无刷直流电机为动力源的小型伺服驱动系统，提出计及电机换相转矩波动和齿轮时变啮合刚度的机电耦合动力学模型。基于电流-速度双闭环比例积分(Proportional-integral, PI)控制策略，研究机械参数、电气参数和驱动控制参数对系统动态特性的影响。构建小型伺服驱动系统动态响应测试平台，分析母线电流变化规律，验证模型的正确性。结果表明：无刷直流电机非理想换相是小型伺服驱动系统输出轴振动和转矩波动的重要因素，受换相转矩波动影响，系统振动随转速升高、负载减小而加剧；适当增大传动轴扭转刚度和逆变器载波频率、减小电机绕组电感，有利于加快系统响应速度并抑制振动。

关键词: 伺服驱动系统, 换相转矩波动, 机电耦合, PI控制, 动态特性

Abstract: Small servo drive system is the core component of small drones, service robots, intelligent medical care and other precision intelligent equipment. Its dynamic characteristics directly affect the overall accuracy, sensitivity and noise of the equipment. Aiming at the small servo drive system powered by brushless DC motor(BLDCM), an electromechanical coupling model is proposed, considering the BLDCM commutation torque ripple and time-varying gear meshing stiffness. The influences of mechanical, electrical and control parameters on the system dynamic characteristics are studied under the proportional-integral(PI) control strategy. A dynamic response testing platform for small servo drive system is built to analyze the bus current and verify the model. The results indicate that the non-ideal commutation of BLDCM is an important factor contributing to the vibration and torque ripple of the output shaft of a small servo drive system. Under the influence of commutation torque ripple, system vibration intensifies with higher speed and lower load. To speed up the system response and suppress vibration, the torsional stiffness of the drive shaft and the carrier frequency of the inverter can be increased appropriately, and the inductance of the motor windings can be reduced.

Key words: servo drive system, commutation torque ripple, electromechanical coupling, PI control, dynamic characterizatio

中图分类号:

TH13

周长江, 夏宁伟, 方安舒, 侯圣文. 含换相转矩波动的小型伺服驱动系统机电耦合模型及动态特性分析[J]. 机械工程学报, 2025, 61(8): 374-383.

ZHOU Changjiang, XIA Ningwei, FANG Anshu, HOU Shengwen. Modeling and Dynamic Characterization of Electromechanical Coupling of Small Servo Drive System with Commutation Torque Ripple[J]. Journal of Mechanical Engineering, 2025, 61(8): 374-383.

参考文献

[1] 姜卫东，廖玉茗，王培侠，等. 减小无刷直流电机换相转矩波动和换相时间的协调控制方法[J]. 中国电机工程学报，2017，37(7)：2120-2131. JIANG Weidong，LIAO Yuming，WANG Peixia，et al. A corporative control method to reduce commutation torque ripple and commutation time for brushless DC motor[J]. Proceedings of the CSEE，2017，37(7)：2120-2131.
[2] CARLSON R，LAJOIE-MAZENC M，FAGUNDES J. Analysis of torque ripple due to phase commutation in brushless DC machines[J]. IEEE Transactions on Industry Applications，1992，28(3)：632-638.
[3] 夏长亮，俞卫，李志强. 永磁无刷直流电机转矩波动的自抗扰控制[J]. 中国电机工程学报，2006，26(24)：137-142. XIA Changliang，YU Wei，LI Zhiqiang. Torque ripple reduction of PM brushless DC motors based on auto-disturbances-rejection controller[J]. Proceedings of the CSEE，2006，26(24)：137-142.
[4] 夏长亮，张茂华，王迎发，等. 永磁无刷直流电机直接转矩控制[J]. 中国电机工程学报，2008，28(6)：104-109. XIA Changliang，ZHANG Maohua，WANG Yingfa，et al. The direct torque control for permanent magnet brushless DC motors[J]. Proceedings of the CSEE，2008，28(6)：104-109.
[5] MENG G，XIONG H，LI H. Commutation torque ripple reduction in BLDC motor using PWM_ON_PWM mode[C]//Institute of Electrical and Electronics Engineers. 2009 International Conference on Electrical Machines and Systems. Tokyo：IEEE，2009：1-6.
[6] 夏鲲，董斌，卢晶. 一种基于电流反馈的分段式PWM控制无刷直流电机转矩波动抑制方法[J]. 电工技术学报，2017，32(17)：172-179. XIA Kun，DONG Bin，LU Jing. Research on hybrid PWM control method with current feedback for torque-ripple reduction in BLDCM[J]. Transactions of China Electrotechnical Society，2017，32(17)：172-179.
[7] KAHRAMAN A，SINGH R. Non-linear dynamics of a geared rotor-bearing system with multiple clearances[J]. Journal of Sound and Vibration，1991，144(3)：469-506.
[8] 孙月海，张策，潘凤章，等. 直齿圆柱齿轮传动系统振动的动力学模型[J]. 机械工程学报，2000，36(8)：47-50. SUN Yuehai，ZHANG Ce，PAN Fengzhang，et al. Dynamic model of a spur gear transmission system vibration[J]. Journal of Mechanical Engineering，2000，36(8)：47-50.
[9] 常乐浩. 平行轴齿轮传动系统动力学通用建模方法与动态激励影响规律研究[D]. 西安：西北工业大学，2014. CHANG Lehao. A generalized dynamic model for parallel shaft gear transmissions and the influences of dynamic excitations[D]. Xi’an：Northwestern Polytechnical University，2014.
[10] ZHOU C，XIAO Z，CHEN S，et al. Normal and tangential oil film stiffness of modified spur gear with non-newtonian elastohydrodynamic lubrication[J]. Tribology International，2017，109：319-327.
[11] CHEN Q，WANG Y，TIAN W，et al. An improved nonlinear dynamic model of gear pair with tooth surface microscopic features[J]. Nonlinear Dynamics，2019，96(2)：1615-1634.
[12] YOUSSEF K，KAMAL A H. Analysis of the electromechanical vibrations in induction motor drives due to the imperfections of the mechanical transmission system[J]. Mathematics and Computers in Simulation，2003，63(17)：421-433.
[13] ROCHUS V，GEUZAINE C. A primal/dual approach for the accurate evaluation of the electromechanical coupling in MEMS[J]. Finite Elements in Analysis and Design，2012，49(1)：19-27.
[14] KHABOU M，BOUCHAALA N，CHAARI F，et al. Study of a spur gear dynamic behavior in transient regime[J]. Mechanical Systems and Signal Processing，2011，25(8)：3089-3101.
[15] CHEN X，HU J，CHEN K，et al. Modeling of electromagnetic torque considering saturation and magnetic field harmonics in permanent magnet synchronous motor for HEV[J]. Simulation Modelling Practice and Theory，2016，66：212-225.
[16] 刘长钊，秦大同，廖映华. 采煤机截割部机电传动系统动力学特性分析[J]. 机械工程学报，2016，52(7)：14-22. LIU Changzhao，QIN Datong，LIAO Yinghua. Dynamic analysis for the cutting electromechanical transmission system in the long-wall shearer[J]. Journal of Mechanical Engineering，2016，52(7)：14-22.
[17] ZHANG Y，YAN X，LIN Q. Characteristic of torsional vibration of mill main drive excited by electromechanical coupling[J]. Chinese Journal of Mechanical Engineering，2016，29(1)：180-187.
[18] 李杰，谢福贵，刘辛军，等. 机电-刚柔耦合特性作用下线性进给系统动力学分析[J]. 机械工程学报，2017，53(17)：60-69. LI Jie，XIE Fugui，LIU Xinjun，et al. Dynamic modeling of a linear feed axis considering the characteristics of the electro-mechanical and rigid-flexible coupling[J]. Journal of Mechanical Engineering，2017，53(17)：60-69.
[19] LIU C，YIN X，LIAO Y，et al. Hybrid dynamic modeling and analysis of the electric vehicle planetary gear system[J]. Mechanism and Machine Theory，2020，150：103860.
[20] 秦大同，吕雪慧，陈锐博，等. 运行工况下风电传动系统机电耦合建模及其动态特性分析[J]. 中国机械工程，2022，33(3)：253-260. QIN Datong，LÜ Xuehui，CHEN Ruibo，et al. Electromechanical coupling modeling and dynamic characteristic analysis of wind power transmission systems under operation conditions[J]. China Mechanical Engineering，2022，33(3)：253-260.
[21] 李艳，向东，王君英. 桥式起重机双边驱动起升机构机电耦合动力学模型及验证[J]. 机械工程学报，2022，58(11)：170-182. LI Yan，XIANG Dong，WANG Junying. Electromechanical coupling dynamics model and its verification of dual path propelled lifting mechanism of bridge crane[J]. Journal of Mechanical Engineering，2022，58(11)：170-182.
[22] 莫帅，周长鹏，王檑，等. 机器人关节裂纹传动系统机电耦合动态特性研究[J]. 机械工程学报，2022，58(19)：57-67. MO Shuai，ZHOU Changpeng，WANG Lei，et al. Research on dynamic characteristics of electromechanical coupling of robot joint crack transmission system[J]. Journal of Mechanical Engineering，2022，58(19)：57-67.
[23] 莫帅，周长鹏，高瀚君，等. 机器人智能关节机电耦合系统瞬态动力学研究[J]. 华中科技大学学报，2023，51(2)：131-138. MO Shuai，ZHOU Changpeng，GAO Hanjun，et al. Research on transient dynamics of robot intelligent joint electromechanical coupling system[J]. Journal of Huazhong University of Science and Technology，2023，51(2)：131-138.
[24] 郑钰馨，奚鹰，袁浪，等. 直齿轮纯扭转模型弹性动力学分析[J]. 上海交通大学学报，2019，53(3)：285-296. ZHENG Yuxin，XI Ying，YUAN Lang，et al. elastodynamics analysis of pure torsional model of spur gear[J]. Journal of Shanghai Jiao Tong University，2019，53(3)：285-296.