考虑时变啮合刚度的多惯量伺服系统机械谐振分析及抑制方法研究

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振动与冲击 ›› 2021, Vol. 40 ›› Issue (19) : 164-171.

论文

李文礼1,陆宇1，郭栋1，刘永康1，石晓辉1，严海燕2

作者信息 +

Mechanical resonance analysis and suppression method of multi-inertia servo system considering time-varying meshing stiffness

LI Wenli1, LU Yu1, GUO Dong1, LIU Yongkang1, SHI Xiaohui1, YAN Haiyan2

Author information +

文章历史 +

摘要

为了更深入的研究多惯量伺服系统振动的机理，考虑齿轮传动过程中时变啮合刚度对机械谐振的影响，在传统双惯量伺服系统模型基础上建立四惯量伺服系统模型；分析系统机械谐振产生机理，利用时变波形近似表示齿轮副啮合刚度值，对比有无齿轮时变啮合刚度的伺服系统模型机械谐振表现特征。采用模型预测控制方法对包含时变啮合刚度的四惯量伺服系统的机械谐振进行抑制控制；设计了基于状态空间表达式的模型预测控制器，通过仿真试验对比常规PID控制方法进行验证，结果表明利用模型预测控制方法能有效的抑制多惯量伺服系统的机械谐振。

Abstract

Here, to study vibration mechanism of multi-inertia servo system more deeply, considering effects of gear time-varying meshing stiffness on the system’s mechanical resonance in gear transmission process, a 4-inertia servo system model was established based on the traditional dual-inertia servo system model to analyze the mechanism of the system’s mechanical resonance. The time-varying waveform was used to approximately indicate meshing stiffness of gear pair. Mechanical resonance performances of the servo system model with and without gear time-varying meshing stiffness were compared. The model prediction control method was used to control and suppress mechanical resonance of the 4-inertia servo system with gear time-varying meshing stiffness. The model prediction controller based on state space expression was designed. Through simulation tests, the model prediction control method was compared with the conventional PID control method for verification. The results showed that the model prediction control method can be used to effectively suppress mechanical resonance of multi-inertia servo system.

导出引用

李文礼,陆宇，郭栋，刘永康，石晓辉，严海燕. 考虑时变啮合刚度的多惯量伺服系统机械谐振分析及抑制方法研究[J]. 振动与冲击, 2021, 40(19): 164-171

LI Wenli, LU Yu, GUO Dong, LIU Yongkang, SHI Xiaohui, YAN Haiyan. Mechanical resonance analysis and suppression method of multi-inertia servo system considering time-varying meshing stiffness[J]. Journal of Vibration and Shock, 2021, 40(19): 164-171

参考文献

［1］SZABAT K, SERKIES P, ORLOWSKA-KOWALSKA T, et al. Robust torque constraints handling in drive systems with elastic transmission［C］∥2010 IEEE International Conference on Industrial Technology. Viadel Mar： IEEE, 2010.
［2］杨明, 胡浩, 徐殿国. 永磁交流伺服系统机械谐振成因及其抑制［J］. 电机与控制学报, 2012, 16(1): 79-84.
YANG Ming, HU Hao, XU Dianguo. Cause and suppression of mechanical resonance in PMSM servo system［J］. Electric Machines and Control, 2012, 16(1): 79-84.
［3］杨影, 张杰鸣, 徐国卿, 等. 转速负反馈在伺服系统机械谐振抑制中的应用研究［J］. 电工技术学报, 2018, 33(23): 5459-5469.
YANG Ying, ZHANG Jieming, XU Guoqing, et al. Application research on speed negative feedback in mechanical resonance suppression in servo system ［J］. Transactions of China Electrotechnical Society, 2018, 33 (23): 5459-5469.
［4］夏超, 那学智, 柴晓慧, 等. 伺服系统机械谐振机理分析与抑制方法分析［J］. 导航定位与授时, 2016,3(1): 29-35.
XIA Chao, NA Xuezhi, CHAI Xiaohui, et al. Analysis on mechanism and suppression of mechanical resonance in servo system［J］. Navigation Positioning & Timing, 2016, 3 (1): 29-35.
［5］杨明, 郝亮, 徐殿国. 基于自适应陷波滤波器的在线机械谐振抑制［J］. 哈尔滨工业大学学报, 2014, 46(4): 63-69.
YANG Ming, HAO Liang, XU Dianguo. Online suppression of mechanical resonance based on adapting notch filter［J］. Journal of Harbin Institute of Technology, 2014, 46(4):63-69.
［6］THOMSEN S, HOFFMANN N, FUCHS F W. PI control, PI-based state space control, and model-based predictive control for drive systems with elastically coupled loads: a comparative study［J］. IEEE Transactions on Industrial Electronics, 2011, 58(8): 3647-3657.
［7］杜仁慧, 陶春荣, 张伟, 等. 伺服系统机械谐振抑制的自适应模糊控制方法［J］. 电机与控制学报, 2017, 21(10): 116-122.
DU Renhui, TAO Chunrong, ZHANG Wei, et al. Adaptive fuzzy control method for mechanical resonance suppression of servo systems ［J］. Electric Machines and Control, 2017, 21(10): 116-122.
［8］于晶, 冯勇, 郑剑飞. 基于高阶滑模和加速度反馈的机械谐振抑制方法［J］. 控制理论与应用, 2009, 26(10): 1133-1136.
YU Jing, FENG Yong, ZHENG Jianfei. Suppression of mechanical resonance based on higher-order sliding mode and acceleration feedback ［J］. Control Theory & Applications, 2009, 26(10): 1133-1136.
［9］杨明, 王璨, 徐殿国. 基于轴矩限幅控制的机械谐振抑制技术［J］. 电机与控制学报, 2015, 19(4): 58-64.
YANG Ming, WANG Can, XU Dianguo. Mechanical resonance suppression strategy based on shaft torque amplitude limiting control［J］. Electric Machines and Control, 2015, 19(4): 58-64.
［10］SZABAT K, SERKIES P, CYCHOWSKI M. Application of the MPC to the robust control of the two-mass drive system［C］∥2011 IEEE International Symposium on Industrial Electronics. Gdansk: IEEE, 2011.
［11］毛仁超, 沈安文. 基于负载转矩反馈的机械谐振抑制方法［J］. 计算技术与自动化, 2014, 33(1): 19-23.
MAO Renchao, SHEN Anwen. Suppression of mechanical resonance based on load torque feedback［J］. Computing Technology and Automation, 2014, 33(1): 19-23.
［12］WANG S B, REN X M, SUN G F. Suppression of mechanical resonance based on dynamic surface control and acceleration feedback ［C］∥33rd Chinese Control Conference. Nanjing: IEEE, 2014.［16］李宗亚. 交流伺服系统机械谐振抑制研究［D］. 武汉:华中科技大学, 2014.
［17］熊琰. 伺服驱动系统机械谐振问题研究［D］. 武汉: 华中科技大学, 2015.
［18］李润方, 王建军. 齿轮系统动力学［M］. 北京: 科学出版社, 1997.
［19］KIA S H, HENAO H, CAPOLINO G A. Torsional vibration effects on induction machine current and torque signatures in gearbox-based electromechanical system［J］. IEEE Transactions on Industrial Electronics, 2009, 56(11):4689-4699.
［20］陈虹. 模型预测控制［M］. 北京: 科学出版社, 2013.
［13］王建敏, 吴云洁, 刘佑民, 等. 基于数字滤波器的伺服系统谐振抑制方法［J］. 北京航空航天大学学报, 2015, 41(3): 485-491.
WANG Jianmin, WU Yunjie, LIU Youmin, et al. Resonance suppression method based on digital filter for servo system ［J］. Journal of Beijing University of Aeronautics and Astronautics, 2015, 41(3): 485-491.
［14］龚文全, 曾岳南, 黄之锋, 等. 基于改进型陷波器的伺服系统谐振抑制研究［J］. 机电工程, 2020, 37(7): 845-850.
GONG Wenquan, ZENG Yuenan, HUANG Zhifeng, et al. Resonance suppression of servo system based on improved notch filter［J］. Journal of Mechanical ＆ Electrical Engineering, 2020, 37(7): 845-850.
［15］IKEDA H, HANAMOTO T, TSUJI T. Vibration suppression controller for 3-mass system designed by particle swarm optimization［C］∥2009 International Conference on Electrical Machines and Systems. Tokyo: IEEE, 2009.