考虑感应电动机模型的质量偏心单盘转子系统Sommerfeld效应及不平衡响应分析

doi:10.3901/JME.2020.17.137

机械工程学报 ›› 2020, Vol. 56 ›› Issue (17): 137-144.doi: 10.3901/JME.2020.17.137

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考虑感应电动机模型的质量偏心单盘转子系统Sommerfeld效应及不平衡响应分析

孔祥希¹, 牛俊开², 罗园庆¹, 许琦¹

1. 沈阳工业大学机械工程学院沈阳 110870;
2. 东北大学机械工程与自动化学院沈阳 110819

收稿日期:2019-08-13 修回日期:2020-05-15 出版日期:2020-09-05 发布日期:2020-10-19
通讯作者: 孔祥希(通信作者),男,1987年出生,博士,副教授,博士研究生导师。主要研究方向为振动利用、非线性动力学与控制。E-mail:xiangxikong0128@sut.edu.cn
基金资助:
国家自然科学基金（51705337，51675350）和中国博士后科学基金（2017M611258）资助项目。

Sommerfeld Effect and Unbalanced Response Analysis in Single Disk Rotor System with Eccentric Mass Considering Induction Motor Model

KONG Xiangxi¹, NIU Junkai², LUO Yuanqing¹, XU Qi¹

1. School of Mechanical Engineering, Shenyang University of Technology, Shenyang 110870;
2. School of Mechanical Engineering and Automation, Northeastern University, Shenyang 110819

Received:2019-08-13 Revised:2020-05-15 Online:2020-09-05 Published:2020-10-19

摘要/Abstract

摘要： Sommerfeld效应是由于非理想原动机在转子系统临界转速附近无法提供足够的动力而产生的一种非线性跳跃现象。研究了由感应电动机驱动的一个质量偏心单盘转子系统的Sommerfeld效应及不平衡响应。将感应电动机的动力学模型引入到转子系统中，建立了电动机-转子系统动力学模型。在充分考虑电动机与转子系统相互作用的基础上，得到了供电频率与转子转速之间的关系表达式，并进行了稳定性分析。对具有不同质量偏心的电动机-转子系统的不平衡响应进行了分析，并基于Matlab/Simulink进行了仿真验证。结果表明：当转子偏心质量与转子总质量的质量比η<0.026时，电动机能够提供足够动力使转子系统平稳通过临界转速，电动机-转子系统不会出现Sommerfeld效应；当质量比满足0.026 < η < 0.083时，在转子系统临界转速附近，电动机所提供的最大电磁转矩小于转子系统平稳通过临界转速所需输出转矩，电动机-转子系统出现Sommerfeld效应；当η>0.083时，随着感应电动机供电频率的增加，电动机将无法提供足够的动力使转子系统通过临界转速，转子系统转速将始终低于临界转速。通过研究，可以为转子系统的动力设计与选型提供借鉴。

关键词: 转子系统, 感应电动机, Sommerfeld效应, 非线性跳跃

Abstract: Sommerfeld effect is a nonlinear jumping phenomenon caused by the failure of a non-ideal motor to provide enough power near the critical speed of the system to enable the system to pass through the resonance region smoothly. Sommerfeld effect and unbalanced response of an induction motor driven single disk rotor system with eccentric mass are studied. The dynamic model of induction motor is introduced into the rotor system, and the induction motor rotor dynamic model is established. It is found that Sommerfeld effect will occur in the induction motor-rotor system based on fully considering the interaction between induction motor and rotor system. The influences of the eccentric mass on Sommerfeld effect and unbalanced response are analyzed. The results show that when the mass ratio of eccentric mass to total rotor mass η is about less than 0.026, namely η<0.026, since the motor can provide enough power to ensure the rotor system smoothly pass the critical speed, Sommerfeld effect will not occur in the induction motor-rotor system. When 0.026 < η < 0.083, since the max electromagnetic torque provided by the motor is less than the output torque required for the rotor system to smoothly pass the critical speed, Sommerfeld effect will occur. When η>0.083, with the supply frequency increasing, the induction motor will not provide enough power to make the rotor system pass through the critical speed, and the rotor system's speed will always be lower than the critical speed. The research can provide reference for the power design and selection of rotor system.

Key words: rotor system, induction motor, Sommerfeld effect, nonlinear jump

中图分类号:

TH113

孔祥希, 牛俊开, 罗园庆, 许琦. 考虑感应电动机模型的质量偏心单盘转子系统Sommerfeld效应及不平衡响应分析[J]. 机械工程学报, 2020, 56(17): 137-144.

KONG Xiangxi, NIU Junkai, LUO Yuanqing, XU Qi. Sommerfeld Effect and Unbalanced Response Analysis in Single Disk Rotor System with Eccentric Mass Considering Induction Motor Model[J]. Journal of Mechanical Engineering, 2020, 56(17): 137-144.

参考文献

[1] BLEKHMAN I I. Vibrational mechanics:Nonlinear dynamic effects,general approach,applications[M]. Singapore:World Scientific Press,2000.
[2] BHARTI S K,BISOI A,SINHA A,et al. Sommerfeld effect at forward and backward critical speeds in a rigid rotor shaft system with anisotropic supports[J]. Journal of Sound and Vibration,2019,442:330-349.
[3] JHA A K,DASGUPTA S S. Attenuation of Sommerfeld effect in an internally damped eccentric shaft-disk system via active magnetic bearings[J]. Meccanica,2019,54(1-2):311-320.
[4] SAMANTARAY A K,DASGUPTA S S,BHATTA-CHARYYA R. Sommerfeld effect in rotationally symmetric planar dynamical systems[J]. International Journal of Engineering Science,2010,48(1):21-36.
[5] KARTHIKEYAN M,BISOI A,SAMANTARAY A K,et al. Sommerfeld effect characterization in rotors with non-ideal drive from ideal drive response and power balance[J]. Mechanism and Machine Theory,2015,91:269-288.
[6] BISOI A,SAMANTARAY A K,BHATTACHARYYA R. Sommerfeld effect in a gyroscopic overhung rotor-disk system[J]. Nonlinear Dynamics,2017,88(3):1565-1585.
[7] 张微,韩兵兵,李响,等. 基于胞映射算法的转子-挤压油膜阻尼器系统多目标优化设计[J]. 机械工程学报,2019,55(19):68-74. ZHANG Wei,HAN Bingbing,LI Xiang,et al. Multi-objective optimization design of rotor-squeeze film damper system based on cell mapping method[J]. Journal of Mechanical Engineering,2019,55(19):68-74.
[8] 张力豪,何立东,陈钊,等. 整体式弹性环挤压油膜阻尼器结构设计与转子过临界实验研究[J]. 振动与冲击,2019,38(18):72-78,108. ZHANG Lihao,HE Lidong,CHEN Zhao,et al. Structure design of an integral elastic rign squeeze film damper and experiments on the rotor passing through critical speed[J]. Journal of Vibration and Shock,2019,38(18):72-78,108.
[9] YAO H,WANG Y,XIE L,et al. Bi-stable buckled beam nonlinear energy sink applied to rotor system[J]. Mechanical Systems and Signal Processing,2020,138:106546.
[10] YAO H,WANG Y,CAO Y,et al. Multi-stable nonlinear energy sink for rotor system[J]. International Journal of Non-Linear Mechanics,2020,118:103273.
[11] 陈坚. 交流电机数学模型及调速系统[M]. 北京:国防工业出版社,1989. CHEN Jian. Mathematical model and speed adjustment system of alternating motors[M]. Beijing:National Defense Industry Press,1989.
[12] 丁学文. 电力拖动运动控制系统[M]. 北京:机械工业出版社,2013. DING Xuewen. Electric drive motion control system[M]. Beijing:China Machine Press,2013.

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考虑感应电动机模型的质量偏心单盘转子系统Sommerfeld效应及不平衡响应分析

Sommerfeld Effect and Unbalanced Response Analysis in Single Disk Rotor System with Eccentric Mass Considering Induction Motor Model

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