Synchronization Behavior of Secondary Vibration Isolation System with Two Co-Rotating Motors

doi:10.3901/JME.2022.17.170

Abstract

Abstract: To solve the harm caused by the excitation transmission in the vibrating system, the secondary vibration isolation system with two co-rotating motors is proposed. Firstly, the motion differential equations of the system are established by Lagrange equation. Subsequently, the analytical expressions of synchronization criterion and stability criterion are given by adopting the small parameter average method and Routh-Hurwitz criterion. Next, the influence of excitation frequency and structural parameters of the system on synchronous behavior is discussed by numeric analyses. Then, the electromechanical coupling model of the system is established to analyze the influence of electromechanical coupling characteristic on synchronous behavior through Runge-Kutta method of the fourth order. The research results indicate that, when the system operates in the low frequency region, the relative motion amplitude and synchronous phase difference of the system are fluctuated and the coupling moment is gradually increased with the increment of the excitation frequency; when the system operates in the high frequency region, the relative motion amplitude and synchronous phase difference of the system are independence of the excitation frequency, and the coupling moment is stabilized at maximum; besides, the synchronous phase difference of the system is decreased with the increment of mounting distance or with the decrement of installation angle. Finally, the experiment is designed to verify the accuracy of theoretical and simulation analyses.

Key words: synchronization, stability, vibration isolation, motor, phase difference

CLC Number:

TH113

HOU Yongjun, PENG Huan, FANG Pan, HOU Duyu, WANG Dejin. Synchronization Behavior of Secondary Vibration Isolation System with Two Co-Rotating Motors[J]. Journal of Mechanical Engineering, 2022, 58(17): 170-180.

References

[1] PENG Huan，HOU Yongjun，FANG Pan，et al. Synchronization analysis of the anti-resonance system with three exciters[J]. Applied Mathematical Modelling，2021，97：96-112.
[2] 方潘，侯勇俊，张丽萍，等. 转子耦合摆系统的同步行为理论研究[J]. 物理学报，2016(1)：254-265. FANG Pan，HOU Yongjun，ZHANG Liping，et al. Synchronous behavior of a rotor-pendulum system[J]. China Academic Journal Electronic，2016(1)：254-265.
[3] 司纪凯，张露锋，封海潮，等. 异步起动表面-内置式永磁转子同步电机特性分析及优化[J]. 电工技术学报，2017，32(9)：63-69. SI Jikai，ZHANG Lufeng，FENG Haichao，et al. Characteristic analysis and optimization of line-start surface-mounted and interior permanent magnet synchronous motor[J]. Transactions of China Electrotechnical Society，2014，32(9)：63-69.
[4] BLEKHMAN II. Synchronization in science and technology[M]. New York：ASME Press，1988.
[5] 闻邦椿，赵春雨. 工程中的振动同步与控制同步[M]. 北京：科学出版社，2009. WEN Bangchun，ZHAO Chunyu. Vibratory synchronization and controlled synchronization in engineering[M]. Beijing：Science Press，2009.
[6] 闻邦椿. 振动机械理论、技术及其应用[M]. 北京：科学出版社，2010. WEN Bangchun. Theory and techniques of vibrating machinery and their applications[M]. Beijing：Science Press，2010.
[7] ZHANG Xueliang，WEN Bangchun，ZHAO Chunyu. Theoretical study on synchronization of two exciters in a nonlinear vibrating system with multiple resonant types[J]. Nonlinear Dynamics，2016，85(1)：141–154.
[8] ZHANG Xueliang，LI Zhenmin，LI Ming，et al. Stability and sommerfeld effect of a vibrating system with two vibrators driven separately by induction motors[J]. IEEE-ASME Transactions on Mechatronics，2021，26(2)：807-817.
[9] SPERLING L，RYZHIK B，LINZ C，et al. Simulation of two-plane automatic balancing of a rigid rotor[J]. Mathematics and Computers in Simulation，2002，58(4)：351-365.
[10] BALTHAZAR J. Short comments on self-synchronization of two non-ideal sources supported by a flexible portal frame structure[J]. Journal of Vibration and Control，2004，10(12)： 1739-1748.
[11] ZHANG Xueliang，WEN Bangchun，ZHAO Chunyu. Theoretical，numerical and experimental study on synchronization of three identical exciters in a vibrating system[J]. Chinese Journal of Mechanical Engineering，2013，26(4)：746-757.
[12] ZHANG Xueliang，WEN Bangchun，ZHAO Chunyu. Experimental investigation on synchronization of three co-rotating non-identical coupled exciters driven by three motors[J]. Journal of Sound and Vibration，2014，333(13)：2898–2908.
[13] 杜明俊. 基于弹性耦合的三激振电机椭圆振动筛动力学研究[D]. 成都：西南石油大学，2017. DU Mingjun. Investigation on dynamics of an elastically coupled tri-rotor vibration system[D]. Chengdu: Southwest Petroleum University，2017.
[14] 杜明俊，侯勇俊，吴毅，等. 非线性耦合同向回转的双偏心转子振动系统同步行为研究[J]. 机械工程学报，2020，56(23)：150-164. DU Mingjun，HOU Yongjun，WU Yi，et al. Synchronization behavior of two co-rotating rotors in a nonlinear coupled system[J]. Journal of Mechanical Engineering，2020，56(23)：150-164.
[15] KONG Xiangxi，CHEN Changzheng，WEN Bangchun. Composite synchronization of three eccentric rotors driven by induction motors in a vibrating system[J]. Mechanical Systems and Signal Processing，2018，102：158-179.
[16] CHEN Xiaozhe，KONG Xiangxi，ZHANG Xueliang，et al. On the synchronization of two eccentric rotors with common rotational axis：Theory and experiment[J]. Shock and Vibration，2016：1-14.
[17] HOU Duyu，FANG Pan，PENG Huan，et al. Synchronization of a dual-exciter coupling with a torsion spring in far-resonance system[J]. Advances in Mechanical Engineering，2020，12(6)：1-16.
[18] 刘杰，孙光复. 反共振振动机械的理论及应用[J]. 东北大学学报，1995，16(1)：82-86. LIU Jie，SUN Guangfu．Theory of anti-resonant vibrating machine with application[J]. Journal of Northeastern University，1995，16(1)：82-86.
[19] 刘杰，刘劲涛，张金萍，等. 考虑物料质量随机波动的反共振振动机动力学分析[J]. 振动与冲击，2006, 25（6）：76-78, 83, 180. LIU Jie，LIU Jintao，ZHANG Jinping，et al. Dynamic analysis of anti-resonant vibrating machines with random oscillation of material mass[J]. Journal of Vibration and Shock，2006，6：76-78, 83, 180.
[20] HOU Yongjun，PENG Huan，FANG Pan，et al. Synchronous characteristic of three homodromy motors in vibrating isolation system[J]. Journal of Mechanical Science and Technology，2021，35(1)：45-60.
[21] HOU Yongjun，PENG Huan，FANG Pan，et al. Synchronous characteristics of two excited motors in an anti-resonance system[J]. Journal of Advanced Mechanical Design，Systems，and Manufacturing，2019，13(3)：JAMDSM0050-JAMDSM0050.
[22] 李鹤，刘丹，姜来，等. 含二次隔振架的双机驱动振动机的自同步理论研究[J]. 振动与冲击，2014，33(8)：134-140. LI He，LIU Dan，JIANG Lai，et al. Self-synchronization theory of a vibrating system with a two-stage vibration isolation frame driven by two motors[J]. Journal of Vibration and Shock，2014，33(8)：134-140.