非对称双激振器振动同步传动
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摘要
在振动同步理论研究中,存在着一种特殊现象,无直接驱动源的激振器仍能跟随其他有源驱动的激振器进行同步运转,称之为振动同步传动。对同向回转且非对称布置的双激振器振动系统的振动同步传动理论进行了研究。采用拉格朗日方程建立振动系统的运动微分方程。应用小参数平均法获得振动系统的频率俘获方程,进而获得系统实现振动同步传动的同步性判据及振动同步传动状态的稳定性判据。根据理论结果对系统进行数值分析与讨论,得到振动系统的运动选择特性;最后,对该振动系统样机进行试验,验证了理论分析的正确性。
In study on the vibration synchronization theory,there is a specific phenomenon that an exciter without a directly driving source can follow another active drive exciter to operate synchronously. This phenomenon is called the vibratory synchronization transmission. Here,the theory of vibratory synchronization transmission for an asymmetrical twoexciter system was studied. The motion equation of the vibrating system was derived with Lagrange equation. The average method of small parameters was adopted to deduce the frequency capture equation of the vibrating system. Then the criterion of synchronism for the system to realize the vibratory synchronization transmission and the criterion of stability for vibratory synchronization transmission state were obtained. According to the theoretical results,the system was numerically analyzed and discussed to get the motion selection characteristics of the system. Finally,the prototype of this vibrating system was tested to verify the correctness of the theoretical analysis.
In study on the vibration synchronization theory,there is a specific phenomenon that an exciter without a directly driving source can follow another active drive exciter to operate synchronously. This phenomenon is called the vibratory synchronization transmission. Here,the theory of vibratory synchronization transmission for an asymmetrical twoexciter system was studied. The motion equation of the vibrating system was derived with Lagrange equation. The average method of small parameters was adopted to deduce the frequency capture equation of the vibrating system. Then the criterion of synchronism for the system to realize the vibratory synchronization transmission and the criterion of stability for vibratory synchronization transmission state were obtained. According to the theoretical results,the system was numerically analyzed and discussed to get the motion selection characteristics of the system. Finally,the prototype of this vibrating system was tested to verify the correctness of the theoretical analysis.
引文
[1]韩清凯,秦朝烨,闻邦椿.自同步振动系统的稳定性与分岔[J].振动与冲击,2007,26(1):31-34.HAN Qingkai,QIN Zhaoye,WEN Bangchun.Stability and bifurcation of self-synchronous vibration system[J].Journal of Vibration and Shock,2007,26(1):31-34.
[2]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.
[3]赵春雨,赵乾斌,贺斌,等.三质体振动机动力学参数对其性能的影响分析[J].振动与冲击,2015,34(12):70-78.ZHAO Chunyu,ZHAO Qianbin,HE Bin,et al.Effects of dynamic parameters on the performance of a three-mass vibrating machine[J].Journal of Vibration and Shock,2015,34(12),70-78.
[4]陈晓哲,窦景欣,孔祥希,等.两激振器同一旋转轴线振动系统的自同步理论[J].振动与冲击,2017,36(14):19-25.CHEN Xiaozhe,DOU Jingxin,KONG Xiangxi,et al.Selfsynchronization theory about two exciterson the same rotational axis in a vibration system[J].Journal of Vibration and Shock,2017,36(14):19-25.
[5]闻邦椿,林项阳.振动同步传动及其工业应用[J].机械工程学报,1984,20(3):26-41.WEN Bangchun,LIN Xiangyang.Vibration synchronous transmission and its industrial application[J].Journal of Mechanical Engineering,1984,20(3):26-41.
[6]XIONG W L,WEN B C,DUAN Z S.Engineering characteristics and its mechanism explanation of vibratory synchronization transmission[J].Chinese Journal of Mechanical Engineering,2004,17(2):185-188.
[7]XIONG W L,WEN B C,DUAN Z S.Mechanism of electromechanical-coupling on self-synchronous vibration an vibratory synchronization transmission[J].Journal of Vibratory Engineering,2000,13(3):325-330.(下转第64页)
[8]ZHAO C Y,ZHANG Y M.Synchronization and general dynamic symmetry of a vibrating system with two exciters rotating in opposite direction[J].Chinese Physics B,2009,19(3):1-7.
[9]ZHAO C Y,WEN B C.Synchronization control of vibration system with dual-motor drives rotating in the same direction[C]∥Proceedings of the Second Chinese World Congress on Intelligent Control and Intelligent Automation.Xi’an,China,1997.
[10]ZHAO C Y,ZHU H T.Synchronization of two coupled exciters in a vibrating system of spatial motion[J].Acta Mech Sin,2010,26:477-493.
[11]ZHANG X L,WEN B C.Theoretical and experimental study on synchronization of the two homodromy exciters in a nonresonant vibrating system[J].Shock and Vibration,2013,332:2300-2317.
[12]张秀华,张庆灵.非线性微分代数系统的控制理论与应用[M].北京:科学出版社,2007.
[13]MARHOMY A E,SATTAR N E A.Stability analysis of rotor-bearing system via Routh-Hurwitz Criterion[J].Applied Energy,2004,77:287-308.
[14]SENATOR M.Synchronization of two coupled escapementdriven pendulum clocks[J].Journal of Sound and Vibration,2006,291:566-603.
[15]闻邦椿,刘树英.振动机械的理论与动态设计方法[M].北京:机械工业出版社,2001.
[16]赵春雨,闻邦椿.多电机驱动的传动机械系统同步控制理论及应用[J].东北大学学报,1997(增刊1):342-347.ZHAO Chunyu,WEN Bangchun.Multimotor driven synchronous control theory and application of transmission mechanical system[J].Journal of Northeastern University,1997(Sup 1):342-347.
[2]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.
[3]赵春雨,赵乾斌,贺斌,等.三质体振动机动力学参数对其性能的影响分析[J].振动与冲击,2015,34(12):70-78.ZHAO Chunyu,ZHAO Qianbin,HE Bin,et al.Effects of dynamic parameters on the performance of a three-mass vibrating machine[J].Journal of Vibration and Shock,2015,34(12),70-78.
[4]陈晓哲,窦景欣,孔祥希,等.两激振器同一旋转轴线振动系统的自同步理论[J].振动与冲击,2017,36(14):19-25.CHEN Xiaozhe,DOU Jingxin,KONG Xiangxi,et al.Selfsynchronization theory about two exciterson the same rotational axis in a vibration system[J].Journal of Vibration and Shock,2017,36(14):19-25.
[5]闻邦椿,林项阳.振动同步传动及其工业应用[J].机械工程学报,1984,20(3):26-41.WEN Bangchun,LIN Xiangyang.Vibration synchronous transmission and its industrial application[J].Journal of Mechanical Engineering,1984,20(3):26-41.
[6]XIONG W L,WEN B C,DUAN Z S.Engineering characteristics and its mechanism explanation of vibratory synchronization transmission[J].Chinese Journal of Mechanical Engineering,2004,17(2):185-188.
[7]XIONG W L,WEN B C,DUAN Z S.Mechanism of electromechanical-coupling on self-synchronous vibration an vibratory synchronization transmission[J].Journal of Vibratory Engineering,2000,13(3):325-330.(下转第64页)
[8]ZHAO C Y,ZHANG Y M.Synchronization and general dynamic symmetry of a vibrating system with two exciters rotating in opposite direction[J].Chinese Physics B,2009,19(3):1-7.
[9]ZHAO C Y,WEN B C.Synchronization control of vibration system with dual-motor drives rotating in the same direction[C]∥Proceedings of the Second Chinese World Congress on Intelligent Control and Intelligent Automation.Xi’an,China,1997.
[10]ZHAO C Y,ZHU H T.Synchronization of two coupled exciters in a vibrating system of spatial motion[J].Acta Mech Sin,2010,26:477-493.
[11]ZHANG X L,WEN B C.Theoretical and experimental study on synchronization of the two homodromy exciters in a nonresonant vibrating system[J].Shock and Vibration,2013,332:2300-2317.
[12]张秀华,张庆灵.非线性微分代数系统的控制理论与应用[M].北京:科学出版社,2007.
[13]MARHOMY A E,SATTAR N E A.Stability analysis of rotor-bearing system via Routh-Hurwitz Criterion[J].Applied Energy,2004,77:287-308.
[14]SENATOR M.Synchronization of two coupled escapementdriven pendulum clocks[J].Journal of Sound and Vibration,2006,291:566-603.
[15]闻邦椿,刘树英.振动机械的理论与动态设计方法[M].北京:机械工业出版社,2001.
[16]赵春雨,闻邦椿.多电机驱动的传动机械系统同步控制理论及应用[J].东北大学学报,1997(增刊1):342-347.ZHAO Chunyu,WEN Bangchun.Multimotor driven synchronous control theory and application of transmission mechanical system[J].Journal of Northeastern University,1997(Sup 1):342-347.