柔性联轴器对振动系统动态响应影响的研究
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摘要
在旋转设备的动力传递过程中,柔性联轴器是一个极为关键的零件,可广泛应用于化工、矿山、冶金等机械设备的传动系统中。在传动设备中,用柔性联轴器将原动机和工作机联结起来,柔性联轴器在机组中起着传递动力、补偿径向和轴向不对中的作用。柔性联轴器的使用改变了系统的固有频率及响应,因此对柔性联轴器的研究具有重要的理论价值和工程应用前景。
本文以一个典型的振动系统-—振动磨机为研究对象。首先,在不考虑阻尼时,对振动系统中的偏心转子系统进行了分析研究。用拉格朗日方程建立偏心转子系统的动力学方程,求得数值解,根据数值解分析柔性联轴器对偏心转子转动的影响。偏心转子的运动为匀速转动和小幅扭转振动的叠加,其中匀速转动的转速是电动机的转速；扭转振动的频率为柔性连接偏心转子系统的固有频率。然后建立了整个振动系统的动力学方程,根据其动力学方程分析了柔性联轴器对平面振动系统不同时段动态响应的影响。由于柔性联轴器的存在,平面振动系统中振动体在初始阶段的振动除激振频率、振动系统固有频率外,还增加了旋转系统固有频率。在稳态阶段,振动体的振动频率为单一的激振频率。此外,还计算了旋转系统在受到扰动时的响应,并分析柔性联轴器对振动系统抗扰动能力的影响。旋转系统抗扰动的能力随着柔性联轴器阻尼的增大而增强,旋转系统所驱动的振动系统也随之较快恢复到稳定状态。即振动系统抗扰动的能力随着柔性联轴器阻尼的增大而增强。
In the process of power transmission of rotating equipment, flexible coupling is a crucial part, which can be widely used in transmission systems of chemical industry, mining, metallurgical industry and other machinery. In the driving device, the prime mover and driven machine are connected by flexible coupling. The flexible coupling is used to transmit torque from the prime mover to the driven machine and the two connected machines can go under radial or axial misalignment. The application of flexible coupling changes the natural frequency and response of the system, so the study of flexible coupling is of important theoretical value and engineering applications.
In this paper, a typical vibration system-a vibration mill is taken as the object to study. Firstly, without considering the damping, the eccentric rotor system, which is part of the vibration system, is analyzed. The dynamic equation of eccentric rotor system is formulated based on Lagrange equation. The influence of flexible coupling on the rotation of eccentric rotor is analyzed according to the numerical solution of dynamic equation. The movement of eccentric rotor is a superposition of a uniform rotation and a torsional vibration. The speed of the uniform rotation equals to the speed of the electric motor; the frequency of torsional vibration equals to the natural frequency of the flexible connected eccentric rotor system. Then, the dynamics equation of the whole vibrating system is established and the influence of flexile coupling on dynamic response of the plane-vibration system (which is also part of the vibration system) in different periods is analyzed. In the initial stage, because of the the presence of flexible coupling, in addition to the excitation frequency and the natural frequency of the plane-vibration system, there was also natural frequency of the rotation system in the vibration of the vibration-body. In the steady stage there was only the excitation frequency in the vibration of the vibration-body. Besides, the response of the rotation system was calculated when it was perturbed by external disturbance. The influence of flexible coupling on anti-disturbance ability of the vibration system is analyzed. The ability of anti-disturbance of the rotation system enhanced with the increase of damping of flexible coupling, so the vibration system, which is driven by rotation system, returns to steady state faster. Namely the ability of anti-disturbance of the vibration system enhanced as the damping of flexible coupling increases.
本文以一个典型的振动系统-—振动磨机为研究对象。首先,在不考虑阻尼时,对振动系统中的偏心转子系统进行了分析研究。用拉格朗日方程建立偏心转子系统的动力学方程,求得数值解,根据数值解分析柔性联轴器对偏心转子转动的影响。偏心转子的运动为匀速转动和小幅扭转振动的叠加,其中匀速转动的转速是电动机的转速；扭转振动的频率为柔性连接偏心转子系统的固有频率。然后建立了整个振动系统的动力学方程,根据其动力学方程分析了柔性联轴器对平面振动系统不同时段动态响应的影响。由于柔性联轴器的存在,平面振动系统中振动体在初始阶段的振动除激振频率、振动系统固有频率外,还增加了旋转系统固有频率。在稳态阶段,振动体的振动频率为单一的激振频率。此外,还计算了旋转系统在受到扰动时的响应,并分析柔性联轴器对振动系统抗扰动能力的影响。旋转系统抗扰动的能力随着柔性联轴器阻尼的增大而增强,旋转系统所驱动的振动系统也随之较快恢复到稳定状态。即振动系统抗扰动的能力随着柔性联轴器阻尼的增大而增强。
In the process of power transmission of rotating equipment, flexible coupling is a crucial part, which can be widely used in transmission systems of chemical industry, mining, metallurgical industry and other machinery. In the driving device, the prime mover and driven machine are connected by flexible coupling. The flexible coupling is used to transmit torque from the prime mover to the driven machine and the two connected machines can go under radial or axial misalignment. The application of flexible coupling changes the natural frequency and response of the system, so the study of flexible coupling is of important theoretical value and engineering applications.
In this paper, a typical vibration system-a vibration mill is taken as the object to study. Firstly, without considering the damping, the eccentric rotor system, which is part of the vibration system, is analyzed. The dynamic equation of eccentric rotor system is formulated based on Lagrange equation. The influence of flexible coupling on the rotation of eccentric rotor is analyzed according to the numerical solution of dynamic equation. The movement of eccentric rotor is a superposition of a uniform rotation and a torsional vibration. The speed of the uniform rotation equals to the speed of the electric motor; the frequency of torsional vibration equals to the natural frequency of the flexible connected eccentric rotor system. Then, the dynamics equation of the whole vibrating system is established and the influence of flexile coupling on dynamic response of the plane-vibration system (which is also part of the vibration system) in different periods is analyzed. In the initial stage, because of the the presence of flexible coupling, in addition to the excitation frequency and the natural frequency of the plane-vibration system, there was also natural frequency of the rotation system in the vibration of the vibration-body. In the steady stage there was only the excitation frequency in the vibration of the vibration-body. Besides, the response of the rotation system was calculated when it was perturbed by external disturbance. The influence of flexible coupling on anti-disturbance ability of the vibration system is analyzed. The ability of anti-disturbance of the rotation system enhanced with the increase of damping of flexible coupling, so the vibration system, which is driven by rotation system, returns to steady state faster. Namely the ability of anti-disturbance of the vibration system enhanced as the damping of flexible coupling increases.
引文
[1]Alan Dean. Taming vibration demons with flexible couplings [J], World Pumps,2005,65: 44-47.
[2]K.M. Al-Hussain. Dynamic stability of two rigid rotors connected by a flexible coupling with angular misalignment [J]. Journal of Sound and Vibration,2003,266 (2):217-234.
[3]李伟伟.采用弹性联轴：节的推土机传动轴系扭转振动分析[D].山东理工大学,2007.
[4]马建敏,杨万东.柔性联轴器非线性阻尼对扭转减振的影响[J].振动与冲击,2006,25(3)：11-13.
[5]毕国军.高弹性联轴器动态特性试验台研究[D].哈尔滨工程大学,2010.
[6]申屠留芳.关节轴承式叠片联轴器的设计研究[D].南京理工大学,2008.
[7]申屠留芳,张相炎.关节联轴器结构最优化设计[J].中国机械工程,2003,14(19)：1637-1639.
[8]李晓俊.电动潜油螺杆泵专用联轴器性能研究及优化设[D].西安石油大学,2008.
[9]辛宗生,吴晓峰.数字可编程式高速柔性联轴器的设计[J].林业机械与木工设备,2007,35(10)：37-38.
[10]梅庆,力宁.弹性联轴器动力特性分析与实验研究[J].振动与冲击,2008,27(6)：128-131.
[11]ZHU Ke-ke, ZHU Ru-pengAn analytic solution to asymmetrical bending problem of diaphragm coupling [J], Applied Mathematics and Mechanics,2008,29(12):1643-1649.
[12]宣旗,郭会.弹性膜盘联轴器膜盘受力分析与转矩应力关系式的建立[J].机械设计与制造,2004,(4)：85-87.
[13]J. Y. Liu, J. Z. Hong. Geometric stiffening effect on rigid-flexible coupling dynamics of an elastic beam[J], Journal of Sound and Vibration,2004,278 (4-5):1147-1162.
[2]K.M. Al-Hussain. Dynamic stability of two rigid rotors connected by a flexible coupling with angular misalignment [J]. Journal of Sound and Vibration,2003,266 (2):217-234.
[3]李伟伟.采用弹性联轴：节的推土机传动轴系扭转振动分析[D].山东理工大学,2007.
[4]马建敏,杨万东.柔性联轴器非线性阻尼对扭转减振的影响[J].振动与冲击,2006,25(3)：11-13.
[5]毕国军.高弹性联轴器动态特性试验台研究[D].哈尔滨工程大学,2010.
[6]申屠留芳.关节轴承式叠片联轴器的设计研究[D].南京理工大学,2008.
[7]申屠留芳,张相炎.关节联轴器结构最优化设计[J].中国机械工程,2003,14(19)：1637-1639.
[8]李晓俊.电动潜油螺杆泵专用联轴器性能研究及优化设[D].西安石油大学,2008.
[9]辛宗生,吴晓峰.数字可编程式高速柔性联轴器的设计[J].林业机械与木工设备,2007,35(10)：37-38.
[10]梅庆,力宁.弹性联轴器动力特性分析与实验研究[J].振动与冲击,2008,27(6)：128-131.
[11]ZHU Ke-ke, ZHU Ru-pengAn analytic solution to asymmetrical bending problem of diaphragm coupling [J], Applied Mathematics and Mechanics,2008,29(12):1643-1649.
[12]宣旗,郭会.弹性膜盘联轴器膜盘受力分析与转矩应力关系式的建立[J].机械设计与制造,2004,(4)：85-87.
[13]J. Y. Liu, J. Z. Hong. Geometric stiffening effect on rigid-flexible coupling dynamics of an elastic beam[J], Journal of Sound and Vibration,2004,278 (4-5):1147-1162.
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