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中文核心期刊

基于伺服电机驱动的进给传动系统扭转振动的Lie群分析方法

LIE GROUP ANALYSIS FOR TORSIBNAL VIBRATION OF SERVE MOTOR DRIVEN FEEDER DRIVE SYSTEM

  • 摘要: 激光切割机进给传动系统是一个伺服电机驱动的进给传动系统, 其传动部件在高速和高加速度进给过程中, 因外部激励或系统的自激振荡产生振动, 影响数控设备的定位精度和表面加工质量, 降低数控设备使用效率和使用寿命, 甚至会对数控系统造成损坏. 文章引入变换Lie群, 以江苏亚威机床股份有限公司生产的HLH 2040激光切割机进给传动系统为例研究伺服驱动的进给传动系统扭转振动问题的Noether对称性理论, 并给出了该问题的运动规律和状态响应特性. 通过寻找激光切割机伺服电机驱动的滚珠丝杆进给传动系统扭转振动的动能与势能, 构造Lagrange 函数, 建立系统的Lagrange方程. 引入关于时间和广义坐标的无限小变换, 提出并证明伺服电机驱动的滚珠丝杆进给传动系统扭转振动的Noether定理, 发现系统存在的守恒量, 且在得到的守恒量中存在对称关系. 根据该系统扭转振动存在的守恒量给出了运动规律, 分析该进给传动系统扭转振动的动态响应特性, 并数值模拟了动态响应, 得出系统在给定具体的技术参数之后, 文章所用的对称性方法的加入使得在极短的时间, 约10 ms, 系统能够迅速稳定, 效果显著. 这项研究有效地降低及控制伺服电机驱动的进给过程中扭转振动问题, 对提高数控设备的加工质量和效率以及提高数控设备的使用寿命具有十分重要的意义.

     

    Abstract: The laser cutting machine feed drive system is a servo motor-driven system, where its transmission components generate vibrations during high-speed and high-acceleration feeding processes due to external excitation or self-induced oscillations of the system. These vibrations adversely affect the positioning accuracy and surface processing quality of the CNC equipment, decrease the operational efficiency and lifespan of CNC equipment, and may even result in damage to the CNC system. In this paper, the transformation Lie group is introduced to study the Noether symmetry theory of torsional vibration problem using the HLH 2040 laser cutting machine manufactured by Jiangsu Yawei Machine Tool Co., China as an example. In addition, the motion law and state response characteristics of the problem are given. The Lagrange equation of the system is established by finding the kinetic and potential energies of torsional vibration of the servo-driven ball screw feed transmission system and constructing the Lagrange function. By introducing infinitesimal transformations about time and generalized coordinates, Noether’s theorem of torsional vibration of the system is proposed and proved. The conserved quantities of the system are found to exist, and symmetry relations exist in the obtained conserved quantities. The principle behind movements is given according to the conserved quantities existing in the torsional vibration of the system. The dynamic response characteristics of the system are analyzed, and the dynamic response is numerically simulated. In conclusion, results prove that, after the system is supplied with specific technical parameters and the effect is remarkable, along with using the symmetry method in this study, the system can able to stabilize rapidly in about 10ms. This study effectively reduces and manages the torsional vibration issue in the servo motor-driven feeding process, which holds significant importance in enhancing the machining quality and efficiency of CNC equipment, as well as extending the operational lifespan of CNC systems.

     

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