基于拉格朗日方法的缠绕复合运动动力学方程

A Composite Winding Movement Dynamic Equation Based On Lagrange

基于拉格朗日方法,以缠绕过程中的运动体为研究对象,以缠绕体的运动状态及形变为研究重点,分析了缠绕体在缠绕过程中动能和势能的变化,得到了绕制过程中缠绕体的拉格朗日函数,建立了动力学方程。通过分析给出了动力学方程成立的条件,同时对方程的相关应用进行了分析。动力学方程的建立,使缠绕复合运动机械结构的力学设计更加精细化,可作为确定缠绕过程中影响缠绕体力学性能参数的理论依据,对精密线圈、光纤环等缠绕体缠绕工艺的控制系统设计具有一定的指导作用。

Based on the Lagrange method, taking moving object in the winding process as research object and taking winding movement state and the strain as research priorities, the winding body dynamic and potential energy are analyzed, and the Lagrange function of winding object during winding process was obtained. On top of that, a dynamic equation was established. Analyzing the dynamic equation presupposition, the conditions for the establishment of the dynamic equation is obtained,and at the same time, the application of dynamic equation was analyzed. The establishment of dynamic equation makes the mechanical design about complex winding movement of mechanical structure more refined. That can be the theoretical basis of factors impacting mechanical performance in winding process, which has a guiding role for winding process control system design, such as precision coil, optic fiber ring etc.