三杆混联数控机床的动力学

为了考察3-TPS型立卧转换式混联数控机床的动态特性、解决机床构件结构参数的选择和优化以及机床的控制等技术问题,使用拉格朗日方法研究了该种混联数控机床的动力学问题。首先根据机床的结构特点将拉格朗日动力学方程展开成表示在笛卡尔坐标中的标准形式,并将机床按照其结构特点分为动平台、三个驱动支链和平行约束机构三个子系统,然后分别推导了三个子系统的动能和势能的计算模型,在此基础上建立了机床在笛卡尔坐标中的拉格朗日动力学方程,并根据拉格朗日动力学方程的标准形式用递推方法得出了动力学方程中三个子系统的惯量矩阵M、科氏项系数V和重力系数G等各系数的计算公式,最后总结出了相应的算法。机床的这种动力学模型概念清楚,计算比较简单,可以满足机床的控制要求。

DYNAMICS OF 3-CHAIN HYBRID CNC MACHINE TOOL

The dynamic problem of the 3-TPS vertical-horizontal conversion hybrid CNC machine tool is studied by using the Lagrange method to analyze the dynamic behavior, study or realize the technology sectors, such as selecting and optimizing the structure parameters, control the machine, and so on. The Lagrange dynamic equation is firstly developed into a standard form expressed in the Cartesian space according to the machine's structure feature. The machine tool is divided into three subsystems: The moving platform, the three limbs and the parallel locking mechanism according to the machine's structure feature. Then the kintic energy and potential energy models of the three subsystems are deduced respectively. The dynamic equation expressed in the Cartesian space of the machine is founded on the base of that. To compute the terms of the dynamic equation, such as the inertia matrix M, the Coriolis centrifugal term V, the gravity term G, and so on, of the three subsystems, the recursion formulas are deduced according to the standard form of the Lagrange dynamic equation. The recursive algorithm to compute the terms is given finally. This dynamic model of the hybrid machine is of clear concept and the calculation is relatively simple. This can satisfy the needs of the machine's control.