基于并行计算的三自由度并联机床动力学解析模型

Analytical dynamic model for three-DOF parallel machine tool based on parallel calculation

基于运动学分析、凯恩动力学方程和数字-符号方法,建立了三自由度并联机床的动力学解析模型.将广义坐标、构件的质量和转动惯量处理为符号量.将动力学模型矩阵的推导问题转化为特定条件下运用运动学和动力学计算公式求解驱动力的问题,由计算机自动生成动力学模型矩阵中的各元素的实时代码.文中引入了一种新的标量矩阵与矢量矩阵的乘法运算,研究了广义坐标和构件的质量对驱动力的影响规律.构造了动力学解析模型的并行算法,节省了计算时间.给出了动力学模型矩阵元素的实时代码生成和驱动力矩与参数关系的具体数值实例.

An analytical dynamic model for three-DOF parallel machine tool is established based on kinematic analysis, Kane dynamic equation and numeric-symbolic approach. The generalized coordinates, mass and moment of inertia of the links are treated as the symbols. The problem of deriving model matrix elements is transformed into the problem of solving for driving force under specified conditions by kinematic and dynamic formulae. Real-time codes of dynamic model matrix elements are generated automatically on computer. A new multiplication operation is introduced. The effects of the generalized coordinates and mass of the links on driving forces are investigated. The procedures of dynamic modeling can be performed off-line and the parallel calculation structure is adopted, therefore computing time can be reduced greatly. The numerical examples of real-time code generation for dynamic model matrix elements and simulation calculation are given for illustration.