五轴机床运动学建模与几何误差补偿

Kinematic modeling and geometric error compensation for five-axis machine tools

相对三轴机床,五轴机床包含三个线性轴和两个旋转轴,轴数和轴类型的增加使得五轴机床的几何误差建模更加复杂。本文基于齐次坐标变换理论,构建各线性轴和旋转轴的DH矩阵和误差矩阵,通过运动链配置关系获得考虑几何误差的五轴机床的运动学模型;基于梯度方法,构建轴空间和笛卡尔空间的微分运动映射雅克比矩阵;结合考虑误差的正运动学和误差映射模型,获得末端位姿偏差与轴端位置偏差的补偿量映射关系;实现考虑误差的通用五轴机床逆运动学迭代求解。仿真和分析证明所提方法可以有效改善机床各运动轴装配偏差引起的加工轮廓误差。

Compared with three-axis machine tools,five-axis machine tools contain three linear axes and two rotating axes,and the increase in the number of axes and axis type makes the geometric error modeling of five-axis machine tools more complicated.In this paper,based on the theory of homogeneous coordinate transformation,DH matrix and error matrix of each linear axis and rotation axis were constructed,and the kinematic model of five-axis machine tools considering geometric errors was obtained through the kinematic chain configuration relationship.Based on the gradient method,the differential motion mapping Jacobian matrix of axis space and Cartesian space was constructed.Aided by forward kinematics and the error mapping model,the mapping relationship between the position deviation of the axis and the position deviation of the end was obtained.The iterative solution of in verse kinematics considering geometric errors for the general five-axis machine tool was realized.Simulation and analysis show that the proposed method can effectively improve the machining profile error caused by the assembly deviation of each moving axis.