基于商空间的五轴数控机床几何误差标定与补偿算法

A Geometric Errors Calibration and Compensation Model for A 5-axis Machine Tool Based on Quotient Space

提出了一种基于商空间和指数积的五轴数控机床几何误差标定与补偿算法。首先,利用提出的机床几何误差标定模型可以快速、准确识别出机床各运动轴的实际旋量坐标,采用商空间法去除伴随变换冗余参数,避免了旋量坐标重复正交化和归一化。其次,采用基于微分法的雅克比矩阵补偿算法,可以在不求取机床运动学逆解的情况下,对机床几何误差进行补偿。最后,通过MATLAB仿真对误差标定模型和补偿算法模型进行验证。

This paper proposes a geometric errors calibration and compensation model for a 5-axis machine tool based on Quotient Space and Products of Exponentials (POE).Firstly,the proposed geometric errors calibration model can be used to identify the actual twists coordinates of the five drives.In order to avoiding the repeated normalization andorthogonalization of twist coordinates,Quotient Space is used to minimize the parameters of Adjoint transformation. Secondly,the manipulator Jacobian matrices of tool axis and tool tip position are achieved by differentiate the actual forward kinematics.Then the Jacobian matrices are used to compensate the geometric error without solving inverse kinematics.What's more,simulations based on MATLAB software are used to verify the efficiency of the proposed geometric errors calibration and compensation model.