Abstract:

A new modeling method for multi-axis CNC machines was proposed based on differential transformation theory,where the geometric errors were equivalent to the differential movement relative to its ideal position.Meanwhile, the Jacobian matrix was adopted to describe the mapping relation between tool pose error vectors and compensation error vectors, and all elements in the matrix could be solved by differential transformation. Thus the compensation error vectors were calculated by computing the generalized inverse of Jacobian martix. And then, an automatic error decoupling procedure was developed herein. Finally, an experiment was conducted on a five-axis CNC machine to test and verify this method. The results show that the overall position accuracy of the test path is improved dramatically.

Key words: multi-axis CNC machine, differential transformation, Jacobian matrix, error decoupling

摘要：

基于几何误差可等效为微分运动的原理，提出了基于微分变换的多轴数控机床几何误差建模的方法;运用雅可比矩阵建立了补偿值与刀具位姿误差之间的映射关系，矩阵中的元素可通过微分变换进行求解，由此利用雅可比矩阵的广义逆建立误差解耦模型。在此基础上，设计了多轴数控机床通用的自动化解耦计算流程。最后进行了五轴联动测试轨迹的误差补偿实验，补偿后的轨迹精度得到了显著的提高，验证了误差模型及解耦算法的有效性。

关键词: 多轴数控机床, 微分变换, 雅可比矩阵, 误差解耦