五轴机床旋转轴几何误差分析与补偿

五轴机床旋转轴之间装配所导致的位置无关几何误差（PIGEs—Position independent geometric error）是决定机床精度的关键因素，如何量化PIGEs对位姿精度的影响程度以及误差项之间的耦合作用强弱，从而合理地确定补偿值的权重系数是目前机床误差补偿技术所关注的热点问题。为降低五轴机床装配导致的PIGEs对机床精度的影响，首先，基于多体系统理论及齐次坐标变换方法建立了混合式五轴机床几何误差综合模型，表征了空间误差向量与几何误差项之间的映射关系。其次，考虑几何误差的分布特性，引入Morris全局灵敏度分析方法量化几何误差的作用效果及误差参数间的耦合强弱，通过灰色关联度分析表征误差的敏感性系数与位置向量、姿态向量间的关联程度，基于分析结果确定位置无关几何误差补偿值的权重系数。最后，以摆头-转台为特征的混合式五轴机床为例，进行基于球杆仪(DBB-Double ball bar)的几何误差测量辨识实验，利用辨识值进行虚拟圆锥台轨迹测量、误差补偿和复杂曲面零件加工实验。结果显示：十项几何误差对姿态误差的直接作用效果最为明显，利用基于敏感性分析的修正补偿值进行误差补偿后，虚拟圆锥台测量轨迹的半径偏差减小了65.1%，圆度误差降低了58.8%。基于误差分析实施误差补偿后，“S”型工件的轮廓精度平均提升了49.9%，误差补偿结果验证了误差分析结果的准确性和有效性。

Geometric Error Analysis and Compensation of Rotary Axes of Five-axis Machine Tools

The position independent geometric errors (PIGEs) of the rotating axes of five-axis machine tools which caused by the assembly are the key factor to determine the accuracy of the machine. Quantization analysis the influence of PIGEs on the accuracy of error vector, the coupling effect and determine the weight coefficient of the compensation value is the key technology of machine tool error compensation technology. In order to reduce the impact of PIGEs on machine tool accuracy caused by the assembly of five-axis machine tools, according to the distribution characteristics of the rotary axes of five-axis machine tool, the geometric error model is established based on multi-body system theory and homogeneous coordinate transformation method, and the mapping relationship between spatial error vector and geometric error terms is characterized. Secondly, by considering the distribution characteristics of geometric error, and Morris global sensitivity analysis method is introduced to quantify the effect of geometric error and coupling strength. The correlation coefficient between the sensitivity coefficient and the error vector is characterized by gray correlation analysis. The weighting factors of the position-independent geometric errors compensation value are determined. Finally, the measurement and identification experiment was conducted on five-axis machine tool with swiveling head is carried out, and the virtual cone-shaped trajectory measurement and error compensation experiment with DBB are carried out by using the identification value. The results show that the direct effect of ten geometric errors on attitude errors is the most obvious, and the error compensation based on the sensitivity analysis was performed, the radius deviation of the virtual cone measuring trajectory is reduced by 65.1%, and the roundness error is reduced by 58.8%. After error compensation based on error analysis, the contour accuracy of S-shaped test workpiece has been improved by 49.9% on average. The error compensation results verify the validity of the error analysis results.