中文摘要：

五轴机床万能主轴头空间误差建模的传统方法采用齐次变换矩阵（HTM）进行运算,计算过程复杂,物理意义很难理解。提出了一种主轴头空间误差的简化建模方法。综合考虑了主轴头两个旋转轴的运动误差和刀具热误差对主轴头空间精度造成的影响。优化了机床运动坐标系设置,从而降低了空间误差模型的复杂性。基于刚体运动学原理,描述了主轴头的运动误差传递关系。结合实例,推导出了主轴头空间误差的数学表达式,其建模过程简单,物理意义明确。

英文摘要：

The traditional method for modeling volumetric errors of the universal spindle head of a five-axis CNC machine tool adopts the homogeneous transformation matrix to calculate the volumetric errors. The computation is complex, and it is difficult to understand its physical meaning. We propose a simple method for modeling the volu- metric errors by taking into consideration the influence of errors of two rotational axis and errors of the CNC machine tool on the volumetric precision of the spindle head. We optimize the coordinate system of the motion of the CNC machine tool, thus reducing the computational complexity of the model. We use the rigid body kinematics to de- scribe the error propagation of the universal spindle head and set up the model of its volumetric errors. We deduce their mathematical expressions, which are simple and have clear physical meanings.