考虑零部件制造误差的精密主轴几何回转精度计算方法

A Calculating Method for the Geometric Rotation Accuracy of Precision Spindles Considering the Manufacturing Errors of Component Parts

提出一种通过精密主轴的结构及零部件制造误差预测其几何回转精度的计算方法。首先利用零部件之间的约束定位关系建立精密主轴的有向图模型,以此筛选出误差累积路径及关键公差;进而使用小位移旋量对各关键公差建模,通过齐次坐标变换的方法分析了4种主轴零件之间典型配合的误差传递过程;再将误差累积路径上的关键公差联系起来,得到主轴几何回转误差分析模型;在此基础上,结合蒙特卡洛模拟仿真方法,统计分析得到主轴几何回转精度的变动范围,得到其公差值;继而通过灵敏度分析,获得对各零件公差对回转精度的贡献度大小,为公差设计结果的改进提供依据。结果表明,该方法可以有效预测精密主轴的几何回转精度以及各零件公差对其影响程度。

A method calculating the geometric rotation accuracy of a precision spindle is proposed.Both the spindle structure and the manufacturing errors of component parts are involved.Firstly,a directed graph of the spindle is built according to the relation among the parts.Error accumulating path and key tolerances are selected based on the graph.Then,key tolerances are modeled with small displacement torsors and the variation propagation within 4 kinds of typical assembly relation between parts is analyzed with the homogeneous coordinate transformation method.Next,key tolerances along the path are linked to complete the geometric rotation error analysis model of the spindle.On this basis,combining with the Monte Carlo method,the vibration ranges of the rotation errors are obtained by statistical analysis and the tolerances are reached.The contribution degree of every tolerance to geometric rotation accuracy is calculated through sensitivity analysis to improve the tolerance allocation.The result shows that this method can predict the geometric rotation accuracy of a high precision spindle and the contribution rate of each tolerance to it effectively.