符合阿贝原则的数控机床几何误差建模

为提高现有数控机床空间误差分析方法的准确度, 本文基于阿贝原则对齐次转换矩阵(HTM)几何误差补偿模型进行优化。首先, 推导出XYFZ型三轴机床适用的HTM几何误差补偿模型并给出模型正确使用的前提条件; 然后, 基于阿贝原则分析了三轴机床的空间误差传递机理, 指出阿贝误差对机床定位精度的影响, 给出理论计算公式并在机床运动轴上进行实验验证; 最后, 基于阿贝原则和布莱恩原则对现有的HTM几何误差补偿模型进行优化, 采用该模型拟合体对角线空间误差, 并与实测机床体对角线误差进行对比验证。现有HTM几何补偿模型可将机床空间误差由41.15 μm补偿至16.37 μm, 补偿率为60.22%; 优化后的补偿模型可将机床空间误差补偿至5.32 μm, 补偿率为87.07%, 提高了26.85%。实验结果表明, 优化后的补偿模型更加合理, 进一步改善了空间误差的补偿精度。

Abstract

In order to address the shortcomings of the existing space error analysis methods of CNC machine tools, the geometry error compensation model was optimized based on Abbe principle. First, the geometry error compensation model of the three-axis machine tool was deduced, and the precondition for the correct usage of the model was provided. Second, the mechanism of spatial error transfer of three-axis machine tool was analyzed, based on the Abbe principle. The influence of Abbe error on the positioning accuracy of machine tool was determined, and the theoretical calculation formula was provided and verified by conducting experiments on the moving axis of machine tool. Finally, the existing geometric error compensation model of HTM was optimized based on the Abbe principle and Bryan principle.This model was used to fit the diagonal space error, and compared with the actual measured diagonal error of the machine tool. The existing HTM geometric compensation model can compensate for the machine tool space error, altering it from 41.15 μm to 16.37 μm, with a compensation rate of 60.22%. The optimized compensation model can compensate for the machine tool space error, altering it to 5.32 μm, with a compensation rate of 87.07%, which is an increase of 26.85%. The experimental results show that the optimized compensation model is more reasonable, and further improves the accuracy of space error compensation.

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