基于张量理论的数控机床误差补偿模型

Error Compensation Model of CNC Machine-tool Based on Tensor Theory

为了进一步提高数控机床多体运动学误差模型的精度,提出了基于张量理论的机床误差补偿模型。首先面向数控系统列表插值补偿方式,提出了应用张量理论设定基础阶、扩展阶和误差阶来建立机床误差张量模型。然后,提出了采用设定机床信息、建立张量模型及设定检测参数3个流程实施误差补偿,并通过多元回归分析提出了采用4阶多项式拟合机床空间误差。最后,以某重型车铣复合机床实验为例,提出了分轴步进对角线法下的张量误差模型,采用球杆仪进行了圆度误差检测实验,结果表明该方法能够有效地提高机床精度,比多体运动学误差模型的补偿效果更优。

In order to improve the geometric accuracy of high-end CNC machine tools, a machine tool error compensation model based on tensor theory was proposed. Firstly, the error tensor model was established by setting the basic order, the extended order and the error order, which was applicable for error compensation table. Secondly, the error compensation was carried out in three processes, which were setting machine tool information, establishing tensor model and setting detection parameter. Referring to the ISO 230 - 2 standard, the modeling flow and detection parameters of the error tensor model were presented. Using multiple regression analysis, the linear fitting and residual errors were 2.5 p.m, while the four polynomial fit residuals were 1 p,m. Finally, taking CNC turn-milling machine experiment as an example, the error tensor model by step-diagonal measurement was proposed. The analysis of experimental data showed that the pitch error by three order fitting can improve the fitting precision by 59.4% - 92.5% , the sum of squared residuals was less than 0. 000 03 ; the straightness error needed five order fitting for nonlinear characteristics. The ballbar experiment of roundness error showed that roundness error was increased by 12.2% - 27.7% , while only compensated the pitch error. For example, the compensation using error tensor model can be reduced by 22.3% of roundness error at XY plane by three order fitting, which was optimized by 26.4% -95.5% compared with that of the linear interpolation. The experiment showed that the error compensation should be paid more attention to the straightness error. The method of error tensor model can effectively improve the accuracy of machine tools for both pitch error and straightness error.