A novel global sensitivity analysis method for vital geometric errors of five-axis machine tools

Abstract

Geometric error is one of the important errors that affect the machining of five-axis machine tools and how to identify th8e vital geometric error is effective for compensation. For this reason, the global sensitivity analysis of geometric errors for five-axis machine tools is an effective means to find the vital geometric error items that affect the machining accuracy of machine tools. However, it is difficult to deal with the higher order items of error parameter coupling in the global sensitivity analysis. In this paper, a novel global sensitivity analysis method for vital geometric error based on multi-body theory and truncated Fourier expansion is proposed. First, multi-body system (MBS) and homogeneous transformation matric (HTM) methods are used to establish the position error of the machine tool. Then, the output value of the error parameter is represented as the amplitude of the truncated Fourier series and the global sensitivity index is represented by the ratio of its amplitude variance to the total function variance through normalization processing. Moreover, the global sensitivity analysis method is presented to calculate the sensitivity index of each geometric error parameter and the vital geometric error parameters have been identified. Finally, an experiment on compensating for vital geometric error parameters is performed and the experimental results show that the proposed method is feasible and accurate.

Appendices

Appendix 1

Table 4 Position transformation matrix between adjacent bodies

Table 5 Position motion transformation matrix between adjacent bodies

Appendix 2

$$ {\delta}_{\mathrm{x}}(x)=\frac{-0.0129x}{5000}+0.0046\sin \left(\frac{2.2633\pi x}{5000}-0.6332\right) $$

$$ {\displaystyle \begin{array}{c}{\delta}_{\mathrm{y}}(x)=0.0296\sin \left(\frac{2.5828\pi x}{5000}+1.4918\right)+0.4288\sin \left(\frac{5.0024\pi x}{5000}-3.3295\right)\\ {}+0.4245\sin \left(\frac{5.0331\pi x}{5000}-0.2304\right)\end{array}} $$

$$ {\displaystyle \begin{array}{c}{\delta}_{\mathrm{z}}(x)=0.0376\sin \left(\frac{0.0136\pi x}{5000}+3.0638\right)+0.0124\sin \left(\frac{2.6840\pi x}{5000}+3.5962\right)\\ {}+0.0145\sin \left(\frac{6.2096\pi x}{5000}+2.3885\right)\end{array}} $$

$$ {\displaystyle \begin{array}{c}{\varepsilon}_{\mathrm{z}}(x)=2.9529\times {10}^{-5}\sin \left(\frac{0.5271\pi x}{5000}+2.7075\right)+7.4715\times {10}^{-6}\sin \left(\frac{4.3723\pi x}{5000}+2.9819\right)\\ {}+7.7088\times {10}^{-6}\sin \left(\frac{7.4411\pi x}{5000}-0.5413\right)\end{array}} $$

$$ {\displaystyle \begin{array}{c}{\varepsilon}_{\mathrm{y}}(x)=2.9990\times {10}^{-6}\sin \left(\frac{2.0054\pi x}{5000}+2.4608\right)+4.1933\times {10}^{-17}\sin \left(\frac{3.5549\pi x}{5000}+0.2324\right)\\ {}+7.3236\times {10}^{-6}\sin \left(\frac{6.000\pi x}{5000}-0.9056\right)\end{array}} $$

$$ {\displaystyle \begin{array}{c}{\varepsilon}_{\mathrm{x}}(x)=1.0384\times {10}^{-4}\sin \left(\frac{0.1089\pi x}{5000}+5.9992\right)+2.7342\times {10}^{-5}\sin \left(\frac{0.6971\pi x}{5000}+2.0011\right)\\ {}+3.4038\times {10}^{-6}\sin \left(\frac{4.7893\pi x}{5000}+1.9626\right)\end{array}} $$