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According to experimental data, the model of fixed Joints stiffness in machine tools was built by least square of relative error. The new regression equations were obtained by regression analysis. Compared to the original equations with Gaussian least-square, the relative error of new regression equations is within 3.5%, which reduces by 12.5% and the mean absolute percentage error (MAPE) decreases by 18.0%, 12.4%and 19.0% respectively.

With the experimental data of positioning precision of high-speed precision NC machine tool, a linear mathematical model of positioning error is established. Based on gray model and Cauchy problem formula, a nonlinear mathematical model is also established. The two models are evaluated by fuzzy comprehensive evaluation method to find the optimal prediction model. Compensated with a selection of positioning error compensation model, the confidence interval of 0.95 of positioning error is less than 3μm, meets the design requirements of the machine tool.