A novel linear virtual temperature constructing method for thermal error modeling of machine tools

When a thermal error model of a machine tool is established, selecting the appropriate temperature measurement point is a very difficult problem. This paper proposes a novel method for constructing a linear virtual temperature. The proposed method can overcome the problem of selecting the temperature measurement point. First, temperature-thermal expansion hysteresis characteristics are used to divide the temperature measurement points into two groups. Each temperature variable is then chosen through a principal component analysis (PCA). Finally, using two temperature-variable weights and the correlative coefficient thermal displacement as the maximum optimal indexes, two temperature-weighted coefficients are calculated, and a linear virtual-temperature variable related to the thermal error linearity is then formed. In establishing the proposed thermal error model, the linear virtual temperature formed can serve as a system input variable. The proposed method was tested on a three-axis milling machine to determine the spindle Z-axial thermal error, and the results show that the root mean square error (RMSE) is reduced by 11 % and the sum of the squares of the error (SSE) is reduced by 39 % in comparison with a direct application of a temperature variable when establishing such a model. In the proposed method, only two temperature measurement points are used to establish a model, through which the complexity in determining the optimal measurement points through a traditional method, along with the number of temperature measurement points required, is greatly reduced.