Thermal Positioning Error Modeling of Servo Axis Based on Empirical Modeling Method

Abstract

In order to investigate the thermal effect of a servo axis’ positioning error on the accuracy of machine tools, an empirical modeling method was proposed, which considers both the geometric and thermal positioning error. Through the analysis of the characteristics of the positioning error curves, the initial geometric positioning error was modeled with polynomial fitting, while the thermal positioning error was built with an empirical modeling method. Empirical modeling maps the relationship between the temperature points and thermal error directly, where the multi-collinearity among the temperature variables exists. Therefore, fuzzy clustering combined with principal component regression (PCR) is applied to the thermal error modeling. The PCR model can preserve information from raw variables and eliminate the effect of multi-collinearity on the error model to a certain degree. The advantages of this modeling method are its high-precision and strong robustness. Experiments were conducted on a three-axis machine tool. A criterion was also proposed to select the temperature-sensitivity points. The fitting accuracy of the comprehensive error modeling could reach about 89%, and the prediction accuracy could reach about 86%. The proposed modeling method was proven to be effective and accurate enough to predict the positioning error at any time during the machine tool operation.

A Novel Methodology for Measuring Ambient Thermal Effects on Machine Tools

“…As a refined statistical tool, the PCA boasts widespread applicability across a diverse array of disciplines. Its versatility is demonstrated in applications ranging from the thermal monitoring of MTs [33] and enhancing the efficiency of sen-networks [34] to the sophisticated analysis of thermal errors in complex mechatronic systems, frequently in conjunction with principal component regression (PCR) [11,35]. Consequently, the PCA method is considered one of the oldest and most widely used techniques for reducing the number of variables in large data sets while minimising information loss.…”

A novel approach for decoupling and separating the thermal positioning errors of machining center linear axes

“…Meanwhile, machine tool thermal errors are also impacted by geometric errors, inducing the relative deviations between the ideal and actual cutting points [19]. Thus, thermal positioning errors of a linear axis must be regarded as the synthetic results of geometric and thermal errors [20,21] since the manufacturing inaccuracies of the ball screws, the assemble errors of the feeding system, and the thermal deformations of the screw-nut mechanism have all contributed to the exhibited positioning errors. However, most of the reported studies barely covered the former two factors, resulting in insufficient compensation in the phase of engineering applications.…”

Spindle Thermal Error Prediction Based on LSTM Deep Learning for a CNC Machine Tool

“…The axes positioning was periodically readjusted by the control of the machine tool, based on the received compensation value. Multiple linear regression (MLR) is a common algorithm for creating mathematical prediction models of thermal displacement [17][18][19][20][21][22][23]. Some neural network modeling techniques have also been proposed to obtain more robust and accurate predictions [24][25][26][27][28][29][30][31][32].…”