The Research On Measurement And Analysis Method Of Thermal Error Of CNC Machine Tools' Linear Axis

With the development of science and technology,the precision of functional parts is higher and higher,which requires the machine tools to have high machining precision to ensure the precision of the processed parts.Error compensation is a cost-efficient method to enhance the accuracy of machine tools,whose prerequisite is an accurate,stable,and robust thermal error model.Experiments were carried out on a 3-axis experiment bench developed by our team,where the positioning errors under different temperatures were measured and the error modeling was studied.The correctness and feasibility of the proposed modeling methods are verified by the verification tests.This paper focuses on the selection of temperature-sensitivity points and the establishment of an error model in the field of thermal error modeling.A 3-axis experiment bench developed by our team was taken as the object to study the effective modeling of positioning errors under different temperatures.In order to improve the efficiency and stability of error compensation,the error modeling methods with strong robustness and high predictive accuracy are presented systematically.The main research contents of this paper are as follows:The generation mechanism of positioning error under different temperature distribution is analyzed,whose shape and slope can be attributed to different error components,that is,geometric positioning error and the thermal positioning error.Therefore,the separate modeling method for positioning error is proposed.Positioning error is separated into geometric error and thermal error,which are modeled respectively and then combined into the compound error model.The feasibility of the separate modeling method is verified.Geometric positioning error is fitted by polynomial.The order of a polynomial is usually chosen empirically without the theoretical guidance,while in this paper,F test is proposed to choose the best order of the polynomial.The F value of different order polynomial is calculated,and the polynomial with the maximum F value which is the most significant is chosen as the mathematical expression of geometric positioning error.For thermally induced positioning error,empirical modeling is applied to model the thermal-variant slopes.Empirical modeling of thermal error generally contains two contents: selection of the temperature-sensitivity points and establishment of the error model.Group search is used to optimize the temperature variables.In this paper,K-harmonic mean clustering and fuzzy C-means clustering are introduced to cluster the temperature variables,and clustering validity indexes are employed.The statistical numerical experiments are carried out to test the performances of these two clustering algorithms.For the establishment of the error model,this paper focuses on the application of fusion algorithm in error modeling.A single mathematical model has inevitable disadvantages.Therefore,reconstructed variable regression and bat algorithm-based BP neural network thermal error modeling are proposed.These two methods belong to the embedded fusion algorithm,which are the improvements of basic multiple linear regression and basic BP neural network in order to overcome the disadvantages of applying multiple linear regression or BP neural network individually.Multi-collinearity exists among the independent variables of MLR mode,which will affect the stability and predictive accuracy of the MLR model.To address this problem,reconstruction variable regression is proposed.Multi-collinearity among the independent variables can be reduced by the selection of temperature-sensitivity points and model optimization.FCM clustering and correlation analysis are used to select the temperature-sensitivity points which are reconstructed,and the thermal error is predicted by the unitary linear regression model of the reconstructed variable.The validity of the model is verified by the experiments.In view of the difficulty in determining the number of hidden nodes and the sensitivity to initial weights and thresholds of the basic BP neural network,a bat algorithm-based BP neural network is presented in this paper.BA is efficient on the searching ability,which is introduced to optimize the BP neural network to obtain the number of nodes in the hidden layer and the optimal weights and thresholds.FCM clustering combining with MIV selects the temperature-sensitivity points as the inputs of the optimized BP neural network.It is proved that the performance of bat algorithm optimized BP neural network is better than that of the basic BP neural network.Least squares support vector machine is especially suitable for thermal error modeling with the small-sample property and non-linearity characteristic.The performance of the LSSVM model mainly depends on the penalty parameters and kernel function parameters,which are difficult to be determined.To solve this problem,GWO-LSSVM is proposed.Grey wolf optimizer is utilized to search the optimal values of the penalty parameter and kernel function parameter,and the optimized model builds the thermal error model.Experimental results show that GWO is able to optimize the parameters of the LSSVM,and the GWO-LSSVM is competent for the job of thermal error modeling.