Thermal-Induced Errors Prediction and Compensation for a Coordinate Boring Machine Based on Time Series Analysis

Abstract

To improve the CNC machine tools precision, a thermal error modeling for the motorized spindle was proposed based on time series analysis, considering the length of cutting tools and thermal declined angles, and the real-time error compensation was implemented. A five-point method was applied to measure radial thermal declinations and axial expansion of the spindle with eddy current sensors, solving the problem that the three-point measurement cannot obtain the radial thermal angle errors. Then the stationarity of the thermal error sequences was determined by the Augmented Dickey-Fuller Test Algorithm, and the autocorrelation/partial autocorrelation function was applied to identify the model pattern. By combining both Yule-Walker equations and information criteria, the order and parameters of the models were solved effectively, which improved the prediction accuracy and generalization ability. The results indicated that the prediction accuracy of the time series model could reach up to 90%. In addition, the axial maximum error decreased from 39.6 μm to 7 μm after error compensation, and the machining accuracy was improved by 89.7%. Moreover, theX/Y-direction accuracy can reach up to 77.4% and 86%, respectively, which demonstrated that the proposed methods of measurement, modeling, and compensation were effective.

High-precision modeling of CNCs’ spatial errors based on screw theory

“…Study of error detection, modeling and compensation of 3-axis CNCs [24][25][26] is relatively comprehensive while some problems remain challenging so far. As those error modeling methods were based on the multi-body theory and homogeneous coordinate transformation, the measurement points were constrained but the positional relationship between the measurement and compensation points and effects of angular errors on the spatial errors were not taken into account in actual measurement.…”

Thermal error prediction of ball screw feed system based on inverse heat transfer analysis

“…The common method of error prediction is to establish a thermal error model through the temperature and thermal error data obtained from experiments to describe the relationship between temperature and thermal error. Generally, various data-driven model are widely used to establish thermal error models, including time series method [11][12], grey theory [13], neural network [14][15][16], support vector machine [17,18]. Miao et al [11] used the time series method to establish a thermal error model, predicted the change of time series by studying the variables and their inference mechanism, gave greater weight to the data near the prediction, and increased the impact of short-term parameters on the model, so as to improve the prediction accuracy.…”

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

“…Empirical modeling is different from theoretical modeling, where the relationship between the thermal errors and the temperature measurements was mapped by the data-driven models such as the neural network [ 12 , 13 ], gray model [ 14 ], support vector model [ 15 ], and time series model [ 16 ]. A thermal error model with the four key temperature points was proposed by Guo et al [ 17 ] using an ant colony algorithm-based back propagation neural network (ACO-BPN).…”