Robust modelling and prediction of thermally induced positional error based on grey rough set theory and neural networks

Abstract

Thermal errors adversely affect the precision of a machine tool operation. Therefore, reduction of thermal errors is essential for improving of machining accuracy. In this paper, in order to realize real-time compensation, taking a multi-axis machine tool as an example and a method for robust modeling and predicting thermally induced positional error is proposed. First of all, the number of temperature measuring points required in thermal error’s model was reduced based on the rough set theory, which greatly reduced variable searching and modeling time. Then through grey relation theory, systematic analysis of the similarity degree between thermal error and temperature data was carried out to select sensitive temperature measuring points, and the temperature variables in the thermal error’s model were reduced from 24 to 7 after optimization, which eliminated the coupling problems. For reducing the influence of unpredictable noises, radial basis function (RBF) and back propagation (BP) neural network modeling methods were adopted to predict thermally induced positional errors, and in comparison, the prediction accuracy of RBF neural network was found superior to that of traditional BP neural network. Finally, some measured data were selected to verify the validity of the proposed method, and the results showed that prediction accuracy of the proposed thermally induced positional error model was reliable.