Modelling and prediction of machining errors using ARMAX and NARMAX structures

Forecasting compensatory control, which was first proposed by Wu ASME J. Eng. Ind. 99 (1977) 708], has been successfully employed to improve the accuracy of workpieces in various machining operations. This low-cost approach is based on on-line stochastic modelling and error compensation. The degree of error improvement depends very much on the accuracy of the modelling technique, which can only be performed on-line in a real-time recursive manner. In this study, the effect of the control input (i.e. the cutting force) is considered in the development of the error models, and the formulation of recursive exogenous autoregressive moving average (ARMAX) models becomes necessary. The nonlinear ARMAX or NARMAX model is also used to represent this nonlinear process. ARMAX and NARMAX models of different autoregressive (AR), moving average (MA) and exogenous (X) orders are proposed and their identifications are based on the recursive extended least square (RELS) method and the neural network (NN) method, respectively. An analysis of the computational results has confirmed that the NARMAX model and the NN method are superior to the ARMAX model and the RELS method in forecasting future machining errors, as indicated by its higher combined coefficient of efficiency.