Application of autoregressive distributed lag model to thermal error compensation of machine tools

Abstract

Since Thermal error in precision CNC machine tools cannot be ignored, it is essential to construct a simple and effective thermal error compensation mathematical model. In this paper, three modeling methods are introduced in detail. The first is multiple linear regression model; the second is congruence model, which combines multiple linear regression model with AR model of its residual error; and the third is autoregressive distributed lag model(ADL), which is compared and analyzed. Multiple linear regression analysis is used most commonly in thermal error compensation, since it is a simple and quick modeling method. But thermal error is nonlinear and interactive, so it is difficult to model a precise least squares model of thermal error. The congruence model and autoregressive distributed lag model belong to time series analysis method which has the advantage of establishing a precise mathematical model. The distinctions between the two models are that: the congruence model divides the parameter into two parts to estimate them respectively, but autoregressive distributed lag model estimates parameter uniformly, so congruence model is less accurate than autoregressive distributed lag model in modeling. This paper, based upon an actual example, concludes that autoregressive distributed lag model for thermal error of precision CNC machine tools is a good way to improve modeling accuracy.