Thermal error is the major factor in restricting the accuracy of CNC machining. The modeling accuracy is the key of thermal error compensation which can achieve precision machining of CNC machine tool. The traditional thermal error compensation models mostly focus on the fitting accuracy without considering the robustness of the models, it makes the research results into practice is difficult. In this paper, the experiment of model robustness is done in different spinde speeds of leaderway V-450 machine tool. Combining fuzzy clustering and grey relevance selects temperature-sensitive points of thermal error. Using multiple linear regression model (MLR) and distributed lag model (DL) establishes model of the multi-batch experimental data and then gives robustness analysis, demonstrates the difference between fitting precision and prediction precision in engineering application, and provides a reference method to choose thermal error compensation model of CNC machine tool in the practical engineering application.
KEYWORDS: Autoregressive models, Thermal modeling, Mathematical modeling, Error analysis, Systems modeling, Data modeling, Instrument modeling, Time series analysis, Temperature metrology, Statistical modeling
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.
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