Dynamic performance modelling and measuring for machine tools with continuous-state wear processes

Abstract

In this paper, we consider the problem of using empirical continuous-state wear data of machine tools to estimate the dynamic lifetime distribution and to measure the performance of a machining process subject to stochastic tool-wear evolution. Machining systems are dynamic processes whose performance variable is usually characterised by the amount of tool wear that advances gradually with a continuous range of values. To accurately capture the performance of these continuous-state wear processes, neither traditional models such as the binary-state models nor multi-state models are suitable. In this paper, an exponential mixed-effects (EME) model is first developed. The EME model is subsequently transformed into a linear mixed-effects (LME) model to enhance the fit and predictability of the wear process data. The LME models take into consideration the correlations among repeated wear measurements collected at different time points within each subject. We then implement the expectation-maximisation (EM) algorithm to obtain the full maximum likelihood estimates (MLEs) of the parameters of the LME models whose asymptotic normal distributions can be used to acquire approximate confidence intervals and a testing hypothesis for the parameters. In addition, to measure the dynamic performance of tools, the amount of wear over time estimated from LME models is compared with a given tool-failure threshold. Consequently, we obtain the reliability of the tool and the estimation of its residual-lifetime distribution, which is critical information for the tool replacement or maintenance strategy. Finally, the lower and upper wear prediction limits of the 95% confidence level are presented. A practical application of the proposed methodology is illustrated throughout the paper.