Compilation of NC lathe dynamic cutting force spectrum based on two-dimensional mixture models

The load spectrum of numerical control machine tool (NCMT) is the basis data of reliability design, life prediction, and reliability bench test with simulated actual load conditions. Static cutting force spectrum, which can be compiled by empirical formula, cannot accurately reflect the real load conditions. Hence, a method for compiling the spectrum of dynamic turning force is proposed by using two-dimensional mixture models. Dynamic turning force is measured in the laboratory based on a large amount of cutting process data collected in the user field. Mean–frequency and amplitude–frequency matrices of dynamic turning force are obtained by the rainflow counting method. The probability distributions of mean and amplitude are established by using Weibull mixture models (WMM) according to the characteristics of the dynamic turning force, and the two main problems of this method are the determination of the number of mixture components and the estimation of parameters. Gray relation analysis is used to quantify the multi-objective evaluation matrix, and thus the number of mixture components is determined. Parameters are estimated using the improved expectation maximization (EM) algorithm, where the initial values of parameters are obtained by the K-means++ and Bayesian random classification. Finally, the joint probability distribution function between the mean and amplitude is established by the Copula function. Thus, the dynamic cutting force spectrum is compiled. Case analysis results show that the mean and amplitude distribution models with high fitting precision can be obtained using the proposed method. Furthermore, the precision of the load spectrum of NCMT is improved.

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