Stochastic approach for modeling machining process variables

Abstract

In metal cutting industries and research organizations, empirical models of machining process variables are developed for their use in machining optimization, adaptive control and computer aided manufacturing. The conventional least square technique which has found a wide use in modeling estimates the mean values of the model parameters and therefore result in models which do not show the observed random nature of the various process responses. Since the variability in a process response is expected to be reflected in the parameters of the model, it is essential to treat the model parameters as random variables associated with some probability distributions. This thesis develops a statistical technique which can fit models whose parameters are random variables. To facilitate the implementation of the proposed technique, a software package has been developed which identifies the distributions of the model parameters from the experimental data of the process response and the input variables. Models which express the relationship between each of the four surface profile features, namely, center-line-average, variance of heights, variance of slopes, and variance of curvatures, and the three fine turning machining variables, i.e., cutting speed, feed rate and depth of cut, are developed from experimental data using the proposed modeling technique. The probability distributions of the surface profile features and the single, 2-factor, and 3-factor effects of the cutting conditions on the features are also investigated. The newly developed models of the surface roughness features show that the proposed technique is capable of capturing the variability of the machining responses which are not measurable by the conventional least square modeling technique.