Optimal modeling of end-mill spindle for improving the cutting stability

Abstract

The prediction of the dynamic stability at the tip of the cutting tool is an essential factor in estimating the cutting stability of the machine tool at the design stage. In the present paper, an optimal design approach is presented to improvise the dynamic stability of the machining process. The integrated spindle-tool unit is initially analyzed with finite element modelling using the Timoshenko beam theory and the corresponding tool tip frequency responses are evaluated. In order to maximize the chatter-free regions in the stability lobe diagram (SLD), an optimization study is carried-out by considering spindle parameters such as bearing locations on spindle shaft along with tool-overhang as parametric design variables. Experimental simulations are carried out for the modelling data to arrive the output response parameters such as the fundamental frequencies and limiting average stable depth of cut for several combinations of the tool overhang and bearing span values with design of experiments (DOE). Analysis of variance and Taguchi’s signal to noise ratios are used to estimate the influence on the response parameters.  End-milling experiments are carried-out to validate the stability states corresponding to various axial depths of cut. Furthermore, the simulated data is generalized by using the feed-forward neural network model and it can be used as functional approximation. A global meta-heuristic optimization scheme namely genetic algorithm (GA) is employed to achieve the spindle design data corresponding to maximize the limiting stable depth of cut.