# Stability Analysis of Model Regenerative Chatter of Milling Process Using First Order Least Square Full Discretization Method

Ezugwu, C. A and Okonkwo, Ugochukwu C. and Sinebe, J.E. and Okokpujie, I.P. (2016) Stability Analysis of Model Regenerative Chatter of Milling Process Using First Order Least Square Full Discretization Method. International Journal of Mechanics and Applications, 6 (3). pp. 49-62.

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## Abstract

Regenerative chatter is an instability phenomenon in machining operation that must be avoided if high accuracy and greater surface finish is to be achieved. It comes with its own consequences such as poor surface finish, low accuracy, excessive noise, tool wear and low material removal rate (MRR). In this paper, an analytical method base on first order least square approximation full-discretization method is use for the stability analysis on the plane of axial depth and radial depths of cut. A detail computational algorithm has been developed for the purpose of delineating stability lobe diagram into stable and unstable regions using mathematical models. These algorithms enabled the performance of sensitivity analysis. From the results axial depth of cut enhances the unstable region and suppresses the stable region. This means that inverse relationship exists between the axial and limiting radial depths of cut thus highlighting the need to determine the maximum value of their product for achieving maximized MRR thereby reducing the chatter in the milling process. It is also seen that the peak radial depths of cut occasioned by the lobbing effects occur at fixed spindle speeds irrespective of the axial depth of cut. Similarly, the rise in spindle speed enhances the stable region and suppresses the unstable region. This means that for us to have chatter-free milling process, parameters like axial and radial depths of cut should be carefully selected together at high machining speed. With these behaviour, one can locate the productive spindle speed at which the lobbing effects occur and depths of cut combination for the operator. Keywords Delineation, Regenerative chatter, Full discretization, Stability lobs diagram, Milling

Item Type: Article T Technology > TJ Mechanical engineering and machinery Mr DIGITAL CONTENT CREATOR LMU 09 Oct 2019 13:12 09 Oct 2019 13:12 https://eprints.lmu.edu.ng/id/eprint/2512