Analytical Prediction of Stability Lobes for Passively Damped Boring Bars

Abstract

AbstractThe present article proposes the closed-form solution for analytical prediction of stability lobes in internal turning process. The passively damped boring bar is modeled as a cantilevered Euler-Bernoulli beam with constant cross sectional properties in which a Tuned Mass Damper (TMD) is embedded for the purpose of chatter suppression. The non-dimensional equations of motion are derived, assuming that the boring bar dynamics is well-represented by the fundamental mode of vibration. The stability of equivalent two-DOF dynamic model, i.e. boring bar with TMD, is analyzed in frequency domain. The closed- form expressions for critical depth of cut and spindle speed are presented in terms of boring bar and TMD characteristics. The proposed solution considers the effects of boring bar's structural damping and cutting geometry of insert on the stability behavior of passively damped cutting tool. An unconstrained optimization method is utilized to compute the most optimal set of tuning parameters for anti-chatter TMD. In order to improve the boundary of stability in a global sense, maximization of minimum critical depth of cut is selected as the objective of optimization. The superior performance of anti-chatter TMD is compared to H∞and H2TMDs for a wide range of applications. Moreover, the achieved results show a remarkable improvement of stability boundary compared to recent research works.