Abstract
A simple modified dynamic model of nonlinear cutting forces considering the geometry of orthogonal cutting, the relationship of cutting angles, the effects of tool cutting on a wavy surface of workpiece and the variations of cutting angles in the cutting process, is derived for predicting the nonlinear chatter phenomenon. Firstly, the linear stability of the cutting process was determined by normal mode analysis. The results show that the cutting feed presents a stabilizing effect, and that larger stiffness of the cutting tool structure gives a more stable region in the W- V (cutting thickness-cutting velocity) plane, secondly, the multiple scale method is used to study the weak nonlinear stability of the cutting process. The results show that the behavior of the cutting process in the linearly stable region is nonlinearly stable, but in the linearly unstable region the amplitude of chatter does not grow infinitely, i.e. supercritical stability exists in the nonlinear region. In the supercritical region, the nonlinear chatter frequency is smaller than that of linear prediction, and when cutting width increases the chatter frequency decreases slowly.
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