Stability and Bifurcation Analysis in Turning of Flexible Parts with Spindle Speed Variation Using FEM Simulation Data

Abstract

This study investigates the effect of variable spindle speed with sinusoidal modulation on chatter vibrations generated in turning of flexible parts. The Euler–Bernoulli beam theory is assumed for mathematical modeling of the slender workpiece that is clamped at the chuck and pinned at the tailstock. The induced force as interaction between tool and workpiece (A2024-T351) during chip formation is calculated using finite element simulation. Numerical-based semi-discretization approach is utilized to seek stability regions and chatter frequencies regarding coupled dynamic model of tool and workpiece, in the form of delay differential equations with time varying delay term. The simulated data are validated and compared with those for a rigid part. The results indicate the efficiency of periodic modulation in improvement of machining stability especially for low spindle speeds. The stability charts for different interaction location and also time history response are studied, extensively. Finally, detection of period-one, flip and secondary Hopf bifurcations for different spindle speeds at instability borders are analyzed and discussed by solving corresponding eigenvalue problem.