Investigation of rotary inertial dynamic effects on chatter boundary in milling process using three-dimensional Timoshenko tool model

Chatter prediction is essential to conduct stable machining. Many of the previous studies made to simulate milling process have not considered gyroscopic and rotary inertial dynamics effects. The aim of this research is to investigate the effects of rotary inertial dynamics on prediction of chatter in the milling operation. For this purpose, a three-dimensional rotating cantilever Timoshenko beam is considered for modeling the cutting tool. In the proposed model, cutting forces are applied at the end of the beam. Imposing spectral finite element model, the governing delay partial differential equations of the system reduce to nondelay ordinary differential equations. The main contributions of the current research are modeling the cutting tool as a continuous model by Timoshenko beam theory, finding and solving nondelay ordinary differential equations of the cutter via spectral finite element model, and studying the effects of gyroscopic and rotary inertial dynamics, completely. For validating, the system stability predictions obtained from the presented model are compared with experimental outcomes from the literature. Besides the common stability lobe diagram which is in terms of depth of cut and the spindle speed, other stability diagrams based on cutter length and diameter are illustrated. Using this model, influences of rotary inertial dynamics on these stability diagrams are investigated. The results show that ignoring the rotary inertial dynamics causes significant errors in prediction of chatter boundaries especially in high angular velocity of the tool. In addition, the effect of number of the cutter teeth on the stability of milling process is studied. The presented stability diagram may help a machinist to choose a better set of parameters, such as tool length and diameter, number of cutter flutes, depth of cut, and spindle velocity, for doing a stable milling process.