Chatter modelling in micro-milling by considering process nonlinearities

Abstract

This paper presents a new approach for chatter modelling in micro-milling. The model takes into account: the nonlinearity of the uncut chip thickness including the run-out effect; velocity dependent micro-milling cutting forces; the dynamics of the tool-holder-spindle assembly. The uncut chip thickness is determined after considering the full kinematics of the cutting tool including the run-out effect. The micro-milling cutting forces are determined by: (i) a finite element (FE) prediction of the cutting forces in orthogonal cutting at different cutting velocities and uncut chip thicknesses; (ii) describing the relationship between cutting forces, cutting velocities and uncut chip thicknesses into a nonlinear equation; (iii) incorporating the uncut chip thickness model into the relationship of the cutting forces as function of the cutting velocity and the uncut chip thickness. The modal dynamic parameters at the cutting tool tip are determined for the tool-holder-spindle assembly and used for solving the equation of motion. The micro-milling process is modelled as two degrees of freedom system where the modal dynamic parameters for the tool-holder-spindle assembly and the micro-milling cutting forces are considered. Due to nonlinearities in the micro-milling cutting forces, the equation of motion is integrated numerically in the time domain using the Runge–Kutta fourth order method. The displacements in the x and y directions are obtained for one revolution-per-tool. Statistical variances are then employed as a chatter detection criterion in the time-domain solution. Scanning electron microscope (SEM) inspection is carried out to observe potential chatter marks on the micro-milled AISI 4340 steel surfaces at different spindle speeds and depths of cut. The predicted stability lobes and the experimentally obtained stability limits resulted in satisfactory agreement. The influence of the run-out effect on the stability lobes at different feed rates was investigated, which demonstrated the capability of the developed chatter model to consider quantitatively the run-out phenomenon. The results showed that the stability limits decrease by increasing the run-out length.