An accurate regenerative chatter model in the ball-end milling process that considers high feed rate and shallow axial immersion conditions

Abstract

This paper proposes an accurate model of a ball-end milling process that considers high feed rate and shallow axial immersion conditions with multiple varying time delays (VTDs) to determine the stability of the system. The criteria that the time delay must satisfy are derived. The effect of the feed motion on the entry and exit cutting angles is discussed herein for the first time to the authors' knowledge in the ball-end milling process. The system dynamics are described by a set of delay differential equations (DDEs) with periodic coefficients and multiple VTDs. In this paper, an improved semi-discretization method (ISDM) is also proposed to determine the stability of the VTD system, which greatly extends the computational efficiency. Then, a discrete dynamical map is deduced to establish the state transition matrix over one time period to predict the stability via the Floquet theory. The improvement of the proposed ISDM is validated by comparing the results with those in other studies.