Chatter suppression analysis in milling process with variable spindle speed based on the reconstructed semi-discretization method

Abstract

Milling chatter is a harmful phenomenon, which seriously affects the quality of the workpiece and limits the processing efficiency. The milling with variable spindle speed is an effective method for chatter suppression. In this paper, the reconstructed semi-discretization method (RSDM) is proposed to analyze the stability of the delay differential equations with varying delay term (VDDE) established based on the milling process with variable spindle speed. Firstly, the modulation period is discretized, and the time periodic delay term in VDDE is approximated at the discrete intervals based on the Shannon orthogonal basis. Secondly, the transition matrix is constructed, and the Floquet theory is used to build the stability boundary of milling system. The validity of the proposed method is verified by comparing with the well-accepted semi-discretization method (SDM) via a single degree of freedom milling system. Considering the limit of the acceleration of the spindle speed of machine tool, the modulation parameters RVF and RVA with sinusoidal and triangular wave modulations are optimized. Finally, the chatter frequencies and chatter types are analyzed and compared based on the reconstructed semi-discretization method.