Identifying the transient milling force coefficient of a slender end-milling cutter with vibrations

Milling is a complex process during the coupling effect for multiple physical fields, especially for slender endmilling cutters. Because of the weak rigidity of its process system, it is easily affected by the physical behavior such as the milling force. In addition, it produces large vibrations and deformations, which affects the machining quality. To accurately predict the milling force of a slender end-milling cutter, a method to identify the milling force coefficients while considering vibrations is proposed. When considering the small diameter of the milling cutter edge, it is difficult to install sensors to measure the vibration. By combining the measured frequency response function of the cutter handle end and the cutter's Timoshenko beam finite element model, the interface dynamics parameters between the cutter and the cutter handle are identified. This is based on the receptance coupling substructure analysis, and the cutter edge's frequency response function is established. When considering the measured milling force data and the state equation of the cutter edge vibration, the realtime vibration of the cutter edge during the milling process is predicted. In addition, the undeformed cutting thickness during the superposition of the cutter edge vibration is obtained. The milling force coefficients are identified based on the undeformed cutting thickness of the coupled vibration, and the influence of the process parameters on the variation of the milling force coefficient is examined. The prediction accuracy and the average milling force coefficient without the vibrations are compared to verify the accuracy.