Subdivision of chatter-free regions and optimal cutting parameters based on vibration frequencies for peripheral milling process

• Relationships between vibration frequencies and phase angle are investigated.
• Chatter-free regions are subdivided according to four kinds of spindle speeds.
• Optimal control theory is employed to obtain the optimal cutting parameters.
• The optimal cutting parameters obtained can achieve the most stable cutting process.

Considering the self-excited and forced vibrations in peripheral milling processes, a novel optimization method of cutting parameters is presented. The optimization method proposed, which is based on the vibration frequency analysis during milling processes, can achieve the most stable cutting process in relative stable region (or conditional stable region). First, relationships between vibration frequencies and phase angle of tooth of cutter in milling processes are investigated. Four kinds of spindle speeds associated with several bifurcations and vibrations are defined. Second, chatter-free regions are subdivided according to these spindle speeds. It is shown that in the so-called subregion C, cutting parameters can be simultaneously optimized for higher material removal rate (MRR) and higher surface accuracy. Third, optimal control theory is employed to determine the optimal cutting parameters, which can achieve the most stable cutting process in relative stable region. Optimizations of spindle speeds and depth of cut are conducted by using the stability charts and performance contours diagrams. The results show that the optimal cutting parameters can also be obtained in the so-called subregion C. Finally, the numerical results are verified and analyzed through milling experiments.