Critical speed analysis for nonlinear effects of rotor system and ball end milling

The critical speed analysis for nonlinear effects of rotor-bearing system and ball end milling are studied in this paper. The nonlinear cutting force can be calculated by using the Tlusty proposed 3/4 rule for chip thickness. The rotor system is supported by bearings with nonlinear spring effects. The critical speeds obtained from this study are compared with two sets of experimental data to validate the proposed four cases. The effects of design parameters on system dynamic behaviors, including critical speeds and tool displacements under the dynamic cutting forces, are numerically investigated in the time domain. The results show that the critical speeds of system are proportional to the corresponding system natural frequencies, but inversely to the cycle number of tool vibration multiplying by the number of flutes during the cutting time from one flute to another. For the linear system and the nonlinear system with small depth-of-cut under linear cutting force milling, their critical speeds are almost identical. With large feed-per-tooth, the differences of the critical speeds become larger between linear and nonlinear rotor systems and so are the dynamic responses at critical speeds milling. The critical speed under nonlinear cutting force milling is found to be always higher than that under linear cutting force. Furthermore, the chatter stability lobes are studied for various cutting conditions. The intervals between critical speeds increase gradually, and the axial depths of cut of nonlinear system for stability are lower than those of linear system.