Comparing Chatter Stability of End-Milling Processes of Different Number of Teeth

Abstract

The cutting forces and dynamic stability of end milling of full radial immersion are compared for end-millers of one to ten teeth. The parameters; tool mass  tool natural frequency , tool damping ratio  and feed speed  are considered fixed for the millers. An end-milling tooth normally has positive rake angle and small cutting edge radius thus workpiece material cutting coefficient  is also considered fixed since ploughing effect is not expected to be noticeably affected by change in number of teeth. It is seen that periodic cutting force reduces as the number of teeth increases. A method of milling stability analysis as proposed by Ding et al known as full-discretization is utilized in generating the stability charts. Use is made of the Simpson’s rule in establishing for the studied system that chatter stability decreases as the number of teeth increases in the low spindle speed range  and that lowest chatter stability at high spindle speed range  occurs for the five tooth miller. Recommendations are made for the machinist based on these findings. The critical characteristic multipliers at single minimum point of each secondary Hopf bifurcation lobe (SHBL) are postulated to leave the unit circle along imaginary axis when number of teeth of slotting miller is greater than two. This phenomenon is noticed for the one and two tooth millers at two turning points that are not necessarily local minima of each SHBL.

Keywords: Chatter, delay, full-discretization, periodic cutting force, discrete time map, bifurcation