Nonlinear Feed Effect in Machining Chatter Analysis

Regenerative chatter is a major limitation to the productivity and quality of machining operations due to the excessive rate of tool wear and scrap parts which are produced. Machining chatter analysis techniques examine the stability of the closed-loop model (force process and machine tool-part structure) of the machining operation to determine the stable process parameter space. Almost all chatter analysis techniques assume a linear force process and develop stability lobe diagrams (i.e., plots of the stable and unstable regions in the process parameter space) for a specific feed. It is well known that machining force processes inherently contain a nonlinear relationship between the force and the feed, which is typically described by a power law. In this paper, the linear chatter analysis technique developed by Budak and Altintas is extended to account for the force-feed nonlinearity. The analysis provides insight into the effect feed has on chatter in machining operations. Also, by directly including the force-feed nonlinearity in the chatter analysis, the need to calibrate the force process model at different feeds is alleviated. The analysis is developed for turning and face milling operations and is validated via time domain simulations for both operations and by experiments for a face milling operation. The analyses show excellent agreement with both the time domain simulations and the experiments. Further, several end milling experiments were conducted that illustrate the nonlinear effect feed has on chatter in machining operations.