Milling bifurcations for strongly asymmetric, symmetric, and weakly asymmetric system dynamics

This paper uses time domain simulation to predict milling behavior for three distinct dynamic system configurations: 1) strongly asymmetric; 2) symmetric; and 3) weakly asymmetric. These correspond to physical setups that include: 1) a single degree-of-freedom flexure used to simplify in-process metrology for model validation; 2) long, flexible endmill dynamics; and 3) tool or workpiece-dominated dynamics with weak asymmetry in the plane of the cut. The time domain simulation displacement and velocity outputs are sampled at the tooth period to produce Poincaré maps and subharmonic sampling is combined with a numerical stability metric to produce stability maps. These Poincaré and stability maps are used to characterize the milling behavior and identify period-n bifurcations. Experimental validation is provided for the flexure-based setups.