Propagation of Johnson-Cook flow stress model uncertainty to milling force uncertainty using finite element analysis and time domain simulation

Abstract

This paper describes the propagation of uncertainty in the parameters for a 6061-T6 aluminum Johnson-Cook flow stress model to, first, the uncertainty in the corresponding mechanistic cutting force model obtained by orthogonal cutting finite element simulation and, second, the milling force predicted by time domain simulation using the force model. The approach includes five key elements: 1) a literature review to identify the means and standard deviations for the 6061-T6 aluminum Johnson-Cook model parameters; 2) structured light scanning to measure an endmill’s cutting edge macro-geometry along the tool axis; 3) structured light scanning to identify the cutting edge cross-sectional rake and relief profiles for the same endmill; 4) orthogonal cutting finite element analysis to determine the mechanistic force model coefficients that relate the force components to chip area and width using the tool’s rake and relief profiles and random samples from the Johnson-Cook parameter distributions; and 5) time domain simulation with inputs that include the measured cutting edge macro-geometry, uncertain finite element-based force model, and measured structural dynamics. Distributions for milling force predictions are determined by Monte Carlo simulation and compared to in-process measurements for an indexable endmill-collet holder to demonstrate the approach. It is observed that 95% confidence intervals on the predicted forces bound the measured time-dependent force profile peaks in over half of the cases tested. It is also seen that the Johnson-Cook flow stress model-based force predictions performed as well as predictions based on a calibrated mechanistic force model.