Uncertainty Propagation Through An Empirical Model of Cutting Forces in End Milling

Empirical mathematical models of cutting forces in machining processes use experimentally determined input parameters to make predictions. A general method for propagation of input parameter uncertainties through such predictive models is developed. Sources of uncertainty are identified and classified. First, a classical uncertainty procedure is employed to estimate uncertainties associated with the data reduction equation using a first-order Taylor series expansion. Small values of input parameter uncertainties justify this local linearization. Coverage factors required to estimate confidence intervals are computed based on appropriate underlying statistical distributions. A root sum of squares method yields the overall expanded uncertainty in force predictions. A popular model used for predicting cutting forces in end milling is selected to demonstrate the procedure, but the demonstrated approach is general. The analysis is applied to experimental data. Force predictions are quoted along with a confidence interval attached to them. An alternative analysis based on Monte Carlo simulations is also presented. This procedure yields different insights compared with the classical uncertainty analysis and complements it. Monte Carlo simulation provides combined uncertainties directly without sensitivity calculations. Classical uncertainty analysis reveals the impacts of random effects and systematic effects separately. This information can prompt the user to improve the experimental setup if the impact of systematic effects is observed to be comparatively large. The method of quoting an estimate of the uncertainty in force predictions presented in this paper will permit users to assess the suitability of given empirical force prediction models in specific applications.