An Explicit Coupling Model for Accurate Prediction of Force-Induced Deflection in Thin-Walled Workpiece Milling

Cutting force-induced vibrations in thin-walled parts milling may cause violation of dimensional tolerance while accurate modeling of the milling error distribution is still a challenging work because of the coupling effect between the dynamic cutting forces and the resulting steady-state vibrations. It greatly increases the computational complexity to capture the true cutter-workpiece engagement with classic time domain or iteration method. This paper proposes a novel explicit model to predict the error distribution considering this coupling relationship without iterative calculation. A new cutting force model with variable coefficients with respect to the deflections is developed to describe the dynamic cutting forces. The effectiveness of the force model is verified by a group of calibration experiments. The analytical solution of the dynamic model is discussed and a semi-analytical method is constructed to predict the error distribution directly. Machined surface as well as the deformation errors are derived and thin-walled workpiece milling experiments for verification are conducted. Comparisons between simulations and experiments show that the proposed method is accurate and efficient.