Mathematical modelling of chip thickness in micro-end- milling: A Fourier modelling

This study developed a model of undeformed chip thickness in micro-end-milling for the use in estimating cutting constants based on measured cutting forces. The proposed estimation method is based upon the invertibility of the average milling force model. In this paper, chip thickness in micro-end-milling was estimated by summing the thicknesses of the conventional chip component and the additional chip component. Thickness was then expressed in terms of Fourier series. The analyses showed that the fast convergence of Fourier series gives the Fourier chip thickness model sufficient accuracy when using only five terms of the truncated Fourier series for common micro-end-milling processes. The Fourier coefficients can be expressed in terms of the ratio of feed per tooth to cutter radius for different numbers of cutter teeth. The accuracy and conciseness of the chip thickness model enables the modelling of average cutting force in a closed form, which can be applied to identify the cutting constants. Cutting force experiments verify that the model prediction agrees very well with the experimental results.