Upgraded closed-form cutting force models for general-helix cylindrical milling tools with application to cutting power and energy demand modeling

Abstract

This paper upgrades the original closed-form models of cutting force for general-helix milling tools for higher accuracy and demonstrates an application of the upgraded models in closed-form modeling of cutting power. The proposed models are shown to be numerically exact for the conventional fixed helix angle milling tools while the original models are not even though they are more accurate than the numerical methods. Errors of 0.00%, 12.15%, and 50.66% are recorded for an upgraded closed-form model, the equivalent original closed-form model, and an equivalent numerical method. Higher accurate applicability of the upgraded closed-form models to variable helix tools is also demonstrated for the harmonic case. Typical errors of 1.37%, 4.84%, and 9.94% are recorded for an upgraded closed-form model, the equivalent original closed-form model, and an equivalent numerical method. The proposed closed-form cutting force models are used to formulate new closed-form cutting power models for general-helix cylindrical milling tools which are applied in numerical evaluation of average cutting power. Evaluated data sets of average cutting power (seen to agree with published values) and spindle speed are then used in empirical calibration of average milling machine power demand. The high goodness-of-fit of the models with three published measured data sets are reflected in the high ${\mathrm{R}}^2$ values of 0.9980, 0.9834, and 0.9472 and low mean percentage errors (MPE) of −0.1247, −0.4137, and −0.6242.