Closed-form models for the cutting forces of general-helix cylindrical milling tools

Cutting force is the predictor of the performance indicators of machining processes, therefore, the measurement and modeling accuracy have received sustained research attention. The existing closed-form models for milling cutting force are useful for an analytical design process and optimization (over large parametric ranges) but the methods are not applicable to milling tools with arbitrary helix angle variation (general-helix). On the other hand, numerical methods are available for general-helix tools but are only applicable in an analytical design process and optimization when they are used to create surrogate models. The aim of this work is to develop closed-form models that retain the benefits of both approaches for computing the cutting forces of general-helix cylindrical milling tools by combining the properties of the analytical and numerical approaches. The proposed closed-form modeling approach is shown to be more accurate and more convergent than the numerical approach and checked using published experimental data for a fixed helix angle milling tool. For this illustrative case, the percentage error of a proposed closed-form model for the unsegmented (1-segment) tool model relative to the 500-segment model (considered exact) is 0.00% when the error for the equivalent numerical method is 1.90%. Higher accurate applicability of the proposed closed-form models to variable helix tools is also demonstrated for the harmonic case. The percentage error of a proposed closed-form model for the 1-segment tool model relative to the 500-segment model (considered exact) is 0.28% when the error of the equivalent numerical method is 1.05% for this illustrative case. The advantage in terms of generalized applicability and the disadvantage in terms of minor discretization error are highlighted against the backdrop of an existing close-form model for fixed helix angle tools.