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

Abstract

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.

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

“…This paper upgrades the predictive accuracy of the original closed-form models of cutting force proposed in Ozoegwu and Eberhard 44 for general-helix milling tools. The upgraded and the original closed-form models consider any milling tool as a series of axial segments having discrete helix angles.…”

“…The original closed-form cutting force models Closed-form models of cutting force have been presented in Ozoegwu and Eberhard 44 for cylindrical milling tools with flutes that are defined with arbitrary variable helix angle b(z) where z is the axial position of a cutting edge point from the tool tip. The models consider milling tools to be made up of series of axial segments S p for p = 0, 1, 2, 3, .…”

“…. and not in cutting action when g p (t) = 0 where u s and u e are the entry and exit angular positions of a cutting edge point into and out of the cutting zone which are determined by the radial immersion r = B=D where B is the radial depth of cut, see Ozoegwu and Eberhard 44 for details. These models are more accurate and convergent than the usual numerical methods and easy to implement because of the equally-spaced segmental endpoints.…”

“…While the models retain the benefits of the numerical approaches (universal applicability to all helix angle functions) while predicting cutting forces more accurately, minor errors are introduced by the partially engaged (incoming/outgoing into/from the cutting zone) segments that are fully discarded or fully included based on mid-segment values of the screening functions. This paper proposes upgraded versions of the methods in Ozoegwu and Eberhard 44 to eliminate the error by accounting for the partial segmental engagements and shows numerical illustrations of improved prediction accuracy and generic applicability. The new models are applied in closed-form modeling of cutting power with numerical illustrations of application to milling machine power demand modeling.…”

“…The common limitation of these closed-form models of cutting force is that they are limited to tools with fixed helix angle. To overcome this common limitation of the existing closed-form models of cutting force, direct integration-based closed-form models were proposed in Ozoegwu and Eberhard 44 for cylindrical milling tools having flutes that are defined with helix angles that vary arbitrarily with axial position of the cutting edge points. The models consider milling tools as series of axial segments with fixed axial or angular position limits.…”