Angle and frequency domain force models for a roughing end mill with a sinusoidal edge profile

Wang, Jiunn-Jyh Junz; Yang, C. S.

doi:10.1016/s0890-6955(03)00163-9

Cited by 19 publications

(4 citation statements)

References 6 publications

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“…4. Evaluate the average cutting power P using equation (31) and then evaluate the average milling machine power demand P m and the milling machine energy consumption E m (t) using equations (32) and (34).…”

Section: Milling Power Demand Modelingmentioning

confidence: 99%

“…A related class of closed-form models with similar limitations are based on the angular convolution of the time-varying component functions of cutting force (like chip thickness, angular position of cutting edge, and the screening function) and/or Fourier transform leading to expressions in the frequency domain in terms of conditions and tool/workpiece geometry, see Junz Wang et al, 30 Zheng et al, 31,32 Junz Wang and Zheng, 33 and Junz Wang and Yang. 34 Another class of closed-form models of cutting force include those that derive from direct integration of the distributed forces leading to the models that are given in terms of the instantaneous limits of angular position of the cutting edge in the cutting zone [35][36][37][38][39] and the models that are given in terms of the instantaneous limits of lag angle of the cutting edge in the cutting zone. [40][41][42][43] In Bhattacharyya et al, 37 edge forces were not considered and two versions of the simplified closed-form model are presented to show alternative ways of accounting for the time-dependence of the limits of angular position of the cutting edge in cut: one is based on analytical expressions of the limits using Heaviside unit step function while the other exploits truncated Fourier series expressions.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Ozoegwu

2023

Proceedings of the Institution of Mechanical Engineers, Part B:

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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 [Formula: see text] values of 0.9980, 0.9834, and 0.9472 and low mean percentage errors (MPE) of −0.1247, −0.4137, and −0.6242.

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Section: Milling Power Demand Modelingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Ozoegwu

2023

Proceedings of the Institution of Mechanical Engineers, Part B:

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“…They include those based on the convolution integral and Fourier series/ transform analysis. [36][37][38][39][40] The analytical integration of milling forces in Zheng et al, 37 Yucesan and Altintas, 41 Bayoumi et al, 42 Liu et al, 43 and Liu et al 44 utilized lag angle as the variable of the definite integration while those in Budak, 4 Altintas, 16 Altintas et al, 45 and Moufki et al 46 are based on the use of the angular position of the cutting edge as the integration variable. Table 1 summarizes the publication years, analytical methods and limitations of the available closed-form models of milling cutting force.…”

Section: Introductionmentioning

confidence: 99%

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

Ozoegwu

Eberhard

2022

Proceedings of the Institution of Mechanical Engineers, Part B:

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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.

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Analysis and prediction of cutting forces in end milling by means of a geometrical model

Tsai

2006

Int J Adv Manuf Technol

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Angle and frequency domain force models for a roughing end mill with a sinusoidal edge profile

Cited by 19 publications

References 6 publications

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

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

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

Analysis and prediction of cutting forces in end milling by means of a geometrical model

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