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Experimental verification of mechanistic force models for endmilling: the impact of the size effect on cutting coefficients

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Abstract

A survey of popular cutting force models for endmilling, published over a period of four decades, has revealed that experimental validation of mechanistic cutting force models for endmilling is largely restricted to low or half radial immersion (RI) milling. It is found that the use of constant (averaged) cutting coefficients yields satisfactory results for low immersion milling. It is shown that low immersion experimental validations do not reveal the inadequacy of constant cutting coefficient models for very high immersion, as well as for full immersion slotting, of ductile metallic alloys. The use of instantaneous cutting coefficients yields more accurate force predictions in high immersion milling of such alloys. The reason is that instantaneous coefficients account for the size effect due to variable chip thickness. Though these facts are known, we provide extensive experimental evidence to support them. Experimental results are presented covering a range of radial immersion from 5% RI to 100% RI. These experimental force signals are graphically overlayed on force predictions made by both the types of models using established models from the literature. These plots are laid side by side to allow the reader to visually sense the stated differences between the predictive powers of the two classes of force model, namely, the constant coefficient models and the instantaneous coefficient models.

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Availability of data and materials

Data has been compiled, presented graphically, and tabulated in this manuscript.

Change history

Abbreviations

A a :

Projected axial chip area

A c :

Chip area

A f :

Projected frontal chip area

D :

Diameter of the endmill

F a :

Axial component of the cutting force

F n :

Normal (radial) component of the cutting force

F t :

Tangential component of the cutting force

F x,y,z :

x,y,z components of the instantaneous cutting force

\(\overline{F}_{x,y,z}\)  :

x,y,z components of the average cutting force

K ac :

Axial cutting coefficient

K ae :

Axial edge coefficient

K nc :

Normal (radial) cutting coefficient

K ne :

Normal (radial) edge coefficient

K tc :

Tangential cutting coefficient

K te :

Tangential edge coefficient

RI :

Radial immersion

a :

Nominal axial depth of cut

a r :

Radial depth of cut

b :

Instantaneous chip width

f T :

Nominal feed per tooth

h :

Instantaneous chip thickness for a straight fluted endmill

\(\overline{h}\) :

Average chip thickness for a straight fluted endmill

h m :

Mean instantaneous chip thickness in helical milling

\(\overline{h}_{m}\)  :

Averaged mean instantaneous chip thickness in helical milling

p :

Subscript denoting the \(p^{th}\) tooth

t,n,a :

Subscripts denoting tangential, normal (radial) and axial components

x,y,z :

Subscripts denoting x, y, and z components

\(\Gamma _{tc,nc,ac}\)  :

Invariant cutting constants

\(\lambda\) :

Helix angle

\(\theta\) :

Angular orientation (rotation angle) of an arbitrary point on the cutting edge in the tool-chip contact zone measured from a suitable reference

\(\theta _{ex}\) :

Rotation angle when the tooth exits the cut in a straight fluted endmill

\(\theta _p\) :

Cutter rotation angle, i.e., the angular orientation of the leading point of the reference helical tooth (the \(p^{th}\) tooth)

\(\theta _{st}\) :

Rotation angle when the tooth enters the cut in a straight fluted endmill

\(\Omega\) :

Angular spindle speed

\(\Psi _{tc,nc,ac}\) :

Invariant cutting constants

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Acknowledgements

Mr. Vadim Tymianski’s generosity in helping us set up the DAQ card is gratefully acknowledged.

Funding

One of the authors (AB) acknowledges the support of the University of Florida Alumni Fellowship.

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Authors and Affiliations

  1. Halliburton Jet Research Center, Alvarado, TX, 76009, USA

    Scott W. T. Payne

  2. Department of Mechanical Engineering, Mahindra University, Hyderabad, 500043, India

    Palash Roy Choudhury & Abhijit Bhattacharyya

  3. Department of Mechanical & Aerospace Engineering, University of Florida, Gainesville, FL, 32611, USA

    John K. Schueller

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  4. Abhijit Bhattacharyya
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Contributions

Scott W. T. Payne: experimental plan, initial experiments, data extraction algorithm, and data analysis. Palash Roy Choudhury: conceptualization, comparative summary of the literature, and manuscript writing. John K. Schueller: model development, resources, editing, funding, and supervision. Abhijit Bhattacharyya: experimental plan, completion of the experiment, data analysis, model development, and manuscript writing.

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Correspondence to Abhijit Bhattacharyya.

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The original online version of this article was revised: The correct city in affiliation 3 is Gainesville.

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Payne, S.W.T., Choudhury, P.R., Schueller, J.K. et al. Experimental verification of mechanistic force models for endmilling: the impact of the size effect on cutting coefficients. Int J Adv Manuf Technol 121, 7147–7165 (2022). https://doi.org/10.1007/s00170-022-09622-1

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