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Force modelling in shallow cuts with large negative rake angle and large nose radius tools—application to hard turning

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Abstract

In finish turning, the applied feedrate and depth of cut are generally very small. In some particular cases, such as the finishing of hardened steels, the feedrate and depth of cut are much smaller than tool nose radius. If a tool with a large tool nose radius and large negative rake angle is used in finish turning, the ploughing effect is pronounced and needs to be carefully addressed. Unfortunately, the ploughing effect has not yet been systematically considered in force modelling in shallow cuts with large negative rake angle and large nose radius tools in 3-D oblique cutting. In this study, in order to model the forces in such shallow cuts, first the chip formation forces are predicted by transforming the 3-D cutting geometry into an equivalent 2-D cutting geometry, then the ploughing effect mechanistic model is proposed to calculate the total 2-D cutting forces. Finally, the 3-D cutting forces are estimated by a geometric transformation. The proposed approach is verified in the turning of hardened 52100 steel, in which cutting conditions are typified as shallow cuts with negative rake angle and large nose radius tools. The workpiece material property of hardened 52100 steel is represented by the Johnson-Cook equation, which is determined from machining tests. The comparison between the experimental results and the model predictions is presented.

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Abbreviations

A cutting :

Cutting cross section area

a 0, a 1, a 2, a 3 :

Constants of the ploughing effect coefficient K c

b 0, b 1, b 2, b 3 :

Constants of the ploughing effect coefficient K t

C s :

Side cutting edge angle

\({C^{*}_{s} }\) :

Equivalent side cutting edge angle

d :

Depth of cut

\({F^{*}_{c} ,F^{*}_{t} }\) :

Tangential and thrust chip formation forces

F c , F t :

Total cutting forces with the ploughing effect considered

f :

Feedrate

i*:

Equivalent inclination angle

K c , K t :

Ploughing effect coefficients

P 1, P 2, P 3 :

Forces in cutting, axial and radial directions

P 1,m , P 2,m , P 3,m :

Measured 3-D cutting forces

P c,measure , P t,measure :

Measured 2-D cutting forces

P 1,p , P 2,p , P 3,p :

Predicted 3-D cutting forces

P c,prediction , P t,prediction :

Predicted 2-D cutting forces

r :

Tool nose radius

t*:

Equivalent undeformed chip thickness

t max :

Maximum undeformed chip thickness along the tool nose

T :

Temperature

T m :

Melting point temperature

T r :

Reference temperature for measuring σ0

w*:

Equivalent width of cut

α n :

Cutting edge normal rake angle

\({\alpha ^{*}_{n} }\) :

Equivalent cutting edge normal rake angle

ε :

Uniaxial (effective) strain

\({\dot{\varepsilon }}\) :

Strain rate

\({\eta ^{*}_{c} }\) :

Equivalent chip flow angle

σ :

Flow stress

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Acknowledgements

The authors wish to express their gratitude to Mr. Anand Ramesh at Georgia Tech for the orthogonal hard grooving data and Mr. Ty G. Dawson at Georgia Tech for his discussion during the machining experiments. The authors also thank the reviewers for their inputs and comments.

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Authors and Affiliations

  1. George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA, 30332-0405, USA

    Yong Huang & Steven Y. Liang

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  1. Yong Huang
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  2. Steven Y. Liang
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Correspondence to Steven Y. Liang.

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Huang, Y., Liang, S.Y. Force modelling in shallow cuts with large negative rake angle and large nose radius tools—application to hard turning. Int J Adv Manuf Technol 22, 626–632 (2003). https://doi.org/10.1007/s00170-003-1550-0

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  • DOI: https://doi.org/10.1007/s00170-003-1550-0

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