| Sign up

PDF (2.3 MB)

Cite

EndNote(RIS) BibTeX

Collect

Collect

Submit Manuscript

Show Outline

Figures (14)

Fig. 1

Fig. 2

Fig. 3

Fig. 4

Fig. 5

Fig. 6

Fig. 7

Fig. 8

Fig. 9

Tables (2)

Table 1

Table 2

Research Article | Open Access

Influence of contact curvature on frictional energy dissipation under varying tangential loads

Sumin BAEK, Seunghun BAEK()

School of Mechanical Engineering, Pusan National University, Pusan 46241, Republic of Korea

Show Author Information

Graphical Abstract

View original image Download original image

Abstract

This study investigates the effect of contact surface curvatures on the friction response under varying tangential loadings using a finite element (FE) model. The results showed that the geometry of the surface influences the contact force at the interface and reduces the friction effect through an unsteady distribution of the contact force. The relationship between the friction effect, excitation, and contact surface shape was also examined, revealing a linear inverse relationship between the friction and curvature. The findings provide a comprehensive understanding of the frictional interactions between elastic bodies and highlight the role of curvature as a design parameter for regulating the friction effect.

Keywords

frictional contact curvelinear contact frictional energy dissipation contact curvature

References

[1]

Lontin

K

, Khan

M

. Interdependence of friction, wear, and noise: A review. Friction 9(6): 1319–1345 (2021)

Crossref Google Scholar

[2]

Griffin

J H

. A review of friction damping of turbine blade vibration. Int J Turbo Jet Engines 7(3–4): 297–307 (1990)

Crossref Google Scholar

[3]

Lee

D

, Jang

Y H

, Kannatey-Asibu

E

. Numerical analysis of quasistatic frictional contact of an elastic block under combined normal and tangential cyclic loading. Int J Mech Sci 64(1): 174–183 (2012)

Crossref Google Scholar

[4]

Baek

S

. Dynamic response predictions of frictionally constrained lap joints subjected to cyclic loading. Int J Mech Mater Des 18(2): 491–507 (2022)

Crossref Google Scholar

[5]

Jang

Y H

, Barber

J R

. Effect of phase on the frictional dissipation in systems subjected to harmonically varying loads. Eur J Mech A 30(3): 269–274 (2011)

Crossref Google Scholar

[6]

Putignano

C

, Ciavarella

M

, Barber

J R

. Frictional energy dissipation in contact of nominally flat rough surfaces under harmonically varying loads. J Mech Phys Solids 59(12): 2442–2454 (2011)

Crossref Google Scholar

[7]

Hertz

H

. On the contact of elastic solids. J Reine Angew Math 92: 156–171 (1882)

Crossref Google Scholar

[8]

Galin

L A

. Plane Static Isotropic Contact Problems. Dordrecht: Springer, 2008: 33–60.

[9]

Golden

J M

. The effect of surface curvature on the friction coefficient. Wear 48(1): 73–86 (1978)

Crossref Google Scholar

[10]

Mindlin

R D

, Deresiewicz

H

. Elastic spheres in contact under varying oblique forces. J Appl Mech 20(3): 327–344 (1953)

Crossref Google Scholar

[11]

Cattaneo

C

. Sul contatto di due corpi elastici: Distribuzione locale degli sforzi. Rendiconti dell’Aecademia Nazionale dei Lincei 6: 342–349 (1938) (in Italian)

[12]

Johnson

K L

. Surface interaction between elastically loaded bodies under tangential forces. Proc R Soc Lond A 230(1183): 531–548 (1955)

Crossref Google Scholar

[13]

Etsion

I

. Revisiting the cattaneo–mindlin concept of interfacial slip in tangentially loaded compliant bodies. J Tribol 132(2): 1 (2010)

Crossref Google Scholar

[14]

Ciavarella

M

. Transition from stick to slip in Hertzian contact with “Griffith” friction: The Cattaneo-Mindlin problem revisited. J Mech Phys Solids 84: 313–324 (2015)

Crossref Google Scholar

[15]

Davies

M

, Barber

J R

, Hills

D A

. Energy dissipation in a frictional incomplete contact with varying normal load. Int J Mech Sci 55(1): 13–21 (2012)

Crossref Google Scholar

[16]

Persson

A

. On the stress distribution of cylindrical elastic bodies in contact. Ph.D. Thesis. (Gothenburg) Sweden: Chalmers University of Technology, 1964.

[17]

Noble

B

, Hussain

M A

. Exact solution of certain dual series for indentation and inclusion problems. Int J Eng Sci 7(11): 1149–1161 (1969)

Crossref Google Scholar

[18]

Ciavarella

M

, Decuzzi

P

. The state of stress induced by the plane frictionless cylindrical contact. I. The case of elastic similarity. Int J Solids Struct 38(26–27): 4507–4523 (2001)

Crossref Google Scholar

[19]

Iyer

K

. Solutions for contact in pinned connections. Int J Solids Struct 38 (50–51): 9133–9148 (2001)

Crossref Google Scholar

[20]

Ayyub

B M

, McCuen

R H

. Probability, Statistics, and Reliability for Engineers and Scientists. Boca Raton (USA): CRC Press, 2011.

Volume 12 Issue 2,
February 2024

Pages 363-374

DOI: 10.1007/s40544-023-0788-9

Cite this article:

BAEK S, BAEK S. Influence of contact curvature on frictional energy dissipation under varying tangential loads. Friction, 2024, 12(2): 363-374. https://doi.org/10.1007/s40544-023-0788-9

10.1007/s40544-023-0788-9.F001 Fig. 1Material properties of FE model. d is the Y-coordinate of the middle point.
10.1007/s40544-023-0788-9.F002 Fig. 2FE model including the illustration of detailed mesh on (i) concave and (ii) convex surface.
10.1007/s40544-023-0788-9.F003 Fig. 3(a) Friction energy dissipation and (b) relative errors between cycles at a flat contact surface (κ = 0.00) with w/L = 0.5.
10.1007/s40544-023-0788-9.F004 Fig. 4(a) Friction energy dissipation and (b) relative errors between cycles at a flat contact surface (κ = 0.02 ) with w/L = 0.5.
10.1007/s40544-023-0788-9.F005 Fig. 5Contact traction distribution of flat surface when w/L = 0.5, F/P = 0.4 at time steps of (a) t/T = 0.2, (b) t/T = 0.3, (c) t/T = 0.7, and (d) t/T = 0.8.
10.1007/s40544-023-0788-9.F006 Fig. 6Contact state evolution over a cycle with w/L = 0.5 and varying F/P.
10.1007/s40544-023-0788-9.F007 Fig. 7Contact traction distribution when loading condition is w/L = 0.5, F/P = 0.4 at the time step of t/T = 0.2 at curved surface with the curvature (a) κ = 0.01 (b) κ = 0.02.
10.1007/s40544-023-0788-9.F008 Fig. 8Force traction on curved contact surface.
10.1007/s40544-023-0788-9.F009 Fig. 9Contact state evolution with varying κ under different loading conditions (a) w/L =0.5, F/P = 0.4; (b) w/L = 0.5, F/P = 0.6.
10.1007/s40544-023-0788-9.F010 Fig. 10(a) Contact state evolution and (b) a corresponding energy dissipation E_cyc with respect to curvature (κ) (F/P = 0.4, w/L = 0.5).
10.1007/s40544-023-0788-9.F011 Fig. 11Energy dissipation for various values of $κ$ when $w / L = 0.5$ .
10.1007/s40544-023-0788-9.F012 Fig. 12Contour plot of correlation coefficient (R).
10.1007/s40544-023-0788-9.F013 Fig. 13Loading conditions making full-stick and slip-stick states at surfaces with the curvatures (a) κ = 0.00 (flat) and (b) κ = 0.02.
10.1007/s40544-023-0788-9.F014 Fig. 14Schematic of a motor bolted to the foundation.

Return

10.1007/s40544-023-0788-9.T001Table 1Material properties of FE model.

Material property	Value
Young’s modulus (Pa)	2×10¹¹
Poisson ratio	0.3
Friction coefficient	0.35

10.1007/s40544-023-0788-9.T002Table 2Pearson correlation coefficient value and indication [20].

Correlation coefficient value	Indication
$0.8 \leq R \leq 1.0$	High correlation
$0.6 \leq R \leq 0.8$	Moderately high correlation
$0.4 \leq R \leq 0.6$	Moderate correlation
$0.2 \leq R \leq 0.4$	Low correlation
$0.1 \leq R \leq 0.2$	Negligible correlation

About Us

Learn about Open Access

Tsinghua University Press

Publish with Us

Peer Review Policy

Copyright and Licensing

Article Processing Charge

Contact Us

Journal Collaboration: Yao Meng (Ms.)✉️ +86-10-83470574

Technical Support: Kuo Zhao (Mr.)✉️ +86-10-83470507

Media Contact: Hao Jin (Mr.)✉️ +86-10-83470559

Address: Floor 6, Tower B, Xueyan Building, Shuangqing Road, Haidian District, Beijing 100084, China.

SciOpen——中国科技期刊卓越行动计划支持项目

Copyright © 2025 Tsinghua University Press Ltd.

京ICP备 10035462号-42 京公网安备11010802044758号