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Tribology Letters

, 67:33 | Cite as

Deformation of Rough Surfaces in Point EHL Contacts

  • Ivan Krupka
  • Martin Hartl
  • Kenji Matsuda
  • Hiroshi Nishikawa
  • Jing Wang
  • Feng Guo
  • Peiran Yang
  • Motohiro KanetaEmail author
Methods
  • 71 Downloads

Abstract

The film thickness profile obtained by the optical interferometry technique merely represents a separation between contact surfaces and does not give the surface shape of contact surfaces. It has been pointed out that the actual shape of the surface roughness in rolling and/or sliding EHL contacts must be evaluated by separately obtaining the surface shape of contact bodies. The degree of the amplitude reduction in actual roughness depends on the mechanical properties of both contacting surfaces. That is, the deformation of roughness and the pressure at which roughness locates are controlled by the interrelationship between the rough surface and the mating surface caused by rolling and/or sliding motion. The method of finding surface profiles of both bodies separately and also the pressure distribution from the interferogram obtained by the optical interferometry technique is proposed in “Appendix”.

Keywords

Surface roughness Deformation Optical interferometry Elastohydrodynamics 

List of symbols

a

Radius of Hertzian contact circle, (m)

Aa,b

Height of ridge or depth of groove on surfaces a and b, (m)

Ba,b

Base half-width of ridge or groove on surfaces a and b, (m)

Ea, Eb

Elastic moduli of solids, (Pa)

Eʹ

Equivalent elastic modulus, (Pa)  =  2{(1 − νa2)/Εa + (1 − νb2)/Εb }−1

G

Material parameter, (–) G = α E

h

Film thickness s, (m)

ha, hb

Surface shapes of bodies a and b, (m)

h00

Rigid film thickness s, (m)

hini

Initial central impact gap, (m)

H

Dimensionless film thickness, (–) H = h/R

ISA, ISB

Original shapes of bodies a and b, (m)

La,b

Wavelength of ridge or groove on surfaces a and b, (m)

m

Mass of moving body, (kg)

N

Number of time step, (–)

p

Film pressure, (Pa)

pH

Maximum Hertzian pressure, (Pa)

P

Dimensionless film pressure, (–) P = p/pH

R

Reduced radius of contact bodies, [m] R = \({R_{\text{a}}}{R_{\text{b}}}/({R_{\text{a}}}+{R_{\text{b}}})\)

Ra, Rb

Radii of contact bodies, (m)

t

Time, (s)

t0

Time required to wmax, (s)

T

Temperature, (K)

T0

Ambient temperature, (K)

u, v

Flow velocities in x and y directions, (m/s)

ua, ub

Surface velocities of solids in x-direction, (m/s)

ue

Entrainment velocity, (m/s) ue = (ua + ub)/2

U

Velocity parameter, (–) U = ue/(ER)

wA

Applied load, (N)

wmax

Maximum load, (N)

W

Load parameter, (–) W = wA/(ER2)

x, y

Coordinates, (m)

xin, xout

Domain boundaries in x-direction, (m)

X

Dimensionless coordinate, (–) X = x/a

Y

Dimensionless coordinate, (–) Y = y/a

yin, yout

Domain boundaries in y-direction, (m)

α

Viscosity-pressure coefficient, (Pa−1)

β

Viscosity-temperature coefficient, (K−1)

δa, δb

Roughness on surfaces, (m)

Δ

Total elastic deformation, (m)

νa, νb

Poisson’s ratios of solids, (–)

η

Viscosity of lubricant, (Pa s)

η0

Ambient viscosity of lubricant, (Pa s)

ρ

Density of lubricant, (kg/m3)

ρ0

Ambient density of lubricant, (kg/m3)

τx, τy

Shear stresses along x- and y-directions, (Pa)

τ0

Eyring stress, (Pa)

Notes

Acknowledgements

The authors would like to express their thanks to the financial support from Czech Science Foundation 15-24091S.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • Ivan Krupka
    • 1
  • Martin Hartl
    • 1
  • Kenji Matsuda
    • 2
  • Hiroshi Nishikawa
    • 2
  • Jing Wang
    • 3
  • Feng Guo
    • 3
  • Peiran Yang
    • 3
  • Motohiro Kaneta
    • 2
    Email author
  1. 1.Faculty of Mechanical EngineeringBrno University of TechnologyBrnoCzech Republic
  2. 2.School of EngineeringKyushu Institute of TechnologyKitakyushuJapan
  3. 3.School of Mechanical and Automotive EngineeringQingdao University of TechnologyQingdaoPeople’s Republic of China

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