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Damping characteristics of thermal elastohydrodynamic lubricated point contacts

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Abstract

The present work envisaged the development of a novel method for computing the damping coefficients of thermal elastohydrodynamic lubricated point contacts based on energy conservation. The effects of load, entrainment velocity, and slide–roll ratio were studied, and the results were compared with the ISO thermal results. Multi-level method and discrete convolution fast Fourier transform method were employed to improve the solution convergence efficiency, and a sequential column sweeping technique was employed to solve the energy equations. The results indicated an increase in the damping coefficients with an increase in the load, and a corresponding decrease with an increase in the speed. When the entrainment velocity was relatively low, or the slide–roll ratio was relatively small, the influence of the slide–roll ratio was negligible. Subsequently, the relation between the damping coefficients and the load, speed, and slide–roll ratio was established using the least-square method.

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Abbreviations

α :

Pressure–viscosity coefficient (Pa−1)

β :

Temperature–viscosity coefficient (K−1)

kf :

Lubricant thermal conductivity (W/mK)

k a,b :

Solid thermal conductivities (W/mK)

c f :

Lubricant specific heat (J/kgK)

c a,b :

Solid specific heat (J/kgK)

D :

Kernel elastic deformation

T :

Temperature (K)

T 0 :

Ambient temperature, 313 (K)

η :

Viscosity of lubricant (Pa·s)

η 0 :

Ambient viscosity of lubricant (Pa·s)

ρ :

Density of lubricant (kg/m3)

ρ 0 :

Ambient density of lubricant (kg/m3)

ρ a,b :

Densities of solids ‘a’ and ‘b’ (kg/m3)

b H :

Half-width of Hertzian contact zone (m)

p :

Oil film pressure (Pa)

p h :

Maximum Hertzian contact pressure (Pa)

F 2 :

Elliptical integral of second kind

E′:

Equivalent Young’s modulus (Pa)

k e :

Elliptical ratio

d :

Damping coefficient (N·s/m)

H c :

Center film thickness (m)

f :

Applied load (N)

W 0 :

Dimensionless load, f/E′Rx2

u,v :

Film velocities (m/s)

u a,b :

Velocities of surfaces ‘a’ and ‘b’ (m/s)

u e :

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

s :

Slide-roll ratio, (ua−ub)/ue

u :

Entrainment velocity (m/s)

U 0 :

Dimensionless velocity, uη0/E′Rx

G 0 :

Material parameter, αE’′

h :

Film thickness (m)

δ :

Mutual approach (m)

Δ:

Dimensionless mutual approach

R x :

Ellipsoid radius in x-direction (m)

R y :

Ellipsoid radius in y-direction (m)

R :

Equivalent radius, 1/R = 1/Rx + 1/Ry

x,y :

Coordinates (m)

X,Y :

Dimensionless coordinates

z :

Coordinate across the film (m)

Z :

Dimensionless coordinate across the film

z a,b :

Coordinates in solids ‘a’ and ‘b’ (m)

Z a,b :

Dimensionless coordinates in solids

t :

Time (s)

ω:

Excitation frequency (rad/s)

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Acknowledgments

This work was supported financially by the Natural Science Basic Research Plan in Shaanxi Province of China (Program No. 2019JM535).

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Authors and Affiliations

  1. School of Mechanical Engineering, Xi′an Aeronautical University, Xi’an, 710077, People’s Republic of China

    Guihua Dong

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  1. Guihua Dong
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Correspondence to Guihua Dong.

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Technical Editor: Wallace Moreira Bessa, D.Sc..

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Dong, G. Damping characteristics of thermal elastohydrodynamic lubricated point contacts. J Braz. Soc. Mech. Sci. Eng. 43, 137 (2021). https://doi.org/10.1007/s40430-021-02842-8

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