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Non-classical Elastohydrodynamic Lubricating Film Shape Under Large Slide-roll Ratios

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The authors showed in previous experiments with high viscosity polymeric lubricants that a non-classical elastohydrodynamic (EHL) film, which featured an inlet dimple, could be generated under pure sliding conditions. The phenomenon was tentatively attributed to boundary slippage. In this paper, much greater sliding is introduced in the experiments to gain further insight into film formation under boundary slippage. By putting all of the results on a load versus entrainment speed chart, it is found that the required conditions for the formation of the inlet dimple fall into an open triangular region in the chart. The existence of the inlet dimple can be maintained for a larger speed range with a higher load. The minimum speed required (the lower speed bound for the dimple existence) decreases only marginally with an increase in load but the speed of the disappearance of the dimple (the upper speed bound) increases with an increasing load. Interferograms show that with an increase in the slide-roll ratio, i.e., expanded boundary slippage, a bump occurs before the exit constriction, which indicates an obvious drop in film thickness, and the location of the minimum film thickness in the whole EHL contact moves from the outlet constriction to the center of the bump. The observed inlet dimple and bump have already been described in the previous numerical results that consider boundary slippage, and provide more justification for the boundary slippage postulation in the experimental films.

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b :

Radius of the Hertzian contact, m


Reduced elastic modulus, Pa

G :

Dimensionless material parameter, G = α E

H :

Dimensionless film thickness, H = h/R

H cen :

Dimensionless central film thickness, H cen = h cen/R

H min :

Dimensionless minimum film thickness, H min = h min/R

h :

Film thickness, m

h cen, h min :

The central and minimum film thickness, m

p H :

The maximum Hertzian pressure, Pa

S :

Slide-roll ratio, \( S = {{\left( {u_{\hbox{d}} - u_{\hbox{b}} } \right)} \mathord{\left/ {\vphantom {{\left( {u_{\hbox{d}} - u_{\hbox{b}} } \right)} {u_{\hbox{e}} }}} \right. \kern-\nulldelimiterspace} {u_{\hbox{e}} }} \)

U e :

Dimensionless entrainment speed, \( U_{\hbox{e}} = {{u_{\hbox{e}} \eta _0 } \mathord{\left/ {\vphantom {{u_{\hbox{e}} \eta _0 } {\left( {E'R} \right)}}} \right. \kern-\nulldelimiterspace} {\left( {E'R} \right)}} \)

u d, u b :

Speed of the surfaces of the disc and the ball, m/s

u e :

Entrainment speed, \( u_{\hbox{e}} = {{\left( {u_{\hbox{d}} + u_{\hbox{b}} } \right)} \mathord{\left/ {\vphantom {{\left( {u_{\hbox{d}} + u_{\hbox{b}} } \right)} 2}} \right. \kern-\nulldelimiterspace} 2} \), m/s

W :

Dimensionless load, \( W = {w \mathord{\left/ {\vphantom {w {\left( {E'R^2 } \right)}}} \right. \kern-\nulldelimiterspace} {\left( {E'R^2 } \right)}} \)

w :

Load, N

X :

Dimensionless coordinate along the central entrainment direction, X = x/b

Y :

Dimensionless coordinate cross the central entrainment direction, Y = y/b

x :

Coordinate along the central entrainment direction, m


Pressure-viscosity coefficient, Pa−1

η0 :

Ambient viscosity of the lubricant, Pa s


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The work described in this paper was supported by the Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. CityU 121405) and the National Natural Science Foundation of China (Project No. 50475165 -05-2-P-4).

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Correspondence to F. Guo.

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Fu, Z., Guo, F. & Wong, P.L. Non-classical Elastohydrodynamic Lubricating Film Shape Under Large Slide-roll Ratios. Tribol Lett 27, 211–219 (2007). https://doi.org/10.1007/s11249-007-9227-8

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  • EHL
  • Non-Newtonian behavior
  • Boundary slippage
  • Interferometry