Tribology Letters

, Volume 50, Issue 3, pp 349–364 | Cite as

Balancing Wedge Action: A Contribution of Textured Surface to Hydrodynamic Pressure Generation

  • Kazuyuki Yagi
  • Joichi Sugimura
Original Paper


This paper suggests a new mechanism called ‘balancing wedge action’, which is based on the hydrodynamic lubrication theory for textured surfaces. While past studies have considered the local wedge film action produced by textured feature, this new mechanism is based on the promotion of a wedge film action between surfaces by the incorporation of a textured feature. The analytical model used in the current study is a one-dimensional centrally pivoted pad bearing having a single dimple on the pad, which considers the equilibrium of the moment applied to the surfaces. Analytical equations are derived for the pressure, shear stress, load, friction, and moment by integrating the Reynolds equation. A series of parametric simulations of the depth, width, and location of a dimple were conducted. The analytical results showed that the incorporation of a single dimple on the pad surface increases the convergence ratio between the surfaces, producing a load capacity and reducing the friction. No negative pressure can be found within the dimple, where a positive pressure with a greater positive gradient causes a higher shear stress than that outside the dimple. The trends for the load and friction in relation to the dimple depth and location are complex. The creation of the dimple closer to the centre results in a failure to obtain an equilibrium solution for the moment.


Hydrodynamic lubrication Texture Moment Balance 



Dimensionless friction, F = fh 0/(ηlu)


Dimensionless film thickness, H = h/h 0


Dimensionless film thickness at inlet, H 1 = h 1/h 0


Dimensionless film thickness at left side of dimple, H 2 = h 2/h 0


Dimensionless film thickness at left side of dimple, H 2d = h 2d/h 0


Dimensionless film thickness at right side of dimple, H 3 = h 3/h 0


Dimensionless film thickness at right side of dimple, H 3d = h 3d/h 0


Dimensionless dimple depth, H d = h d/h 0


Convergence ratio, K = (h 1h 0)/h 0


Dimensionless position at left side of dimple, L 2 = l 2/l


Dimensionless position at right side of dimple, L 3 = l 3/l


Dimensionless position of pivot, L pv = l pv/l


Dimensionless moment, M = h 0 2 m/(6ηl 3 u)


Dimensionless pressure, P = h 0 2 p/(6ηlu)


Dimensionless minimum pressure


Dimensionless mass flow rate, Q = q/(h 0 u)


Dimensionless Couette flow rate, Q c = q c/(h 0 u)


Dimensionless Poiseuille flow rate, Q p = q p/(h 0 u)


Dimensionless shear stress, S = −h 0 s/(ηu)


Dimensionless shear stress by Couette flow, S c = 1/H


Dimensionless shear stress by Poiseuille flow, S p = H/2(dP/dX)


Dimensionless coordinate in direction of surface motion, X = x/l


Dimensionless load, W = h 0 2 w/(6ηl 2 u)


Friction (N/m)


Film thickness (m)


Film thickness at inlet (m)


Film thickness at left side of dimple (m)


Film thickness at left side of dimple (m), h 2d = h 2 + h d


Film thickness at right side of dimple (m)


Film thickness at right side of dimple (m), h 3d = h 3 + h d


Minimum film thickness (m)


Dimple depth (m)


Width of pad (m)


Position at left side of dimple (m)


Position at right side of dimple (m)


Position of pivot (m)


Maximum number of series terms


Pressure of fluid film (Pa)


Mass flow rate, q = q c + q p (m3/(ms))


Couette mass flow rate (m3/(ms))


Poiseuille mass flow rate (m3/(ms))


Shear stress (N/m)


Sliding speed of moving surface (m)


Coordinate in direction of surface motion (m)


Load (N/m)


Viscosity (Pas)


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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Department of Mechanical Engineering, Faculty of EngineeringKyushu UniversityFukuokaJapan

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