1. Tribology Lecture I

2. Tribology From:  = rubbing Tribology deals with all aspects of
interacting surfaces in relative motion
Friction
Wear
Lubrication
- bearings

3. Friction Loss of energy due to rubbing. Energy is converted to heat
Extra energy and force required to overcome friction
Causes wear and failure

4. Friction: Amonton’s Law
Ffriction V

5. Origin of Friction Surface Roughness Solid to solid contact Adhesion
Deformation

6. Lubrication Replace Solid to solid contact
Fluid Layer
with a fluid layer - i.e. a lubricant

7. Lubrication
Solid rubbing replaced by
Fluid Layer
viscous shearing

8. To be useful must support some loadW
Fluid Layer

9. To be useful must support some loadW

10. To be useful must support some loadW
Fluid Layer p
Need pressure in the fluid to support the load

11. Hydrodynamic LubricationW
Fluid Layer p
Pressure is generated by motion and geometry of the the bearing in concert with the viscosity of the lubricant

12. 1-D Reynolds Equation W z
h(x) ho x U

13. z h h0 p t
Infinitesimal element U p x B

14. Force balance
Viscosity equation
Combine:

15. Integrate wrt z
Apply BC’s:
No-slip: ux = U at z = 0, ux = 0 at z = h
yields
Volumetric flow rate (per unit width)
Incompressible flow, q = const. Evaluate at dp/dx = 0:
Solve for dp/dx

16. 1-D Reynolds Equation Integrate over x to get p(x)wn z
h(x) ho x U
Reynold’s Equation
Integrate over x to get p(x)
Integrate over x again to get Wn
Result gives ho in terms of U, , Wn

17. Example Exponential h B wn z h(x) ho x U integrate wrt x; apply BC’s
p = 0 at x = 0 and at x = -B
solve for p(x), integrate to get
Wn/L, then solve for h0

18. 2-D Reynolds Equation w Sphere R z Fluid Layer x U For sphere P(x)hc
P(x) x U
For sphere
Exact solution

19. Hydrodynamic Lubrication Point ContactW
Sphere R
Fluid Layer hc U

20. Hydrodynamic Lubrication (Refinement: Both surfaces moving)W
Sphere R U1
Fluid Layer hc U2
“Entrainment” or
“Rolling Velocity”

21. Hydrodynamic Lubrication (Refinement: two spheres)hc U2
Where R is now
“reduced” radius R2 1

22. Hydrodynamic LubricationW R1 U1
Nice theory but as a rule it
greatly under estimates hc hc U2
Pressure is very high near contact
P >>1000atm ( 108 Pa)
Pressure Dependence of 
Elastic Deformation of Sphere R2

23. Hydrodynamic Lubrication Elasto-Hydrodynamic Lubrication