Title: Tribology Lecture I
1TribologyLecture I
2From ?????? rubbing
Tribology
Tribology deals with all aspects of
interacting surfaces in relative motion
- Friction
- Wear
- Lubrication
- bearings
3Friction
- Loss of energy due to rubbing. Energy is
converted to heat - Extra energy and force required to overcome
friction - Causes wear and failure
4Friction Amontons Law
W
Ffriction
A
V
5Origin of Friction
- Surface Roughness
- Solid to solid contact
- Adhesion
- Deformation
6Lubrication
Replace Solid to solid contact
Fluid Layer
with a fluid layer - i.e. a lubricant
7Lubrication
Solid rubbing replaced by
Fluid Layer
viscous shearing
8To be useful must support some load
W
Fluid Layer
9To be useful must support some load
W
10To be useful must support some load
W
Fluid Layer
p
Need pressure in the fluid to support the load
11Hydrodynamic Lubrication
W
Fluid Layer
p
Pressure is generated by motion and geometry of
the the bearing in concert with the viscosity of
the lubricant
121-D Reynolds Equation
W
z
h(x)
ho
x
U
13z
h
h0
p
t
Infinitesimal element
U
p
x
B
0
14Force balance
Viscosity equation
Combine
15Integrate wrt z
Apply BCs
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
161-D Reynolds Equation
wn
z
h(x)
ho
x
U
Reynolds Equation
- Integrate over x to get p(x)
- Integrate over x again to get Wn
- Result gives ho in terms of U, ?, Wn
17Example Exponential h
B
wn
z
h(x)
ho
x
integrate wrt x apply BCs p 0 at x 0 and
at x -B
solve for p(x), integrate to get Wn/L, then solve
for h0
182-D Reynolds Equation
w
Sphere
R
z
Fluid Layer
hc
x
For sphere
Exact solution
19Hydrodynamic LubricationPoint Contact
W
Sphere
R
Fluid Layer
hc
20Hydrodynamic Lubrication(Refinement Both
surfaces moving)
W
Sphere
R
U1
Fluid Layer
hc
U2
Entrainment or Rolling Velocity
21Hydrodynamic Lubrication(Refinement two spheres)
W
R1
U1
hc
U2
Where R is now reduced radius
R2
1
22Hydrodynamic Lubrication
W
R1
U1
Nice theory but as a rule it greatly under
estimates hc
hc
U2
- Pressure is very high near contact
- P gtgt1000atm ( 108 Pa)
- Pressure Dependence of ?
- Elastic Deformation of Sphere
R2
23Hydrodynamic Lubrication
Elasto-Hydrodynamic Lubrication