Tribology Lecture I

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TribologyLecture I
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From ?????? rubbing
Tribology
Tribology deals with all aspects of
interacting surfaces in relative motion

• Friction
• Wear
• Lubrication

- bearings
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Friction

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

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Friction Amontons Law
W
Ffriction
A
V
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Origin of Friction

• Surface Roughness
• Solid to solid contact
• Adhesion
• Deformation

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Lubrication
Replace Solid to solid contact
Fluid Layer
with a fluid layer - i.e. a lubricant
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Lubrication
Solid rubbing replaced by
Fluid Layer
viscous shearing
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To be useful must support some load
W
Fluid Layer
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To be useful must support some load
W
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To be useful must support some load
W
Fluid Layer
p
Need pressure in the fluid to support the load
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Hydrodynamic Lubrication
W
Fluid Layer
p
Pressure is generated by motion and geometry of
the the bearing in concert with the viscosity of
the lubricant
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1-D Reynolds Equation
W
z
h(x)
ho
x
U
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z
h
h0
p
t
Infinitesimal element
U
p
x
B
0
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Force balance
Viscosity equation
Combine
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Integrate 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
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1-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

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Example 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
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2-D Reynolds Equation
w
Sphere
R
z
Fluid Layer
hc
x
For sphere
Exact solution
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Hydrodynamic LubricationPoint Contact
W
Sphere
R
Fluid Layer
hc
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Hydrodynamic Lubrication(Refinement Both
surfaces moving)
W
Sphere
R
U1
Fluid Layer
hc
U2
Entrainment or Rolling Velocity
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Hydrodynamic Lubrication(Refinement two spheres)
W
R1
U1
hc
U2
Where R is now reduced radius
R2
1
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Hydrodynamic 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
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Hydrodynamic Lubrication
Elasto-Hydrodynamic Lubrication