Tribology Lecture I

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# Tribology Lecture I - PowerPoint PPT Presentation

Tribology Lecture I. Tribology. From:  = rubbing. Friction Wear Lubrication. Tribology deals with all aspects of . interacting surfaces in relative motion. - bearings. Friction. Loss of energy due to rubbing. Energy is converted to heat

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## Tribology Lecture I

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Presentation Transcript

### TribologyLecture I

Tribology

From:  = rubbing
• Friction
• Wear
• Lubrication

Tribology deals with all aspects of

interacting surfaces in relative motion

- bearings

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

Origin of Friction

• Surface Roughness
• Solid to solid contact
• Deformation

Lubrication

Replace Solid to solid contact

Fluid Layer

with a fluid layer - i.e. a lubricant

Lubrication

Solid rubbing replaced by

Fluid Layer

viscous shearing

To be useful must support some load

W

Fluid Layer

p

Need pressure in the fluid to support the load

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

z

h

h0

p

t

Infinitesimal element

U

p

x

0

B

Force balance

Viscosity equation

Combine:

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

1-D Reynolds Equation

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 hoin terms of U, , Wn

U

Example Exponential h

B

wn

z

h(x)

ho

x

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

U

P(x)

2-D Reynolds Equation

w

Sphere

R

z

Fluid Layer

hc

x

For sphere

Exact solution

U

Hydrodynamic LubricationPoint Contact

W

Sphere

R

Fluid Layer

hc

Hydrodynamic Lubrication(Refinement: Both surfaces moving)

W

Sphere

R

U1

Fluid Layer

hc

U2

“Entrainment”

or

“Rolling Velocity”

Hydrodynamic Lubrication(Refinement: two spheres)

W

R1

U1

hc

U2

Where R is now

R2

1

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 >>1000atm ( 108 Pa)
• Pressure Dependence of 
• Elastic Deformation of Sphere

R2

Hydrodynamic Lubrication

Elasto-Hydrodynamic Lubrication