1. Tribology Lecture II Elastohydrodynamic Lubrication

2. Hydrodynamic Lubricationw
Fluid Layer p
Pressure required to support the load is generated by motion and geometry of the bearing in concert with the viscosity of the lubricant

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

4. Hydrodynamic Lubrication Point Contactw
Sphere R
Fluid Layer hc U

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

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

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

8. Pressure and Temperature Dependence of Viscosity
Viscosity increases exponentially with pressure:
Barus Equation:
 pressure viscosity coefficient
0 (cp) 
SAE x10-8
SAE x10-8

9. Large stresses lead to elastic deformationw w R1 R1 R2 R2
Contact Circle (radius a)
Contact Point
Point Contact
Conformal Contact

10. Large stresses lead to elastic deformationw w R1 R1 R2 R2
Contact Circle (radius a)
Contact Point
Point Contact
Conformal Contact

11. w Elastic Deformation of Sphere 2a R1 R is the reduced radius
E* contact modulus 2a R2

12. Either way contact becomes conformal
E2>>E1
E1>>E2
Either way contact becomes conformal

13. Surfaces are parallel at contact - i.e. “conformal”
Because of rise in viscosity with pressure deformation is about the same with the lubricating fluid present E2 E1 hc E1 hc E2
Surfaces are parallel at contact - i.e. “conformal”
Lower E* ( larger a for same load )  larger hc

14. w Elastohydrodynamic Lubrication (EHD L)
To variables for hydrodynamic lubrication E1 U1
add hc E2 U2
How does hc depend on these parameters?

15. Elastohydrodynamic Lubrication (EHD L) Dimensional Analysis
speed
load
material
Hamrock & Dowson Equation
Dependence on load is very weak =1.048

16. Hamrock & Dowson Equation (clarification from lab manual)
where
u = rolling velocity
OIL= zero pressure oil viscosity,  = oil viscosity at higher pressure
 = pressure-viscosity index from the equation,  = OILexp( P)
Note factor of 2

17. Tribology Lab Measure hc as a function of U and W
Compare result with Hamrock Dowsen equation

18. ME 4053
Tribology Lab
Objectives: Characterize elastohydrodynamic (EHD) lubrication using an optical technique. The study involves:
Measurement of the lubricating film thickness as a function of:
rolling velocity
normal load
Comparison of the measured film thickness with a theoretical film thickness (from the Hamrock & Dawson equation)
Experimental Setup:
Light Source:
Camera
Monitor
Camera
Light
Source
aperture
Loading
Mechanism
Semi-
reflective
Surface Nd
Glass plate (connected to motor)
Steel ball
Fiberoptic
Cable
condenser
Contact Area

19. Experimental Setup (cont’d)
Camera
top view:
side view:
Light
Beam Nd
glass
disc u
oil
film rc
Fringe pattern h
W(load)
Nd: rpm; u: rolling velocity; h: film thickness
Rolling velocity:
Measured oil film thickness:
, where:
: wavelength of light in air (600nm) N: fringe order
n: refractive index of oil (1.5) : phase shift constant (0.1)

20. Theoretical Thickness, ht: The Hamrock & Dowson Equation
Experimental Procedure: obtain the following table for W=16N & W=30N
measured
computed from Nd, N
computed from
HD equation
Theoretical Thickness, ht: The Hamrock & Dowson Equation
R: ball radius W*: dimensionless load parameter
U*: dimensionless speed parameter G*: dimensionless material parameter

21. Results Presentation:
Theoretical/Experimental Comparison:
ln(h/R)
ln(U*)
*Practical note on load adjustment:
Load = 2 x (spring value - tare value)
(tare = 3.2N)
Ex: to get W=16N, set spring value to 11.2N
16 = 2 x ( )