Tribology Lecture IIElastohydrodynamic

Lubrication

Hydrodynamic Lubrication

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

w

Hydrodynamic Lubrication

Fluid Layer p

Pressure is generated by motion and geometry of the bearing in concert with the viscosity of the lubricant

w

Hydrodynamic LubricationPoint Contact

hc

R

288 2

25

UR

2W

2

Fluid Layer hc

U

R

Sphere

w

Hydrodynamic Lubrication(Refinement: Both surfaces moving)

hc

R

288 2

25

U R

W

2

Fluid Layer hc

U2

R

Sphere

U1

U 1

2U1 U2

“Entrainment”or

“Rolling Velocity” 2

0 21

UUU

w

Hydrodynamic Lubrication(Refinement: two spheres)

hc

R

288 2

25

U R

W

2

hc

R1

U1

1

R

1

R1

1

R2

Where R is now “reduced” radius

12 RRR

R2

U2

w

Hydrodynamic Lubrication

hc

R

288 2

25

U R

W

2

hc

R

288 2

25

U R

W

2

hc

R1

U1

R2

U2

Nice theory but as a rule itgreatly under estimates hc

•Pressure is very high near contact

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

Nice theory but as a rule itgreatly under estimates hc

•Pressure is very high near contact

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

w

Pressure and Temperature Dependence of Viscosity

Viscosity increases exponentially with pressure:

Barus Equation:

0eP

pressure viscosity coefficient

0 (cp)

SAE 10 266 2.51x10-8

SAE 30 105 3.19x10-8

larger larger hc for a given load

Large stresses lead to elastic deformation

R1

R2

Conformal Contact

Contact Circle (radius a)Contact Point

Point Contact

R1

R2

ww

Large stresses lead to elastic deformation

R1

R2

R1

R2

Conformal Contact

Contact Circle (radius a)Contact Point

Point Contact

w w

R1

R2

Elastic Deformation of Sphere

a3 3WR

4E*

2aR is the reduced radiusE* contact modulus

1

E* 1 1

2

E1

1 2

2

E2

w

E1

E2 E2

E1

E2

1

E* 1 1

2

E1

1 2

2

E2

E2>>E1

E* E1

1 12

E1>>E2

E* E2

1 22

E1

•Either way contact becomes conformal

Because of rise in viscosity with pressure deformation is about the same with the lubricating fluid present

E1

E2

hc

E2

E1E1

hc

•Surfaces are parallel at contact - i.e. “conformal”•Lower E* ( larger a for same load ) larger hc

E1

E2

hc

U2

U1

Elastohydrodynamic Lubrication (EHD L)

To variables for hydrodynamic lubrication

R, W , 0, U

add , E*

•How does hc depend on these parameters?

w

Hamrock & Dowson Equation

hc

RK E*

a 0U

E*R

b

W

E*R2

c

hc

RK E*

a 0U

E*R

b

W

E*R2

c

material speed load

Elastohydrodynamic Lubrication (EHD L)Dimensional Analysis

02

0.67 .0670.53*1.9 2* *2 2

ch U WE

R E R E R

0

2

0.67 .0670.53*1.9 2* *2 2

ch U WE

R E R E R

•Dependence on load is very weak 2.067=1.048

Hamrock & Dowson Equation (clarification from lab manual)

H* hP /R 1.90 U * 0.67W * 0.067

G * 0.53

where

U* uOIL

E R, W *

WE R2 , G* E , R Rb

u = rolling velocityOIL= zero pressure oil viscosity, = oil viscosity at higher pressure = pressure-viscosity index from the equation, = OILexp( P)

1E

1

2

1 d2

Ed

1 b

2

Eb

Note factor of 2

*2E E

Tribology Lab

•Measure hc as a function of U and W•Compare result with Hamrock Dowsen equation

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:

ME 4053

Nd Glass plate (connected to motor)

Steel ball

LightSource

MonitorCamera

LoadingMechanism

Light Source:

Contact Area

FiberopticCable

Camera

aperture

condenser

Semi-reflectiveSurface

Experimental Setup (cont’d)

rc

Nd

top view: side view:

W(load)

Fringe pattern

Camera

LightBeam

h

oilfilm

glassdisc u

Nd: rpm; u: rolling velocity; h: film thickness

Rolling velocity:60

2 dc Nru

Measured oil film thickness: )(2

N

nh , where:

: wavelength of light in air (600nm) N: fringe order

n: refractive index of oil (1.5) : phase shift constant (0.1)

fringes)(dark 0.5,1.5,

)fringesbright(,3,2,1

Experimental Procedure: obtain the following table for W=16N & W=30N

Fringe N Nd (rpm) Nd (rpm) u (m/s) h (nm) ht (nm)fringe order trial 1 trial2 velocity experimental theoretical

Dark 0.5 2 2 80Bright 1 180Dark 1.5 280Bright 2 380Dark 2.5 480Bright 3 580Dark 3.5 680Bright 4 780

measured computed from Nd, N computed fromHD equation

Theoretical Thickness, ht: The Hamrock & Dowson Equation

])()()(9.1[ 53.0*067.0*67.0* GWURht

R: ball radius W*: dimensionless load parameterU*: dimensionless speed parameter G*: dimensionless material parameter

-12.5

-12.0

-11.5

-11.0

-10.5

-10.0

-9.5

-27.0 -26.5 -26.0 -25.5 -25.0 -24.5 -24.0 -23.5 -23.0 -22.5

ln(U*)

ln(h

/R)

data model upper lim lower lim prediction

Results Presentation:

*Practical note on load adjustment:

Load = 2 x (spring value - tare value)

Ex: to get W=16N, set spring value to 11.2N16 = 2 x (11.2 - 3.2)

(tare = 3.2N)

Theoretical/Experimental Comparison:

ln(h

/R)

ln(U*)