tribology lecture ii elastohydrodynamic lubrication
TRANSCRIPT
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Tribology Lecture IIElastohydrodynamic
Lubrication
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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
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Hydrodynamic Lubrication
Fluid Layer p
Pressure is generated by motion and geometry of the bearing in concert with the viscosity of the lubricant
w
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Hydrodynamic LubricationPoint Contact
hc
R
288 2
25
UR
2W
2
Fluid Layer hc
U
R
Sphere
w
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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
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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
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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
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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
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Large stresses lead to elastic deformation
R1
R2
Conformal Contact
Contact Circle (radius a)Contact Point
Point Contact
R1
R2
ww
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Large stresses lead to elastic deformation
R1
R2
R1
R2
Conformal Contact
Contact Circle (radius a)Contact Point
Point Contact
w w
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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
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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
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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
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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
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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
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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
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Tribology Lab
•Measure hc as a function of U and W•Compare result with Hamrock Dowsen equation
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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
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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
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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
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-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*)