Tribology Lecture II Elastohydrodynamic Lubrication

Hydrodynamic Lubrication w 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

Hydrodynamic Lubrication w Fluid Layer p Pressure is generated by motion and geometry of the bearing in concert with the viscosity of the lubricant

Hydrodynamic Lubrication Point Contact w Sphere R Fluid Layer hc U

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

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

Hydrodynamic Lubrication w 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

Pressure and Temperature Dependence of Viscosity Viscosity increases exponentially with pressure: Barus Equation:  pressure viscosity coefficient 0 (cp)  SAE 10 266 2.51x10-8 SAE 30 105 3.19x10-8

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

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

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

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

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

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

Elastohydrodynamic Lubrication (EHD L) Dimensional Analysis speed load material Hamrock & Dowson Equation Dependence on load is very weak 2.067=1.048

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

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

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

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)

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

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 (11.2 - 3.2)