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Tribology Lecture I

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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  1. TribologyLecture I

  2. Tribology From:  = rubbing • Friction • Wear • Lubrication Tribology deals with all aspects of interacting surfaces in relative motion - bearings

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

  4. Friction: Amonton’s Law W Ffriction A V

  5. Origin of Friction • Surface Roughness • Solid to solid contact • Adhesion • Deformation

  6. Lubrication Replace Solid to solid contact Fluid Layer with a fluid layer - i.e. a lubricant

  7. Lubrication Solid rubbing replaced by Fluid Layer viscous shearing

  8. To be useful must support some load W Fluid Layer

  9. To be useful must support some load W

  10. To be useful must support some load W Fluid Layer p Need pressure in the fluid to support the load

  11. 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

  12. 1-D Reynolds Equation W z h(x) ho x U

  13. z h h0 p t Infinitesimal element U p x 0 B

  14. Force balance Viscosity equation Combine:

  15. 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

  16. 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

  17. 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

  18. U P(x) 2-D Reynolds Equation w Sphere R z Fluid Layer hc x For sphere Exact solution

  19. U Hydrodynamic LubricationPoint Contact W Sphere R Fluid Layer hc

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

  21. Hydrodynamic Lubrication(Refinement: two spheres) W R1 U1 hc U2 Where R is now “reduced” radius R2 1

  22. 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

  23. Hydrodynamic Lubrication Elasto-Hydrodynamic Lubrication

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