Hydrodynamic lubrication By Khairul Bashar

Lubrication Engineering

1. Presented By : BASHAR MD KHAIRUL Student ID: 15595901 Masters Student Graduate School of Science & Engineering Saga University 1 Advanced Lubrication Engineering Hydrodynamic lubrication (Friday J anuary 22, 2016 @ multipurpose lecture room)

2. Hydrodynamic lubrication Hydrodynamic lubrication implies there is a (comparatively) thick film of fluid between the moving surfaces, so no contact occurs between the surfaces. It requires that there be sufficient speed differential between the surfaces, which causes the formation of the "oil wedge“. There has to be pressure buildup in the film due to relative motion of the surfaces. Fluid friction is substituted for sliding friction. Hydrodynamic lubrication doesn't need an oil pump or pressurized lubricant source to happen, but will be reached if a shaft spins fast enough in a bearing supplied with sufficient lubricant flow. Prevalent in journal and thrust bearings. Shaft/Journal Oil wedge Bearing + W Bearing center + Shaft center 2

3. 7.2.2. Reynolds’ equation There is a relationship between the build-up of pressure, the sliding speed , the operational viscosity and the geometry of the hydrodynamic film. Considering a simple Taper geometry of the type shown in fig. (a). Oil wedge W h i h o U L h u Fig. (a) u u Fig. (b) U s distribution Fig: The velocity and pressure distribution in an inclined pad bearing . 3

4. Fig. c X=0 X=X m X=L dp /dx is + ve dp /dx is - ve dp /dx=0 Pressure distribution U p is + ve U p is + ve U p is 0 U p distribution Fig. d u h m u u Fig. e Velocity distribution u=us+ up Fig: The velocity and pressure distribution in an inclined pad bearing . 4

5. The fluid that is in contact with the moving surface moves with the moving surface with the velocity U surface . The film to a continuous shearing so that the velocity Us of the film at any value of Y is given by u s = U   The form of u s is shown in fig b; u s is +U at y=0 and zero at y=h. This is known as Couette flow. With converging walls the relationship between the fluid flow and the pressure build-up ( Poiseuille flow) is , u p = ( ) y(h-y)   7.1 The values of dp /dx vary with x , and assume that this variation is as shown in figure c . The form of u p is according to fig. d and u p is zero at y=0 and y=h . At the entry section dp /dx will be positive, near the center it will be zero , and after this point it will be negative . This gives rise to the patterns of up shown in fig. d. The pressure gradient and the shear flow are the only two causes of fluid flow , the resultant velocity of the fluid follows the patterns shown in fig. e is given by u = u s + u p = U + ( ) y(h-y)   7.1 7.2 7.3 5

6. Neglecting any side flow , the area of an element of film is 1×dy per unit width of the film. The quantity flowing per unit time is thus u dy for each element area and the total flow q is given by q= Substituting for u from equation (7.3) and integrating = =   . 7.4 At some point the pressure is maximum and =0 ; let the value of h at this point be h m (maximum) whence , = =0 [As some point the pressure is maximum; =0] = h( ) [ note : let the value of h at this point be h m ] q m = h m ( )   . 7.5 . 6 . So,

7. But the flow through the film must be the same at all values of h so that, q m = q and thus , = = h m ( ) So , = h m ( ) = = - = ( ) ( )   7.4 7.5 7.6 7.7 7

8. ど うもありがとうございま す . Thank you very much. 8