CHAPTER 8 DYNAMIC ANALYSIS OF …

1 CHAPTER 8 DYNAMIC ANALYSIS OF hydrodynamic BEARING In this CHAPTER the analyses of the hydrodynamic bearings such as plane slider bearing and journal bearing are discussed. Briefly different types of lubrications are described and the mechanism of pressure development in the oil film is studied. The Petroff s equation for a lightly loaded journal bearing is derived. The derivation of Reynold s equation is carried out and it is applied to idealized plane slider bearing with fixed and pivoted shoe and journal bearings.

2 lubrication lubrication is the science of reducing friction by application of a suitable substance called lubricant, between the rubbing surfaces of bodies having relative motion. The main motive of using a lubricant is to reduce friction, to reduce or prevent wear and tear, to carry away heat generated in friction and to protect against corrosion. The basic modes of lubrication are thick and thin film lubrication . Thick Film lubrication : Thick film lubrication describes a condition of lubrication , where two surfaces of bearing in relative motion are completely separated by a film of fluid.

3 Since there is no contact between the surfaces, the properties of surface have little or no influence on the performance of the bearing. The resistance to the relative motion arises from the viscous resistance of the fluid. Therefore, the performance of the bearing is only affected by the viscosity of the lubricant. Thick film lubrication is further divided into two groups: hydrodynamic and hydrostatic lubrication . hydrodynamic Bearing: hydrodynamic lubrication is defined as a system of lubrication in which the supporting fluid film is created by the shape and relative motion of the sliding surfaces.

4 The principal of hydrodynamic bearing is shown in Initially the shaft is at rest (a) and it sinks to the bottom of the clearance space under the action of load W. As the journal starts to rotate, it will climb the bearing surface (b) and as the speed is further increased, it will force the fluid into the wedge-shaped region (c). 142 (a) (b) (c) Figure 1 Formation of Continuous Film in a Journal Bearing Figure 2. hydrodynamic lubrication (Oil Wedge Region) Since more and more fluid is forced into the wedge-shaped clearance space, pressure is generated within the system.

5 Shows the pressure distribution around the periphery of a journal. Since, the pressure is created within the system due to rotation of the shaft, this type of bearing is known as self acting bearing. The pressure generated supports the external load W. This mode of lubrication is seen in bearings mounted on engines and centrifugal pumps. 143 Figure 3 Pressure Distribution in hydrodynamic Bearing Hydrostatic lubrication : Hydrostatic lubrication is defined as a system of lubrication in which the load supporting fluid film, separating the two surfaces, is created by an external source, like a pump, supplying sufficient fluid under pressure.

6 Since the lubricant is supplied under pressure, this type of bearing is called externally pressurized bearing. Hydrostatic bearings are used on vertical turbo-generators, centrifuges and ball mills. Thin Film lubrication : Thin fluid lubrication , also known as boundary lubrication , is defined as a condition of lubrication , where the lubricant film is relatively thin and there is partial metal to metal contact. This mode of lubrication is seen in door hinges and machine tool slides. The conditions of boundary lubrication are excessive load, insufficient surface area or oil supply, low speed and misalignment.

7 Figure 4 Boundary lubrication 144 The hydrodynamic bearing also operates under the boundary lubrication condition when the speed is very low or when the load is excessive. Under the extreme conditions of load and temperature, the fluid film gets completely ruptured, direct contact between the two metallic surfaces takes place and thus, extreme boundary lubrication exists. Figure 5 Contacts at High Points (Extreme Boundary lubrication ) The phenomenon of extreme boundary lubrication is based on the theory of hot spots. These hot spots, also known as high spots are the spots on the metallic surfaces where the welding of the two surfaces takes place, owing to extreme temperature conditions, which is a consequence of the shearing action of the high points.

8 However, due to the relative motion between the two surfaces, the welding too gets ruptured. As a consequence of the phenomenon of the high spots, occurring at extreme conditions of load and temperature, the physical properties get severely damaged. LIGHTLY LOADED JOURNAL BEARINGS: The following assumptions are made while deriving the characteristic equations for the lightly loaded journal bearings: 1. The radial load is almost zero. 2. Viscosity of the lubricant is very high. 3. Journal speed approaches very large values. 4. Film thickness is very small as compared to radius of the journal h <<< r.

9 145 Figure 6 Journal Bearing Figure 7: Unwrapped Film shows the unwrapped film. The length is 2 r and the width is L into the plane of the paper. Also, the film thickness is equal to the clearance h = C. Now, we have 2UN' =andFA = (1) where N = journal speed = shear stress acting on the fluid A = 2 rL, area of the journal surface. Assuming constant coefficient of viscosity of the fluid and from Newton s law, we have Uh = (2) or 2rNh' = (2a) Hence, 224'NLrFC = (3) Further, the frictional torque may be obtained as 146234'.

10 FNLrTFrC == (4) This equation is known as the Petroff s equation, for lightly loaded journal bearings. The coefficient of friction may be obtained as FfW= (5) We define unit bearing load P as the radial load per unit projected area. 2 WPrL= (6) Hence, the coefficient of frictional is 2'2 NrfPC = (7) PRESSURE DEVELOPMENT IN THE OIL FILM: Consider two parallel surfaces, one stationary and the other moving with uniform velocity U, as shown in Figure 8 Two Parallel Surfaces in Motion Here, we assume that the two surfaces are very large in a direction perpendicular to the plane of motion and therefore, their velocity in this direction is zero.