Brief overview of bearings
Bearings are broadly categorized into two types, fluid film and rolling contact type.
Fluid Film bearings
In fluid film bearing the entire load of the shaft is carried by a thin film of fluid present between the rotating and non-rotating elements. The types of fluid film bearings are as follows,
Sliding contact type
Rolling contact bearings
In rolling contact bearings, the rotating shaft load is carried by a series of balls or rollers placed between rotating and non-rotating elements. The rolling contact type bearings are of two types, namely,
Comparison of bearing frictions
The Fig. 14.1.1 shows a plot of Friction vs. Shaft speed for three bearings. It is observed that for the lower shaft speeds the journal bearing have more friction than roller and ball bearing and ball bearing friction being the lowest. For this reason, the ball bearings and roller bearings are also called as anti friction bearings. However, with the increase of shaft speed the friction in the ball and roller bearing phenomenally increases but the journal bearing friction is relatively lower than both of them. Hence, it is advantageous to use ball bearing and roller bearing at low speeds. Journal bearings are mostly suited for high speeds and high loads.
The ball and roller bearings require less axial space but more diametrical space during installation and low maintenance cost compared to journal bearings. Ball bearings and roller bearing are relatively costly compared to a journal bearing. The reliability of journal bearing is more compared to that of ball and roller bearings.
Here, we will discuss only about journal, ball and roller bearings, being most commonly used in design.
Fig. 14.1.2 describes the operation of a journal bearing. The black annulus represents the bush and grey circle represents the shaft placed within an oil film shown by the shaded region. The shaft, called journal, carries a load P on it. The journal being smaller in diameter than the bush, it will always rotate with an eccentricity.
When the journal is at rest, it is seen from the figure that due to bearing load P, the journal is in contact with the bush at the lower most position and there is no oil film between the bush and the journal. Now when the journal starts rotating, then at low speed condition, with the load P acting, it has a tendency to shift to its sides as shown in the figure. At this equilibrium position, the frictional force will balance the component of bearing load. In order to achieve the equilibrium, the journal orients itself with respect to the bush as shown in figure. The angle θ, shown for low speed condition, is the angle of friction. Normally at this condition either a metal to metal contact or an almost negligible oil film thickness will prevail. At the higher speed, the equilibrium position shifts and a continuous oil film will be created as indicated in the third figure above. This continuous fluid film has a converging zone, which is shown in the magnified view. It has been established that due to presence of the converging zone or wedge, the fluid film is capable of carrying huge load. If a wedge is taken in isolation, the pressure profile generated due to wedge action will be as shown in the magnified view.
Hence, to build-up a positive pressure in a continuous fluid film, to support a load, a converging zone is necessary. Moreover, simultaneous presence of the converging and diverging zones ensures a fluid film continuity and flow of fluid. The journal bearings operate as per the above stated principle.
The background of hydrodynamic theory of lubrication
Petroff (1883) carried out extensive experimental investigation and showed the dependence of friction on viscosity of lubricant, load and dimensions of the journal bearing. Tower (1883 and later) also conducted experimental investigation on bearing friction and bearing film pressure.
The experimental investigations by Petroff and Tower form the background of the hydrodynamic theory. Later on Osborne Reynolds conducted experiments and published the findings in the form of present day hydrodynamic theory of lubrication and the corresponding mathematical equation is known as Reynolds’ equation.
The Reynolds’ equation (simplified form)
U : surface speed of the wedge, in x-direction
p : pressure at any point(x,z) in the film
μ : Absolute viscosity of the lubricant
h : film thickness, measured in y-direction
The left hand side of the equation represents flow under the pressure gradient. The corresponding right hand side represents a pressure generation mechanism. In this equation it has been assumed that the lubricant is incompressible and Newtonian. The wedge shape, that was discussed earlier, is assumed to be a straight profile as shown in Fig.14.1.3. The bearing is very long in the Z direction and the variation of pressure is in the X and Z direction.
Let us have a look at the right hand term in details.
There are two moving surfaces 1 and 2 as indicated in Fig. 14.1.4. For 1 the velocities are u1, v1 and w1 along the three coordinate axes X, Y and Z respectively. For 2, similarly the velocities are u2, v2 and w2 respectively. Equation (14.1.2) represents the full form of the right hand side of Reynolds’ equation. For the purpose of explanation, partial derivative of only the first term of equation (14.1.2) is written in equation (14.1.3). Here u1+ u2 have been replaced by U.
The first term of (14.1.3), , represents a physical wedge. The second term is known as the stretch. All the three terms of (14.1.3) contribute in pressure generation mechanism.
The term, in equation (14.1.2) is called squeeze film; with respect to time how the film thickness is changing is given by this term.
The last term, is the compressibility of the fluid with time and it is termed as compression.
The simplified form of the Reynolds’s equation, (14.1.1), has only the physical wedge term,