Journal-bearing problem

To obtain governing equations and boundary conditions, we adopt the circular cylindrical coordinate system that is shown, along with a top view of the eccentric cylinder system, in Fig. 5-1. In this system, the origin of the coordinate system is chosen to be coincident with the central axis of the inner cylinder, which is assumed to have a radius a and an angular velocity 2 in the direction shown. The radius of the outer cylinder is assumed to be a( 1 + e), and its center is offset along the 0 = 0 axis relative to the center of the inner cylinder by an amount ask. In the journal-bearing problem, the outer cylinder does not rotate ( 2 = 0). The surface of the inner cylinder is thus... 

It is evident that uP depends both on y and 6, though the velocity field has the same form locally (that is, for fixed 0) as for unidirectional flow between parallel plane boundaries. In this journal-bearing problem, the motion is due to the motion of the boundary only. The pressure gradient is a consequence of this motion and the fact that the gap width is not constant. 

For purposes of nondimensionalizing, we follow the journal-bearing problem of the preceding section. An appropriate choice for the characteristic velocity when the boundary moves in its own plane is the magnitude of the boundary velocity, uc = U. (We will return to the case in which the boundary moves in the normal direction shortly.) We denote the horizontal length scale characteristic of the distance for 0((h)) changes in the gap width as tc. Hence,... 

The core of the computationally crucial part of CONNFFESSIT calculations has been described in great detail in Sections III and IV. The remaining elements in a CONNFFESSIT calculation are relatively straightforward. Two recent references describe in detail specific applications to the journal bearing problem (Laso et al. 1997) and to the planar contraction flow (Laso 1998) as well as the implementation on parallel and vector machines. 

During inspection, all journal bearings should be closely inspected. If the machine has not suffered from excessive vibrations or lubrication problems, the bearings can be reinstalled and utilized. 

It is perhaps worthwhile to dwell briefly on the use of the journal-bearing configuration in practical lubrication applications. In such circumstances, the rotating inner cylinder is normally allowed to float to seek a position in which the hydrodynamic force precisely balances the load. We have analyzed the eccentric cylinder problem based on the picture in Fig. 5-1, in which the line of centers between the two cylinders is in the horizontal direction. In that configuration, there is a net vertical force but no horizontal force. Moreover, examination of (5-48) shows that the magnitude of the vertical force for a given pair of cylinders (so that a and e are fixed) is determined by 9 and A. The A dependence is contained in the factor... 

Let us examine the problem for a familiar engineering device, namely the plain journal bearing, shown in diagrammatic cross-section in Fig. 1-1. The bearing a is fixed in position and supported its bounding... 

Analysis of the externally pressurized gas-lubricated journal bearing is involved, tedious and quite specific to the particular problem. Details can be found in the monograph by Pinkus and Sternlicht [4]. 

Thrust bearings which are usually larger than the journal bearings mounted on the same machine have correspondingly higher surface velocities and are more prone to thermal problems. 

In order to solve this problem, some workers have Investigated the oil film pressure distribution in journal bearings under dynamic load (2-5), and one of the authors has also presented two papers ii.,5) which had dealt with this problem. Nevertheless, the boundary condition for dynamic loading has remained a big question, because there is infinite combinations of experimental parameters and the measurement of an oil film pressure under dynamic condition is a difficult task. 

This paper considers various aspects oi bearing development for sea water lubricated thrust and journal bearings. Section 2 discusses theoretical aspects of bearing design with low viscosity lubricants and makes reference to experimental and practical evidence. Section 3 considers aspects of bearing materials and indicates an approach which has been found to be helpful in material selection. Section 4 illustrates some of the problems to be overcome in the manufacture of bearing components to the required accuracy. 

One of the most challenging problems in tribology is the determination of mathematical models to describe the dynamics of bearing oil-films in vibration - sometimes referred to as the problem of bearing identification. The central problem of bearing identification involves the determination of the linearised coefficients associated with a journal bearing oil-film. However, there are are other problems currently of Interest, notably the Identification of the linearised dynamics of the squeeze-film vibration isolator. It is this latter problem which will be considered here. 

The similitude concept may be illustrated by considering an example. The problem of journal bearing load capacity is convenient for this purpose. In this problem, the minimum film thickness h) is related to a number of other variables, already defined in Ch. 5, Sec. 6.0 as follows ... 

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