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Article Excerpt
This study presents a theoretical model of the remarkably good lubrication characteristics of the thrust slide-bearings found in scroll compressors experimentally by Ishii et al. (2007). It has been suggested that the thrust plate undergoes elastic deformation due to axial loading. As a result of this deformation, a fluid wedge is believed to form at the periphery of the thrust plate. The fluid wedge angle between the sliding surfaces was calculated with a finite element method analysis and then used in the average Reynolds equation from Patir and Cheng (1978, 1979) to analyze the fluid lubrication on rough sliding surfaces. The plastic and elastic contacts between the orbiting and fixed thrust plates were analyzed using the solid contact theory from Greenwood and Williamson (1966). The derived theoretical model permitted the calculation of the oil film pressure, the solid contact force, the fluid frictional force, and the solid shearing drag force. These results were used, in turn, to determine the resultant friction coefficient at the thrust slide-bearing. Finally, it is shown that the predicted theoretical results agree well with the experimental lubrication test results of Ishii et al. (2007). The proposed theoretical development appears to model accurately the essential mechanism for the remarkably good mixed fluid-and-solid lubrication in a thrust slide-bearing.
INTRODUCTION
A lubrication mechanism for thrust slide-bearings in scroll compressors, which in recent years have been widely used in room air-conditioners, was first proposed in experimental studies described in Ishii et al. (2004, 2007). In the proposed mechanism, the thrust plate undergoes an elastic deformation due to axial loadings caused by the pressure difference between the inner and outer regions of the thrust slide-bearing, which forms a fluid wedge between the sliding surfaces. This fluid wedge drastically improves the lubrication performance of these bearings. In order to clarify more fully the essential aspects of the proposed lubrication mechanism, a theoretical model of the lubrication process is needed for these thrust slide-bearings. A limited number of theoretical studies of thrust slide-bearings in scroll compressors have been reported by Kulkarni (1990a, 1990b) and Morishita and Sugihara (1986). In addition, an experimental study was undertaken by Nishiwaki et al. (1996). In these previous studies, however, the formation of the fluid wedge was not considered, and, hence, the essential characteristics of the lubrication in thrust slide-bearings, such as the bearing clearance, the oil-film force, the solid contact force, the resulting bearing load capacity, and so on, have not yet been definitively determined.
In the present study, a theoretical analysis of the proposed mechanism from Ishii et al. (2004) is presented. In the study by Ishii et al. (2007), the fluid wedge angle was calculated from the pressure difference between the inner and outer regions of the thrust slide-bearing using a finite element method analysis. In the present theoretical development, the orbiting thrust plate with elastic deformation is represented by a rigid, fixed thrust plate with an equivalent geometrical wedge at its periphery. The second plate, assumed to be flat and rigid, is then forced to perform the orbiting motion. The relative motion of these thrust plates is exactly the same as that of an operational scroll compressor. Such simplified modeling makes the mathematics in the theoretical development tractable, thus permitting theoretical analysis of the lubrication performance of the thrust slide-bearing in a scroll compressor.
It is postulated that the thrust slide-surfaces are under a state of mixed lubrication composed of fluid lubrication and solid friction. This mixed fluid/solid lubrication is analyzed using the average Reynolds equation developed by Patir and Cheng (1978, 1979)--applicable to any general roughness structure--for the fluid lubrication at the thrust slide-bearing, and using the solid contact theory from Greenwood and Williamson (1966) for the plastic contact between the orbiting and fixed thrust plates. These analytical methods for mixed lubrication have been well validated by the respective authors. Since the thrust slide-bearing is basically axisymmetric, the average Reynolds equation was transformed into polar coordinates. Solution of the axisymmetric average Reynolds equation yields the oil film force, permitting calculation of oil film viscous frictional force. The solid contact force and the solid shearing force can be calculated using the solid contact theory. The attitude of the thrust plate can be determined such that it satisfies the equilibrium equations (second order ordinary differential equations) of the resulting forces and moments. To reach this equilibrium condition in theory, these equilibrium equations should be solved simultaneously with the average Reynolds equations while, in practice, the solution is accomplished numerically.
The numerical calculations were undertaken for the same conditions as in the reported experiments by Ishii et al. (2007). The solution procedure involved initially assuming an attitude (mean floating height and inclination angle) of the thrust slide-bearing. Then the oil film pressure and viscous frictional force were calculated numerically solving the average Reynolds equation reduced to a finite difference approximation with the method of successive over-relaxation. At the same time, the solid contact and frictional forces were calculated with the solid contact theory. Subsequently, repetitive convergence calculations with the Runge-Kutta method were carried out for the equilibrium equations of these forces and resulting moments, thus deriving periodic solutions over a revolution of the crankshaft. Finally, repetitive convergence calculations were carried out for the thrust plate attitude, until the correct attitude was obtained. Ultimately, the calculated oil film viscous and solid frictional forces permitted calculation of the resultant frictional forces and the friction coefficient, both of which compared well with the previously measured experimental data from Ishii et al. (2007).
Finally, within the framework of the developed theoretical model, detailed examination of the effect of the ratio of fluid lubrication to solid friction on the resultant friction coefficient, bearing load capability, and bearing clearance was undertaken to further clarify the essential role mixed lubrication plays in enhancing the lubrication characteristics of thrust slide-bearings in scroll compressors.
THRUST SLIDE-BEARINGS AND A MODEL FOR LUBRICATION TESTS
The compression mechanism of a high-pressure type scroll compressor is shown in Figure 1a, where the orbiting thrust plate is pressed against the fixed thrust plate by the high and intermediate pressure oil. The orbiting thrust plate, made of aluminum alloy, undergoes an elastic deformation because of the axial loading along the axis of rotation. The deformation of the orbiting thrust plate results in the formation of an oil wedge near the outer periphery of the thrust slide-bearing. In addition, the pressure difference between the intermediate and suction pressures across the...
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