Abstract
In a previous study handling this subject, a series of six papers has been published covering the fitted type (equal radii of this sort of bearings) with its configurations in details. The present study handles the same subject investigating the clearance type of this sort of bearings starting with the un-recessed one. The clearance type of bearings, where the sphere radius is smaller than that of the seat, provides plenty of complications and great divergence in its behavior compared with the fitted one. The study investigates theoretically the bearing behavior under the lubricant viscosity variation in the presence of the centripetal inertia due to the shaft rotation and the surface roughness. Solutions have been derived for the un-recessed clearance type of bearings with hemispherical and partial hemispherical seats in addition to its two special cases using capillary tube and orifice restrictors. Unlike other studies, using the conventional integration (i.e., without using the Sommerfeld substitution), only one equation with one form for the pressure gradient is derived to cover the positive and negative eccentricity ratios. Expressions for the pressure distribution, temperature distribution in turn the temperature rise, load carrying capacity; volume flow rate, frictional torque, friction factor, power losses and stiffness factor are obtained. The study shows the combined effects of the viscosity variation, the centripetal inertia and the surface roughness on the bearing performance. The optimum design (with constant viscosity) based on the minimum power losses, minimum flow rate and the optimal restrictor dimensions, in a previous study is checked where it is found out that designing this type of bearings on such basis only is not sufficient in despite of the bearing consistency. A natural dynamic phenomenon ignored in the previous study is revealed and briefly touched.
Highlights
Because of their fabrication simplicity, potential characteristics of low running friction, high load carrying capacity, high stiffness, small viscous dissipation, self aligning property and ability to accept thrust and radial loads, the externally pressurized spherical bearings are preferably used in heavy duty and high speed devices as machine tools, gyroscope gimbals, radar tracking units, craft engines, dynamometers and telescopes
Yacout [1,2,3,4] studied the combined effects of the surface roughness and the centripetal inertia on the hydrostatic thrust spherical bearing performance where it is concluded that the central pressure ratio should be (2/3) showing the bearing behavior in details and offering an example of a bearing designed on the minimum power losses, minimum flow rate and optimal restrictor dimensions
Variable Lubricant Viscosity (Un-recessed Clearance Type) example of the designed bearing was checked showing that the temperature rise is less than 14 degrees centigrade in addition to the bearing consistency which proved the reliability of the design technique [2,3]
Summary
Because of their fabrication simplicity, potential characteristics of low running friction, high load carrying capacity, high stiffness, small viscous dissipation, self aligning property and ability to accept thrust and radial loads, the externally pressurized spherical bearings are preferably used in heavy duty and high speed devices as machine tools, gyroscope gimbals, radar tracking units, craft engines, dynamometers and telescopes. Yacout [1,2,3,4] studied the combined effects of the surface roughness and the centripetal inertia on the hydrostatic thrust spherical bearing performance (fitted and clearance) where it is concluded that the central pressure ratio should be (2/3) showing the bearing behavior in details and offering an example of a bearing designed on the minimum power losses, minimum flow rate and optimal restrictor dimensions. The effect of the viscosity variability on fitted type bearing behavior in the presence of the surface roughness and the centripetal inertia has been studied showing the temperature distribution and calculating the temperature rise through introducing the energy equation. The clearance type (un-recessed) bearing behavior under the surface roughness and the centripetal inertia has been studied where a single equation with two forms for the pressure is derived to cover the negative and positive eccentricity ratios, in turn a single equation with two forms for the load [4]
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More From: International Journal of Mechanical Engineering and Applications
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