Design of Self-restriction Hydrostatic Thrust Spherical Bearing (Fitted Type)

Abstract

This is the last part of the series studying the fitted hydrostatic thrust spherical bearing. It handles an unconventional design of this type of bearings. The conception of this design is to break the rules controlling the bearing restrictions, where it is believed that without restrictors no hydrostatic bearing could be got (axiom). The paper focused the effort to derive a general characteristic equation that can control the design in turn the bearing performance and behavior. This general characteristic equation, through its simple form, gives the designer the ability to get a comprehensive conception about his problem and widely opens the door in front of him to design a conventional or unconventional bearing whatever the bearing purpose. The effective parameters; needed to be known for designing the bearing; were concentrated into three items; the rotor speed, the seat dimensions and the lubricant properties. The characteristic equation shows that the seat radius and the inlet angle play the major role in determining the supply pressure, in turn the load carrying capacity. The inertia, the recess angle and the lubricant viscosity have the major effect on determining the bearing stiffness in case of the partial hemispherical seats while in case of the hemispherical seats the stiffness has slightly been affected. The design shows that the bearings with hemispherical seats have extremely low stiffness, practically zero stiffness and very high temperature rise, which make this bearing configuration invalid to be self restriction bearing; while the bearings with partial hemispherical seats have a very wide stiffness range allowing the designer to control and design the bearing with the stiffness needed for any purpose (from zero stiffness to extremely high stiffness). The lubricant temperature rises about three degrees centigrade which practically means that the bearing operates at constant temperature.

Kugel ball as an interesting application of designing the hydrosphere

“…Looking at the few data mentioned by Snoeijer and van der Weele [12] about this example, it could be realized the agreement with the present results. However, despite the lack of information about the specifications of this example, the results reveal that the Kugel ball is a self-restriction hydrosphere Yacout [11].…”

“…The fountain specifications are: Ball radius (R) = 0,5 m fitted with the seat. Material, granite, specific weight (  ) = 2.75x10 4 N/m 3 Following the previous design procedures:  i  2.31 deg, Ke = 1/775, mor = 1 for self-restriction [11] and  =2/3 for consistency [6][7][8][9][10][11], water lubricant  = 10 3 Kg/m 3 ,  = 0.001 N.s 2 /m 4 From eq. ( 7…”

“…All mathematical equations related to the hydrosphere could be found in Yacout [6][7][8][9][10][11] and the necessary ones which serve this design are listed.…”

“…Dowson and Taylor [4][5] offered a more complete theoretical analysis by starting with the equations of motion and reducing them to a usable form retaining only the centripetal inertia terms. Yacout [6][7][8][9][10][11] developed Dowson form to be able to handle this type of bearings with its different configurations, in presence of the surface roughness centripetal inertia and the lubricant variable viscosity, investigating its performance in details and offering a single equation covers this type and a design for restricted and self-restriction fitted bearing ,which the Kugel ball is to be considered a partially hemispherical configuration of the hydrosphere. Snoeijer and Weele [12] offered mathematical analysis for the Kugel ball and concluded that, as a matter of fact, the kugel fountain can be thought of as a giant ball bearing.…”

“…---------------------------------------------------------------------------------------------------------1. Expressions Needed Simplifying the expressions in Yacout (6)(7)(8)(9)(10)(11) gives the simplest forms of the equations needed for the Kugel ball at the appendix, which cover the un-recessed fitted hydrosphere. Equating the parameter: ( , , , ,…”