By Pradeep K. Gupta (auth.)
In any rotating equipment approach, the bearing has usually been a crit ical member of the total process, because it is the part that enables the relative movement among the desk bound and relocating elements. counting on the appliance, a couple of diversified bearing varieties were used, corresponding to oil-lubricated hydrodynamic bearings, fuel bearings, magnetic suspensions, rolling point bearings, and so on. Hydrodynamic bearings supplies any wanted load help, yet they're constrained in stiffness and the linked strength loss will be fairly huge. gasoline bearings are used for high-precision functions the place the supported quite a bit are quite mild, bearing energy losses are very low, and the rotating speeds often excessive. For large precision elements the place no frictional dissipation or bearing strength loss could be tolerated, magnetic suspensions are hired; back, the weight help specifications are very low. Rolling point bearings were ordinary for these functions that require larger bearing versatility, as a result of the standards for high-load and high-stiffness features, whereas permitting reasonable strength loss and allowing variable speeds. A research of the dynamic interplay of rolling components is, for that reason, the topic of this article. Texts overlaying the research and layout method of rolling parts are very restricted. impressive works comprise research of Stresses and Deflections (Jones, 1946, Vols. I and II), Ball and curler Bearings, Their idea, layout and alertness (Eschmann, Hasbargen, and Weigand, 1958), Ball and curler Bearing Engineering (Palmgren, 1959, third ed. ), complex Bearing expertise (Bisson and Anderson, 1965), and Rolling Bearing research (Harris, 1966).
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Extra info for Advanced Dynamics of Rolling Elements
General Motion Simulation 19 relative to the bearing coordinate frame be r, the position of the origin of the bearing coordinate frame relative to a point fixed in space be r o , and the applied force on the bearing element be F. 24) where m is the mass of the bearing element and the accelerations at and an generally called the acceleration of transport and the acceleration of Coriolis respectively, are given by at =nx R + n(n . 26) where R = r + ro Thus if the motion of the bearing coordinate is prescribed the accelerations of the various bearing elements can be determined in the coordinate frame fixed in the bearing.
However, as will be seen below, an average interaction will be deter- Rolling Element/Cage Interactions 47 mined for each contact and the corresponding hydrodynamic or dry contact force will be determined. Thus, variation within the contact zone, as computed for the rolling element/race interaction, will not be considered. This is reasonable in view of the fundamental assumptions outlined above. 1 Geometric and Kinematic Considerations For high-speed angular-contact ball bearings and cylindrical roller bearings, the cage is usually guided on one of the races.
81) may be solved for ~o by setting Pi (~o) = O. The resultant algebraic equation will be nonlinear, but the solution is straightforward by the conventional bisection method. 0 - as a function of ( and 2. Figure 3-16 shows ¢o as a function of, and Figure 3-17 shows the pressure profile, at , = 0, for the different values of the parameter 2. 81), over the entire contact region -1::; ~ ::; ~o and -(0::; ( ::; ~o, where the coordinate indicates the point of maximum film. ; ~2~! 82) where R = 1/22 + (2 + ~'2 and a = 1/22 + (2.
Advanced Dynamics of Rolling Elements by Pradeep K. Gupta (auth.)