By Pradeep K. Gupta (auth.)
In any rotating equipment approach, the bearing has frequently been a crit ical member of the complete method, because it is the part that allows the relative movement among the desk bound and relocating components. counting on the appliance, a couple of assorted bearing kinds were used, comparable to oil-lubricated hydrodynamic bearings, gasoline bearings, magnetic suspensions, rolling point bearings, and so on. Hydrodynamic bearings promises any wanted load aid, yet they're constrained in stiffness and the linked strength loss could be fairly huge. gasoline bearings are used for high-precision functions the place the supported so much are particularly mild, bearing strength losses are very low, and the rotating speeds typically excessive. For great precision parts the place no frictional dissipation or bearing strength loss will be tolerated, magnetic suspensions are hired; back, the burden help requisites are very low. Rolling point bearings were primary for these functions that require larger bearing versatility, because of the standards for high-load and high-stiffness features, whereas permitting reasonable strength loss and allowing variable speeds. A examine of the dynamic interplay of rolling components is, for this reason, the topic of this article. Texts overlaying the research and layout technique of rolling parts are very restricted. outstanding works contain research of Stresses and Deflections (Jones, 1946, Vols. I and II), Ball and curler Bearings, Their concept, layout and alertness (Eschmann, Hasbargen, and Weigand, 1958), Ball and curler Bearing Engineering (Palmgren, 1959, third ed. ), complicated Bearing expertise (Bisson and Anderson, 1965), and Rolling Bearing research (Harris, 1966).
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Additional resources for Advanced Dynamics of Rolling Elements
The traction coefficient, when multiplied by the normal load, gives the traction force. Both the normal and traction forces can now be added vectorially to determine the net force vector acting between the interacting elements. The moment vector acting on the element is determined by the cross product of the vector that locates the point of interaction with respect to the element's mass center and the net force vector. 1 Rolling Element/Race Interactions Since the geometry of the bearing plays an important role in formulating the interaction between various elements, the considerations in ball and roller bearings will be discussed separately.
Vector rrg locates the race geometric center RG relative to the mass center, and vector rgc locates the center of race land R[ relative to the race geometric center R G • Similarly, the mass center of the roller BM is located by rb relative to the inertial frame and rbg locates the roller geometric center relative to the mass Rolling Element/Race Interactions 35 Race Roller Frame z x~ 0 ~ Inertial Frame y Figure 3-8 Exaggerated view of roller/race interaction. center. The vectors rrg and rbg , respectively, will generally be prescribed in the race-fixed frame (x,y,z) and the roller-fixed frame (:R,y,i).
In terms of the scaled variable (x,y), the elliptical contact zone is transformed into a unit circle, as shown in Figure 3-7. 23) 32 Geometric Interactions in Rolling Bearings Contact Ellipse y CSt ~. I • ·1 Tractive Forces / / / ",-",- f',~ ~ '\ ( 1\ Normal Forces / / ",-/ i'f', i'f'\ t\ ( '\ Slip Distributions x = x/a Figure 3-6 Typical variation of ball/race slip velocity in the rolling direction. where ds = rde and The term ~, resulting from the Hertzian elasticity solution, cannot be Rolling Element/Race Interactions 33 y t10f Direction Rolling Figure 3-7 Elliptical contact zone transformed into a unit circle.