By Pradeep K. Gupta (auth.)
In any rotating equipment process, the bearing has often been a crit ical member of the whole process, because it is the part that allows the relative movement among the desk bound and relocating components. looking on the appliance, a few varied bearing varieties were used, similar to oil-lubricated hydrodynamic bearings, fuel bearings, magnetic suspensions, rolling aspect bearings, and so on. Hydrodynamic bearings delivers any wanted load help, yet they're restricted in stiffness and the linked energy loss could be relatively huge. fuel bearings are used for high-precision purposes the place the supported quite a bit are quite gentle, bearing strength losses are very low, and the rotating speeds as a rule excessive. For large precision elements the place no frictional dissipation or bearing strength loss should be tolerated, magnetic suspensions are hired; back, the weight aid standards are very low. Rolling aspect bearings were popular for these purposes that require larger bearing versatility, as a result of specifications for high-load and high-stiffness features, whereas permitting reasonable energy loss and allowing variable speeds. A learn of the dynamic interplay of rolling parts is, for this reason, the topic of this article. Texts masking the research and layout technique of rolling parts are very constrained. extraordinary works comprise research of Stresses and Deflections (Jones, 1946, Vols. I and II), Ball and curler Bearings, Their conception, 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
It will, therefore, be convenient to define ~g and rgg as the body-fixed vectors locating the geometric center relative to the mass center for the cage and ball respectively. 68) where [1i~] is defined as the transformation matrix between the inertial and ball frames. 69) Rolling Element/Cage Interactions 49 Figure 3-13 Exaggerated pocket geometry for a ball riding cage. 70) where d is the ball diameter and [T;b] is the transformation from the inertial to ball frame. 67). Ball/Cage Interactions with Ball Guidance.
With the above assumptions, the rolling element/cage interaction can be considered in three basic parts: (i) the determination of geometric interaction or minimum clearance between interacting elements, (ii) postulation of hydrodynamic models for prescribed clearances, and (iii) postulation of dry contact models in the case of contact. The geometric interaction or the minimum film is determined by the prescribed position vectors and geometry of the elements. Once a minimum clearance, the geometry of the elements, and the velocity vectors are known, the hydrodynamic interaction is determined by solving the Reynolds equation in the contact zone.
Depending on the degree of approximation acceptable, two cases may be considered. Case 1: No Variation in Traction Along the y Axis. 10). 21) can be easily integrated numerically using the conventional Gaussian Quadrature formulae. Treatment of discontinuities in components of K will require some care. When due to curvature of the ball/race interaction surface there are one or two points of pure rolling, the slip component changes sign; Figure 3-6 shows a typical variation. Because of this change in sign there is a corresponding discontinuity in K and a subdivision of the domain -1 :5: x:5: 1 into the two or three regions separated by the discontinuities becomes convenient.
Advanced Dynamics of Rolling Elements by Pradeep K. Gupta (auth.)