Advanced Dynamics of Rolling Elements by Pradeep K. Gupta (auth.)

By Pradeep K. Gupta (auth.)

In any rotating equipment approach, the bearing has normally been a crit­ ical member of the whole approach, because it is the part that allows the relative movement among the desk bound and relocating components. counting on the applying, a couple of assorted bearing kinds were used, similar to oil-lubricated hydrodynamic bearings, fuel bearings, magnetic suspensions, rolling aspect bearings, and so forth. Hydrodynamic bearings grants any wanted load aid, yet they're constrained in stiffness and the linked strength loss might be relatively huge. gasoline bearings are used for high-precision functions the place the supported quite a bit are rather gentle, bearing strength losses are very low, and the rotating speeds in most cases excessive. For great­ precision elements the place no frictional dissipation or bearing energy loss may be tolerated, magnetic suspensions are hired; back, the weight aid specifications are very low. Rolling point bearings were common for these purposes that require higher bearing versatility, end result of the necessities for high-load and high-stiffness features, whereas permitting average 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 components are very restricted. extraordinary works contain 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. ), complicated Bearing expertise (Bisson and Anderson, 1965), and Rolling Bearing research (Harris, 1966).

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38) becomes a little difficult. In view of this difficulty, Lund berg [71] has determined an empirical equation based on actual load deflection measurements in line contact. 39). 40); however, when J is prescribed, some type of iterative procedure will be necessary in order to compute Q. 41 ) In terms of results, the above two relations are fairly close. 41) and, under such conditions, the iteration will converge rather rapidly. Tractive Forces and Moments. For the purposes of computing the traction, it will be necessary to define the position vector locating the center of the elementary disk in the contact zone relative to the roller geometric center and the local slip velocities.

An attractive feature of such a simplification is that the integration required for the computation of the total tractive forces and moments is necessary only along the x axis. It is generally agreed that for oil-lubricated elastohydrodynamic conditions (to be discussed in Chapter 4) such an assumption is quite realistic, especially in view of the assumptions in the traction/slip models. However, for a dry contact or for solid-lubricated conditions the point-to-point variation in the traction force must be considered and a generalized two-dimensional integration must be performed.

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.

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