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Rolling-element bearing analysis

Rolling-element bearing analysis
Issue Time:2018-06-12

Rolling-element bearing analysis

A rolling-element bearing, also known as a rolling bearing, is a bearing which carries a load by placing rolling elements (such as balls or rollers) between two bearing rings called races. The relative motion of the races causes the rolling elements to roll with very little rolling resistance and with little sliding.

Rolling-element bearings have the advantage of a good trade off between cost, size, weight, carrying capacity,durability, accuracy, friction, and so on. Other bearing designs are often better on one specific attribute, but worse in most other attributes, although fluid bearings can sometimes simultaneously outperform on carrying capacity,durability, accuracy, friction, rotation rate and sometimes cost. Only plain bearings are used as widely as rolling-element bearings.

Ball bearing

A particularly common kind of rolling-element bearing is the ball bearing. The bearing has inner and outer races between which balls roll. Each race features a groove usually shaped so the ball fits slightly loose. Thus, in principle, the ball contacts each race across a very narrow area. However, a load on an infinitely small point would cause infinitely high contact pressure. In practice, the ball deforms(flattens) slightly where it contacts each race much as a tire flattens where it contacts the road. The race also yields slightly where each ball presses against it. Thus, the contact between ball and race is of finite size and has finite pressure. Note also that the deformed ball and race do not roll entirely smoothly because different parts of the ball are moving at different speeds as it rolls. Thus, there are opposing forces and sliding motions at each ball/race contact. Overall, these cause bearing drag.

Roller bearings

Cylindrical roller

Roller bearings are the earliest known type of rolling-element-bearing, dating back to at least 40 BC.Common roller bearings use cylinders of slightly greater length than diameter.Roller bearings typically have higher radial load capacity than ball bearings,but a lower capacity and higher friction under axial loads. If the inner and outer races are misaligned, the bearing capacity often drops quickly compared to either a ball bearing or a spherical roller bearing.

As in all radial bearings, theouter load is continuously re-distributed among the rollers. Often, only lessthan half of the total number of rollers carries a significant portion of theload at all time. The animation on the right shows how a static radial load issupported by the bearing rollers as the inner ring rotates.

Spherical roller

Spherical roller bearings havean outer ring with an internal spherical shape. The rollers are thicker in themiddle and thinner at the ends. Spherical roller bearings can thus accommodateboth static and dynamic misalignment. However, spherical rollers are difficultto produce and thus expensive, and the bearings have higher friction than anideal cylindrical or tapered roller bearing since there will be a certainamount of sliding between rolling elements and rings.



Gear bearing

Gear bearing is roller bearingcombining to epicyclical gear. Each element of it is represented by concentricalternation of rollers and gearwheels with equality of roller(s) diameter(s) togearwheel(s) pitch diameter(s). The widths of conjugated rollers and gearwheelsin pairs are the same. The engagement is herringbone or with the skew end facesto realize efficient rolling axial contact. The downside to this bearing ismanufacturing complexity. Gear bearings could be used, for example, asefficient rotary suspension, kinematically simplified planetary gear mechanismin measuring instruments and watches.

Tapered roller

Tapered roller bearings useconical rollers that run on conical races. Most roller bearings only takeradial or axial loads, but tapered roller bearings support both radial andaxial loads, and generally can carry higher loads than ball bearings due togreater contact area. Tapered roller bearings are used, for example, as thewheel bearings of most wheeled land vehicles. The downsides to this bearing isthat due to manufacturing complexities, tapered roller bearings are usuallymore expensive than ball bearings; and additionally under heavy loads thetapered roller is like a wedge and bearing loads tend to try to eject the roller;the force from the collar which keeps the roller in the bearing adds to bearingfriction compared to ball bearings.

Needle roller

Needle roller bearings use very long and thin cylinders. Often the ends of the rollers taper to points, and these are used to keep the rollers captive, or they may be hemispherical and not captive but held by the shaft itself or a similar arrangement. Since the rollers are thin, the outside diameter of the bearing is only slightly larger than the hole in the middle. However, the small-diameter rollers must bend sharply where they contact the races, and thus the bearing fatigues relatively quickly.