Surface roughness, loads, speeds, and lubrication type are just some of the factors to look at when sizing rolling-element and oil-film bearings.
M. M. Khonsari
Dow Chemical Endowed Chair in
Professor, Dept. of Mechanical
Louisiana State Univ.
Baton Rouge, La.
E. R. Booser
Vero Beach, Fla.
Numerous oil and grease-lubricated bearing designs rely on adequate lubricant film thickness for smooth and trouble-free operation. Engineers must check that films are sufficiently thick so asperities peaks of surface roughness between mating surfaces don't touch. Otherwise, bearings can rapidly wear and fail.
Step one is to estimate film thickness. A film thickness parameter, , quantifies the composite surface roughness for mating surfaces:
where hmin = minimum film thickness, R1 and R2 = the rms surface finishes of surface 1 and 2, respectively. When starting with a normal distribution of surface heights, multiply the arithmetic roughness average value, Ra by 1.25 to get the rms value, Rq.
For full-film lubrication of journal and thrust bearings, is typically above the range of 3 to 10. Misalignment, thermal, and elastic distortions can raise that to about 10 to 20.
Keep >3 when lubricating precision-finish journal bearings with a low-viscosity fluid such as water. This is because maximum asperity heights range up to 3 the rms value. Lower values boost wear or can make bearings fail prematurely. As a rule, hmin with oil-film bearings should be at least 10 to 20 the combined surface roughness of the shaft and bearing surfaces.
Unfortunately, for machinery bearings is not always well defined. Shaft journals in industrial electric motors, for example, typically have an initial Ra = 32 in. surface. Such shafts commonly run on soft babbitt bearings with an Ra = 64 in.
Using the 1.25 factor to convert arithmetic-average roughness to rms, and with nominal hmin = 0.0008 in., = 9.
After a few start-ups and running hours, babbitt typically polishes to about Ra = 16 in., while the journal burnishes to the same or better surface finish. An initial (and marginal) = 9, then climbs quickly to about 28 in service.
For journal bearings, a minimum film thickness can be estimated for small fluid-film thickness in the range of 0.5 to 20% of the radial internal clearance, C by:
where L = bearing length, in., D = bearing diameter, in., and S = the Sommerfeld dimensionless load-speed number:
in which = viscosity, reyns (lbf-sec/in. 2 ); N = speed in rev/sec; P = projected load = W/(LD), lbf/in. 2 ; and R and C are the shaft radius and radial clearance in inches.
For thrust bearings, minimum film thickness can be estimated from the relation:
where U = runner surface speed at its mean radius, in./sec, and P = pad average unit load, lb/in. 2 The coefficient, Kh, reaches a maximum of 0.26 for centrally pivoted pad thrust bearings with equal radial L and circumferential B pad dimensions. Kh drops to about 0.15 to 0.20 for tapered-land and step-thrust bearings, and 0.04 to 0.08 for flat lands. This minimum film thickness is proportional to the square root of both and U, and inversely proportional to P. Film thickness drops roughly 30% when load doubles, but remains unchanged if either speed or viscosity is simultaneously doubled.
BALL AND ROLLER BEARINGS
Load in ball and roller bearings is distributed on extremely small contact areas. Contact stresses elastically deform the surfaces to accommodate formation of an oil film. For these reasons, estimating film thickness in such bearings is a lot more involved. In both types of rolling-element bearings, film thickness is rather insensitive to rising load. For example, raising load by a factor of four on a ball bearing cuts minimum film thickness just 10%. Hydrodynamic journal or thrust bearings, by comparison, see a 50% reduction in film thickness for the same load increase.
At ball and roller bearing contacts, composite surface roughness, R can be taken as 0.12 m for aerospace bearings, 0.25 m for off-the-shelf bearings, and 0.65 m for extremely large industrial bearings. Wear generally becomes negligible when exceeds about 3.0 because a full film forms. Above 3.0, fatigue life is roughly 4 greater than values given in bearing catalogs. For high-speed aerospace applications, values of 6.0 or higher can give infinite fatigue life. Bearings with values between 1.0 and 3.0 may see minor surface glazing and distress. Then fatigue life is on par with lifetimes published in bearing catalogs. For below 1.0, wear and surface deformation are possible along with reduced fatigue life. In these cases, use extreme-pressure and antiwear additives and higher-viscosity oil to minimize wear.