EngineeringMechanical EngineeringPart 02 of 15
Rolling Element Bearing Selection
A bearing selection is a life calculation, not a strength calculation. Get the equivalent dynamic load and the design life right and the rest of the procedure is arithmetic — but the checks that follow the life calculation are where most specifications quietly fail.
- ISO 281 method
- L10 rating life
- Four bearing families
- Worked example
Executive summary
Rolling element bearings are selected against fatigue life. The governing quantity is the basic rating life L10 — the life in millions of revolutions that ninety per cent of a large group of apparently identical bearings will attain or exceed under a given load. Ten per cent are expected to fall short; the average life is several times the L10 figure.
The ISO method relates life to load alone. Modern manufacturer methods extend it to account for reliability, bearing steel, lubricant viscosity, contamination and a fatigue load limit below which fatigue is not expected to occur at all. This page sets out the classical method in full, then explains what the extended methods add and when they matter.
The four families worth knowing first
Bearing catalogues list dozens of types. Four cover the large majority of general mechanical design, and the selection arithmetic differs between them only in how the equivalent load is formed.
Deep groove ball
The default. High speed capability, moderate radial load, useful axial capacity in both directions. Available pre-sealed and pre-lubricated, which removes a whole class of maintenance risk.
Self-aligning ball
Two rows of balls on a spherical outer raceway. Tolerates shaft and housing misalignment that would destroy a rigid bearing. Often supplied with a tapered bore and adaptor sleeve.
Cylindrical roller
Line contact gives high radial capacity in a compact envelope. Flangeless variants carry no axial load at all; flanged variants carry a limited amount.
Spherical (self-aligning) roller
High radial capacity combined with misalignment tolerance. The workhorse of heavy plant, conveyors and mill equipment.
Choose the type from load direction, speed, alignment, noise, friction and sealing requirements first. Only then size it. Reversing the order produces bearings that satisfy a life calculation while being fundamentally unsuited to the application.
Design life and the life equation
Begin with the life the equipment must achieve, expressed in operating hours. This depends on whether the machine runs continuously or intermittently and on the expected service life of the equipment; in general mechanical design a ten-year target is common. Convert the hours to millions of revolutions.
- L
- design life, millions of revolutions
- N
- average operating speed, rev/min
- h
- design life, hours
The bearing achieves a basic rating life determined by the ratio of its dynamic load rating to the equivalent dynamic load acting on it.
- C
- basic dynamic load rating from the manufacturer's table
- P
- equivalent dynamic bearing load
The selection is then a comparison: if L10 falls short of L the bearing is too small; if it greatly exceeds L the bearing is probably larger, heavier and more expensive than the duty requires.
Forming the equivalent dynamic load
Bearings are rated for pure radial load. Real bearings usually carry a combination of radial load Fr and axial load Fa, so the two are combined into a single equivalent load P that would produce the same fatigue life. The combination rule depends on the bearing family and on the ratio Fa/Fr relative to a limiting value e.
| Family | When Fa/Fr ≤ e | When Fa/Fr > e | Notes |
|---|---|---|---|
| Deep groove ball | P = Fr | P = X Fr + Y Fa | X and Y, and e itself, are read against Fa/C0 from the manufacturer's chart for normal clearance. |
| Self-aligning ball | P = Fr + Y1 Fa | P = 0.65 Fr + Y2 Fa | e, Y1, Y2 and Y0 are listed per bearing designation. |
| Cylindrical roller | P = Fr | P = 0.92 Fr + Y Fa | Flangeless (NU) types take no axial load; Fa/Fr should not exceed about 0.5 on flanged types. |
| Spherical roller | P = Fr + Y1 Fa | P = 0.67 Fr + Y2 Fa | Factors are tabulated per designation, as for self-aligning ball. |
In most machine designs the bearing loads are simply the shaft reaction forces at the bearing positions. Where the drive imposes dynamic loading — reciprocating machinery, crushing duty, frequent direction reversal — apply a shock factor to the steady reactions before forming P.
The selection procedure
- State the required life in hoursDerived from duty pattern and expected equipment life.
- Convert to millions of revolutionsUsing L = 60 N h / 106.
- Establish Fr and FaNormally the shaft reactions, with shock factors applied where dynamic loads occur.
- Compute Fa/FrThis decides which equivalent load expression applies.
- Trial a bearing for the shaft sizeFrom the table for that bore, take a mid-range bearing and record C and C0 together with the calculation factors.
- Determine e and the load factorsFor deep groove ball bearings these follow from Fa/C0; for the other families they are tabulated.
- Form P and calculate L10Compare against the required life L.
- Iterate up or down the tableMove to higher capacity if short of life, lower capacity if substantially over.
- Check the static caseForm the equivalent static load P0 and confirm it is below C0 — or below C0/1.5 for roller types. If P0 computes below Fr, take P0 = Fr.
- Check the minimum loadRolling elements must be loaded enough to roll rather than skid.
- Check the speed ratingConfirm maximum shaft speed is within the reference speed for the bearing and lubrication method.
- Check sleeve and seal limitsWhere an adaptor sleeve is used, verify the permissible axial load on the sleeve.
- Note
- More accurate minimum-load expressions based on lubricant viscosity and speed are published by bearing manufacturers and should be used for high-speed or lightly loaded arrangements.
Worked example
A shaft runs at 1450 rev/min carrying a radial reaction of 4.5 kN and negligible axial load at one bearing position. The machine operates two shifts, six days a week, and a ten-year life is required.
The required dynamic rating follows directly from rearranging the life equation: C = P · L1/3 = 4.5 × 34801/3 ≈ 68.5 kN. The designer then reads down the table for the chosen bore until a bearing with C at or above that value appears, and proceeds to the static, minimum-load and speed checks.
A 68.5 kN rating at a modest bore may push the bearing into a heavy series. If the resulting envelope is unacceptable, the honest options are to reduce the design life, accept a lower reliability, improve lubrication and cleanliness so an adjusted life method applies, or redesign the shaft layout to lower the reaction. Quietly reducing the assumed load is not one of them.
Beyond the basic rating life
The classical method considers load only. Decades of testing established that three further factors materially change bearing life.
Bearing steel
ISO ratings assume standardised material. Commercial bearing steels generally equal or exceed that assumption, and special steels can be specified where duty demands it.
Lubrication
Lubricant type, additives, viscosity at operating temperature, delivery and circulation method, and replacement interval. Viscosity falls as temperature rises, so the operating temperature must be estimated, not assumed.
Cleanliness
Environmental contaminants, ingressed dirt and metallic debris, water contamination, filtration quality and sealing method. Many of these are the same problem viewed from different angles: a well sealed bearing stays clean.
Three levels of life calculation
| Method | Accounts for | Use when |
|---|---|---|
| Basic rating life | Load only. | First-pass sizing, comparison between candidates, and general-purpose duty. |
| Adjusted rating life | Load, plus reliability, material and lubricant viscosity through life adjustment factors. | Non-standard reliability targets, or where lubrication is known and controlled. |
| Manufacturer life theory | All of the above plus contamination and a fatigue load limit below which fatigue is not expected. | Critical or high-value machines where cleanliness and lubrication are genuinely managed. |
The adjusted life is formed by multiplying the basic rating life by life adjustment factors for reliability, material and operating conditions. At the conventional ninety per cent reliability the reliability factor is unity, so the adjustment reduces to a combined material and lubrication factor determined from viscosity ratio — the actual lubricant viscosity at operating temperature divided by the viscosity required for adequate film formation at that speed and bearing size.
An adjusted life method is only honest if the conditions it assumes are actually delivered. Claiming a lubrication-enhanced life on a machine with no filtration, no scheduled oil change and marginal sealing is a specification failure waiting to be discovered in service.
Specification checklist
- Bearing type justified against load direction, speed, alignment, noise and sealing requirements.
- Design life stated in hours and converted to millions of revolutions.
- Radial and axial loads derived from shaft reactions, with shock factors applied where relevant.
- Equivalent dynamic load formed with the correct expression for the bearing family.
- Basic rating life compared against required life, and the trial iterated.
- Equivalent static load checked against the static rating.
- Minimum radial load satisfied so rolling elements do not skid.
- Maximum operating speed within the bearing and lubrication limits.
- Adaptor sleeve axial limit checked where a tapered bore is used.
- Lubrication method, quantity and interval specified alongside the bearing designation.
- All rating values re-verified against the current manufacturer catalogue.