Rolling-Element Bearings

Rolling-element bearings use balls or rollers between inner and outer raceways. The bearing type is selected from load direction, magnitude, speed, stiffness, accuracy, misalignment, available space, temperature, and environment.

Types and arrangements

Deep-groove ball bearings accept radial and moderate axial load. Angular-contact ball and tapered-roller bearings carry combined load and are often mounted in pairs. Cylindrical and spherical rollers provide high radial capacity; spherical types tolerate misalignment. A shaft usually uses a locating bearing and a non-locating bearing to accommodate thermal expansion.

Equivalent load and life

Dynamic equivalent load is written

$$P=XF_r+YF_a.$$

Basic rating life is

$$L_{10}=\left(\frac{C}{P}\right)^p10^6\ \text{revolutions},$$

where \(p=3\) for ball bearings and \(p=10/3\) for roller bearings. In hours, \(L_{10h}=10^6L_{10}/(60n)\). Static safety is checked from \(s_0=C_0/P_0\).

Fits, clearance, and lubrication

A ring under rotating load normally requires an interference fit. Fit, temperature, and preload alter internal clearance. Lubricant selection depends on speed, load, temperature, sealing, and relubrication interval.

Failures

Typical failures include rolling-contact fatigue, false brinelling, smearing, wear, electrical erosion, cage damage, overheating, and corrosion. Correct mounting force, alignment, cleanliness, sealing, preload, and shaft/housing tolerances are as important as the catalog life equation.

Contact angle and internal load distribution

The contact angle controls the relation between radial and axial capacity. Under combined load, only a subset of rolling elements may carry substantial force. Internal clearance, preload, ring deformation, and housing stiffness change this distribution and therefore stiffness, temperature, and life.

Bearing pairs

Angular-contact and tapered-roller bearings can be arranged back-to-back, face-to-face, or in tandem. Back-to-back sets provide a wide effective support span and high moment stiffness; face-to-face sets are more tolerant of some misalignment; tandem sets share axial load in one direction. Preload must be established by controlled spacers, springs, or adjustment.

Modified rating life

Basic \(L_{10}\) life corresponds to 90% reliability for a sufficiently large group under idealized conditions. Practical methods may modify it for reliability, lubrication quality, contamination, fatigue load limit, and material. Life calculations remain statistical and do not predict the exact failure time of one bearing.

Variable loads

For operating intervals with loads \(P_i\) lasting \(L_i\) revolutions, an equivalent load can be formed from damage accumulation:

$$P_{eq}=\left(\frac{\sum P_i^pL_i}{\sum L_i}\right)^{1/p}.$$

Speed and temperature intervals must be treated consistently with the duty cycle.

Static safety and minimum load

Static rating protects against permanent raceway indentation during high peaks, shock, or standstill. High-speed bearings also require a minimum load to prevent rolling-element skidding and smearing. Very lightly loaded large bearings may therefore need preload or a different type.

Speed and thermal limits

Permissible speed depends on bearing type, cage, size, load, preload, lubricant, and heat removal. Grease quantity should be controlled because overfilling raises churning temperature. At high speed, centrifugal effects and gyroscopic moments become important, especially for balls and large rollers.

Mounting and diagnostics

Mounting force is applied only to the ring being fitted. Induction heating, hydraulic nuts, tapered sleeves, and controlled pressing prevent damage. Condition monitoring uses temperature, vibration, noise, lubricant debris, and envelope analysis; diagnosis should distinguish bearing defects from imbalance, misalignment, looseness, and gear excitation.

Selection sequence

1. Determine radial, axial, moment, peak, and variable loads.
2. Select type and locating arrangement from speed, stiffness, alignment, and space.
3. Calculate equivalent dynamic load, life, and static safety.
4. Choose clearance or preload and shaft/housing fits.
5. Verify speed, minimum load, heat, lubrication, sealing, and contamination.
6. Specify mounting, axial retention, inspection, monitoring, and replacement.