Shown are plots of representative bearing types with   standard inner and outer race curvatures. Such plots allow designers to   calculate approximate relationships between radial play, contact angle,   and end play. Bearings with special curvatures have different relationships.   Also, end play values are not applicable to single-angular-contact bearings.

Shown are plots of representative bearing types with standard inner and outer race curvatures. Such plots allow designers to calculate approximate relationships between radial play, contact angle, and end play. Bearings with special curvatures have different relationships. Also, end play values are not applicable to single-angular-contact bearings.


Radial play, end play, and contact angle all provide a measure of bearing movement. But, it's not always clear which is the best way to typify movement for a specific application. Of the three, radial play is the most commonly used because the other two are functions of it.

Radial play
Radial play, Pr, is the total theoretical radial movement of a bearing outer ring with respect to a fixed inner ring:

Pr = A - B - 2d

When calculating radial play, also consider how the bearing mounts. Loose or line-to-line fits don't affect radial play whereas tight or interference fits can reduce it by about 80% of interference. Bearing makers such as Timken Super Precision (MPB), Keene, N.H., suggest a "standard" radial play, although certain applications require different values.

For example, interference fits may demand a looser radial play. So do bearings that see axial loads. Here, more radial play increases contact angle and lowers ball/race contact stresses and bearing torque for a given axial load. A larger radial play accommodates greater bearing misalignment as well. On the other hand, a tighterthan-standard value reduces potential misalignment, especially important when a preloaded bearing pair isn't an option. In general, keep radial play within manufacturer-prescribed limits (typically ±0.0003 in.). Specifying tighter values can make things unnecessarily expensive because bearing makers typically assemble ball bearings to a radial-play range.

Timken Super Precision, for instance, measures balls and inner rings to the nearest 0.00005-in. diameter, then sorts them into groups. Outer-ring tracks matched to these size-sorted parts give a theoretical fit-up. Several trial bearings are built to this theoretical fit-up and gauged on a specially designed radial-play instrument. The instrument centers the bearing in a fixture and applies a small radial load to the outer ring to seat balls into ball grooves. An indicator is zeroed and the machine applies an opposing radial load equal to the above load plus a gauge load. Gauge load is proportional to bearing size.

Next, more bearings are assem-bled to the theoretical fit-up. Improper fit-ups are corrected by changing balls or other components. When any of the component-size groups are consumed during a build, another theoretical fit-up and certification (with a new component or components) must take place before production resumes. Tighter radial plays require more fit-up adjustments which, in turn, shrinks the pool of usable parts and increases cost.

Contact angle
Contact angle is the angle between the ball/race contact points — with end play removed — and a line perpendicular to the bearing axis. The initial contact angle for bearings is measured at zero axial load and depends on radial play, raceway curvature, and ball diameter.

However, some applications with tighter deflection specs may hold contact angle to within ±1.5° or tighter. In these cases, contact angle is measured directly. First, a small axial load applied to the outer ring (with the inner ring held stationary) removes both radial and axial play. A special gauging tool rotates the outer ring about 20 revolutions and simultaneously tracks revolutions of the retainer or ball set. These counts are used to calculate initial bearing contact angle, b0, from:

End play
End play is the total axial movement of the inner ring (race) with respect to the fixed outer ring under a reversing axial gage load. End play, Pe, is a function of radial play, track curvature, and ball diameter according to:

Alternatively, it may be derived from the contact angle:

End play is typically not specified because it's controllable with radial play. Shimming is the preferred method to lower end play to required values. Bearing end plays less than 0.0001 in. are difficult to measure and may result in higher operating torque and shorter life.

Timken Super Precision can use various gages to measure end play of bearings with a controlled end play requirement. As with radial-play gaging, loads are matched to bearing size to prevent excessive deflection.

Information for this article supplied by John Mullett, Jr., product engineer at Timken Super Precision (MPB), Keene, N.H.