Engineering Reference

Miniature & Instrument Ball Bearings

Internal Bearing Geometry

When a ball bearing is running under a load, force is transmitted from one bearing ring to the other through the balls. Since the contact area between each ball and the rings is relatively small, moderate loads can produce stresses of tens, even hundreds of thousands of pounds per square inch. These internal stresses have a significant impact on a bearing's life and performance. The internal geometry of a bearing—its radial play, raceway curvature and contact angle—must be carefully chosen so loads will be distributed for optimal performance.

Radial and Axial Play

Most ball bearings are assembled so that a slight amount of looseness exists between the balls and the raceways. This looseness is referred to as radial play and axial play. Radial play is the maximum distance that one bearing ring can be displaced with respect to the other in a direction perpendicular to the bearing axis when the bearing is in an unmounted state. Axial Play, or end play, is the maximum relative displacement between the two rings of an unmounted ball bearing in a direction parallel to the bearing axis.

Since radial play and axial play are both consequences of the same degree of looseness between the components, they bear a mutual dependence, yet their values are usually quite different in magnitude. Radial play often varies between .0002 and .0020 in, while axial play may range from .001 to .010 in. The suggested radial play ranges for typical applications should always be consulted when a device is in the initial design phase.

In most ball bearing applications, radial play is functionally more critical than axial play. While radial play has become the standard purchasing specification, you may also specify axial play requirements. Keep in mind, however, the values of radial play and axial play for any given bearing design are mathematically interdependent. Radial play is affected by any interference fit between the shaft and bearing I.D. or between the housing and bearing O.D. Since the important condition is the actual radial play remaining after assembly of the complete device, the radial play specification for the bearing must be modified in accordance with the discussion in the mounting and coding section.

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Radial play and axial play.

Standard Radial Play Ranges 

DescriptionRadial Play Range*NHBB Code
Tight.0001 to .0003P13
Normal.0002 to .0005P25
Loose.0005 to .0008P58
Extra loose.0008 to .0011P811

*Measurement in inches.
Non-standard ranges may be specified.

Suggested Radial Play 

Typical ApplicationSuggested Radial Play*
Small precision high speed electric motors.0005 to .0008
Tape guides, belt guides, low speed.0002 to .0005
Tape guides, belt guides, high speed.0005 to .0008
Gyro gimbals, horizontal axis.0002 to .0005
Gyro gimbals, vertical axis.0005 to .0008
Precision gear trains, low speed electric motors, synchros and servos.0002 to .0005
Gyro spin bearings, ultra-high speed turbines and spindlesConsult factory

*Measurement in inches.

Free Angle of Misalignment

As a result of the previously described looseness or play, which is permitted to exist between the components of most ball bearings, the inner ring can be cocked or tilted a small amount with respect to the outer ring. This displacement is called free angle of misalignment. The amount of misalignment allowable in a given ball bearing is determined by its radial play and track curvature values. Misalignment has positive practical significance because it enables a ball bearing to accommodate small dimensional variations that may exist in associated shafts and housings. The performance of a misaligned bearing will be degraded to a certain extent, but for slight misalignments under reasonably light loads, the effects are not significant in most cases. In general, the amount of misalignment a bearing is subject to by the shaft and housing's physical arrangement should never exceed the bearing's free angle of misalignment. Free angle of misalignment is typically less than one degree.

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Free angle of misalignment.

Raceway Curvature

Raceway curvature is the ratio of the raceway radius to ball diameter. Typically, raceway curvature values are either 52 to 54 percent or 57 percent. The lower 52 to 54 percent curvature implies close ball-to-raceway conformity and is useful in applications where heavy loads are encountered. The higher 57 percent curvature is more suitable for torque sensitive applications.

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Raceway curvature.

Contact Angle

Contact angle is the angle between a plane perpendicular to the ball bearing axis and a line joining the two points where the balls make contact with the inner and outer raceways. The initial contact angle of the bearing is directly related to radial play—the higher the radial play, the higher the contact angle-as well as its inner and outer track curvatures. A low contact angle is desirable for pure radial loads; a higher contact angle is recommended when thrust loading is predominant.

The contact angle of thrust loaded bearings provides an indication of ball position inside the raceways. When a thrust load is applied to a ball bearing, the balls move away from the median planes of the raceways and assume positions somewhere between the deepest portions of the raceways and their edges.

The table of contact angles shown below gives nominal values under no load.

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Contact angle.

Table of Contact Angles 

Ball size
Radial Play Code
0.02518°24 1/2°30°
1/32 & 0.8 mm16 1/2°22°27°
1mm14 1/2°20°24°


3/329 1/2°13°15 1/2°
1/812 1/2°17°20°
9/6412°16°19 1/2°
5/3211°15°18 1/2°
3/1610°14°16 1/2°

*The contact angle is given for the mean radial play of the range shown, i.e., for P25 (.0002 to .0005), contact angle is given for .00035.

Formulas for Radial Play, Axial Play and Contact Angle

Radial Play

PD = 2Bd (1 - cos β0)

PD = 2Bd - √((2Bd)2 - P2E)

Axial Play

PE = 2Bd sin β0

PE = √(4BdPD - P2D)

Contact Angle

β0 = cos-1 (2Bd - PD / 2Bd)

β0 = sin-1 PE / 2Bd


PD = Radial play

PE = Axial play

β0 = Contact angle

B = Total curvature = (fi + fo - 1)

fi = Inner ring curvature*

fo = Outer ring curvature*

d = Ball diameter

* Expressed as the ratio of race radius to ball diameter.