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Koyo Technical Information

7. Internal clearance

• Internal clearance of bearing
• Operating clearance
• Clearance specifications
• Recommended internal clearance

a. Internal clearance of bearing

1) Radial internal clearance and axial internal clearance
A bearing’s inner ring or outer ring is movable even if the other ring is fastened. The amount of movement the ring can make is called clearance.
The amount of radial movement the ring can make is called radial internal clearance, while that of axial movement the ring can make is called axial internal clearance.

Relationship between radial internal clearance and axial internal clearance

Regarding deep groove ball bearings and matched pair and double-row angular contact ball bearings, equations of the relationship between radial internal clearance and axial internal clearance are shown as follows.

• Deep groove ball bearings

• Double-row angular contact ball bearings

• Matched pair angular contact ball bearings

• Double/four-row and matched pair tapered roller bearings

2) Measured clearance
Bearing internal clearance is measured under a specific amount of loading, exerted to obtain reliable measurements. The measured clearance may be slightly greater than real clearance due to elastic deformation caused by the load. In case of roller bearings, however, the deformation is so small as to be ignorable.

3) Initial clearance
The internal clearance of the bearing is provided with at the time of shipment is called initial clearance. It is specified in the Table of Clearance Specifications.

4) Residual clearance
When the bearing is mounted on the shaft or housing by interference fit, the bearing ring expands or contracts, making the internal clearance smaller. This smaller clearance is called “residual clearance” or “residual clearance after mounting”.

5) Effective clearance, operating clearance
Bearing temperature rises during operation, causing thermal expansion and making the clearance smaller. The reduced clearance is called effective internal clearance.
The clearance obtained by taking into account elastic deformation due to loads is called “operating clearance” or “residual clearance during operation.”

6) Selection of initial clearance
The value of the internal clearance may have a great impact on the bearing during operation, with regard to such aspects as bearing fatigue life, heating and noise.
As Fig. 7-1 shows, bearing service life is longest when the operating clearance is slightly negative. However, when the operating clearance is negative beyond a specific extent, bearing service life is extremely short. The initial clearance should therefore be determined such that the operating clearance will be slightly positive. The dispersion of permissible values should also be considered.

Fig. 7-1 Relationship between operating clearance and fatigue life

b. Operating clearance

The operating clearance can be calculated as specified below.
To calculate the operating clearance for actual applications, use the Menu entitled Clearance Calculation.

Operating clearance (S)	S=So-(Sf+St1+St2)+Sw	Sw (increase of clearance due to load) is generally small, and thus may ignored, although there is an equation for determining the value.
Decrease of clearance due to fitting (Sf)	(In the case of hollow shaft) (In the case of Dh≠∞) (In the case of solid shaft) (In the case of Dh=∞)
Decrease of clearance due to temperature differentials between inner and outer rings (St1)	The amount of decrease varies depending on the state of housing; however, generally the amount can be approximated by the following equation on the assumption that the outer ring will not expand: St1=α(Di · ti–De · te)	where: De=Di+2Dw Consequently, St1+St2 will be determined by the following equation: St1+St2=α · Di · t1+2α · Dw · t2 Temperature differential between the inner and outer rings, t1, can be expressed as follows: t1=ti–te Temperature differential between the rolling element and outer ring, t2, can be expressed as follows: t2=tw–te
Decrease of clearance due to temperature rise of rolling element (St2)	St2=2α · Dw · tw

S	: operating clearance	mm
So	: clearance before mounting	mm
Sf	: decrease of clearance due to fitting	mm
Sfi	: expansion of inner ring raceway contact diameter	mm
Sfo	: contraction of outer ring raceway contact diameter	mm
St1	: decrease of clearance due to temperature differentials between inner and outer rings	mm
St2	: decrease of clearance due to temperature rise of the rolling elements	mm
Sw	: increase of clearance due to load	mm
Δdeff	: effective interference of inner ring	mm
d	: nominal inner ring bore diameter(shaft diameter)	mm
do	: bore diameter of hollow shaft	mm
Di	: inner ring raceway contact diameter	mm
	ball bearingDi0.2(D+4d) roller bearingDi0.25(D+3d)
ΔDeff	: effective interference of outer ring	mm
Dh	: outside diameter of housing	mm
De	: outer ring raceway contact diameter	mm
	ball bearingDe0.2(4D+d) roller bearingDe0.25(3D+d)
D	: nominal outer ring outside diameter	mm
α	: linear expansion coefficient of bearing steel(12.5X10-6)	1/K
Dw	: average diameter of rolling elements	mm
	ball bearingDw0.3(D–d) roller bearingDw0.25(D–d)
ti	: temperature rise of the inner ring	K
te	:temperature rise of the outer ring	K
tw	: temperature rise of rolling elements	K

c. Clearance specifications

1) Mathched pair angular contact ball bearings

Table 7-3 Axial internal clearance of matched pair angular contact ball bearings (measurement clearance)  ¹⁾ 

Unit: µm

[Note] 1) Including increase of clearance caused by measurement load.

2) Double-row angular contact ball bearings

Table 7-4 Radial internal clearance of double row angular contact ball bearings

Unit: µm

d. Recommended internal clearance

Standard values for bearing internal clearance are generally described as CN clearance.
Table 7-9 shows examples of clearance selection excluding CN clearance.

Table 7-9 Examples of non-standard clearance selection