Gamet BearingsExclusive North American distributor for Gamet Bearing.

Koyo Technical Information

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.

Radial internal clearance

Radial internal clearance


Axial internal clearance

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

Double-row angular contact ball bearings

  • Matched pair angular contact ball bearings

Matched pair angular contact ball bearings

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

Double/four-row and matched pair tapered roller bearings

where:
Δ a: axial internal clearancemm
Δ r: radial internal clearancemm
α:: nominal contact angle
e: limit value of Fa/Fr (shown in the bearing specification table.)
mo=re+ri –Dw
re: outer ring raceway groove radiusmm
r i: inner ring raceway groove radiusmm
Dw: ball diametermm

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

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)+Swasteriskasterisk 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≠∞)
Operating clearanceOperating clearance
(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 · tiDe · 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=tite
Temperature differential between the rolling element and outer ring, t2, can be expressed as follows:
t2=twte

Decrease of clearance due to temperature rise of rolling element (St2)St2=2α · Dw · tw

 

S: operating clearancemm
So: clearance before mountingmm
Sf: decrease of clearance due to fittingmm
Sfi: expansion of inner ring raceway contact diametermm
Sfo: contraction of outer ring raceway contact diametermm
St1: decrease of clearance due to temperature differentials between inner and outer ringsmm
St2: decrease of clearance due to temperature rise of the rolling elementsmm
Sw: increase of clearance due to loadmm
Δdeff: effective interference of inner ringmm
d: nominal inner ring bore diameter(shaft diameter)mm
do: bore diameter of hollow shaftmm
Di: inner ring raceway contact diametermm
ball bearingDi0.2(D+4d)
roller bearingDi0.25(D+3d)
ΔDeff: effective interference of outer ringmm
Dh: outside diameter of housingmm
De: outer ring raceway contact diametermm
ball bearingDe0.2(4D+d)
roller bearingDe0.25(3D+d)
D: nominal outer ring outside diametermm
α: linear expansion coefficient of bearing steel(12.5X10-6)1/K
Dw: average diameter of rolling elementsmm
ball bearingDw0.3(Dd)
roller bearingDw0.25(Dd)
ti: temperature rise of the inner ringK
te:temperature rise of the outer ringK
tw: temperature rise of rolling elementsK
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

Nominal bore diameter
d, mm
Contact angle: 15°Contact angle: 30°Contact angle: 40°
C2CNC2CNC3C4C2CNC3C4
overup tomin.max.min.max.min.max.min.max.min.max.min.max.min.max.min.max.min.max.min.max.

10
18
10
18
24
13
15
20
33
35
40
33
35
45
53
55
65
3
3
3
14
16
20
10
10
20
30
30
40
30
30
40
50
50
60
50
50
60
70
70
80
2
2
2
10
12
12
6
7
12
18
21
26
16
18
20
30
32
40
26
28
30
40
44
50
24
30
40
30
40
50
20
20
20
40
40
40
45
45
50
65
65
70
3
3
3
20
20
20
20
25
30
40
45
50
40
45
50
60
65
70
60
70
75
80
90
95
2
2
2
14
14
14
12
12
12
26
26
30
20
25
30
40
45
50
40
45
50
60
65
70
50
65
80
65
80
100
30
30
35
55
55
60
65
70
85
90
95
110
9
10
10
27
28
30
35
40
50
60
65
75
60
70
80
85
95
105
90
110
130
115
135
155
5
6
6
17
18
20
17
18
20
35
40
45
35
40
55
60
65
80
60
70
85
85
95
110
100
120
140
120
140
160
40
45
45
65
75
75
100
110
125
125
140
155
12
15
15
37
40
40
65
75
80
90
105
110
100
120
130
125
150
160
150
180
210
175
210
240
6
7
7
25
30
30
25
30
35
50
60
65
60
75
85
85
105
115
100
125
140
125
155
170
160
180
180
200
50
50
80
80
140
160
170
190
15
20
45
50
95
110
125
140
140
170
170
200
235
275
265
305
7
7
31
37
45
60
75
90
100
110
130
140
155
170
185
200

[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

Nominal bore diameter
d, mm
Clearance
CD2CDNCD3
overup tomin.max.min.max.min.max.
2.5
10
18
10
18
24
0
0
0
7
7
8
2
2
2
10
11
11
8
9
10
18
19
21
24
30
40
30
40
50
0
0
0
8
9
10
2
3
4
13
14
16
10
11
13
23
24
27
50
65
80
65
80
100
0
0
0
11
12
12
6
7
8
20
22
24
15
18
22
30
33
38
100
120
140
120
140
160
0
0
0
13
15
16
9
10
11
25
26
28
24
25
26
42
44
46
160
180
180
200
0
0
17
18
12
14
30
32
27
28
47
48