Gamet BearingsExclusive North American distributor for Gamet Bearing.

Koyo Technical Information

a. Purpose and selection

The purpose of fit is to prevent harmful sliding between two mating bodies, by securely fastening a bearing ring, which rotates under loads, on the shaft or housing.

This harmful sliding is called creep. It may induce excessive heating, wear in the contact area of the mating surfaces, ingress of wear debris into the bearing, vibration, and other unwanted phenomena.

To determine what class of fit is optimal, examine the following:
1) The characteristics and sizes of loads
2) Temperature distribution during rotation
3) Bearing internal clearance
4) The material, finishing, and strength of the shaft and housing
5) Mounting and dismounting methods
6) Whether shaft thermal expansion needs to be accommodated between the mating surfaces of the fit
7) Bearing type and dimensions

b. Load characteristics

To prevent creeping, interference fit is used on the ring that is rotated. The table below shows the possible load combinations along with the classes of fit that is suitable for the individual combinations.

Rotation patternDirection of loadLoading conditionsFitTypical application
Inner ring &
shaft
Outer ring &
housing

Inner ring : rotating
Outer ring : stationary

Stationary
Rotating inner ring load
Stationary outer ring load
Interference fit necessary
(k, m, n, p, r)
Clearance fit acceptable
(F, G, H, JS)
Spur gear boxes,
motors

Inner ring: stationary
Outer ring: rotating

Rotating with outer ring
Greatly unbalanced wheels

Inner ring: stationary
Outer ring: rotating

Stationary
Stationary inner ring load
Rotating outer ring load
Clearance fit acceptable
(f, g, h, js)
Interference fit necessary
(K, M, N, P)
Running wheels& pulleys with stationary
shaft

Inner ring: rotating
Outer ring: stationary

Rotating with inner ring
Shaker screens unbalanced vibration)
IndeterminateRotating or stationaryIndeterminate direction loadInterference fitInterference fitCranks
c. Load magnitude

The inner ring contracts in the radial direction due to radial loads, while it expands in the circumferential direction. The interference at the time of assembly may, therefore, slightly decrease.

The decrease in the interference can be calculated by the following equations:


(In the case of Fr≤0.25Co)

(In the case of Fr>0.25Co)


where:
ΔdF:reduction of inner ring interferencemm
d:bore diameter of bearingmm
B:inner ring widthmm
Fr:radial loadN
Co:basic static load ratingN
d. Surface roughness

The effective interference obtained after fitting differs from calculated interference due to plastic deformation of the ring-fitting surface. When the inner ring is fitted, the effective interference, subject to the effect of the fitting surface finish, can be approximated by the following equations:


(In the case of a ground shaft)

ΔdeffΔd Small dotd/(d+2)

(In the case of a turned shaft)

ΔdeffΔd Small dotd/(d+3)


where:
Δdeff: effective interference mm
Δd: calculated interference mm
d: bore diameter of bearing mm
e. Temperature

The inner ring of a bearing rotating under loads may be heated beyond the temperature of the shaft. The thermal expansion of the ring may reduce effective interference.

Experiments have proved that the difference in temperature between the shaft and inner ring is equivalent to 10% to 15% of that between the inside bearing and housing periphery. The reduction in the interference due to the thermal expansion can be, therefore, calculated by the following equation:


Δdt=(0.10 to 0.15)ΔtSmall dotαSmall dotd
0.0015ΔtSmall dotd×10-3

where :
Δdt:reduction of interference due to temperature differencemm
Δt:temperature difference between the inside of the bearing and
the surrounding housing
K
α:linear expansion coefficient of bearing steel (12.5×10-6)1/K
d:bore diameter of bearingmm
f. Maximum stress of bearing

When a bearing ring is assembled with interference fit, a stress may be occurred as the ring expands or contracts.
If the stress is excessively large, the ring may break down.
If the ring is made from bearing steel, it is safe if the stress can be controlled at 120 MPa or less.
The maximum possible stress can be estimated by the following equations:

Maximum fitting – generated stress in bearings

 

Shaft and inner ringHousing bore and outer ring
(In the case of hollow shaft)
(In the case of Dh≠∞)
(In the case of solid shaft)
(In the case of Dh=∞)

 

where :
:maximum stressMPa
d:nominal bore diameter of inner ring(shaft diameter)mm
Di:raceway contact diameter of inner ringmm
for ball bearingDi0.2(D+4d )
for roller bearingDi0.25(D+3d )
Δdeff:effective interference of inner ringmm
do: bore diameter of hollow shaftmm
De:raceway contact diameter of outer ringmm
for ball bearingDe0.2(4D+d )
for roller bearingDe0.25(3D+d )
D:nominal outside diameter of outer ring
(bore diameter of housing)
mm
ΔDeff:effective interference of outer ringmm
Dh:outside diameter of housingmm
E:young’s modulus  2.08×105 MPa

[Remark] The above equations are applicable when the shaft and housing are steel. When other materials are used, Koyo should be consulted.