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Koyo Technical Information

6 .Fits

• Purpose and selection
• Load characteristics
• Load magnitude
• Surface roughness
• Temperature
• Maximum stress of bearing

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 pattern	Direction of load	Loading conditions	Fit		Typical 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)
Indeterminate	Rotating or stationary	Indeterminate direction load	Interference fit	Interference fit	Cranks

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 F_r≤0.25C_o)

(In the case of F_r>0.25C_o)

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)

Δd_effΔd d/(d+2)

(In the case of a turned shaft)

Δd_effΔd d/(d+3)

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)Δtαd
		0.0015Δtd×10-3

where :
Δdt:	reduction of interference due to temperature difference	mm
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 bearing	mm

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 ring	Housing 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 stress	MPa
d:	nominal bore diameter of inner ring(shaft diameter)	mm
Di:	raceway contact diameter of inner ring	mm
	for ball bearingDi0.2(D+4d )
	for roller bearingDi0.25(D+3d )
Δdeff:	effective interference of inner ring	mm
do:	bore diameter of hollow shaft	mm
De:	raceway contact diameter of outer ring	mm
	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 ring	mm
Dh:	outside diameter of housing	mm
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.