Page 39 - needle bearings

Bearing Fits
NTN

Where,
6.5 Interference Calculation ϶dT : Required effective interference for temperature
(1) Load and required interference difference Жm
When radial load acts on a bearing, the interference ϶T : Difference between bearing temperature and
required to prevent a clearance between its inner ring and ambient temperature ˚C
a steel solid shaft can be expressed in formulas (6.1) d : Bearing bore diameter mm
and (6.2).
(3) Fitting surface roughness and required
For Frʽ0.3 Cor, interference
The fitting surface is smoothed (surface roughness is
made less) by bearing fits so that the interference
dɾFr dɾFr
ʕʕʕʕ
ʕʕʕʕ
0.25
϶dFʹ0.08 ˽ʉʉʉ ʢ ˽ʉʉʉ ʣ ʜʜʜʜʜʜ(6.1) reduces correspondingly. The interference reduced value
B B
differs depending on the fitting surface roughness and
For Frʼ0.3 Cor, generally the following reduction values must be
prospected.
ʣ
ʢ
Fr
Fr
϶dFʹ0.02ʕʕ 0.2ʕʕ ʜʜʜʜʜʜʜʜʜʜʜʜ(6.2) For ground shafts : 1.0 to 2.5mm
B B For lathe-turned shafts : 5.0 to 7.0 mm
Where, (4) Maximum interference
϶dF : Required effective interference mm Bearing ring fitted, with interference, on a shaft or in a
d : Bearing bore diameter mm housing results in tensile stress or compressive stress.
B : Inner ring width mm Over-interference could cause cracking /splitting of
Fr : Radial load N (kgf) bearing and short fatigue life of bearing. Therefore, in
C0r : Basic static load rating N (kgf) general the maximum interference is secured at 1/1000
and less of shaft diameter or otherwise it is secured so
(2) Temperature rise and required interference the circumferential maximum stress generating on the
When temperature rise of bearing (difference between fitting surface comes to 130MPa or less. (See Table 6.4)
bearing temperature and ambient temperature) is
inevitable incurred by bearing running, the interference (5) Stress and deformation caused by interference
required to prevent a clearance between the inner ring When bearing ring (solid) is fitted with interference, it
and a steel shaft can be expressed in formula (6.3). deforms elastically and this elastic deformation results in
stress.(See Fig.6.2) The fitting surface pressure of
϶dFʹ0.0015ɾdɾ϶Tʜʜʜʜʜʜʜʜʜʜʜʜʜʜ(6.3) bearing ring, circumferential tensile stress (inner ring),
compressive stress (outer ring) and radial expansion of
raceway (inner ring), and shrinkage(outer ring) can be
calculated from Table 6.4.
Table 6.4 Deformation and stress caused by bearing fit
Item Inner ring Outer ring
Surface E ϶deff ʢ1ʵk ʣʢ1ʵk0 ʣ E ϶Deff ʢ1ʵh ʣʢ ʵh0 ʣ
2
2
2
2
pressure piʹʕʕ ʕʕʕʕ ʕʕʕʕʕʕʕʕʕʕ peʹʕʕ ʕʕʕʕ ʕʕʕʕʕʕʕʕʕʕʕ ϶
2
2
pɹMPa 2 d 1ʵk k0 2 2 D 1ʵh h0 2 М
Circumferential 1ʴk 2 2
maximum stress Мiʹpi ʕʕʕʕ (Tensile stress) Мeʹpe ʕʕʕʕ (Compressive stress)
МɹMPa 1ʵk 2 1ʵh 2 p
Radial elastic 2 2
1ʵh0
1ʵk0
deformation of ϶iʹ϶deffɾk ʕʕʕʕʕ (Expansion) ϶eʹ϶Deffɾh ʕʕʕʕʕ (Shrinkage)
2
2
raceway ϶ 1ʵk k0 2 1ʵh h0 2
Where,ɹ Remarks (Symbol representation)
ɹd ɿInner ring bore diameter (shaft diameter) mm
d d0 De D
kʹʕʕɼk0ʹʕʕɼhʹʕʕɼh0ʹʕʕ ɹd0 ɿ Hollowed shaft bore diameter
di d D D0
ɹ ɹ(For solid shaft, d0ʹ0) mm
ɹdi ɿInner ring raceway diameter mm
ɹ϶deff ɿEffective interference for inner ring mm
ɹD ɿOuter ring outer diameter
ɹ (housing hole diameter) mm Fig.6.2
ɹD0 ɿ Housing outer diameter
ɹ (For sufficient housing size, D0ʹʿ) mm
ɹDe ɿOuter ring raceway diameter mm
ɹ϶Deff ɿEffective interference for outer ring mm
ɹE ɿModulus of elasticity (Young factor)
6
ɹ ɹ2.07ʷ10 (21200)
ɹ MPa (kgf/mm ) 2
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