Page 58 - needle bearings

Technical Data
NTN

2) Inscribed circle diameter after complete bearing fit
11.3 Calculation Examples in the housing on actual machine
11.3.1 Shrinkage factor and post-installation
clearance of drawn cup needle roller bearing [1] Inscribed circle diameter in press-fitting of master ring
The recommended fit data for the standard bearings is
as described in Table 1 on page B-33. This paragraph
describes hereunder the calculation methods to be used
when the bearing fit conditions are reviewed in detail.
T
1) Calculation of bearing shrinkage factor
For the drawn cup bearings, the shrinkage factor is
calculated using the following method. H D

Fig. 11.5

H ɿHousing inner diameter mm
T ɿRoller diameter + plate thickness mm
D ɿOuter diameter of drawn cup needle roller bearing mm
Li ɿPost press-fit inscribed circle diameter mm
When the master ring is press-fitted, the dimension of
DH de "roller diameter + plate thickness" remains unchanged.
Housing Drawn cup bearing Hence, the inscribed circle diameter Li is determined by
the following formula.
LiʹDʵ2TʵЕʢDʵHʣʹʢ1ʵЕʣDʵ2TʴЕH ʜʜ(11.2)
Determine the mean value of "roller diameter + plate
thickness" (=T) and standard deviation from formula
(11.2). The mean value of formula (11.2) is determined
dnom as follows.
mLiʹʢ1ʵЕʣmDʵm2TʴЕmH ʜʜʜʜʜʜʜʜ(11.3)
Fig. 11.4
Standard deviation of formula (11.2)

1ʵS 2 МLi2ʹʢ1ʵЕʣ2ɾМD2ʴМ2T 2ʴЕ2МH 2 ʜʜʜʜʜ(11.4)
2t
2 ʜʢ11.1ʣ
Еʹɹɾ ʢ0.7S ʴ1.3ʣʢ1ʵt ʣʢ0.7ʴ1.3t ʣʢ1ʵS ʣ In the case of master ring, due to МH 2=0 the formula
2
2
2
E 2 ʴ
E 1 E 2 (11.4) is expressed as follows.
МLi2ʹʢ1ʵЕʣ2ɾМD2ʴМ2T 2 ʜʜʜʜʜʜʜʜʜʜ(11.5)
The unknown values in formulas (11.3), (11.5) are only
Where,
m T and М2T . Hence, substitute the known numerical
2
Е ɿOuter ring shrinkage factor
values for formulas (11.3), (11.5) to determine m2T and
DH ɿHousing outer diameter mm
М2T .
2
dnomɿNominal diameter of fitting portion mm
de ɿRolling surface diameter of outer ring mm
[2] Even when bearing ring is press-fitted in the housing
E ɿ Modulus of housing vertical elasticity
on actual machine, consider the inscribed circle
2
(Young’s modulus) MPa (kgfʗmm )
diameter similarly to the master ring press-fit.
E ɿModulus of outer ring vertical elasticity
Herein, the calculation formulas for press-fit in the
(Young’s modulus)
6
2
2.07ʷ10 MPa (21 200kgfʗmm ) housing on actual machine can be discriminated as
follows from formula (11.3), (11.4) by adding " " to
each formula.
dnom
S ʹʕʕʕ
DH mLi ʹʢ1ʵЕ ʣmDʵm2TʴЕ mH ʜʜʜʜʜʜʜ(11.6)
МLi 2ʹʢ1ʵЕ ʣ2ɾМD2ʴМ2T 2ʴЕ 2МH 2 ʜʜʜʜ(11.7)
de
t ʹʕʕʕ [3] For m2T and М2T in formula (11.6), (11.7), substitute
2
dnom
the values determined previously for the respective
formula.
[4] From the calculations, the inscribed circle diameter in
press-fitting in the housing on actual machine can be
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