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IS0
INTERNATIONAL OR GAN I ZATl O N FOR ÇTAN DARD IZATl O N
IS0 RECOMMENDATION
R 281
ROLLING BEARINGS
METHODS OF EVALUATING DYNAMIC LOAD RATINGS
,
1st EDITION
November 1962
COPYRIGHT RESERVED
The copyright of IS0 Recommendations and IS0 Standards
belongs to IS0 Member Bodies. Reproduction of these
documents, in any country, may be authorized therefore only
by the national standards organization of that country, being
of ISO.
a member
For each individual country the only valid standard is the national standard of that country.
Printed in Switzerland
Also issued in French and Russian. Copies to be obtained through the national standards organizations.
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BRIEF HISTORY
The IS0 Recommendation R 281, Rolling Bearings-Methods of Evaluating Dynamic Load Rat-
ings, was drawn up by Technical Committee ISO/TC 4, Ball and Roller Bearings, the Secretariat
of which is held by the Sveriges Standardiseringskommission (SIS).
Work, on this question by the Technical Committee began in 1952 and led, in 1959, to the
adoption of a Draft IS0 Recommendation.
IS0 Recommendation (No. 278) was circulated to all the IS0
In December 1959, this Draft
Member Bodies for enquiry. It was approved by the following Member Bodies:
Austria France Poland
Belgium India
Portugal
Burma Italy Romania
Chile Japan Spain
Colombia Netherlands Sweden
Czechoslovakia New Zealand Switzerland
Finland Pakistan U.S.A.
Yugoslavia
Four Member Bodies opposed the approval of the Draft:
Germany, Hungary, United Kingdom, U.S.S.R.
The Draft IS0 Recommendation was then submitted by correspondence to the IS0 Council,
which decided, in November 1962, to accept it as an IS0 RECOMMENDATION.
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IÇOIR 281 - 1962 (E)
IS0 Recommendation R 281 November 1962
ROLLING BEARINGS
METHODS OF EVALUATING DYNAMIC LOAD RATINGS
I NT RO D U CTO RY NOTE
This IS0 Recommendation covers methods of evaluating dynamic load ratings for
Radial ball bearings . see section 1, page 3,
Radial roller bearings . see section 2, page 8,
Thrust ball bearings . see section 3, page 11,
Thrust roller bearings . see section 4, page 14,
giving for each part the following items:
Definitions,
Calculation of basic load rating,
Calculation of rating life,
Calculation of equivalent load.
It is recognized that revisions of the calculations may be required from time to time as
the result of improvements or new developments.
METHOD OF EVALUATING DYNAMIC LOAD RATINGS
1.
OF RADIAL BALL BEARINGS
1.1 Definitions
1.1.1 The Zife of an individual ball bearing is defined as the number of revolutions (or hours at
some given constant speed) which the bearing runs before the first evidence of fatigue
develops in the material of one of the rings or any of the rolling elements.
1.1.2 The rating life of a group of apparently identical ball bearings is defined as the number
of revolutions (or hours at some given constant speed) that 90 per cent of that group of
bearings will complete or exceed before the first evidence of fatigue develops.
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ISOIR 281 - 1962 (E)
1 .I .3 The basic load rating is that constant stationary radial load which a group of apparently
identical ball bearings with stationary outer ring can endure for a rating life of one
million revolutions of the inner ring. In single-row angular-contact ball bearings, the
basic load rating relates to the radial component of that load, which causes a purely
radial displacement of the bearing rings in relation to each other.
1.1.3.1 Load ratings, if given for specific speeds, should be based on a rating life of 500 hours.
1 .I .4 The equivalent load is defined as that constant stationary radial load which, if applied to
a bearing with rotating inner ring and stationary outer ring, would give the same life as
that which the bearing will attain under the actual conditions of load and rotation.
1.2 Calculation of basic load rating
The magnitude of the basic load rating C for radial- and angular-contact ball bearings, except
filling-slot bearings, is given by the following formulae :
(a) with balls of diameter not larger than 25.4 mm or 1 in:
C =fc (i cos ~t)'.~ Z2/3 DI.'
(b) with balls of diameter larger than 25.4 mm, when kilogramme and millimetre units are
used :
C = fc (i COS Z2/3 X 3.647
(c) with balls of dianieter larger than 1 in, when pound and inch units are used:
C = fc (i cos tc)0.7 Z2/3 D'.4
where i = number of rows of balls in any one bearing,
tc = nominal angle of contact = nominal angle between the line of action of the ball
load and a plane perpendicular to the bearing axis,
Z = number of balls per row,
D = ball diameter,
fc = factor which depends on the units used, the geometry of the bearing components,
the accuracy to which the various bearing parts are made and the material.
Values off, are obtained by multiplying
f,
the values of ~ , from the appropriate column of Table 1,
f
by a factorf, covered in the note below.
NOTE. - Current tests of ball bearings of good quality, hardened ball-bearing stec., indicate
that the value of the factorfis:
10 when kilogramme and millimetre units are used,
f =
f = 7450 when pound and inch units are used.
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IÇOIR 281 - 1962 (E)
fc
TABLE 1. - Factor -
f
Dcos U *
for single-row, radial- I for single-row,
___
for double-row,
~ radial-contact,
contact, groove ball
dm
bearings and single- and radial-contact, for self-aligning separable ball
groove ball ball bearings
bearings
double-row, angular-contact,
bearings**
groove ball bearings ** (magneto bearings)
I
0.05 0.476 0.451 O. 176 0.165
0.06 0.500 0.474 0.190 0.177
0.203 I 0.189
0.07 0.521 0.494
0.21 5 0.199
0.08 0.539 0.51 1
0.09 0.524 0.227 I 0.210
0.554
0.10 0.566 0.537 0.238 0.219
0.12 0.586 0.555 0.261 0.239
0.258
0.14 0.600 0.568 0.282
0.608 0.276
0.16 0.576 0.303
0.61 1 0.294
0.18 0.579 0.323
0.20 0.61 1 0.579 0.342 0.311
~
0.22 0.608 0.576 0.359 0.327
0.24 0.375 0.343
0.26 0.593 0.562 0.390 I 0.358
0.402 I 0.372
0.28 0.583 0.552
l
0.41 1 l
0.541 0.386
0.30 0.571
0.32 0.558 0.530 0.418 0.397
0.34 O. 543 0.515 0.420 0.406
0.36 0.527 0.500 0.421 0.412
5
0.38 0.510 0.484 0.418 0.41
0.492 0.412 0.4 17
0.40 0.467
* dm = pitch diameter of the ball set.
Dcos ci fc .
For values of -- ----~, other than given inTable 1, ~ is obtained by linear interpolation.
dm f
** (U) When calculating the basic load rating for a unit consisting of two similar single-row radial-contact ball bearings
in a duplex mounting, the unit is considered as one double-row radial-contact ball bearing.
(b) When calculating the basic load rating for a unit consisting of two similar single-row angular-contact ball bearings
or “back-to-back”, the unit is considered as one double-row angular-
in a duplex mounting, “face-to-face”
contact ball bearing.
(c) When calculating the basic load rating for a unit consisting of two or more similar single-row angular-contact
ball bearings mounted “in tandem”, properly manufactured and mounted for equal load distribution, the rating
of the unit is the number of bearings to the 0.7 power times the load rating of a single-row ball bearing.
If for some technical reason the unit may be treated as a number of individually interchangeable single-row bear-
ings, this paragraph (c) does not apply.
f.
The values of factor ~~ given in Table 1 apply to bearings whose ring raceways have a cross-
f
sectional radius not larger than,
52 per cent of the
in radial contact and angular contact groove ball bearing inner rings,
bail diameter
in radial contact and angular contact groove ball bearing outer rings, 53 per cent of the
ball diameter
in self-aligning ball bearing inner rings, 53 per cent of the
bail diameter.
The basic load rating is not necessarily increased by the use of smaller groove radii, but is reduced
by the use of larger radii than those given above.
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ISOIR 281 - 1962 (E)
1.3 Calculation of rating life
The approximate magnitude of the rating life L for ball bearings, except filling-slot bearings,
is given by the formula :
million revolutions
where P = equivalent load.
1.4 Calculation of equivalent load
The magnitude of the equivalent load P for radial- and angular-contact ball bearings of con-
ventional type, except filling-slot bearings, under combined constant radial and constant
thrust loads, is given by the formula:
P = XVF, +YFa
where X = radial factor,
V = rotation factor,
Y = thrust factor,
F, = radial load,
Fa = thrust load.
Values of factors V, X and Y are given in Table 2, page 7.
FOOT-NOTES OF TABLE 2 (PAGE 7):
(1) Co is the static basic load rating.
(2) Values of X, Y and e for a load or a contact angle, other th n shown in Table 2, are obtained by linear interpolation.
Fa
(3) For single-row bearings, when--- < e, use X = 1 and Y = O.
YFr =
(a) When calculating the equivalent load for a unit consisting of two similar single-row angular-contact ball bearings
in a duplex mounting, “face-to-face” or “back-to-back”, the unit is considered as one double-row angular-contact
ball bearing.
(b) When calculating the equivalent load for a unit consisting of two or more single-row radial- or angular-contact
ball bearings mounted “in tandem”, the Xand Yvalues for single-row ball bearings are used. Attention is called to
footnote * * (c) under Table 1.
(4) Double-row bearings are presumed to be symmetrical.
(5) Permissible maximum value of adepends on the bearing design.
Co
(6) Because experimental data are incomplete, no correct value of factor V for radial and angular contact groove ball
bearings with inner ring stationary in relation to the load can be stated. The values shown in the Table are, however,
well on the safe side.
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ISO/R 281 - 1962 (E)
TABLE 2. - Factors V, X and Y
_.
-
V
-~~
Fa
~-
Fa f, in relation
~~ -~
ZD2 for double-
or single-
iFa
to the load,
Fa
Z D2
units row
-
row
Bearing
the inner
units
sed: bearings(4)
CO earings(3) e
ring is
type
used :
ound!
(9
ounds and
and
I
inches
when 1 when 1 when
nches
otat- ~ statior
Fa /Fa ka ,
VFT> e IVF~~~~VF,
ing I
- -
-
Non-filling- 25 2.30 I 1 2.30 0.19
1.014
slot 1.028 50 1.99 I 1.99 0.22
1.71 1 1.71 0.26
assembly, 1.056 1 O0
0.28
radial- 1.084 150 1 1.2 0.56 1 ' 0.56 1.55 O
i ;::;
1.45 0.30
contact, 1.11 200
groove ball 1.17 300 1.31 1.31 0.34
P)
500 1.15 1.15 0.38
bearings(5) 1.28
1.42 750 1 .O4 i 1.04 0.42
1 .O0 1 .O0 0.44
1.56 O00
--
-
For this For this 2.78 ' 3.74 0.23
0.014 25
0.26
0.028 50 type, use 2.40 1 3.23
me, use
the X, Y the X, Y 2.07 2.78 0.30
0.056 I O0
0.085 150 and and 1.87 2.52 0.34
e values e values 1.75 2.36 0.36
0.1 1 200
h=5" 0.17 300 1.2 pplicable 10.78 pplicable 1.58 2.13 0.40
O single- .O single- 1.39 1.87 0.45
0.28 500
0.42 750 row, row, 1.26 1.69 0.50
(9
m-filling on-filling 1.21 1.63 0.52
0.56 1 O00
slot slot
ssembly, issembly,
radial- radial-
contact, contact,
groove groove
ball
hgu- ball
lar- bearings bearings
~~ ~ ~ -~ ~
con-
0.29
tact 0.014 25 2.18 3.06
1.98 2.78 0.32
Sroovf 0.029 50
ball 0.057 1 O0 1.76 2.47 0.36
1.63 2.29 0.38
bear- 0.086 150
0.40
ings x=10 0.11 200 1 ' 1.2 0.46 I .55 2.18
1.42 2.00 0.44
0.17 300
(5)
0.29 500 1.27 1.79 0.49
~ (9
1.17 1.64 0.54
0.43 750
0.54
0.57 1 O00 1.16 1.63
~~
~ __ ~ ~~
0.38
0.01 5 25 1.47 1.65 2.39
0.029 1.40 1.57 2.28 0.40
50
0.43
0.058 1 O0 1.30 1.46 2.11
1.23 1.38 2.00 0.46
0.087 150
%=I5 0.12 200 0.44 0.72 1.19 1.34 1.93 0.47
1.12 1.26 1.82 0.50
0.17 300
0.55
0.29 500 1 .O2 1.14 1.66
1 .O0 1.12 1.63 0.56
0.44 750
0.58 1 O00 1 .O0 1.12 1.63 0.56
__ - __ ~ -~ -~
0.57
r=20 1 1.2 0.43 1 .O0 1 .O9 1.63
0.87 0.92 1.41 0.68
r=25 1 1.2 0.41
0.80
%=30 1 1.2 0.39 0.76 0.78 1.24
1.2 0.66 0.66 1 .O7 0.95
a=35 1 0.37
1.14
U =40 1.2 0.35 0.57 0.55 0.93
1
- -
Self-aligning 0.40 I 0.65 0.4cot a 0.42 0.65
cot a cot
ball bearings
-
Single-row
radial-contact
2.5 0.2
separable 0.5
ball bearings
(magneto
bearings)
- -- -
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ISOlR 281 - 1962 (E)
2. METHOD OF EVALUATING DYNAMIC LOAD RATINGS
OF RADIAL ROLLER BEARINGS
2.1 Definitions
2.1.1 The life of an individual roller bearing is defined as the number of revolutions (or hours
at some given constant speed) which the bearing runs before the first evidence of fatigue
develops in the material of one of the rings or any of the rolling elements.
2.1.2 The rating life of a group of apparently identical roller bearings is defined as the number
of revolutions (or hours at some given constant speed) that 90 per cent of that group of
bearings will complete or exceed before the first evidence of fatigue develops.
2.1.3 The basic load rating is that constant stationary radial load which a group of apparently
identical roller bearings with stationary outer ring can endure for a rating life of one
million revolutions of the inner ring. In single-row angular-contact roller bearings the
basic load rating relates to the radial component of that load, which causes a purely
radial displacement of the bearing rings in relation to each other.
2.1.3.1 Load ratings, if given for specific speeds, should be based on a rating life of 500 hours.
2.1.4 The equivalent load is defined as that constant stationary radial load which, if applied to
a bearing with rotating inner ring and stationary outer ring, would give the same life as
that which the bearing will attain under the actual conditions of load and rotation.
2.2 Calculation of basic load rating
The magnitude of the basic load rating C for radial roller bearings is given by the formula :
C = fc (iIeff cos u)’/9 z3/4 oZ9/27
where i = number of rows of rollers in any one bearing,
M = nominal angle of contact = nominal angle between the line of action of the
roller resultant load and a plane perpendicular to the bearing axis,
2 = number of rollers per row,
D = roller diameter (mean diameter of tapered rollers),
Zeff = effective length of contact between one roller and that ring where the contact
is the shortest (overall roller length minus roller chamfers, or minus grinding
undercuts),
SC = factor which depends on the units used, the exact geometrical shape of the
load-carrying surfaces of the rollers and rings, the accuracy to which the various
bearing parts are made and the material.
Values off, are obtained by multiplying
...