|
SIST-TP ISO/TR 1281-2:2009
01-junij-2009
.RWDOQLOHåDML3RMDVQLORNVWDQGDUGX,62GHO 0RGLILFLUDQDGREDWUDMDQMD
L]UDþXQDQDQDRVQRYLXWUXMHQRVWQLKQDSHWRVWL
Rolling bearings - Explanatory notes on ISO 281 - Part 2: Modified rating life calculation,
based on a systems approach to fatigue stresses
Wälzlager - Erläuternde Anmerkungen zur ISO 281 - Teil 2: Berechnung der erweiterten
modifizierten Lebensdauer, basierend auf dem Ansatz der Ermüdungsspannung
Roulements - Notes explicatives sur l'ISO 281 - Partie 2: Calcul modifié de la durée
nominale de base fondé sur une approche système du travail de fatigue
Ta slovenski standard je istoveten z: ISO/TR 1281-2:2008
ICS:
21.100.20 Kotalni ležaji Rolling bearings
SIST-TP ISO/TR 1281-2:2009 en
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.
---------------------- Page: 1 ----------------------
SIST-TP ISO/TR 1281-2:2009
---------------------- Page: 2 ----------------------
SIST-TP ISO/TR 1281-2:2009
TECHNICAL ISO/TR
REPORT 1281-2
First edition
2008-12-01
Rolling bearings — Explanatory notes on
ISO 281 —
Part 2:
Modified rating life calculation, based on
a systems approach to fatigue stresses
Roulements — Notes explicatives sur l'ISO 281 —
Partie 2: Calcul modifié de la durée nominale de base fondé sur une
approche système du travail de fatigue
Reference number
ISO/TR 1281-2:2008(E)
©
ISO 2008
---------------------- Page: 3 ----------------------
SIST-TP ISO/TR 1281-2:2009
ISO/TR 1281-2:2008(E)
PDF disclaimer
This PDF file may contain embedded typefaces. In accordance with Adobe's licensing policy, this file may be printed or viewed but
shall not be edited unless the typefaces which are embedded are licensed to and installed on the computer performing the editing. In
downloading this file, parties accept therein the responsibility of not infringing Adobe's licensing policy. The ISO Central Secretariat
accepts no liability in this area.
Adobe is a trademark of Adobe Systems Incorporated.
Details of the software products used to create this PDF file can be found in the General Info relative to the file; the PDF-creation
parameters were optimized for printing. Every care has been taken to ensure that the file is suitable for use by ISO member bodies. In
the unlikely event that a problem relating to it is found, please inform the Central Secretariat at the address given below.
COPYRIGHT PROTECTED DOCUMENT
© ISO 2008
or by any means,
electronic or mechanical, including photocopying and microfilm, without permission in writing from either ISO at the address below or
ISO's member body in the country of the requester.
ISO copyright office
Case postale 56 • CH-1211 Geneva 20
Tel. + 41 22 749 01 11
Fax + 41 22 749 09 47
E-mail [email protected]
Web www.iso.org
Published in Switzerland
ii © ISO 2008 – All rights reserved
---------------------- Page: 4 ----------------------
SIST-TP ISO/TR 1281-2:2009
ISO/TR 1281-2:2008(E)
Contents Page
Foreword. iv
Introduction . v
1 Scope . 1
2 Normative references . 1
3 Symbols . 1
4 Life modification factor for reliability, a . 3
1
4.1 General. 3
4.2 Derivation of the life modification factor for reliability. 3
5 Background to the life modification factor, a . 7
ISO
5.1 General. 7
5.2 The lubrication factor, η . 7
b
5.3 The contamination factor, η . 10
c
5.4 Experimental results. 14
5.5 Conclusions . 18
5.6 Practical application of the contamination factor according to Reference [5],
Equation (19.a) . 19
5.7 Difference between the life modification factors in Reference [5] and ISO 281. 26
[3]
6 Background to the ranges of ISO 4406 cleanliness codes used in ISO 281, Clauses A.4
and A.5 . 26
6.1 General. 26
6.2 On-line filtered oil . 28
6.3 Oil bath. 28
6.4 Contamination factor for oil mist lubrication.28
7 Influence of wear. 29
7.1 General definition . 29
7.2 Abrasive wear. 29
7.3 Mild wear. 29
7.4 Influence of wear on fatigue life . 29
7.5 Wear with little influence on fatigue life . 30
7.6 Adhesive wear. 30
8 Influence of a corrosive environment on rolling bearing life. 32
8.1 General. 32
8.2 Life reduction by hydrogen . 32
8.3 Corrosion. 34
9 Fatigue load limit of a complete rolling bearing. 37
9.1 Influence of bearing size. 37
9.2 Relationship fatigue load limit divided by basic static load rating for calculating
the fatigue load limit for roller bearings. 39
10 Influence of hoop stress, temperature and particle hardness on bearing life . 41
10.1 Hoop stress . 41
10.2 Temperature . 41
10.3 Hardness of contaminant particles. 41
11 Relationship between κ and Λ. 42
11.1 The viscosity ratio, κ . 42
11.2 The ratio of oil film thickness to composite surface roughness, Λ. 42
11.3 Theoretical calculation of Λ. 42
Bibliography . 46
© ISO 2008 – All rights reserved iii
---------------------- Page: 5 ----------------------
SIST-TP ISO/TR 1281-2:2009
ISO/TR 1281-2:2008(E)
Foreword
ISO (the International Organization for Standardization) is a worldwide federation of national standards bodies
(ISO member bodies). The work of preparing International Standards is normally carried out through ISO
technical committees. Each member body interested in a subject for which a technical committee has been
established has the right to be represented on that committee. International organizations, governmental and
non-governmental, in liaison with ISO, also take part in the work. ISO collaborates closely with the
International Electrotechnical Commission (IEC) on all matters of electrotechnical standardization.
International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part 2.
The main task of technical committees is to prepare International Standards. Draft International Standards
adopted by the technical committees are circulated to the member bodies for voting. Publication as an
International Standard requires approval by at least 75 % of the member bodies casting a vote.
In exceptional circumstances, when a technical committee has collected data of a different kind from that
which is normally published as an International Standard (“state of the art”, for example), it may decide by a
simple majority vote of its participating members to publish a Technical Report. A Technical Report is entirely
informative in nature and does not have to be reviewed until the data it provides are considered to be no
longer valid or useful.
Attention is drawn to the possibility that some of the elements of this document may be the subject of patent
rights. ISO shall not be held responsible for identifying any or all such patent rights.
ISO/TR 1281-2 was prepared by Technical Committee ISO/TC 4, Rolling bearings, Subcommittee SC 8, Load
ratings and life.
This first edition of ISO/TR 1281-2, together with the first edition of ISO/TR 1281-1, cancels and replaces the
first edition of ISO/TR 8646:1985, which has been technically revised.
ISO/TR 1281 consists of the following parts, under the general title Rolling bearings — Explanatory notes on
ISO 281:
⎯ Part 1: Basic dynamic load rating and basic rating life
⎯ Part 2: Modified rating life calculation, based on a systems approach of fatigue stresses
iv © ISO 2008 – All rights reserved
---------------------- Page: 6 ----------------------
SIST-TP ISO/TR 1281-2:2009
ISO/TR 1281-2:2008(E)
Introduction
[25]
Since the publication of ISO 281:1990 , more knowledge has been gained regarding the influence on
bearing life of contamination, lubrication, fatigue load limit of the material, internal stresses from mounting,
stresses from hardening, etc. It is therefore now possible to take into consideration factors influencing the
fatigue load in a more complete way.
Practical implementation of this was first presented in ISO 281:1990/Amd.2:2000, which specified how new
additional knowledge could be put into practice in a consistent way in the life equation. The disadvantage was,
however, that the influence of contamination and lubrication was presented only in a general fashion.
ISO 281:2007 incorporates this amendment, and specifies a practical method of considering the influence on
bearing life of lubrication condition, contaminated lubricant and fatigue load of bearing material.
In this part of ISO/TR 1281, background information used in the preparation of ISO 281:2007 is assembled for
the information of its users, and to ensure its availability when ISO 281 is revised.
For many years the use of basic rating life, L , as a criterion of bearing performance has proved satisfactory.
10
This life is associated with 90 % reliability, with commonly used high quality material, good manufacturing
quality, and with conventional operating conditions.
However, for many applications, it has become desirable to calculate the life for a different level of reliability
and/or for a more accurate life calculation under specified lubrication and contamination conditions. With
modern high quality bearing steel, it has been found that, under favourable operating conditions and below a
certain Hertzian rolling element contact stress, very long bearing lives, compared with the L life, can be
10
obtained if the fatigue limit of the bearing steel is not exceeded. On the other hand, bearing lives shorter than
the L life can be obtained under unfavourable operating conditions.
10
A systems approach to fatigue life calculation has been used in ISO 281:2007. With such a method, the
influence on the life of the system due to variation and interaction of interdependent factors is considered by
referring all influences to the additional stress they give rise to in the rolling element contacts and under the
contact regions.
© ISO 2008 – All rights reserved v
---------------------- Page: 7 ----------------------
SIST-TP ISO/TR 1281-2:2009
---------------------- Page: 8 ----------------------
SIST-TP ISO/TR 1281-2:2009
TECHNICAL REPORT ISO/TR 1281-2:2008(E)
Rolling bearings — Explanatory notes on ISO 281 —
Part 2:
Modified rating life calculation, based on a systems approach to
fatigue stresses
1 Scope
ISO 281:2007 introduced a life modification factor, a , based on a systems approach to life calculation, in
ISO
addition to the life modification factor for reliability, a .These factors are applied in the modified rating life
1
equation
L =aa L (1)
nm1ISO10
For a range of reliability values, a is given in ISO 281:2007 as well as the method for evaluating the
1
modification factor for systems approach, a . L is the basic rating life.
ISO 10
This part of ISO/TR 1281 gives supplementary background information regarding the derivation of a and a .
1 ISO
NOTE The derivation of a is primarily based on theory presented in Reference [5], which also deals with the fairly
ISO
complicated theoretical background of the contamination factor, e , and other factors considered when calculating a .
C ISO
2 Normative references
The following referenced documents are indispensable for the application of this document. For dated
references, only the edition cited applies. For undated references, the latest edition of the referenced
document (including any amendments) applies.
ISO 281:2007, Rolling bearings — Dynamic load ratings and rating life
ISO 11171, Hydraulic fluid power — Calibration of automatic particle counters for liquids
3 Symbols
Certain other symbols are defined on an ad hoc basis in the clause or subclause in which they are used.
A scaling constant in the derivation of the life equation
a life modification factor, based on a systems approach to life calculation
ISO
a stress-life factor in Reference [5], based on a systems approach to life calculation (same as the life
SLF
modification factor a in ISO 281)
ISO
a life modification factor for reliability
1
C basic dynamic load rating, in newtons
C fatigue load limit, in newtons
u
© ISO 2008 – All rights reserved 1
---------------------- Page: 9 ----------------------
SIST-TP ISO/TR 1281-2:2009
ISO/TR 1281-2:2008(E)
C basic static load rating, in newtons
0
c exponent in the stress-life equation (in Reference [5] and ISO 281, c = 31/3 is used)
D pitch diameter, in millimetres, of ball or roller set
pw
dV elementary integration volume, in cubic millimetres
e Weibull's exponent (10/9 for ball bearings and 9/8 for roller bearings)
e contamination factor
C
F bearing radial load (radial component of actual bearing load), in newtons
r
L life, corresponding to n percent probability of failure, in million revolutions
n
L modified rating life, in million revolutions
nm
L effective roller length, in millimetres, applicable in the calculation of load ratings
we
L basic rating life, in million revolutions
10
N number of load cycles
n probability of failure, expressed as a percentage
P dynamic equivalent load, in newtons
P fatigue load limit, in newtons (same as C )
u u
Q maximum load, in newtons, of a single contact
max
Q fatigue load, in newtons, of a single contact
u
Q maximum load, in newtons, of a single contact when bearing load is C
0 0
S reliability (probability of survival), expressed as a percentage
s uncertainty factor
w exponent in the load-stress relationship (1/3 for ball bearings and 1/2,5 for roller bearings)
x contamination particle size, in micrometres, with ISO 11171 calibration
Z number of rolling elements per row
α nominal contact angle, in degrees
β lubricant cleanliness degree (in Reference [5] and Clause 5)
cc
β filtration ratio at contamination particle size x (see symbol x above)
x(c)
NOTE The designation (c) signifies that the particle counters — of particles of size x µm — shall be an APC (automatic
optical single-particle counter) calibrated in accordance with ISO 11171.
η lubrication factor
b
η contamination factor (same as the contamination factor e in ISO 281)
c C
κ viscosity ratio, ν /ν
1
Λ ratio of oil film thickness to composite surface roughness
ν actual kinematic viscosity, in square millimetres per second, at the operating temperature
ν reference kinematic viscosity, in square millimetres per second, required to obtain adequate
1
lubrication
τ fatigue stress criterion of an elementary volume, dV, in megapascals
i
τ fatigue stress limit in shear, in megapascals
u
2 © ISO 2008 – All rights reserved
---------------------- Page: 10 ----------------------
SIST-TP ISO/TR 1281-2:2009
ISO/TR 1281-2:2008(E)
4 Life modification factor for reliability, a
1
4.1 General
In the context of bearing life for a group of apparently identical rolling bearings, operating under the same
conditions, reliability is defined as the percentage of the group that is expected to attain or exceed a specified
life.
The reliability of an individual rolling bearing is the probability that the bearing will attain or exceed a specified
life. Reliability can thus be expressed as the probability of survival. If this probability is expressed as S %, then
the probability of failure is (100 − S) %.
The bearing life can be calculated for different probability of failure levels with the aid of the life modification
factor for reliability, a .
1
4.2 Derivation of the life modification factor for reliability
4.2.1 Two parameter Weibull relationship
Endurance tests, which normally involve batches of 10 to 30 bearings with a sufficient number of failed
bearings, can be satisfactorily summarized and described using a two parameter Weibull distribution, which
can be expressed
1/ e
⎡⎤
⎛⎞100
L = η ln (2)
n⎢⎥⎜⎟
S
⎝⎠
⎣⎦
nS=−100 (3)
where
S is the probability, expressed as a percentage, of survival;
n is the probability, expressed as a percentage, of failure;
e is the Weibull exponent (set at 1,5 when n < 10);
η characteristic life.
With the life L (corresponding to 10 % probability of failure or 90 % probability of survival) used as the
10
reference, L /L can be written, with the aid of Equation (2), as
n 10
1/ e
⎡⎤
ln 100/ S
()
LL= (4)
⎢⎥
n 10
ln 100 /90
()
⎢⎥
⎣⎦
By including the life modification factor for reliability, a , Equation (4) can be written
1
L =aL (5)
n 110
The life modification factor for reliability, a , is then given by
1
1/ e
⎡⎤
ln 100/ S
()
a = (6)
⎢⎥
1
ln()100/90
⎢⎥
⎣⎦
© ISO 2008 – All rights reserved 3
---------------------- Page: 11 ----------------------
SIST-TP ISO/TR 1281-2:2009
ISO/TR 1281-2:2008(E)
4.2.2 Experimental study of the life modification factor for reliability
References [6], [7], and [8] confirm that the two parameter Weibull distribution is valid for reliabilities up to
90 %. However, for reliabilities above 90%, test results indicate that Equation (6) is not accurate enough.
Figures 1 and 2 are reproduced from Reference [8] and illustrate a summary of the test results from
References [6] to [8] and others. In Figure 1, the test results, represented by a reliability factor designated a ,
1x
are summarized. The curves are calculated as mean values of the test results. In Figure 2, a represents the
1Ix
lower value of the (±3σ) range confidence limits of reliability of the test results, where σ is the standard
deviation.
Figure 1 indicates that all mean value curves have a values above 0,05, and Figure 2 confirms that the
1x
asymptotic value a = a = 0,05 for the life modification factor for reliability is on the safe side.
1 1Ix
Key Key
a reliability factor a lower limit of the ±3σ confidence range for reliability
1x 1lx
S reliability S reliability
1 Reference [8] (total) 1 Reference [8] (total)
2 Reference [8] (ball bearings) 2 Reference [8] (ball bearings)
3 Reference [8] (roller bearings) 3 Reference [8] (roller bearings)
4 Reference [6] 4 Reference [6]
5 Reference [7] 5 Reference [7]
6 Okamoto et al. 6 Okamoto et al.
7 ISO 281 7 ISO 281
Figure 1 — Factor a Figure 2 — Factor a
1x 1Ix
Reproduced, with permission, from Reference [8] Reproduced, with permission, from Reference [8]
4 © ISO 2008 – All rights reserved
---------------------- Page: 12 ----------------------
SIST-TP ISO/TR 1281-2:2009
ISO/TR 1281-2:2008(E)
4.2.3 Three parameter Weibull relationship
The tests (4.2.2) indicate that a three parameter Weibull distribution would better represent the probability of
survival for values > 90 %.
The three parameter Weibull relationship is expressed by
1/ e
⎡⎤100
⎛⎞
L −=γη ln (7)
n ⎢⎥
⎜⎟
S
⎝⎠
⎣⎦
where γ is the third Weibull parameter.
By introducing a factor C to define γ as a function of L , γ can be written
γ 10
γ =CL (8)
γ 10
1/ e
⎡⎤
ln 100 / S
()
LC−=L L−CL (9)
()⎢⎥
nγγ10 10 10
ln 100/ 90
()
⎢⎥
⎣⎦
L =aL (10)
n 110
with the new life modification factor for reliability, a , defined as
1
1/ e
⎡⎤
ln 100/ S
()
aC=−1 +C (11)
()⎢⎥
1 γ γ
ln 100 /90
()
⎢⎥
⎣⎦
The factor C represents the asymptotic value of a in Figure 2, i.e. 0,05. This value and a selected Weibull
γ 1
slope, e = 1,5, give a good representation of the curves in Figure 2. With these values inserted in
Equation (11), the equation for the life modification factor for reliability can be written
2/3
⎡⎤
ln 100/ S
()
a=+0,95 0,05 (12)
⎢⎥
1
ln 100 /90
()
⎢⎥
⎣⎦
Table 1 lists reliability factors calculated by Equation (11) for C = 0 and e = 1,5, and by Equation (12), along
γ
[25]
with the life adjustment factor for reliability, a , in ISO 281:1990 . The calculations are made for reliabilities,
1
S, from 90 % to 99,95 %.
Values of a calculated by Equation (12) are adopted in ISO 281:2007.
1
© ISO 2008 – All rights reserved 5
---------------------- Page: 13 ----------------------
SIST-TP ISO/TR 1281-2:2009
ISO/TR 1281-2:2008(E)
Table 1 — The life modification factor for reliability, a , for different Weibull distributions
1
Reliability factor
Reliability
a
1
C = 0 C = 0,05
S
γ γ
[25]
ISO 281:1990
% e = 1,5 e = 1,5
90 1 1 1
95 0,62 0,62 0,64
96 0,53 0,53 0,55
97 0,44 0,44 0,47
98 0,33 0,33 0,37
99 0,21 0,21 0,25
99,5 — 0,13 0,17
99,9 — 0,04 0,09
99,95 — 0,03 0,08
Figure 3 shows the probability of failure and the probability of survival as functions of the life modification
factor for reliability, a , by means of one curve for C = 0 and e = 1,5 and one curve for C = 0,05 and e = 1,5.
1 γ γ
Key
a life modification factor for reliability
1
C asymptotic value of a
γ 1
e Weibull exponent
n probability of failure
S probability of survival (S = 100 − n)
Figure 3 — Weibull distributions with C = 0 and C = 0,05
γ γ
6 © ISO 2008 – All rights reserved
---------------------- Page: 14 ----------------------
SIST-TP ISO/TR 1281-2:2009
ISO/TR 1281-2:2008(E)
5 Background to the life modification factor, a
ISO
5.1 General
The derivation of the life modification factor, a , in ISO 281 is described in Reference [5], where the same
ISO
factor is called stress-life factor and designated a . In this part of ISO/TR 1281, further information of the
SLF
derivation of the factor a is given, based on Reference [22].
SLF
According to Reference [5], Section 3.2, based on the conditions valid for ISO 281 (i.e. the macro-scale factor
η = 1 and A = 0,1), the equation for a can be written
a SLF
−ce/
w
P
⎛⎞
u
a =−0,1 1 ηη (13)
SLF ⎜⎟b c
P
⎝⎠
The background to the lubrication factor, η , and the contamination factor, η , is explained in 5.2 and 5.3
b c
respectively. The contamination factor, η , corresponds to the factor e in ISO 281.
c C
5.2 The lubrication factor, η
b
This subclause covers the relationship between the lubrication quality, which is characterized by the viscosity
ratio, κ, in ISO 281, and its influence on the fatigue stress.
For this purpose, the fatigue life reduction resulting from an actual rolling bearing (with standard raceway
surface roughness) compared with one characterized by an ideally smooth contact, as from purely Hertzian,
friction-free, stress distribution hypothesis, needs to be quantified.
This can be done by comparing the theoretical fatigue life between a real bearing (with standard raceway
surface roughness) and the fatigue life of a hypothetical bearing with ideally smooth and friction-free
contacting surfaces. Thus the life ratio of Equation (14) has to be quantified
La
10,rough SLF,rough
= (14)
La
10,smooth SLF,smooth
p
with (C/P) constant in the life equation. The ratio in Equation (14) can be evaluated numerically using the
Ioannides-Harris fatigue life stress integral of Equation (15) (see Reference [21]):
c
ττ−
100
e i u
ln ≈ ANVd (15)
∫
h
S
z′
V
R
where
h is a depth exponent;
z′ is a stress-weighted average depth;
τ represents stress criteria.
In Equation (15), the relevant quantity affecting the life ratio in Equation (14) is the volume-related stress
integral I, which can be expressed
c
ττ−
i u
I = dV (16)
∫ h
′
z
V
R
© ISO 2008 – All rights reserved 7
---------------------- Page: 15 ----------------------
SIST-TP ISO/TR 1281-2:2009
ISO/TR 1281-2:2008(E)
By means of Equations (15) and (16), the life equation can be written
1/ e
⎛⎞
ln()100/90
−−61 −1
L=≈10 Nu u (17)
⎜⎟
10
⎜⎟
AI
⎝⎠
The basic rating life in number of revolutions in Equation (17) is expressed as the number of load cycles
obtained with 90 % probability, N, divided by the number of over-rolling per revolution, u.
In Equation (17), the stress integral, I, can be computed for both standard roughness and for an ideally
smooth contact, and it can be used for estimation of the expected effect of raceway surface roughness on
bearing life with the aid of Equations (14) and (17). The following derivation then applies
1/ e
⎛⎞La⎛ ⎞ ⎛ ⎞
I
10,rough SLF,rough
smooth
⎜⎟==⎜ ⎟ ⎜ ⎟ (18)
⎜⎟ ⎜ ⎟ ⎜ ⎟
LI a
10,smooth rough SLF,smooth
⎝⎠ ⎝ ⎠ ⎝ ⎠
mn,,mn mn,
() () ()
In general, this ratio depends on the surface topography (index m) and amount of surface separation or
amount of interposed lubricant film (index n).
The lubrication factor can now be directly derived from Equation (18) by introducing the stress-life factor
according to Equation (13). For standard-bearing roughness and under the hypothesis of an ideally clean
lubricant represented by setting the factor η = 1, the stress-life factor can be written
c
−ce/
w
⎛⎞P
u
a =−0,1 1 η (19)
SLF,rough ⎜⎟b
P
⎝⎠
Similarly, in the case of a well lubricated, hypothetical bearing with ideally smooth surfaces, κ W 4, and η = 1
b
according to the definition of the ranges of η in Reference [5]. Equation (19) can then be written
b
−ce/
w
⎛⎞P
u
a =−0,1 1 (20)
SLF,smooth ⎜⎟
P
⎝⎠
By inserting Equations (19) and (20) into Equation (18), the following equation is derived
1/ w
−1/ c
w
⎛⎞
PI
P ⎛⎞
usmooth
η =−11− ⎜⎟ (21)
⎜⎟
b,()mn
⎜⎟
PP I
⎝⎠
u rough
⎝⎠
mn,
()
Equation (21) shows that a (m × n) matrix of numerically derive
...