ISO/TS 31657-3:2020

TECHNICAL ISO/TS
SPECIFICATION 31657-3
First edition
2020-06
Plain bearings — Hydrodynamic plain
journal bearings under steady-state
conditions —
Part 3:
Functions for calculation of tilting pad
journal bearings
—
Reference number
©
ISO 2020
© ISO 2020
All rights reserved. Unless otherwise specified, or required in the context of its implementation, no part of this publication may
be reproduced or utilized otherwise in any form or by any means, electronic or mechanical, including photocopying, or posting
on the internet or an intranet, without prior written permission. Permission can be requested from either ISO at the address
below or ISO’s member body in the country of the requester.
ISO copyright office
CP 401 • Ch. de Blandonnet 8
CH-1214 Vernier, Geneva
Phone: +41 22 749 01 11
Email: copyright@iso.org
Website: www.iso.org
Published in Switzerland
ii © ISO 2020 – All rights reserved

Contents Page
Foreword .iv
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
4 Functions for calculation of multi-lobed journal bearings . 1
4.1 General . 1
4.2 Tilting-pad journal bearings with four tilting pads . 4
4.3 Tilting-pad journal bearings with five tilting pads .39
Annex A (informative) Characteristic curves for tilting-pad bearings with five pads .62
Bibliography .73
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.
The procedures used to develop this document and those intended for its further maintenance are
described in the ISO/IEC Directives, Part 1. In particular, the different approval criteria needed for the
different types of ISO documents should be noted. This document was drafted in accordance with the
editorial rules of the ISO/IEC Directives, Part 2 (see www .iso .org/ directives).
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. Details of
any patent rights identified during the development of the document will be in the Introduction and/or
on the ISO list of patent declarations received (see www .iso .org/ patents).
Any trade name used in this document is information given for the convenience of users and does not
constitute an endorsement.
For an explanation of the voluntary nature of standards, the meaning of ISO specific terms and
expressions related to conformity assessment, as well as information about ISO's adherence to the
World Trade Organization (WTO) principles in the Technical Barriers to Trade (TBT), see www .iso .org/
iso/ foreword .html.
This document was prepared by Technical Committee ISO/TC 123, Plain bearings, Subcommittee SC 8,
Calculation methods for plain bearings and their applications.
A list of all parts in the ISO/TS 31657 series can be found on the ISO website.
Any feedback or questions on this document should be directed to the user’s national standards body. A
complete listing of these bodies can be found at www .iso .org/ members .html.
iv © ISO 2020 – All rights reserved

TECHNICAL SPECIFICATION ISO/TS 31657-3:2020(E)
Plain bearings — Hydrodynamic plain journal bearings
under steady-state conditions —
Part 3:
Functions for calculation of tilting pad journal bearings
1 Scope
This document specifies the characteristic values for selected tilting-pad journal bearings with four or
five centrally or eccentrically supported tilting pads and with angular spans of pad sliding surfaces of
Ω = 80°, 60° and 45°.
The functions plotted and listed in table form below are required for the operationally safe design
of hydrodynamic tilting-pad journal bearings according to ISO/TS 31657-1. They are based on the
presumptions and boundary conditions indicated there and only apply to stationary operating states.
The symbols used are explained in ISO/TS 31657-1; calculation examples are also included there.
The calculation method described in ISO/TS 31657-1 can also be used for other tilting-pad journal
bearing designs, if the numerical solutions of the basic equations are available in the same manner for
these designs.
2 Normative references
There are no normative references in this document.
3 Terms and definitions
No terms and definitions are listed in this document.
ISO and IEC maintain terminological databases for use in standardization at the following addresses:
— ISO Online browsing platform: available at https:// www .iso .org/ obp
— IEC Electropedia: available at http:// www .electropedia .org/
4 Functions for calculation of multi-lobed journal bearings
4.1 General
The characteristic values for symmetrically loaded tilting-pad journal bearings with four and five
*
centrally (relative angular distance between leading edge and pivot position of pad Ω = 0,5) or
F
*
eccentrically (Ω = 0,6) supported tilting pads are indicated below in table form.
F
The characteristic values were calculated for the geometrical parameters summarised in Figure 1
(angular spans of pad sliding surface Ω, angular coordinates of pivot position of pad ϕ , profile factors
F ,1
* *
K , bearing width ratios B ) in the operating range 0,02 ≤ h ≤ 1. The following (dimensionless)
P min
characteristic values are individually listed in table form:
a) Static characteristic values
Sommerfeld number:
F⋅ψ
eff
So=
BD⋅⋅ηω⋅
eff
Relative eccentricity:
e
ε =
C
R,eff
Attitude angle β in ° .
Product of maximum lubricant film pressure parameter and Sommerfeld number:
p ⋅ψ
max eff
*
pS⋅=o
max
ηω⋅
eff
Minimum relative lubricant film thickness:
h
min
*
h =
min
C
R,eff
Friction force parameter:
f
*
F =⋅So
f
ψ
eff
Lubricant flow rate parameter due to hydrodynamic pressure build-up:
Q
*
Q =
Q
Lubricant flow rate parameter due to supply pressure:
Q
p
*
Q =
p
*
PQ⋅
en 0
Lubricant flow rate parameter at the exit of the lubricant gap:
Q
*
Q =
Q
Non-dimensional difference between maximum temperature of lubricant film and lubricant
temperature in the lubricant pocket:
ρψ⋅⋅c
p eff
*
ΔΔT = ⋅ T
max max
pf⋅
b) Dynamic characteristic values
Non-dimensional lubricant film stiffness coefficients:
2 © ISO 2020 – All rights reserved

ψ
eff
*
c = ⋅c    (i, k = 1, 2)
ik, ik,
2⋅⋅Bηω⋅
eff
Non-dimensional lubricant film damping coefficients:
ψ
eff
*
d = ⋅⋅ω d  (i, k = 1, 2)
ik, ik,
2⋅⋅Bηω⋅
eff
*
For some selected tilting-pad journal bearings (Ω = 0,6, Ω = 45°, ϕ = 36°), these characteristic
F F ,1
values are shown graphically as a function of the Sommerfeld number So and the profile factor K
P
in Annex A, Figures A.1 to A.11.
Figure 1 — Geometrical parameters of selected tilting-pad journal bearings
* *
(Ω = 0,5 and Ω = 0,6)
F F
4.2 Tilting-pad journal bearings with four tilting pads
Characteristic values for tilting-pad journal bearings with four centrally or eccentrically supported
tilting pads and angular spans of pad sliding surface of Ω = 80° or 60° are contained in Tables 1 to 34.
4 © ISO 2020 – All rights reserved

*
Table 1 — Characteristic values of a tilting-pad bearing with four centrally (Ω = 0,5) supported tilting pads (Ω = 80°, φ = 45°, K = 2,
F,1 P
F
B* = 0,5)
* * * *
* * * * * * * * * * *
So ε β [°] F
pS⋅ o h Q Q Q ΔT c c c c d d d d
f
max min 3 P 2 max 11 12 21 22 11 12 21 22
0,000 0,000 0,00 0,278 0,829 2,785 0,909 0,000 1,730 1,02 0,283 0,000 0,000 0,283 0,335 0,000 0,000 0,335
0,021 0,050 0,00 0,308 0,796 2,789 0,909 0,000 1,730 1,10 0,286 0,000 0,000 0,286 0,337 0,000 0,000 0,337
0,042 0,100 0,00 0,342 0,763 2,800 0,907 0,000 1,730 1,18 0,295 0,000 0,000 0,295 0,342 0,000 0,000 0,342
0,086 0,200 0,00 0,426 0,698 2,846 0,902 0,000 1,732 1,36 0,330 0,000 0,000 0,330 0,362 0,000 0,000 0,362
0,136 0,300 0,00 0,539 0,632 2,925 0,893 0,000 1,735 1,58 0,397 0,000 0,000 0,397 0,399 0,000 0,000 0,399
0,197 0,400 0,00 0,692 0,567 3,043 0,881 0,000 1,739 1,84 0,505 0,000 0,000 0,505 0,456 0,000 0,000 0,456
0,273 0,500 0,00 0,907 0,503 3,210 0,863 0,000 1,744 2,15 0,678 0,000 0,000 0,678 0,546 0,000 0,000 0,546
0,374 0,600 0,00 1,216 0,440 3,436 0,841 0,000 1,752 2,51 0,954 0,000 0,000 0,954 0,686 0,000 0,000 0,686
0,512 0,700 0,00 1,674 0,378 3,741 0,812 0,000 1,760 2,93 1,403 0,000 0,000 1,403 0,905 0,000 0,000 0,905
0,713 0,800 0,00 2,392 0,317 4,157 0,776 0,000 1,773 3,51 2,167 0,000 0,000 2,167 1,253 0,000 0,000 1,253
1,023 0,900 0,00 3,587 0,259 4,735 0,732 0,000 1,788 4,34 3,562 0,000 0,000 3,562 1,841 0,000 0,000 1,841
1,245 0,950 0,00 4,501 0,230 5,111 0,707 0,000 1,796 4,88 4,707 0,000 0,000 4,707 2,299 0,000 0,000 2,299
1,541 1,000 0,00 5,768 0,202 5,568 0,679 0,000 1,806 5,65 6,389 0,000 0,000 6,389 2,931 0,000 0,000 2,931
1,943 1,050 0,00 7,584 0,174 6,134 0,648 0,000 1,816 6,49 8,951 0,000 0,000 8,951 3,848 0,000 0,000 3,848
2,512 1,100 0,00 10,311 0,147 6,850 0,613 0,000 1,829 7,76 13,077 0,000 0,000 13,077 5,241 0,000 0,000 5,241
3,358 1,150 0,00 14,651 0,121 7,787 0,575 0,000 1,842 9,64 20,191 0,000 0,000 20,191 7,500 0,000 0,000 7,500
4,708 1,200 0,00 22,167 0,095 9,074 0,532 0,000 1,857 12,41 33,852 0,000 0,000 33,852 11,308 0,000 0,000 11,308
7,086 1,250 0,00 36,774 0,070 10,962 0,482 0,000 1,874 16,96 63,748 0,000 0,000 63,748 19,069 0,000 0,000 19,069
12,031 1,300 0,00 71,724 0,046 14,101 0,422 0,000 1,895 26,41 148,095 0,000 0,000 148,095 37,650 0,000 0,000 37,650
26,371 1,350 0,00 197,100 0,024 20,706 0,346 0,000 1,923 51,75 535,824 0,000 0,000 535,824 107,479 0,000 0,000 107,478
58,756 1,380 0,00 571,372 0,012 31,042 0,284 0,000 1,945 109,29 2 141,057 0,000 0,000 2 141,055 306,671 0,000 0,000 306,670

6 © ISO 2020 – All rights reserved
*
Table 2 — Characteristic values of a tilting-pad bearing with four eccentrically (Ω = 0,6) supported tilting pads (Ω = 80°, φ = 45°, K = 2,
F,1 P
F
B* = 0,5)
*
* * * * * * * * * * * * * *
So ε β [°] F
pS⋅ o h Q Q Q ΔT c c c c d d d d
f
max min 3 P 2 max 11 12 21 22 11 12 21 22
0,000 0,000 0,00 0,443 0,664 2,789 1,572 0,000 1,542 1,07 0,473 0,000 0,000 0,473 0,459 0,000 0,000 0,459
0,025 0,050 0,00 0,481 0,643 2,792 1,572 0,000 1,542 1,14 0,477 0,000 0,000 0,477 0,461 0,000 0,000 0,461
0,051 0,100 0,00 0,522 0,622 2,803 1,570 0,000 1,544 1,23 0,486 0,000 0,000 0,486 0,468 0,000 0,000 0,468
0,106 0,200 0,00 0,623 0,582 2,844 1,567 0,000 1,545 1,42 0,528 0,000 0,000 0,528 0,496 0,000 0,000 0,496
0,166 0,300 0,00 0,752 0,540 2,916 1,561 0,000 1,546 1,64 0,605 0,000 0,000 0,605 0,545 0,000 0,000 0,545
0,234 0,400 0,00 0,925 0,496 3,016 1,544 0,000 1,553 1,91 0,728 0,000 0,000 0,728 0,621 0,000 0,000 0,621
0,320 0,500 0,00 1,159 0,450 3,164 1,533 0,000 1,556 2,25 0,920 0,000 0,000 0,920 0,735 0,000 0,000 0,735
0,440 0,600 0,00 1,491 0,402 3,381 1,527 0,000 1,556 2,65 1,222 0,000 0,000 1,222 0,902 0,000 0,000 0,902
0,595 0,700 0,00 1,982 0,352 3,666 1,512 0,000 1,560 3,14 1,707 0,000 0,000 1,707 1,150 0,000 0,000 1,150
0,819 0,800 0,00 2,751 0,300 4,066 1,494 0,000 1,564 3,77 2,533 0,000 0,000 2,533 1,529 0,000 0,000 1,529
1,164 0,900 0,00 4,056 0,246 4,649 1,474 0,000 1,567 4,81 4,052 0,000 0,000 4,052 2,134 0,000 0,000 2,134
1,412 0,950 0,00 5,059 0,219 5,042 1,463 0,000 1,568 5,45 5,296 0,000 0,000 5,296 2,623 0,000 0,000 2,623
1,737 1,000 0,00 6,449 0,192 5,527 1,449 0,000 1,571 6,18 7,103 0,000 0,000 7,103 3,316 0,000 0,000 3,316
2,175 1,050 0,00 8,424 0,166 6,132 1,434 0,000 1,573 7,14 9,848 0,000 0,000 9,848 4,311 0,000 0,000 4,311
2,791 1,100 0,00 11,376 0,140 6,905 1,416 0,000 1,576 8,33 14,237 0,000 0,000 14,237 5,801 0,000 0,000 5,801
3,700 1,150 0,00 16,040 0,115 7,920 1,395 0,000 1,580 10,23 21,778 0,000 0,000 21,778 8,167 0,000 0,000 8,167
5,133 1,200 0,00 24,049 0,091 9,305 1,372 0,000 1,583 13,00 36,003 0,000 0,000 36,003 12,305 0,000 0,000 12,305
7,634 1,250 0,00 39,539 0,067 11,327 1,343 0,000 1,588 17,56 67,340 0,000 0,000 67,340 20,207 0,000 0,000 20,207
12,774 1,300 0,00 76,100 0,045 14,616 1,308 0,000 1,594 27,05 154,291 0,000 0,000 154,291 39,597 0,000 0,000 39,597
27,474 1,350 0,00 2
...