ISO 31657-3:2025

Plain bearings — Hydrodynamic plain journal bearings under steady-state conditions — Part 3: Characteristic values for calculation of tilting pad journal bearings

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°.

Paliers lisses — Paliers lisses hydrodynamiques radiaux fonctionnant en régime stabilisé — Partie 3: Titre manque

General Information

• Status: Published
• Publication Date: 15-Oct-2025
• ICS: 21.100.10 - Plain bearings
• Technical Committee: ISO/TC 123/SC 8 - Calculation methods for plain bearings and their applications
• Drafting Committee: ISO/TC 123/SC 8 - Calculation methods for plain bearings and their applications
• Current Stage: 6060 - International Standard published
• Start Date: 16-Oct-2025
• Due Date: 05-Aug-2025
• Completion Date: 16-Oct-2025

Standards Content (Sample)

International
Standard
ISO 31657-3
First edition
Plain bearings — Hydrodynamic
2025-10
plain journal bearings under
steady-state conditions —
Part 3:
Characteristic values for calculation
of tilting pad journal bearings
Reference number
© ISO 2025
All rights reserved. Unless otherwise specified, or required in the context of its implementation, no part of this publication may
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or ISO’s member body in the country of the requester.
ISO copyright office
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Phone: [phone]
Email: [e-mail]
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Published in Switzerland
ii
Contents Page
Foreword .iv
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
4 Characteristic values 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

iii
Foreword
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This document was prepared by Technical Committee ISO/TC 123, Plain bearings, Subcommittee SC 8,
Calculation methods for plain bearings and their applications.
This first edition of ISO 31657-3 cancels and replaces ISO/TS 31657-3:2020, which has been technically
revised.
The main changes are as follows:
— the title has been modified;
— Figure 1 has been updated.
A list of all parts in the ISO 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
International Standard ISO 31657-3:2025(en)
Plain bearings — Hydrodynamic plain journal bearings under
steady-state conditions —
Part 3:
Characteristic values 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°.
2 Normative references
The following documents are referred to in the text in such a way that some or all of their content constitutes
requirements 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 31657-1:2025, Plain bearings — Hydrodynamic plain journal bearings under steady-state conditions — Part
1: Calculation of multi-lobed and tilting pad journal bearings
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 https:// www .electropedia .org/
4 Characteristic values for calculation of multi-lobed journal bearings
4.1 General
The characteristic values plotted and listed in this clause are required for the operationally safe design
of hydrodynamic tilting-pad journal bearings in accordance with ISO 31657-1. They are based on the
presumptions and boundary conditions indicated there and only apply to stationary operating states. The
symbols used shall be in accordance with ISO 31657-1:2025, Table 1; calculation examples are also given in
ISO 31657-1:2025, Annex A.
The calculation method described in ISO 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.
NOTE Equivalent calculation procedures exist that enable operating conditions to be estimated and checked
against acceptable conditions. Another calculation procedure is equally admissible.

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)
F
*
or eccentrically (Ω = 0,6) supported tilting pads are indicated.
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 K , bearing
F,1 P
* *
width ratios B ) in the operating range 0,02 ≤ h ≤ 1. The following (dimensionless) characteristic values
min
are individually listed from Tables 1 to 56:
a) Static characteristic values
The Sommerfeld number is given as Formula (1):
F⋅ψ
eff
So= (1)
BD⋅⋅ηω⋅
eff
The relative eccentricity is given as Formula (2):
e
ε = (2)
C
Re, ff
Attitude angle β in °C.
For the product of maximum lubricant film pressure parameter and Sommerfeld number, see
Formula (3):
p ·ψ
* maxeff
pS· o= (3)
max
ηω⋅
eff
For the minimum relative lubricant film thickness, see Formula (4):
h
* min
h = (4)
min
C
Re, ff
For the friction force parameter, see Formula (5):
f
*
F =⋅So (5)
f
ψ
eff
For the lubricant flow rate parameter due to hydrodynamic pressure build-up, see Formula (6):
Q
* 3
Q = (6)
Q
For the lubricant flow rate parameter due to supply pressure, see Formula (7):
Q
p
*
Q = (7)
p
*
PQ⋅
en 0
For the lubricant flow rate parameter at the exit of the lubricant gap, see Formula (8):
Q
*
Q = (8)
Q
For non-dimensional difference between maximum temperature of lubricant film and lubricant
temperature in the lubricant pocket, see Formula (9):

ρψ⋅⋅c
peff
*
ΔΔT = · T (9)
max max
pf⋅
b) Dynamic characteristic values
For non-dimensional lubricant film stiffness coefficients, see Formula (10):
ψ
* eff
c = ⋅c (i, k = 1, 2) (10)
ik, ik,
2⋅⋅B ηω⋅
eff
For non-dimensional lubricant film damping coefficients, see Formula (11):
ψ
* eff
d = ⋅⋅ω d (i, k = 1, 2) (11)
ik, ik,
2⋅⋅B ηω⋅
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 in
P
Annex A, Figures A.1 to A.11.
Figure 1 — Geometrical parameters of selected tilting-pad journal bearings
* *
(ΩΩ = 0,5 andΩΩ = 0,6)
F F
4.2 Tilting-pad journal bearings with four tilting pads
The 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 given in Tables 1 to 34.

Table 1 — Characteristic values of a tilting-pad bearing
*
with four centrally (ΩΩ = 0,5) supported tilting pads (Ω = 80°, φ = 45°, K = 2, B* = 0,5)
F F,1 P
* * * * * * * * * * * * * * *
So ε β [°]
pS⋅ o h F Q Q Q ΔT c c c c d d d d
max min f 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

Table 2 — Characteristic values of a tilting-pad bearing
*
with four eccentrically (ΩΩ = 0,6) supported tilting pads (Ω = 80°, φ = 45°, K = 2, B* = 0,5)
F F,1 P
* * * * * * * * * * * * * * *
So ε β [°]
pS⋅ o h F Q Q Q ΔT c c c c d d d d
max min f 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
...