ISO 31657-2:2025

Plain bearings — Hydrodynamic plain journal bearings under steady-state conditions — Part 2: Characteristic values for calculation of multilobed journal bearings

This document specifies the characteristic values for selected two-, three- and four-lobe bearings.

Paliers lisses — Paliers lisses hydrodynamiques radiaux fonctionnant en régime stabilisé — Partie 2: Valeurs caractéristiques pour le calcul des paliers radiaux multilobés

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 31657-2
First edition
Plain bearings — Hydrodynamic
2025-10
plain journal bearings under
steady-state conditions —
Part 2:
Characteristic values for calculation
of multilobed journal bearings
Paliers lisses — Paliers lisses hydrodynamiques radiaux
fonctionnant en régime stabilisé —
Partie 2: Valeurs caractéristiques pour le calcul des paliers
radiaux multilobés
Reference number
© ISO 2025
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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 Two-lobe bearings .4
4.3 Three-lobe bearings . 20
4.4 Four-lobe bearings .32
Annex A (informative) Characteristic curves for four-lobe bearings .50
Bibliography . 67

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 31657-2 cancels and replaces ISO/TS 31657-2:2020, 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 31657-2:2025(en)
Plain bearings — Hydrodynamic plain journal bearings under
steady-state conditions —
Part 2:
Characteristic values for calculation of multilobed journal
bearings
1 Scope
This document specifies the characteristic values for selected two-, three- and four-lobe bearings.
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 terminology 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 characteristics values plotted and listed in this clause are required for the operationally safe design
of hydrodynamic multi-lobed 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 in this document shall be in accordance with ISO 31657-1:2025, Table 1; calculation examples
are also given ISO 31657-1:2025, Annex A.
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 two-, three- and four-lobe bearings with relative lubrication pocket widths of
*
b = 0,8 are given in 4.2 to 4.4. The characteristic values were calculated for the geometrical parameters
P
summarised in Figure 1 (angular spans of segment sliding surface, Ω, angular coordinates of lubricant
* *
pocket centrelines, ϕ , gap ratios, h , bearing width ratios B*) in the operating range 0,02 ≤ h ≤ 1.
P,1 0,max min
*
The profile factors, K , associated with the indicated gap ratios, h , can be calculated for these bearing
P 0,max
types as shown in Formulae (1) to (3):
for Z = 2
*
Kh= (1)
Pm0, ax
for Z = 3
*
Kh=⋅2 (2)
Pm0, ax
for Z = 4
*
h −
0,max
K = (3)
P
1−
The following (dimensionless) characteristic values are indicated in Tables 1 to 43.
a) Static characteristic values
The Sommerfeld number is given as Formula (4):
F⋅ψ
eff
So= (4)
BD⋅⋅ηω⋅
eff
The relative eccentricity is given as Formula (5):
e
ε = (5)
C
Re, ff
Attitude angle, β, in °.
For the product of maximum lubricant film pressure parameter and Sommerfeld number, see
Formula (6):
p ⋅ψ
*
maxeff
pS⋅ o= (6)
max
ηω⋅
eff
For the minimum relative lubricant film thickness, see Formula (7):
h
*
min
h = (7)
min
C
R,eff
For the friction force parameter, see Formula (8):
f
*
F =⋅So (8)
f
ψ
eff
For the lubricant flow rate parameter due to hydrodynamic pressure build-up, see Formula (9):
Q
* 3
Q = (9)
Q
For the lubricant flow rate parameter due to supply pressure, see Formula (10):

Q
p
*
Q = (10)
p
*
PQ⋅
en 0
For the lubricant flow rate parameter at the exit of the lubrication gap, see Formula (11):
Q
* 2
Q = (11)
Q
For non-dimensional difference between maximum lubricant temperature and lubricant temperature in
the lubricant pockets, see Formula (12):
ρψ⋅⋅c
peff
*
ΔΔT = ⋅ T (12)
max max
pf⋅
b) Dynamic characteristic values
For non-dimensional lubricant film stiffness coefficients, see Formula (13):
ψ
* eff
c = ⋅c (i, k = 1, 2) (13)
ik, ik,
2⋅⋅B ηω⋅
eff
For non-dimensional lubricant film damping coefficients, see Formula (14):
ψ
* eff
d = ⋅⋅ω d (i, k = 1, 2) (14)
ik, ik,
2⋅⋅B ηω⋅
eff
For some selected four-lobe bearings (Ω = 70°, ϕ = 315°), these characteristic values are shown graphically
P,1
* *
as a function of the Sommerfeld number So, the gap ratio h and the bearing width ratio B in Annex A,
0,max
Figures A.1 to A.16.
Figure 1 — Geometrical parameters of selected multi-lobed journal bearings
4.2 Two-lobe bearings
Characteristic values for two-lobe bearings are listed in Tables 1 to 15.

*
Table 1 — Characteristic values of a two-lobe bearing with Ω = 150°, φ = 180°, h = 3, B* = 0,75
P,1 0,max
* * * * * * * * * * * * * * *
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 90,00 0,327 1,000 1,780 0,959 36,868 1,619 1,25 0,364 –0,107 0,174 0,019 0,541 0,168 0,168 0,093
0,014 0,203 15,82 0,364 0,935 1,790 0,971 37,474 1,604 1,35 0,373 –0,106 0,181 0,023 0,548 0,171 0,171 0,099
0,029 0,406 15,38 0,422 0,856 1,822 1,007 39,301 1,560 1,50 0,401 –0,105 0,201 0,035 0,576 0,182 0,182 0,116
0,048 0,607 14,65 0,510 0,768 1,878 1,065 42,339 1,488 1,71 0,455 –0,100 0,241 0,058 0,623 0,202 0,202 0,150
0,073 0,805 13,63 0,639 0,675 1,962 1,145 46,566 1,388 1,99 0,542 –0,089 0,306 0,099 0,699 0,235 0,235 0,206
0,108 1,001 12,36 0,834 0,579 2,083 1,243 52,000 1,265 2,35 0,684 –0,067 0,415 0,174 0,815 0,289 0,289 0,297
0,159 1,195 10,84 1,139 0,485 2,255 1,357 58,643 1,118 2,88 0,916 –0,020 0,599 0,314 0,994 0,376 0,377 0,450
0,241 1,387 9,11 1,645 0,392 2,504 1,482 66,479 0,953 3,64 1,323 0,084 0,932 0,597 1,285 0,525 0,525 0,721
0,384 1,577 7,17 2,569 0,303 2,884 1,616 75,476 0,769 4,80 2,120 0,326 1,599 1,240 1,810 0,801 0,801 1,249
0,677 1,768 5,05 4,546 0,217 3,522 1,755 85,736 0,567 6,73 4,010 1,012 3,194 3,029 2,907 1,371 1,371 2,459
1,478 1,959 2,79 10,341 0,133 4,839 1,898 97,153 0,350 10,97 10,662 3,665 8,585 10,316 6,159 2,978 2,978 6,332
3,840 2,100 1,14 29,250 0,071 7,487 2,003 106,265 0,177 20,77 40,455 15,265 29,531 46,571 17,323 7,373 7,374 20,278
18,558 2,200 0,18 183,912 0,022 16,491 2,079 113,058 0,049 65,04 514,115 142,002 242,523 642,042 124,068 32,520 32,518 154,507
45,130 2,220 0,06 569,417 0,010 26,225 2,095 114,450 0,023 142,08 2 504,109 425,818 779,476 3 114,672 443,694 115,503 115,503 554,368

*
Table 2 — Characteristic values of a two-lobe bearing with Ω = 150°, φ = 180°, h = 5, B* = 0,75
P,1 0,max
* * * * * * * * * * * * * * *
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 90,00 0,342 1,000 1,507 1,787 152,625 1,670 1,25 0,284 –0,038 0,110 0,022 0,315 0,081 0,081 0,039
0,011 0,301 7,29 0,370 0,951 1,518 1,801 154,870 1,650 1,33 0,292 –0,038 0,114 0,024 0,321 0,083 0,083 0,041
0,023 0,602 7,02 0,418 0,883 1,551 1,841 161,614 1,598 1,46 0,315 –0,036 0,125 0,031 0,339 0,089 0,089 0,048
0,038 0,902 6,57 0,493 0,800 1,610 1,905 172,838 1,510 1,64 0,359 –0,033 0,147 0,044 0,373 0,099 0,099 0,062
0,058 1,202 5,93 0,609 0,706 1,703 1,994 188,597 1,388 1,88 0,434 –0,026 0,185 0,069 0,427 0,116 0,116 0,085
0,088 1,500 5,14 0,793 0,604 1,841 2,104 208,778 1,235 2,25 0,564 –0,012 0,252 0,116 0,519 0,145 0,145 0,125
0,134 1,798 4,21 1,106 0,496 2,051 2,234 233,495 1,050 2,78 0,805 0,021 0,373 0,212 0,674 0,194 0,194 0,199
0,218 2,095 3,15 1,701 0,384 2,386 2,380 262,650 0,836 3,69 1,311 0,097 0,623 0,435 0,977 0,287 0,287 0,350
0,321 2,293 2,40 2,463 0,307 2,742 2,486 284,578 0,676 4,64 2,042 0,218 0,968 0,784 1,367 0,401 0,402 0,554
0,517 2,491 1,62 3,996 0,228 3,319 2,597 308,482 0,504 6,29 3,737 0,505 1,725 1,650 2,183 0,611 0,611 0,992
1,004 2,690 0,86 8,151 0,146 4,446 2,713 334,471 0,319 9,97 9,508 1,410 3,958 4,721 4,513 1,177 1,177 2,276
3,915 2,900 0,18 40,203 0,052 8,632 2,842 364,011 0,109 28,23 85,684 10,417 24,374 47,054 24,886 4,356 4,355 13,687
8,457 2,950 0,07 107,659
...