Plain bearings — Hydrodynamic plain journal bearings under steady-state conditions — Part 2: Functions for calculation of multi-lobed journal bearings

This document specifies the characteristic values for selected two-, three- and four-lobe bearings. The functions plotted and listed in table form below are required for the operationally safe design of hydrodynamic multi-lobed 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.

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TECHNICAL ISO/TS
SPECIFICATION 31657-2
First edition
2020-06
Plain bearings — Hydrodynamic plain
journal bearings under steady-state
conditions —
Part 2:
Functions for calculation of multi-
lobed journal bearings
Reference number
ISO/TS 31657-2:2020(E)
ISO 2020
---------------------- Page: 1 ----------------------
ISO/TS 31657-2:2020(E)
COPYRIGHT PROTECTED DOCUMENT
© 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

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Email: copyright@iso.org
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Published in Switzerland
ii © ISO 2020 – All rights reserved
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ISO/TS 31657-2:2020(E)
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 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

© ISO 2020 – All rights reserved iii
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ISO/TS 31657-2:2020(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.

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).

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constitute an endorsement.

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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
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TECHNICAL SPECIFICATION ISO/TS 31657-2:2020(E)
Plain bearings — Hydrodynamic plain journal bearings
under steady-state conditions —
Part 2:
Functions for calculation of multi-lobed journal bearings
1 Scope

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

The functions plotted and listed in table form below are required for the operationally safe design

of hydrodynamic multi-lobed 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.

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 two-, three- and four-lobe bearings with relative lubrication pocket widths

of b = 0,8 are shown in table form below. The characteristic values were calculated for the geometrical

parameters 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

P,1 0,max
* *

0,02 ≤ h ≤ 1. The profile factors,K , associated with the indicated gap ratios, h , can be

min P 0,max
calculated for these bearing types as follows:
Kh= for Z = 2
P 0,max
Kh=⋅21− for Z = 3
P 0,max
© ISO 2020 – All rights reserved 1
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ISO/TS 31657-2:2020(E)
h −
0,max
K = for Z = 4

The following (dimensionless) characteristic values are indicated in Tables 1 to 43:

a) Static characteristic values
Sommerfeld number:
F⋅ψ
eff
So=
BD⋅⋅ηω⋅
eff
Relative eccentricity:
ε =
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:
min
h =
min
R,eff
Friction force parameter:
F =⋅So
eff
Lubricant flow rate parameter due to hydrodynamic pressure build-up:
Q =
Lubricant flow rate parameter due to supply pressure:
Q =
PQ⋅
en 0
Lubricant flow rate parameter at the exit of the lubrication gap:
Q =

Non-dimensional difference between maximum lubricant temperature and lubricant temperature

in the lubricant pockets:
ρψ⋅⋅c
p eff
ΔΔT = ⋅ T
max max
pf⋅
2 © ISO 2020 – All rights reserved
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ISO/TS 31657-2:2020(E)
b) Dynamic characteristic values
Non-dimensional lubricant film stiffness coefficients:
eff
c = ⋅c (i, k = 1, 2)
ik, ik,
2⋅⋅Bηω⋅
eff
Non-dimensional lubricant film damping coefficients:
eff
d = ⋅⋅ω d (i, k = 1, 2)
ik, ik,
2⋅⋅Bηω⋅
eff

For some selected four-lobe bearings (Ω = 70°, ϕ = 315°), these characteristic values are shown

P,1

graphically as a function of the Sommerfeld number So, the gap ratio h and the bearing width ratio

0,max
B in Annex A, Figures A.1 to A.16.
Figure 1 — Geometrical parameters of selected multi-lobed journal bearings
© ISO 2020 – All rights reserved 3
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ISO/TS 31657-2:2020(E)
4.2 Two-lobe bearings
Characteristic values for two-lobe bearings are listed in Tables 1 to 15.
4 © ISO 2020 – All rights reserved
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ISO/TS 31657-2:2020(E)
© ISO 2020 – All rights reserved 5

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 [°] F
pS⋅ o h Q Q Q ΔT c c c c d d d d
max f 3 max
min P 2 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

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ISO/TS 31657-2:2020(E)
6 © ISO 2020 – All rights reserved

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 [°] F
pS⋅ o h Q Q Q ΔT c c c c d d d d
max f 3 max
min P 2 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 0,027 12,809 2,873 371,364 0,056 54,49 334,928 30,443 71,696 186,580 74,182 9,627 9,627 41,342

14,689 2,970 0,03 224,879 0,017 17,027 2,886 374,341 0,035 89,35 926,933 61,807 152,876 517,668 164,982 19,973 19,972 92,317

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ISO/TS 31657-2:2020(E)
© ISO 2020 – All rights reserved 7

Table 3 — Characteristic values of a two-lobe bearing with Ω = 150°, φ = 240°, h = 3, B* = 0,75

P,1
0,max
* * * * * * * * * * * * * *
So ε β [°] F
pS⋅ o h Q Q Q ΔT c c c c d d d d
max f 3 max
min P 2 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 0,135 –0,307 –0,025 0,249 0,351 –0,278 –0,278 0,283

0,024 0,300 65,76 0,343 0,948 1,800 0,986 38,272 1,585 1,30 0,144 –0,316 –0,024 0,259 0,360 –0,279 –0,279 0,296

0,053 0,600 64,93 0,388 0,863 1,862 1,065 42,498 1,483 1,39 0,176 –0,345 –0,021 0,296 0,394 –0,286 –0,285 0,339

0,096 0,900 63,58 0,501 0,756 1,983 1,191 49,575 1,320 1,55 0,239 –0,401 –0,010 0,380 0,458 –0,297 –0,297 0,435

0,195 1,255 61,44 0,833 0,612 2,255 1,387 61,648 1,055 2,00 0,395 –0,528 0,031 0,646 0,603 –0,316 –0,316 0,697

0,337 1,488 59,74 1,406 0,502 2,590 1,535 71,722 0,844 2,77 0,602 –0,683 0,128 1,168 0,780 –0,327 –0,326 1,148

0,647 1,698 58,00 2,889 0,331 3,159 1,675 82,206 0,632 4,44 0,968 –0,912 0,463 2,796 1,054 –0,296 –0,296 2,322

1,449 1,860 56,29 7,683 0,182 4,165 1,784 91,126 0,455 9,19 1,578 –1,003 1,986 9,830 1,400 0,010 0,010 6,279

4,655 1,931 53,56 34,941 0,068 6,408 1,816 94,911 0,372 29,85 3,188 2,998 14,895 75,236 1,592 2,566 2,567 30,672

11,520 1,879 50,12 119,413 0,030 9,298 1,747 90,997 0,431 76,95 7,878 21,587 63,226 403,924 1,955 9,260 9,259 113,638

26,368 1,811 46,94 379,970 0,014 13,580 1,670 86,161 0,509 179,60 19,622 83,789 224,646 1 939,293 3,095 25,234 25,233 393,073

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ISO/TS 31657-2:2020(E)
8 © ISO 2020 – All rights reserved

Table 4 — Characteristic values of a two-lobe bearing with Ω = 150°, φ = 240°, h = 5, B* = 0,75

P,1
0,max
* * * * * * * * * * * * * *
So ε β [°]
pS⋅ o h Q Q Q ΔT c c c c d d d d
max f 3 max
min P 2 11 12 21 22 11 12 21 22

0,000 0,000 90,00 0,342 1,000 1,507 1,787 152,625 1,669 1,25 0,119 –0,206 –0,057 0,188 0,178 –0,160 –0,160 0,175

0,013 0,300 59,79 0,356 0,988 1,517 1,801 154,887 1,650 1,27 0,121 –0,209 –0,058 0,193 0,181 –0,162 –0,162 0,180

0,028 0,600 59,61 0,387 0,951 1,548 1,839 161,674 1,597 1,34 0,130 –0,220 –0,060 0,209 0,189 –0,167 –0,167 0,193

0,046 0,900 59,33 0,442 0,890 1,604 1,902 172,982 1,508 1,44 0,148 –0,240 –0,065 0,240 0,203 –0,176 –0,176 0,218

0,074 1,231 58,89 0,549 0,792 1,703 1,998 190,702 1,371 1,64 0,179 –0,279 –0,073 0,305 0,230 –0,194 –0,194 0,269

0,111 1,518 58,43 0,717 0,683 1,837 2,102 210,507 1,220 1,95 0,225 –0,335 –0,083 0,413 0,268 –0,218 –0,218 0,350

0,171 1,797 57,95 1,021 0,556 2,037 2,219 233,701 1,046 2,47 0,300 –0,428 –0,097 0,630 0,324 –0,255 –0,255 0,499

0,281 2,070 57,47 1,659 0,416 2,354 2,348 260,142 0,851 3,45 0,433 –0,601 –0,115 1,150 0,415 –0,318 –0,318 0,815

0,546 2,341 57,09 3,440 0,264 2,940 2,489 290,060 0,633 5,87 0,710 –1,003 –0,110 2,946 0,588 –0,441 –0,441 1,731

1,816 2,625 56,97 15,037 0,101 4,646 2,652 325,394 0,380 17,84 1,631 –2,658 0,683 21,407 1,044 –0,742 –0,742 8,014

3,419 2,702 57,02 34,428 0,058 6,004 2,699 335,693 0,306 34,13 2,381 –4,050 3,505 65,596 1,325 –0,735 –0,735 19,502

13,503 2,757 56,80 224,496 0,017 10,618 2,731 343,151 0,252 136,17 5,394 6,815 53,808 863,057 1,707 2,358 2,358 132,080

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ISO/TS 31657-2:2020(E)
© ISO 2020 – All rights reserved 9

Table 5 — Characteristic values of a two-lobe bearing with Ω = 150°, φ = 270°, h = 1, B* = 0,5

P,1
0,max
* * * * * * * * * * * * * *
So ε β [°]
pS⋅ o h Q Q Q ΔT c c c c d d d d
max f 3 max
min P 2 11 12 21 22 11 12 21 22

0,000 0,000 90,00 0,000 1,000 2,614 0,000 3,008 1,000 2,00 0,000 –0,262 0,671 0,000 0,523 0,000 0,000 1,342

0,090 0,236 64,91 0,192 0,764 2,430 0,175 3,394 0,796 2,71 0,160 –0,171 0,469 0,163 0,372 0,174 0,174 0,923

0,163 0,361 56,42 0,373 0,639 2,471 0,245 3,784 0,706 3,34 0,292 –0,210 0,674 0,345 0,510 0,339 0,338 1,309

0,260 0,467 50,13 0,643 0,533 2,607 0,291 4,131 0,639 3,93 0,438 –0,204 0,976 0,690 0,599 0,501 0,501 1,868

0,401 0,562 44,64 1,081 0,438 2,833 0,323 4,403 0,588 4,66 0,650 –0,180 1,473 1,332 0,730 0,740 0,740 2,783

0,626 0,649 39,58 1,849 0,351 3,168 0,342 4,584 0,548 5,68 0,983 –0,107 2,338 2,622 0,926 1,120 1,120 4,383

1,011 0,729 34,71 3,317 0,271 3,649 0,351 4,663 0,520 7,20 1,570 0,093 4,007 5,477 1,241 1,791 1,793 7,460

1,783 0,805 29,68 6,656 0,195 4,392 0,350 4,633 0,502 9,89 2,748 0,706 7,804 13,213 1,799 3,154 3,155 14,473

3,709 0,877 24,15 16,512 0,123 5,714 0,335 4,477 0,497 15,89 5,805 3,052 19,273 41,921 3,039 6,768 6,767 35,742

11,175 0,943 17,40 66,166 0,057 8,914 0,303 4,174 0,511 36,26 18,352 19,280 80,457 252,403 6,810 21,690 21,697 148,293

30,369 0,974 12,58 238,937 0,026 13,981 0,273 3,946 0,534 85,56 53,612 93,221 315,937 1 384,251 14,455 64,581 64,585 574,742

59,033 0,985 9,96 568,507 0,015 19,196 0,255 3,837 0,550 155,16 109,469 267,165 805,560 4 501,754 23,051 130,675 130,663 1 433,334

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ISO/TS 31657-2:2020(E)
10 © ISO 2020 – All rights reserved

Table 6 — Characteristic values of a two-lobe bearing with Ω = 150°, φ = 270°, h = 3, B* = 0,5

P,1
0,max
* * * * * * * * * * * * * *
So ε β [°] F
pS⋅ o h Q Q Q ΔT c c c c d d d d
max f 3 max
min P 2 11 12 21 22 11 12 21 22

0,000 0,000 90,00 0,219 1,000 1,737 0,864 50,725 1,052 1,16 0,017 –0,121 0,059 0,244 0,062 –0,107 –0,107 0,330

0,029 0,300 81,39 0,264 0,934 1,758 0,884 52,595 1,030 1,30 0,020 –0,121 0,067 0,259 0,066 –0,102 –0,102 0,346

0,065 0,574 79,98 0,352 0,825 1,819 0,935 57,521 0,972 1,54 0,031 –0,121 0,093 0,310 0,075 –0,088 –0,087 0,394

0,138 0,861 76,57 0,600 0,646 1,967 1,014 65,671 0,879 2,09 0,059 –0,105 0,182 0,481 0,095 –0,040 –0,040 0,549

0,228 1,001 72,54 0,976 0,510 2,132 1,054 70,214 0,825 2,83 0,101 –0,068 0,328 0,784 0,113 0,030 0,030 0,797

0,343 1,066 67,95 1,538 0,404 2,320 1,064 71,688 0,804 3,75 0,160 –0,010 0,551 1,309 0,133 0,121 0,121 1,184

0,505 1,092 62,75 2,424 0,318 2,554 1,052 71,111 0,804 5,03 0,246 0,084 0,904 2,271 0,159 0,240 0,241 1,814

0,756 1,097 56,85 3,974 0,243 2,874 1,026 69,181 0,819 6,99 0,385 0,250 1,532 4,237 0,198 0,418 0,418 2,959

1,208 1,090 50,03 7,147 0,174 3,365 0,989 66,289 0,845 10,42 0,642 0,617 2,852 9,028 0,266 0,735 0,736 5,382

2,202 1,074 41,86 15,349 0,110 4,232 0,940 62,611 0,882 17,84 1,239 1,686 6,465 24,638 0,409 1,478 1,479 12,023

5,666 1,047 30,73 52,233 0,051 6,345 0,876 58,047 0,935 42,44 3,428 7,798 24,121 128,756 0,772 4,047 4,046 43,158

13,560 1,028 22,43 166,704 0,024 9,519 0,837 55,380 0,971 98,25 8,914 30,395 85,418 623,960 1,465 10,802 10,799 150,032

24,443 1,019 17,86 371,567 0,014 12,657 0,819 54,246 0,987 175,92 17,061 74,399 204,567 1 848,538 2,327 21,727 21,726 361,019

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ISO/TS 31657-2:2020(E)
© ISO 2020 – All rights reserved 11

Table 7 — Characteristic values of a two-lobe bearing with Ω = 150°, φ = 270°, h = 5, B* = 0,5

P,1
0,max
* * * * * * * * * * * * * *
So ε β [°]
pS⋅ o h Q Q Q ΔT c c c c d d d d
max f 3 max
min P 2 11 12 21 22 11 12 21 22

0,000 0,000 90,00 0,247 1,000 1,450 1,650 213,796 1,082 1,13 0,017 –0,082 0,023 0,209 0,027 –0,055 –0,055 0,212

0,016 0,250 77,97 0,282 0,941 1,459 1,658 215,843 1,072 1,25 0,018 –0,082 0,025 0,215 0,027 –0,055 –0,055 0,217

0,033 0,470 77,67 0,329 0,874 1,481 1,675 221,018 1,052 1,39 0,019 –0,082 0,031 0,233 0,028 –0,053 –0,053 0,230

0,075 0,854 76,43 0,487 0,718 1,569 1,726 237,424 0,990 1,79 0,026 –0,081 0,057 0,315 0,032 –0,044 –0,044 0,289

0,133 1,118 74,44 0,768 0,567 1,701 1,775 253,621 0,928 2,43 0,039 –0,071 0,115 0,489 0,037 –0,024 –0,024 0,405

0,217 1,270 71,65 1,238 0,438 1,871 1,803 263,800 0,887 3,41 0,060 –0,047 0,222 0,826 0,045 0,011 0,011 0,609

0,338 1,335 68,02 2,019 0,333 2,085 1,806 266,737 0,873 4,79 0,096 0,005 0,409 1,485 0,054 0,063 0,064 0,953

0,524 1,341 63,43 3,385 0,246 2,370 1,790 263,798 0,879 7,04 0,157 0,102 0,755 2,844 0,069 0,147 0,148 1,591

0,846 1,306 57,59 6,119 0,172 2,790 1,758 256,513 0,901 10,80 0,270 0,320 1,476 6,156 0,094 0,293 0,293 2,916

1,534 1,240 49,80 13,089 0,107 3,517 1,714 246,007 0,936 18,85 0,524 0,962 3,420 17,016 0,139 0,603 0,603 6,416

3,824 1,144 38,09 43,390 0,049 5,237 1,659 232,808 0,981 46,29 1,454 4,265 12,856 86,361 0,272 1,777 1,777 23,268

8,906 1,081 28,45 136,265 0,023 7,783 1,627 225,087 1,009 105,72 3,721 15,807 45,042 407,129 0,523 4,864 4,863 81,056

16,009 1,051 22,64 305,473 0,014 10,294 1,613 221,714 1,022 184,85 6,936 40,897 106,192 1 241,172 0,729 8,678 8,678 184,187

---------------------- Page: 15 ----------------------
ISO/TS 31657-2:2020(E)
12 © ISO 2020 – All rights reserved

Table 8 — Characteristic values of a two-lobe bearing with Ω = 150°, φ = 270°, h = 1, B* = 0,75

P,1
0,max
* * * * * * * * * * * * * *
So ε β [°]
pS⋅ o h Q Q Q ΔT c c c c d d d d
max f 3 max
min P 2 11 12 21 22 11 12 21 22

0,000 0,000 90,00 0,000 1,000 2,614 0,000 2,419 1,500 2,00 0,000 –0,397 1,303 0,000 0,793 0,000 0,000 2,604

0,067 0,100 76,62 0,136 0,900 2,503 0,106 2,480 1,370 2,20 0,100 –0,209 0,696 0,112 0,427 0,101 0,101 1,392

0,162 0,225 63,62 0,343 0,775 2,442 0,217 2,685 1,219 2,70 0,252 –0,253 0,871 0,293 0,551 0,273 0,273 1,744

0,290 0,348 54,89 0,648 0,652 2,488 0,299 2,963 1,088 3,38 0,472 –0,332 1,207 0,579 0,794 0,558 0,557 2,425

0,457 0,457 48,98 1,091 0,543 2,635 0,355 3,240 0,985 4,09 0,721 –0,361 1,696 1,103 0,999 0,870 0,871 3,406

0,692 0,555 43,88 1,780 0,445 2,882 0,390 3,475 0,903 4,90 1,042 –0,331 2,442 2,074 1,199 1,247 1,248 4,895

1,051 0,645 39,18 2,936 0,355 3,251 0,410 3,655 0,838 6,02 1,540 –0,234 3,707 3,955 1,496 1,835 1,835 7,407

1,653 0,729 34,54 5,096 0,271 3,797 0,415 3,765 0,788 7,80 2,399 0,043 6,097 8,041 1,966 2,855 2,854 12,140

2,787 0,807 29,76 9,707 0,193 4,637 0,406 3,793 0,755 10,96 4,080 0,888 11,320 18,552 2,781 4,861 4,862 22,404

5,384 0,879 24,49 22,147 0,121 6,098 0,382 3,723 0,742 18,01 8,162 4,039 26,083 54,894 4,462 9,790 9,792 51,020

14,772 0,945 17,77 80,430 0,055 9,630 0,335 3,530 0,761 42,36 24,424 25,423 102,609 311,066 9,486 29,552 29,548 194,465

37,137 0,975 12,88 268,936 0,025 15,046 0,295 3,368 0,797 98,40 67,256 120,183 382,518 1 634,706 18,574 81,019 81,010 695,146

70,430 0,986 10,12 636,223 0,014 20,696 0,272 3,286 0,823 176,24 135,182 347,197 971,881 5 376,094 28,396 158,436 158,420 1 696,999

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ISO/TS 31657-2:2020(E)
© ISO 2020 – All rights reserved 13

Table 9 — Characteristic values of a two-lobe bearing with Ω = 150°, φ = 270°, h = 3, B* = 0,75

P,1
0,max
* * * * * * * * * * * * * *
So ε β [°] F
pS⋅ o h Q Q Q ΔT c c c c d d d d
max f 3 max
min P 2 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 0,019 –0,174 0,107 0,364 0,093 –0,168 –0,168 0,541

0,045 0,300 83,10 0,392 0,942 1,802 0,984 38,266 1,584 1,40 0,025 –0,175 0,117 0,382 0,099 –0,161 –0,160 0,560

0,117 0,638 80,98 0,557 0,808 1,892 1,067 43,136 1,466 1,73 0,046 –0,171 0,165 0,470 0,118 –0,127 –0,126 0,650

0,227 0,900 77,18 0,909 0,632 2,059 1,158 49,062 1,323 2,37 0,091 –0,143 0,291 0,703 0,146 –0,047 –0,046 0,872

0,353 1,026 73,00 1,404 0,499 2,241 1,197 52,183 1,245 3,20 0,148 –0,089 0,483 1,096 0,170 0,055 0,055 1,206

0,510 1,086 68,38 2,114 0,396 2,450 1,198 53,198 1,212 4,30 0,228 –0,007 0,769 1,762 0,195 0,181 0,181 1,718

0,721 1,110 63,23 3,198 0,311 2,709 1,176 52,773 1,210 5,78 0,341 0,119 1,214 2,965 0,228 0,338 0,338 2,533

1,042 1,114 57,40 5,043 0,236 3,065 1,137 51,373 1,230 8,14 0,522 0,341 2,001 5,377 0,280 0,576 0,576 4,004

1,594 1,105 50,69 8,665 0,168 3,600 1,084 49,245 1,268 12,06 0,845 0,828 3,608 11,141 0,363 0,969 0,968 6,955

2,789 1,085 42,46 17,882 0,106 4,546 1,018 46,449 1,326 20,82 1,590 2,224 8,015 29,830 0,542 1,900 1,900 15,036

6,710 1,053 31,31 57,534 0,049 6,779 0,936 43,014 1,409 48,78 4,258 9,513 28,983 147,989 1,032 5,266 5,266 52,508

15,486 1,030 22,73 180,447 0,023 10,111 0,887 40,957 1,467 108,79 10,525 37,762 98,999 719,051 1,718 12,433 12,433 169,558

27,571 1,020 18,00 406,280 0,013 13,447 0,867 40,095 1,493 194,71 20,214 89,574 239,540 2 124,936 2,831 26,132 26,132 419,399

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ISO/TS 31657-2:2020(E)
14 © ISO 2020 – All rights reserved

Table 10 — Characteristic values of a two-lobe bearing with Ω = 150°, φ = 270°, h = 5, B* = 0,75

P,1
0,max
* * * * * * * * * * * * * *
So ε β [°]
pS⋅ o h Q Q Q ΔT c c c c d d d d
max f 3 max
min P 2 11 12 21 22 11 12 21 22

0,000 0,000 90,00 0,342 1,000 1,507 1,787 152,625 1,669 1,25 0,022 –0,110 0,038 0,284 0,039 –0,081 –0,081 0,315

0,029 0,300 78,47 0,399 0,929 1,520 1,799 154,807 1,651 1,40 0,023 –0,110 0,043 0,295 0,039 –0,080 –0,080 0,325

0,049 0,488 78,16 0,453 0,872 1,543 1,817 158,387 1,622 1,54 0,025 –0,110 0,049 0,315 0,041 –0,077 –0,077 0,341

0,108 0,877 76,80 0,656 0,714 1,642 1,879 171,063 1,520 2,02 0,035 –0,107 0,084 0,419 0,046 –0,063 –0,063 0,419

0,187 1,139 74,73 0,998 0,562 1,788 1,934 183,227 1,421 2,79 0,052 –0,094 0,157 0,629 0,054 –0,035 –0,035 0,569

0,294 1,289 71,93 1,548 0,433 1,974 1,962 190,823 1,356 3,86 0,079 –0,061 0,286 1,033 0,063 0,009 0,009 0,815

0,444 1,355 68,35 2,439 0,327 2,209 1,961 193,200 1,330 5,54 0,124 0,003 0,513 1,803 0,076 0,079 0,079 1,245

0,667 1,361 63,83 3,967 0,241 2,519 1,935 191,147 1,338 8,08 0,198 0,129 0,922 3,404 0,093 0,182 0,181 2,001

1,044 1,324 58,10 6,949 0,168 2,971 1,891 185,766 1,371 12,44 0,335 0,400 1,772 7,225 0,123 0,361 0,361 3,568

1,825 1,254 50,39 14,389 0,104 3,743 1,834 177,889 1,425 21,58 0,641 1,169 4,049 19,502 0,180 0,749 0,749 7,686

4,371 1,151 38,56 46,618 0,047 5,555 1,766 167,848 1,499 51,14 1,733 5,058 14,976 97,311 0,343 2,180 2,180 27,196

9,686 1,085 28,94 141,384 0,023 8,110 1,730 162,095 1,544 112,02 4,175 18,270 49,367 439,551 0,591 5,339 5,339 86,992

17,351 1,053 22,89 321,176 0,013 10,739 1,715 159,494 1,565 196,95 7,771 47,131 117,285 1 358,273 0,819 9,579 9,579 199,359

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ISO/TS 31657-2:2020(E)
© ISO 2020 – All rights reserved 15

Table 11 — Characteristic values of a two-lobe bearing with Ω = 150°, φ = 270°, h = 1, B* = 1

P,1
0,max
* * * * * * * * * * * * * *
So ε β [°] F
pS⋅ o h Q Q Q ΔT c c c c d d d d
max f 3 max
min P 2 11 12 21 22 11 12 21 22

0,000 0,000 90,00 0,000 1,000 2,614 0,000 2,108 2,000 2,00 0,000 –0,489 1,949 0,000 0,978 0,000 0,000 3,900

0,099 0,100 75,43 0,202 0,900 2,504 0,122 2,158 1,834 2,21 0,135 –0,259 1,039 0,163 0,528 0,138 0,138 2,084

0,229 0,217 62,56 0,479 0,783 2,451 0,237 2,311 1,651 2,70 0,323 –0,309 1,262 0,399 0,671 0,349 0,348 2,558

0,402 0,338 53,64 0,882 0,662 2,502 0,324 2,531 1,483 3,38 0,597 –0,405 1,685 0,766 0,957 0,704 0,704 3,465

0,624 0,448 47,91 1,451 0,552 2,656 0,382 2,764 1,344 4,23 0,941 –0,501 2,314 1,367 1,318 1,190 1,191 4,826

0,933 0,549 43,19 2,317 0,451 2,919 0,419 2,983 1,228 5,11 1,335 –0,472 3,215 2,548 1,563 1,664 1,665 6,733

1,391 0,642 38,78 3,732 0,358 3,315 0,438 3,166 1,134 6,40 1,936 –0,360 4,718 4,788 1,913 2,386 2,385 9,890

2,118 0,727 34,46 6,227 0,273 3,890 0,440 3,295 1,061 8,35 2,935 –0,048 7,439 9,440 2,463 3,590 3,592 15,533

3,466 0,807 29,85 11,452 0,193 4,788 0,427 3,361 1,010 11,89 4,896 0,934 13,394 21,341 3,419 5,955 5,959 27,630

6,450 0,880 24,68 25,040 0,120 6,339 0,397 3,345 0,988 19,73 9,558 4,626 29,934 61,882 5,316 11,559 11,552 60,213

16,854 0,946 17,96 86,518 0,054 10,043 0,343 3,220 1,011 46,31 27,847 29,359 114,765 343,527 10,933 33,673 33,682 219,295

40,350 0,975 13,08 277,380 0,025 15,534 0,300 3,102 1,058 104,69 74,270 131,880 413,357 1 726,357 21,118 90,642 90,640 754,679

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ISO/TS 31657-2:2020(E)
16 © ISO 2020 – All rights reserved

Table 12 — Characteristic values of a two-lobe bearing with Ω = 150°, φ = 270°, h = 3, B* = 1

P,1
0,max
* * * * * * * * * * * * * *
So ε β [°] F
pS⋅ o h Q Q Q ΔT c c c c d d d d
max f 3 max
min P 2 11 12 21 22 11 12 21 22

0,000 0,000 90,00 0,393 1,000 1,808 0,986 29,398 2,196 1,31 0,019 –0,207 0,147 0,440 0,114 –0,211 –0,211 0,698

0,079 0,400 83,67 0,512 0,918 1,850 1,035 31,411 2,112 1,55 0,031 –0,207 0,166 0,476 0,126 –0,193 –0,193 0,735

0,159 0,675 81,48 0,697 0,796 1,942 1,118 35,083 1,961 1,90 0,057 –0,201 0,221 0,572 0,149 –0,1

...

TECHNICAL ISO/TS
SPECIFICATION 31657-2
First edition
Plain bearings — Hydrodynamic plain
journal bearings under steady-state
conditions —
Part 2:
Functions for calculation of multi-
lobed journal bearings
PROOF/ÉPREUVE
Reference number
ISO/TS 31657-2:2020(E)
ISO 2020
---------------------- Page: 1 ----------------------
ISO/TS 31657-2:2020(E)
COPYRIGHT PROTECTED DOCUMENT
© 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.
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Published in Switzerland
ii PROOF/ÉPREUVE © ISO 2020 – All rights reserved
---------------------- Page: 2 ----------------------
ISO/TS 31657-2:2020(E)
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 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 .............................................................................................................................................................................................................................68

© ISO 2020 – All rights reserved PROOF/ÉPREUVE iii
---------------------- Page: 3 ----------------------
ISO/TS 31657-2:2020(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.

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 PROOF/ÉPREUVE © ISO 2020 – All rights reserved
---------------------- Page: 4 ----------------------
TECHNICAL SPECIFICATION ISO/TS 31657-2:2020(E)
Plain bearings — Hydrodynamic plain journal bearings
under steady-state conditions —
Part 2:
Functions for calculation of multi-lobed journal bearings
1 Scope

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

The functions plotted and listed in table form below are required for the operationally safe design

of hydrodynamic multi-lobed 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.

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 two-, three- and four-lobe bearings with relative lubrication pocket widths

of b = 0,8 are shown in table form below. The characteristic values were calculated for the geometrical

parameters 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

P,1 0,max
* *

0,02 ≤ h ≤ 1. The profile factors ,K , associated with the indicated gap ratios, h , can be

min P 0,max
calculated for these bearing types as follows:
Kh= for Z = 2
P 0,max
Kh=⋅21− for Z = 3
P 0,max
© ISO 2020 – All rights reserved PROOF/ÉPREUVE 1
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ISO/TS 31657-2:2020(E)
h −
0,max
K = for Z = 4

The following (dimensionless) characteristic values are indicated in Tables 1 to 43:

a) Static characteristic values
Sommerfeld number:
F⋅ψ
eff
So=
BD⋅⋅ηω⋅
eff
Relative eccentricity:
ε =
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:
min
h =
min
R,eff
Friction force parameter:
F =⋅So
eff
Lubricant flow rate parameter due to hydrodynamic pressure build-up:
Q =
Lubricant flow rate parameter due to supply pressure:
Q =
PQ⋅
en 0
Lubricant flow rate parameter at the exit of the lubrication gap:
Q =

Non-dimensional difference between maximum lubricant temperature and lubricant temperature

in the lubricant pockets:
ρψ⋅⋅c
p eff
ΔΔT = ⋅ T
max max
pf⋅
2 PROOF/ÉPREUVE © ISO 2020 – All rights reserved
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ISO/TS 31657-2:2020(E)
b) Dynamic characteristic values
Non-dimensional lubricant film stiffness coefficients:
eff
c = ⋅c (i, k = 1, 2)
ik, ik,
2⋅⋅Bηω⋅
eff
Non-dimensional lubricant film damping coefficients:
eff
d = ⋅⋅ω d (i, k = 1, 2)
ik, ik,
2⋅⋅Bηω⋅
eff

For some selected four-lobe bearings (Ω = 70°, ϕ = 315°), these characteristic values are shown

P,1

graphically as a function of the Sommerfeld number So, the gap ratio h and the bearing width ratio

0,max
B in Annex A, Figures A.1 to A.16.
Figure 1 — Geometrical parameters of selected multi-lobed journal bearings
© ISO 2020 – All rights reserved PROOF/ÉPREUVE 3
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ISO/TS 31657-2:2020(E)
4.2 Two-lobe bearings
Characteristic values for two-lobe bearings are listed in Tables 1 to 15.
4 PROOF/ÉPREUVE © ISO 2020 – All rights reserved
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ISO/TS 31657-2:2020(E)
© ISO 2020 – All rights reserved PROOF/ÉPREUVE 5

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 [°] F
pS⋅ o h Q Q Q ΔT c c c c d d d d
max f 3 max
min P 2 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

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ISO/TS 31657-2:2020(E)
6 PROOF/ÉPREUVE © ISO 2020 – All rights reserved

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 [°] F
pS⋅ o h Q Q Q ΔT c c c c d d d d
max f 3 max
min P 2 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 0,027 12,809 2,873 371,364 0,056 54,49 334,928 30,443 71,696 186,580 74,182 9,627 9,627 41,342

14,689 2,970 0,03 224,879 0,017 17,027 2,886 374,341 0,035 89,35 926,933 61,807 152,876 517,668 164,982 19,973 19,972 92,317

---------------------- Page: 10 ----------------------
ISO/TS 31657-2:2020(E)
© ISO 2020 – All rights reserved PROOF/ÉPREUVE 7

Table 3 — Characteristic values of a two-lobe bearing with Ω = 150°, φ = 240°, h = 3, B* = 0,75

P,1
0,max
* * * * * * * * * * * * * *
So ε β [°] F
pS⋅ o h Q Q Q ΔT c c c c d d d d
max f 3 max
min P 2 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 0,135 –0,307 –0,025 0,249 0,351 –0,278 –0,278 0,283

0,024 0,300 65,76 0,343 0,948 1,800 0,986 38,272 1,585 1,30 0,144 –0,316 –0,024 0,259 0,360 –0,279 –0,279 0,296

0,053 0,600 64,93 0,388 0,863 1,862 1,065 42,498 1,483 1,39 0,176 –0,345 –0,021 0,296 0,394 –0,286 –0,285 0,339

0,096 0,900 63,58 0,501 0,756 1,983 1,191 49,575 1,320 1,55 0,239 –0,401 –0,010 0,380 0,458 –0,297 –0,297 0,435

0,195 1,255 61,44 0,833 0,612 2,255 1,387 61,648 1,055 2,00 0,395 –0,528 0,031 0,646 0,603 –0,316 –0,316 0,697

0,337 1,488 59,74 1,406 0,502 2,590 1,535 71,722 0,844 2,77 0,602 –0,683 0,128 1,168 0,780 –0,327 –0,326 1,148

0,647 1,698 58,00 2,889 0,331 3,159 1,675 82,206 0,632 4,44 0,968 –0,912 0,463 2,796 1,054 –0,296 –0,296 2,322

1,449 1,860 56,29 7,683 0,182 4,165 1,784 91,126 0,455 9,19 1,578 –1,003 1,986 9,830 1,400 0,010 0,010 6,279

4,655 1,931 53,56 34,941 0,068 6,408 1,816 94,911 0,372 29,85 3,188 2,998 14,895 75,236 1,592 2,566 2,567 30,672

11,520 1,879 50,12 119,413 0,030 9,298 1,747 90,997 0,431 76,95 7,878 21,587 63,226 403,924 1,955 9,260 9,259 113,638

26,368 1,811 46,94 379,970 0,014 13,580 1,670 86,161 0,509 179,60 19,622 83,789 224,646 1 939,293 3,095 25,234 25,233 393,073

---------------------- Page: 11 ----------------------
ISO/TS 31657-2:2020(E)
8 PROOF/ÉPREUVE © ISO 2020 – All rights reserved

Table 4 — Characteristic values of a two-lobe bearing with Ω = 150°, φ = 240°, h = 5, B* = 0,75

P,1
0,max
* * * * * * * * * * * * * *
So ε β [°]
pS⋅ o h Q Q Q ΔT c c c c d d d d
max f 3 max
min P 2 11 12 21 22 11 12 21 22

0,000 0,000 90,00 0,342 1,000 1,507 1,787 152,625 1,669 1,25 0,119 –0,206 –0,057 0,188 0,178 –0,160 –0,160 0,175

0,013 0,300 59,79 0,356 0,988 1,517 1,801 154,887 1,650 1,27 0,121 –0,209 –0,058 0,193 0,181 –0,162 –0,162 0,180

0,028 0,600 59,61 0,387 0,951 1,548 1,839 161,674 1,597 1,34 0,130 –0,220 –0,060 0,209 0,189 –0,167 –0,167 0,193

0,046 0,900 59,33 0,442 0,890 1,604 1,902 172,982 1,508 1,44 0,148 –0,240 –0,065 0,240 0,203 –0,176 –0,176 0,218

0,074 1,231 58,89 0,549 0,792 1,703 1,998 190,702 1,371 1,64 0,179 –0,279 –0,073 0,305 0,230 –0,194 –0,194 0,269

0,111 1,518 58,43 0,717 0,683 1,837 2,102 210,507 1,220 1,95 0,225 –0,335 –0,083 0,413 0,268 –0,218 –0,218 0,350

0,171 1,797 57,95 1,021 0,556 2,037 2,219 233,701 1,046 2,47 0,300 –0,428 –0,097 0,630 0,324 –0,255 –0,255 0,499

0,281 2,070 57,47 1,659 0,416 2,354 2,348 260,142 0,851 3,45 0,433 –0,601 –0,115 1,150 0,415 –0,318 –0,318 0,815

0,546 2,341 57,09 3,440 0,264 2,940 2,489 290,060 0,633 5,87 0,710 –1,003 –0,110 2,946 0,588 –0,441 –0,441 1,731

1,816 2,625 56,97 15,037 0,101 4,646 2,652 325,394 0,380 17,84 1,631 –2,658 0,683 21,407 1,044 –0,742 –0,742 8,014

3,419 2,702 57,02 34,428 0,058 6,004 2,699 335,693 0,306 34,13 2,381 –4,050 3,505 65,596 1,325 –0,735 –0,735 19,502

13,503 2,757 56,80 224,496 0,017 10,618 2,731 343,151 0,252 136,17 5,394 6,815 53,808 863,057 1,707 2,358 2,358 132,080

---------------------- Page: 12 ----------------------
ISO/TS 31657-2:2020(E)
© ISO 2020 – All rights reserved PROOF/ÉPREUVE 9

Table 5 — Characteristic values of a two-lobe bearing with Ω = 150°, φ = 270°, h = 1, B* = 0,5

P,1
0,max
* * * * * * * * * * * * * *
So ε β [°]
pS⋅ o h Q Q Q ΔT c c c c d d d d
max f 3 max
min P 2 11 12 21 22 11 12 21 22

0,000 0,000 90,00 0,000 1,000 2,614 0,000 3,008 1,000 2,00 0,000 –0,262 0,671 0,000 0,523 0,000 0,000 1,342

0,090 0,236 64,91 0,192 0,764 2,430 0,175 3,394 0,796 2,71 0,160 –0,171 0,469 0,163 0,372 0,174 0,174 0,923

0,163 0,361 56,42 0,373 0,639 2,471 0,245 3,784 0,706 3,34 0,292 –0,210 0,674 0,345 0,510 0,339 0,338 1,309

0,260 0,467 50,13 0,643 0,533 2,607 0,291 4,131 0,639 3,93 0,438 –0,204 0,976 0,690 0,599 0,501 0,501 1,868

0,401 0,562 44,64 1,081 0,438 2,833 0,323 4,403 0,588 4,66 0,650 –0,180 1,473 1,332 0,730 0,740 0,740 2,783

0,626 0,649 39,58 1,849 0,351 3,168 0,342 4,584 0,548 5,68 0,983 –0,107 2,338 2,622 0,926 1,120 1,120 4,383

1,011 0,729 34,71 3,317 0,271 3,649 0,351 4,663 0,520 7,20 1,570 0,093 4,007 5,477 1,241 1,791 1,793 7,460

1,783 0,805 29,68 6,656 0,195 4,392 0,350 4,633 0,502 9,89 2,748 0,706 7,804 13,213 1,799 3,154 3,155 14,473

3,709 0,877 24,15 16,512 0,123 5,714 0,335 4,477 0,497 15,89 5,805 3,052 19,273 41,921 3,039 6,768 6,767 35,742

11,175 0,943 17,40 66,166 0,057 8,914 0,303 4,174 0,511 36,26 18,352 19,280 80,457 252,403 6,810 21,690 21,697 148,293

30,369 0,974 12,58 238,937 0,026 13,981 0,273 3,946 0,534 85,56 53,612 93,221 315,937 1 384,251 14,455 64,581 64,585 574,742

59,033 0,985 9,96 568,507 0,015 19,196 0,255 3,837 0,550 155,16 109,469 267,165 805,560 4 501,754 23,051 130,675 130,663 1 433,334

---------------------- Page: 13 ----------------------
ISO/TS 31657-2:2020(E)
10 PROOF/ÉPREUVE © ISO 2020 – All rights reserved

Table 6 — Characteristic values of a two-lobe bearing with Ω = 150°, φ = 270°, h = 3, B* = 0,5

P,1
0,max
* * * * * * * * * * * * * *
So ε β [°] F
pS⋅ o h Q Q Q ΔT c c c c d d d d
max f 3 max
min P 2 11 12 21 22 11 12 21 22

0,000 0,000 90,00 0,219 1,000 1,737 0,864 50,725 1,052 1,16 0,017 –0,121 0,059 0,244 0,062 –0,107 –0,107 0,330

0,029 0,300 81,39 0,264 0,934 1,758 0,884 52,595 1,030 1,30 0,020 –0,121 0,067 0,259 0,066 –0,102 –0,102 0,346

0,065 0,574 79,98 0,352 0,825 1,819 0,935 57,521 0,972 1,54 0,031 –0,121 0,093 0,310 0,075 –0,088 –0,087 0,394

0,138 0,861 76,57 0,600 0,646 1,967 1,014 65,671 0,879 2,09 0,059 –0,105 0,182 0,481 0,095 –0,040 –0,040 0,549

0,228 1,001 72,54 0,976 0,510 2,132 1,054 70,214 0,825 2,83 0,101 –0,068 0,328 0,784 0,113 0,030 0,030 0,797

0,343 1,066 67,95 1,538 0,404 2,320 1,064 71,688 0,804 3,75 0,160 –0,010 0,551 1,309 0,133 0,121 0,121 1,184

0,505 1,092 62,75 2,424 0,318 2,554 1,052 71,111 0,804 5,03 0,246 0,084 0,904 2,271 0,159 0,240 0,241 1,814

0,756 1,097 56,85 3,974 0,243 2,874 1,026 69,181 0,819 6,99 0,385 0,250 1,532 4,237 0,198 0,418 0,418 2,959

1,208 1,090 50,03 7,147 0,174 3,365 0,989 66,289 0,845 10,42 0,642 0,617 2,852 9,028 0,266 0,735 0,736 5,382

2,202 1,074 41,86 15,349 0,110 4,232 0,940 62,611 0,882 17,84 1,239 1,686 6,465 24,638 0,409 1,478 1,479 12,023

5,666 1,047 30,73 52,233 0,051 6,345 0,876 58,047 0,935 42,44 3,428 7,798 24,121 128,756 0,772 4,047 4,046 43,158

13,560 1,028 22,43 166,704 0,024 9,519 0,837 55,380 0,971 98,25 8,914 30,395 85,418 623,960 1,465 10,802 10,799 150,032

24,443 1,019 17,86 371,567 0,014 12,657 0,819 54,246 0,987 175,92 17,061 74,399 204,567 1 848,538 2,327 21,727 21,726 361,019

---------------------- Page: 14 ----------------------
ISO/TS 31657-2:2020(E)
© ISO 2020 – All rights reserved PROOF/ÉPREUVE 11

Table 7 — Characteristic values of a two-lobe bearing with Ω = 150°, φ = 270°, h = 5, B* = 0,5

P,1
0,max
* * * * * * * * * * * * * *
So ε β [°]
pS⋅ o h Q Q Q ΔT c c c c d d d d
max f 3 max
min P 2 11 12 21 22 11 12 21 22

0,000 0,000 90,00 0,247 1,000 1,450 1,650 213,796 1,082 1,13 0,017 –0,082 0,023 0,209 0,027 –0,055 –0,055 0,212

0,016 0,250 77,97 0,282 0,941 1,459 1,658 215,843 1,072 1,25 0,018 –0,082 0,025 0,215 0,027 –0,055 –0,055 0,217

0,033 0,470 77,67 0,329 0,874 1,481 1,675 221,018 1,052 1,39 0,019 –0,082 0,031 0,233 0,028 –0,053 –0,053 0,230

0,075 0,854 76,43 0,487 0,718 1,569 1,726 237,424 0,990 1,79 0,026 –0,081 0,057 0,315 0,032 –0,044 –0,044 0,289

0,133 1,118 74,44 0,768 0,567 1,701 1,775 253,621 0,928 2,43 0,039 –0,071 0,115 0,489 0,037 –0,024 –0,024 0,405

0,217 1,270 71,65 1,238 0,438 1,871 1,803 263,800 0,887 3,41 0,060 –0,047 0,222 0,826 0,045 0,011 0,011 0,609

0,338 1,335 68,02 2,019 0,333 2,085 1,806 266,737 0,873 4,79 0,096 0,005 0,409 1,485 0,054 0,063 0,064 0,953

0,524 1,341 63,43 3,385 0,246 2,370 1,790 263,798 0,879 7,04 0,157 0,102 0,755 2,844 0,069 0,147 0,148 1,591

0,846 1,306 57,59 6,119 0,172 2,790 1,758 256,513 0,901 10,80 0,270 0,320 1,476 6,156 0,094 0,293 0,293 2,916

1,534 1,240 49,80 13,089 0,107 3,517 1,714 246,007 0,936 18,85 0,524 0,962 3,420 17,016 0,139 0,603 0,603 6,416

3,824 1,144 38,09 43,390 0,049 5,237 1,659 232,808 0,981 46,29 1,454 4,265 12,856 86,361 0,272 1,777 1,777 23,268

8,906 1,081 28,45 136,265 0,023 7,783 1,627 225,087 1,009 105,72 3,721 15,807 45,042 407,129 0,523 4,864 4,863 81,056

16,009 1,051 22,64 305,473 0,014 10,294 1,613 221,714 1,022 184,85 6,936 40,897 106,192 1 241,172 0,729 8,678 8,678 184,187

---------------------- Page: 15 ----------------------
ISO/TS 31657-2:2020(E)
12 PROOF/ÉPREUVE © ISO 2020 – All rights reserved

Table 8 — Characteristic values of a two-lobe bearing with Ω = 150°, φ = 270°, h = 1, B* = 0,75

P,1
0,max
* * * * * * * * * * * * * *
So ε β [°]
pS⋅ o h Q Q Q ΔT c c c c d d d d
max f 3 max
min P 2 11 12 21 22 11 12 21 22

0,000 0,000 90,00 0,000 1,000 2,614 0,000 2,419 1,500 2,00 0,000 –0,397 1,303 0,000 0,793 0,000 0,000 2,604

0,067 0,100 76,62 0,136 0,900 2,503 0,106 2,480 1,370 2,20 0,100 –0,209 0,696 0,112 0,427 0,101 0,101 1,392

0,162 0,225 63,62 0,343 0,775 2,442 0,217 2,685 1,219 2,70 0,252 –0,253 0,871 0,293 0,551 0,273 0,273 1,744

0,290 0,348 54,89 0,648 0,652 2,488 0,299 2,963 1,088 3,38 0,472 –0,332 1,207 0,579 0,794 0,558 0,557 2,425

0,457 0,457 48,98 1,091 0,543 2,635 0,355 3,240 0,985 4,09 0,721 –0,361 1,696 1,103 0,999 0,870 0,871 3,406

0,692 0,555 43,88 1,780 0,445 2,882 0,390 3,475 0,903 4,90 1,042 –0,331 2,442 2,074 1,199 1,247 1,248 4,895

1,051 0,645 39,18 2,936 0,355 3,251 0,410 3,655 0,838 6,02 1,540 –0,234 3,707 3,955 1,496 1,835 1,835 7,407

1,653 0,729 34,54 5,096 0,271 3,797 0,415 3,765 0,788 7,80 2,399 0,043 6,097 8,041 1,966 2,855 2,854 12,140

2,787 0,807 29,76 9,707 0,193 4,637 0,406 3,793 0,755 10,96 4,080 0,888 11,320 18,552 2,781 4,861 4,862 22,404

5,384 0,879 24,49 22,147 0,121 6,098 0,382 3,723 0,742 18,01 8,162 4,039 26,083 54,894 4,462 9,790 9,792 51,020

14,772 0,945 17,77 80,430 0,055 9,630 0,335 3,530 0,761 42,36 24,424 25,423 102,609 311,066 9,486 29,552 29,548 194,465

37,137 0,975 12,88 268,936 0,025 15,046 0,295 3,368 0,797 98,40 67,256 120,183 382,518 1 634,706 18,574 81,019 81,010 695,146

70,430 0,986 10,12 636,223 0,014 20,696 0,272 3,286 0,823 176,24 135,182 347,197 971,881 5 376,094 28,396 158,436 158,420 1 696,999

---------------------- Page: 16 ----------------------
ISO/TS 31657-2:2020(E)
© ISO 2020 – All rights reserved PROOF/ÉPREUVE 13

Table 9 — Characteristic values of a two-lobe bearing with Ω = 150°, φ = 270°, h = 3, B* = 0,75

P,1
0,max
* * * * * * * * * * * * * *
So ε β [°] F
pS⋅ o h Q Q Q ΔT c c c c d d d d
max f 3 max
min P 2 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 0,019 –0,174 0,107 0,364 0,093 –0,168 –0,168 0,541

0,045 0,300 83,10 0,392 0,942 1,802 0,984 38,266 1,584 1,40 0,025 –0,175 0,117 0,382 0,099 –0,161 –0,160 0,560

0,117 0,638 80,98 0,557 0,808 1,892 1,067 43,136 1,466 1,73 0,046 –0,171 0,165 0,470 0,118 –0,127 –0,126 0,650

0,227 0,900 77,18 0,909 0,632 2,059 1,158 49,062 1,323 2,37 0,091 –0,143 0,291 0,703 0,146 –0,047 –0,046 0,872

0,353 1,026 73,00 1,404 0,499 2,241 1,197 52,183 1,245 3,20 0,148 –0,089 0,483 1,096 0,170 0,055 0,055 1,206

0,510 1,086 68,38 2,114 0,396 2,450 1,198 53,198 1,212 4,30 0,228 –0,007 0,769 1,762 0,195 0,181 0,181 1,718

0,721 1,110 63,23 3,198 0,311 2,709 1,176 52,773 1,210 5,78 0,341 0,119 1,214 2,965 0,228 0,338 0,338 2,533

1,042 1,114 57,40 5,043 0,236 3,065 1,137 51,373 1,230 8,14 0,522 0,341 2,001 5,377 0,280 0,576 0,576 4,004

1,594 1,105 50,69 8,665 0,168 3,600 1,084 49,245 1,268 12,06 0,845 0,828 3,608 11,141 0,363 0,969 0,968 6,955

2,789 1,085 42,46 17,882 0,106 4,546 1,018 46,449 1,326 20,82 1,590 2,224 8,015 29,830 0,542 1,900 1,900 15,036

6,710 1,053 31,31 57,534 0,049 6,779 0,936 43,014 1,409 48,78 4,258 9,513 28,983 147,989 1,032 5,266 5,266 52,508

15,486 1,030 22,73 180,447 0,023 10,111 0,887 40,957 1,467 108,79 10,525 37,762 98,999 719,051 1,718 12,433 12,433 169,558

27,571 1,020 18,00 406,280 0,013 13,447 0,867 40,095 1,493 194,71 20,214 89,574 239,540 2 124,936 2,831 26,132 26,132 419,399

---------------------- Page: 17 ----------------------
ISO/TS 31657-2:2020(E)
14 PROOF/ÉPREUVE © ISO 2020 – All rights reserved

Table 10 — Characteristic values of a two-lobe bearing with Ω = 150°, φ = 270°, h = 5, B* = 0,75

P,1
0,max
* * * * * * * * * * * * * *
So ε β [°]
pS⋅ o h Q Q Q ΔT c c c c d d d d
max f 3 max
min P 2 11 12 21 22 11 12 21 22

0,000 0,000 90,00 0,342 1,000 1,507 1,787 152,625 1,669 1,25 0,022 –0,110 0,038 0,284 0,039 –0,081 –0,081 0,315

0,029 0,300 78,47 0,399 0,929 1,520 1,799 154,807 1,651 1,40 0,023 –0,110 0,043 0,295 0,039 –0,080 –0,080 0,325

0,049 0,488 78,16 0,453 0,872 1,543 1,817 158,387 1,622 1,54 0,025 –0,110 0,049 0,315 0,041 –0,077 –0,077 0,341

0,108 0,877 76,80 0,656 0,714 1,642 1,879 171,063 1,520 2,02 0,035 –0,107 0,084 0,419 0,046 –0,063 –0,063 0,419

0,187 1,139 74,73 0,998 0,562 1,788 1,934 183,227 1,421 2,79 0,052 –0,094 0,157 0,629 0,054 –0,035 –0,035 0,569

0,294 1,289 71,93 1,548 0,433 1,974 1,962 190,823 1,356 3,86 0,079 –0,061 0,286 1,033 0,063 0,009 0,009 0,815

0,444 1,355 68,35 2,439 0,327 2,209 1,961 193,200 1,330 5,54 0,124 0,003 0,513 1,803 0,076 0,079 0,079 1,245

0,667 1,361 63,83 3,967 0,241 2,519 1,935 191,147 1,338 8,08 0,198 0,129 0,922 3,404 0,093 0,182 0,181 2,001

1,044 1,324 58,10 6,949 0,168 2,971 1,891 185,766 1,371 12,44 0,335 0,400 1,772 7,225 0,123 0,361 0,361 3,568

1,825 1,254 50,39 14,389 0,104 3,743 1,834 177,889 1,425 21,58 0,641 1,169 4,049 19,502 0,180 0,749 0,749 7,686

4,371 1,151 38,56 46,618 0,047 5,555 1,766 167,848 1,499 51,14 1,733 5,058 14,976 97,311 0,343 2,180 2,180 27,196

9,686 1,085 28,94 141,384 0,023 8,110 1,730 162,095 1,544 112,02 4,175 18,270 49,367 439,551 0,591 5,339 5,339 86,992

17,351 1,053 22,89 321,176 0,013 10,739 1,715 159,494 1,565 196,95 7,771 47,131 117,285 1 358,273 0,819 9,579 9,579 199,359

---------------------- Page: 18 ----------------------
ISO/TS 31657-2:2020(E)
© ISO 2020 – All rights reserved PROOF/ÉPREUVE 15

Table 11 — Characteristic values of a two-lobe bearing with Ω = 150°, φ = 270°, h = 1, B* = 1

P,1
0,max
* * * * * * * * * * * * * *
So ε β [°] F
pS⋅ o h Q Q Q ΔT c c c c d d d d
max f 3 max
min P 2 11 12 21 22 11 12 21 22

0,000 0,000 90,00 0,000 1,000 2,614 0,000 2,108 2,000 2,00 0,000 –0,489 1,949 0,000 0,978 0,000 0,000 3,900

0,099 0,100 75,43 0,202 0,900 2,504 0,122 2,158 1,834 2,21 0,135 –0,259 1,039 0,163 0,528 0,138 0,138 2,084

0,229 0,217 62,56 0,479 0,783 2,451 0,237 2,311 1,651 2,70 0,323 –0,309 1,262 0,399 0,671 0,349 0,348 2,558

0,402 0,338 53,64 0,882 0,662 2,502 0,324 2,531 1,483 3,38 0,597 –0,405 1,685 0,766 0,957 0,704 0,704 3,465

0,624 0,448 47,91 1,451 0,552 2,656 0,382 2,764 1,344 4,23 0,941 –0,501 2,314 1,367 1,318 1,190 1,191 4,826

0,933 0,549 43,19 2,317 0,451 2,919 0,419 2,983 1,228 5,11 1,335 –0,472 3,215 2,548 1,563 1,664 1,665 6,733

1,391 0,642 38,78 3,732 0,358 3,315 0,438 3,166 1,134 6,40 1,936 –0,360 4,718 4,788 1,913 2,386 2,385 9,890

2,118 0,727 34,46 6,227 0,273 3,890 0,440 3,295 1,061 8,35 2,935 –0,048 7,439 9,440 2,463 3,590 3,592 15,533

3,466 0,807 29,85 11,452 0,193 4,788 0,427 3,361 1,010 11,89 4,896 0,934 13,394 21,341 3,419 5,955 5,959 27,630

6,450 0,880 24,68 25,040 0,120 6,339 0,397 3,345 0,988 19,73 9,558 4,626 29,934 61,882 5,316 11,559 11,552 60,213

16,854 0,946 17,96 86,518 0,054 10,043 0,343 3,220 1,011 46,31 27,847 29,359 114,765 343,527 10,933 33,673 33,682 219,295

40,350 0,975 13,08 277,380 0,025 15,534 0,300 3,102 1,058 104,69 74,270 131,880 413,357 1 726,357 21,118 90,642 90,640 754,679

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ISO/TS 31657-2:2020(E)
16 PROOF/ÉPREUVE © ISO 2020 – All rights reserved

Table 12 — Characteristic values of a two-lobe bearing with Ω = 150°, φ = 270°, h = 3, B* = 1

P,1
0,max
* * * * * * * * * * * * * *
So ε β [°] F
pS⋅ o h Q Q Q ΔT c c c c d d d d
max f 3 max
min P 2 11 12 21 22 11 12 21 22
0,000 0,000 90,00 0,393 1,000 1,808 0,986
...

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