Hydrodynamic plain journal bearings under steady-state conditions — Circular cylindrical bearings — Part 2: Functions used in the calculation procedure

This document specifies the values of the basic functions used in the calculation procedure for oil-lubricated circular cylindrical hydrodynamic bearings under conditions of full lubrication. The values are given for the assumptions and boundary conditions given in ISO 7902-1. The values necessary for the calculation can be determined from the tables of bearing characteristics, the graphs and from the formulae. The descriptions of the symbols used and calculation examples are given in ISO 7902-1.

Paliers lisses hydrodynamiques radiaux fonctionnant en régime stabilisé — Paliers circulaires cylindriques — Partie 2: Fonctions utilisées pour le calcul

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04-Jun-2020
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16-Apr-2020
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INTERNATIONAL ISO
STANDARD 7902-2
Second edition
2020-06
Hydrodynamic plain journal bearings
under steady-state conditions —
Circular cylindrical bearings —
Part 2:
Functions used in the calculation
procedure
Paliers lisses hydrodynamiques radiaux fonctionnant en régime
stabilisé — Paliers circulaires cylindriques —
Partie 2: Fonctions utilisées pour le calcul
Reference number
ISO 7902-2:2020(E)
ISO 2020
---------------------- Page: 1 ----------------------
ISO 7902-2:2020(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

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below or ISO’s member body in the country of the requester.
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Published in Switzerland
ii © ISO 2020 – All rights reserved
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ISO 7902-2:2020(E)
Contents Page

Foreword ........................................................................................................................................................................................................................................iv

1 Scope ................................................................................................................................................................................................................................. 1

2 Normative references ...................................................................................................................................................................................... 1

3 Terms and definitions ..................................................................................................................................................................................... 1

4 Tables of basic bearing characteristics ......................................................................................................................................... 1

5 Graphs of basic bearing characteristics ....................................................................................................................................11

6 Friction power loss ..........................................................................................................................................................................................61

7 Lubricant flow rate resulting from feed pressure...........................................................................................................61

7.1 General ........................................................................................................................................................................................................61

7.2 Lubrication hole located opposite to direction of load .....................................................................................62

7.3 Lubrication hole located at 90° to direction of load ............................................................................................62

7.4 Lubrication holes located at 90° to direction of load ..........................................................................................63

7.5 Circumferential groove (full groove) ................................................................................................................................63

7.6 Circumferential groove (partial groove) ........................................................................................................................64

7.7 Lubrication pocket, located opposite to direction of load ..............................................................................65

7.8 Lubrication pocket located at 90° to direction of application load ........................................................65

7.9 Two lubrication pockets at ±90° to direction of load .........................................................................................66

8 Effective dynamic viscosity, η , of the lubricant as a function of effective bearing

eff

temperature, T ................................................................................................................................................................................................66

eff

Bibliography .............................................................................................................................................................................................................................68

© ISO 2020 – All rights reserved iii
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ISO 7902-2:2020(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.

This second edition cancels and replaces the first edition (ISO 7902-2:1998), of which it constitutes a

minor revision. The changes compared to the previous edition are as follows:
— adjustment to ISO/IEC Directives, Part 2:2018;
— correction of typographical errors.
A list of all parts in the ISO 7902 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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INTERNATIONAL STANDARD ISO 7902-2:2020(E)
Hydrodynamic plain journal bearings under steady-state
conditions — Circular cylindrical bearings —
Part 2:
Functions used in the calculation procedure
1 Scope

This document specifies the values of the basic functions used in the calculation procedure for oil-

lubricated circular cylindrical hydrodynamic bearings under conditions of full lubrication.

The values are given for the assumptions and boundary conditions given in ISO 7902-1. The values

necessary for the calculation can be determined from the tables of bearing characteristics, the graphs

and from the formulae.

The descriptions of the symbols used and calculation examples are given in ISO 7902-1.

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 7902-1, Hydrodynamic plain journal bearings under steady-state conditions Circular cylindrical

bearings — Part 1: Calculation procedure
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 Tables of basic bearing characteristics

ISO 7902-1:2020, Table 1 shall be referenced to identify the meaning of the symbols used in this

document.
Tables 1 to 30 give
— the attitude angle, β,
— the Sommerfeld number, So,

— the specific coefficient of friction, taking account of the unloaded area of lubricant film, f′/φ,

— the specific coefficient of friction in the loaded area of the lubricant film, f/φ, and

© ISO 2020 – All rights reserved 1
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ISO 7902-2:2020(E)

— the coefficient of lubricant flow rate, parameter Q , due to generation of the internal pressure, as a

function of angular span, Ω, relative eccentricity ε and relative bearing width B/D for various values

of ε, Ω and B/D.
Table 1 — Values of the basic characteristics for Ω = 360° and B/D = 1,5
ε β So f′/φ f/φ
0,2 72,523 6 0,427 3 7,599 2 4,968 4 0,047 7
0,4 62,658 8 1,000 5 3,603 5 2,658 2 0,093 5
0,6 51,969 2 1,972 4 2,227 2 1,669 5 0,136 1
0,8 38,160 1 4,682 4 1,365 3 1,073 6 0,175 9
0,9 27,961 10,138 2 0,921 8 0,760 4 0,193 9
0,925 24,618 4 13,825 6 0,790 6 0,667 8 0,198
0,95 19,800 7 22,044 0,617 3 0,535 9 0,201
0,975 13,597 1 48,842 9 0,404 0,358 6 0,203 6
Table 2 — Values of the basic characteristics for Ω = 360° and B/D = 1,25
ε β So f′/φ f/φ
0,2 73,342 7 0,341 9,497 8 6,201 6 0,044 4
0,4 62,653 3 0,815 5 4,380 8 3,245 7 0,087 6
0,6 51,390 1 1,671 5 2,583 7 1,925 7 0,128 7
0,8 37,247 4 4,210 7 1,485 5 1,128 5 0,167 9
0,9 27,270 1 9,462 1 0,967 8 0,794 9 0,186
0,925 23,958 6 13,083 9 0,819 7 0,69 0,190 1
0,95 19,304 5 21,127 1 0,633 2 0,548 4 0,193 6
0,975 13,315 4 47,533 2 0,409 7 0,363 1 0,195 9
Table 3 — Values of the basic characteristics for Ω = 360° and B/D = 1
ε β So f′/φ f/φ
0,2 74,208 0,249 2 12,958 8,448 9 0,039 4
0,4 62,574 4 0,611 5,786 8 4,272 1 0,078 5
0,6 50,454 5 1,318 2 3,210 2 2,376 1 0,116 4
0,8 36,027 8 3,595 5 1,691 5 1,276 6 0,153 3
0,9 26,368 5 8,520 3 1,045 7 0,853 7 0,170 8
0,925 23,072 6 12,034 2 0,868 2 0,727 5 0,174 8
0,95 18,639 2 19,799 0,659 9 0,569 6 0,178 3
0,975 12,938 8 45,572 1 0,419 3 0,371 0,180 8
2 © ISO 2020 – All rights reserved
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ISO 7902-2:2020(E)
Table 4 — Values of the basic characteristics for Ω = 360° and B/D = 0,75
ε β So f′/φ f/φ
0,2 75,022 0,158 4 20,390 9 13,237 2 0,032 6
0,4 62,258 4 0,399 3 8,760 6 6,183 0,065
0,6 49,355 4 0,915 5 4,516 7 3,316 1 0,097 2
0,8 34,514 4 2,784 8 2,106 7 1,571 2 0,129 2
0,9 25,188 7 7,161 4 1,197 9 0,969 6 0,144 7
0,925 21,882 3 10,461 1 0,962 7 0,801 0,148 3
0,95 17,739 3 17,736 3 0,711 9 0,611 4 0,151 6
0,975 12,426 4 42,382 9 0,438 4 0,386 9 0,153
Table 5 — Values of the basic characteristics for Ω = 360° and B/D = 0,5
ε β So f′/φ f/φ
0,2 75,818 8 0,077 9 41,264 1 26,832 2 0,023 3
0,4 61,762 8 0,202 6 17,087 12,010 1 0,046 8
0,6 47,970 3 0,499 5 8,083 7 5,856 1 0,070 3
0,8 32,965 3 1,74 3,226 7 2,369 8 0,093 8
0,9 23,503 7 5,157 9 1,576 8 1,260 4 0,105 4
0,925 20,317 1 7,916 8 1,205 0,992 0,108 2
0,95 16,529 2 14,175 7 0,844 9 0,719 8 0,110 7
0,975 11,716 4 36,438 0,487 0,415 0,112 8
Table 6 — Values of the basic characteristics for Ω = 360° and B/D = 0,25
ε β So f′/φ f/φ
0,2 75,852 2 0,020 9 153,245 99,557 1 0,012 3
0,4 61,484 3 0,056 61,556 7 41,887 9 0,024 6
0,6 47,407 6 0,146 27,106 5 18,705 8 0,036 8
0,8 31,289 6 0,605 3 8,857 7 6,396 1 0,049 2
0,9 21,531 5 2,203 7 3,435 6 2,697 2 0,055 3
0,925 18,530 6 3,670 7 2,399 4 1,942 4 0,056 8
0,95 15,078 7,346 6 1,493 1 1,254 6 0,058 2
0,975 10,779 2 22,666 5 0,714 9 0,563 2 0,059 5
© ISO 2020 – All rights reserved 3
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ISO 7902-2:2020(E)
Table 7 — Values of the basic characteristics for Ω = 180° and B/D = 1,5
ε β So f′/φ f/φ
0,2 66,676 7 0,378 1 8,571 8 4,556 5 0,038 5
0,4 54,239 5 0,871 1 4,097 2 2,442 4 0,062 8
0,6 44,217 1 1,752 8 2,449 6 1,680 3 0,075 5
0,8 32,582 4,353 1 1,418 2 1,139 1 0,075
0,9 24,256 9,698 7 0,916 1 0,796 0,067 5
0,925 21,517 7 13,445 1 0,784 6 0,678 2 0,063 2
0,95 18,655 7 20,525 9 0,642 3 0,549 5 0,058 9
0,975 12,665 2 47,276 1 0,405 9 0,370 1 0,050 1
Table 8 — Values of the basic characteristics for Ω = 180° and B/D = 1,25
ε Β So f′/φ f/φ
0,2 67,708 5 0,310 6 10,415 5,514 6 0,036 9
0,4 55,202 7 0,732 6 4,843 1 2,866 6 0,061 5
0,6 44,364 2 1,531 2 2,774 4 1,893 1 0,074 8
0,8 32,449 1 3,981 9 1,529 6 1,224 8 0,074 7
0,9 24,033 7 9,227 9 0,964 3 0,822 0,068 2
0,925 21,247 12,858 4 0,810 6 0,707 5 0,064 2
0,95 18,433 19,947 1 0,654 9 0,558 9 0,060 1
0,975 12,347 1 46,753 5 0,406 6 0,370 6 0,050 7
Table 9 — Values of the basic characteristics for Ω = 180° and B/D = 1
ε β So f′/φ f/φ
0,2 69,018 2 0,232 8 13,868 3 7,306 8 0,033 8
0,4 56,409 3 0,560 1 6,286 1 3,687 3 0,057 5
0,6 44,589 1,244 8 3,365 2 2,279 7 0,072 9
0,8 32,368 1 3,451 4 1,731 2 1,379 9 0,073 5
0,9 23,770 1 8,403 7 1,039 0,906 1 0,067 9
0,925 20,898 1 11,940 5 0,857 4 0,744 6 0,064
0,95 18,135 1 18,577 5 0,691 0,589 4 0,060 1
0,975 11,901 7 45,771 0,409 4 0,375 4 0,051 3
4 © ISO 2020 – All rights reserved
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ISO 7902-2:2020(E)
Table 10 — Values of the basic characteristics for Ω = 180° and B/D = 0,75
ε β So f′/φ f/φ
0,2 70,534 9 0,151 3 21,282 4 11,151 3 0,028 9
0,4 57,855 8 0,381 9,166 3 5,320 7 0,051 3
0,6 45,012 4 0,888 3 4,632 8 3,107 8 0,066
0,8 32,312 8 2,698 7 2,154 1,705 0,069 8
0,9 23,336 7 7,137 5 1,188 1,032 2 0,064 9
0,925 20,438 4 10,425 2 0,954 6 0,827 8 0,061 7
0,95 17,579 3 16,746 5 0,746 9 0,639 0,058
0,975 11,294 8 43,512 8 0,420 4 0,380 1 0,051 3
Table 11 — Values of the basic characteristics for Ω = 180° and B/D = 0,5
ε β So f′/φ f/φ
0,2 72,293 9 0,074 7 43,011 7 22,402 8 0,021 3
0,4 58,192 8 0,200 2 17,289 7 9,961 0,039 4
0,6 45,697 1 0,49 8,228 4 5,451 8 0,052 2
0,8 31,575 6 1,722 2 3,249 8 2,550 2 0,057 3
0,9 22,246 5,167 6 1,566 6 1,335 2 0,054 7
0,925 19,751 4 7,843 6 1,210 4 1,039 0,053
0,95 16,593 5 13,85 2 0,862 0,741 9 0,050 8
0,975 10,769 1 38,05 5 0,460 1 0,412 0,045 1
Table 12 — Values of the basic characteristics for Ω = 180° and B/D = 0,25
ε β So f′/φ f/φ
0,2 73,936 4 0,019 169,077 87,621 5 0,011
0,4 59,674 3 0,053 7 64,035 4 36,513 5 0,021 4
0,6 45,563 1 0,146 5 27,014 5 16,989 1 0,029 5
0,8 30,521 4 0,605 4 8,852 2 6,047 2 0,033 9
0,9 21,448 2 2,172 5 3,482 1 2,703 6 0,033 4
0,925 19,517 5 3,461 7 2,543 2,011 9 0,033 2
0,95 14,938 5 7,348 5 1,491 6 1,260 3 0,032 1
0,975 9,461 7 23,426 6 0,683 7 0,566 8 0,029 9
© ISO 2020 – All rights reserved 5
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ISO 7902-2:2020(E)
Table 13 — Values of the basic characteristics for Ω = 150° and B/D = 1,5
ε β So f′/φ f/φ
0,2 61,770 3 0,305 8 10,574 2 4,767 8 0,028 8
0,4 47,933 7 0,738 4,793 3 2,489 0,044 5
0,6 39,850 8 1,554 7 2,718 1 1,659 9 0,052 1
0,8 30,215 2 4,061 6 1,490 5 1,108 2 0,050 1
0,9 23,445 9 9,207 3 0,961 8 0,771 2 0,043 7
0,925 20,432 13,050 8 0,794 9 0,655 1 0,040 3
0,95 17,262 20,569 9 0,630 1 0,525 0,036 5
0,975 12,396 46,556 5 0,408 3 0,35 0,032 5
Table 14 — Values of the basic characteristics for Ω = 150° and B/D = 1,25
ε β So f′/φ f/φ
0,2 62,776 5 0,258 8 12,478 5,604 0,028 3
0,4 48,877 3 0,637 4 5,528 2 2,850 1 0,044 5
0,6 40,280 1 1,380 6 3,038 3 1,843 6 0,052 6
0,8 30,231 1 3,747 2 1,598 7 1,184 4 0,050 9
0,9 23,432 6 8,690 6 1,008 3 0,800 2 0,044 7
0,925 20,295 4 12,474 1 0,823 2 0,680 5 0,041 3
0,95 17,159 2 19,833 7 0,647 4 0,542 5 0,037 5
0,975 12,298 7 45,382 6 0,415 4 0,370 5 0,033 4
Table 15 — Values of the basic characteristics for Ω = 150° and B/D = 1
ε β So f′/φ f/φ
0,2 64,170 8 0,202 2 15,945 7,122 8 0,026 8
0,4 50,190 4 0,509 9 6,875 9 3,51 0,043 4
0,6 41,135 1 1,143 4 3,631 8 2,175 7 0,052 6
0,8 30,244 5 3,296 7 1,789 7 1,318 9 0,051 1
0,9 22,963 4 8,078 7 1,067 7 0,886 2 0,045
0,925 20,115 11,598 6 0,871 9 0,748 8 0,041 9
0,95 16,946 5 18,783 7 0,674 1 0,563 6 0,038 3
0,975 12,184 4 43,302 6 0,429 4 0,376 0,033 9
6 © ISO 2020 – All rights reserved
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ISO 7902-2:2020(E)
Table 16 — Values of the basic characteristics for Ω = 150° and B/D = 0,75
ε β So f′/φ f/φ
0,2 65,961 1 0,136 7 23,553 7 10,449 6 0,023 8
0,4 51,996 3 0,356 1 9,782 7 4,927 4 0,04
0,6 42,117 4 0,837 2 4,891 8 2,887 7 0,05
0,8 30,636 7 2,606 8 2,211 1,615 4 0,049 7
0,9 22,669 5 6,943 8 1,211 4 1,000 8 0,044 3
0,925 19,853 4 10,166 2 0,970 4 0,815 5 0,041 5
0,95 16,681 2 16,940 9 0,730 2 0,608 0,038 2
0,975 11,904 4 40,595 3 0,448 8 0,380 9 0,033 7
Table 17 — Values of the basic characteristics for Ω = 150° and B/D = 0,5
ε β So f′/φ f/φ
0,2 67,982 1 0,070 6 45,488 2 20,028 9 0,018 4
0,4 54,289 6 0,189 9 18,209 7 9,021 1 0,032 3
0,6 43,007 8 0,477 5 8,429 1 4,915 2 0,041 2
0,8 30,304 7 1,692 7 3,295 1 2,378 5 0,043 1
0,9 22,185 9 5,033 5 1,601 8 1,293 0,040 2
0,925 19,66 7,583 4 1,246 1,022 0,038 5
0,95 16,378 1 13,255 2 0,894 6 0,738 3 0,036 1
0,975 11,467 3 34,970 3 0,501 2 0,424 5 0,031 7
Table 18 — Values of the basic characteristics for Ω = 150° and B/D = 0,25
ε β So f′/φ f/φ
0,2 70,141 7 0,018 5 173,657 75,891 2 0,009 9
0,4 56,480 4 0,052 9 65,001 8 31,701 1 0,018 5
0,6 43,946 4 0,144 7 27,351 15,684 6 0,024 8
0,8 29,809 3 0,600 8 8,914 3 6,343 3 0,026 9
0,9 21,215 2 2,153 9 3,509 2,611 2 0,025 9
0,925 18,326 8 3,587 1 2,450 4 1,911 4 0,025 1
0,95 15,853 8 6,827 2 1,603 5 1,270 1 0,024 4
0,975 10,791 7 21,429 5 0,751 0,631 5 0,022 1
© ISO 2020 – All rights reserved 7
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ISO 7902-2:2020(E)
Table 19 — Values of the basic characteristics for Ω = 120° and B/D = 1,5
ε β So f′/φ f/φ
0,2 56,676 3 0,219 6 14,682 2 5,394 3 0,019 5
0,4 42,036 2 0,553 6 6,325 8 2,743 3 0,028 4
0,6 34,566 2 1,267 2 3,269 2 1,713 3 0,033 5
0,8 27,097 3 3,610 8 1,632 3 1,085 8 0,030 8
0,9 21,230 1 8,726 1 0,988 9 0,768 0,025 4
0,925 19,173 2 12,258 2 0,826 4 0,667 3 0,023 5
0,95 16,245 9 19,760 5 0,642 0,514 8 0,020 9
0,975 12,526 3 42,612 1 0,437 5 0,353 7 0,018 1
Table 20 — Values of the basic characteristics for Ω = 120° and B/D = 1,25
ε β So f′/φ f/φ
0,2 58,210 3 0,184 8 17,438 2 6,371 7 0,019 1
0,4 42,953 0,486 9 7,176 7 3,091 1 0,028 7
0,6 35,068 9 1,144 9 3,602 3 1,873 2 0,033 8
0,8 27,206 7 3,366 5 1,738 2 1,151 4 0,031 3
0,9 21,216 3 8,307 8 1,030 4 0,798 4 0,026 3
0,925 19,068 1 11,786 9 0,852 6 0,691 1 0,024 3
0,95 16,196 2 19,095 2 0,659 4 0,530 5 0,022 3
0,975 12,497 1 41,177 5 0,448 8 0,375 1 0,018 9
Table 21 — Values of the basic characteristics for Ω = 120° and B/D = 1
ε β So f′/φ f/φ
0,2 59,398 7 0,153 21,036 7,650 6 0,018 8
0,4 44,128 5 0,407 5 8,550 6 3,649 7 0,028 8
0,6 35,883 7 0,977 9 4,191 5 2,157 8 0,033 6
0,8 27,36 3,009 4 1,923 7 1,266 5 0,031 6
0,9 21,254 9 7,658 1 1,104 3 0,852 5 0,027
0,925 18,998 1 11,022 2 0,900 7 0,728 2 0,025 1
0,95 16,145 2 18,053 6 0,689 4 0,541 8 0,022 5
0,975 12,470 2 39,792 4 0,460 6 0,389 6 0,019 7
8 © ISO 2020 – All rights reserved
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ISO 7902-2:2020(E)
Table 22 — Values of the basic characteristics for Ω = 120° and B/D = 0,75
ε β So f′/φ f/φ
0,2 61,304 5 0,110 2 29,196 2 10,540 9 0,017 5
0,4 45,817 9 0,301 11,530 2 4,858 3 0,027 7
0,6 37,124 9 0,747 1 5,437 2 2,756 5 0,032 8
0,8 27,997 8 2,440 1 2,333 6 1,518 5 0,031 8
0,9 21,183 6 6,656 1 1,245 4 0,956 1 0,027 3
0,925 18,901 5 9,760 2 0,996 9 0,766 5 0,025 5
0,95 15,968 8 16,405 7 0,744 0,590 5 0,022 9
0,975 12,355 1 37,152 8 0,484 9 0,401 0,020 2
Table 23 — Values of the basic characteristics for Ω = 120° and B/D = 0,5
ε β So f′/φ f/φ
0,2 63,707 2 0,061 1 52,602 18,817 3 0,014 4
0,4 48,359 7 0,171 3 20,155 8,330 5 0,023 8
0,6 39,012 5 0,444 6 9,021 4 4,469 2 0,029 5
0,8 27,961 1,641 3 3,377 6 2,166 4 0,029 7
0,9 20,901 3 4,956 1 1,614 8 1,227 2 0,026 3
0,925 18,945 4 7,410 6 1,265 9 0,962 4 0,025
0,95 15,685 6 13,250 3 0,887 8 0,691 3 0,022 7
0,975 11,904 8 31,950 5 0,548 1 0,436 5 0,019 9
Table 24 — Values of the bas
...

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