# ISO 12130-1-2001

Reference numberISO 12130-1:2001(E)©ISO 2001INTERNATIONAL STANDARD ISO12130-1First edition2001-11-15Plain bearings — Hydrodynamic plain tilting pad thrust bearings under steady-state conditions — Part 1: Calculation of tilting pad thrust bearings Paliers lisses — Butées hydrodynamiques à patins oscillants fonctionnant en régime stationnaire — Partie 1: Calcul des butées à patins oscillants --`,```,,,,``,,,```,``,``,,,,`,`-`-`,,`,,`,`,,`---ISO 12130-1:2001(E) PDF disclaimer This PDF file may contain embedded typefaces. In accordance with Adobe s licensing policy, this file may be printed or viewed but shall not be edited unless the typefaces which are embedded are licensed to and installed on the computer performing the editing. In downloading this file, parties accept therein the responsibility of not infringing Adobe s licensing policy. The ISO Central Secretariat accepts no liability in this area. Adobe is a trademark of Adobe Systems Incorporated. Details of the software products used to create this PDF file can be found in the General Info relative to the file; the PDF-creation parameters were optimized for printing. Every care has been taken to ensure that the file is suitable for use by ISO member bodies. In the unlikely event that a problem relating to it is found, please inform the Central Secretariat at the address given below. © ISO 2001 All rights reserved. Unless otherwise specified, no part of this publication may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying and microfilm, without permission in writing from either ISO at the address below or ISO s member body in the country of the requester. ISO copyright office Case postale 56 • CH-1211 Geneva 20 Tel. + 41 22 749 01 11 Fax + 41 22 749 09 47 E-mail copyright@iso.ch Web www.iso.ch Printed in Switzerland © ISO 2001 – All rights reserved --`,```,,,,``,,,```,``,``,,,,`,`-`-`,,`,,`,`,,`---ISO 12130-1:2001(E) iiiContents Page Foreword.iv 1 Scope 1 2 Normative references1 3 Fundamentals, assumptions and premises2 4 Symbols, terms and units.3 5 Calculation procedure.6 5.1 Loading operations .6 5.2 Coordinate of centre of pressure7 5.3 Load-carrying capacity 7 5.4 Frictional power9 5.5 Lubricant flow rate .9 5.6 Heat balance.10 5.7 Minimum lubricant film thickness and specific bearing load .13 5.8 Operating conditions .13 5.9 Further influence factors .14 Annex A (normative) Examples of calculation.15 A.1 Example 15 A.2 Example 19 Bibliography24 ISO 12130-1:2001(E) © ISO 2001 – All rights reserved 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. International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part 3. Draft International Standards adopted by the technical committees are circulated to the member bodies for voting. Publication as an International Standard requires approval by at least 75 % of the member bodies casting a vote. Attention is drawn to the possibility that some of the elements of this part of ISO 12130 may be the subject of patent rights. ISO shall not be held responsible for identifying any or all such patent rights. International Standard ISO 12130-1 was prepared by Technical Committee ISO/TC 123, Plain bearings, Subcommittee SC 4, Methods of calculation of plain bearings. ISO 12130 consists of the following parts, under the general title Plain bearings — Hydrodynamic plain tilting pad thrust bearings under steady-state conditions: Part 1: Calculation of tilting pad thrust bearings Part 2: Functions for calculation of tilting pad thrust bearings Part 3: Guide values for the calculation of tilting pad thrust bearings Annex A forms a normative part of this part of ISO 12130. --`,```,,,,``,,,```,``,``,,,,`,`-`-`,,`,,`,`,,`---INTERNATIONAL STANDARD ISO 12130-1:2001(E)1Plain bearings — Hydrodynamic plain tilting pad thrust bearings under steady-state conditions — Part 1: Calculation of tilting pad thrust bearings 1 Scope The aim of ISO 12130 is to achieve designs of plain bearings that are reliable in operation by the application of a calculation method for oil-lubricated hydrodynamic plain bearings with complete separation of the thrust collar and plain bearing surfaces by a film of lubricant. This part of ISO 12130 applies to plain thrust bearings with tilting-type sliding blocks (tilting pads), where a wedge-shaped lubrication clearance gap is automatically formed during operation. The ratio of width to length of one pad can be varied in the range B/L = 0,5 to 2. The calculation method described in this part of ISO 12130 can be used for other gap shapes, e.g. parabolic lubrication clearance gaps, as well as for other types of sliding blocks, e.g. circular sliding blocks, when for these types the numerical solutions of Reynolds differential equation are present. ISO 12130-2 gives only the characteristic values for the plane wedge-shaped gap; the values are therefore not applicable to tilting pads with axial support. The calculation method serves for designing and optimizing plain thrust bearings e.g. for fans, gear units, pumps, turbines, electric machines, compressors and machine tools. It is limited to steady-state conditions, i.e. load and angular speed of all rotating parts are constant under continuous operating conditions. This part of ISO 12130 is not applicable to heavily loaded tilting pad thrust bearings. 2 Normative references The following normative documents contain provisions which, through reference in this text, constitute provisions of this part of ISO 12130. For dated references, subsequent amendments to, or revisions of, any of these publications do not apply. However, parties to agreements based on this part of ISO 12130 are encouraged to investigate the possibility of applying the most recent editions of the normative documents indicated below. For undated references, the latest edition of the normative document referred to applies. Members of ISO and IEC maintain registers of currently valid International Standards. ISO 3448:1992, Industrial liquid lubricants — ISO viscosity classification ISO 12130-2, Plain bearings — Hydrodynamic plain tilting pad thrust bearings under steady-state conditions —Part 2: Functions for calculation of tilting pad thrust bearings ISO 12130-3, Plain bearings — Hydrodynamic plain tilting pad thrust bearings under steady-state conditions —Part 3: Guide values for the calculation of tilting pad thrust bearings --`,```,,,,``,,,```,``,``,,,,`,`-`-`,,`,,`,`,,`---ISO 12130-1:2001(E) © ISO 2001 – All rights reserved 3 Fundamentals, assumptions and premises The calculation is always carried out with the numerical solutions of Reynolds differential equations for sliding surfaces with finite width, taking into account the physically correct boundary conditions for the generation of pressure. 336p ph+ = U hhxxzz xh∂∂ ∂∂ ∂Êˆ Ê ˆ¥¥¥Á˜ Á ˜Ë¯ Ë ¯∂∂∂∂ ∂(1) Reference is made, e.g., to [1]for the derivation of Reynolds differential equation and to [2]for the numerical solution. For the solution to equation (1), the following idealizing assumptions and premises are used, the reliability of which has been sufficiently confirmed by experiment and in practice [3]: a) the lubricant corresponds to a Newtonian fluid; b) all lubricant flows are laminar; c) the lubricant adheres completely to the sliding surfaces; d) the lubricant is incompressible; e) the lubrication clearance gap is completely filled with lubricant; f) inertia effects, gravitational and magnetic forces of the lubricant are negligible; g) the components forming the lubrication clearance gap are rigid or their deformation is negligible; their surfaces are completely even; h) the lubricant film thickness in the radial direction (z-coordinate) is constant; i) fluctuations in pressure within the lubricant film normal to the sliding surfaces (y-coordinate) are negligible; j) there is no motion normal to the sliding surfaces (y-coordinate); k) the lubricant is isoviscous over the entire lubrication clearance gap; l) the lubricant is fed in at the widest lubrication clearance gap; m) the magnitude of the lubricant feed pressure is negligible as compared to the lubricant film pressures themselves; n) the pad shape of the sliding surfaces is replaced by rectangles. The boundary conditions for the solution of Reynolds differential equation are the following: 1) the gauge pressure of the lubricant at the feeding point is p(x = 0, z) = 0 2) the feeding of the lubricant is arranged in such a way that it does not interfere with the generation of pressure in the lubrication clearance gap 3) the gauge pressure of the lubricant at the lateral edges of the plain bearing is ( )=0,5 = 0p x,z B ± 4) the gauge pressure of the lubricant is p(x = L, z) = 0 at the end of the pressure field. --`,```,,,,``,,,```,``,``,,,,`,`-`-`,,`,,`,`,,`---ISO 12130-1:2001(E) 3The application of the principle of similarity in hydrodynamic plain bearing theory results in dimensionless parameters of similarity for such characteristics as load carrying capacity, friction behaviour and lubricant flow rate. The use of parameters of similarity reduces the number of necessary numerical solutions of Reynolds differential equation which are compiled in ISO 12130-2. In principle, other solutions are also permitted if they satisfy the conditions given in this part of ISO 12130 and have the corresponding numerical accuracy. ISO 12130-3, contains guide values according to which the calculation result is to be oriented in order to ensure the functioning of the plain bearings. In special cases, guide values deviating from ISO 12130-3, may be agreed for specific applications. 4 Symbols, terms and units See Table 1 and Figure 1. Table 1 — Symbols, terms and units Symbol Term Unit aFDistance between supporting point and inlet of the clearance gap in the direction of motion (circumferential direction) m *FaRelative distance between supporting point and inlet of the clearance gap in the direction of motion (circumferential direction) 1 A Heat-emitting surface of the bearing housing m2B Width of one pad m cpSpecific heat capacity of the lubricant (p = constant) J/(kg⋅K) CwedWedge depth m D Mean sliding diameter m DiInside diameter over tilting pads m DoOutside diameter over tilting pads m f*Characteristic value of friction 1 F Bearing force (load) at nominal rotational frequency N F*Characteristic value of load carrying capacity 1 FstBearing force (load) at standstill N h Local lubricant film thickness (clearance gap height) m hlimMinimum permissible lubricant film thickness during operation m hlim,trMinimum permissible lubricant film thickness on transition into mixed lubrication m hminMinimum lubricant film thickness (minimum clearance gap height) m k Heat transfer coefficient related to the product B ¥ L ¥ Z W/(m2⋅K) kAExternal heat transfer coefficient (reference surface A) W/(m2⋅K) L Length of one pad in circumferential direction m M Mixing factor 1 N Rotational frequency (speed) of thrust collar s-1p Local lubricant film pressure Pa --`,```,,,,``,,,```,``,``,,,,`,`-`-`,,`,,`,`,,`---ISO 12130-1:2001(E) © ISO 2001 – All rights reserved Table 1 (continued) Symbol Term Unit p Specific bearing load p= F/(B L Z)¥¥ Pa limp Maximum permissible specific bearing load Pa PfFrictional power in the bearing or power generated heat flow rate W Pth,ambHeat flow rate to the environment W Pth,LHeat flow rate in the lubricant W Q Lubricant flow rate m3/s Q*Characteristic value of lubricant flow rate 1 Q0Relative lubricant flow rate min0= B U ZQh¥¥¥ m3/s Q1Lubricant flow rate at the inlet of the clearance gap (circumferential direction) m3/s *1Q Characteristic value of lubricant flow rate at the inlet of the clearance gap 1 Q2Lubricant flow rate at the outlet of the clearance gap (circumferential direction) m3/s *2Q Characteristic value of lubricant flow rate **13QQ at the outlet of the clearance gap 1 Q3Lubricant flow rate at the sides (perpendicular to circumferential direction) m3/s *3Q Characteristic value of lubricant flow rate at the sides 1 Rz Average peak-to-valley height of thrust collar mm Re Reynolds number 1 TambAmbient temperature °C TBBearing temperature °C TeffEffective lubricant film temperature °C TenLubricant temperature at the inlet of the bearing °C TexLubricant temperature at the outlet of the bearing °C TlimMaximum permissible bearing temperature °C T1Lubricant temperature at the inlet of the clearance gap °C T2Lubricant temperature at the outlet of the clearance gap °C U Sliding velocity relative to mean diameter of bearing ring m/s wambVelocity of air surrounding the bearing housing m/s x Coordinate in direction of motion (circumferential direction) m y Coordinate in direction of lubrication clearance gap (axial) m z Coordinate perpendicular to the direction of motion (radial) m Z Number of tilting-pads 1 h Dynamic viscosity of the lubricant Pa⋅s heffEffective dynamic viscosity of the lubricant Pa⋅s r Density of the lubricant kg/m3--`,```,,,,``,,,```,``,``,,,,`,`-`-`,,`,,`,`,,`---ISO 12130-1:2001(E) 5Key 1 Thrust collar 2 Tilting-pad 3 Centre of pressure (supporting surface) Figure 1 — Schematic view of a tilting-pad thrust bearing --`,```,,,,``,,,```,``,``,,,,`,`-`-`,,`,,`,`,,`---ISO 12130-1:2001(E) © ISO 2001 – All rights reserved 5 Calculation procedure 5.1 Loading operations 5.1.1 General Calculation means the mathematical determination of the correct functioning using operational parameters (see Figure 2) which has to be compared with guide values. Thereby, the operational parameters determined under varying operation conditions shall be permissible as compared to the guide values. For this purpose, all continuous operating conditions shall be investigated. 5.1.2 Wear Safety against wear is assured if complete separation of the mating bearing parts is achieved by the lubricant. Continuous operation in the mixed lubrication range results in early loss of functioning. Short-time operation in the mixed lubrication range, such as starting up and running down machines with plain bearings, is unavoidable and can result in bearing damage after frequent occurence. When subjected to heavy loads, an auxiliary hydrostatic arrangement may be necessary for starting up or running down at low speed. Running-in and adaptive wear to compensate for surface geometry deviations from ideal geometry are permissible as lon