# ISO 7902-1-2013

BS ISO 7902-1:2013© ISO 2013Hydrodynamic plain journal bearings under steady-state conditions — Circular cylindrical bearings —Part 1: Calculation procedurePaliers lisses hydrodynamiques radiaux fonctionnant en régime stabilisé — Paliers circulaires cylindriques —Partie 1: Méthode de calculINTERNATIONAL STANDARDISO7902-1Second edition2013-11-01Reference numberISO 7902-1:2013(E)BS ISO 7902-1:2013ISO 7902-1:2013(E)ii © ISO 2013 – All rights reservedCOPYRIGHT PROTECTED DOCUMENT© ISO 2013All rights reserved. Unless otherwise specified, 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.ISO copyright officeCase postale 56 • CH-1211 Geneva 20Tel. + 41 22 749 01 11Fax + 41 22 749 09 47E-mail copyright@iso.orgWeb www.iso.orgPublished in SwitzerlandBS ISO 7902-1:2013ISO 7902-1:2013(E)© ISO 2013 – All rights reserved iiiContents PageForeword iv1 Scope . 12 Normative references 13 Basis of calculation, assumptions, and preconditions 14 Calculation procedure 35 Symbols and units . 56 Definition of symbols . 66.1 Load-carrying capacity 66.2 Frictional power loss . 96.3 Lubricant flow rate . 106.4 Heat balance . 116.5 Minimum lubricant film thickness and specific bearing load .136.6 Operational conditions 146.7 Further influencing factors 15Annex A (normative) Calculation examples .17Bibliography .32BS ISO 7902-1:2013ISO 7902-1:2013(E)ForewordISO (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. 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. 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.The committee responsible for this document is ISO/TC 123, Plain bearings, Subcommittee SC 4, Methods of calculation of plain bearings.This second edition cancels and replaces the first edition (ISO 7902-1:1998), which has been technically revised.ISO 7902 consists of the following parts, under the general title Hydrodynamic plain journal bearings under steady-state conditions — Circular cylindrical bearings:— Part 1: Calculation procedure— Part 2: Functions used in the calculation procedure— Part 3: Permissible operational parametersiv © ISO 2013 – All rights reservedBS ISO 7902-1:2013INTERNATIONAL STANDARD ISO 7902-1:2013(E)Hydrodynamic plain journal bearings under steady-state conditions — Circular cylindrical bearings —Part 1: Calculation procedure1 ScopeThis part of ISO 7902 specifies a calculation procedure for oil-lubricated hydrodynamic plain bearings, with complete separation of the shaft and bearing sliding surfaces by a film of lubricant, used for designing plain bearings that are reliable in operation.It deals with circular cylindrical bearings having angular spans, Ω, of 360°, 180°, 150°, 120°, and 90°, the arc segment being loaded centrally. Their clearance geometry is constant except for negligible deformations resulting from lubricant film pressure and temperature.The calculation procedure serves to dimension and optimize plain bearings in turbines, generators, electric motors, gear units, rolling mills, pumps, and other machines. It is limited to steady-state operation, i.e. under continuously driven operating conditions, with the magnitude and direction of loading as well as the angular speeds of all rotating parts constant. It can also be applied if a full plain bearing is subjected to a constant force rotating at any speed. Dynamic loadings, i.e. those whose magnitude and direction vary with time, such as can result from vibration effects and instabilities of rapid-running rotors, are not taken into account.2 Normative referencesThe following documents, in whole or in part, are normatively referenced in this document and are indispensable for its application. For dated references, only the edition cited applies. For undated references, the latest edition of the referenced document (including any amendments) applies.ISO 3448, Industrial liquid lubricants — ISO viscosity classificationISO 7902-2:1998, Hydrodynamic plain journal bearings under steady-state conditions — Circular cylindrical bearings — Part 2: Functions used in the calculation procedureISO 7902-3, Hydrodynamic plain journal bearings under steady-state conditions — Circular cylindrical bearings — Part 3: Permissible operational parameters3 Basis of calculation, assumptions, and preconditions3.1 The basis of calculation is the numerical solution to Reynolds’ differential equation for a finite bearing length, taking into account the physically correct boundary conditions for the generation of pressure:∂∂∂∂+∂∂∂∂=+()∂∂xhpxxhpzuuhxJB336η (1)The symbols are given in Clause 5.See References [1] to [3] and References [11] to [14] for the derivation of Reynolds’ differential equation and References [4] to [6], [12], and [13] for its numerical solution.© ISO 2013 – All rights reserved 1BS ISO 7902-1:2013ISO 7902-1:2013(E)3.2 The following idealizing assumptions and preconditions are made, the permissibility of which has been sufficiently confirmed both experimentally and in practice.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 lubricant clearance gap in the loaded area is completely filled with lubricant. Filling up of the unloaded area depends on the way the lubricant is supplied to the bearing.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 ideal circular cylinders.h) The radii of curvature of the surfaces in relative motion are large in comparison with the lubricant film thicknesses.i) The lubricant film thickness in the axial direction (z-coordinate) is constant.j) Fluctuations in pressure within the lubricant film normal to the bearing surfaces (y-coordinate) are negligible.k) There is no motion normal to the bearing surfaces (y-coordinate).l) The lubricant is isoviscous over the entire lubrication clearance gap.m) The lubricant is fed in at the start of the bearing liner or where the lubrication clearance gap is widest; the magnitude of the lubricant feed pressure is negligible in comparison with the lubricant film pressures.3.3 The boundary conditions for the generation of lubricant film pressure fulfil the following continuity conditions:— at the leading edge of the pressure profile: pzϕ10,()= ;— at the bearing rim: pzBϕ, =±()=20;— at the trailing edge of the pressure profile: pzzϕ20()=, ;— ∂∂()=pzzϕϕ20, .For some types and sizes of bearing, the boundary conditions may be specified.In partial bearings, if Formula (2) is satisfied:ϕpiβpi22−−()41,3R,DCeff(for example as a result of high peripheral speed), higher loss coefficients and bearing temperatures shall be expected. Calculations for bearings with turbulent flow cannot be carried out in accordance with this part of ISO 7902.4.7 The plain bearing calculation takes into account the following factors (starting with the known bearing dimensions and operational data):— the relationship between load-carrying capacity and lubricant film thickness;— the frictional power rate;— the lubricant flow rate;— the heat balance.All these factors are mutually dependent.The solution is obtained using an iterative method; the sequence is outlined in the flow chart in Figure 1.For optimization of individual parameters, parameter variation can be applied; modification of the calculation sequence is possible.5 Symbols and unitsSee Figure 2 and Table 1.Minimum lubricant film thickness, hmin:hmin=−−= −()DDeDJ0,512ψε (5)where the relative eccentricity, ε, is given byε =−eDDJ2(6)Ifϕpiβpi22−− 1,2 m/skVAa=+712 (19)(See References [3] and [14].)Should the area of the heat-emitting surface, A, of the bearing housing not be known exactly, the following can be used as an approximation:— for cylindrical housingsADDDB=−()+2422pipiHHH(20)— for pedestal bearingsAHBH=+piH2(21)— for bearings in the machine structureADB=()15 20to (22)whereBHis the length of the axial housing;DHis the length of the outside diameter of the housing;H is the length of the total height of the pedestal bearing.6.4.2 Heat dissipation via the lubricantIn the case of force-feed lubrication, heat dissipation is via the lubricant:PcQT Tth,L ex en=−()ρ (23)For mineral lubricants, the volume-specific heat is given by:ρcx=⋅()18 1063,/JmK (24)From the heat balance, it follows thatPPth fthamb,,= 12 © ISO 2013 – All rights reservedBS ISO 7902-1:2013ISO 7902-1:2013(E)for pressureless-lubricated bearings andPPth fthL,,= for pressure-lubricated bearings.This gives bearing temperature, TB(see Reference [15]), and lubricant outlet temperature, Tex(see Reference [15]). The effective film lubricant temperature with reference to the lubricant viscosity isa) in the case of pure convection: Teff= TBb) in the case of heat dissipation via the lubricant: Teff= TL= 0,5 (Ten+ Tex)At high peripheral speed, it is possible to select, instead of these mean values, a temperature which lies nearer to the lubricant outlet temperature. The values calculated for TBand Texshall be checked for their permissibility by comparison with the permissible operational parameters, Tlim, given in ISO 7902-3.In the sequence of calculations, at first only the operational data Tambor Tenare known, but not the effective temperature, Teff, which is required at the start of the calculation. The solution is obtained by first starting the calculation using an estimated temperature rise, i.e.a) TB,0− Tamb= 20 Kb) Tex,0− Ten= 20 Kand the corresponding operating temperatures, Teff. From the heat balance, corrected temperatures, TB,1or Tex,1, are obtained, which, by averaging with the temperatures previously assumed (TB,0or Tex,0), are iteratively improved until the difference between the values with index 0 and 1 becomes negligibly small, for example 2 K. The condition then attained corresponds to the steady condition. During the iterative steps, the influencing factors given in 6.7 shall be taken into account. As a rule, the iteration converges rapidly. It can also be replaced by graphical interpolation in which, for calculating Pth,fand Pth,ambor Pth,L, several temperature differences are assumed. If the heat flows Pth,amb= f (TB) or Pth,L= f (Tex) are plotted, then the steady condition is given by the intersection of the two curves (see Figure A.1).6.5 Minimum lubricant film thickness and specific bearing loadThe clearance gap, h, in a circular cylindrical journal bearing with the shaft offset is a function given by:hD=+()05 1,cosψεϕeff(25)starting with ϕϕ=1, in the widest clearance gap (see Figure 1).The minimum lubricant film thicknesshD=−()05 1, ψεeff(26)shall be compared with the permissible operational parameter, hlim, specified in ISO 7902-3.The specific bearing load:pFDB= (27)shall be compared with the permissible operational parameter, plim, specified in ISO 7902-3.© ISO 2013 – All rights reserved 13BS ISO 7902-1:2013ISO 7902-1:2013(E)6.6 Operational conditionsShould the plain bearing be operated under several, varying sets of operating conditions over lengthy periods, then they shall be checked for the most unfavourable p , hmin, and TB. First, a decision shall be reached as to whether or not the bearing can be lubricated without pressure and whether or not the heat dissipation by convection suffices. The most unfavourable thermal case shall be investigated, which, as a rule, corresponds to an operating condition at high rotary frequency together with heavy loading. If, for pure convection, excessive bearing temperatures occur, which even by increasing the dimensions of the bearing or of the surface area of the housing to their greatest possible extent cannot be lowered to permissible values, then force-feed lubrication and oil cooling are necessary.If an operating condition under high thermal loading (low dynamic lubricant viscosity) is followed directly by one with high specific bearing load and low rotary frequency, this new operating condition should be investigated while keeping the thermal condition from the preceding operating point.The transition to mixed friction is due to contact of the roughness peaks of the shaft and bearing under the criteria for hlimspecified in ISO 7902-3, whereby deformation is also to be taken into account. A transition eccentricity:εψueff=−12hDlim(28)and a transition Sommerfeld number:SoFDBfBDueffeffhu==ψηωε2,,Ω (29)(see ISO 7902-2)can be assigned to this value. Thus, the individual transition conditions (load, viscosity, and rotary speed) can be determined. The transition condition can be described by just three coexistent parameters. In order to be able to determine one of them, the two others have to be substituted in the manner appropriate to this condition. For rapid run-down of the machine, the thermal state corresponds mostly to the previous continuously driven operating condition of high thermal loading. If cooling is shut off immediately when the machine is switched off, this can result in an accumulation of heat in the bearing, so that a yet more unfavourable value has to be selected for heff. If the machine runs down slowly, lowering of the temperature of the lubricant or bearing is to be expected.14 © ISO 2013 – All rights reservedBS ISO 7902-1:2013ISO 7902-1:2013(E)6.7 Further influencing factorsThe calculation procedure