1、BSI Standards Publication PD ISO/TR 15144-2:2014 Incorporating corrigendum September 2015 PD ISO/TR 15144-2:2014 Calculation of micropitting load capacity of cylindrical spur and helical gears Part 2: Examples of calculation for micropittingPD ISO/TR 15144-2:2014 PUBLISHED DOCUMENT National foreword
2、 This Published Document is the UK implementation of ISO/TR 15144-2:2014. The UK participation in its preparation was entrusted to Technical Committee MCE/5/-/15, Micropitting. A list of organizations represented on this committee can be obtained on request to its secretary. This publication does no
3、t purport to include all the necessary provisions of a contract. Users are responsible for its correct application. The British Standards Institution 2015. Published by BSI Standards Limited 2015 ISBN 978 0 580 91717 2 ICS 21.200 Compliance with a British Standard cannot confer immunity from legal o
4、bligations. This British Standard was published under the authority of the Standards Policy and Strategy Committee on 31 October 2014. Amendments/corrigenda issued since publication Date Text affected 30 September 2015 Implementation of ISO corrected text 15 January 2015: errors in symbols and equat
5、ions have been corrected ISO 2014 Calculation of micropitting load capacity of cylindrical spur and helical gears Part 2: Examples of calculation for micropitting Calcul de la capacit de charge aux micropiqres des engrenages cylindriques dentures droite et hlicodale Partie 2: Exemples de calcul pour
6、 micropiqres TECHNICAL REPORT ISO/TR 15144-2 Reference number ISO/TR 15144-2:2014(E) First edition 2014-10-01 Corrected version 2015-01-15 PD ISO/TR 15144-2:2014 ISO/TR 15144-2:2014(E)ii ISO 2014 All rights reserved COPYRIGHT PROTECTED DOCUMENT ISO 2014 All rights reserved. Unless otherwise specifie
7、d, 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 ISOs
8、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 copyrightiso.org Web www.iso.org Published in Switzerland PD ISO/TR 15144-2:2014 ISO/TR 15144-2:2014(E)Contents Page Foreword iv Introduction v 1 Sc
9、ope . 1 2 Normative references 1 3 T erms, definitions, s ymbols, and units 1 3.1 Terms and definitions . 1 3.2 Symbols and units 1 4 Example calculation 4 4.1 Example 1 Spur gear . 5 4.1.1 Input data . 6 4.1.2 Calculation according to method B 7 4.1.3 Calculation according to method A .12 4.1.4 Cal
10、culation of the permissible lubricant film thickness13 4.2 Example 2 Spur gear 19 4.2.1 Input data 20 4.2.2 Calculation according to method B .21 4.3 Example 3 Helical gear .28 4.3.1 Input data 29 4.3.2 Calculation according to method B .30 4.3.3 Calculation according to method A .36 4.4 Example 4 S
11、peed increaser 37 4.4.1 Input data 38 4.4.2 Calculation according to method B .39 4.4.3 Calculation according to method A .45 Bibliogr aph y .47 ISO 2014 All rights reserved iii PD ISO/TR 15144-2:2014 ISO/TR 15144-2:2014(E) Foreword ISO (the International Organization for Standardization) is a world
12、wide 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 t
13、hat 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 do
14、cument 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 Direct
15、ives, 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 develop
16、ment 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 on the meaning of ISO s
17、pecific terms and expressions related to conformity assessment, as well as information about ISOs adherence to the WTO principles in the Technical Barriers to Trade (TBT) see the following URL: Foreword - Supplementary information The committee responsible for this document is ISO/TC 60, Gears, Subc
18、ommittee SC 2, Gear capacity calculation. This corrected version of ISO/TR 15144-2:2014 incorporates the following corrections: errors in symbols and equations have been corrected. ISO/TR 15144 consists of the following parts, under the general title Calculation of micropitting load capacity of cyli
19、ndrical spur and helical gears: Part 1: Introduction and basic principles Part 2: Examples of calculation for micropittingiv ISO 2014 All rights reserved PD ISO/TR 15144-2:2014 ISO/TR 15144-2:2014(E) Introduction This part of ISO/TR 15144 provides worked examples for the application of the calculati
20、on procedures defined in ISO/TR 15144-1. The example calculations cover the application to spur and helical cyclindrical involute gears for both high-speed and low-speed operating conditions, determining the micropitting safety factor for each gear pair. The calculation procedures used are consisten
21、t with those presented in ISO/TR 15144-1. No additional calculations are presented here that are outside of the technical report. Four worked examples are presented with the necessary input data for each gear set provided at the beginning of the calculation. The worked examples are based on real gea
22、r pairs where either laboratory or operational field performance data has been established, with the examples covering several applications. When available, pictures and measurements are provided of the micropitting wear, experienced on the gear sets when run under the conditions used in the worked
23、examples. Calculation details are presented in full for several of the initial calculations after which only summarized results data are included. For better applicability, the numbering of the formulae follows ISO/TR 15144-1. Several of the worked examples are presented with the calculation procedu
24、res performed in accordance with the application of both methods A and B. ISO 2014 All rights reserved v PD ISO/TR 15144-2:2014PD ISO/TR 15144-2:2014 Calculation of micropitting load capacity of cylindrical spur and helical gears Part 2: Examples of calculation for micropitting 1 Scope The example c
25、alculations presented here are provided for guidance on the application of the technical report ISO/TR 15144-1 only. Any of the values or the data presented should not be used as material or lubricant allowables or as recommendations for micro-geometry in real applications when applying this procedu
26、re. The necessary parameters and allowable film thickness values, GFP , should be determined for a given application in accordance with the procedures defined in ISO/TR 15144-1. 2 Normative references The following documents, in whole or in part, are normatively referenced in this document and are i
27、ndispensable 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 1122-1:1998, Vocabulary of gear terms Part 1: Definitions related to geometry ISO 6336-1:2006, Calcula
28、tion of load capacity of spur and helical gears Part 1: Basic principles, introduction and general influence factors ISO 6336-2:2006, Calculation of load capacity of spur and helical gears Part 2: Calculation of surface durability (pitting) ISO 21771:2007, Gears Cylindrical involute gears and gear p
29、airs Concepts and geometry ISO/TR 15144-1:2014, Calculation of micropitting load capacity of cylindrical spur and helical gears Part 1: Introduction and basic principles 3 T erms, d efinitions , s ymbols, and units 3.1 T erms and definiti ons For the purpose of this document, the terms and definitio
30、ns given in ISO 1122-1, ISO 6336-1, and ISO 6336-2 apply. 3.2 S ymbols and units The symbols used in this technical report are given in Table 1. The units of length metre, millimetre, and micrometre are chosen in accordance with common practice. The conversions of the units are already included in t
31、he given formulae. TECHNICAL REPORT ISO/TR 15144-2:2014(E) ISO 2014 All rights reserved 1 PD ISO/TR 15144-2:2014 ISO/TR 15144-2:2014(E) T a b l e 1 S y m b o l s a n d u n i t s S y m b ol Description Unit a centre distance mm B M1 thermal contact coefficient of pinion N/(ms 0,5 K) B M2 thermal cont
32、act coefficient of wheel N/(ms 0,5 K) b face width mm C a1 tip relief of pinion m C a2 tip relief of wheel m c M1 specific heat per unit mass of pinion J/(kgK) c M2 specific heat per unit mass of wheel J/(kgK) c maximum tooth stiffness per unit face width (single stiffness) of a tooth pair N/(mmm) c
33、 mean value of mesh stiffness per unit face width N/(mmm) d a1 tip diameter of pinion mm d a2 tip diameter of wheel mm d b1 base diameter of pinion mm d b2 base diameter of wheel mm d w1 pitch diameter of pinion mm d w2 pitch diameter of wheel mm d Y1 Y-circle diameter of pinion mm d Y2 Y-circle dia
34、meter of wheel mm E r reduced modulus of elasticity N/mm 2 E 1 modulus of elasticity of pinion N/mm 2 E 2 modulus of elasticity of wheel N/mm 2 F bt nominal transverse load in plane of action (base tangent plane) N F t (nominal) transverse tangential load at reference cylinder per mesh N G M materia
35、l parameter - g Y parameter on the path of contact (distance of point Y from point A) mm g length of path of contact mm H v load losses factor - h Y local lubricant film thickness m K A application factor - K H transverse load factor - K H face load factor - K v dynamic factor - n 1 rotation speed o
36、f pinion min 1 P transmitted power kW p et transverse base pitch on the path of contact Mm p dyn,Y local Hertzian contact stress including the load factors K N/mm 2 p H,Y local nominal Hertzian contact stress N/mm 2 Ra effective arithmetic mean roughness value m Ra 1 arithmetic mean roughness value
37、of pinion m Ra 2 arithmetic mean roughness value of wheel m S GF,Y local sliding parameter -2 ISO 2014 All rights reserved PD ISO/TR 15144-2:2014 ISO/TR 15144-2:2014(E) S y m b ol Description Unit S safety factor against micropitting - S ,min minimum required safety factor against micropitting - T 1
38、 nominal torque at the pinion Nm U Y local velocity parameter - u gear ratio - v g,Y local sliding velocity m/s v r1,Y local tangential velocity on pinion m/s v r2,Y local tangential velocity on wheel m/s v ,C sum of tangential velocities at pitch point m/s v ,Y sum of tangential velocities at point
39、 Y m/s W W material factor - W Y local load parameter - X but,Y local buttressing factor - X Ca tip relief factor - X L lubricant factor - X R roughness factor - X S lubrication factor - X Y local load sharing factor - Z E elasticity factor (N/mm 2 ) 0,5 z 1 number of teeth of pinion - z 2 number of
40、 teeth of wheel - t transverse pressure angle wt pressure angle at the pitch cylinder B,Y pressure-viscosity coefficient at local contact temperature m 2 /N M pressure-viscosity coefficient at bulk temperature m 2 /N 38 pressure-viscosity coefficient at 38 C m 2 /N b base helix angle max maximum add
41、endum contact ratio - transverse contact ratio - n virtual transverse contact ratio - overlap ratio - total contact ratio - 1 addendum contact ratio of the pinion - 2 addendum contact ratio of the wheel - B,Y dynamic viscosity at local contact temperature Ns/m 2 M dynamic viscosity at bulk temperatu
42、re Ns/m 2 oil dynamic viscosity at oil inlet/sump temperature Ns/m 2 38 dynamic viscosity at 38 C Ns/m 2 B,Y local contact temperature C fl,Y local flash temperature C M bulk temperature CT a b l e 1 (continued) ISO 2014 All rights reserved 3 PD ISO/TR 15144-2:2014 ISO/TR 15144-2:2014(E) S y m b ol
43、Description Unit oil oil inlet/sump temperature C GF,min minimum specific lubricant film thickness in the contact area - GF,Y local specific lubricant film thickness - GFP permissible specific lubricant film thickness - GFT limiting specific lubricant film thickness of the test gears - M1 specific h
44、eat conductivity of pinion W/(mK) M2 specific heat conductivity of wheel W/(mK) m mean coefficient of friction - B,Y kinematic viscosity at local contact temperature mm 2 /s M kinematic viscosity at bulk temperature mm 2 /s 1 Poissons ratio of pinion - 2 Poissons ratio of wheel - 100 kinematic visco
45、sity at 100 C mm 2 /s 40 kinematic viscosity at 40 C mm 2 /s M1 density of pinion kg/m 3 M2 density of wheel kg/m 3 n,C normal radius of relative curvature at pitch diameter mm n,Y normal radius of relative curvature at point Y mm t,Y transverse radius of relative curvature at point Y mm t1,Y transv
46、erse radius of curvature of pinion at point Y mm t2,Y transverse radius of curvature of wheel at point Y mm B,Y density of lubricant at local contact temperature kg/m 3 M density of lubricant at bulk temperature kg/m 3 15 density of lubricant at 15 C kg/m 3 S ub s c r i p t s t o s y m b o l s Y Par
47、ameter for any contact point Y in the contact area for method A and on the path of contact for method B (all parameters subscript Y has to be calculated with local values). 4 Example calculation The following presents examples for the calculation of the safety factor against micropitting, S . Each e
48、xample is first calculated according to method B and examples 1, 3, and 4 subsequently calculated according to method A. The calculation sequence for method B has been provided to follow a logical approach in relation to the input data. Beside the formulae itself, the formula numbers related to ISO/
49、TR 15144-1 are given. The examples calculate the safety factor S of a specific gear set when compared to an allowable GFPvalue. For the examples 1, 2, and 4, the permissible specific oil film thickness, GFP , was determined from the test result of the lubricant in the FZG-FVA micropitting test. 1For these calculations medium values for the standard FZG b
