1、BRITISH STANDARDBS EN 15302:2008Railway applications Method for determining the equivalent conicityICS 17.040.20; 45.060.01g49g50g3g38g50g51g60g44g49g42g3g58g44g55g43g50g56g55g3g37g54g44g3g51g40g53g48g44g54g54g44g50g49g3g40g59g38g40g51g55g3g36g54g3g51g40g53g48g44g55g55g40g39g3g37g60g3g38g50g51g60g53
2、g44g42g43g55g3g47g36g58+A1:2010National forewordThis British Standard is the UK implementation of EN 15302:2008+A1:2010. It supersedes BS EN 15302:2008, which is withdrawn.The start and finish of text introduced or altered by amendment is indicated in the text by tags. Tags indicating changes to CEN
3、 text carry the number of the CEN amendment. For example, text altered by CEN amendment A1 is indicated by !“.The UK participation in its preparation was entrusted by Technical Committee RAE/1, Railway applications, to Panel RAE/1/-/8, Vehicle/track interaction.A list of organizations represented on
4、 this committee can be obtained on request to its secretary.Definitions of normative and informative.“Normative” A (mandatory) requirement defined as an expression in the content of a document conveying criteria to be fulfilled if compliance with the document is to be claimed and from which no devia
5、tion is permitted CEN/CENELEC Internal Regulations, Part 3: Rules for the Structure and Drafting of European Standards (PNE-Rules).“Informative” Information (not mandatory) intended to assist the understanding or use of the document. Informative annexes shall not contain requirements, except as opti
6、onal requirements. (For example, a test method that is optional may contain requirements but there is no need to comply with these requirements to claim compliance with the document.)This publication does not purport to include all the necessary provisions of a contract. Users are responsible for it
7、s correct application.Compliance with a British Standard cannot confer immunity from legal obligations.BS EN 15302:2008+A1:2010This British Standard was published under the authority of the Standards Policy and Strategy Committee on 30 June 2008 BSI 2011Amendments/corrigenda issued since publication
8、Date Comments 31 January 2011 Implementation of CEN Amendment A1:2010ISBN 978 0 580 70853 4EUROPEAN STANDARD NORME EUROPENNE EUROPISCHE NORM EN 15302:2008+A1 November 2010 ICS 17.040.20; 45.060.01 Supersedes EN 15302:2008English Version Railway applications - Method for determining the equivalent co
9、nicity Applications ferroviaires - Mthode de dtermination de la conicit quivalente Bahnanwendungen - Verfahren zur Bestimmung der quivalenten Konizitt This European Standard was approved by CEN on 7 February 2008 and includes Amendment 1 approved by CEN on 28 September 2010.CEN members are bound to
10、comply with the CEN/CENELEC Internal Regulations which stipulate the conditions for giving this European Standard the status of a national standard without any alteration. Up-to-date lists and bibliographical references concerning such national standards may be obtained on application to the CEN Man
11、agement Centre or to any CEN member. This European Standard exists in three official versions (English, French, German). A version in any other language made by translation under the responsibility of a CEN member into its own language and notified to the CEN Management Centre has the same status as
12、 the official versions. CEN members are the national standards bodies of Austria, Belgium, Bulgaria, Croatia, Cyprus, Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Rom
13、ania, Slovakia, Slovenia, Spain, Sweden, Switzerland and United Kingdom. EUROPEAN COMMITTEE FOR STANDARDIZATION COMIT EUROPEN DE NORMALISATION EUROPISCHES KOMITEE FR NORMUNG Management Centre: Avenue Marnix 17, B-1000 Brussels 2010 CEN All rights of exploitation in any form and by any means reserved
14、 worldwide for CEN national Members. Ref. No. EN 15302:2008+A1:2010: EEN 15302:2008+A1:2010 (E) 2 Contents Page Foreword 9Introduction 101 Scope . 132 Normative references . 133 Symbols . 144 Principle of determining the equivalent conicity . 154.1 Integration of the equation of the wheelset movemen
15、t of a conical profile . 154.2 Determining the wavelength of a conical profile . 164.3 Definition of equivalent conicity for nonlinear profiles 175 Description of the reference procedure . 175.1 General principles. 175.2 Determining the wheel and rail profiles . 185.2.1 Principles of measurement 185
16、.2.2 Accuracy of the measuring system 185.3 Determining the rolling radius difference function r 185.4 Determining the equivalent conicity . 196 Benchmark calculation 196.1 Overview 196.2 Validation of evaluation method . 19Annex A (informative) Example of presentation of r function and conicity . 2
17、1Annex B (informative) Example of method for determining the equivalent conicity by integration of the nonlinear differential equation . 22B.1 Principle . 22B.2 Steps of the procedure . 25B.3 Special cases 26Annex C (informative) Example of method for determining the equivalent conicity by linear re
18、gression of the r function 28C.1 Principles . 28C.2 Steps of the procedure . 28C.3 Particularities 28Annex D (normative) Reference profiles 29D.1 Wheel A 29D.1.1 Drawing 29D.1.2 Analytic definition . 29D.1.3 Cartesian coordinates 30D.2 Wheel B 31D.2.1 Drawing 31D.2.2 Analytic definition . 31D.2.3 Ca
19、rtesian coordinates 32D.3 Wheel H 33D.3.1 Drawing 33D.3.2 Analytic definition . 33D.3.3 Cartesian coordinates 34D.4 Wheel I . 35D.4.1 Drawing 35D.4.2 Analytic definition . 35BS EN 15302:2008+A1:2010EN 15302:2008+A1:2010 (E) 3 D.4.3 Cartesian coordinates . 36D.5 Rail A . 37D.5.1 Drawing. 37D.5.2 Anal
20、ytic definition . 37D.5.3 Cartesian coordinates . 38Annex E (normative) Calculation results with reference profiles 39E.1 Wheel A / Rail A . 40E.1.1 Diagram of r, tana, tanefunctions and representation of contact points 40E.1.2 Representation of the curves of kinematic rolling movement of the wheels
21、et on track . 41E.1.3 Numerical values for r function . 42E.1.4 Numerical values for tanefunction . 43E.2 Wheel B / Rail A . 44E.2.1 Diagram r, tana, tanefunctions and representation of contact points . 44E.2.2 Representation of the curves of kinematic rolling movement of the wheelset on track . 45E
22、.2.3 Numerical values for r function . 46E.2.4 Numerical values for tanefunction . 47E.3 Wheel H / Rail A . 48E.3.1 Diagram of r, tana, tanefunctions and representation of contact points . 48E.3.2 Representation of the curves of kinematic rolling movement of the wheelset on track . 49E.3.3 Numerical
23、 values for r function . 50E.3.4 Numerical values for tanefunction 51E.4 Wheel I / Rail A . 52E.4.1 Diagram of r, tana, tanefunctions and representation of contact points . 52E.4.2 Representation of the curves of kinematic rolling movement of the wheelset on track . 53E.4.3 Numerical values for r fu
24、nction . 54E.4.4 Numerical values for tanefunction . 55E.5 Modified Wheel A (-2 mm on left wheel diameter) / Rail A 56E.5.1 Diagram of r, tana, tanefunctions and representation of contact points . 56E.5.2 Representation of the curves of kinematic rolling movement of the wheelset on track . 57E.5.3 N
25、umerical values for r function . 58E.5.4 Numerical values for tanefunction 59E.6 Modified Wheel B (-2 mm on left wheel diameter) / Rail A 60E.6.1 Diagram of r, tana, tanefunctions and representation of contact points . 60E.6.2 Representation of the curves of kinematic rolling movement of the wheelse
26、t on track . 61E.6.3 Numerical values for r function . 62E.6.4 Numerical values for tanefunction 63E.7 Modified Wheel H (-2 mm on left wheel diameter) / Rail A 64E.7.1 Diagram of r, tana, tanefunctions and representation of contact points . 64E.7.2 Representation of the curves of kinematic rolling m
27、ovement of the wheelset on track . 65E.7.3 Numerical values for r function . 66E.7.4 Numerical values for tanefunction 67E.8 Modified Wheel I (-2 mm on left wheel diameter) / Rail A 67E.8.1 Diagram of r, tana, tanefunctions and representation of contact points . 67E.8.2 Representation of the curves
28、of kinematic rolling movement of the wheelset on track . 69E.8.3 Numerical values for r function . 70E.8.4 Numerical values for tanefunction 71E.9 (Right Wheel A Left Wheel B) / Rail A . 72E.9.1 Diagram of r, tana, tanefunctions and representation of contact points . 72E.9.2 Representation of the cu
29、rves of kinematic rolling movement of the wheelset on track . 73E.9.3 Numerical values for r function . 74E.9.4 Numerical values for tanefunction 75Annex F (normative) Tolerances on equivalent conicity 76F.1 Wheel A / Rail A . 77BS EN 15302:2008+A1:2010EN 15302:2008+A1:2010 (E) 4 F.1.1 Diagram 77F.1
30、.2 Numerical values 78F.2 Wheel B / Rail A . 80F.2.1 Diagram 80F.2.2 Numerical values 81F.3 Wheel H / Rail A . 83F.3.1 Diagram 83F.3.2 Numerical values 84F.4 Wheel I / Rail A 86F.4.1 Diagram 86F.4.2 Numerical values 87F.5 Modified Wheel A (-2 mm on left wheel diameter) / Rail A . 89F.5.1 Diagram 89F
31、.5.2 Numerical values 90F.6 Modified Wheel B (-2 mm on left wheel diameter) / Rail A . 92F.6.1 Diagram 92F.6.2 Numerical values 93F.7 Modified Wheel H (-2 mm on left wheel diameter) / Rail A . 95F.7.1 Diagram 95F.7.2 Numerical values 96F.8 Modified Wheel I (-2 mm on left wheel diameter) / Rail A . 9
32、8F.8.1 Diagram 98F.8.2 Numerical values 99F.9 (Right Wheel A Left Wheel B) / Rail A 101F.9.1 Diagram 101F.9.2 Numerical values 102Annex G (informative) Examples of calculation results with introduced errors 104G.1 Wheel A / Rail A Random error in mm . 104G.2 Wheel A / Rail A Random error in mm . 105
33、G.3 Wheel A / Rail A Random error in mm . 106G.4 Wheel A / Rail A Grid error in mm 107G.5 Wheel A / Rail A Grid error in mm 108G.6 Wheel A / Rail A Grid error in mm 109G.7 Wheel H / Rail A Random error in mm . 110Annex H (informative) Guideline for application of errors . 111H.1 Grid error . 111H.2
34、Random error 114Annex I (informative) Guidelines for application 117Annex ZA (informative) !Relationship between this European Standard and the Essential Requirements of EU Directive 2008/57/EC of the European Parliament and of the Council of 17 June 2008 on the interoperability of the rail system w
35、ithin the Community (Recast)“ 119Bibliography . 124Figures Figure 1 Benchmark process, Step 1 11Figure 2 Benchmark process, Step 2 11Figure 3 Benchmark process, Step 3 12Figure 4 Dimensions on the wheelset . 15Figure 5 y = f(x) function . 16Figure A.1 r = f(y) function and tane= f(y) . 21BS EN 15302
36、:2008+A1:2010EN 15302:2008+A1:2010 (E) 5 Figure B.1 Representation of dx, dy 22Figure B.2 Representation of ds, d . 22Figure B.3 Representation of r1, r2, e . 23Figure B.4 r = f(y) characteristic with negative slope . 26Figure B.5 Calculation of rdy integral . 26Figure B.6 Determination of yem, calc
37、ulation of rdy and determination of y27Figure B.7 Determination of yemin= f( y ) and yemax= f( y ) functions . 27Figure B.8 Determination of C constant 27Figure D.1 Wheel A 29Figure D.2 Wheel B . 31Figure D.3 Wheel H 33Figure D.4 Wheel I 35Figure D.5 Rail A 37Figure E.1a Diagram of r, tana, tanefunc
38、tions and representation of contact points Wheel A / Rail A . 40Figure E.1b Representation of the curves of kinematic rolling movement of the wheelset on track Wheel A / Rail A . 41Figure E.2a Diagram r, tana, tanefunctions and representation of contact points Wheel B / Rail A . 44Figure E.2b Repres
39、entation of the curves of kinematic rolling movement of the wheelset on track Wheel B / Rail A . 45Figure E.3a Diagram of r, tana, tanefunctions and representation of contact points Wheel H / Rail A . 48Figure E.3b Representation of the curves of kinematic rolling movement of the wheelset on track W
40、heel H / Rail A . 49Figure E.4a Diagram of r, tana, tanefunctions and representation of contact points Wheel I / Rail A . 52Figure E.4b Representation of the curves of kinematic rolling movement of the wheelset on track Wheel I / Rail A . 53Figure E.5a Diagram of r, tana, tanefunctions and represent
41、ation of contact points Modified Wheel A / Rail A . 56Figure E.5b Representation of the curves of kinematic rolling movement of the wheelset on track Modified Wheel A / Rail A . 57Figure E.6a Diagram of r, tana, tanefunctions and representation of contact points Modified Wheel B / Rail A . 60Figure
42、E.6b Representation of the curves of kinematic rolling movement of the wheelset on track Modified Wheel B / Rail A . 61Figure E.7a Diagram of r, tana, tanefunctions and representation of contact points Modified Wheel H / Rail A . 64Figure E.7b Representation of the curves of kinematic rolling moveme
43、nt of the wheelset on track Modified Wheel H / Rail A . 65BS EN 15302:2008+A1:2010EN 15302:2008+A1:2010 (E) 6 Figure E.8a Diagram of r, tana, tanefunctions and representation of contact points Modified Wheel I / Rail A 68Figure E.8b Representation of the curves of kinematic rolling movement of the w
44、heelset on track Modified Wheel I / Rail A 69Figure E.9a Diagram of r, tana, tanefunctions and representation of contact points (Right Wheel A Left Wheel B) / Rail A 72Figure E.9b Representation of the curves of kinematic rolling movement of the wheelset on track (Right Wheel A Left Wheel B) / Rail
45、A 73Figure F.1 Diagram Wheel A / Rail A . 77Figure F.2 Diagram Wheel B / Rail A . 80Figure F.3 Diagram Wheel H / Rail A . 83Figure F.4 Diagram Wheel I / Rail A . 86Figure F.5 Diagram modified Wheel A / Rail A . 89Figure F.6 Diagram modified Wheel B / Rail A . 92Figure F.7 Diagram modified Wheel H /
46、Rail A . 95Figure F.8 Diagram modified Wheel I / Rail A . 98Figure F.9 Diagram (Right Wheel A Left Wheel B) / Rail A . 101Figure G.1 Wheel A / Rail A Random error in mm . 104Figure G.2 Wheel A / Rail A Random error in mm . 105Figure G.3 Wheel A / Rail A Random error in mm . 106Figure G.4 Wheel A / R
47、ail A Grid error in mm 107Figure G.5 Wheel A / Rail A Grid error in mm 108Figure G.6 Wheel A / Rail A Grid error in mm 109Figure G.7 Wheel H / Rail A Random error in mm . 110Figure H.1 Transformation of the point P (x, y) to grid with grid widths y, z . 111Figure H.2 Grid transformation with grid widths of 0,5 mm . 112Figure H.3 Variation of the grid origin. 112Figure H.4 50 variants of grid origins 114Figure H.5 Random error of measuring points 116Tables Table D.1 Wheel profile: R-UIC 519-A Right wh
