1、ANSI/AGMA ISO 23509-A08Identical to ISO 23509:2006American National StandardBevel and Hypoid GearGeometryANSI/AGMAISO23509-A08iiBevel and Hypoid Gear GeometryANSI/AGMA ISO 23509-A08ApprovalofanAmericanNationalStandardrequiresverificationbyANSIthattherequire-ments for due process, consensus, and othe
2、r criteria for approval have been met by thestandards developer.Consensusisestablishedwhen,inthejudgmentoftheANSIBoardofStandardsReview,substantial agreement has been reached by directly and materially affected interests.Substantialagreementmeansmuchmorethanasimplemajority,butnotnecessarilyuna-nimit
3、y. Consensus requires that all views and objections be considered, and that aconcerted effort be made toward their resolution.TheuseofAmericanNationalStandardsiscompletelyvoluntary;theirexistencedoesnotin any respect preclude anyone, whether he has approved the standards or not, frommanufacturing, m
4、arketing, purchasing, or using products, processes, or procedures notconforming to the standards.The American National Standards Institute does not develop standards and will in nocircumstances give an interpretation of any American National Standard. Moreover, noperson shall have the right or autho
5、rity to issue an interpretation ofan American NationalStandardinthenameoftheAmericanNationalStandardsInstitute. Requestsforinterpre-tation of this standard should be addressed to the American Gear ManufacturersAssociation.CAUTION NOTICE: AGMA technical publications are subject to constant improvemen
6、t,revision, or withdrawal as dictated by experience. Any person who refers to any AGMAtechnical publication should be sure that the publication is the latest available from theAssociation on the subject matter.Tablesorotherself-supportingsectionsmaybereferenced. Citationsshouldread: SeeANSI/AGMAISO2
7、3509-A08,BevelandHypoidGearGeometry,publishedbytheAmeri-can Gear Manufacturers Association, 500 Montgomery Street, Suite 350, Alexandria,Virginia 22314, http:/www.agma.org.Approved May 20, 2008ABSTRACTThisstandardspecifiesthegeometryofbevelgears.Thetermbevelgearsisusedtomeanstraight,spiral,zerolbeve
8、l and hypoid gear designs. If the text pertains to one or more, but not all, of these, the specific forms areidentified.This standard is intended for use by anexperienced geardesigner capableofselectingreasonablevalues for the factors based on his knowledge and background. It is not intended for use
9、 by the engineeringpublic at large.Published byAmerican Gear Manufacturers Association500 Montgomery Street, Suite 350, Alexandria, Virginia 22314Copyright 2008 by American Gear Manufacturers AssociationAll rights reserved.No part of this publication may be reproduced in any form, in an electronicre
10、trieval system or otherwise, without prior written permission of the publisher.Printed in the United States of AmericaISBN: 978-1-55589-927-1AmericanNationalStandardANSI/AGMA ISO 23509-A08AMERICAN NATIONAL STANDARDiii AGMA 2008 - All rights reservedContentsPageForeword iv.1 Scope 12 Normative refere
11、nces 13 Terms, definitions and symbols 14 Design considerations 10.5 Tooth geometry and cutting considerations 13.6 Pitch cone parameters 227 Gear dimensions 35.8 Undercut check 48AnnexesA Structure of ISO formula set for calculation of geometry data ofbevel and hypoid gears 52B Pitch cone parameter
12、s 58C Gear dimensions 68.D Analysis of forces 75.E Machine tool data 78.F Sample calculations 79.Figures1 Bevel gear nomenclature - axial plane 2.2 Bevel gear nomenclature - mean transverse section 4.3 Hypoid nomenclature 54 Straight bevel 115 Spiral bevel 116 Zerol bevel 127 Hypoid 128 Bevel gear t
13、ooth tapers 149 Root line tilt 1510 Bevel gear depthwise tapers 17.11 Tooth tip chamfering on the pinion 1712 Angle modification required because of extension in pinion shaft 1813 Geometry of face milling and face hobbing processes 19.14 Hypoid geometry 20.15 Crossing point for hypoid gears 22.16 Ba
14、sic rack tooth profile of wheel 36Tables1 Symbols used in ISO 23509 8.2 Initial data for the calculation of the pitch cone parameters 22.3 Additional data for calculation of gear dimensions 35.4 Relations between data type I and data type II 36ANSI/AGMA ISO 23509-A08 AMERICAN NATIONAL STANDARDiv AGM
15、A 2008 - All rights reservedForewordThe foreword, footnotes and annexes, if any, in this document are provided forinformational purposes only and are not to be construed as a part of ANSI/AGMA ISO23509-A08, Bevel and Hypoid Gear Geometry.For many decades, information on bevel, and especially hypoid,
16、 gear geometry has beendeveloped and published by the gear machine manufacturers. It is clear that the specificformulas for their respective geometries were developed for the mechanical generationmethodsoftheirparticularmachinesandtools.Inmanycases,theseformulascouldnotbeused in general for all beve
17、l gear types. This situation changed with the introduction ofuniversal,multi-axis,CNC-machines,whichinprincipleareabletoproducenearlyalltypesof gearing. The manufacturers were, therefore, asked to provide CNC programs for thegeometries of different bevel gear generation methods on their machines.Thi
18、s standard integrates straight bevel gears and the three major design generationmethods for spiral bevel gears into one complete set of formulas. In only a few places dospecificformulasforeachmethodhavetobeapplied.Thestructureoftheformulasissuchthat they can be programmed directly, allowing the user
19、 to compare the different designs.Theformulasofthethreemethodsaredevelopedforthegeneralcaseofhypoidgearsandcalculate the specific case of spiral bevel gears by entering zero for the hypoid offset.Additionally,thegeometriescorrespondsuchthateachgearsetconsistsofageneratedornon-generatedwheelwithoutof
20、fsetandapinionwhichisgeneratedandprovidedwiththetotal hypoid offset.An additional objective of this standard is that on the basis of the combined bevel geargeometries an ISO hypoid gear rating system can be established in the future.ANSI/AGMA ISO 23509-A08 represents an identical adoption of ISO 235
21、09:2006.ThefirstdraftofANSI/AGMAISO23509-A08wasmadeinJuly,2007. ItwasapprovedbytheAGMAmembershipinMarch,2008andapprovedasanAmericanNationalStandardonMay 20, 2008.Suggestionsforimprovementofthisstandardwillbewelcome. TheyshouldbesenttotheAmericanGearManufacturersAssociation,500MontgomeryStreet,Suite3
22、50,Alexandria,Virginia 22314.ANSI/AGMA ISO 23509-A08AMERICAN NATIONAL STANDARDv AGMA 2008 - All rights reservedPERSONNEL of the AGMA Bevel Gearing CommitteeChairman: Robert F. Wasilewski, Arrow Gear Company.Vice Chairman: George Lian, Amarillo Gear CompanyACTIVE MEMBERST. Guertin Liebherr Gear Techn
23、ology Company.J. Kolonko Rexnord Industries. LLC.T.J. Krenzer Consultant.P.A. McNamara Caterpillar, Inc.K. Miller Dana Spicer Off Highway Products.W. Tsung Dana CorporationANSI/AGMA ISO 23509-A08 AMERICAN NATIONAL STANDARDvi AGMA 2008 - All rights reserved(This page is intentionally blank) AGMA 2008
24、 All rights reserved 1 AMERICAN GEAR MANUFACTURERS ASSOCIATION ANSI/AGMA ISO 23509-A08American National Standard - Bevel and hypoid gear geometry 1 Scope This International Standard specifies the geometry of bevel gears. The term bevel gears is used to mean straight, spiral, zerol bevel and hypoid g
25、ear designs. If the text pertains to one or more, but not all, of these, the specific forms are identified. The manufacturing process of forming the desired tooth form is not intended to imply any specific process, but rather to be general in nature and applicable to all methods of manufacture. The
26、geometry for the calculation of factors used in bevel gear rating, such as ISO 10300, is also included. This International Standard is intended for use by an experienced gear designer capable of selecting reasonable values for the factors based on his knowledge and background. It is not intended for
27、 use by the engineering public at large. Annex A provides a structure for the calculation of the methods provided in this International Standard. 2 Normative references The following referenced documents are indispensable for the application of this document. For dated references, only the edition c
28、ited 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 10300-1:2001, Calculation of load capacity of bevel gears Part 1: Introduction and general inf
29、luence factors ISO 10300-2:2001, Calculation of load capacity of bevel gears Part 2: Calculation of surface durability (pitting) ISO 10300-3:2001, Calculation of load capacity of bevel gears Part 3: Calculation of tooth root strength 3 Terms, definitions and symbols For the purposes of this document
30、, the terms and definitions given in ISO 1122-1 and the following terms, definitions and symbols apply. NOTE 1 The symbols, terms and definitions used in this International Standard are, wherever possible, consistent with other International Standards. It is known, because of certain limitations, th
31、at some symbols, their terms and definitions, as used in this document, are different from those used in similar literature pertaining to spur and helical gearing. NOTE 2 Bevel gear nomenclature used throughout this International Standard is illustrated in Figure 1, the axial section of a bevel gear
32、, and in Figure 2, the mean transverse section. Hypoid nomenclature is illustrated in Figure 3. Subscript 1 refers to the pinion and subscript 2 to the wheel. ANSI/AGMA ISO 23509-A08 AMERICAN NATIONAL STANDARD 2 AGMA 2008 All rights reserved Figure 1 Bevel gear nomenclature Axial plane AMERICAN NATI
33、ONAL STANDARD ANSI/AGMA ISO 23509-A08 AGMA 2008 All rights reserved 3 Key 1 back angle 10 front angle 19 outer pitch diameter, de1, de2 2 back cone angle 11 mean cone distance, Rm 20 root angle, f1, f2 3 back cone distance 12 mean point 21 shaft angle, 4 clearance, c 13 mounting distance 22 equivale
34、nt pitch radius 5 crown point 14 outer cone distance, Re 23 mean pitch diameter, dm1, dm26 crown to back15 outside diameter, dae1, dae2 24 pinion 7 dedendum angle, f1, f2 16 pitch angle, 1, 2 25 wheel 8 face angle a1, a2 17 pitch cone apex 9 face width, b 18 crown to crossing point, txo1, txo2 NOTE
35、See Figure 2 for mean transverse section, A-A. Figure 1 Bevel gear nomenclature Axial plane (continued) ANSI/AGMA ISO 23509-A08 AMERICAN NATIONAL STANDARD 4 AGMA 2008 All rights reserved Key 1 whole depth, hm5 circular pitch9 working depth, hmw 2 pitch point 6 chordal addendum 10 addendum, ham3 clea
36、rance, c 7 chordal thickness 11 dedendum hfm 4 circular thickness 8 backlash12 equivalent pitch radiusFigure 2 Bevel gear nomenclature Mean transverse section (A-A in Figure 1) AMERICAN NATIONAL STANDARD ANSI/AGMA ISO 23509-A08 AGMA 2008 All rights reserved 5 Key 1 face apex beyond crossing point, t
37、zF17 outer pitch diameter, de1, de2 13 mounting distance2 root apex beyond crossing point, tzR18 shaft angle, 14 pitch angle, 2 3 pitch apex beyond crossing point, tz19 root angle, f1, f2 15 outer cone distance, Re 4 crown to crossing point, txo1, txo210 face angle of blank, a1, a216 pinion face wid
38、th, b1 5 front crown to crossing point, txi111 wheel face width, b2 6 outside diameter, dae1, dae212 hypoid offset, a NOTE 1 Apex beyond centreline of mate (positive values). NOTE 2 Apex before centreline of mate (negative values). Figure 3 Hypoid nomenclature ANSI/AGMA ISO 23509-A08 AMERICAN NATION
39、AL STANDARD 6 AGMA 2008 All rights reserved 3.1 Terms and definitions 3.1.1 pinion wheel mean normal chordal addendum hamc1, hamc2height from the top of the gear tooth to the chord subtending the circular thickness arc at the mean cone distance in a plane normal to the tooth face 3.1.2 pinion wheel
40、mean addendum ham1, ham2height by which the gear tooth projects above the pitch cone at the mean cone distance 3.1.3 outer normal backlash allowance jenamount by which the tooth thicknesses are reduced to provide the necessary backlash in assembly NOTE It is specified at the outer cone distance. 3.1
41、.4 coast side by normal convention, convex pinion flank in mesh with the concave wheel flank 3.1.5 cutter radius rc0nominal radius of the face type cutter or cup-shaped grinding wheel that is used to cut or grind the spiral bevel teeth 3.1.6 sum of dedendum angles fsum of the pinion and wheel dedend
42、um angles 3.1.7 sum of constant slot width dedendum angles fCsum of dedendum angles for constant slot width 3.1.8 sum of modified slot width dedendum angles fMsum of dedendum angles for modified slot width taper 3.1.9 sum of standard depth dedendum angles fSsum of dedendum angles for standard depth
43、taper 3.1.10 sum of uniform depth dedendum angles fUsum of dedendum angles for uniform depth 3.1.11 pinion wheel mean dedendum hfm1, hfm2depth of the tooth space below the pitch cone at the mean cone distance AMERICAN NATIONAL STANDARD ANSI/AGMA ISO 23509-A08 AGMA 2008 All rights reserved 7 3.1.12 m
44、ean whole depth hmtooth depth at mean cone distance 3.1.13 mean working depth hmwdepth of engagement of two gears at mean cone distance 3.1.14 direction of rotation direction determined by an observer viewing the gear from the back looking toward the pitch apex 3.1.15 drive side by normal convention
45、, concave pinion flank in mesh with the convex wheel flank 3.1.16 face width b length of the teeth measured along a pitch cone element 3.1.17 mean addendum factor chamapportions the mean working depth between wheel and pinion mean addendums NOTE The gear mean addendum is equal to chamtimes the mean
46、working depth. 3.1.18 mean radius of curvature mradius of curvature of the tooth surface in the lengthwise direction at the mean cone distance 3.1.19 number of blade groups z0number of blade groups contained in the circumference of the cutting tool 3.1.20 number of teeth in pinion wheel z1, z2number
47、 of teeth contained in the whole circumference of the pitch cone 3.1.21 number of crown gear teeth zpnumber of teeth in the whole circumference of the crown gear NOTE The number may not be an integer. 3.1.22 mean normal chordal pinion wheel tooth thickness smnc1, smnc2chordal thickness of the gear t
48、ooth at the mean cone distance in a plane normal to the tooth trace ANSI/AGMA ISO 23509-A08 AMERICAN NATIONAL STANDARD 8 AGMA 2008 All rights reserved 3.1.23 mean normal circular pinion wheel tooth thickness smn1, smn2length of arc on the pitch cone between the two sides of the gear tooth at the mea
49、n cone distance in the plane normal to the tooth trace 3.1.24 tooth trace curve of the tooth on the pitch surface 3.2 Symbols Table 1 Symbols used in ISO 23509 Symbol Description Unit a hypoid offset mm b1, b2 face width mm be1, be2 face width from calculation point to outside mm bi1, bi2 face width from calculation point to inside mm c clearance mmcbe2face width factor chammean addendum factor of wheel dae1, dae2 outside diameter mm de1, de2 outer p
