AGMA 23509-B17-2017 Bevel and Hypoid Gear Geometry.pdf

1、 ANSI/AGMA ISO 23509-B17ANSI/AGMA ISO 23509-B17 (Identical to ISO 23509:2016) American National Standard Bevel and Hypoid Gear Geometry AMERICAN NATIONAL STANDARD ANSI/AGMA ISO 23509-B17 AGMA 2017 All rights reserved i Bevel and Hypoid Gear Geometry ANSI/AGMA ISO 23509-B17 Identical to ISO 23509:201

2、6 Approval of an American National Standard requires verification by ANSI that the requirements for due process, consensus and other criteria for approval have been met by the standards developer. Consensus is established when, in the judgment of the ANSI Board of Standards Review, substantial agree

3、ment has been reached by directly and materially affected interests. Substantial agreement means much more than a simple majority, but not necessarily unanimity. Consensus requires that all views and objections be considered, and that a concerted effort be made toward their resolution. The use of Am

4、erican National Standards is completely voluntary; their existence does not in any respect preclude anyone, whether they have approved the standards or not, from manufacturing, marketing, purchasing or using products, processes or procedures not conforming to the standards. The American National Sta

5、ndards Institute does not develop standards and will in no circumstances give an interpretation of any American National Standard. Moreover, no person shall have the right or authority to issue an interpretation of an American National Standard in the name of the American National Standards Institut

6、e. Requests for interpretation of this standard should be addressed to the American Gear Manufacturers Association. CAUTION NOTICE: AGMA technical publications are subject to constant improvement, revision or withdrawal as dictated by experience. Any person who refers to any AGMA Technical Publicati

7、on should be sure that the publication is the latest available from the Association on the subject matter. Tables or other self-supporting sections may be referenced. Citations should read: See ANSI/AGMA ISO 23509-B17, Bevel and Hypoid Gear Geometry, published by the American Gear Manufacturers Asso

8、ciation, 1001 N. Fairfax Street, Suite 500, Alexandria, Virginia 22314, http:/www.agma.org. Approved December 12, 2017 ABSTRACT This standard specifies the geometry of bevel gears. The term bevel gears is used to mean straight, spiral, zerol bevel and hypoid gear designs. If the text pertains to one

9、 or more, but not all, of these, the specific forms are identified. This standard is intended for use by an experienced gear designer capable of selecting reasonable values for the factors based on his/her knowledge and background. It is not intended for use by the engineering public at large. Publi

10、shed by American Gear Manufacturers Association 1001 N. Fairfax Street, Suite 500, Alexandria, Virginia 22314 Copyright 2017 by American Gear Manufacturers Association All rights reserved. No part of this publication may be reproduced in any form, in an electronic retrieval system or otherwise, with

11、out prior written permission of the publisher. Printed in the United States of America ISBN: 978-1-64353-002-4 American National Standard AMERICAN NATIONAL STANDARD ANSI/AGMA ISO 23509-B17 AGMA 2017 All rights reserved ii Contents Foreword . iv 1 Scope 1 2 Normative references . 1 3 Terms, definitio

12、ns and symbols 1 3.1 Terms and definitions . 5 3.2 Symbols 7 4 Design considerations 11 4.1 General . 11 4.2 Types of bevel gears 11 4.2.1 General 11 4.2.2 Straight bevels . 11 4.2.3 Spiral bevels 11 4.2.4 Zerol bevels . 12 4.2.5 Hypoids 12 4.3 Ratios 13 4.4 Hand of spiral 13 4.5 Preliminary gear si

13、ze 13 5 Tooth geometry and cutting considerations . 13 5.1 Manufacturing considerations . 13 5.2 Tooth taper . 13 5.3 Tooth depth configurations . 15 5.3.1 Taper depth . 15 5.3.2 Uniform depth 16 5.4 Dedendum angle modifications 18 5.5 Cutter radius . 18 5.6 Mean radius of curvature 18 5.7 Hypoid de

14、sign . 19 5.8 Most general type of gearing 19 5.9 Hypoid geometry . 20 5.9.1 Basics 20 5.9.2 Crossing point 22 6 Pitch cone parameters 22 6.1 Initial data for pitch cone parameters . 22 6.2 Determination of pitch cone parameters for bevel and hypoid gears . 23 6.2.1 Method 0 23 6.2.2 Method 1 23 6.2

15、.3 Method 2 27 6.2.4 Method 3 32 7 Gear dimensions. 35 7.1 Initial data for tooth profile parameters . 35 7.2 Determination of basic data 37 7.3 Determination of tooth depth at calculation point . 39 7.4 Determination of root angles and face angles 40 7.5 Determination of pinion face width, b1 41 AM

16、ERICAN NATIONAL STANDARD ANSI/AGMA ISO 23509-B17 AGMA 2017 All rights reserved iii 7.6 Determination of inner and outer spiral angles . 43 7.6.1 Pinion . 43 7.6.2 Wheel . 45 7.7 Determination of tooth depth 46 7.8 Determination of tooth thickness 47 7.9 Determination of remaining dimensions . 48 8 U

17、ndercut check . 49 8.1 Pinion 49 8.2 Wheel 52 Annexes Annex A (informative) Structure of ISO formula set for calculation of geometry data of bevel and hypoid gears 54 Annex B (informative) Pitch cone parameters . 60 Annex C (informative) Gear dimensions 71 Annex D (informative) Analysis of forces .

18、78 Annex E (informative) Machine tool data . 81 Annex F (informative) Sample calculations 82 Tables Table 1 Symbols used in this document . 7 Table 2 Initial data for pitch cone parameters 22 Table 3 Initial data for tooth profile parameters 36 Table 4 Conversions between data type I and data type I

19、I 36 Figures Figure 1 Bevel gear nomenclature Axial plane 2 Figure 2 Bevel gear nomenclature Mean transverse section 3 Figure 3 Hypoid nomenclature . 4 Figure 4 Straight bevel . 11 Figure 5 Spiral bevel . 12 Figure 6 Zerol bevel 12 Figure 7 Hypoid 12 Figure 8 Bevel gear tooth tapers 14 Figure 9 Root

20、 line tilt . 15 Figure 10 Bevel gear depthwise tapers 17 Figure 11 Tooth tip chamfering on the pinion . 17 Figure 12 Angle modification required because of extension in pinion shaft . 18 Figure 13 Geometry of face milling and face hobbing processes 19 Figure 14 Hypoid geometry 21 Figure 15 Crossing

21、point for hypoid gears . 22 Figure 16 Basic rack tooth profile of wheel at calculation point . 37 AMERICAN NATIONAL STANDARD ANSI/AGMA ISO 23509-B17 AGMA 2017 All rights reserved iv Foreword The foreword, footnotes and annexes, if any, in this document are provided for informational purposes only an

22、d are not to be construed as a part of ANSI/AGMA ISO 23509-B17, Bevel and Hypoid Gear Geometry. For many decades, information on bevel, and especially hypoid, gear geometry has been developed and published by the gear machine manufacturers. It is clear that the specific formulae for their respective

23、 geometries were developed for the mechanical generation methods of their particular machines and tools. In many cases, these formulae could not be used in general for all bevel gear types. This situation changed with the introduction of universal, multi-axis, CNC-machines, which in principle are ab

24、le to produce nearly all types of gearing. The manufacturers were, therefore, asked to provide CNC programs for the geometries of different bevel gear generation methods on their machines. This document integrates straight bevel gears and the three major design generation methods for spiral bevel ge

25、ars into one complete set of formulae. In only a few places do specific formulae for each method have to be applied. The structure of the formulae is such that they can be programmed directly, allowing the user to compare the different designs. The formulae of the three methods are developed for the

26、 general case of hypoid gears and to calculate the specific case of spiral bevel gears by entering zero for the hypoid offset. Additionally, the geometries correspond such that each gear set consists of a generated or non-generated wheel without offset and a pinion which is generated and provided wi

27、th the total hypoid offset. An additional objective of this document is that, on the basis of the combined bevel gear geometries, an ISO hypoid gear rating system can be established in the future. ISO 23509:2016 was developed by Technical Committee ISO TC 60, Gears. The changes in the new document i

28、nclude: minor corrections of several formulae; the figures have been reworked; explanations have been added in 4.4; the structure of Formula (129) has been changed to cover the case m 0 = ; a formula for the calculation of cbe2 has been added as Formula (F.160); the values for nC and nC in Formulae

29、(F.318) and (F.319) have been extended to three decimal digits to prevent rounding errors. The AGMA Bevel Gearing Committee approved the adoption of ISO 23509:2016 in June 2017. It was approved as an American National Standard, ANSI/AGMA ISO 23509-B17, on December 12, 2017. ANSI/AGMA ISO 23509-B17 r

30、eplaces ANSI/AGMA ISO 23509-A08. The new document represents an identical adoption of ISO 23509:2016, which replaced ISO 23509:2006. Suggestions for improvement of this standard will be welcome. They may be submitted to techagma.org. AMERICAN NATIONAL STANDARD ANSI/AGMA ISO 23509-B17 AGMA 2017 All r

31、ights reserved v PERSONNEL of the AGMA Bevel Gearing Committee Chairman: Robert F. Wasilewski Arrow Gear Company ACTIVE MEMBERS B. Bijonowski Bison Gear see B.3. If there is sufficient offset, the shafts may pass one another and a compact straddle mounting can be used on the wheel and pinion. Hypoid

32、 gears can also have their tooth surfaces precision-finished. Figure 7 Hypoid AMERICAN NATIONAL STANDARD ANSI/AGMA ISO 23509-B17 AGMA 2017 All rights reserved 13 4.3 Ratios Bevel gears may be used for both speed-reducing and speed-increasing drives. The required ratio shall be determined by the desi

33、gner from the given input speed and required output speed. For power drives, the ratio in bevel and hypoid gears may be as low as 1, but should not exceed approximately 10. High-ratio hypoids from 10 to approximately 20 have found considerable usage in machine tool design where precision gears are r

34、equired. In speed-increasing applications, the ratio should not exceed 5. 4.4 Hand of spiral The hand of spiral should be selected to give an axial thrust that tends to move both the wheel and pinion out of mesh when operating in the predominant working direction. Often, the mounting conditions will

35、 dictate the hand of spiral to be selected. For spiral bevel and hypoid gears, both members should be held against axial movement in both directions. A right-hand spiral bevel gear is one in which the outer half of a tooth is inclined in the clockwise direction from the axial plane through the midpo

36、int of the tooth as viewed by an observer looking at the face of the gear. Figure 5 shows a right-hand wheel. A left-hand spiral bevel gear is one in which the outer half of a tooth is inclined in the anticlockwise (counterclockwise) direction from the axial plane through the midpoint of the tooth a

37、s viewed by an observer looking at the face of the gear. Figure 5 shows a left-hand pinion. To avoid the loss of backlash, the hand of spiral should be selected to give an axial thrust that tends to move the pinion out of mesh. See Annex D. For relation of the hand of spiral and the direction of hyp

38、oid offset, see B.3. 4.5 Preliminary gear size Once the preliminary gear size is determined (see B.4.3), the tooth proportions of the gears should be established and the resulting design should be checked for bending strength and pitting resistance. See ISO 10300 (all parts). 5 Tooth geometry and cu

39、tting considerations 5.1 Manufacturing considerations This clause presents tooth dimensions for bevel and hypoid gears in which the teeth are machined by a face mill cutter, face hob cutter, a planing tool or a cup-shaped grinding wheel. The gear geometry is a function of the cutting method used. Fo

40、r this reason, it is important that the user is familiar with the cutting methods used by the gear manufacturer. The following section is provided to familiarize the user with this interdependence. 5.2 Tooth taper Bevel gear tooth design involves some consideration of tooth taper because the amount

41、of taper affects the final tooth proportions and the size and shape of the blank. It is advisable to define the following interrelated basic types of tapers (these are illustrated in Figure 8, in which straight bevel teeth are shown for simplicity). Depth taper refers to the change in tooth depth al

42、ong the face measured perpendicular to the pitch cone. AMERICAN NATIONAL STANDARD ANSI/AGMA ISO 23509-B17 AGMA 2017 All rights reserved 14 Slot width taper refers to the change in the point width formed by a V-shaped cutting tool of nominal pressure angle, whose sides are tangent to the two sides of

43、 the tooth space and whose top is tangent to the root cone, along the face. Space width taper refers to the change in the space width along the face. It is generally measured in the pitch plane. Thickness taper refers to the change in tooth thickness along the face. It is generally measured in the p

44、itch plane. Key 1 depth 2 slot width 3 thickness 4 space width Figure 8 Bevel gear tooth tapers The taper of primary consideration for production is the slot width taper. The width of the slot at its narrowest point determines the point width of the cutting tool and limits the edge radius that can b

45、e placed on the cutter blade. The taper which directly affects the blank is the depth taper through its effect on the dedendum angle, which is used in the calculation of the face angle of the mating member. The slot width taper depends upon the lengthwise curvature and the dedendum angle. It can be

46、changed by varying the depth taper, i.e. by tilting the root line as shown in Figure 9, in which the concept is simplified by illustrating straight bevel teeth. In spiral bevel and hypoid gears, the amount by which the root line is tilted is further dependent upon a number of geometric characteristi

47、cs including the cutter radius. AMERICAN NATIONAL STANDARD ANSI/AGMA ISO 23509-B17 AGMA 2017 All rights reserved 15 This relationship is discussed more thoroughly in 5.3. The root line is generally rotated about the mid-section at the pitch line in order to maintain the desired working depth at the

48、mean section of the tooth. Key 1 pitch cone apex Figure 9 Root line tilt 5.3 Tooth depth configurations 5.3.1 Taper depth 5.3.1.1 Standard depth Standard depth pertains to the configuration where the depth changes in proportion to the cone distance at any particular section of the tooth. If the root

49、 line of such a tooth is extended, it intersects the axis at the pitch cone apex, as illustrated in Figure 10, but the face cone apex does not. The sum of the dedendum angles of pinion and wheel for standard depth taper, fS, does not depend on cutter radius. Most straight bevel gears are designed with standard depth taper. 5.3.1.2 Constant slot width This taper represents a tilt of the root line such that the slot width is constant while maintaining the proper space width tape