AGMA+913-A98-美标-齿轮标准设计规范

A G M A 9 1 3 - A 9 8 AGMA INFORMATION SHEET (This Information Sheet is NOT an AGMA Standard) AGMA 913-A98 AMERICAN GEAR MANUFACTURERS ASSOCIATION Method for Specifying the Geometry of Spur and Helical Gears ii Method for Specifying the Geometry of Spur and Helical Gears AGMA 913--A98 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 Publication 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 quoted or extracted. Credit lines should read: Extracted from AGMA 913--A98, Method for Specifying the Geometry of Spur and Helical Gears,with the permission of the publisher, the AmericanGear Manufacturers As- sociation, 1500 King Street, Suite 201, Alexandria, Virginia 22314.] Approved March 13, 1998 ABSTRACT This information sheet provides information to translate tooth thickness specifications which are expressed in terms of tooth thickness, center distance or diameter into profile shift coefficients, as that term is used in international standards. Published by American Gear Manufacturers Association 1500 King Street, Suite 201, Alexandria, Virginia 22314 Copyright 1998 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, without prior written permission of the publisher. Printed in the United States of America ISBN: 1--55589--714--2 American Gear Manufacturers Association AGMA 913--A98AMERICAN GEAR MANUFACTURERS ASSOCIATION iii Contents Page Foreword iv. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Scope 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Terms and symbols 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Definitions 3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Profile shift 6. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Internal gear pair calculations 11. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Tables 1 Symbols used in equations 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Obsolete terms 3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Figures 1 The basic rack 3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Hypothetical tool 4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Profile shift of a helical gear 5. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Effect of profile shift on involute tooth profiles 7. . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Distances along the line of action 9. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Root radii cut with rack tool 10. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Distances along the line of action for an internal gear pair 12. . . . . . . . . . . . . . . Annexes A Tool proportions 15. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B Calculation of profile shift 19. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Bibliography 25. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . AGMA 913--A98 AMERICAN GEAR MANUFACTURERS ASSOCIATION iv Foreword [The foreword, footnotes and annexes, if any, in this document are provided for informational purposes only and are not to be construed as a part of AGMA Information Sheet 913--A98, Method for Specifying the Geometry of Spur and Helical Gears.] This information sheet is intended to provide sufficient information to allow its users to be able to translate tooth thickness specifications which are expressed in terms of tooth thickness, center distance or diameter into profile shift coefficients, as that term is used in international standards. This AGMA information sheet and related publications are based on typical or average data, conditions or application. AGMA 913--A98 was approved by the AGMA membership on March 13, 1998. Suggestions for improvement of this standard will be welcome. They should be sent to the American Gear Manufacturers Association, 1500 King Street, Suite 201, Alexandria, Virginia 22314. AGMA 913--A98AMERICAN GEAR MANUFACTURERS ASSOCIATION v PERSONNEL of the AGMA Nomenclature Committee Chairman: John R. Colbourne University of Alberta. . . . . . . Vice Chairman: D. McCarroll Gleason Works. . . . . . . . . ACTIVE MEMBERS W.A. Bradley III Consultant. . . . . . . . . . . . . . . . . . . . R.L. Errichello GEARTECH. . . . . . . . . . . . . . . . . . . . . . D. Gonnella Texaco Lubricants Company. . . . . . . . . . . . . . . . . . . . . . . . D.R. McVittie Gear Engineers, Inc.. . . . . . . . . . . . . . . . . . . . . . . O.A. LaBath Cincinnati Gear Company. . . . . . . . . . . . . . . . . . . . . . . I. Laskin Irving Laskin, P.E.. . . . . . . . . . . . . . . . . . . . . . . . . . . G.W. Nagorny Nagorny & Associates. . . . . . . . . . . . . . . . . . . . . . J.W. Polder Delft University of Technology. . . . . . . . . . . . . . . . . . . . . . . . L.J. Smith Invincible Gear Company. . . . . . . . . . . . . . . . . . . . . . . . . R.E. Smith R.E. Smith & Co., Inc.. . . . . . . . . . . . . . . . . . . . . . . . . ASSOCIATE MEMBERS K. Acheson The Gear Works -- Seattle, Inc.. . . . . . . . . . . . . . . . . . . . . . . . M. Allard UNITRAM. . . . . . . . . . . . . . . . . . . . . . . . . . M.R. Chaplin Contour Hardening, Inc.. . . . . . . . . . . . . . . . . . . . . . . A.S. Cohen Engranes y Maquinaria. . . . . . . . . . . . . . . . . . . . . . . . L. Faure CMD. . . . . . . . . . . . . . . . . . . . . . . . . . . R. Green Eaton Corporation. . . . . . . . . . . . . . . . . . . . . . . . . . T. Okamoto Nippon Gear. . . . . . . . . . . . . . . . . . . . . . . . AGMA 913--A98 AMERICAN GEAR MANUFACTURERS ASSOCIATION vi (This page is intentionally left blank.) 1 AGMA 913--A98AMERICAN GEAR MANUFACTURERS ASSOCIATION American Gear Manufacturers Association -- Method for Specifying the Geometry of Spur and Helical Gears 1 Scope This information sheet provides a general method for specifying profile shift and rack shift, with gear nomenclature and definitions. This document describes the effect that profile shift has on the geometry and performance of gears, but does not make specific design recommendations. The equations in the first part of this document (clauses 3 and 4) apply to external gear pairs only. The corresponding equations for internal gear pairs are contained in clause 5. Annexes A andB provide practical examples on the calculation of tool proportions and profile shift. 2 Terms and symbols 2.1 Terms The terms used, wherever applicable conform to the following standards. ISO 701:1998, International gear notation ---- Symbols for geometrical data ANSI/AGMA 1012--F90,Gear Nomenclature, Def- initions of Terms with Symbols 2.2 Symbols This information sheet uses the ISO symbols in table 1. In cases where there are no ISO symbols, or the definitions are different, other symbols are used. NOTE: The symbols, definitions and terminologyused in this information sheet may differ from other AGMA publications. The user should not assume that familiar symbols can be used without a careful study of these definitions. Table 1 -- Symbols used in equations ISO Symbols Other Symbols Terms Units Where first used C1 Distance to SAP mm Eq 23 C2, C3, C4 Distances along line of action mm Eq 27 C5 Distance to EAP mm Eq 23 C6 Distance between interference points mm Eq 23 YJ1, YJ2 Bending strength geometry factor, pinion and gear ---- Eq 30 aref Reference center distance mm Eq 5 aw Operating center distance mm Eq 16 c Root clearance mm Eq 42 ci2 Required clearance at the tooth root of the internal gear mm Eq 70 d Diameter mm Eq 4 ha0 Addendum of the tool mm Eq 22 ha1, ha2 Addendum, pinion and gear mm Eq 34 haP0 Distance on the cutting tool from the reference line to the point near the tooth tip where the straight part of the pro- file ends and the circular tip begins mm Eq 21 (continued) AGMA 913--A98 AMERICAN GEAR MANUFACTURERS ASSOCIATION 2 Table 1 (concluded) ISO Symbols Other Symbols Terms Units Where first used jn Normal operating circular backlash mm Eq 31 k Tip--shortening coefficient ---- Eq 32 m Module mm Eq 3 p Circular pitch mm Eq 1 r1, r2 Reference radius, pinion and gear mm Eq 5 ra1, ra2 Outside radius, pinion and gear mm Eq 25 rb1, rb2 Base circle radius, pinion and gear mm Eq 13 rf1, rf2 Root radius, pinion and gear mm Eq 42 rfP1 Radius of the pinion fillet circle mm Eq 60 s Tooth thickness mm Eq 2 sn1, sn2 Reference normal circular tooth thickness, pinion and gear mm Eq 7 u Gear ratio ∫ 1.0 ---- Eq 10 xE1, xE2 Generating rack shift coefficient, pinion and gear ---- Eq 46 x1, x2 Profile shift coefficient, pinion and gear ---- Eq 6 x1min Minimum pinion profile shift coefficient to avoid undercut ---- Eq 20 y Profile shift mm Eq 6 yE Rack shift ---- Eq 8 y1min Minimum pinion profile shift to avoid undercut mm Eq 20 z1, z2 Number of teeth, pinion and gear ---- Eq 4 ∼n Reference normal pressure angle ---- Eq 7 ∼t Reference transverse pressure angle ---- Eq 9 ∼wt Operating transverse pressure angle ---- Eq 9 ϒ Reference helix angle ---- Eq 1 ∆aref Center distance modification mm Eq 32 ∆sn Amount of tooth thinning mm Eq 8 ∆sn1, ∆sn2 Tooth thinning for backlash, pinion and gear mm Eq 31 ±a0 Radius of the circular tip of the tool mm Eq 22 ±fP Fillet radius of the basic rack mm Fig 1 Σx Sum of profile shift coefficients ---- Eq 53 ΣxE Sum of generating rack shift coefficients ---- Eq 52 σF1, σF2 Allowable bending stress, pinion and gear MPa Eq 30 Subscript conversion (none) At reference diameter a At addendum (tip) diameter b At base cylinder diameter f At root diameter n Normal plane t Transverse plane w Operating, running or working y At any (undefined) diameter 0 Tool dimensions 1 Pinion 2 Gear or rack AGMA 913--A98AMERICAN GEAR MANUFACTURERS ASSOCIATION 3 3 Definitions This information sheet provides definitions of profile shift and rack shift and shows the relations between them and other gear quantities. The terms profile shift and rack shift are used in this information sheet for standardization. The intention is to replace the similar or related terms listed in table 2. 3.1 Basic rack The standard basic rack tooth profile is the tooth profile normal section through the teeth of a basic rack which corresponds to an external gear with number of teeth z =  and diameter d = , see figure 1. A gear with normal module, mn, and normal pressure angle, ∼n, has a basic rack whose normal circular pitch, pn, is πmn andwhose normal pressure angle is ∼n. The referenceplaneof thebasic rack isparallel to its tooth tip plane and is the plane on which the normal circular tooth thickness, sn, is equal to one half the normal circular pitch. From this definition it follows that the normal circular tooth thickness on the reference plane is equal to the normal circular space width. Table 2 -- Obsolete terms Addendum correction Addendum elongation Addendum increment Addendum modification Addendum ratio Basic rack offset Cutter offset Delta addendum Delta teeth Drop--tooth design Enlargement/reduction Enlarged/reduced center distance Enlarged/reduced number of teeth Half pitch hob pull High/low addendum Hob offset Hob pull Increase/decrease Involute shift Long/short addendum Nonstandard addenda Over/undersize Profile displacement Profile withdrawal Rack withdrawal Tool shift Tool withdrawal Unequal addenda X factor A d d e n d u m π mn 2 Normal circular pitch, pn = π mn Reference line Normal pressure angle Normal base pitch, pbn w P ∼n D e d e n d u m Normal circular thickness, sn ± fP h π mn 2 cP h a P 0 h fP h a P Figure 1 -- The basic rack AGMA 913--A98 AMERICAN GEAR MANUFACTURERS ASSOCIATION 4 If the basic rack is oriented so that its teeth make an angle βwith the gear axis, see figure 3, the section through the basic rack perpendicular to the gear axis is called the transverse section. On this section, the transverse circular pitch, pt, and the transverse tooth thickness, st, are given by: pt= pn cosβ ...(1) st= sn cosβ ...(2) and the transverse module, mt, is defined by: mt= mn cosβ ...(3) The basic rack represents the theoretical gear tooth form, not the form of the cutting tool. No allowance ismade for backlash, finishing stock or manufactur- ing method. The standard 20 normal pressure angle basic rack of ISO53 is commonly used. This document is valid for that basic rack and for any other basic rackwhich meets the criteria of figure 1. 3.2 Reference cylinder of the gear (standard pitch cylinder) The reference cylinder of a gear is defined as the pitch cylinder where circular pitch of the gear is equal to circular pitch of the basic rack. If the gear has z teeth and the rack is oriented with its teeth making an angle β with the gear axis, then the diameter, d, of the reference cylinder is given by d= z mn cosβ ...(4) The pitch plane of the basic rack is parallel to the reference plane and is the plane that is tangent to the reference cylinder of the gear. Thehelix angleof the gear at its reference cylinder is equal to β. 3.3 Reference center distance The reference center distance of an external gear pair is defined as half the sum of the reference diameters. aref= �d1+ d2� 2 = r1+ r2 ...(5) where r1 and r2 are the radii of the reference cylinders. The reference center distance is not necessarily equal to the operating center distance. It is one of the advantages of involute gears, that the operating center distance can vary from the reference center distance without change in operation. 3.4 Hypothetical tool The hypothetical tool is the complement of thebasic rack as shown in figure 2. The reference line of the hypothetical tool is the line at which its normal circular tooth thickness is equal to π mn 2 . The use of the phrase “hypothetical tool” in this document refers to a rack--type cutter. For additional information and an example calculation, see annexes A and B. A d d e n d u m h a 0 π mn 2 Normal circular pitch, pn Reference line Profile angle∼n Hypothetical tool tooth Basic rack π mn 2 h a P 0 h a P ±a0 D e d e n d u m h f0 Figure 2 -- Hypothetical tool AGMA 913--A98AMERICAN GEAR MANUFACTURERS ASSOCIATION 5 3.5 Zero backlash gear pair A zero backlash gear pair is one which operates in tight mesh (has no backlash) on the operating center distance. 3.6 Profile shift The profile shift, y, of the gear is defined as the amount by which the reference plane of the hypothetical tool (conjugate to the basic rack) is displaced from the reference cylinder of the gear. In other words, the gear has profile shift y if the reference plane of the hypothetical tool lies a distance (r + y) from thegear axis, where r is half the diameter, d. Profile shift, y, can be either plus or minus depending on whether the profile shift is to the outside or to the inside of the reference diameter. See figure 3. 3.7 Profile shift coefficient The profile shift coefficient, x, of the gear is defined as the profile shift divided by the normal module. x= y mn ...(6) 3.8 Tooth thickness The normal circular tooth thickness, sn, of the zero backlash gear at its reference cylinder is equal to the normal circular space width of the hypothetical tool at its pitch plane when in tight mesh with the zero backlash gear. sn= 1 2 π mn+ 2y tanαn ...(7) NOTE: Equations 7, 8 and 9 are for external gears only. The corresponding equations for internal gears are given in 5.1. 3.9 Rack shift It is customary to first choose the tooth thicknesses in a gear pair, assuming there is no backlash, and to then reduce the tooth thicknesses to allow for backlash. The phrase “profile shift” will be used for the value of y corresponding to the tooth thickness before thinning, and the phrase “rack shift” for the value of y after thinning. Since the rack shift determines the actual tooth thickness at the time of cutting or generating, the symbol yE is used for the rack shift and xE for the rack shift coefficient. If the amount of thinning is ∆sn, the relationship between rack shift and profile shift is: Normal plane Base circle Transverse plane Profile shift “y” Hypothetical tool reference line Gear reference pitch cylinder Zero backlash gear without tooth thinning Hypothetical tool Basic rack in tight mesh with zero backlash gear β Helix angle r Figure 3 -- Profile shift of a helical gear AGMA 913--A98 AMERICAN GEAR MANUFACTURERS ASSOCIATION 6 yE= y − ∆ sn 2 tan αn ...(8) If two external gears are to mesh with no backlash, their profile shift values must satisfy: y1+ y2= aref (inv αwt − inv αt) tan αt ...(9) where aref is the reference center distance; ∼wt is the operating transverse pressure angle; ∼t is the reference transverse pressure angle. 3.10 Addendum values The gear addendum, measured from the reference cylinder, is usually chosen as (haP + y). This value depends on the profile shift rather than the rack shift and is therefore independent of the value chosen for backlash. In certain designs, particularly when the center distance is significantly larger than the reference standard center distance, the gear ad- dendummay need to be reduced to allow adequate clearance at the roots of the meshing gear, see 4.10. For internal gear pair equations which replace equations 7 through 9, see 5.1. 4 Profile shift 4.1 Profile shift calculation Profile shift is selected considering the following criteria: -- avoiding undercut; -- avoiding narrow top lands; -- balanced specific sliding; -- balanced flash temperature; -- balanced bending fatigue life. The profile shift should be large enough to avoid undercut and small enough to avoid narrow top lands. The profile shifts required for balanced specific sliding, balanced flash temperature and balanced bending fatigue life are usually different. Therefore, the value used should be based on the criterion that is judged to be the most important for the particular application. Figure 4 illustrates how the shape of a gear tooth is influenced by the number of teeth on the gear and the value of the profile shift coefficient. The influence that the number of teeth has on tooth form can be seen by viewing the teeth within any given column of figure 4. With small numbers of teeth, the tooth has larger curvatureand the relative thickness of the teeth at the topland and at the form diameter is smaller. As the number of teeth increases, the topland and tooth thicknesses in- crease and the curvature of the profiles decrease. Tooth thicknesses are maximum for a rack with straight--sided profiles and theoretically infinite number of teeth. Viewing figure 4 horizontally within any given row shows how profile shift changes tooth form. Rows near the top of figure 4 show that gears with few teethhave