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1、AGMA913-A98 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 Return to Menu ii Method for Specifying the Geometry of Spur and Helical Gears AGMA 913-A98 CAUTION NO
2、TICE: 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 se
3、lf-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 ManufacturersAs- sociation, 1500 King Street, Suite 201, Alexandria, Virginia
4、 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
5、 American Gear Manufacturers Association 1500 King Street, Suite 201, Alexandria, Virginia 22314 Copyright1998 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 writ
6、ten 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 Forewordiv. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7、 . . . . . . . . . . . . . . . . . . . . 1Scope1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2Terms and symbols1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3Definitions3.
8、. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4Profile shift6. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5Internal gear pair calculations11. . . . . . . . . . . . . .
9、 . . . . . . . . . . . . . . . . . . . . . . . . . Tables 1Symbols used in equations1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2Obsolete terms3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Figures 1Th
10、e basic rack3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2Hypothetical tool4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3Profile shift of a helical gear5. . . . . . . . . . . . . .
11、 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4Effect of profile shift on involute tooth profiles7. . . . . . . . . . . . . . . . . . . . . . . . . . . 5Distances along the line of action9. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6Root radii cut with rack t
12、ool10. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7Distances along the line of action for an internal gear pair12. . . . . . . . . . . . . . . Annexes ATool proportions15. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
13、 . . . . BCalculation of profile shift19. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Bibliography25. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . AGMA 913- -A98AMERICAN GEAR MANUFACTURERS
14、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
15、 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
16、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
17、, Suite 201, Alexandria, Virginia 22314. AGMA 913- -A98AMERICAN GEAR MANUFACTURERS ASSOCIATION v PERSONNEL of the AGMA Nomenclature Committee Chairman: John R. ColbourneUniversity of Alberta. . . . . . . Vice Chairman: D. McCarrollGleason Works. . . . . . . . . ACTIVE MEMBERS W.A. Bradley IIIConsult
18、ant. . . . . . . . . . . . . . . . . . . . R.L. ErrichelloGEARTECH. . . . . . . . . . . . . . . . . . . . . . D. GonnellaTexaco Lubricants Company. . . . . . . . . . . . . . . . . . . . . . . . D.R. McVittieGear Engineers, Inc . . . . . . . . . . . . . . . . . . . . . . O.A. LaBathCincinnati Gear Co
19、mpany. . . . . . . . . . . . . . . . . . . . . . . I. LaskinIrving Laskin, P.E . . . . . . . . . . . . . . . . . . . . . . . . . . G.W. NagornyNagorny wtis the operating transverse pressure angle; tis the referencetransverse pressureangle. 3.10 Addendum values The gear addendum, measured from the re
20、ference cylinder, is usually chosen as (haP+ y). This value dependsontheprofileshiftratherthantherackshift andisthereforeindependentofthevaluechosenfor backlash. In certain designs, particularly when the center distance is significantly larger than the reference standard center distance, the gear ad
21、- dendum may 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
22、 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 f
23、lash 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
24、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, thetoothhaslargercurvatureandtherelative thickness of the teeth at the topland and at the f
25、orm 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 an
26、y given row shows how profile shift changes tooth form. Rows near the top of figure 4 show that gears with few teethhaveatoothformthatdependsstronglyonthe value of the profile shift coefficient. For gears with few teeth, the sensitivity to profile shift narrows the choice for profile shift coefficie
27、nt because too little profile shift results in undercut teeth, whereas too much profile shift gives teeth with toplands that are too narrow. For example, the acceptable values of profileshiftcoefficientfora12toothgearrangefrom x = 0.4 near undercut, to x = 0.44 for a topland thickness equal to 30% o
28、f the module. In contrast, rows near the bottom of figure 4 show that gears withlargenumbersof teetharerelativelyinsensitive to profile shift. This means that the gear designer has wider latitude when choosing profile shift for gears with a large number of teeth. As a limiting case, the shape of the
29、 teeth of a rack are independent of profile shift. Generally, the performance of a gear is enhanced with increasing numbers of teeth and the optimum value of profile shift. Fora fixedgear diameter, with the exception of bending strength, load capacity is increased when the number of teeth increases
30、and the profile shift is designed properly. Resistance to macropitting, adhesive wear and scuffing is im- proved and the gears usually operate more quietly. Themaximumnumberof teethislimitedbybending strength because a large number of relatively small teeth have high bending stresses. Therefore, the
31、 gear designer must limit the number of teeth in the pinion based on maintaining adequate bending strength.Load capacity can be maximized by balancing the pitting resistance and the bending AGMA 913- -A98AMERICAN GEAR MANUFACTURERS ASSOCIATION 7 strength of the gearset (see AGMA 901-A92). A balanced
32、 design has a relatively large number of teeth in the pinion.This makes the gearset relatively insensitive to profile shift, and allows the designer to select the profile shift to minimize specific sliding, minimize flash temperature or balance the bending fatigue life of the pinion and gear. Number
33、 of teeth Profile shift coefficient 12 15 20 30 50 100 -0.40.00.4 0.8 Figure 4 - - Effect of profile shift on involute tooth profiles AGMA 913- -A98AMERICAN GEAR MANUFACTURERS ASSOCIATION 8 4.2 Basic gear geometry .(10)u = z2 z1, where z2 z1 .(11) r1= z1mn 2 cos .(12) r2= z2mn 2 cos = r1u .(13)rb1=
34、r1cos t .(14)rb2= r2cos t= rb1u .(15)t= arctan?tan n cos ? .(16)wt= arccos?aref cost aw ? .(17)inv t= tan t t .(18)inv wt= tan wt wt 4.3Sum of profile shift coefficients for zero backlash NOTE: The equations to follow in this section are for external gearpairs only.The corresponding equations for in
35、ternal gear pairs are given in 5.2.1. .(19)x1+ x2= aref(inv wt inv t) mntan t 4.4 Avoiding involute undercut teeth There are a number of design options to compen- sate for undercut teeth, including profile shift. Undercut is a condition in generated gear teeth where any part of the fillet curve lies
36、 inside a line drawn tangent to the working profile at its point of juncturewiththefillet.Forsuchgears, theendofthe cutting tool has extended inside of the point of tangency of the base circle and the line of action, and removed an excessive amount of material. This removal of material can weaken th
37、e tooth and also may reduce the length of contact, since gear action can only take place on the involute portion of the flank.Should a gear be made by another method that would not undercut the flanks, there may be interference of material and generally the gear would not mesh or roll with another g
38、ear. See AGMA 908-B89, Geometry Factors for Determin- ing the Pitting Resistance and Bending Strength of Spur, Helical and Herringbone Gear Teeth. The minimum profile shift coefficient (to avoid undercut) for the pinion is given by: .(20)x1 min= y1 min mn .(21) y1 min= haP0 r1sin2t where haP0isthedi
39、stanceonthecuttingtooltoothfrom the reference line to the point near the tool tooth tip where the straight part of the profile ends and the circular tip begins. .(22)haP0= ha0 ?a0+ ?a0sin n where ha0is the addendum of the tool; a0is the radius of the circular tip of the tool. 4.5 Avoiding narrow top
40、 lands The maximum permissible profile shift coefficients are obtained by iteratively varying the profile shift coefficientsof thepinionandgearuntiltheirtopland thicknesses are equal to the minimum allowable. 4.6 Balanced specific sliding Specific sliding is defined as the ratio of the sliding veloc
41、ity to rolling velocity at a particular point of contact on the gear of interest. Maximumpittingandwearresistanceisobtainedby balancingthespecificslidingateachendof thepath of contact. This is done by iteratively varying the profile shift coefficients of the pinion and gear until the following equat
42、ion is satisfied: .(23)?C6 C1 1?C6 C5 1?= u2 where C6is the distance between interference points (see figure 5); C1is the distance to SAP (see figure 5); C5is the distance to EAP (see figure 5). .(24)C6=?rb1+ rb2?tanwt= awsinwt .(25) C1= C6r2 a2 r2 b2 ? .(26) C5=r2 a1 r2 b1 ? .(27)C2= C5 pbt .(28)C3
43、= rb1tan wt .(29)C4= C1+ pbt AGMA 913- -A98AMERICAN GEAR MANUFACTURERS ASSOCIATION 9 HPSTC rb2wt pbt pbt C6 ra1 C1 C2 C3 C4 C5 rb1 P aw EAP LPSTC SAP ra2 Line of action Figure 5 - - Distances along the line of action for external gear pair 4.7 Balanced flash temperature According to Bloks theory, th
44、e maximum scuffing resistance is obtained by minimizing the contact temperature. This is done by iteratively varying the profile shift coefficients of the pinionand gear, while calculatingtheflashtemperaturebyBloksequation (see annex A of ANSI/AGMA 2101-C95, Funda- mental Rating Factors and Calculat
45、ion Methods for InvoluteSpurandHelicalGearTeeth),untiltheflash temperature peaks in the approach and recess portions of the line of action are equal. The flash temperatureshouldbecalculatedatthepointsSAP, LPSTC, HPSTC, EAP and at several points in the two pair zones (between points SAP and LPSTC and
46、betweenpoints HPSTCand EAP, see figure5). 4.8 Balanced bending strength Maximum bending resistance is obtained by itera- tively varying the profile shift coefficients of the pinion and gear until the ratio of the bending strength geometry factors equals the ratio of allowable bending stresses, i.e.,
47、 .(30) YJ1 YJ2 = F2 F1 See ANSI/AGMA 2101-C95, clause 5.2 through 5.2.3, for an explanation of YJ1,YJ2,F1and F2. AGMA 913- -A98AMERICAN GEAR MANUFACTURERS ASSOCIATION 10 4.9 Tooth thinning for backlash The small adjustments of the position of the cutting tool to thin the gear teeth for backlash are
48、considered independently of the profile shift coeffi- cients (x1and x2) by specifying the amount the pinion and gear teeth are thinned for backlash,sn1 and sn2.This way, the outside diameters are independent of tooth thinning for backlash.The total thinning coefficients are selected such that: .(31)
49、 sn1+ sn2= jn?aref aw? where jnis normal operating circular backlash A common convention among gear manufacturers is to reduce the normal tooth thickness of each memberbythesameamount,whichmaybeavalue in ?m or a function of the normal module, such as 0.024mn. This maintains the same whole depth for both members. However, for other directions of tooth thickness measurement, see ANSI/AGMA 2002-B88. 4.10Tip- -shortening coefficient for external gearsets Forgearsoperatingonextended centers(aw aref), the outside radii