AGMA 901-A92-1992 Rational Procedure for the Preliminary Design of Minimum Volume Gears《最小体积齿轮初步设计的合理程序》.pdf

1、AGHA 901-A 92 m Ob87575 00031110 7T5 m AGMA 901492 AMERICAN GEAR MANUFACTURERS ASSOCIATION A Rational Procedure for the Preliminary Design of Minimum Volume Gears AGMA INFORMATION SHEET (Thk Information Sheet is NOT an AGMA Sraadard) AGMA 901-A 72 = Ob87575 0003L4L 831 AGMA 901-A92, A Rational Proce

2、dure for the Preliminary Design of Minimum Volume Gears CAUTION NOTICE: AGMA standards 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

3、Association on the subject matter. Tables or other self-supporting sections may be quoted or extracted in their entirety. Credl lines should read Extracted from AGMA 901-A92, A Ratbnd Prvcedure forthe PreliminatyDesignofMinimum Volume Gem, with the permission of the publisher, the American Gear Manu

4、facturers Association, 1500 King Street, Suite 201 , Alexandria, Virginia 223141. ABSTRACT: A simple, closed-form procedure is presented as 8 first step in the design of minimum vdume spur and helical gearsets. The procedure includes methods for selecting geometry and dimensions, considering maximum

5、 pitting resistance, bending strength, and scuffing resistance. It also includes methods for selecting profile Shift. Copyright 9, 1992 by American Gear Manuiacturers Association Published by American Gear Manufacturers Association 1500 King Street, Suite 201, Alexandria, Vlrginla, 22314 ISBN: 1-555

6、89-579-4 ii AGMA 90%-A 92 Ob87575 0003142 778 m Contents Page Foreword . v 1 Scope . 1 1.1 Procedure 1 1.2 Exceptions . 1 2 Definitionandsymbols 1 2.1 Definitions . 1 2.2 Symbols . 1 3 Inputvariables 1 3.1 Materials and heat treatment . 1 3.2 Design life . 5 3.3 Aspectratio 5 3.4 Inputpower 6 3.5 Co

7、mbined derating factors. Cd and IQ . 6 3.6 Geomettyfactors 8 3.7 Gearratio 8 3.8 Cutter profile angle . 9 3.9 Toolselection . 10 3.1 O Selecting a helix angle . 10 3.11 Factorofsafety 10 4 Preferred number of pinion teeth . 11 5 Design algorithm . 13 7 Considerations for improved rating . 14 Improve

8、 scuffing resistance . 15 6 Designaudit . 14 7.1 Improve bending fatigue resistance . 14 7.2 Improve pitting fatigue resistance 15 7.3 7.4 Profileshfi . 15 7.5 Summary . 15 Tables 1 Symbols used in equations 2 2 Allowable contact stress number9 for steel gears . 4 3 Allowable bending stress numbers

9、for steel gears . 5 4 5 Typical load distribution factors . 7 6 Effects of helix angle in parallel shat gearing . 11 Typical application factors, Ca and Ka 6 i iii AGHA 901-A 92 Ob87575 0003343 b04 Contents (cont) Page Figures 1 2 3 4 5 Two branch double stage gearing . 6 Preferred number of pinion

10、teeth . 11 Preferred number of pinion teeth for spur gear (unmodified) 12 Preferred number of pinion teeth for spur gear (modified) 13 Preferred number of pinion teeth for spur gear where redesign shouldbeconsidered 13 Annexes A Profileshift 17 B C E Ratio split for minimum volume 23 Ratio split for

11、 an existing two stage box 27 D Exampleproblems 31 References and bibliography 37 N AGMA 901-A 92 Ob87575 0003344 540 FOREWORD The foreword, footnotes, and annexes are provided for informational purposes only and should not be const rued as a part of AG MA 90 1 -A92, A Rational Procedure for the Pre

12、liminary Design of Minimum Volume Gears, Gear design is a process of synthesis where gear geometry, materials, heat treatment, manufacturing methods, and lubrication are selected to meet the performance requirements of a given application. The designer must design the gearset with adequate pitting r

13、esistance, bending strength, and scuffing resistance to transmit the required power for the design life. With the algorithm presented here, one can select materials and heat treatment within the economic constraints and limitations of manufacturing facilities, and select the gear geometry tosatisfy

14、constraints on weight, size and configuration. The gear designer can minimize noise level and operating temperature by minimizing the pitchline velocity and sliding velocity. This is done by specifying high gear accuracy and selecting material strengths consistent with maximum material hardness, to

15、obtain minimum volume gearsets with teeth no larger than necessary to balance the pitting resistance and bending strength. Gear design is not the same as gear analysis. Existing gearsets can only be analyzed, not designed. While design is more challenging than analysis, current textbooks do not prov

16、ide proceduresfor designing minimum volume gears. They usually recommend that the number of teeth in the pinion be chosen based solely on avoiding undercut. This information sheet, based on the workof R. Errichello 1*, will show why this practice, or any procedure which arbitrarily selects the numbe

17、r of pinion teeth, will not necessarily result in minimum volume gearsets. Although there have been many technical papers on gear design (for example 2 and 3), most advocate using computer-based search algorithms which are unnecessary. Tucker 4 came the closest to an efficient algoriithm, but he did

18、 not show how to find the preferred number of teeth for the pinion. This information sheet includes the design of spur and helical gears. Other gear types could bedesigned by a similar algoriithm with some slight modifications to the one presented here. AGMA 901-A92 was approved by the Helical Gear

19、Rating Committee in March, 1992 and approved by the AGMA Board of Directors as of May, 1992. Suggestions for the improvement of this information sheet will be welcome. They should be sent to the American Gear Manufacturers Association, 1500 King Street, Suite 201 , Alexandria, Virginia, 2231 4. * Nu

20、mbers in brackets refer to the list of references in annex E. V AGHA 901-A 92 0687575 0003345 487 PERSONNEL of the AGMA Committee for Helical Gear Rating Chairman: D. McCarthy . Doms Company Vice Chairman: N. Hube . . General Electric ACTIVE MEMBERS K. E. Acheson . . The Gear Works-Seattle M. Antosi

21、ewicz . . Falk J. Bentley Peerless-Winsmith E. S. Berndt C - required torque capacity; - specified center distance; - material selection. This method could be extended to other gear types given the appropriate constants and factors. 1.1 Procedure The simple closed form of the procedure allows the de

22、signer to explore options with a minimum of computation so that the important design decisions regarding loads, overloads, material, and tooling selections are not obscured by the need to spend a long time calculating each possibility. This information sheet will demonstrate to the user that the tra

23、ditional beginning point for gear design, selecting the minimum number of pinion teeth to avoid undercut, will rarely lead to the best design. As this procedure is approximate, it is necessary to audit the design (see clause 6). 1.2 Exceptions The procedure described herein incorporates major design

24、 considerations and leads toward minimum volume gear designs based upon the criteria chosen. For the final gear design, additional influencing factors beyond those in this infomation sheet include shaft deflection limits, sound level, cost, etc. Any of these could influence the design of the gear en

25、velope and final volume. It is not the intent of this information sheet to include the calculation of the profile shift coefficient (adden- dum modification coefficient). It is, however, neces- sary to inform the reader that profile shift exists, how it can affect gear design, and where it comes int

26、o play in designing a gearset. Some of the important factors relating to profile shift are discussed in 7.4. Overhung pinions or gears are not covered by this information sheet because of the difficulty in deter- mining an accurate value for the load distribution factor. 2 Definitions and symbols 2.

27、1 Definitions The terms used, wherever applicable, conform to the following standards: ANSI Y1 0.3-1 968, Letter Symbols for Quantities Used in Mechanics of Solids ANSVAGMA 1 O1 2-F90, Gear Nomenclature, Definitions of Terms with Symbols AGMA 9WB89, Metric Usage 2.2 Symbols The symbols used in this

28、information sheet are shown in table 1. NOTE -The symbols, definitions and terminology used in this information sheet may difier from other AGMA publications. The user should not assume that familiar symbols can be used without a careful study of these definitions. 3 Input variables This clause disc

29、usses the significant parameters relating to a preferred gear design. It is not intended to be all inclusive, but to be limited by the scope of this information sheet. 3.1 Materlals and heat treatment Many materials have been used in gearing, but the most common today is steel. This information shee

30、t only applies to steel gearing. There are two commonly used types of heat treatment for steel gear materials, surface hardening and through hardening. The choice of steel alloy must be compatible with the chosen heat treatment process. 1 AGHA 901-A 72 = 0687575 0003147 25T AGMA 901-A92 Table 1 - Sy

31、mbols used in equations Symbols AGMA IS0 Terms number of power paths application factor - pitting combined derating factor - pitting pitting resistance life factor load distribution factor - pitting elastic coefficient operating center distance dynamic factor - pitting operating pitch diameter of pi

32、nion net face width (without gap for double helical) Brinell hardness pitting resistance geometry factor bending strength geometry factor application factor - bending rim thickness factor pitting resistance constant combined derating factor - bending bending strength lie factor load distribution fac

33、tor - bending bending strength constant dynamic factor - bending gear life face contact ratio gear ratio (mG) 1) gear ratio of high speed gearset (mG1 1 1) normal module overall gear ratio of double stage gear drive (Moil) total number of load cycles in gear lie number of teeth in gear number of tee

34、th in pinion preferred number of pinion teeth speed pining resistance factor of safety bending strength factor of safety input power normal diametral pitch aspect (Hd) ratio Units Equation where first used 8 9 30 26 9 32 21 30 10 25 1 11 12 31 31 32 31 27 9 33 31 3 4 25 4 15 25M 15 3 6 6 34 3 32 33

35、7 25 The symbol Ky is also used for the dynamic factor in IS0 standards. However, its value is the inverse (equal to IlKy) of the value used in ANSVAGMA 2001-688. continue 2 AGHA 901-A 92 Ob87575 000311i8 196 Symbols - 1 2 n G P r (4 IS0 N4 OHP 6FP o“ OFN Ti TP %o nl AGMA 901492 Table 1 (concluded)

36、Terms number of contacts per revolution allowable contact stress number allowable bending stress number contact strength bending strength torque on high speed shaft transmitted pinion toque, per mesh normal profile angle of cutter standard hei angle Equation Units where first - IWin2 (Nmm2) IWin2 (N

37、mm2) lidin2 (Nmm2) IMn2 (Nmm2) in Ibs (Nm) in Ibs (Nm) degrees degrees 3 1 2 28 29 7 8 11 25 SubscriptsSign convention high speed (pinion) low speed (wheel) normal (no subscript indicates transverse) gear (wheel) pinion operating or running upper sign external gearsets, lower sign internal gearsets

38、3.1.1 Surface hardening Surface hardening takes place after tooth cutting, usually on gears made from hot rolled bar or forged steel. 3.1.1.1 Carburized Carburized steel is most commonly used for highly loaded, compact designs such as aircraft gears, vehicle transmissions of all types, machine tools

39、, industrial gear driwes, mining machines and similar uses. This material has the highest strength and greatest overload capacity, but carburized gears must be carefully manufactured. Cariiurized gears often result in the least expensive overall transmis- sion design, if their advantage in small siz

40、e for a given capacity can be utilized. Few manufacturers can produce carburized gears larger than 40 inches in diameter, though some can make them over 1 O0 inches in diameter. Secondary finishing operations after carburizing, such as tooth grinding, are often required to achieve the desired tooth

41、form. This is often required to eliminate the distortions caused by heating and cooling employed in the carburizing process. 3.1.1 2 Nitrided Nitrided steel is most commonly used for small gears, finer than 10 diametral pitch (2.5 module) because the maximum case depth is limited. Some large gears a

42、re nitrided to avoid the distortion inherent in the carburizing process. Typical applica- tions are industrial gear drives and small machine tools. Nitrided gears have limited shock resistance. This information sheet does not address nitrided gears, as reference 5 does not provide life factor curves

43、 for nitrided gears. 3.1.1 3 Induction and flame hardened Induction and flame hardened steels are used to achieve intermediate capacities between car- burized and through hardened gears. These processes are difficult to control, but give good results when carefully controlled. This information sheet

44、 does not address induction or flame hardened gears, as they are not recommended for inexperienced designers. 3.1.2 Through hardening Through hardened gears typically have teeth cut in pre-heat-treated gear blanks, with no further heat treatment after cutting. The raw material can be hot 3 AGUA 901-

45、A 92 W Ob87575 0003349 O22 AGMA 901-A92 rolled, cast, or forged. Hardness is chosen on the basis of machinability, using the lowest hardness which will carry the load on the required center distance. Theallowable stress numbers shall be based on the lowest hardness in the heat treatment specifica- t

46、ions. Typical heat treatment specifications have a 40 BHN tolerance between the minimum and maximum hardnesses. The hardest heat treatment range that can be machined without special techniques is 320460 BHN. The normal lowest range of hardness is 180-220 BHN, because lower values are difficult to ma

47、chine. Through hardened gear sizes commonly range from less than one inch to over 20 feet in diameter. Typical applications vary from instrument gears to girth gears on large mills and kilns. When gears cannot be of minimum size because of required center distance, rigidity requirements or thermal l

48、imits, or when loads are low, through hardened gears are commonly used. Internal gears are often through hardened. The selection of a proper alloy for hardenability and reliability as well as the qual* control of the steel manufacturing and heat treatment process are beyond the scope of this informa

49、tion sheet. Guid- ance can be found in section 14 of 5, as well as 161 and il. 3.1.3 Elastic coefficient, C, The rating of gears also depends on the elastic coefficient, C, . Further information can be found in section 1 O of 5. The elastic coefficient for a steel pinion and gear is 230Olbs/in20.5 (191 N/mm20.5). 3.1.4 Allowable stress numbers The allowable stress numbers for some heat treatments, surface hardness and steel quality grades are shown in tables 2 and 3. There are two grades of allowables shown in tables 2 and 3. The allowable stress numbers are