AGMA 927-A01-2001 Load Distribution Factors - Analytical Methods for Cylindrical Gears《负载分布系数.圆柱齿轮用分析法》.pdf

1、AGMA 927-AO1 AMERICAN GEAR MANUFACTURERS ASSOCIATION Load Distribution Factors = Analytical Methods for Cylindrical Gears AGMA INFORIMATION SHEET (This Information Sheet is NOT an AGMA Standard) Am er can Gear Manufacturers Association Load Distribution Factors - Analytical Methods for Cylindrical G

2、ears 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 As- sociation on the subject matter. Fa

3、bles or other self-supporting sections may be quoted or extracted. Credit lines should read: Extracted from AGMA 927-AO1, Load Distribution Factors -Analytical Methods for Cylindrical Gears, with the permission of the publisher, the American Gear Manufacturers Association, 1500 King Street, Suite 20

4、1, Alexandria, Virginia 2231 4.1 AGMA 927-A01 Approved October 22, 2000 ABSTRACT This information sheet describes an analytical procedure for the calculation of the face load distribution. The iterative solution that is described is compatible with the definitions of the term face load distribution

5、(KH) of AGMAstandards and longitudinal load distribution (KH and KF) of the IS0 standards. The procedure is easily programmable and flow charts of the calculation scheme as well as examples from typical software are presented. Published by American Gear Manufacturers Association 1500 King Street, Su

6、ite 201, Alexandria, Virginia 22314 Copyright O 2000 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 Sta

7、tes of America ISBN: i -55589-779-7 ii AMERICAN GEAR MANUFACTURERS ASSOCIATION AGMA 927-AO1 Contents Page Foreword . iv 1 Scope . 1 2 References 1 3 4 5 6 8 Gapanalysis 15 Definitions and symbols 2 Iterative analytical method 3 Shaft bending deflections 9 7 Shaft torsional deflection 14 9 Load distr

8、ibution . 19 1 O Future considerations 21 Annexes A B Figures Coordinate system. sign convention. gearing forces and moments . 4 Flowcharts for load distribution factor . 22 Load distribution examples 26 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Base tangent coordinate system for CW driven rotation fro

9、m reference end . 5 Base tangent coordinate system for CCW driven rotation from reference end 6 Hand of cut for gears and explanation of apex for bevel gears . 7 Gearing force sense of direction for positive value from equations 8 Example general case gear arrangement (base tangent coordinate system

10、) . 8 View A-A from figure 5 9 Example shaft . 11 Calculated shaft diagrams . 13 Torsional increments . 15 Shaftnumber3gap 17 Shaftnumber4gap 17 Total meshgap 18 Tooth section with spring constant Cy,. load L. and deflection cd . 19 Meshgapsection grid 20 Relative mesh gap . 18 Deflection sections .

11、 19 Tables 1 2 4 Symbols and definitions 2 Values for factors hand. apex. rotation. and drive 7 3 Calculation data and results . 10 Evaluation of mesh gap for mesh #3. pm 16 iii AGMA 927-AO1 AMERICAN GEAR MANUFACTURERS ASSOCIATION Foreword rhe foreword, footnotes and annexes, if any, in this documen

12、t are provided for informational purposes only and are not to be construed as a part of AGMA Information Sheet 927-AO1, Load Distribution Factors - Analytical Methods for Cylindrical Gears. This information sheet provides an analytical method to calculate a numeric value for the face load distributi

13、on factor for cylindrical gearing. This is a new document, which provides a description of the analytical procedures that are used in several software programs that have been developed by various gear manufacturing companies. The method provides a significant improvement from the procedures used to

14、define numeric values of face load distribution factor in current AGMA standards. Current AGMA standards utilize either an empirical procedure or a simplified closed form analytical calculation. The empirical procedure which is used in ANWAGMA 21 O1 -C95 only allows for a nominal assessment of the i

15、nfluence of many parameters which effect the numeric value of the face load distribution factor. The closed form analytic formulations which have been found in AGMA standards suffer from the limitation that the shape of the load distribution across the face width is limited to a linear form. The lim

16、itations of the previous AGMA procedures are overcome by the method defined in this information sheet. This method allows for including a sufficiently accurate representation of many of the parameters that influence the distribution of load along the face width of cylindrical gears. These parameters

17、 include the elastic effects due to deformations under load, and the inelastic effects of geometric errors as well as the tooth modifications which are typically utilized to offset the deleterious effects of the deformations and errors. The analytical method described in this information sheet is ba

18、sed on a”thin slice” model of a gear mesh. This model treats the distribution of load across the face width of the gear mesh as being independent of the any transverse effects. The method also represents all of the elastic effects of a set of meshing teeth (tooth bending, tooth shear, tooth rotation

19、, Hertzian deflections, etc.) by one constant, .e., mesh stiffness (Cy,). Despite these simplifying assumptions, this method provides numeric values of the face load distribution factor that are sufficiently accurate for industrial applications of gearing which fall within the limitations specified.

20、 The first draft of this information sheet was made in February, 1996. This version was approved by the AGMA membership on October 22,2000. Special mention must be made of the devotion of Louis Lloyd of Lufkin for his untiring efforts from the submittal of the original software code through the prod

21、ding for progress during the long process of writing this information sheet. Without his foresight and contributions this information sheet may not have been possible. Suggestions for improvement of this document will be welcome. They should be sent to the American Gear Manufacturers Association, 15

22、00 King Street, Suite 201, Alexandria, Virginia 2231 4. iv AMERICAN GEAR MANUFACTURERS ASSOCIATION AGMA 927-AO1 PERSONNEL of the AGMA Helical Rating Committee and Load Distribution SubCommittee Chairman: D. McCarthy . Dorris Company Vice Chairman: M. Antosiewicz The Falk Corporation SubCommittee Cha

23、irman: J. Lisiecki The Falk Corporation SUBCOMMITTEE ACTIVE MEMBERS K.E. Acheson . The Gear Works - Seattle W.A. Bradley Consultant M.F. Dalton . General Electric Company G.A. DeLange . Prager, Inc. O. LaBath The Cincinnati Gear Co. L. Lloyd Lufkin Industries, Inc. COMMITTEE ACTIVE MEMBERS K.E. Ache

24、son . The Gear Works-Seattle, Inc. J.B. Amendola . . MAAG Gear AG T.A. Beveridge . . Caterpillar, Inc. W.A. Bradley Consultant M.J. Broglie . Dudley Technical Group, Inc. A.B. Cardis . Mobil Technology Center M.F. Dalton . General Electric Company G.A. DeLange. Prager, Incorporated D.W. Dudley Consu

25、ltant R.L. Errichello . GEARTECH D.R. Gonnella . Equilon Lubricants M.R. Hoeprich . . The Timken Company O.A. LaBath The Cincinnati Gear Co. COMMITTEE ASSOCIATE MEMBERS M. Bartolomeo . . New Venture Gear, Inc. A.C. Becker Nuttall Gear LLC E. Berndt . Besco E.J. Bodensieck . Bodensieck Engineering Co

26、. D.L. Borden D.L. Borden, Inc. M.R. Chaplin Contour Hardening, Inc. R.J. Ciszak . Euclid-Hitachi Heavy Equip. Inc. A.S. Cohen . Engranes y Maquinaria Arco SA S. Copeland Gear Products, Inc. R.L. Cragg . Consultant T.J. Dansdill General Electric Company F. Eberle . Rockwell Automation/Dodge L. Faure

27、 C.M.D. C. Gay . Charles E. Gay - tooth alignment and crowning modification; - alignment of the axes of rotation of the pinion and gear, including bearing clearances and housing bore alignment; - mesh elastic deflections due to Hertzian contact and tooth bending; - shaft elastic deflections due to t

28、wisting and bending, resulting from the target mesh loads and loads external to the mesh. Influences that may be accounted for by estimating values and including them as equivalent misalign- ments of the target shaft axes are: elastic deflection of a gear body if it is not a - solid disk (such as a

29、spoke gear); 3 AGMA 927-AO1 AMERICAN GEAR MANUFACTURERS ASSOCIATION - elastic deflection of the housing and foundations; - displacements of the gearing due to bearing deflection; - thermal or centrifugal effects; - running-in or lapping effects. The method does not consider the following influences:

30、 - tooth profile, spacing and runout deviations; - total tooth load including increases due to application influences and tooth dynamics; - variations of stiffness of the gear teeth; - double helical gears with one helix overloaded. 4.1 Methodology The iterative analytical method consists of the fol

31、lowing basic steps: 1) Calculate the mesh gap resulting from an initial uniform load distribution; 2) Calculate a new load distribution by mathe- matically closing the mesh gap. This is accom- plished by compressing the springs until the sum of the spring forces equals the total tooth force; 3) Calc

32、ulate a new mesh gap resulting from the new load distribution; 4) Repeat steps 2 and 3 until the change in load distribution from the previous iteration is negligible; 5) The load distribution factor is then calculated from this final load distribution. 4.1.1 Calculated elastic deflections Deflectio

33、ns which are calculated within the iterative method include the elastic deflections of the pinion and gear shafts, plus the mesh. Elastic shaft deflections include shaft twist and bending. Elastic tooth deflections include Hertzian contact and tooth bending. 4.1.2 Equivalent misalignment inputs Othe

34、r displacements that are treated by combining them as an equivalent deflection at the target mesh include: - alignment deviations and modifications of pinion and gear teeth; - equivalent elastic deflection of non-solid body gears (such as a spoke gear); - elastic deflection of the housing and founda

35、tions; - displacements due to bearing clearance, alignment and deflection; - thermal or centrifugal effects; - running-in or lapping effects. 4.2 Assumptions and simplifications The following assumptions and simplifications are used: - the weight of components is ignored; - effects of uneven distrib

36、ution of load on meshes other than the target mesh are ignored; load on these meshes is treated as concentrated in the center of the mesh; - shear coupling between the mesh gap com- pression springs representing the mesh stiffness is ignored; - mesh stiffness is a constant across the full width of t

37、ooth; - all shafts are supported on two bearings; - for double helical gears the net thrust force is zero as the thrust force from each helix cancels each other; - for double helical gears the tangential and separating force is distributed equally on each hand helix; this is generally true as long a

38、s one member can float with respect to the other with no external axial load applied. 5 Coordinate system, sign convention, gearing forces and moments 5.1 Rules The rules that govern the coordinate system, sign convention, gearing forces and moments are: - the target mesh shafts are mutually paralle

39、l; - the coordinate system for all calculations lies in the base tangent plane; - the base tangent plane is a plane tangent to the base circles of the target mesh; - the driving element is the element for which contact first occurs in the root of the tooth and traverses to the tip of the tooth; 4 AM

40、ERICAN GEAR MANUFACTURERS ASSOCIATION AGMA 927-AO1 - a modified Timken sign convention is followed; - each analysis includes only the two shafts under consideration; - the origin of the shaft is the bearing or point of application of a force or moment on the target pinion shaft which is most remote

41、from the target mesh toward the reference end of the shaft (see 5.2); - the input torque to the driving element enters the shaft from one side only and is fully balanced by torque in the target mesh. 5.2 Coordinate system and sign convention The coordinate system is aligned with the base tangent pla

42、ne, BTP, of the target mesh and is defined as the base tangent coordinate system, BTCS. The BTCS is comprised of three orthogonal axes: BT, BTN (base tangent normal), and BTZ. The BTZ axis is parallel to the axes of the target mesh shafts. The BT axis lies in the BTP and is perpendicular to the BTZ

43、axis. The BTN axis is perpendicular to both the BT and the BTZ axes (normal to the base tangent plane). The origin of the BTCS lies at the intersection of the base tangent plane and the edge of the target mesh face closest to the reference end (see figures 1 and 2). For consistency in defining the p

44、ositive direction of the BTCS axes and in calculating the mesh loads, a “reference end” needs to be identified. For purposes of this information sheet, the reference end is the end of the driving element shaft opposite the torque input end. Using this definition of the refence end, the positive dire

45、ctions of the BTCS axes are determined as follows: + BTZ: away from the reference end; + BTN: toward the driven element; + BT obtained by right hand rule; BTN to BTZ. Figures 1 and 2 illustrate the base tangent plane and the base tangent coordinate system for a typical target mesh. In figure 1, the

46、input torque is clockwise when viewed from the reference end. In figure 2, the input torque is counterclockwise when viewed from the reference end. The force, moment and deflection along the positive direction of BT, BTN and BTZ are assigned positive values. Along the negative direction of BT, BTN a

47、nd BTZ, they are assigned negative values. Base tangent plane Base diameter - Base diameter - driven element Figure 1 - Base tangent coordinate system for CW driven rotation from reference end 5 AGMA 927-AO1 AMERICAN GEAR MANUFACTURERS ASSOCIATION Target shaft - Base diameter - driven element Target

48、 shaft - Driven driven Figure 2 - Base tangent coordinate system for CCW driven rotation from reference end 5.3 Gearing forces and signs Meshing gear members transmitting torque will cause forces and moments to develop on the shafts that carry these gear members. These forces and moments will cause

49、deflections of the shafts that will tend to affect the alignment and ultimately the distribution of the load across the face width of the mesh. These elastic deflections need to be com- bined with all other sources of potential misalign- ment. The forces on the gear member are given by equations 1 through 3. In these equations, the values of factors H, A, R, and D are obtained using table 2. When properly applied, these factors will ensure that the proper direction of the forces are determined. The directions obtained will be consistent with the BTCS definition presented in 5.2. The