1、STD-AGHA SSFTM3-ENGL li995 811 Ob87575 0004b73 843 4 7SFTM3 The Effect of Manufacturing Errors on the Predicted Dynamic Factors of Spur Gears by: Jonny Harianto and Donald Houser, Ohio State University American Gear Manufacturers TECHNICAL PAPER COPYRIGHT American Gear Manufacturers Association, Inc
2、.Licensed by Information Handling ServicesSTD*AGflA 75FTfl3-ENGL 1995 Ob87575 0004b74 78T The Effect of Manufacturing Errors on the Predicted Dynamic Factors of Spur Gears - Jonny Harianto and Donald Houser, Ohio State University me statements and opiaionS contained herein are those of the author an
3、d should not be consmed as an official action or opinion of the American Gear Manufacturers Associarion. Abstract Thispaperstudiestheeffectofmanufacturingemorsonpredicteddynamicfatorsofspurgears. Three typesofdynamic factors are defined and studid dynamic bad factors, dynamic tooth force factors, an
4、d dynamic bending moment factors. Three diferent computer programs for predicting dynamic facm are introuced. These programs are a MATLAB forced vibration analysis using a six degree of freedom model, a multi-degree of freedom Dynamic Transmission Error Program (DYTEM) tha uses a six dem of freedom
5、modei, and the Geared Rotor Dynamics Rogram (GRD) that uses a finite element method. After comparing the three programs results with experimental data provided by Nationai Aeronautics and Space Adminisazition (NASA), the DYTEM program is used for dynamic factors prediction. The effects of Merent pro
6、file tolerances for AGMA quality 10,12, and 14 gears are presented. Copyright O 1995 American Gear Manufactums Association 1500 King Street, Suite 201 Alexandria, Virginia, 22314 October, 1995 ISBN 1-55589451-0 COPYRIGHT American Gear Manufacturers Association, Inc.Licensed by Information Handling S
7、ervices. STD.AGMA 75FTM3-ENGL L975 9 b87575 0004b75 blb m The Effect of Manufacturing Errors on Predicted Dynamic Factors of Spur Gears Dr. Donald R Houser Professor, Depi. of Mechanical Engineering The Ohio Stare Universi9 Columbus, Ohio 43210 and Jonny Harianto Graduaie Research Associate The Ohio
8、 State Universig Columbus, Ohio 43210 INTRODUCTION The dynamic factor used in gear design has been the subject of many studies, and has resulted in many formulations. The existing factors used by AGMA (American Gear Manufacturers Association) and IS0 (International Standard Organization) are empiric
9、al in nature. Aithough accuracy is a consideration, it has not been studied to any great extent. The advent of many relatively simple models and available analysis procedures aliows for dynamic factors to be predicted by a variety of methods. This paper uses three different modeling procedures that
10、predict dynamic factors and then uses one of the procedures to compare the effects of profe accuracy with the values used in present AGMA standards. The development of the dynamic factor, using either experimental and theoretical methods, can be traced back more than one century ago. Walker introduc
11、ed a factor which was reformulated by Barth as the ratio of static load to dynamic load l. Buckingham has performed systematic studies in the prediction of dynamic tooth loads for designing gears 2. The formulation of dynamic factor has changed as more factors, such as operational speeds, tooth prec
12、ision, and gear geometry, are considered. The AGMA 2001 standard provides some standard equations for the computation of the dynamic actor based on the gear quality numbers of the gears 3. The AGMA Standard recognizes that it does not consider system resonances and is empirical in nature. Thus, more
13、 intensive investigations in the analytical prediction of dynamic factors have been performed by many investigators. Kubo 4 presented a method whose results compared favorably with his experimental data. Kubos measured results are presented by Dudley 5 in his fairly detailed discussion of dynamic fa
14、ctors. Lin, et al. 161 have conducted an investigation in predicting the effects of both hear and parabolic tooth profile modifications on the dynamic response using a four degree of freedom torsional model. Rebbechi, et. al. 7 have performed some experimental studies to predict the gear dynamic beh
15、avior. These experimental results were compared with the computer program developed at NASA (National Aeronautics and Space Administration) for a four degree of freedom model SI. Wang 9 has also applied time domain torsional dynamic modeling for the prediction of dynamic factors. Although not applie
16、d directly to dynamic factor modeling, Kahraman and Singh lo and Padmanabhan and Singh i I have studied dynamic modeling procedures for gears that have non-lieu effects near system resonances. Ozguven and Houser 12 have developed a computer program, DYTE (Dynamic Transmission Error Program) that use
17、s either measured or computed static transmission errors to excite a single degree of freedom non-hear time domain model. This program determines the dynamic factors, dynamic tooth forces, and dynamic transmission errors. This computer program has been extended to a Si degree of freedom non- linear
18、model caiied DYTEM (Dynamic Transmission Error Program for Multi-degree of fieedom model that provides more complete results 13. In addition to the dynamic factors, dynamic tooth forces, and dynamic transmission errors predicted by DYTE, dynamic bearing forces, bearing displacement, and torsional sh
19、aft motions are also predicted with this time domain program. A computer program calied GRD (Gear Rotor Dynamics Program) has been developed by Kahraman, et. al. 14. This procedure uses finite elements to analyze the dynamics of a system consisting of two shafts supported on bearings and coupled by
20、a spur or helical gears 1 COPYRIGHT American Gear Manufacturers Association, Inc.Licensed by Information Handling Servicesmesh. This program uses honk components of transmission error to predict the dynamic loads in using a fiequency domain approach. The three programs can be used to determine sever
21、al types of dynamic factors of gears in mesh. More specifically, the following dynamic factor effects may be predicted: Dynamic Load Factor, Dynamic Tooth Force Factor, Dynamic Bending Moment Factor, Dynamic Contact Stress Factor, and Dynamic Root Stress Factor. These factors are defined below. The
22、DyMmic Load Factor is the ratio of the static load carried by a gear pair to the peak dynamic load. This dynamic load usually does not consider load sharing between teeth SO it is possible to have the highest dynamic load where two pairs of teeth are in contact, hence providing a conservative value.
23、 This is the factor used by AGMA in its standards. The Dynomic Tooth Force Factor method considers each tooth pair as a separate entity and then computes the highest ratio of static force carried by one tooth relative to the highest dynamic force carried by the same tooth. This i 320 10 O rm (sec) F
24、ig. 4. Dynamic Bending Moment at Different Operating Speed using 196.93 Ib-in Torque. I I I o 2ooo 4wo 6Mx) woo loo60 12Km 14mO 18ooo M.rhFnquncyW) J PM (RPM) Fig. 5. Comparisons of the Dynamic Loads Predicted by the Three Mkrent Dynamic Models. t 8 COPYRIGHT American Gear Manufacturers Association,
25、 Inc.Licensed by Information Handling ServicesHPSTC = 23.18 -0.oo01 - -0.0002 - -0.0003 - - C ._ ; 0.0004 - O L PPT- Pitch Point LPSTG Lowen Point of Single-Tooth Contra i HPSTC= Highest Point of Side-Tooth Contact 4.001 10 12.5 15 17.5 20 22.5 25 27.5 30 32.5 Roll Angle (degree) Fig. 6. K-Chart of
26、Spur Gear for Optimum Profile Moddcation. OB- -. .,=. - I-,_-_,-i-_-_- - 0.81 , , , , , , , 4 O 1000 2000 9oM) 4ooo 5000 6ooo . 7000 8000 Mesh Frequency (Hz) I I o Moo 4Mx) Mxx) ao00 1ww 12000 14000 16000 Pinion Speed (RPM) Fig. 8. Comparison of Dynamic Tooth Force Factors of the Perfect involute Sp
27、ur Gear and Optimum Modified spur Gear. O 10W Zoo0 3000 -4000 5000 &MO 7000 8M)O Mesh Frequency (Hz) I 1 o 2000 4wa 6Ooo 8ooo loo00 1moo 14000 16wo Piion Speed (RPM) Fig. 9a. Comparison of Dynamic Bending Moment Factors of the Perfect Involute Spur Gear and Optimum Modified Spur Gear (Pinion Tooth).
28、 0.8 i O 1000 2000 3wo (o00 5000 6000 7000 8000 Mesh Fmquency (Hz) L I O 2WO 4wO 6W 8ooo 10W 1- 14000 16W Pinion Speed (RPM) Fig. 9b. Comparison of Dynamic Bending Moment Factors of the Perfect Involute Spur Gear and Optimum Modified Spur Gear (Gear Tooth). O -0.0002 p -0.0004 1- - c O .- 3 -0.0006
29、!E U O 2 -0.0008 -0.001 -0.0012 Fig. 10. 10 12.5 15 17.5 20 22.5 25 27.5 30 32.5 Roll Angle (degree) K-Chart of Spur Gear for AGMA Class 14. 9 COPYRIGHT American Gear Manufacturers Association, Inc.Licensed by Information Handling Services- A.- *+ + . 1. TI441 2. T1W :+ . Fig. 11. Comparison of Dyna
30、mic Load Factors for the Class 14. 10 125 15 17.5 20 22.5 25 27.5 30 32.5 4.0014 Roll Angle (degree) Fig. 12. K-Chart of Spur Gear for AGMA Class 12. . L l o 5001wo15002ooo9Qoo95QouKIo45005ooo - spwd (RPW Fig. 13. Comparison of Dynamic Load Factors for the Class 12 Profles. I 1 o 500 low 15w 2ooo 25
31、00 3MxI 3500 4wo - 5000 Fig. 14. Comparison of Dynamic Tooth Force Factors for Pinon Sped (RPH) the Class 12 Profiles. o 500lmol5w3ow4500 Pinion Speed (RPM) Fig. 15a. Comparison of Dynamic Bending Moment Factors for the Class 12 Profiles (Pion). Fig. 15b. Comparison of Dynamic Bending Moment Factors
32、 for the Class 12 Proies (Gear). IO COPYRIGHT American Gear Manufacturers Association, Inc.Licensed by Information Handling ServicesO 4.0002 -0.0004 STD-ALMA 95FTM3-ENGL 1795 b87575 0004b85 5b5 m 10 125 15 17.5 20 22.5 25 27.5 30 3.5 4.0012 4.0014 4.0016 Roll Angle (degree) Fig. 16. K-Chari of Spur
33、Gear for AGMA Class 10. O lo00 1500 2000 2500 Frequemy W Fig. 17. Cornpanson of Dynamic Load Factors for the Class 1 O Profues. loo0 - 900 - 800- 700 - E 8 600- D 500- U 400- 300 - I I I I I, - , I Tooh Farie ._ 200 - 100- O Tirne(sac). Fig. 18a. Dynamic Mesh and Tooth Forces Trace of the Perfect In
34、volute Spur Gear at Pion Speed of 3214 RPM. Time (sec) Fig. 18b. Static and Dynamic Moment Trace of the Perfect involute Spur Gear at Pinion Speed of 3 2 14 RPM. s I I 200 - 100 . I - 01 / , Time (sec) Fig. 19a. Dynamic Mesh and Tooth Forces Trace of the Case 4 (T1004) of AGMA Class 10 Spur Gear at
35、Pinion Speed of 3214 RPM. 200 I Gear Static Moment .- d 120- 8 =loo- D 40- Time (sec) Fig. 19b. Static and Dynamic Moment Trace of the Case 4 (T1004) of AGMA Class 10 Spur Gear at Pinion Speed of 3214 RPM. 11 COPYRIGHT American Gear Manufacturers Association, Inc.Licensed by Information Handling Ser
36、vicesSTD-AGHA 95FTfl3-ENGL 2995 m Ob87575 0009bBb 9T1 v - 4001 / i Fig. 20a. Dynamic Mesh and Tooth Forces Trace of the Optimum Modified Spur Gear at Pinion Speed of 3214 RPM. 60- 40- 20- O * Turi. (tic) Fig. 20b. Static and Dynamic Moment Trace of the Optimum Modified Spur Gear at Pinion Speed of 3214 RPM. COPYRIGHT American Gear Manufacturers Association, Inc.Licensed by Information Handling Services
