AGMA-06FTM11-2006.pdf
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1、06FTM11 On Tooth Failure Analysis in Small- -Teeth- -Number Gearing: An Analytical Approach by: Dr. S.P. Radzevich, Eaton | Automotive, Innovation Center TECHNICAL PAPER American Gear Manufacturers Association Copyright American Gear Manufacturers Association Provided by IHS under license with AGMA
2、Licensee=Boeing Co/5910770001 Not for Resale, 07/25/2008 04:28:13 MDTNo reproduction or networking permitted without license from IHS -,-,- On Tooth Failure Analysis in Small- -Teeth- -Number Gearing: An Analytical Approach Dr. Stephen P. Radzevich, Eaton | Automotive, Innovation Center The statemen
3、ts and opinions contained herein are those of the author and should not be construed as an official action or opinion of the American Gear Manufacturers Association. Abstract The paper pertains to analytical study of the major reasons that cause tooth failure in gearing having small teethnumber. Bel
4、ow,gearswithsmallteethnumberarereferredtoSTN-gears. Fortheanalysisofgeartooth failure, tooth contact stresses, and the combined contact/shear stresses (CS-stresses) are investigating. Thestudyisbasedonthein-depthanalysisofthegeartoothloadingandonaccountingofvariationintimeof thetoothloadingandofothe
5、rgearparametersinvariousphasesoftoothmeshing. Theearlierdevelopedby theauthorDG/K-method1ofsurfacegenerationisusedinthestudy. Forthecomputationofthecontactloads of parallel-axis gears, a novel load distribution model is proposed in the paper, as well as a novel analytical method for computation (a)
6、of contact stresses, and (b) of combined CS-stresses in STN-gearing is discussed. The CS-stresses are caused by simultaneous impact of (a) contact stresses together with (b) stresses caused by the pinion/gear tooth profile sliding. To use the developed method of computation, minimum of preliminary a
7、ssumptions are required. While developed for use in STN-gearing, the method is also recommended for the accurate computation of stresses in gearing having regular teeth number. Using commercialsoftwareMathCAD/Scientific,acomputercodesforcomputationofbothofcontactstresses,and of the combined CS-stres
8、ses are worked out. The reported results of the research could be used for extending of the existed standard AGMA 908-B-89 to the area of gear drives comprised of STN-gears, e.g. comprised of gears having teeth number less than Ng= 12. The developed method for the computation is ready to put in prac
9、tice. Copyright 2006 American Gear Manufacturers Association 500 Montgomery Street, Suite 350 Alexandria, Virginia, 22314 October, 2006 ISBN: 1-55589-893-9 1 The DG/K-method is based on fundamental results obtained in differential geometry of surfaces, and on kinematics of multi- parametric motion o
10、f a rigid body in theE3space. Theinterested readermay wishto gofor detailsto themonograph: Radzevich,S.P., FundamentalsofSurfaceGeneration,Monograph,Kiev,Rastan,2001,592p. CopyofthemonographisavailablefromThe Libraryof Congress. Copyright American Gear Manufacturers Association Provided by IHS under
11、 license with AGMA Licensee=Boeing Co/5910770001 Not for Resale, 07/25/2008 04:28:13 MDTNo reproduction or networking permitted without license from IHS -,-,- 1 On Tooth Failure Analysis in Small- -Teeth- -Number Gearing: An Analytical Approach Dr. Stephen P. Radzevich, Eaton | Automotive, Innovatio
12、n Center Introduction Gears fail by pitting and wear as well as by tooth breakage. Gears having small teeth number are considering in this paper. Often, those involute gears are referredto asSTN- gears, base diameter db.gof which exceeds the gear limit diameter dl.g. When the inequality db.g dl.gobs
13、erves, then not the entire active tooth profile is shaped properly following the involute profile. The AGMA standard 1 encompasses involute gears having the minimal teeth number Ng= 12. It could be supposed that according to 1, the STN- gearsarethosehavingteethnumberNg dfobserves for STN-gears. An e
14、xample of application of small-teeth-number- involute gears (further STN-gears) is depicted in Fig. 1. A gearset ofthe Truetracdifferential (Fig.1) is comprised of two side-gears (having Ng= 15/28 teeth number, normal pressure angle n= 30, and pitch helix angle = 38), which are engaged in mesh with
15、four to six pinions (having Np= 5/7 teeth number) 2, 3. Gears of the automotive differentials are a good example of STN-gears. Because of small teeth number, many features of the STN-gearing observe when operating. Thisre- sults in that conventional approach for computation contactstressesisnotappli
16、cableforcomputationof STN-gearing. This is due to the known approach was developed for gearing with ordinary teeth number. Figure 1. An example of application of helical STN- -gears 2, 3. Copyright American Gear Manufacturers Association Provided by IHS under license with AGMA Licensee=Boeing Co/591
17、0770001 Not for Resale, 07/25/2008 04:28:13 MDTNo reproduction or networking permitted without license from IHS -,-,- 2 Literary Survey Thestressescausedbythepressurebetweenelas- tic bodies are of importance in connection with the designand/orinvestigationofSTN-gears. Hertz4 was the first who develo
18、ped the mathematical theory for the surface stresses and deformations produced by pressure between curved bodies, and the results of his analysis are supported by experi- ment. Formulasbasedonthistheorygivethemaxi- mum compressive stresses, which occur at the center of the tooth surfaces contact ell
19、ipse. Unfor- tunately, they allow computation neither the maxi- mum shear stresses, which occur in the interiors of the compressed teeth, nor the maximum tensile stresses,whichoccurattheboundaryofthecontact area and are normal thereto. Hertz based his work on the assumption that the contact area was
20、 small compared with the radii of curvature of the contacting bodies. Because of the very small area involved in what initially approxi- mates a point or line contact, contact stresses for even light loads are very high; but as the formulas show,stressesdonotincreaseinproportionofload- ing.Furthermo
21、re, because of the facts that the stress is highly localized and triaxial, the actual stress intensity can be very high without producing apparentdamage. Tomakeuseofthe Hertzformu- las for purposes of design or safe-load determina- tion, it is necessary to know the relationship between theoretical s
22、tresses and likelihood of failure, whether from excessive deformation or fracture. Bothsurfaceand subsurfacestresses werestudied byBelayev 5. Timoshenko6 wasamong thefirst who used the Hertzs method for investigation of strength of gear teeth. Tons of research had been carried out in the field since
23、 the first publications on the topic 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, and others. Many efforts have been taken aiming use of FEM (Finite Element Method) for solving the problem of com- putationofcontactstressesingeartooth. However, most of research pertained to computation of just contact stresses
24、in gearing with relatively big num- ber of teeth. No relativemotions (sliding)of thepin- ion and of the gear teeth are put into account. If the motion involved is a true rolling without any slip,thenunderconditionsofslowmotion thestress conditions are comparable with those produced by staticloading.
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