1、92 FTM 5Gears:I The Design of Non-Involute Spur Gears to Improve theIby: Jo_e Hlebanja, University of Ljubljana, SloveniaAmerican Gear Manufacturers AssociationTECHNICAL PAPERMain Advantages of Non-Involute Spur Gears: The Designof Non-Involute Spur Gears to Improve the Condition ofContactJo_e Hieba
2、njaUniversity of Ljubljana, SloveniaThe statementsand opinions containedherein are thoseof theauthorand should notbe construed as an officialaction oropinion of the American Gear Manufacturers Association.ABSTRACT:The main cause for the limitation of gear durability in highly loaded and high speed w
3、orking gears is scuffing. Theprincipal way to avoid scuffing of tooth flanks is an oil-film of sufficient thickness between the mating flanks. In thecalculation rules for the oil-fdm thickness and surface durability, the curvature radius and sliding velocities affectdecisively the forming of the oil
4、-film between the flanks. Both the curvature radius and the sliding velocity depend onthe shape of the tooth flanks. By shaping the line of action properly, better gear flank shapes can be achieved, thusimplying improved durability. In this paper the tooth shapes, generated by a progressive crooked
5、path of contact, will beshown and discussed.Copyright 1992American Gear Manufacturers Association1500 King Slreet, Suite 201Alexandria, Virginia, 22314October, 1992ISBN: 1-55589-585-9MAIN ADVANTAGES OFNON-INVOLUTE SPUR GEARSTHE DESIGN OF NON-INVOLUTE SPUR GEARSTO IMPROVE THE CONDITION OF CONTACTJo_e
6、 Hlebanja, ProfessorUniversity of Ljubljana,Faculty of Mechanical Engineering,Ljubljana, SloveniaINTRODUCTION Centers of curvatures SH t2 =Vrl Vr2 (9)As a criterion to estimate the danger of scuffing we use the Bloks If we take into account the value for cylindrical Hertzian contactformula, which is
7、, if both gears are made of similar material, as of steel flanks with (5)follows (7,9):0,50o(10)k J Vrl - Vr2 then the time of contact duration will be:-C-ft. ( v-_R1 +v_R2) (4)We calculate the coefficient of friction according to DIN 3990 = w)5 pr0e5(8,9): tl, 2 3,02 _ Vrl,2 (11)w R .0.25_ The infl
8、uence of the shape of the path of contact to the contact“(vx“ Predf0“25/ (5) duration will be expressed by:/a 0,1205P_dWe take eq. 5 into eq. 4, and after some rearrangements we get: _btl,2 =Vrl,2 (12)f Ra 1025 1 1 The value 1 belongs to addendum, while 2 belongs to dedendum.0fl = 0,024 w. )_ “_“ 0
9、5Pred The charge of tooth flank will be smaller when the time of contactduration is shorter.v25 (6) ESSENTIAL PROPERTIES OF PATHOF CONTACTThe productAs a rule, to a concavely shaped path of contact belongs a concave1 . v,/_-rl- v4_r_ - convexly shaped tooth flank, which means their better conforma-q
10、bfl = 0 5 v0,25 tion. The reduced radii of curvature for pitch point C have to be thePred (7) same for any kind of path of contact, if the pressure angle c_C independs on the shape of the path of contact. If _fl increases, the this point is the same (4):flash temperature will be greater. Therefore,
11、the danger of seuffmgwill be greater, too. r 1 “r 2Pred C = _ sin_Xc (13)The adaptabilityof tooth flanks willbe betterif the path ofcontact . is more crooked, This is especially important for the beginning of _ i _ /the teeth mesh. In case the path of contact is strongly crooked atthe addendum, then
12、 the oil-film thickness in this part of tooth - / m=_,z.t0 f_/ jmeshing will be greater. “- _: / “DESIGN OF A PROGRESSIVELY CROOKEDPATH OF CONTACTWe wish to obtain a strongly accommodated tooth flank at thebeginning of the mesh, and a standard type of tooth flank in thepitch point. We started by cho
13、osing a standardpressure angle anda short straight part of the path of contact, Fig. 3. Then wecontinued with a short arc with a great radius. Further arcs were Figure 5graduated by smaller and smaller radii. There belong such shapesof gear tooth and rack tooth to this path of contact, asshown in Fi
14、g. - . q- -4. We are going on to manufacture such a gear pair (Fig. 5) and _. i , /_compare it to an involute gear pair, shown in Fig. 6. This two , f ! /Z, /)differenttypesofgears, will be compared according to the criterion , “, /m=61z=9 /_/,_,/treated in the previous chapter. , _= _/-“/“ “ J_“ _
15、,)i_. “_. _ - _ _/_Figure 3 gears according ro Fig 6:z1= z2 = 9;COMPARISON OF TI-IEPARAMETERS m= 6a = 55mmThese parameters will be calculated for the following data: _w = 25n 1 = n2 = 1450 graingears according to Fig 5:The Hertzian stress (eq,1) depends mostly on the reduced radiuszI =z2 = 10; of to
16、othcurvatures.The magnitudeof it will beexpressedby them = 5,5 value_p_a. Ifthevalueof Predisgreater,theHertzianstresswilla = 55ram be smaller. The relation of value of Predbelonging to each path ofCtC= 20 contact is shown in Fig. 7. It is evident that the progressive path ofnI = n2 = 1450 grain con
17、tact demonstrates much more reduced radius of curvature.x“._ /., ,Figure 44Figure 9_s/_Figure 7Fig. 8 shows the distribution of the sum of relative velocities vx. _We observe, especially at the beginning of the tooth mesh, that thevr is very high. The negative specific sliding velocity _gl,2belong-h
18、agto progressive path of contact is at the beginning of the mesh * _especially small (Fig. 9), meanwhile it is always high at involute _ “,_ii:_:_)_0gears.The nature of the path of contact according to the oil-film thickness p_could be expressed by (eq.3) and is, for both cases, shown in Fig1.Incase
19、of the progressivepathof contactcanbe seen,especially Figure 10at the beginning of the mesh, that the value of it is extremely parison to the involute gears. 0_3_6 _ftoM_“_ “ 0-nmff-_/_50rflln-_ (_16_ /I0,78Figure 11Fig. 11shows the distribution of dpfl,(eq. 7). Its value is extremelysmall if the pa
20、th of contact is progressive and very high at involutegears in the beginning of tooth mesh. The distribution of the timeof contact duration is shown in Fig 12. For the involute gears atthe beginning of the mesh we can see that the contact duration onFigure 8 dedendum is very high in relation to that
21、 on the addendum. Thecontact duration on the gears according to progressive path ofcontact is much better distributed to addendum and dedendum.:_ _ _.t/.r_l 5. J.E. Shigley, C.R. Mishke: Handbook of Machine Design, McG-= . raw-Hill Book Company, New York, 19866. D.Dowson, G.R. Higginson: Theorie der
22、 Evolventen Zahnrad-_-_s Maschinenbautecl, nik 20, 1971 Heft 4, 185/190schmierung, PP_ I 7. F.IL Theyse: Die Blitztemperaturhypothese naeh Blok und ihre_1 / “Y.,._/_l tl praktische Anwendung bei Zahnriider. Schmiertechnik 14 (1967)Heft 1, pp 22/788. DIN 3990 Teil 4: Tragf_ihigkeitsberechung von Stim
23、riider, Be-7 reehnung der Fresstragffihigkeit, Normenauschuss, Antriebsteclmik_12 (MAN) in DIN Deutsehes Instimt ftir Normen, 19879. Magg Gear book, Maag gear Company ltd. Zurich, 1990I08ct_8/1_ 10. H. Winter, K. Michaelis and H. F. Collenberg: Investigation on6 thescuffingResistanceofhigh-speedGear
24、s,AGMAFTM8,Tech-nical paperFigure 12 NOMENCLATURE AND SYMBOLSF load, normal to the tooth flank;E module of elasticity;1 length of contact;w load per unit length;CONCLUSION ho oil-fihnthickness;This paper presents some criteria, wkich can be used to estimate Pred reduced radius of curvature;the quali
25、ty of gears in view of conformity of gear teeth at the mesh PE, PH, P0 radius of curvature of tooth flanksand in view of sliding condition. A progressive crooked path of (addendum, dedendum, and rack);contact was presented, and a corresponding gear pair was shown, a pressure exponent of viscosity;Fo
26、r this gear pair charged in certain working conditions, the mesh I0 oil viscosity at condition inof gear teeth and also the sliding condition were calculated and entry point of contact;1compared to the values of similar involute gear pair. It was shown u=_Vrl + vr21 the mean vahe of relative velocit
27、y;that the progressive crooked path of contact gives a mueh better vz = (vrt + va) the sum of relative velocity;mesh and sliding condition of lubricated gears. It can be concludedthat it is possible to design non-involute gears suitable for special Vrl,2 relative velocity of teeth surfacesin contact
28、 point;duty, _t coefficientof frictionincontactpoint;_-= XpcHowever, we cannot claim that non-involute gears have only X thermal conductivity;advantages, some problems are e.g. influence of changes in center P material density of surface;distance, length of contact path. etc. Therefore there exists
29、a need c specific heat;for further investigations of such newly designed non-involute a C pressure angle in pitch point;gears, bH a halfHertziancontactwidth;Ra surface roughness;REFERENCES tl, 2 time of contact duration;aph oil-film thickness factor;1. d. Hlebanja: Influence of the path of contact s
30、hape on sliding apfl flash temperature factor;conditions between Tooth flanks. Proceedings of MPT 91, Nov. apt duration of contact factor;1991, Hiroshima2. J. Hlebanja: Konkav-konvexe Verzahnung-Ermitlung der Zahn-flanken und einige Grenzf_ille. Antriebs-Technik, 16 Jahrg. (1976)Nr.63. A. Sehiebel und W. Lindner: Zahnrdder, Bd/, S. 7, SpringerVerlag, 19544. J. Hlebanja: Die Grenze der Tragffihigkeit der beiderseitigen Kon-vex-Konkaven Verzahnungen, IFTOMM-JUDEKO World Sympo-sium on Gears, Dubrovnik, 19786
