1、93FTM7New Developments in Design,Manufacturing and Applicationsof Cylkro-(Face) Gearsby: Guus Basstein and Anne SijtstraCrown Gears b.v., The NetherlandsAmerican Gear Manufacturers AssociationTECHNICAL PAPERNew developments in Design, Manufacturing andApplications of Cylkro-(Face) GearsGuus Basstein
2、 and Anne SijtstraCrown Gear b.v., The NetherlandsThestatements andopinions containedherein arethose of theauthor and should notbe construed asan officialaction oropinion of the American Gear ManufacturersAssociation.ABSTRACT:The geometry of both Cylkro-gear and pinion are calculatedand optimized co
3、ncerningcontact ratio, linesof action andcontact. By means of F.E.M. analysisand use of aload distributionprogram, the DIN 3990 (ISO/DIS6336) calculationmethods for bending strength and pitting resistance were adapted to include Cylkro-gear calculations. The methoddeveloped is tested on a back test
4、bench.Copyright 1993American Gear Manufacturers Association1500 King Street, Suite 201Alexandria, Vkgiuia, 22314October, 1993ISBN: 1-55589-619-7NEW DEVELOPMENTS IN DESIGN,MANUFACTURING AND APPLICATIONSOF CYLKRO-(FACE) GEARSGuus Basstein, Manager R _ _ direction of the tooth flank/_ilTrrlrfliliiiliil
5、liiiiliiiliiiliiililillllllTlJ._ _ Influence f the psitin relative t the suD-illllllllllllllllllllllllllllllllljiiiii _llII_ portinq faceP_-“_.ii.LtlJ.LLL!_JJ.Lt.lXl_-“- _ “_ E E Aos _TIV_ PITCH D_A_ION MINOS CACCUrATED _O_OOT _ _- _f _II.LI.IIUJ-ILIJ.IIIJ-UJ._UJJJJJJJJ_UJ.LL_ _,.I,o, _ /Fig. 34 : P
6、resentation of the cumulative pitchdeviationsThe inspection reports correspond well with theevaluation of the quality of parallel gears.However the tolerances for bevel gears according Fig. 37: The effect of vertical and horizontaldeviations in normal direction of the toothto DIN 3965 are larger tha
7、n those for parallelgears of the same quality class. Therefor a flank.parallel gear which satisfies quality class N A deviation of the position relative to the sup-according to DIN 3962, can be compared with a porting face (the face distance Afd) arises fromCylkro-gear which has quality class N-I (D
8、IN a position of the cutting tool which is not in3965). accordance with the nominal value. The measuringmachine establishes a deviation Afd in the vet-Besides giving a mark to the gear, it is possible tical direction of every point of the networkto “translate“ the deviations of the inspection Figure
9、 37. The theoretical component normal toreport into corrections of the setting of the the surface of the left and right tooth flanksgear cutting machine. To this end the influences can be calculated with:of the deviations of the machine-setting on the Aft4 = Afdxsin(_z)-sin(_) 19inspection charts ar
10、e analyzed.Influence of the deviation of the shaft anqle4.5.3. Manufacturinq deviations and their effectson the inspection charts, d_ L8Zi- Afd _ Asa dmzi _ /l di2 4 saFig. 38 : Effect of a deviation of the shaftangle.A deviation of the shaft angle Asa arises whenthe angular path of the cutting tool
11、 does notFig. 35: Deviations in the distance to the sup- coincide with the nominal shaft angle. It can beporting face (Afd), in the shaft angle (Asa), in regarded as a variable distance to the supportingthe offset (Aos) face over the facewidth Figure 38. The theoret-ical component (equal for left an
12、d right flanks)The effect of the deviations in the distance normal to the tooth flank can be calculated with:relative to the supporting face (Afd), the shaft Af_a -tan(Asa)x (4 - d_) xsin(_z) 20angle (Asa) and the position relative to the axis 2(offset Aos) Figure 35 have been determinedFigure 36.i0
13、Influence of offset of the teeth The inverse-symmetrical deviation has to be com-pensated by a _os (offset) setting and the sym-metrical deviation by Afd (face distance) and Asa_/ (shaft angle) settings. After correcting, a theo-retical residual-deviation e will remain becauseof the geometry of the
14、hob, the elasticity of thegear cutting machine and mounting of the gear:eI = (s_ - Afrd,1 - Af_,_) + (ki - Afo,.1) 23O With the aid of a numerical optimization the_ values of Afd, _sa and Aos are calculated in suchj a way that the sum of the squares of the resldu-al-deviation is minimum:_e_(Afd, Asa
15、,Aos)Z=minlmal 24It is possible to use the calculated machinecorrections and the residual-deviations to evalu-ate the quality of a Cylkro-gear according toquality classes which have to be standardized forface gears.5. USE OF CYLKRO-GEARTRANSMISSIONSFig. 39: Effect of a deviation in the offsetOffset
16、of the teeth arises when the cutting tool 5.1. Introductionfollows a path which does not cross the axis ofthe Cylkro-gear at the nominal value. Figure 39 Cylkro-gear transmissions can be used where an-shows that this deviation is inverse-symmetric, gular transmissions are needed. Two fields of useTh
17、e theoretical component normal to the tooth can be defined, i.e. substitution of bevel gearsflank Figure 37 can be calculated with: and new use. Substitution is only of interest_ when not only the gears, but the complete struc-Afos=Aosx(l- )xcos(_2) 21 ture of the transmission can be optimized. The-
18、_ latter is possible on account of the characteris-Influence of runout of the Cylkro-qear tics of Cylkro-transmissions, i.e. axial freedomof the pinion and lack of axial forces on thepinion, permitting cheaper bearings and housingand easier mounting. The market for new use ofCylkro-transmissions is
19、much larger on account ofthe unique properties, which allow in many casescheaper solutions. Some examples of new uses aredemonstrated with the following representations.5.2. Multi Power Take-Off (MPTO)For that purpose different systems are known.Cylkro-gears offer a simple solution because thepinion
20、 has axial freedom; only one Cylkro-gearhas to be adjusted. This property allows morethan one pinion to engage with one Cylkro-gear ortwo Cylkro-gears to engage with one pinion.The most recent use is a split torque design ofthe helicopter drive of Lucas-Western Inc 5,8.Figure 41. In this design two
21、pinions are eachcoupled directly to two turbines. Each pinionFig. 40: Influence of run-out of the Cylkro-gear drives two face gears which in turn drive a plan-In a position in which the runout of the gear is etary gear. This drive is possible due to themaximum Figure 40, the effect is observed as an
22、 axial freedom of the pinion and advantageous inoffset position of the cutting tool. Rotated comparison with a design with bevel gears. Thethrough an angle of 90, the tooth space is on- claimed advantages of this drive are:center, but will be measured at a different ra- 40% reduction of weight;dius
23、compared with the radius calculated with the 10 dB reduction of work-points.Incorrectly, this can be translated into a devia-tion of the shaft angle or position relative tothe supporting face.It is therefore advisable to calculate correctedmachine settings from the mean values of measure-ments of se
24、veral teeth, evenly distributed aroundthe circumference of the Cylkro-gear.4.5.4. The “translation“ of the inspection reportinto corrections of the machine-settinq:First of all the measured deviations have to besplit into a symmetrical and an inverse-sym-metrical part, according to:r_+/_ i = Cross s
25、ection i Fig. 41: Helicopter split torque designs_= 2 ri = Deviation right flank;r_ll i = Deviation left flank;k_= 2 s = Symmetrical deviation;22 ki = Inverse symmetrical deviation11Mother use is the ship propulsion system with 5.3. Shaft anqles _ 90 Contra Rotating Propellers (C_). Figures 42 and43
26、 show two designs which, by using _ikro-trans- Every drive with a shaft angle between 0 and_ssions, are capable to drive two propellers in ii0 can be achieved with Cylkro-transmissions.opposite directions and, if desired, with two The solution with Cylkro-gears is especiallydifferent speeds, suited
27、to shaft angles between i0 and 20 .example of a propeller drive with a Cylkro-rsonuehtransmission can be used in mixer drives.iFig. 42: Contra Rotating Propellers_ Fig“ 45: Prpeller _i_ with shaft angle 20The above mentioned examples are meant to showvarious solutions with Cylkro-transmissions.6._fe
28、_nces1 Y.-J.D. Chen; Kine_tic stu_ of the face_ gear; Meas, Arizona, February 15, 1990;_ _ Prepared for the AS_ 1990 design automationconference, Paper No. 90-DAC-95.2 D. Overdijk; De driedimensionale constructievan Reuleaux, een wiskundige methodetoegepast op de kroonwieloverbrenging;Ein_oven, 1988
29、; Doctors Thesis.3 Deutsches Institut fur No_ung e.v.; DIN3990, Tragf_higkeitsberechnung vonStirnr_dern.Fig. 43: Contra Rotat_g Propellers 4 International organization for standar-dization; ISO/DIS 6336; Calculation of loadFibre 44 shows a shaft with two pinions, each capacity of spur and helical ge
30、ars.driving a Cylkro-gear. 5 F.L. Litvin, Y. Zhang, J.-C Wang, R.B.Bossler Jr., Y.-J.D. Chen; Design andgeometry of face-gear drives; Transactionsof the AS_, Vol. 114, December 1992, p.642-647.6 E.W. Miller; Hobbing by a toroidal hob; USAPatent 2,304,586; Dec. 8, 1942;_ _ _, 7 The art of generating
31、with a reciprocatingI tool - The Fellows Gear Shaper Company,U.S.A. 1945_ _ 8 F.L. Litvin, J.-C Wang, R.B. Bossier Jr.,I I Y.-J.D. Chen, G. Heath, D.G. Lewicki, Face-gear drives: desi_, analysis and testingfor helicopter trans_ssion applications;AGMA-paper 92FTM2 1992.Fig. 44: Shaft with two pinions12
