1、92 FTM2Face Gear Drives: Design, Analysis,and Testing for HelicopterTransmission Applicationsby: F. L. Litvin and J.-C. Wang, University of Illinois at ChicagoR. B. Bossler, Jr., Lucas Western, Inc.Y.-J. D. Chen and G. Heath, McDonnell Douglas Helicopter Co.D. C. Lewicki, NASA Lewis Research Centerr
2、L _idIAmerican Gear Manufacturers AssociationTECHNICAL PAPERFace Gear Drives: Design, Analysis, and Testing forHelicopter Transmission ApplicationsF. L. Litvin and J.-C. Wang, University of Illinois at ChicagoR. B. Bossier, Jr., Lucas Western, Inc.Y.-J.D.Chen and G. Heath, McDonnell Douglas Helicopt
3、er Co.D. C. Lewicki, NASA Lewis Research CenterThe_tatementsand opinionscontainedhereinare thoseof theauthor andshouldnotbe construed asan officialaction oropinion of the American Gear Manufacturers Association.ABSTRACT:The use of face-gearsin helicopter transmissions was explored. A light-weight sp
4、lit-torque transmission designutilizing face -gears is described. Face-gear design and geometry were investigated. Topics included tooth generation,limiting inner and outer radii, tooth contact analysis, contact ratio, gear eccentricity, grinding and structural stiffness.Design charts were developed
5、 to determine minimum and maximum face-gear inner and outer radii. An analyticalstudy showed that the face-gear drive is relatively insensitiveto gear misalignment withrespect totransmission errors,but the tooth contact is affected by misalignment. A method of localizing the bearing contact to permi
6、t operation withmisalignment was explored. Two new methodsfor grindingof theface-gear tooth surfaceswere also investigated. Theproper choice of shaft stiffness enabled good load sharing in the split torque transmission design. Face-gearexperimental studies were also conducted. These tests demonstrat
7、ed the feasibility of face-gears in high-speed,high-load applications such as helicopter transmissions.Copyright 1992American Gear Manufacturers Association1500 King Street, Suite 201Alexandria, Virginia, 22314October, 1992ISBN: 1-55589-582-4FACE-GEAR DRIVES: DESIGN, ANALYSIS, AND TESTINGFOR HELICOP
8、TER TRANSMISSION APPLICATIONSF. L. Litvin and J.-C. Wang (University of Illinois at Chicago)R. B. Bossler, Jr. (Lucas Western, Inc.)Y.-J. D. Chen and G. Heath (McDonnell Douglas Helicopter Co.)D. G. Lewicki (NASA Lewis Research Center)Introductionquirement for the spiral bevel pinions (fig. 2). Stat
9、ement (iii)is based on the advantage of involute gearing to have a corn-The Advanced Rotorcraft Transmission (ART) program mon normal for those teeth that are finishing and startingis an Army funded, joint Army / NASA program to develop the meshing. The analysis shows that the face-gear drivesand de
10、monstrate lightweight, quiet, durable drivetrain sys- maintain the conjugate action because the face-gear teeth areterns for next generation rotorcraft 1. One contract team generated as conjugated to the pinion teeth. The amount ofparticipant, McDonnell Douglas Helicopter Co. (MDHC) / misalignment t
11、hat can be tolerated is easily controlled byLucas Western Inc., developed a novel split torque ART con- the manufacturing process. The comparison made was forfiguration using face-gears 2, 3. The geometry and design misalignments greater than spiral bevel gears can tolerate.of face-gears and compute
12、rized simulation of their meshing The majority of the work in this paper has been presentedhave been developed by another member of the team, the in reference 8, with the exception of face-gear grinding in-University of Illinois at Chicago. vestigations. This paper showsthat with proper design face-
13、Manufacturing of face-gears was proposed many years gear drives can find a successful application in high power ap-ago by the Fellows Corporation. Face-gears have had wide- plications. The results of computerized simulation of mesh-spread use in low power applications (fig. 1) but have not ing and b
14、earing contact and experimental test of face-gearhad much development for design and manufacturing prac- drives confirm that such drives can be successfully applied.rices necessary for high power use. The paper covers application of face-gear drives in he-The theory of face-gear drives has not been
15、developed licopter transmission. The advantage of this design is thesufficiently for the needs of the designers and manufacturers, possibility to split the torque between two face-gear drives.Publications in this area in English by E. Buckingham 4, This results in a significant savings in transmissi
16、on weight.D.W. Dudley 5 can be considered only as a brief descrip- The design of face-gear drives, simulation of meshing andtion of face-gear drives. J. Davidov 6, F.L. Litvin and L.J. bearing contact, and grinding of the face-gear tooth surfaces,Liburkin 7 have published the results of their invest
17、igation have been analytically described. Computer programs andof face-gear drives in Russian literature, but these works are design charts have been developed. The torque split hasnot familiar in the western world, been confirmed by finite element structural analysis. Proto-The advantages of face-g
18、ear drives are: (i) reduced sen- type face-gear drives have been successfully tested at NASAsitivity of the bearing contact to gear misalignment, (ii) re- Lewis Research Center.duced level of noise due to the very low level of transmission All types of gears, including face-gears, have niches wheree
19、rrors, (iii) more favorable conditions of transfer of load from their advantages are greater than competing types. Thisone pair of teeth to the next pair of teeth, (iv) accurate axial program is an attempt to explore an application where face-location of the pinion is not required in contrast to suc
20、h re- gears appear to offer an advantage.spllTorqueDesin iThe idea of torque split is illustrated in fig. 2. Fig. 2ashows an alternative version of the torque splitting by twospiral bevel pinions, a and b, designed as one rigid body.Fig. 2b shows the second version of the split of torque whena singl
21、e spur (or helical) pinion is in mesh with two face-gears. The advantage of the face-gear version is that thesame transmitted power results in a reduced load on thebearings in comparison with the spiral bevel version shown (c)in fig. 2a. A second advantage is the pinion is a conventional _:_!“_.spur
22、 (or helical) gear compared to a complex spiral bevel _._;designwithtwopinions. : _ The general configuration of the MDHC/Lucas ART de- _;,_i,*_sign is illustrated conceptuallyin fig. 3. There are two en-gines rated at 2500 HP each which combine to drive therotor shaft with 5000 HP. The transmission
23、 is designed tocarry 3000 HP per side for a one engine inoperative condi- Fig. 1. Examples of the application of face-gear drives.tion. Power flows from the engine through an overrunningpositive-engagement clutch to a spur pinion, which is lightlyrestrained radially. The spur pinion drives a downwar
24、d- (_)facing face-gear and an upward-facing face-gear. The face _J_ Combm,_oa_gear shafts terminate in spur pinions, which drive a large , _ ,/ Ycombining gear. The hub of the combining gear is attached _lvto the sun gear of a high contact ratio planetary gear set _ I /_k_ _ _where the carrier is th
25、e output member and is attached to .-/_f_ “-_the rotor shaft. A small pinion is driven at the aft side of the imain combining gear. This pinion drives another face-gearmounted on the NOTAR TM (notail rotor) driveshaft, which sp,_ s_l g_leads aft directly to a NOTAR TM fan. (b)The concept of torque s
26、plit appears to be a significant de- c_ Co_bi_g _o_velopment wherein an input spur gear pinion drives two face- _ “/ I “_ t Igears arranged to provide an accurate division of power. This _/_ division greatly reduces the size and weight of the corner-turning hardware as well as the size and weight of
27、 the next _reduction stage. The predicted payoffis greatly reduced _ _weight and cost compared to conventional design.The pinion which serves the two face-gears is a conven- F_-_g_tional spur gear with an even number of teeth. If the spur Fig. 2. Different versions of torque split.gear were rigidly
28、located between the two face-gears, precisetorque splitting would be very unlikely. The spur gear has afree-floating mount which allows self-centering between thetwo face-gears. The effect of normal manufacturing inaccu- Rotor_t outputracy on torque split will be compensated by automatic relo- s_ go
29、_cation of the input pinion to its balanced position as long ascompliant support is provided for the front end of the pinionshaft. It will be shown analytically (see next section) that NOTAR“precise torque splitting (with =kl.0%) will take place, o_twtMore importantly, torque splitting between two d
30、rivengears by a free-floating spur-gear pinion has been used formany years in truck transmissions. The first known truckapplication was the experimental Road Ranger transmission Combi_gg_produced by the Fuller Transmission Division of the EatonManufacturing Company in 1961. Truck transmissions us- D
31、rivlngspu_p .ing this principle have been in production since 1963. In _-so_addition to accurate torque splitting, it was found that gear E_w_ ,_p_tnoise was reduced and gear life was increased. Thus the useof a free floating pinion as a torque-splitting device is well Fig. 3. Three-stage split-torq
32、ue single planetarysubstantiated, transmission.The gear chain formed by the input pinion, two face-gears, two spur pinions and the combining gear is a closedloop locked train. Errors of gear tooth orientation may causea nonsatisfactory system backlash or even the imposibilityto assemble the closed l
33、oop train. However, since the face-gears and the combining gear are provided with prime num-ber teeth, indexing by assembly will enable to change thetooth angular orientation inside of the chain and provide thesatisfactory system backlash. This is similiar to the prac-tice of assembly of locked trai
34、ns used in marine drives. Inreality, there is a need in ofie test assembly only. Then, therequired indexing can be accomplished in accordance withthe developed chart.Finite Element Structural Analysis for the SplitTorque Gear Drive Fig. 4. Finite element model of the split-torque drive.The success o
35、f a split-torque gear train design dependson the equal division of the torque to the two output shafts.Conceptually, the floating pinion design makes the system ferent support conditions as shown in Table I. The stiffnessof the pinion shaft a two-force member. The transmitted of the front and rear s
36、upport of the pinion shaft were variedforces on the two diametrically opposite meshing points on to determine their effect on torque split (cases 1 through 4,the pinion have to balance each other to achieve equal torque table I). The contacts between the pinion and the two face-splitting, gears were
37、 modeled using gap elements. The torque split wasThe analytical effort to validate the split torque concept determined using gap element reaction forces as calculatedwas conducted through use of the finite element method. To using finite element analysis. Among the cases studied, theanalyze the defl
38、ection and the percentage of torque splitting, most even torque split was provided in case 9 when the stiff-the elasticity of the gear structure and pinion shaft support hess of the shafts front support was 6 104 lb/in. This ishave to be considered first. The finite element model pro- an order of ma
39、gnitude less than a typical bearing support.rides an accurate approach to include the stiffness and the The use of backlash control to compensate for the differ-deflection of the gear structure. The overall model of the ence in the tangential stiffness between the two output shaftssplit-torque gear
40、train is shown in fig. 4. This model has was investigated. In reality, the exact compliance betweenbeen used to analyze the torque splitting percentage for dif- the teeth of the three gears is not practical. The deviationTable I. Advanced rotorcraft transmission torque splitting percentagesSupport o
41、f Pinion Shaft Gear Meshing Clearance (inch) Split Torque PercentageCase Due to Backlash Adjustment (%)No. front-end Rear-end face-down face-up face-down face-upspringrate springrate gear gear gear gear(lb/in) (lb/in)1 K = 0 K= co 0.0 0.0 51.58 48.42(free float) (restrained)2 K = oo K = co 0.0 0.9 5
42、6.87 43.13(restrained) (restrained)3 K = 6.0.10 s # K = 6.0.10 s # 0.0 0.0 53.11 46.894 K = 6.0 104 K = 6.0 * 10s 0.0 0.0 51.41 48.595 K = 6.0 * 104 K = 6.0 * l0 s 0.0 0.0005 51.55 48.456 K = 6.0 * 104 K = 6.0 * 105 02 0.005 52.86 47.147 K = co K = 6.0 * l0 s 0.0 0.005 81.66 18.348 K = 6.0 * 104 K =
43、 6.0 * l0 s 0.003 0.0 50.54 49.469 K = 6.0 * 104 K = 6.0 * l0 s 0.005 0.0 49.97 50.03_: 6.0 * 105 lb/in is the translational spring rate for typical bearing and housing support in helicoptertransmission.In addition to the analysis of torque splitting, the ac-mi curate rating system for the face-gear
44、 is under development,40: using TCA and finite element method. Conservative approx-120: imation in calculating bending stresses and contact stresses_ has been used in the current design. The calculation showss0- that the strengthof the face-gearsis competitiveto others _ types of gears. Moreover,the
45、 feasibilityin constructinga2 ,0 split torque configuration make the gear train a more corn-=: pactdesignthan the others. Theriskofscoringiseliminatedby localization of bearing contact. The accomplishment of a-2o0 _ 2 3 4 _ 6 7 8 .9 t0 circumstantial rating system will further promote the appli-e. ,
46、t cations of face-gears.Fig. 5. Typical transmission errors for a face-gear mesh.Influence of Gear Eccentricityfrom the common engagement is caused not only by the dif-ferent stiffness of the two paths but also by the indexing The influence of gear eccentricity is important for de-problem associated
47、 with the closed-loop gear train design, termination of conditions of the split of torque when oneAdditional analyses have been performed to incorporate the pinion is in mesh with two face-gears, and the pinion andinitial clearance on any one side of the pinion to simulate the gears have eccentricit
48、y. Due to transmission errors theunequal backlash conditions. This was done by setting an driven face-gears will perform rotation with slightly differentinitial clearance in the appropriate gap element. The influ- angular velocities, and this means that the torque split willence of unequal backlash
49、on load sharing in the split-torque be accompanied with deflections of tooth surfaces.drive system is also given in Table I. The effect of clearance The function of transmission errors is defined as,on torque split was small but should be considered whenN1flne-tuning a design for optimal load sharing. The analysis A_ = 2 - _(1 - ) (l)results are the baseline for using backlash control in assem-bling an equal torque-splitting drive in practice, where N1 and N2 are the number of teeth of the pinion andA structural dynamic analysis was carried
