1、96FTM6 I - The F-22AMAD Gear Drive - Optimization of Resonance Characteristics by Detuning, it does not require an evahmiion of mdividual natural frequencies and their associated mode shapes to determine if they are likely to be excited by applicable gear forcing functions to cause damage. As an fks
2、t attempt, we therefore decided to apply this Frequency Shatmg technique to ail AMAD gears. However it soon became apparent that it was not avalid option for all gears of the F-22 AMAD due to wide speed range and existence of multipleiesovertheentirerangeasweU.asjust below and just above the operati
3、ug speed range. The number of natural fiequencieS were so many for some gears that it wouid have been hpossiile to shift aIl of themoutoftheoperaImgrangewithoutvioiating weight hits. We also found some gears withjust 2 or 3 fquemkwithinthe entirerange. Howevethey were placed athe upper and lower end
4、 of the wide operating band where an attempt to shift frequency at lower end caused frequencies from above the upper end to creep weninside the speed range and viceversa Additionaliy, physical- placedbyotherAMAD oomponents made it impossiile to make minor geometric modifbions for demiug natural freq
5、uencies judged to be damagkg. A systematic anayticd approach was therefredevehped and applied to each AMAD gear to achieve an optimum lightweight gear design free of damagingresponseswithinthe 0perain.g speed range. Our overd analysis and evaluation involved several intexreiated and at times iterati
6、ve steps as foIlows: STD-AGMA SbFTflb-ENGL L77b Ob87575 OOOi887 LTT D 1) Develop an FEM (finite element model) of the gear under consideration, perform free-free modal anaiysis and identify natural frequencies that are candidates for potential resonances through the use of Campbell (1) Diagram withi
7、n the operating speed range of the gear. If no such frequencies exist, the gear is acceptable from view pomt of resonance characteristics. 2) If natural frequencies for potential resonances are identified within the operating range from step 1 above, evaluate mode shapes to separate them m thee cate
8、gories: A. Insimiificant modes such as shaft bending, shaft torsion and coqlex modes unlikely to be excited by gear contact forces. B. Complex modes and wupled modes ( such as rim out of plane bendmg coupled with secondary diametral response ) which may or may not be signicant for known gear forcing
9、 functions. C. Simple modes which are clearly gear teeth sensitive (e.g., 20 or 3D radial rim modes m toothed region, etc.) 3) No action is required on gears m category A since they involve insignificant modes or the modes unlikely to be excited by gear forcing functiom. 4) conduct forced response a
10、nalyses (2) on the gem in category 2B to determine if any of he identifed modes cause damaging resonances with the speed range of interest andlor large unacceptable displacement responses which are likely to be significant enough to warrant either damping or detunmg. 5) For gears m category 2C and f
11、or those found unsatisfactory by the forced response analysis m category 4, dehe geometry changes to shift resonant frequencies out of the speed range and conrm (by fdresponseifnecessary) thatthere areno damaging resonances in the operating range. 6) Dene dampmg ring weights and locations, to damp o
12、ut damaging resonant responses, for gears in category 5 which could not pass the resonance acceptability critaia by pracicai changes to gear blank geometry. ANALYICAL MODELS AND METHODS A full 360 degree NASW finite element model 0 was developed for each gear Usmg 8 noded solid (CHEXA) and a few 6 n
13、oded wedge (m transition regions) elements. A 2D CATIA geometry of the gear was imported into PATRAN preprocessor for building the model Each FEM mcluded gear rim, web and the integrai shaft. in earlier models, gear teeth were simulated by a solid ring from gear root to pitch diameter based on our p
14、ast experience (mostly with Helicopter main power gears, Reference 3) that this idealizaton of gear teeth was adequate for the purposes of gear resonance analysis. Subsequent analytical and experimental comparison of natural frequencies with other applications mvohring light weight gears (especially
15、 those with smaller rim to tooth height ratio) however, mdicated that .this idealization could over predict naturai hquencies by as much 20% or more. All AMAD gear modeis were therefore revised to include a detailed hite element representaion of gear teeth. The element mesh size was generally dictat
16、ed by complexity of gear geometry, number of teeth and the importance of tooth mesh fkquency m the gear resonance analysis rather thaninumber of modes require and the operaag speed range. A fke-ftee modal analysis was performed for each gear (as a fist step of the overall analytical approach) Usmg s
17、oMon procedure 103 of NAS“. The Lanczos frequency exraclion with genemked dynamic reduction was used for the modal analysis. Ail frequencies m O to 20000 Hz range were extracted to covez PTO speed range up to 15% above the maximum speed. Mode shapes were plotted by importing NASTRAN soMon data mto P
18、ATRAN. A modal analysis with Phed boundary conditions at bearings was also perfomed for those gears which required a forced response analysis evaluation. A forced response analysis was therefme perfomed (using 5% of aitical dampmg) to quantitativeiy assess whether these modes would cause damaging re
19、sonances due to gear tooth excitation. A ford response analysis was perfonned for all gears mvolving modes which couid not be classified as hsignicant based on inspection of mode shapes alone. The forced response analysis was perfonned by simultaneously applying radial and tangential forces at the g
20、ear tooth contact. The rigid body responses were removed from the analysis by specis.mgresaints at the bearings and constraining one of the two bearings m UX (axiai) and RX (rotation about x-axis) degree of fieedom. A modal analysis with these boundary condition inned) was also perfomed to aid m mte
21、qmehg forced response results. APPLICATION The anaiyticai approach developed for the AMAD gears is jllustrakd tbrough application to Generator, Idler 4 t- 5% I Figure 20 - Campbell Diagram for Idler 4, Original Configuration gum 21 - Campbell Diagram for Idler 5, Original Configuration The CampbeU d
22、iagram for Idler 4 identitied three potential resonant frequencies m the lower operating speed range and several in the upper operating speed range. A review of the mode shapes reveaied that four modes m the upper speed range involve a simple m- plane 2D response at 6308,6387,7216 and 7285 Hz. Figur
23、e 22 depicts a typicai mode shape at one of these frequencies (7285 Hz) which shows a clear m-phe second diametral (2D) response of both Idler 4 gear rim as well as the mtegrai shaft. ese highly gear teeth sensitive modes can be excite by spur gear tooth loading and a forced response analysis will s
24、how a Since these modes occur wen with the operating speed range of Idler 4, a geomegic modification was necessary to shift these modes out of the operahg range. signjf.caatresponseamplincationatthesefrequencies. I Figure 22 - Idler 4/5 Original Configuration, 2D Mode at 7285 Hz -8- STD-AGMA SbFTMb-
25、ENGL L99b A fmal geometric configuration (Figure 23) was developed for the cluster gear after several iterations to drive the damaging gear rim and shaft 2D m-plane modes out of the range of interest. Figure 23 Idler 415 Final, Detuned Configuration An isometric view showing a 36 degree segment of t
26、he fuil model is presented m Figure 24. The Campbell diagrams for this revised gear (Rev 2) Idler 4 and 5 based on a they do not invoive gear teeth response and both are above the maximum operating speed. Idler 5 is therefore free of any damaging resonances within its operating speed range. I Raw LE
27、Mr Figure 25 - Campbell Diagram For Idler 4, Final Detuned Configuration 59211 SB+ WB 5sz42Dry)rpR -1 SR Figure 26 Campbell Diagram For Idler 5, Final Detuned Configuration -9- STD.AGMA SbFTMb-ENGL L99b b87575 0001i894 33T in contrast, Idler 4 (Figure 25) shows a number of frequencies, some of them
28、closely spaced, within the operating speed range. However, a careful review of mode shapes indicated thai most of them were imlikely to be problematic based on the modal response they exhiiite. eumbreiamodes at 1631,7386, and 9115 Hz mostly mvohre web bending in the axial direction and cannot be exc
29、ited by the radial and tangential gear tooth loads. A typicalurnbrella mode is shown m Figure 27. Figure 27 - Idler 4/5 Final Detwned Configuration, Umbrella Mode at 1,631 Hz The 2D modes at the bearings at 7479 Hz (Fgure 28) and the shaft rocking mode at 1481 Hz (Figure 29) are of no concern becaus
30、e of the restraining effect of the bearings and the absence of imbalanced forces to excite the rocking mode. Figure 28 - Idler 4/5 Final Detuned Configuration, 20 Mode At Bearing Journal The shaft bending mode at 5928 Hz is tmwreEy to be excited at the lower harmonics and die torsional mode at 4487
31、Hz is meffde m the absence of torsional constraint Furthermore, we do not beiieve that the mixed modes at 8246 and 8247 Hz, which show a complex 3D coupled response (see Figure 30 for a typical mixed mode), can be excited by the copianar combmation of tangential and radial gear tooth forces. igure 2
32、9 - Idler 4/5 Final Detuned Congurson, Shaft Rocking Mode At 1,481 Hz Figure 30 - Idler 4/5 Final Detuned Configuration, Complex, Mixed Mode At 8,246 Hz The remahhg modes at 1618, 4038, and bending modes with coupled secondary rim diametral responses; Fm 31 exhiits a typical out-of-plane bendiug res
33、ponse shown by these modes. While these modes aredikeiy to resuit m signifcant ampijcation of deimenal gear teeth response, we could not conchidewithdiythatthey areofno consequence withou further evaluation. A forced response analysis wasthereforepefinmed (using 5% of critical damping) to q- iy asse
34、ss whetha these modes wouid cause damghg resonances due to gear tooth exciktior Theforcedresponsewasperformedbysmiultaneously applying radiai and tangential forces at a gear tooth contact. The rigid body responses were removed from the analysis by specifyiug restrants at the bearings and 7482n484nm
35、HZ pred0-e gw rim -10- STD-AGHA SbFTMb-ENGL 1SSb H Ob7575 0004875 27b W constraining one of the two bearings m UX (axiai) and RX (rotation about x-axis) degree of freedom. A modal analysis with these boundary condition was also pexformed to aid m mterpreting forced response results. Figure 31 - Idle
36、r 4/5 Final Detuned Configuration, Out of Plane Bending Mode At 4,038 Hz The computed forced response for Idler 4 at gear tooth contact (most critical area) is shown in Figure 32 and the Campbell diagram based on modal analysis with Tinned boundary conditions (same as those m the forced response) is
37、 presented in Figure 33. Note that here are no radial or tangential direction resonances due to the 1618,4038, and 7482/7484/7518 Hz coupled modes substmtbhg thab they are not signincant modes. The radiai and tangentiai responses exceeding the corresponding static load response are shown by crosshat
38、ched (I/ = radial the other mode at 4862 Hz is similar. These modes fully mvohie gear teethandmustbetoavoidanyproblemwhenthe gear is operated at these speeds. The rst choice was, of course, to detunefhe gear by geometric modifications to drive &ese modes out of the operatmg speed range. This was acc
39、omplished, as the Campbell diagram for the odined geometry, Figures 36 shows. BallnGur *.-a igure 34 - RiH PTO Campbell Diagram, Original Configuration Notice ?hat both gear teeh semitive 2D modes have been driven out above the 115% maximum speed. Howevery due to spline and decouphg mechanism passin
40、g through the bore of this geary this modincation was impractiCa. Adding mated to the ontside diameter wouid have required significant chauges to the AMAD gear box besides being mecient and much heavier. Because detmiing is not practical, and m view of potentialy damaging naine of the two modes, it
41、was mxmyto add damping rings totbis gear asmdid in step 6 of the analytical approach discussed previous. Figme 37 shows the modincaions required to add damping rings to this gear. The total additional weights (ring phis mrbenal to form the ring grooves) reqnired to damp this gear is about 0.33 Ib. i
42、gure 35 - PTO Gear Onginal Configuration, 2D Mode At 4,637 Hz, Fully Tooth Involved gum 36 - RRI PTO Campbell Diagram, Proposed Detuned Configuration REFINED FEM MODELS The baseiine fmite model of the FUH PTO was later refned to replace simplifd gear tooth representaim with a much more accurate fini
43、te element mesh to bpmve auaiyticaiiy prediced frequencies. The rened model also preaiCtea 2D and 3D modes m the operating speed range asideiitified unCarnpbeU iagramm Figure -12- STD-ALMA SbFTMb-ENGL L77b 38. The 2D and 3D modes at 4343 and 10796 Hz are shown m Figures 39 and 40. A comparison of th
44、e Campbell diagrams based on frequencies predicted by the original and the refined models show between 3 to 7% difference in fiequencies, as seen fiom Figures 34 and 37. The differences between the baseline and refined model predictions for other gears, in which the gear rim was supported by a thin
45、web, were found to be as high as 20% indicating that the simplified gear tooth simulalion for light weight gears may lead to significant maccuracies m computed frequencies. Figure 37 - WH PTO Gear, Final Configuration (Shaded Area Shows Material Added To Accommodate Addition Of Damping Rings) igure
46、38 - RRI PTO Gear Campbell Diagram, Improved Model Wdh Material Added For Damping Rings These are very significant diferences since resonant responses tend to be very narrow. A small error m preicting the fkquency at which a particular mode WilI occur can, therefore, result m operation on the resona
47、nce with perhaps undesirable results. b87575 0004897 O49 For this reason, it is important to carefully model ail of the gear teeth and other small geometric details of any gear when evaluating its resonance behavior. This is particularly true for mali gears. In generai, wherever the size of the teet
48、h is significant m terms of the overail size of the part, very detailed models are required. Where the size (or mass) of the teeth is relatively insignificant m comparison to the rest of the part a coarser model may be acceptable. The best guide, however7 is to create a fully detaed model, mcluding
49、all gear teeth, m all cases. Practical consideraiions of model size and solution time may limit this methodology for very large gears. in such cases, it would be best to model the teeth more coarsely rather than to ignore them altogether. The determination of a suitable model configuration is a matter of experience but the range can be explored by domg simple sensitivity studies of a particular model. ANALYTICAL FREQUENCY VERIFICATION To verify analytically predicted fiequencies and mode shapes, we performed laborat
