1、07FTM02Study of the Correlation Between Theoretical andActual Gear Fatigue Test Data on a Polyamideby: S. Wasson, DSM Engineering PlasticsTECHNICAL PAPERAmerican Gear Manufacturers AssociationStudy of the Correlation Between Theoretical andActual Gear Fatigue Test Data on a PolyamideSteve Wasson, DS
2、M Engineering PlasticsThe statements and opinions contained herein are those of the author and should not be construed as anofficial action or opinion of the American Gear Manufacturers Association.AbstractDSMEngineeringPlasticsisaproducerofnylonplasticmaterialsusedforgears. Inthepasttwoyears,theyha
3、vebeenrunningfatiguetestsonactualmoldedgearsinordertoprovidedesigndata.Thisexperimentusedspur gears that are fully lubricated and temperature controlled. Testing for the materials has been done atDSMResearch,whilethegeartestsarebeingconductedattheUniversityofBerlin. Thepurposeofthetestingis to see i
4、fthere is a good correlation between fatigue data,generated on testbars,versusthe actualfatigueperformance in a gear.In order to do this, the theories of gear calculations to get root stresses also had to be examined. AdvancedFEA showed that there are corrections needed to account for high loading o
5、r high temperatures in plasticgears. This corroborates other work within the industry.With proper corrections to get accurate root stresses, there can be shown good correlation between tensilebar fatigue and actual spur gear fatigue.Thechemistryofvariousnylonsusedingearsisexplained. Ahighcrystalline
6、nylonhasbeenfoundwhichisan excellent material for gears in demanding applications and can withstand high torques and operatingtemperatures. The material has a crystallinity of 70%, which results in very good wear properties andexcellent retention of mechanical properties (strength, stiffness, and fa
7、tigue) especially at elevatedtemperatures.Several commercial gear applications are currently utilizing these properties. These will be shown todemonstrate the benefits and manufacturability of this material.Copyright 2007American Gear Manufacturers Association500 Montgomery Street, Suite 350Alexandr
8、ia, Virginia, 22314October, 2007ISBN: 978-1-55589-906-61Study of the Correlation Between Theoretical and Actual Gear Fatigue Test Dataon a PolyamideSteve Wasson, DSM Engineering PlasticsIntroductionPlastic gears have gained in their use and are nowseen in the home, office, and automobile. Theyhave g
9、ained acceptance due to manufacturingmethods such as injection molding which produceseconomical yet very reproducible gears. Noise re-duction and corrosion resistance are also reasonswhy plastic gears are used. Plastic gears are nownot only used for light loaded applications such asprinters and toys
10、, but for highly loaded or elevatedtemperature environments, such as automotivestarter gears, turbo actuators, electronic throttlecontrol, etc.With the higher demands it would be desirable tohave increased predictive ability especially with re-gards to long term endurance capability. To thisend, a s
11、tudy was done to look at fatigue on actualplastic gears and relate that to tensile bar fatigue.Tensile fatigue is quicker and easier to generate.The materials suppliers usually have this data al-ready available. It is also independent of geometryasthestressontensilespecimensissimplytheloaddivided by
12、 the cross sectional area. The goal is tohave a method where root stresses could be calcu-lated and compared to the more readily availabletensile fatigue for prediction of gear life.Critical to this predictive capability then is the meth-odsforcalculationofgeartoothrootbendingstress.Finite Element A
13、nalysis (FEA) and semi-analytic(e.g. ISO standards, KISSsoft) must be comparedand validated for use in heavily loaded or high tem-perature plastic gears.MethodsThe portion of the fatigue study that is on the actualplastic gears was conducted at the University ofBerlin in Germany, while the tensile b
14、ar fatigue wasperformed at DSM Engineering Plastics in Geleen,the Netherlands. The gear test parameters wereselected to minimize wear and thus isolate the fail-uremodeinthegeartotruefatigue. The testrig isa2closed-loop(4-square)testerwithdiplubrication.The oil lubrication is maintained at 140 C. Thi
15、s istypical automotive under hood temperatures andmotoroilwasutilizedasthelubricant. Thegearsarespur with the driver being steel and the driven plas-tic. Theyarebothmoduleof2,facewidthof12mm,witha 20degree pressureangle. A standardprofileaccording to DIN 867 was used.The FEA was conducted on the sam
16、e gear pair us-ing a commercially available software package,MSC.MARC. The gears were modeled as 2 discswith 4 teeth each, under plain strain conditions.80,000 first order quads were used, with mesh re-finementsinthetoothandatthesurfacesinordertoalso capture contact stresses, see figures 1, 2 and3.
17、Linear elastic modeling was used for the initialruns.Figure 1. Finite element mesh2Figure 2. Mesh refinementFigure 3. Mesh refinement for contactstressesResultsCalculationsIngeneralcontactratiosoftwospurgearsare intherangeof1to2. Thismeansthatinpartof themesh-ing cycle, 1 tooth will carry the entire
18、 transmittedtorque load. The classic theory shows this as1/3-2/3-3/3 rule. That is, at first contact, the toothcarries 1/3 of the load and increases its sharesteadily to 2/3 until the preceding tooth leaves themesh and then it carries the entire load for a shortperiod and then symmetrically reverses
19、 this loadcycle. Our FEA shows this to be more like2/5-3/5-5/5 for a steel gear pair, with a modulus of206 GPa. This is reinforced in other literature also.Whenweintroduceaplasticdrivengearwithasteeldriver gear, the load sharing is quite different thanthe theory. The curve skews to later in the rota
20、tion.Thesharefollows1/3inthefirstpartofrotation,and2/3 in the second part of rotation through the meshcycle. However, thesymmetry is lostandtheshareof the load never reaches 1 as the modulus (at140C) falls below 10GPa, figure 4.Figure 4. Load share vs. roll angleThedeflectionoftheloadedtoothonthepla
21、sticdriv-en gear is the cause of this skewed load sharecurve. Astheloadedtoothisdeflected,therotation-al angle of meshing is moved out of phase, thiscauses both preliminary contact by the next toothentering mesh and prolonged contact at the end ofmesh by the preceding tooth. That preceding toothisbe
22、ingunloadedandisstraighteningbacktoitsun-deflected form, see figure 5.Figure 5. Deformed mesh3This increased contact, both entering and leavingmesh, will increase load sharing and thus lower theroot stresses. Table 1, shows the results given bythe FEA and the semi-analytic methods. You cansee the ef
23、fect, as the modulus decreases the FEAshows the actual stress decrease. The differencebetween the theoretical and actual (FEA) also be-comes more significant. While most semi-analyticapproaches allow no dependency for root bendingstresses on modulus, the FEA shows there is in-deed an effect of tooth
24、 deflection which is indirectlydependent on modulus.Fatigue tests correlationLoads were selected by using FEA to get a reason-able number of cycles. Thetorques of4, 5,6, 8Nmwere run in the Berlin test rig. The gears were runconstantly at 3000 rpm and 140C. Two materialswere molded and tested; an unf
25、illed PA46 andPEEK. Based on the torque levels, the rootstresses were calculated using the FEA and ISO6336. They are then being compared to tensile barfatigue data. As you can see in figure 6, the rootstresses generated with FEA (labeled corrected)correlate well with the tensile specimens while theI
26、SO6336calculationsexhibitmuchlessofacorrela-tion. Since the uncorrected or ISO6336 equationsyield apparently higher allowable stress values,caution in utilizing previously generated gear datamustbeused,asitmayportrayafalsesafetyfactor.This will depend on the loads, modulus based ontemperature, and r
27、esulting tooth deflection.Table 1. FEA and semi-analytic method resultsStress Modulus ISO 6336 VDI 2545 KISSsoft FEARoot 206 GPa 74.8 42 77.4 73.410 74.8 42 77.4 70.73 74.8 42 77.4 65.10.7 74.8 42 77.4 51.7Contact 206 609 609 609 80010 193 193 193 2303 107 107 107 1200.7 54 54 54 50Figure 6. Fatigue
28、 results4Tooth deflection vs. load and modulusThe effect of a lower material modulus has beenshown to be that the tooth deflects under load. Themodulusmaybelowerasamatterofmaterialselec-tion, for example an elastomer versus a thermo-plastic. However the modulus of thermoplastics istemperature depend
29、ent and therefore may also belower due to exposure to higher operating environ-ment temperatures or increased frictionally gener-atedtemperatures. Forexample3GPaisthemodu-lusofanunfilledPA46at23C,whereat140Cithasamodulus of .7GPa. Modulus and load are recipro-cally linked in this tooth deflection be
30、havior. Stiffermaterials will exhibit the same behavior as lowermodulus materials when the corresponding load isincreased. Figure 7 shows two identical resultsdemonstrated with two different loads and modulii.Figure 7. Load share vs. modulus and loadAdditional workUp to thispoint, workhas beendone o
31、na steeldriv-erand plasticdriven gearpair. Employing thenoiseand economical advantages of plastic gears ofteninvolvesaplasticonplasticgearpair. Theeffectsoftooth deflection is now able to be exhibited in bothgears, the driver and the driven. If we look at ourload share curve again, in Figure 8, we s
32、ee that thecurve now retains its symmetry. Also the 1/3-2/3portion of the curve now falls back on the “theoreti-cal” values. The prolonged tooth contact, early andlateintherollangle,resultin theload sharepeakingat 2/3 and not 1.Figure 9 shows the increased contact ratio and thedeviated contact path
33、that results first from oneplastic gear, and increases as two plastic gears areused.Figure 8. Load share plastic on steel vs. allplasticFigure 9. Contact pathAs previously pointed out, two unfilled materialswere fatigue tested in injection molded gears at theUniversity of Berlin on the test rig. The
34、 two unfilledmaterials,aPA46andPEEK,wereselectedfortheirknownapplicabilityand usein theengine andunderthe hood in automotive. Exposure to the oil lubrica-tion and 140 C should not be a concern for eithermaterial. Shown below are the fatigue results fromthese tests.PA46showsimpressiveresultsongeartes
35、ts. PA46is a highly crystalline polyamide in the same familywith PA66 (nylon). It gains crystallinity of 70% vs.the 50% of PA66 or PA6 due to symmetrically re-5peating CH4. This allows more rapid and frequentcoupling of the amide groups (CONH). See Figure11. The speed of this crystallization allows
36、this tohappen regardless of injection molding toolingtemperatures.This high crystalline nylon then sees an increase innearly allproperties importantfor gears.Wear isre-duced while temperature capability is increased.Fatigue, especially in elevated temperatureenvironments, is also dramatically improv
37、ed.Figure 10. Fatigue of PA46 vs. peakFigure 11. Molecular structure of PA46 and PA66Figure 12. Wear and friction chart6Figure 13. Thermal properties of PA46, PA66 and PA6Fatigue resistance at 140C of glass fibre reinforced engineering plasticsFigure 14. Fatigue of PA46, PPA and PA66ConclusionsLab g
38、enerated tensile fatigue data can be used topredict plastic gear life. However, in order to utilizethis data, it must be known what the actual rootstresses in the plastic gear are.Iffatiguedatawasgeneratedfromactualgears,andthatdataistakenbacktoatypicalS-Ncurve,know-ing how the root stresses were ca
39、lculated and if thestress values were corrected for tooth deflection isparamount.Toothdeflectioncancauselargevariancesbetweenthe actual root stresses versus theoretical. There-fore,geartoothdeflectionmustbeanalyzedandac-counted for. This will require understanding the an-ticipated load, operating temperature plusfrictionallyinducedheat,andthecorrespondingma-terial modulus at that cumulative temperature.
