1、08FTM01AGMA Technical PaperParametric Study of theFailure of Plastic GearsBy M. Cassata, Winzeler Gearand Dr. M. Morris, BradleyUniversityParametric Study of the Failure of Plastic GearsMike Cassata, Winzeler Gear and Dr. Martin Morris, Bradley UniversityThe statements and opinions contained herein
2、are those of the author and should not be construed as anofficial action or opinion of the American Gear Manufacturers Association.AbstractResearchersatBradleyUniversityhavebeencollaboratingwithengineersatWinzelerGeartodeveloptoolsfor the prediction of plastic gear tooth failure for any given set of
3、 operating conditions and to classify failuremodes of these gears. The goal of the project is to characterize and predict the failureof plastic gears overarangeofgivenparameters. Theexperimentstocharacterizetheperformancehavebeenconductedonageardynamometer. Thedynamometerusestwopolymerspurgearsinmes
4、h;onegearattachedtothedriveshaftwhich is driven by a digitally controlled DC motor and the other attached to a parallel driven shaft which iscoupledtoadigitallycontrolledhysteresisbrake. Thedynamometerisequippedwithasetofopticalencoderswhich are attached to each of the shafts. Since temperature of t
5、he gear is a primary concern, thedynamometer is also equipped with an infrared temperature sensor. The sensor allows for measurement ofthetoothflanktemperatureasittraversesintoandoutofthemeshzoneforeitherthedriveordrivengear. Tohelpcontrolthetemperatureofthegears,afanwasmountedabovethemeshandblowsco
6、olingaironthetestgears.A test plan was developed to explore the effect of rotational speed, root stress, and flank temperature on thelifeofthesegears.Insteadofusingaclassicaltestplan,aLatinSquaretestdesignandanalysiswas usedtoreduce the number of experiments and the time required. The torque (or roo
7、t stress) was tested at threelevels, the cooling air velocity at three levels, andthe rotationalspeed atfour levels.The dependentvariablefor the experiments was the number of cycles (or rotations) until failure.Three different gears were used in this test protocol. Each of the gears was injection mo
8、lded from Delrin311DPatWinzelerGear. Thethreegeargeometriesweredesignedtohavethesamecenterdistancesothatthe dynamometer did not need to be adjusted during the length of the test. Each of the three gears had adifferentnumberofteethcorrespondingtoadifferentmodule. TheLatinSquarewasrunoneachofthegearsa
9、ndalinearizingandleastsquarestechniquewasusedtofitapowerequationtothedata. Thedatashowedanaverageerrorinthe15-20%rangewhich,accordingtoengineersatDuPont,is similartotheerrorintheirdog bone test specimens.Copyright 2008American Gear Manufacturers Association500 Montgomery Street, Suite 350Alexandria,
10、 Virginia, 22314October, 2008ISBN: 978-1-55589-931-83Parametric Study of the Failure of Plastic GearsMike Cassata, Winzeler Gear and Dr. Martin Morris, Bradley UniversityIntroductionOver the last seven years, Bradley University hasbeen working with Winzeler Gear Company ofChicagoIllinoisthroughaseri
11、esofgraduateandun-dergraduate research projects. Much of the workhas been centered on a parallel-shaft, rotary geardynamometer. Winzeler Gear manufactures vari-ous plastic gears mostly for automotive systemuses. Many of these gears are used for windowactuators, door locks and HVAC control systems to
12、name a few of the systems. The long-term goal oftheprojectsatBradleyistocharacterizeandpredictthefailureofplasticgearsoverasetofgivenoperat-ing parameter.The dynamometerAs already noted, most of the testing has been per-formed on a parallel-shaft rotary gear dynamome-ter which was designed and assem
13、bled through acollaborative effort between Bradley and WinzelerGear. The dynamometer can be seen in Figure 1.Thedynamometerusestwopolymergearsinmesh.The gear mesh is shown in Figure 2. The gear ontherightisconnectedtothedriveshaftwhichisdriv-en by a digitally controlled DC motor. The motorcontroller
14、 allows the user to dynamically control thespeed of the drive shaft between 0 and 500 RPM.Directionalcontrolisalsoavailable. Thegearontheleft is attached to the driven shaft which is coupledto a digitally controlled hysteresis brake. The hys-teresis brake has its own controller which is con-nectedto
15、thedataacquisitioncomputer. Thetorquecan be digitally varied from 0 to 3.6 Nm. Thedynamometercontrolleralsohasmeasuredoutputsof speed and applied torque. It also has an internalPID control for the applied torque.The dynamometer is equipped with a set of opticalencoders that are attached to each of t
16、he shafts.TheencodersfeatureZreferencingand5000incre-mentsperrevolution. Withtheencoders,theshiftinthe relative angular position between the gears canbe measured to within about 0.1 as the test prog-resses. This is particularly usefulinformation inthetestingofplasticgearssinceplasticgearscanexpe-rie
17、nce significant deformation during operation andbefore failure.Figure 1. DynamometerFigure 2. Gear meshHeating a plastic gear to a temperature higher thanthe limits of its normal operating range has asignifi-cant effect on the properties of the gears and canlead to a significant reduction in gear li
18、fe. Since thetemperature of the gear is such an important con-cern, the dynamometer is also equipped with an in-frared temperature sensor that measures the sur-face temperatureof thegear flank. Thisis showninFigure 3. The sensor is mounted onan orbitaltrackwhich allows for temperature measurements4a
19、round the outer radius of the drive or driven gearand keeps the sensor at the required 6 inches fromthe surface of the gear teeth. The measurementareaofthedetectorisapproximately1mm.TheIRsensorisalsomountedtoatranslationaltrackwhichallowsthesensortobepositionedacrossthefaceofthe teeth. The control f
20、or the sensor can beadjusted for different radiation emmisivities to com-pensate for variations due to different materials.There is an analog output from the controller whichis attached to the data acquisition computer tocontinuously log the temperature.Figure 3. Infrared temperature sensorAs might
21、be expected an important variable tocontrolduringatestwouldbethetemperatureofthegear. Unfortunately, the gear temperature was avariable dependent upon all of the other test vari-ables proving difficult to control to a target value.Furthermore, the tests for this study wereconducted such that a norma
22、l lifetime of a gearoperation was compressed into a much shorterduration. As a result, a relatively large amount ofheat was generated during each test and couldresult in elevated temperatures. In an effort to con-trol the influence the gear temperature the gearswere air cooled. A computer fan was mo
23、untedabovethemeshasshowninFigure4. Asetofthreedifferentconeswasdesignedandbuiltusingarapidprototypemachine. These coneswere mountedonthefantochangethecoolingairvelocityandsubse-quently achieve different cooling rates. Thisapproach did not control the gear temperature, butinstead controlled the conve
24、ctive velocity of thecooling air.Figure 4. Cooling fan and coneTest gearsThree different test gears were used for the tests; a53 tooth 0.6 module gear, a 40 tooth 0.8 modulegear and a 32 tooth 1.0 module gear. The gearsweredesigned sothat theywould allhave thesamemounting center distance. This was d
25、one so thatthe dynamometer would not require adjustmentwhen testing each of the different gears. ThegearsusedforthetestswereinjectionmoldedbyWinzelerGear. The gears were made from Delrin 311DPwhich is an acetal polymer made by the DuPontCompany. Delrin is a popularthermoplastic usedinpowertransmissi
26、ongearsbecauseDelrinexhibitsarelatively high strength due to its semi-crystallinestructure. A picture of the test gears is shown inFigure 5. The gears are currently being testedwithout any type of lubrication to facilitate anaccelerated test.Figure 5. Dynamometer test gears5Test procedureInordertopr
27、edictthecyclestofailureofthegears,atest plan was designed so that the acquired datacould be used to define an equation using aregression scheme. To reduce the number ofexperiments, a Latin Square analysis was used.This approach is a design of experiments that isused to reduce the number of experimen
28、ts neededtocorrelatedata. Forexample,ifthreeindependentvariablesaretestedatfourdifferentlevels,thereare34or 81 combinations of variables that would berequired for a complete classical test plan. UsingLatinSquareapproachreduces thenumber ofteststo 44or16tests.Thethreeindependentinputsthatwereusedfort
29、heexperiments of this study were torque, rotationalspeed, and cooling velocity. The torque wasassigned to one of three levels (2.5, 3.0, 3.5Nm),the rotation speed to 4 levels (300, 360, 400,450RPM) and the cooling velocity to three levels(250, 375, 750ft/min). The dependent output wasthe number of g
30、ear rotations until failure. The tablebelow shows the Latin Square test plan that wasused for this study. The columns represent threetorque levels, the rows represent the four levels ofthe rotational speed and the numbers in the matrixrepresent the cooling velocities. Each of the cellsmatrixes corre
31、sponds to a test and each test wasrun twice.Torque2.500 3.000 3.500RPM300250 375 750360 750 250 375400 375 750 250450 250 375 750This Latin Square test matrix was applied for eachof the three gears.The program used to test the gears was a cyclicramptestwhereboththespeedandthetorquewerelinearly chang
32、ed to target levels. Figure 6 showsthegraphofthespeed andtorque versustime. Thespeed and torque are ramped from 0 to the maxi-mum values over a 3 second time interval, theywere held constant for 3 seconds, then they wereramped back down to 0 over 3 another seconds. Asimilar cycle was then repeated b
33、ut in the oppositedirection. Thiscounter-rotatingcyclewasrepeateduntil the gear set failed. This protocol was usedbecauseitresemblestheconditionsexperiencedbymanyofWinzelerGearsproducts;forexample,thegears which control a window going up and down.The tooth temperature, phase shift, instantaneousrota
34、tional speed, instantaneous torque, and cyclesto failure were logged. Upon gear failure, theprogram shuts down the brake and drive motor andthen saves the data.Figure 6. Torque-speed profileLeast squares power analysisOncethedatawasacquired,itwasprocessedusinga Least Squares regression routine. This
35、 programwill fit an exponential equation to the data using alinearizingleastsquaresregressiontechnique. Thefollowing equation format was assumed.Y = a0xa11xa22 xannWhere Y is the dependent variable, the xs are theindependentvariablesandtheasaretheconstantswhich the technique calculates.As mentioned
36、previously, the purpose of the testingwas to predict the failure of plastic gears for a set ofgiven operating parameters. Therefore, the set ofparameters needed to fully define included not onlythedescription ofthe conditionsexperienced bythegears during the experiment, but also a descriptionof the
37、physical geometry of the gears. Theseparameterswereusedintheabovepowerequation.The first parameter was the average mesh temper-ature. This was represented as the average of themeasured temperature recorded from the IRsensor. The second parameter was the rotational6speed which was represented by the
38、maximumspeed during the test. The third parameter was thegear tooth root stress. The root stress was calcu-lated using the Lewis Bending equation. Two addi-tionalparameterswereusedtodefinethegeometryof the gears. The first was the contact ratio. Thiswas calculated using the known center distance oft
39、he gears and the tooth geometry. The secondgeometry parameter was created to define theshape of the gear teeth and, consequently, is de-fined as the “Shape Ratio”. We define the ShapeRatio as the tooth whole depth divided by the tooththickness. Since Delrin gears have a crystallineskinduetowallshear
40、during themolding process,atall and thin tooth will have a higher ratio of crystal-line skin relative to the amorphous center material.ThepurposeoftheShapeRatiowastocharacterizethis condition.These parameters were then input into the powerequation as shown below.CTF = a0(RPM)a1()a2(T)a3(CR)a4(SR)a5W
41、hereCTF is thecycles tofailure, RPM is therota-tional speed, is the root stress, T is the averagemeshtemperature,CRisthecontactratioandSRisthe shape ratio. After running the Least Squaresprogram on the data, the following equation wasdetermined to fit the data, (CR) 4.13(SR)12.84CTF = 1.57 106(RPM)0
42、.02() 5.26(T) 13.17From the equation it can be seen that the ShapeRatio and the Temperature had the strongestinfluenceonlife. Basedonthedatafromthisstudyitis not clear why the Contact Ratio has a negativevalue. The negative value for the exponent wouldsuggest that the contact ratio is inversely rela
43、ted togear life. One would expect that the life of a gearwould likely increase when increasing the contactratio. The graph shown in Figure 7 shows a 3 di-mensional plot of the data and the curve which wasgenerated by the least squares regression routine.Figure 7. Surface plot7The average error betwe
44、en the data and the equa-tion was found to be 23.7%. This was close to theaverage error between all of the measurementswhich was 19.4%. This suggests a reasonablygood fit of the data.Future plans and testsA second generation gear dynamometer is current-ly being built by Winzeler Gear. The dynamomete
45、rwillallowforthegearstobeputintoathermalcham-ber where the conditions ofthe atmosphere,includ-ing temperature and humidity, can be monitoredand controlled. The torque capacity will be 6.4 Nmwhich is almost double the capability of the existingdynamometer. The next step for testing will be touse diff
46、erent polymers in an effort to be able tocompare the life expectancy for gears of differentmaterials under similar loading conditions. Tests inwhich the gear set is lubricated will also beincludedin the follow-on testing. The tests in which thegears are lubricated will most likely be run on thesecond-generation dynamometer since the torquecapacityishigher. Highertorqueswillbeusedinthetestsusinglubricatedgearsinanefforttoreducetherelatively long testing time that is expected.
