1、07FTM01Estimation of Lifetime for Plastic Gearsby: Dr. S. Beermann, KISSsoft AGTECHNICAL PAPERAmerican Gear Manufacturers AssociationEstimation of Lifetime for Plastic GearsDr. Stefan Beermann, KISSsoft AGThe statements and opinions contained herein are those of the author and should not be construe
2、d as anofficial action or opinion of the American Gear Manufacturers Association.AbstractTheimportanceofplasticgearsformodern industryis growingevery year.The engineersizing plasticgearshasaverydifficulttask.Thereisnointernationalstandardavailableforthestrengthanalysis.Theonlymethodpubliclyacceptedi
3、stheGermanguidelineVDI2545.Inadditiontoalackofcalculationmethodsthereisaneedfor measuring material properties.This paper shall give an overview over the current situation and will provide some guidelines how to rateplasticgears,howtohandlethelackofmaterialdataavailableandhowtoconductmeasurementsofma
4、terialproperties to make them suitable for the available calculation methods.Copyright 2007American Gear Manufacturers Association500 Montgomery Street, Suite 350Alexandria, Virginia, 22314October, 2007ISBN: 978-1-55589-905-91Estimation of Lifetime for Plastic GearsDr. Stefan Beermann, KISSsoft AGIn
5、troductionThe number of gears produced out of plastic is get-ting dramatically larger. This is primarily due to theimprovement of plastic materials strength. Theproperties of plastic can be varied in a large range,especially when compared to steel. It is now pos-sible to select an optimal material f
6、or a specific taskbased on the following properties: strength, wear,stiffness, damping and noise production.Inspiteofthegrowinguseofplasticgearsthescien-tific research is astonishingly low, especiallycompared to the resources used for research onmetalgears.Amirrorofthissituationistheavailabil-ity of
7、 standards. The standard used for the strengthanalysis of cylindrical plastic gears is the Germanguideline VDI 2545 and is poor compared to the re-spective standards AGMA 2001 and ISO 6336 formetal gears. AGMA 909-A06, ANSI/AGMA1006-A97 and ANSI/AGMA 1106-A97 addressplastic gears, but only the geome
8、try. ANSI/AGMA920-A01offersmuchgeneralinformationabouttheapplicability of plastic material for gears and pres-ents the typical test procedures. The VDI 2545 iscurrently invalid and fits into the overall lack of re-search into plastic gearing.One of the major restrictions of the VDI 2545 is theavaila
9、bility of data for only three different materials(PA12, PA66, POM). Currently several groups areattempting to produce reliable data for modernmaterials. These experiments have proven to beexpensive and are very time consuming. A designengineer therefore needs to know how he candesign new plastic gea
10、rs successfully without theuse of a valid standard and without scientificmaterials research data. The engineer must rely onknowledge gained from past experience.Usually metal gears are produced in a generatingprocess. Plastic gears most often are injectionmolded. If the insert for the mold is manufa
11、cturedwith EDM (e.g. wire erosion) the tooth form can beoptimized without additional costs. For generatedgears this is only possible with special tools, whichincreases the costs. On the other hand, typicalinjection molded gears have a relatively low quality(ISO 9-10), a problem, however, which can b
12、ehandled with special arrangements. Optimizedplastic gear tooth forms arealso designated“hybridtoothing” in literature.Strength analysisMaterial data for plastic gears (Whler curvesor S-N curves)Forthesizingandoptimizationofgears,thecalcula-tion of root, flank and wear strength for the pre-scribed l
13、ifetime are of large importance.In the same way as with steel gears, for plastic ma-terials the specific parameters (root pulsatingstrength and flank strength) are dependant on thenumber of load cycles. For plastic gears these pa-rameters depend strongly on temperature and thetype of lubrication (oi
14、l, grease or dry running).Whereonevalueforthetoothstrengthcalculationissufficient for steel, a plastic material requires thenecessity of several S-N curves (e.g. for POMfigure 1).The method according to VDI 2545 1 for thestrengthanalysisofcylindricalgearsmadeofplasticis the only worldwideknown metho
15、dfor thecalcula-tion solution. Even though it was cancelled someyearsagoitisstillincommonuseduetothelackofareplacement. Currently Prof. Werner Krause andDr. Jrgen Wassermann in Germany along withtheir associates have plans to develop a replace-ment for the guideline but it is in the very earlystages
16、 of development.Todays materials are much more numerous thanthe materials mentioned in the VDI 2545. Some ofthem show a significantly higher strength, e.g. rein-forcedmaterial. Typically,the producerof themate-rial will only provide values for the tensile strength,theaforementioneddataforagearcalcul
17、ationisnotknown and can not be derived from the tensilestrength.Changingtherecipeofaplasticmightleadto higher ultimate strength, thus increasing the rootstrength, while the flank or wear resistance is de-creasingatthesametimeduetotribologicaleffects.2Figure 1. Temperature dependent Whler curves for
18、POM.A simple solution for the problem is not available.The material properties have to be verified usingprototypes or by means of a long term test on a testrig. In most cases it is not necessary to conducthundreds of measurements, to get enough datapoints for a diagram like in figure 1 but by determ
19、in-ing some data pointsthe diagramcan begeneratedby interpolation with good accuracy. These datapoints can be derived from experience with pro-duced gear boxes or experiments on test rigs. Stillthe effort is significant.General layout of the strength calculation ofplastic gearsThe mechanical propert
20、ies of plastic parts arestrongly dependant on temperature. So for ratingplasticgearsfirsttherelevanttemperaturehastobedetermined. This means that based on the environ-mentaltemperature,thelocalheatproductioninthemeshing of the gear due to frictional and viscoelas-tic power losses and the dissipation
21、 of the heat, thefinalstateofequilibriummustbesearched. Figure2shows the general layout of the calculation proce-dure (according to Erhard 2).Figure 2. General layout of the strengthcalculation procedure for plastic parts.3Estimation of the temperatureSeveral models are available for the calculation
22、 ofsurface and body temperature. For metal gears theflash temperature concept of Blok is used for thecalculation of the scoring safety factor. For plasticgears this model wasadapted bySiedke 3.Practi-cal experience however shows that this model maynot be appropriate for plastic gears. Takanashi de-v
23、eloped equations with an approach containing afriction and adeformation part.The heatproductionout of the deformation part is based on the modelaccordingtoVoigt(spring-damping-model).Tobal-ance the heat production the dissipation has to becalculated.Thedifferencebetween heatproductionand heat dissip
24、ation thenleads tosurface andbodytemperature. The model according to Takanashi 4proved to be precise enough for practical applica-tion. However, several of the parameters neededarehardtodetermine.Forthisreasonanothermod-el prevailed, based on work of Hachmann andStrickle 5. The calculation is also b
25、ased on heatbalancing.Theassumptionis,thattheheatquantityQ1,whichisproducedbythepower lossin thetoothmeshingisequaltotheheatquantityQ2thatisdissi-pated to the inner space of the gearbox housing.ThisinturnisequaltothequantityQ3which isdissi-pated by the housing to the environment. This ap-proach lead
26、s to a formula, which is also used in theVDI guideline. The factors in the formula differslightly between original publication, the formula inthe VDI guideline and other publications.17100bz1,2k2( m)+ 6.3k3A1,2= a+ 136(P)(m)u+ 1z2+ 5Where1,2C is the surface or body temperature ofgear i, i=1,2,aC is
27、the ambient temperature,P kW is the power transmitted,m - is a coefficient taking friction into ac-count (not the friction coefficient!),zi- number of teeth of gear i, i =1,2,u - transmission ratio z2/z1,b mmface width, m/scircumferential speed,m mmnormal module,k2, - factors described in the VDI254
28、5, seebelow,k3- takes the influence of the housing intoaccount (none, open, partially open orclosed),A m2 is the surface of the housing.Comparison of the results of the temperature cal-culation according to Hachmann and Strickle andmeasured temperaturesin testsshow slightlylowercalculatedtemperature
29、sintherootarea,andsignifi-cantly higher calculated temperature of the flanksurface. Frequently, thecalculated temperatureex-ceeds the melting temperature of the material, al-though the test showed no melting of the flank. Er-hard and Weiss 6 proposed a modified calculationof the temperature, taking
30、the ratio of the power-on-time into account. Based on measurements,they defined continuous power-on-time of 75 min-utes to be permanent running. For all cases withshorter periods they introduced a factor fEDto re-duce the calculated temperature. Since this workwas done after the publication of the V
31、DI guideline,this correction factor is not included in thecalculation formula of the temperature in theVDI 2545.The factors k2and show up during the derivationofthe formula.They takethe materialcombinationsand lubrication type into account. The factor k2alsodetermines whether the calculated temperat
32、ure isthe body or the surface temperature. For k2, k3, and m tables are provided in the guideline.The temperature calculation is one of the criticalpointsnotonlyintheVDI2545,butinthecalculationofplasticpartsingeneral.Duetotheproblemsmen-tioned above it is recommended to use a fixed tem-perature when
33、ever possible to supersede theseproblems. For slow running gears (circumferentialspeed= 3.5 1,000 . 1,0000 VDI 2545 with Tp2.0 . 3.5 1,000 . 1,0000 VDI 2545 with Tpand VDI 2545with Td 2.0 1,000 . 1,0000 VDI 2545 with Tpand VDI 2545with TdTp: Peak (maximum) torqueTd: Nominal (endurance) torqueBold: T
34、he most common cases(*) : Number of load cycles with Tp (during full life period)Strength calculation taking the real toothform into accountThe endurance safety against root failure is highlyinfluenced by an optimized transformation from theinvolute to the root circle. The manufacturing of agear wit
35、h a generating process, even with a wellrounded tip of the tool, an optimal rounding oftencannot be achieved. With a modification, which ofcourse has to be adapted to the contact behaviorwith the counter gear, the root strength can be in-creasedsignificantly.Forthe strengthanalysis are-liable algori
36、thm was developed based on literature,hints in standards and comparable calculations byFEA software. With this algorithm the complexeffort of a FEA calculation usually can be skipped.All standardized calculationmethods determinetheroot stress based on a simplified model. Accordingto VDI 2545 (in ana
37、logy to DIN 3990), the criticalcross section is determined by the tangent on theinside of the root curve which intersects the middleline of the tooth at an angle of 30 degrees. Depend-ing on the root rounding, the position of the realcriticalcrosssectionmightdeviatemoreorless.Inapaper by B. Obsieger
38、 8 years ago, an approachwas proposed for a significant improvement of thecalculation method. Depending on the real toothformforeachpointintherootareathetoothformYFand the stress correction YSfactors are calculatedand the point is determined at which the productYFYSreaches a maximum (see fig. 4). Th
39、is leadstoamuchmoreprecise calculationmethod andcanbe applied without problems to non-involute toothforms as well.Applying the formula forYSas defined in the DIN ortheISOstandardasproposedbyObsiegerexceedsthe defined limits for the formula. It is valid only forthe point of the 30 degrees tangent, sh
40、ould not beused for a graphical method and is only for involutetooth forms. However, comparing YSin a graphicalmethod and FEA results showed a very goodmatch, so that in most cases the accuracy of bothmethods should be the same. In addition, the de-scribed method is a “worst-case” method, i.e. theca
41、lculated safety factors are by definition alwayssmaller than those calculated by the standard: theone point treated in the standard calculation is in-cluded in the list of points to be checked accordingto Obsieger. In contrast to the standard method dif-ferent root forms can be compared and the bene
42、fitornegativesofarootmodificationcanbeevaluated.7Following the approach of Obsieger it is possible tolocate the critical cross section of the tooth. As anoption, the force can be applied at the tip as in ISO6336 Method C, or at the point of single tooth con-tact method B.The strengthanalysis accordi
43、ngtoVDI 2545 can be carried out later with this specificdata. In addition, it is possible to visualize the geo-metricalcourseofthestressintherootareaandthecourse of the maximum stress in the root area dur-ing the meshing of the gears (figure 5).The calculation of the Hertzian stress can also becondu
44、cted along the tooth flank based on the realtooth form. Here for each point of contact the re-spectiveradiiofbothgearsaredeterminedandwiththis the Hertzian stress is calculated. The samedataallowsthecalculationoftheslidingvelocity,thelocal heating, theefficiency andthe heatproductionof these tooth f
45、orms. With these additional informa-tion it is much easier tooptimize thetooth formthanonly with the standard calculation that only givesin-formation about one point of contact.Figure 4. Graphical method for the determination of the worst case in the root area.Figure 5. Course of stresses in flank a
46、nd root during meshing of the gears.8Strength analysis of non involute gearsThe algorithms described above are derived fromthe base law of gearing and can be used for modi-fied involute profiles as well as for non involute pro-files. Although the large majority of gears used arebasedonaninvolutedesi
47、gn,sometimesanalterna-tive tooth form can be beneficial. For example for agear pump in a formula-1-car; the weight could bereduced significantly by replacing the metal gearswith an involute profile by plastic gears with a cy-cloid profile. The Hertzian stress and the sliding ve-locity were reduced d
48、ue to the optimal curvature ofcycloids (figure 6) by nearly 50%, especially in thecritical areas at tip and root circle.Optimization of the tooth contourThe geometry of the tooth can be changed in differ-ent ways to achieve the optimal situation duringmeshing.Dependingonthetargeteddesignspecifi-cati
49、ons like minimum noise, vibration reduction,highest strength, low sliding velocity and even stiff-nessorsmoothnessoftherotation,oneor theotheraction may be preferred.Thefollowingaretypicalactionsfortheoptimizationof the geometry and give suggestions to which cal-culation methods should be applied:Figure 6. Comparison of an involute design with a cycloid design. Above: stresses during themeshing. Below: sliding velocities.91. Change of geometry with a given referenceprofileThe geometry of the meshin
