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1、07FTM01 Estimation of Lifetime for Plastic Gears by: Dr. S. Beermann, KISSsoft AG TECHNICAL PAPER American Gear Manufacturers Association Copyright American Gear Manufacturers Association Provided by IHS under license with AGMA Licensee=Boeing Co/5910770001 Not for Resale, 07/25/2008 03:14:51 MDTNo
2、reproduction or networking permitted without license from IHS -,-,- Estimation of Lifetime for Plastic Gears Dr. Stefan Beermann, KISSsoft AG The statements and opinions contained herein are those of the author and should not be construed as an official action or opinion of the American Gear Manufac
3、turers Association. Abstract The importance of plastic gears for modern industry is growing every year. The engineer sizing plastic gears hasaverydifficulttask.Thereisnointernationalstandardavailableforthestrengthanalysis.Theonlymethod publiclyacceptedistheGermanguidelineVDI2545.Inadditiontoalackofc
4、alculationmethodsthereisaneed for measuring material properties. This paper shall give an overview over the current situation and will provide some guidelines how to rate plasticgears,howtohandlethelackofmaterialdataavailableandhowtoconductmeasurementsofmaterial properties to make them suitable for
5、the available calculation methods. Copyright 2007 American Gear Manufacturers Association 500 Montgomery Street, Suite 350 Alexandria, Virginia, 22314 October, 2007 ISBN: 978-1-55589-905-9 Copyright American Gear Manufacturers Association Provided by IHS under license with AGMA Licensee=Boeing Co/59
6、10770001 Not for Resale, 07/25/2008 03:14:51 MDTNo reproduction or networking permitted without license from IHS -,-,- 1 Estimation of Lifetime for Plastic Gears Dr. Stefan Beermann, KISSsoft AG Introduction The number of gears produced out of plastic is get- ting dramatically larger. This is primar
7、ily due to the improvement of plastic materials strength.The properties of plastic can be varied in a large range, especially when compared to steel. It is now pos- sible to select an optimal material for a specific task based on the following properties: strength, wear, stiffness, damping and noise
8、 production. Inspiteofthegrowinguseofplasticgearsthescien- tificresearchisastonishinglylow,especially compared to the resources used for research on metalgears.Amirrorofthissituationistheavailabil- ity of standards. The standard used for the strength analysis of cylindrical plastic gears is the Germ
9、an guideline VDI 2545 and is poor compared to the re- spective standards AGMA 2001 and ISO 6336 for metalgears.AGMA909-A06,ANSI/AGMA 1006-A97 and ANSI/AGMA 1106-A97 address plastic gears, but only the geometry. ANSI/AGMA 920-A01offersmuchgeneralinformationaboutthe applicability of plastic material f
10、or gears and pres- ents the typical test procedures. The VDI 2545 is currently invalid and fits into the overall lack of re- search into plastic gearing. One of the major restrictions of the VDI 2545 is the availability of data for only three different materials (PA12, PA66, POM). Currently several
11、groups are attempting to produce reliable data for modern materials. These experiments have proven to be expensive and are very time consuming. A design engineer therefore needs to know how he can design new plastic gears successfully without the use of a valid standard and without scientific materi
12、als research data. The engineer must rely on knowledge gained from past experience. Usually metal gears are produced in a generating process. Plastic gears most often are injection molded. If the insert for the mold is manufactured with EDM (e.g. wire erosion) the tooth form can be optimized without
13、 additional costs. For generated gears this is only possible with special tools, which increases the costs. On the other hand, typical injection molded gears have a relatively low quality (ISO 9-10), a problem, however, which can be handled with special arrangements. Optimized plastic gear tooth for
14、ms arealso designated“hybrid toothing” in literature. Strength analysis Material data for plastic gears (Whler curves or S- -N curves) Forthesizingandoptimizationofgears,thecalcula- tion of root, flank and wear strength for the pre- scribed lifetime are of large importance. In the same way as with s
15、teel gears, for plastic ma- terials the specific parameters (root pulsating strength and flank strength) are dependant on the number of load cycles. For plastic gears these pa- rameters depend strongly on temperature and the type of lubrication (oil, grease or dry running). Whereonevalueforthetooths
16、trengthcalculationis sufficient for steel, a plastic material requires the necessity of several S-N curves (e.g. for POM figure 1). The method according to VDI 2545 1 for the strengthanalysisofcylindricalgearsmadeofplastic is the only worldwideknown methodfor thecalcula- tion solution. Even though i
17、t was cancelled some yearsagoitisstillincommonuseduetothelackofa replacement. Currently Prof. Werner Krause and Dr. Jrgen Wassermann in Germany along with their associates have plans to develop a replace- ment for the guideline but it is in the very early stages of development. Todays materials are
18、much more numerous than the materials mentioned in the VDI 2545. Some of them show a significantly higher strength, e.g. rein- forcedmaterial. Typically,the producerof themate- rial will only provide values for the tensile strength, theaforementioneddataforagearcalculationisnot known and can not be
19、derived from the tensile strength.Changingtherecipeofaplasticmightlead to higher ultimate strength, thus increasing the root strength, while the flank or wear resistance is de- creasingatthesametimeduetotribologicaleffects. Copyright American Gear Manufacturers Association Provided by IHS under lice
20、nse with AGMA Licensee=Boeing Co/5910770001 Not for Resale, 07/25/2008 03:14:51 MDTNo reproduction or networking permitted without license from IHS -,-,- 2 Figure 1. Temperature dependent Whler curves for POM. A simple solution for the problem is not available. The material properties have to be ver
21、ified using prototypes or by means of a long term test on a test rig. In most cases it is not necessary to conduct hundreds of measurements, to get enough data points for a diagram like in figure 1 but by determin- ing some data pointsthe diagramcan begenerated by interpolation with good accuracy. T
22、hese data points can be derived from experience with pro- duced gear boxes or experiments on test rigs. Still the effort is significant. General layout of the strength calculation of plastic gears The mechanical properties of plastic parts are strongly dependant on temperature. So for rating plastic
23、gearsfirsttherelevanttemperaturehastobe determined. This means that based on the environ- mentaltemperature,thelocalheatproductioninthe meshing of the gear due to frictional and viscoelas- tic power losses and the dissipation of the heat, the finalstateofequilibriummustbesearched. Figure2 shows the
24、general layout of the calculation proce- dure (according to Erhard 2). Figure 2. General layout of the strength calculation procedure for plastic parts. Copyright American Gear Manufacturers Association Provided by IHS under license with AGMA Licensee=Boeing Co/5910770001 Not for Resale, 07/25/2008
25、03:14:51 MDTNo reproduction or networking permitted without license from IHS -,-,- 3 Estimation of the temperature Several models are available for the calculation of surface and body temperature. For metal gears the flash temperature concept of Blok is used for the calculation of the scoring safety
26、 factor. For plastic gears this model wasadapted bySiedke 3.Practi- cal experience however shows that this model may not be appropriate for plastic gears. Takanashi de- veloped equations with an approach containing a friction and adeformation part.The heatproduction out of the deformation part is ba
27、sed on the model accordingtoVoigt(spring-damping-model).Tobal- ance the heat production the dissipation has to be calculated.Thedifferencebetween heatproduction and heat dissipation thenleads tosurface andbody temperature. The model according to Takanashi 4 proved to be precise enough for practical
28、applica- tion. However, several of the parameters needed arehardtodetermine.Forthisreasonanothermod- el prevailed, based on work of Hachmann and Strickle 5. The calculation is also based on heat balancing.Theassumptionis,thattheheatquantity Q1,whichisproducedbythepower lossin thetooth meshingisequal
29、totheheatquantityQ2thatisdissi- pated to the inner space of the gearbox housing. ThisinturnisequaltothequantityQ3which isdissi- pated by the housing to the environment. This ap- proach leads to a formula, which is also used in the VDI guideline. The factors in the formula differ slightly between ori
30、ginal publication, the formula in the VDI guideline and other publications. 17100 bz1,2 k2 ( m) + 6.3 k3 A 1,2= a+ 136(P)(m) u + 1 z2+ 5 Where 1,2C is the surface or body temperature of gear i, i=1,2, aC is the ambient temperature, PkW is the power transmitted, m-is a coefficient taking friction int
31、o ac- count (not the friction coefficient!), zi-number of teeth of gear i, i = 1,2, u-transmission ratio z2/z1, bmmface width, m/scircumferential speed, mmmnormal module, k2, -factors described in the VDI2545, see below, k3-takes the influence of the housing into account (none, open, partially open
32、or closed), Am2 is the surface of the housing. Comparison of the results of the temperature cal- culation according to Hachmann and Strickle and measured temperaturesin testsshow slightlylower calculatedtemperaturesintherootarea,andsignifi- cantly higher calculated temperature of the flank surface.
33、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 calculation of the temperature, taking the ratio of the power- on-time into account. Based on measurements, they define
34、d continuous power-on-time of 75 min- utes to be permanent running. For all cases with shorter periods they introduced a factor fEDto re- duce the calculated temperature. Since this work was done after the publication of the VDI guideline, thiscorrectionfactorisnotincludedinthe calculation formula o
35、f the temperature in the VDI 2545. The factors k2and show up during the derivation ofthe formula.They takethe materialcombinations and lubrication type into account. The factor k2also determines whether the calculated temperature is the body or the surface temperature. For k2, k3, and m tables are p
36、rovided in the guideline. The temperature calculation is one of the critical pointsnotonlyintheVDI2545,butinthecalculation ofplasticpartsingeneral.Duetotheproblemsmen- tioned above it is recommended to use a fixed tem- perature whenever possible to supersede these problems. For slow running gears (c
37、ircumferential speed= 3.51,000 . 1,0000VDI 2545 with Tp 2.0 . 3.5 1,000 . 1,0000VDI 2545 with Tp and VDI 2545 with Td 2.0 1,000 . 1,0000VDI 2545 with Tp and VDI 2545 with Td Tp: Peak (maximum) torque Td: Nominal (endurance) torque Bold: The most common cases (*) : Number of load cycles with Tp (duri
38、ng full life period) Strength calculation taking the real tooth form into account The endurance safety against root failure is highly influenced by an optimized transformation from the involute to the root circle. The manufacturing of a gear with a generating process, even with a well rounded tip of
39、 the tool, an optimal rounding often cannot be achieved. With a modification, which of course has to be adapted to the contact behavior with the counter gear, the root strength can be in- creasedsignificantly.Forthe strengthanalysis are- liable algorithm was developed based on literature, hints in s
40、tandards and comparable calculations by FEA software. With this algorithm the complex effort of a FEA calculation usually can be skipped. All standardized calculationmethods determinethe root stress based on a simplified model. According to VDI 2545 (in analogy to DIN 3990), the critical cross secti
41、on is determined by the tangent on the inside of the root curve which intersects the middle line of the tooth at an angle of 30 degrees. Depend- ing on the root rounding, the position of the real criticalcrosssectionmightdeviatemoreorless.Ina paper by B. Obsieger 8 years ago, an approach was propose
42、d for a significant improvement of the calculation method. Depending on the real tooth formforeachpointintherootareathetoothformYF and the stress correction YSfactors are calculated and the point is determined at which the product YFYSreaches a maximum (see fig. 4). This leads toamuchmoreprecise cal
43、culationmethod andcan be applied without problems to non-involute tooth forms as well. Applying the formula for YSas defined in the DIN or theISOstandardasproposedbyObsiegerexceeds the defined limits for the formula. It is valid only for the point of the 30 degrees tangent, should not be used for a
44、graphical method and is only for involute tooth forms. However, comparing YSin a graphical method and FEA results showed a very good match, so that in most cases the accuracy of both methods should be the same. In addition, the de- scribed method is a “worst-case” method, i.e. the calculated safety
45、factors are by definition always smaller than those calculated by the standard: the one point treated in the standard calculation is in- cluded in the list of points to be checked according to Obsieger. In contrast to the standard method dif- ferent root forms can be compared and the benefit ornegat
46、ivesofarootmodificationcanbeevaluated. Copyright American Gear Manufacturers Association Provided by IHS under license with AGMA Licensee=Boeing Co/5910770001 Not for Resale, 07/25/2008 03:14:51 MDTNo reproduction or networking permitted without license from IHS -,-,- 7 Following the approach of Obs
47、ieger it is possible to locate the critical cross section of the tooth. As an option, the force can be applied at the tip as in ISO 6336 Method C, or at the point of single tooth con- tact method B.The strengthanalysis accordingto VDI 2545 can be carried out later with this specific data. In additio
48、n, it is possible to visualize the geo- metricalcourseofthestressintherootareaandthe course 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 be conducted along the tooth flank based on the real tooth form. Here for each point of contact the re- spectiveradiiofbothgearsaredeterminedandwith this the Hertzian stress is calculated. The same dataallowsthecalculationoftheslidingvelocity,the local heating, theefficiency andthe heatproduction of these tooth forms. With these additional informa