AGMA-06FTM03-2006.pdf
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1、06FTM03 Detailed Procedure for the Optimum Design of an Epicyclic Transmission Using Plastic Gears by: I. Regalado and A. Hernndez, CIATEQ TECHNICAL PAPER American Gear Manufacturers Association Copyright American Gear Manufacturers Association Provided by IHS under license with AGMA Licensee=Boeing
2、 Co/5910770001 Not for Resale, 07/25/2008 04:31:34 MDTNo reproduction or networking permitted without license from IHS -,-,- Detailed Procedure for the Optimum Design of an Epicyclic Transmission Using Plastic Gears Isaias Regalado, Ph.D. and Alfredo Hernndez, CIATEQ The statements and opinions cont
3、ained herein are those of the author and should not be construed as an official action or opinion of the American Gear Manufacturers Association. Abstract This paper shows all the steps suggested to get an optimum (volume based) design for an epicyclic (planetary) transmission using plastic material
4、s. The design was developed using the tooth proportions proposed in ANSI/AGMA 1006-A97, Tooth Proportions for Plastic Gears and taking into account the recommendations given in AGMA 6023-A88, Design Manual for Enclosed Epicyclic Gear Drives and ANSI/AGMA2101-C95,FundamentalRatingFactorsandCalculatio
5、nMethodsforInvoluteSpurandHelical Gears taking into account the effect of changing the number of planets, the bending fatigue and contact strength of the plastic materials, and the temperature effects on the size of the gears. The design procedure starts with a preliminary analysis of the performanc
6、e of the gears in a proposed (not optimized)transmission,goingstepbysteptoanoptimumdesignforthegivenloadconditions andexpected minimum life. Copyright 2006 American Gear Manufacturers Association 500 Montgomery Street, Suite 350 Alexandria, Virginia, 22314 October, 2006 ISBN: 1-55589-885-8 Copyright
7、 American Gear Manufacturers Association Provided by IHS under license with AGMA Licensee=Boeing Co/5910770001 Not for Resale, 07/25/2008 04:31:34 MDTNo reproduction or networking permitted without license from IHS -,-,- 1 Detailed Procedure for the Optimum Design of an Epicyclic Transmission Using
8、Plastic Gears Isaias Regalado Ph. D. and Alfredo Hernndez, CIATEQ Introduction The design of an epicyclic transmission involves some special considerations like assemblingpossi- bility, factorizing, and idler planets considerations not necessary for a conventional parallel axles transmission. If add
9、itionally we include the expan- sion characteristic of a plastic material, the design ofaplasticepicyclictransmissionmaybecomevery involving. Byfollowinganexamplesystematically,wewillcov- eralltheconsiderationsneededfor thedesign ofan optimum epicyclic transmission. Nomenclature NSNumber of teeth in
10、 the sun NPNumber of teeth in the planet NRNumber of teeth in the rim SRotating speed of the sun PRotating speed of the planet RRotating speed of the rim CRotating speed of the carrier Mg Overall gear ratio NP Number of equally distributed planets CR Ratio operating/theoretical center distance FWOpe
11、rating face width Problem Description Type of transmissionPlanetary Gear ratio4 (3%) Rim pitch diameter70 mm (Max) Face widthMinimize Sun input speed600 RPM Sun torque (Max.)6.25 Nm Bending durability2000 Hr Carrier materialAluminum Ambient temperature25C Operating temperature75C LubricationOil lubr
12、icated General Design Guidelines The basic speed equations for an epicyclic trans- mission may be found in the literature 1: SNS= RNR+ CNS+ NR( 1) SNS= CNS+ PNP( 2) From eqn. 2, in the planetary: R= 0; Therefore, S C = NS+ NR NS ( 3) And P= S CNS NP ( 4) In addition, for equally distributedplanets w
13、ithstan- dard center distances, the assembly constraints given by eqns. 5 and 6 must be accomplished: NR= NS+ 2 NP( 5) NS+ NR NP = Integer( 6) In practice, designs with non-standard center dis- tances and dropped tooth planets are commonly used; in that case, eqn. 5 may be ignored. Materials Thesele
14、ctionofthetypeofplastictobeusedforthe gears may be information for a full article and is be- yond the scope of this paper. For this example, the selection of the material was based in the recom- mendations of the plastic vendor, who suggested two possibilities: An unfilled high molecular weight acet
15、al copolymer for maximum toughness (HMW POM) and a 25% glass reinforced acetal copolymer (GF POM). One important consideration is that for sliding operation likegears,itisagoodpracticetocombinetwodiffer- ent materials or grades in both members. In this case, due to the application, it is also import
16、ant to haveaverystrongcage(rimgear);therefore,based in their strength, the materials were assigned as follows: Copyright American Gear Manufacturers Association Provided by IHS under license with AGMA Licensee=Boeing Co/5910770001 Not for Resale, 07/25/2008 04:31:34 MDTNo reproduction or networking
17、permitted without license from IHS -,-,- 2 RimGF POM PlanetHMW POM SunGF POM Fromtheinformationprovidedbytheplasticvendor, the properties listed in Table 1 are relevant during the gear design. As may be observed, the Youngs modulus and strength of the plastics reduces with the tempera- tureinagreeme
18、ntwiththebehavior statedinAGMA 2 and shown in Fig. 1. Therefore, for a conserva- tive calculation, we use the material properties at the highest operating temperature highlighted in Table 1. Table 1. Relevant properties of the materials PropertyMaterial HMW POMGF POM Temperature (deg C)40754075 Youn
19、gs Modulus (MPa) 2414.51339.3327001500 Poissons Ratio0.350.350.350.35 Endurance limit 107 cycles (MPa) 6134.925547.97 Contact stress dry (MPa) 1915.91915.9 Contact stress lubri- cated (MPa) 63.252.563.252.5 Linear thermal exp, coeff. 1.2E-041.2E-043.0E-053.0E-05 Aluminum L.T.E.C.2.4E-05 Procedure Th
20、e AGMA 3 suggest thatfor plasticgears theba- sic rack must have the proportions shown in Fig. 2 and summarized as follows: Addendum coefficient1.33 Dedendum coefficient1.00 Tip radius coefficient0.43032 (full) Normal pressure angle20 Allthecalculationsshowninthispaperarebasedon this tooth geometry w
21、ith a non-undercut constrain. Additionally, although the minimum recommended tooththicknessatthetipofthetoothis0.275M4,in order to consider as many options as possible with- out a pointed tooth, during the development of this study a minimum of 0.1M was used. Using eqn. 3 with the nominal gear ratio
22、 and the maximum pitch diameter of the rim, we get the op- tions given in Table 2 iterating from NS=11 to 30. Figure 1. Effect of strain rate and temperature on stress- -strain curves (from AGMA 2). Figure 2. AGMA PT basic rack (from AGMA 2). Copyright American Gear Manufacturers Association Provide
23、d by IHS under license with AGMA Licensee=Boeing Co/5910770001 Not for Resale, 07/25/2008 04:31:34 MDTNo reproduction or networking permitted without license from IHS -,-,- 3 Table 2. Maximum allowable module NS11121314151617181920 NR33363942454851545760 NP11121314151617181920 M2.121.941.791.671.561
24、.461.371.31.231.17 21222324252627282930 63666972757881848790 21222324252627282930 1.111.061.010.970.930.90.860.830.80.78 Ithasbeenshown5thattheperformanceofagear set may be greatly improved by using non standard center distances and tooth proportions in the gears without changing the basic rack geom
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