1、09FTM09AGMA Technical PaperDesigning for Staticand Dynamic Loadingof a Gear ReducerHousing with FEAby M. Davis, Y.S. Mohammed,and A.A. Elmustafa, Old DominionUniversity and P.F. Martin,C. Ritinski, Sumitomo MachineryCorporation AmericaDesigning for Static and Dynamic Loading of a Gear ReducerHousing
2、 with FEAMatt Davis, Yousuf S. Mohammed, and A.A. Elmustafa, Old Dominion Universityand Paul F. Martin, Charles Ritinski, Sumitomo Machinery Corporation AmericaThe statements and opinions contained herein are those of the author and should not be construed as anofficial action or opinion of the Amer
3、ican Gear Manufacturers Association.AbstractA recent trend has been a movement to more user friendly products in the mechanical power transmissionindustry.Oneofthesemoreuserfriendlystylesisahighhorsepower,rightangleshaftmounteddrivedesignedto minimize installation efforts. Commonly referred to as an
4、 alignment free type, it allows the drive packagemountingtobequicker,morecosteffective,andrequirelessexpertiseduringinstallation. Thisfacilitatestheuse ofthe drive in applications,such as in underground mining, where there is little room to maneuver parts.The most common application for the alignmen
5、t free style drive is for powering bulk material handling beltconveyors.Analignmentfreedriveisdirectcoupledtothedrivenshaftonly;itisnotfirmlyattachedtoafoundationorrigidstructure. A connecting link or torque arm connects the drive to a fixed structure, which limits the drivesrotationalmovementaboutt
6、hedrivenshaft. Theelectricmotorissupportedbythereducerhousingthroughafabricatedsteelmotoradapter;thecouplingconnectingthemotorshaftandreducershaftisenclosedbythismotor adapter.Sumitomo Drive Technologies is working on a design of the alignment free system by using Finite ElementAnalysis(FEA)tohelpgu
7、idethedesignprocess. FEAwasusedtotestthecastironhousingtodetermineanypotential problem areas before production begins. Once analyses were completed, the motor adaptor wasredesigned to lower stresses using the information from the FEA and comparing it to field test data.Copyright 2009American Gear Ma
8、nufacturers Association500 Montgomery Street, Suite 350Alexandria, Virginia, 22314September 2009ISBN: 978-1-55589-962-23Designing for Static and Dynamic Loading of a Gear Reducer Housing with FEAMatt Davis, Yousuf S. Mohammed, and A.A. Elmustafa, Old Dominion Universityand Paul F. Martin, Charles Ri
9、tinski, Sumitomo Machinery Corporation AmericaIntroductionGear reducers arekey elementsfor manyindustrialapplications. Alignment free is a common industryterm used for a right angle shaft mounted drivedesigned to be installed with minimal field couplingand electric motor alignments. This particular
10、typeof drive system reduces cost and time of field as-sembly, andminimizes therequired skill level of thefield assemblers. Sumitomo Drive Technologiesgoal is to maximize the use of standard products,andtoexpandthisdesignphilosophytoapplicationsbeyond underground mining.Gear reducers allow electricmo
11、tors producingrela-tively small torque to create high output torquethrough a series of gears. 1-4 The weight of boththe motor and reducer, plus the movement of thecomplete drive assembly can create high stressesontheinterfacebetweenthereducer andthemotoror motor adapter. Motor induced vibrations due
12、 togear meshing, etc. also play a significant role inreducer analysis. 5-10 These vibrations aregreater at start-up, andcanproducelargedynamicforcesandtorques, whichincreases therisk ofgearreducer housing failure at the interface with themotor adapter. A typical practice of stress analysisand design
13、 optimization is the use of finite elementanalysis (FEA) toevaluatehighstress andpossibleproblem areas. 11-15 In order to determine if thecurrent reducer design meets the requirements ofthe proposed alignment free drive systems, thereducer housing was analyzed under both staticand dynamic loads usin
14、g FEA. Pertinent results,structure optimization proposals, and conclusionsare introduced in the following sections.FEA of gear reducer housingFEA modelingInordertosimulatethesystemeffectivelytheentiresystemwasanalyzedasanassembly. Basedonanexisting and operating prototype design, thealignment free d
15、rive was modeled in AutodeskInventor. Figure 1 shows the entire assembly.The drive is connected to the motor adapter, whichvaries in sizedepending onwhat typeand model ofcoupling it houses. The motor is also connected tothe motor adapter on the right side by a series ofbolts.The solid model was conv
16、erted to a step file (.stp)and imported into PTC Pro/Mechanica.Figure 1. Alignment free drive systemThe FEA model was meshed in Pro/Mechanicausing p-type elements and simple linear analysiswas performed. Bolts were modeled using Pro/Mechanicas fastener application. This methodsimulates the bolt as a
17、 spring element passingthrough the two fastened parts. The load is com-pletely transferred through the bolt rather than thetouching components. The entire assembly meshis shown in Figure 2. The FEA model had amaximum of 133,812 elements. Although thisassemblyisverylarge,itwassimplifiedbyremovingmany
18、 structurally insignificant features. Analyzingthe entire system (reducer housing, coupling boxand motor) as an assembly made it very compli-catedtosimulate. Morecomplexity inthe model, intermsoffeatures,meansmoreelementsandhenceless accuracy. Significant effort was made tosimplify the model while m
19、aintaining the structuralproperties of the system.4Figure 2. FEA model meshBoth the static and dynamic analysis wereconducted in this environment. The loads appliedare the weight of the entire system and the torquereaction due to the action of the output shaft. Theinitialtorqueonthesystematstartupis
20、about300%of the rated torque. This factor of three has beentaken into account while applying the loads. Thealignment free system is designed to be both flip-pableandreversible. Theterm“flippable”describesthe reducers capability of operating both right-side-up and upside-down positions. “Reversible”r
21、efers to the reducers ability to operate in bothCWand CCW shaft rotations. Analysis of the housingwas done in such a way as to test with the torqueapplied in both theclockwise andcounterclockwiseon the output shaft.The reducer housing is typically made out of castiron. Themotoradapterismadeoutofplat
22、esofA36and structural tubing. This design allows themotoradapter to be relatively light-weight. Both the topand the bottom of the adapter have a cover platethatcanquicklyandeasilybetakenoffforaccesstothecoupling. Thereducerhousingandthecouplingbox is bolted together. Figure 3 shows cornerbracketstha
23、twereputinplaceasadditionalsupportif needed. Thesecorner brackets were includedonthe prototype units, pending confirmation of thehousing strength analysis.Figure 3. Bracket and bracket located onhousingStatic analysisThe reducer housing is connected to the rest of theassembly by 4 bolts at the high-
24、speed end-face ofthe housing. Besides the bolts there is also a fail-safe in the form of brackets at the four corners ofend-face of the housing. As a conservative ap-proach static analyses were conducted with andwithoutthebrackets. Thefree-bodydiagram oftheentiredrivesystemisgiveninFigure4,anditdeta
25、ilshow the loads were applied.Figure 4. Free-body diagram5The stress without the brackets was high but notfatal. Withthebrackets,however,thestresswasre-duced considerably. Figure 5 shows the stressdistribution around the bolt holes of the reducer in-terface. The stress distribution on the rest of th
26、ehousing shows the area of high stresses.Figure 5. Stress distribution on ReducerInterfaceMany of the high stress areas are the sharp edgesand holes. Higher stresses are due to the stressconcentration in the area where the geometry issmaller and thinner. These arethe particular areasof concern. Two
27、cases arise as a result of variabletorquearm location(seeFigure6). The torquearmis designed in such a way as to only allow slightmovement in the negative Y-direction (see Figure4). When the loads associated with a counter-clockwise output shaft rotation are applied, thereducer is forced down on the
28、torque arm, allowingno further movement along the Y-direction.Figure 6. Torque arm positionsWith the model constrained at the torque armlocation-1(seeFigure 6) with zerodegrees of free-dom in every direction, high stresses were seen onthe structural tubingin Figure7(a). This tubingandthe area surrou
29、nding show stresses above failure.Figure 7(a) shows that stress concentration in twomajor areas; the circular mounting hole and theround corners of the structural tubing. Themaximum stress on the structural tubing is 543MPa, andit occurredontheoutermost edges oftheexterior of the tubing. This stress
30、 concentrationarea is very small and should be omitted due tostress singularities at those points.a) Inner structural tubing b) Bottom bar constrained areaFigure 7. Static analysis stress field6A local maximum stress occurred near the edge ofthe mounting hole of 400 MPa. Because A36 steeltubing has
31、an ultimate tensile strength of around450 MPa, this stress could cause this tubing toyield. With theweight of the system, and theexter-naltorqueapplied,thestructuraltubingof themotoradapter could fail in those areas of high stress.Figure 7(b) shows the mounting hole that wasconstrained during the an
32、alysis. High stresseswereseenontheedgeof thismountingbarduetoapinching effect. When the loads are applied whilethat location is held fixed, a significant amount ofbending stress is created in the area where themountingbar meetsthestructuraltubingandouter-most motor plate shown in Figure 7(b). The lo
33、calmaximum stresses of this outermost plate arearound200MPa, andthereby will not causefailure.Similar analyses were conducted with counter-clockwisetorqueandthetwolocationsofthetorquearm. These analyses, however, showed lowerstresses,andweredisregarded. Inthiswayaworstcase loading scenario was obtai
34、ned.In the static analysis, the plate at this interface,betweenthemotoradapterandthereducerbox,ex-hibited much higher stresses than the reducer, andis thereby the limiting factors of the design. Thegreater thickness of the reducer housing at theinterface allowed that area to produce little stress.In
35、 order to get lower stresses, many of the partswereredesignedinaniterativeprocess. Theplateswere thickened, the structural tubing was thick-ened,butthestresseswerestillhighandthecostofthese modifications would increase the productioncost. Eventually,thesolutionthatprovedtobeeasyand cost effective in
36、 terms of manufacturing was toextendthebottom bar totheentirewidthof thecou-pling box. This causes the reactionforces from thetorque arm to act over the entire coupling boxinstead of a small region thereby lowering thestresses.Figure 8 shows the results from the static analysiswith the extended bar.
37、 With this bar extended thestresses were around 60 MPa. These stresseswere located on the bar mounting hole. With thissmall modification a significant reduction instresses was achieved.Figure 8. Extended bar stress fieldIn order to further verify these stresses, the result-ing reaction force onthe t
38、orquearm was comparedto the forces applied to themodel. The total weightof the reducer ( -11929 N) , coupling box(-7573.3 N), and motor (-23583.2 N) in the Y-direction gave a reaction force on the torque arm intheY-directionof+43085.5N. ApplyingtheFy=0gives the same result, and the model is consiste
39、nt.Dynamic analysisPTC Pro/Mechanica was also used to perform thedynamic analyses. Dynamic analysis measures asystemsresponsetoanumberoftimedrivenloads.In particular, dynamic random analysis was used.Dynamic random analysis measures the responseof a system to a power spectral density function(PSD)16
40、,17. Theloadinputisaforceoraccelera-tionPSDgivenoverarangeoffrequencies. Inorderto conduct a dynamic analysis, a modal analysismust first be run. A modal analysis calculates thefrequencies of failure. 18-20To ascertain the validity of both the assumptionsand the calculations, acceleration vs. freque
41、ncydata was collected in three different planes and invarious locations from the prototype of the align-ment free drive. A magnetic probe and machineryhealth analyzer was connected to the prototype toacquire this information. Figure 9 shows theaccel-eration vs. frequency in graphical form from there
42、adings taken from the prototype.7Figure 9. Acceleration vs. frequency graphThe modes of failure acquired during the prototypetestwereveryclosetothosecalculatedinthemodalanalysis and further verified the accuracy of ouranalysis and can be seen in Table 1.Table 1. Comparison of frequencyMode Estimated
43、(Hz)Experimental(Hz)%error1 28.3 24.9 12.02 51.1 48.6 4.93 137.8 121.8 11.6The results in Table 1 show that the error in theanalysis is comparable to the error computedaccording to 13. Since the FEA model was ex-tremely large, there was a larger window ofacceptable error.The acceleration vs. frequen
44、cy tables were alsoused as inputs in the dynamic random analysis toshow how the system responded to various fre-quencies. The model was constrainedas showninFigure 7(b) and the loads were applied in a similarfashion as the static analysis, except that for thedynamic random analysis, the PSD data was
45、 usedastheinputtotheanalysis. Figure10(a)showsoneof the internal structural tubing members. Thismember showed the maximum stress of the entiresystem. The resulting maximum stress on theinternalstructuraltubingwas450MPa. Thisstress,however, was over a small area and can be disre-gardedduetoasingulari
46、ty regionat that point. Therealistic stress was around 300 MPa.Figure 10(b) shows the stress distribution on themotoradaptorfrontplate. Thisisthelocationwherethe adaptor is bolted to the reducer. This area alsoshowed stresses near 300 MPa under dynamicloading. From these results, it is clear that th
47、erewas a significant reduction in stress on the motoradapter with the new design. The reducer housingand the motor adaptor will not fail under runningloads.Based on the FEA research results, optimizationproposalsaremadetoincreasethestructuralinteg-rity of the alignment free drive and reduce thechanc
48、e of failure. The suggestions are:1. Modify the four (top and bottom) bottom mount-ing bars so that it extends the full length of themotoradapter. Thisallowsforagreaterloaddis-tribution of the reaction forces caused by thefixed torque arm. This larger contact area willnotcausehighstressesontheintern
49、alstructuraltubing. This becomes even more important asthedesignisappliedtolargercapacityreducers,couplings, and motors. These extended barscan also be used as a skid-pad, that will aid intransportation, and will also allow the reducer tosit on the ground, if need be.a) Inner structural tubing b) Reducer side of motor adaptor plateFigure 10. Dynamic random analysis stress distribution82. The analyses shown are for the case where theexternal torque load is applied in the counter-clockwisedirectiontotheoutputshaft, anddriveisconstrainedinthet
