AGMA 06FTM04-2006 Precision Planetary Servo Gearheads《精密行星伺服齿轮头》.pdf

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1、06FTM04Precision Planetary Servo Gearheadsby: G.G. Antony, Neugart USA LPand A. Pantelides, mG miniGears North AmericaTECHNICAL PAPERAmerican Gear Manufacturers AssociationPrecision Planetary Servo GearheadsGerhard G. Antony, Neugart USA LP and Arthur Pantelides, mG miniGearsNorth AmericaThe stateme

2、nts and opinions contained herein are those of the author and should not be construed as anofficial action or opinion of the American Gear Manufacturers Association.AbstractModern automated machineries are increasingly using flexible high dynamic servomotors because of theirability to speed up and f

3、lexibly automate complex motions these machineries need to perform. Planetarygearheadsareusedfrequentlyinconjunctionwithservomotorstomatchtheinertias,lowerthemotorspeed,boost the torque, and at the same time provide a sturdy mechanical interface for pulleys, cams, drums andother mechanical component

4、s.This paper addressing following topics:- main reasons why the planetary (epicyclical gear systems) are the preferred choice for ”servoapplications” (applications using servo motors);- what influencing the positioning accuracy repeatability of a planetary servo gear;- helical gears in planetary sys

5、tems;- the rating practices establishing a transparent ”comparability” of different torque listings;- introduction of a simple reliable method to the required gearbox torque rating for a servo-applicationbased on the selected motor toque data.Copyright 2006American Gear Manufacturers Association500

6、Montgomery Street, Suite 350Alexandria, Virginia, 22314October, 2006ISBN: 1-55589-886-61Precision Planetary Servo GearheadsGerhard G. Antony, PhD, Neugart USA LPwith contributions from Arthur Pantelides, mG miniGears North AmericaBecause of their versatility as well as their ability tospeed-up and a

7、utomate a wide-range of highly-complex motion sequence programs required inmany of todays industries, computer-controlled,programmable, highly dynamic-capable servo mo-tors areincreasinglybeingusedinmodernmachin-ery required in complex automation applications.Precision planetary gearheads are freque

8、ntly usedin conjunction with such servo motors in order to:balance inertial loading conditions seen during fre-quent speed cycling sequences, decrease motorspeeds, and boost torque, while at the same time,provide a robust mechanical interface for pulleys,cams, drums, and other mechanical transmissio

9、ncomponents.This paper shall present a foundation and funda-mental approach for understanding why theplane-tary system is thepreferreddesignchoice for servogearheads; clear up some misconceptions aboutplanetaryservo gearheads;compare ratingpractic-esbyestablishingatransparentcomparabilityofdif-feren

10、ttorquelistings;andintroduceasimpleandre-liable method of determining the required gearboxtorque rating for a selected servo motor/gearboxapplication.Main topics covered in the paper shall be:- The planetary (epicyclic) gear system as the“system of choice” for servo gearheads;- The best “balanced” p

11、lanetary ratio from atorque density point of view;- The gearhead design influence on positioning-accuracy and repeatability;- Typical dynamic servo applications and servogearhead torque ratings;- How to establish comparative torque ratings;- Sizing/selection of servo gearheads for match-ingAC servom

12、otorsinautomationapplications.1. The Planetary (Epicyclical) GearSystem as the “System of Choice” forServo GearheadsFrequent misconceptions regarding planetarygears systems involve backlash: planetary sys-temsareusedforservogearheadsbecause oftheirinherent low backlash; low backlash is the mainchara

13、cteristic requirement for a servo gearboxes;backlash is a measure of the precision of theplane-tary gearbox.The fact is, fixed-axis, standard, “spur” gear ar-rangement systems can be designed and built justas easily for low backlash requirements. Further-more, low backlash is not an absolute require

14、mentforservo-based automationapplications. Amoder-ately-lowbacklashisadvisable(inapplicationswithvery high start/stop, forward/reverse cycles) toavoid internal shock loads in the gear mesh. Thatsaid, with todays high-resolution motor-feedbackdevices andassociatedmotioncontrollersit iseasyto compensa

15、te for backlash anytime there is achange in the rotation or torque-load direction.If,forthe moment,we discountbacklash, thenwhatare the reasons for selecting a more expensive,seeminglymorecomplexplanetarysystemsforser-vo gearheads? What advantages do planetarygears offer?High Torque Density - Compac

16、t DesignAn important requirement for automation applica-tions is hightorquecapability inacompact andlightpackage. This high torque density requirement (ahightorque/volumeor torque/weight ratio) is impor-tant for automation applications with changing highdynamic loads in order to avoid additional sys

17、teminertia.Depending upon the number of planets, planetarysystems distribute the transferred torque throughmultiple gear mesh points. This means a planetarygear withsay three planets cantransfer threetimesthe torque of a similar sized fixed-axis “standard”spur gear system. Reference Figure 1.2Fixed

18、axis “standard” gear Planetary “Epicyclical” gear systemFigure 1.Rotational Stiffness/ElasticityHigh rotational stiffness, or minimal elastic windup,is important for applications with elevated position-ing accuracy and repeatability requirements; espe-cially under fluctuating loading conditions. The

19、 loaddistribution unto multiple gear mesh points meanstheloadissupportedbyNcontacts(whereN=num-ber of planet gears) increasing the torsional stiff-ness of the gearbox by factor N. This means itcon-siderably lowers the lost motion compared to asimilarsizestandardgearbox;andthisiswhatisde-sired.Low In

20、ertiaAdded inertia results in an additional torque/energyrequirement for bothacceleration anddeceleration.Thesmaller gears inplanetary systemresult inlow-er inertia. Compared to a same torque rating stan-dard gearbox, it is a fair approximation to say thatthe planetary gearbox inertia is smaller by

21、thesquare of the number of planets. Again, this advan-tageisrootedinthedistributionor“branching”oftheload into multiple gear mesh locations.High SpeedsServomotors run at high rpm, hence a servo gear-box must also operate in a reliable manner at highinput speeds. For servomotors 3,000 rpm is practi-c

22、ally the standard and in fact speeds are constantlyincreasinginordertooptimizemoreandmorecom-plex application requirements. Servomotors run-ning at speeds in excess of 10,000 rpm are not un-common.Froma ratingpoint ofview withincreasedspeedthepowerdensityofthemotorincreasespro-portionally without an

23、y real size increaseof the mo-tor or electronic drive. Thus Amp rating stays aboutthesamewhileonly theVoltagemust beincreased.An additional, important factor is in regards to lu-brication and operating speed. Fixed-axis spurgears willexhibit lubrication“starvation” andquicklyfailifrunningathighspeed

24、sbecausethelubricantisslung away. Only special means suchasexpensivepressurized forced lubrication systems can solvethis problem. On the other hand, grease lubricationis impractical because of a its “tunneling effect,” inwhich the grease, over time, is pushed away andcannot flow back into the mesh.I

25、nplanetarysystemsthelubricantcannotescapeit is continuously redistributed, “pushed and pulled”or “mixed” into the gear contacts, ensuring safe lu-brication practically inany mountingposition andatany speed. Furthermore, planetary gearboxes canbe grease lubricated. This feature is inherent inplanetar

26、ygearingbecauseoftherelativemotionbe-tween the different gears making up thearrangement.2. The Best “Balanced” Planetary Ratiofrom a Torque Density Point of ViewForeasiercomputationitispreferredthattheplane-tary gearbox ratio is an exact integer (3, 4, 6 .).Since we are so used to the decimal system

27、, wetend to use 10:1 even though this has no practicaladvantaged for the computer/servo/motion control-ler. Actually, as wewill see,10:1orhigher ratiosarethe weakest, using the least “balanced” size gearsand hence have the lowest torque rating.This paper addresses “simple planetary” gear ar-rangemen

28、ts, meaning all gears are engaging in thesame plane. The vast majority of the epicyclicalgears used in servo applications are of this “simpleplanetary” design. Figure 2a illustrates a cross-section of such a planetary gear arrangement withits central sun gear, multiple planets (3), and the3ring-gear

29、. The definition of the ratio of a planetarygearboxshowninthefigureisobtaineddirectlyfromthe unique kinematics of the system. It is obviousthat a 2:1 ratio is not possible in a simple planetarygear system,sincetosatisfy theaboveequationfora ratio of 2:1 the sun gear would need to have thesame diamet

30、er as the ring-gear. Figure 2b showsthesungear sizefor differentratios. Withincreasedratio the sun gear diameter (size) is decreasing.Since gear size effects loadability the ratio is astrong and direct influence factor for the torque rat-ing. Figure 3a below shows the gears in a 3:1, 4:1,and10:1simp

31、lesystem.At3:1ratio, thesun gearislargeandtheplanets aresmall. Theplanets arebe-coming “thin walled” thus limiting the space for theplanet bearings and carrier pins, hence limiting theloadability. The 4:1 ratio is an well-balance ratio,with sunand planets having thesame size. 5:1and6:1 ratios still

32、yield fairly good balanced gear sizesbetween planets and sun. With higher ratios ap-proaching 10:1, the small sun-gear becomes astrong limiting factor for the transferable torque.Simpleplanetary designswith 10:1ratios haveverysmall sun-gears, whichsharply limits torquerating.Addingmoreplanetscanincr

33、easethetorquedensi-tyofthearrangement.Tothiseffectweseethatwithlower ratios additional planet gears can be used;but for higher ratios, such as 10:1, multiple gearsbeyond say 3 planets, would cause interference.This is illustrated in Figure 3b.Ratio =Ring gear DiameterSun gear Diameter+ 1Ratio =Ring

34、gear Number of TeethSun gear Number of Teeth+ 1Figure 2a. Definition of the (Reduction) Ratio for a simple planetary gear arrangement having astationary ring gear. The input is at the sun-gear and output at the planet carrier shaft.Figure 2b. Sun gear size for different ratios4Figure 3a. Planetary g

35、ear ratios and the relationship between sun/planet sizeRatio 3:1 with 5 planets Ratio 4:1 with 4 planets Ratio 10:1max. 3 planets possibleFigure 3b. 10:1 ratios should be avoided unless absolutely necessary from a technical point ofview. If such ratios are used additional consideration must be given

36、 to arrangement/sizevs. rating3. How Positioning-Accuracy and the positioning error is load-dependantsince the wind-up of course depends on the load.Backlash - the clearance between mechanicalcomponents - (such as the backlash of a gearbox)cancontributetothepositioningerrorifthesenseoftherotationort

37、orqueischangedduringtheposition-ing move. Theoverall rotational backlashof agear-box is determined not only by the clearance be-tweenthegearteethinmesh,itisinfluencedalsobythe other components of the gearbox such as thehousing, bearings, shafts, and shaft/hub connec-tion to name a few.Transmission E

38、rror (TE) can be also describedas “the fluctuation of the theoretical reduction ratio”5the output does not follow the input rotation exactlyat the theoretical reduction ratio but fluctuates (+/-)a certain angle during therotation, dueto theincon-sistencies of the gears (gear errors). These includepi

39、tch, lead, profile error, general eccentricity due tonon-optimum positioning/placement, and others.The TE of a gear is directly dependent to the gearprecisionorgearclassoftheparticulargearinques-tion. And, just like the backlash,the overallgearboxTE is influenced by the other components of thegearbo

40、x.Example 1:Given:S Gearhead PLS115S 4:1 ratioS worst case backlash 3 minS rotational stiffness = 20 Nm/arcminS Torque rating 200 NmS Neugart115measuredgearboxtransmissionerror (TE) approximately +/- 1.25 arc min1. WhatistheworstcasepositioningerrorfromtheTE? 1.25 arc min2. What is the worst case po

41、sitioning error due totheBacklashinamotioncyclewithmotiondirec-tion reversal at rated torque load? 3 arc min3. What is the worst case positioning error due tothe Stiffness or “wind-up” in amotion cyclewithmotion direction reversal at nominal torqueload? 200 Nm x 2/20 Nm/arc min= 20 arc minGear Preci

42、sion Class - a number of geometricalmeasurements and associated tolerances anddeviationsforthesedeterminegearprecisionclass.Various national and international organizationshave established standards which define variousgear precision class levels; these include AGMA,ISO, DIN, JIS, and others. It is

43、a frequent miscon-ception that the low backlash is a prerequisite forhigh precision. The fact is that the gear precisionclass has little to no influence on the backlash. Onthe other hand it has a determining influence on theTE as indicated in the example above. Also, asshown, the stiffness can have

44、considerably higherinfluence on the positioning error as opposed to ei-ther the Backlash or the TE, again shown above.Repeatability a measure of how exact a certainpositionis reachedwhenapositioningmotioncycleis repeated a number of times.Influence of the Gearbox Stiffness if therepeated motion cycl

45、e is performed with differentloads the stiffness of the system has a significantinfluence on the repeatability.InfluenceoftheGearboxBacklashIfthemotioncycle is exactly repeated the backlash of the gear-box has theoretically NO influence on the repeat-ability; not even at fluctuating loads.4. Torque

46、Rating of Servo Gearheads inAutomation, Motion Control, and RoboticsApplicationsThe basic limiting factor for electrical devices is thetemperature; more specifically, the instantaneous,orgradualbreakdown ofthe insulationof thedevicedue to temperature, ultimately resulting in a failurecondition. Othe

47、r than the strength of the magnetsused in a particular motor design, or the currents,anddemagnetizationcharacteristics,thetorquerat-ingofanACservomotorismainlydeterminedbyits“thermal loadability.” In a motor the generated heatisproportionalto RxI2xt andtheratinglimitationisthe RMS value of the curre

48、nt (I) and its duration (t).Therefore RMS Torque is proportional to the cur-rent.On the other hand from a mechanical point of view,the basic limiting factors of mechanical devices arethe mechanical stresses, tension, compression,bending, shear, and Hertzian Pressure. The ther-mal loading is secondar

49、y.In virtually all automation applications, frequentlychangingloads createdby duty cycles withmultiplestarts/stops and accelerations/decelerations arepresent and very common in the servo drives asso-ciated with these applications. Even if the externalloads are constant, all major componentsof agear-head are subjected to cyclic mechanical stresses.As an example, we calculate the number of peakload cycles being subjected to the sun gear in amoderate/low cycle automation application. In thecaseofa5:1ratioplanetarygearbox,with3plane