1、10FTM17AGMA Technical PaperSelf-Locking Gears:Design and PotentialApplicationsBy Dr. A.L. Kapelevich, AKGears,LLC and Dr. E. Taye, ETAnalytical Engineering, LLCSelf-Locking Gears: Design and Potential ApplicationsDr. Alexander L. Kapelevich, AKGears, LLC and Dr. Elias Taye, ET AnalyticalEngineering,
2、 LLCThe statements 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.AbstractIn most of the gear drives, when the driving torque is suddenly reduced as a result of power off, torsionalvibra
3、tion, power outage or any mechanical failure at the transmission input side, then gears will be rotatingeither in the same direction driven by the system inertia, or in the opposite direction driven by the resistantoutput load due to gravity, spring load, etc. The latter condition is known as backdr
4、iving. During inertial motionor backdriving, the driven output shaft (load) becomes the driving one and the driving input shaft (load)becomes the driven one. There are many gear drive applications where the output shaft driving is lessdesirable. In order to prevent it, different types of brake or cl
5、utch devices are used. However, there are alsosolutions in gear transmission that prevent inertial motion or backdriving using self-locking gears without anyadditional devices. The most common one is a worm gear with a low lead angle. In self-locking worm gears,torque applied from the load side (wor
6、m gear) is blocked, i.e. cannot drive the worm. However, theirapplication comes with some limitations: the crossed axis shafts arrangement, relatively high gear ratio, lowspeed, low gear mesh efficiency, increased heat generation, etc.The paper describes the design approach as well as potential appl
7、ications of the parallel axis self-lockinggears. These gears, unlike the worm gears dont have such application limitations. They can utilize any gearratio from 1:1 and higher. They can be external, internal, or incorporated into the planetary gear stage ormultistage gear system. Their gear mesh effi
8、ciency is significantly higher than the worm gears and closer toconventional gears. As a result they generate less heat. The self-locking can be designed to prevent either theinertia driving, or backdriving, or both. The paper explains the principle of the self-locking process for gearswith symmetri
9、c and asymmetric teeth profile, and shows their suitability for different applications. It definesthe main parameters of gear geometry and operating conditions. It also describes potential self-locking gearapplications and references to related publications.Copyright 2010American Gear Manufacturers
10、Association1001 N. Fairfax Street, Suite 500Alexandria, Virginia, 22314October 2010ISBN: 978-1-55589-992-93Self- Locking Gears: Design and Potential ApplicationsDr. Alexander L. Kapelevich, AKGears, LLCand Dr. Elias Taye, ET Analytical Engineering, LLCIntroductionIn most gear drives, when driving to
11、rque is suddenlyreduced as a result of power off, torsional vibration,power outage, or any mechanical failure at thetransmission input side, then gears will be rotatingeither in the same direction driven by the systeminertia, or in the opposite direction driven by the res-istant output load due to g
12、ravity, spring load, etc.The latter condition is known as backdriving. Duringinertial motion or backdriving, the driven outputshaft (load) becomes the driving one and the drivinginput shaft (load) becomes the driven one. Thereare many gear drive applications where output shaftdriving is undesirable.
13、 In order to prevent it,different types of brake or clutch devices are used.However, there are also solutions in the gear trans-mission that prevent inertial motion or backdrivingusing self-locking gears without any additionaldevices. The most common one is a worm gear witha low lead angle. In self-
14、locking worm gears, torqueapplied from the load side (worm gear) is blocked,i.e. cannot drive the worm. However, their applica-tion comes with some limitations: the crossed axisshafts arrangement, relatively high gear ratio, lowspeed, low gear mesh efficiency, increased heatgeneration, etc.Also ther
15、e are parallel axis self-locking gears 1, 2.These gears, unlike the worm gears can utilize anygear ratio from 1:1 and higher. They have thedriving mode and self-locking mode, when theinertial or backdriving torque is applied to the outputgear. Initially these gears had very low ( 50%.Another conditi
16、on of self-locking is to have asufficient friction angle, , to deflect the force Fbeyond the center of the pinion O1. It creates theresisting self-locking moment (torque) T1=F L1,L1is a lever of the force F1. This condition can bepresented as L1min0or arctan1(1 + u) tanw u tana2 (1)orf 1(1 + u) tanw
17、 u tana2(2)whereu is gear ratio,=n2n14n2is number of gear teethn1is number of pinion teetha2is involute profile angle at the tip of the geartooth= arccosdb2da2Design of self- locking gearsSelf-locking gears are custom. They cannot be fab-ricated with the standards tooling with, for example,the 20 pr
18、essure and rack. This makes them verysuitable for Direct Gear DesignR5, 6 that providesrequired gear performance and after that definestooling parametersa) Conventional gearsb) Self-locking gearsKey1 Driving pinion2 Driven geardb1,db2Base diametersdp1dp2Pitch diametersda1,da2Outer diametersT1Driving
19、 pinion torqueT2Driven gear torqueT2Driving torque, applied tothe gearT1Driven torque, applied tothe pinionF Driving forceF Driving force, when thedriving torque is applied tothe gearO1Center of the pinionO2Center of the gearL1Lever of the force FL2Lever of the force FwOperating transverse pres-sure
20、 angle Arctan (f) - friction anglef Average friction coefficientNOTE: Blue shows the normal driving operation, red shows the case when the driven gear becomesthe driving by output load.Figure 1. Conventional (a) and self-locking (b) gears driven by output load5a) Conventional gearsb) Self-locking ge
21、arsNOTE: Blue shows the normal driving operation, red shows the case when the driven gear becomesthe driving by inertia.Key1 Driving pinion2 Driven geardb1,db2Base diametersdp1dp2Pitch diametersda1,da2Outer diametersT1Driving pinion torqueT2Driven gear torqueT2Driving torque, applied tothe gearT1Dri
22、ven torque, applied tothe pinionF Driving forceF Driving force, when thedriving torque is applied tothe gearO1Center of the pinionO2Center of the gearL1Lever of the force FL2Lever of the force FwOperating transverse pres-sure angle Arctan (f) - friction anglef Average friction coefficientFigure 2. C
23、onventional (a) and self-locking (b) gears driven by inertiaDirect Gear DesignRpresents the symmetric geartooth formed by two involutes of one base circle(Figure 3). The asymmetric gear tooth is formed bytwo involutes of two different base circles(Figure 3b). The tooth tip circle daallows avoidingth
24、e pointed tooth tip. The equally spaced teeth formthe gear. The fillet profile between teeth is designedindependently to avoid interference and provideminimum bending stress.The operating pressure angle wand the contactratio are defined by the following equations:for gears with symmetric teethinv 2=
25、11 + uinv v1+ u inv v2n1(3)=n12 tan a1+ u tana2 (1 + u) tanw(4)for gears with asymmetric teeth inv 1d+ inv 1c+ uinv 2d+ inv 2c2 n1inv wd+ inv wc=11 + u(5)6a) Symmetric tooth b) Asymmetric toothKeydaTooth tip circle diameterdbBase circle diameter Involute intersection angleSubscriptsd Drive flank of
26、theasymmetric toothc Coast flank of theasymmetric toothFigure 3. Direct Gear DesignRtooth profile definition;d=n12tan ad1+ u tan ad2(1 + u)tan wd(6)c=n12tan ac1+ u tan ac2(1 + u)tan wc(7)whereinv (x) is involute function of the profile angle x(in radians)=tanx - xConditions (1) and (2) show that sel
27、f-lockingrequires high pressure and high sliding friction in thetooth contact. If the sliding friction coefficientf = 0.1 - 0.3, it requires the transverse operatingpressure angle to w=7585.Asaresult,thetransverse contact ratio 1.0 (typically 0.4 0.6).Lack of the transverse contact ratio should be c
28、om-pensated by the axial (or face) contact ratio toguarantee the total contact ratio = + 1.0.This can be achieved by using helical gears(Figure 4a). However, helical gears apply the axial(thrust) force on the gear bearings. The doublehelical (or “herringbone”) gears (Figure 4b) allow tocompensate th
29、is force.a) Helical gear b) Double helical gearsFigure 4. Self-locking gear design7High transverse pressure angles result in increasedbearing radial load that could be up to 4-5 timeshigher than for the conventional 20 pressure anglegears. Bearing selection and gearbox housingdesign should be done a
30、ccordingly to hold thisincreased load without excessive deflection.Application of the asymmetric teeth forunidirectional drives allows for improvedperformance. For the self-locking gears that areused to prevent backdriving, the same tooth flank isused for both driving and locking modes. In thiscase,
31、 asymmetric tooth profiles provide much high-er transverse contact ratio at the given pressureangle than the symmetric tooth flanks. It makes itpossible to reduce the helix angle and axial bearingload. For the self-locking gears that used toprevent inertial driving, different tooth flanks areused fo
32、r driving and locking modes. In this case,asymmetric tooth profile with low-pressure angleprovides high efficiency for driving mode and theopposite high-pressure angle tooth profile is usedfor reliable self-locking.Testing of self-locking gearsSelf-locking helical gear prototype sets were madebased
33、on the developed mathematical models. Thegear data are presented in the Table 1. The testgears are presented in Figure 5.The schematic presentation of the test setup isshown in Figure 6. The 0.5 Nm electric motor wasused to drive the actuator. An integrated speed andtorque sensor was mounted on the
34、high-speedshaft of the gearbox and Hysteresis BrakeDynamometer (HD) was connected to the lowspeed shaft of the gearbox via coupling. The inputand output torque and speed information werecaptured in the data acquisition tool and further ana-lyzed in a computer using data analysis software.The instant
35、aneous efficiency of the actuator wascalculated and plotted for a wide range of speed/torque combination. Average driving efficiency ofthe self- locking gear obtained during testing wasabove 85%. The self-locking property of the helicalgear set in backdriving mode was also tested.During this test th
36、e external torque was applied tothe output gear shaft and the angular transducershowed no angular movement of input shaft, whichconfirmed the self-locking condition.Table 1. Testing of self-locking gearsGear Input OutputNumber of teeth 6 11Normal module, mm 1.500Normal pressure angle 63Helix angle o
37、n the pitchdiameter75Transverse pressureangle82.5Transverse contact ratio 0.50Axial contact ratio 2.00Figure 5. Helical self-locking test gears8Figure 6. Helical self-locking gear actuator test benchPotential applicationsInitially self-locking gears were used in textile in-dustry 2. However, this ty
38、pe of gears has manypotential applications in lifting mechanisms, as-sembly tooling, and other gear drives where thebackdriving or inertial driving is not permissible.One of such application 7 of the self-locking gearsfor a continuously variable valve lift system wassuggested for an automotive engin
39、e.SummaryS A principle of work of the self-locking gears isdescribed.S Design specifics of the self-locking gears withsymmetric and asymmetric profiles are shown.S Testing of the gear prototypes has provedrelatively high driving efficiency and reliableself-locking.S The self-locking gears may find m
40、anyapplications in various industries. For example,in a control systems where position stability isvery important (such as in automotive,aerospace, medical, robotic, agricultural etc.)the self-locking will allow to achieverequired performance.S Similar to the worm self-locking gears, theparallel axi
41、s self-locking gears are sensitive tooperating conditions. The locking reliability isaffected by lubrication, vibration, misalignment,etc.S Implementation of these gears should be donewith caution and requires comprehensivetesting in all possible operating conditions.References1. Popper ,J.B., Coope
42、rating Wedges includingmating worms, US Patent 2973660, 19612. Munster, N.S., Tzarev, G.V., Self-lockingCylindrical Gears, Theory Mechanisms andMachines, Publications of the TashkentPolytechnic Institute, 1968, #30A, 3 15 (inRussian)3. Iskhakov, T.G., Self-locking in GearMechanisms, Publications of
43、the KazanAviation Institute, 1969, #105, Vol. 105, 3 15(in Russian)4. Timofeev, G.A., Panukhin, V.V., Self-lockingCriteria Analysis, Vestnik Mashinostroenia,September 2003, 38(inRussian)5. Kapelevich, A.L., Kleiss, R.E., Direct GearDesign for Spur and Helical Gears, GearTechnology, September/October 2002, 29 - 356. Kapelevich, A.L., Geometry and design ofinvolute spur gears with asymmetric teeth,Mechanism and Machine Theory, 2000, Issue35, pp. 117-1307. Taye, E., Actuator with self-locking helicalgears for a continuously variable valve liftsystem, US Patent #US2009/0283062 A1(pending)
