Introduction toWorm Gearing

J:ames IK. SimonelliiJKS & Associaltes,BrecksvUle, OH

Wonn gears are among the oldest types ofgearing ..but that does not mean they are obso-lete. antiquated technology, The main reasonsfor the bad experiences some engineers havewith worm gearing are misapplication andmisuse. No form of gearing works for everyapplication. Strengths and weaknesses versusthe application must be weighed to decidewhich from of gearing to use. For properapplication and operation of worm gears, cer-tain areas that may differ from other types ofgearing need to be addressed.

The BasicsWorm gear reducers are quiet, compact,

and can have large reduction ratios in a singlestage. The ideal ratio range for worm gear-ing is 5: 1 to 75: 1. This is the general rangefor most catalog reducers. Ratios of 3: 1 to120: I are practical and have applicationsthat are very successful. For ratios below3: 1. worm gearing is not a practical solu-

Axlal Movement

tion for most applications, and other formsof gearing should be considered. Worm gear-ing for ratios above the ranges mentioned aregenerally more practical as part of a multi-stage reduction.

In service, worm gears survive large over-loads and high shocks. When properly ap-plied. worm gearing can offer excellent per-forrnance and cost savings. Worm gearing hasan inherent 200% overload (i.e .• 3x rating)capacity in its rating. Other forms of gearingdo not have this built-in ervice factor. There-fore when sizing a worm gear set. a lowerservice factor than normal can be used.

Explanation of HandThe purpose of left- and righi-hand gearing

is to cbange the relative rotation ofthe worm tothe gear. Hand refers to the direction of axialthread movement as the worm is rotated. Ifyoupoint your thumb in the direction of ax ial move-ment and curl your fingers in the direction of

Axia.i Movement

Worm Thread

Left Hand

Worm Thread

·34 GE-'R TECHNOlOGV

Fig. 1 - Comparison of lett and right hand.

RightHand:

rotation, the hand that corresponds to the wormis the hand of the gear set. (See Figs .. 1&2.)Bolts are a simple example. Normally they areright. handed, and experimenting with a nut andbolt win help to clarify this description.

Right-hand gear sets, like bolts, are theindustry standard. More right-hand gear ratiosare available as standard items, and most manu-facturers win supply right-hand gearing unlessotherwise pecified, This does not mean thereis a flaw in left-hand gearing, but left-handratios may not be as readily available.

B.ack DrivingRunning a worm gear set with the gear

(worm wheel) as the input member is corn-monly caUed back driving, Back drive effi-ciency of a worm gear set is lower than itsforward drive efficiency. By varying design,the back drive efficiency can be reduced tozero, a in a self-tacking or irreversible gearset. ]f the gear tries to drive the worm, internalfriction causes the mesh to lock. NO' matter howmuch torque is applied to tile gear haft, me hfriction increases proportionally, preventingrotation. This is the same principle that keeps anut and bolt from unscrewing under an appliedtension load.

Back driving call occur in many applica-tions. A worm gear speed increaser is the mostobvious, but it is rarely used because of its [owefficiency, It also occurs in lifting applications,such as cranes, hoists, and crank arms ..Whenlowering the load. the gear is the input member.Worm rotation controls the rate of descent.Also, during braking or coast-down, the mo-mentum ofa device will back drive a worm ..

A self-locking worm gear can be designedby making the lead angle le than thefr.ictiollangle, which is defined as the arc tangent ofthe coefficient of friction, The static coeffi-cient of friction i .20 to ,15, equating to afriction angle of 11.3° to 8.5°. Vibration in anon-rotating gear set can induce motion in thetooth contact The mesh velocity is zero, butthe tooth contact is dynamic, At a mesh ve-10cHy of zero, the theoretical dynamic coef-ficient of friction is . J 24, or a friction angleof 7.0° ..TOoprovide a afety factor, a 5.000leadangle is recommended as the upper limit ofself-Iocking.aad a ]5.0° lead angle is recom-mended as the lower limit to assume a worm

,-","","",

*-.....,

,

~~

LeftHand

RightHand

CWWorm(), CW Gear

,-

~ CCWWorm .1ll.1.1(\~ CWGear $

- - - .....::.J

Fig. 2 • Relative rotations.

100

90

801')' 70r;;:

.~ 60.~w 50E-~ 40:i;n, 30

20

10

o0.01

Worm Gear Back Drive 'EfficiencyEfficiency vs. Rubbing Velocity

Various Lead Angles

Iii, , ~,

--- /"1--"-:::1-,

130---- '// /

I ""'r,

~..-/ II/

l-{j,5 ........v //

.1101 /

~ I~ ,

I I

/ II,

0.1 1000 10000 I10 100Rubbing Velocily (fpm)

-

Fig.3 • Worm gear back drive efficiency.

gear will back drive.James K. Simonellii.Back drive efficiency decreases with de- P. E., is a power IraiIS'

creasing speed. The slope of this curve is expo- mission consultant. Henential and is affected by the lead angle. (See has ovenen year . expe-

rience in product designFig. 3.) This factor should be considered when and troubleshooting wtth

sizing a brake and its rate of application. Often ap plications ran gingfrom .I"IIJall COflSU/Ilerllp,

a brake placed on the worm can be smaller than pliances 10 large steelnormally anticipated. Self-locking worm gear mill drives.

MARCH/APRil 1993 :35

sets will coast because of dynamic effects.Using a brake on self-locking designs must

be thoroughly analyzed. Most brakes have anincreasing torque rate when applied. Also, theefficiency will be decreasing during slow down.This double effect can cause the effective brak-ing torque to rise at a surprising rate, causinga sudden stop .. High inertial loads with self-locking designs should have controlled motorspeed ramp down for braking.

On the other hand. back drive efficiencyincreases with increasing speed. Therefore aconstant back driving torque restrained only bya worm gear will havearate of acceleration thatincreases exponentially. This is a very impor-tant point to remember when designing hoists ..Unless it is properly designed, relying solely onself-locking mechanism to suspend a load maybe dangerous. The load may stay suspendeduntil an outside influence starts a vibration inthe gear mesh. At first, the load willcreepslowly. As it falls, it accelerates at an expo-nentially increasing rate.

Since many factors influence the coefficientof friction, gear set designs should be te ted fortheir back drive suitability. Break-in ofagear setwill reduce the coefficient of friction. This maymake a gear set self-locking when it is new andnot self-locking after use. Also, synthetic lubri-cants can have an effect on the coefficient offriction and may be used in the field without theknowledge of the gear designer,

If elf-locking is critical to safety, a brake or"ba.ck stop" should be used, A back stop is aclutch device that permits rotation in one direc-tion only. It is sometimes referred to as a "Sprag"

4b - Full Load

or "roller" dutch and is commonly u ed onconveyors that lift material to prevent reversalif power is lost.

"Plugging" is a method of braking gener-al1y used in large crane wheel drives that usereversal of the drive motor ..Plugging applica-tions can cause extremely high torque spikes.The worm system inertia consists of the worm,drive motor, and any miscellaneous compo-nents. The gear system inertia consists of thegear and the entire braked device ..When plug-ging, the worm can reverse rotation before thedrive train loads ill the back drive direction.The worm system's momentum is in a directionopposite the gear system. At. impact, the wormmust again reverse rotation to follow the gear,crossing a point where the mesh rubbing veloc-ity is zero. The gear system's momentum willgenerate whatever torque spike is required toforce the worm to reverse rotation a.nd over-come the motor plugging torque and the meshback drive efficiency at zero speed.

Torque spikes are a transient impact effectand not a problem when the system is properlydesigned, Plugging designs should limitthe II eof brittle materials, such as grey cast iron.Bolted joints and drive train mountings shouldbe designed for impact. In wheel drives, thewheel slip torque limit torque spike and can beused a a maximum design point. Peak torquecan be reduced by slowing the rate of reversaL

Contact PatternThe area of contact the worm makes on the

gear as it rotates into mesh is the contact pat-tern. The ideal contact pattern for worm gear-ing uses 90% of the full face, with the remain-

Flanks Show Contact FromBI·Dir,ectional Operation

Entering:Side

Entering

4a - INa-Load

Side

4c • Overload

36 GEAR TECHNOLOGV

Fig.4 - Typical contact patterns of a worm gear set.

ing 10% open. on the entering side (Fig. 4b).This has maximum area for load distributionand still allows oll to. be dragged in for Iubrica-tion. Jf the entering side has contact. (Fig. 4c)the oil would be wiped off the worm as It rotatesinto the gear. Without oil being drawn in, thegear set will not generate an oil film and willquickly fail. (See the section on lubrication formore details.)

Under load the gearbox. worm, and gearwill deflect. These deflections cause the con-tact pattern to spread across the gear face to-ward the entering side ..To compensate for CO[l-

tact pattern spread, the gear can be movedaxiaHy in relationship to. the worm ..This willincrease the open face at no. load (Fig. 4a), so asnot to close off the entering side at fun load. Ano-load pattern of approximately 30% of fuUface Dn the leaving side is desirable.

Since deflection . occur in opposite direc-tions for opposite rotations. the two flanks of agear tooth cannot be directly in line ..The flanksneed [0 be shifted axially with respect to eachother when the gear is cut. The axial movementof the gear required for the contact pattern to gofrom 90% full face to 90% full face 01'1 theopposite tooth flank is the total shift. Total shiftanticipates deflections that will occur from fullload forward to full load reverse.

The no-load contact pattern is determinedby lightly coating the worm threads with Prus-sian Blue (i.e .. high spot blue). This transfers tothe gear teeth when rotated by hand. Althoughnot required, coating the gear teeth with amixture of powdered orange paint pigment andgrease makes the pattern easier to. see. Theorange grease paint improves the contrast ofthe blue transfer pattern and adds lubricant tothe mesh. To observe the contact pattern underloaded conditions, a coat of layout blue can besprayed on the gear teeth. This will quicklywear off, revealing the fun load contact pattern.Be sure the surface is oil-free when sprayingand wait until the blue dries before operation ..Oil may wash the coating off if it is not com-pletely dry.

In severe applications under heavy loads.the fuUy loaded pattern should be checked.The amount of shift cut into a gear may notcompensate for an overly flexible housing orhigher-than-anticipated loads. For one direc-

Shim to adjust bearing'r---~-- end play and adjust -~---,

contact pat1ern.

Sa

Shim to adjust bearing end play -

Shim to adjust gear contact

5b

-- -

Fig. 5 - Typical gear shaft assemblies.

tion loading, such as hoists or conveyers, hift-cut into a gear is nota major concern. Since theopposite flank is never loaded, the pattern isadjusted on the drive flank only, ignoring thenon-drive flank. When adjusting the gear tofavor one flank, care must be taken so that thegear does :not lose all of its backlash. If thishappens, the wonn is wedged into the cornerof (be gear. This will generate excessive heatand cause premature failure.

In most reducer designs, axial gear adjust-ment is accomplished by shims placed betweenthe gear shaft bearing caps and the housing(Fig. Sa). First. determine the total shim stockfor proper bearing end play. Then transfer shimsfrom one side to the other until an optimum

MARCH/AP RIL '993 31

38 GfAR TfCHNOLOGY

pattern is obtained. In heavy duty applicationswhere one would like to adjust the gear fullyloaded, moving shims requires disconnectingthe shaft couplings, removing the gearbox fromits mounting, and removing the gear shaft cou-pling. This is a very difficult process in largemachinery. A common method to adjust thegear from one side is to put both thru t bearingsin a carrier on one side (Fig. 5b). The oppositeside is supported by a radial bearing that is freeto move axially. There are other methods ofadjustment, but these are the most common.

PittingGear tooth pitting results from the combina-

tion of several forces. Normal force (referringto a direction 900 to the tooth surface) at thecontact point produces Hertzian stress. Frictionproduces a tangential force, which induces sub-surface shear stress. Friction also generalesheat. Temperature at the contact point is muchhigher than the surroundingarea, Differentialthermal expansion (the phenomenon that cancause a glass to break when a hot liquid ispoured into it) induces stress.

Constant cycling as the tooth goes throughthe mesh can cause a. surface fatigue crack.Oil inthe gear mesh is underextreme pressurefrom contact forces. The oil is forced into thefatigue crack, and hydrostatic pressure tries tolift a piece out. Continuing cycles cause thecrack to encircle the high stress area. Thecrack grows deeper. until a piece literally popsout, leaving a pit

In most gearing, apitted tooth surfacesignals impending failure. For worm gearing,pitting is part of normal operation. Correctivepining is a break-in process. In manufacturinga worm, the thread is generated by a continu-ous line that can be described by the grindingwheel. It produces a continuous (i.e., smoothand uniform) surface curved in all threeplanes ..The gear is hobbed by a gashed cut-ting tool that is in effect a worm having adisconriuuous or interrupted surface. It pro-duces gear teeth which have a series of shortflats or discontinuous surfaces that approxi-mate the desired tooth form. Because of theflats, the gear tooth form is imperfect. Wheretwo flats join there must be a peak. At such apoint, the contact street would be infinite i.fdeformation did not occur,

The break-in process is the gear tooth formbeing improved by the worm. This is done byelastic or inelastic deformation, wearing awaythe high spots or pining them away. After themany high spots are either worn or pittedaway, the worm rides on the larger flat areas.The pit areas retain pools of oil, which helpsupport the load by hydrostatic pressure andaid in lubrication. Corrective pitting ceasesafter a sufficient area has been developed tosustain the load and normal wear takes over.A new worm gear will pitatan alarming rate,then quickly stop. No additionalpitting willoccur for a long time. Then the surface winagain pit rapidly and quickly stop, the cyclerecurring throughout the life of the gear ..

Destructive pitting is a case of the gear notbeing able to correct itself enough to supportthe imposed load. It is the result of overload,improper gear adjustment, improper tooth pro-file, or improper lubrication. In thi case, pit-ting continues until the gear tooth surfaces arecompletely destroyed ..This is not a commonproblem, because most errors large enough tocause failure will normally how up as thegearbox overheating.

MaterialsWorm gearing has a high sliding compo-

nent in its tooth meshing action. Sliding con-tact materials are selected to make one mem-ber hard and trong and theother soft andductile, Friction is generally proportional tothe combined hardness of the mating sur-faces, Two bard surface cannot deform tobroaden the contact area and distribute thecontact stress. By hardening only one partand having the other ductile, the combinedhardne s is increased, while still being ableto distribute stress. Also, using dissimilarhardness reduces the chance for galling. Steeland bronze have been the materials of choicebecau e they balance strength, ductility, lu-bricity. and heat dissipation. Shaft bushingsare common examples of sliding componentsusing this arrangement.

The worm is the hard member, and the gearis the ductile member. There are several rea-sons for this arrangement COil tact stress tinboth members is equal. The worm goes throughmore contact. cycles because of the ratio of thegear set. Compared to steel, bronze has a

lower strength, a lower endurance ratio. and ahigher number of cycle required forinfinitelife. Fig. 6 uses these factors in a generalized,theoretical SoN curve. Stress levels that havea finite life for bronze would have an infiniteIife for teet Since the bronze will fail at afewer cycles, it i .used for the member requir-ing the fewest cycle.

Gear mesh reaction forces are equal andopposi.te in:both members. The worm is muchsmaller in diameter than the gear and has agreater span between supports. Therefore bend-ing stress is greater in the worm, requiring it tobe made from the stronger material.

Manufacturing methodsal 0 playa part inmaterial choice. Grinding is generally usedfor accurate finish of high-hardness, heat-treated steels. Grinding the worm is a simpleprocess, using the flank of a traight-sidedgrinding wheel, Grinding the gear requires acomplicated process using a form dressedgrinding wheel and a three-axis grinder.

Tin bronze has proved to be the most suc-cessful alloy for worm gears. It. has a lowcoefficient of friction and a low rate of wear.Good heat conduction carries away heat gen-eratedin the mesh and dissipates it throughoutthe gear. Aluminum bronzes have higherstrength. but also a higher coefficient of fric-tion. A less obvious disadvantage of tile higherstrength alloys is lower ductility. Theoreticalcontact between a worm and gear is a line. Inpractice. the bronze deflects under load broad-ening the contact line to an area. The materialdeflects. until the contact area broaden enoughto support the load. A low-ductility materialmay have localized failure before reaching alarge enough area .. Small contact areas of alower dnctility material have higher localizedcontact temperature • which further increasethe sub-surface tresses.

The unique properties of tin bronze can betraced to its grain structure. When the bronzesolidifies, partial segregation of the copperand till occurs. High tin area or grains arecommonly called the delta phase. Hardnessof the delta phase :is approximately 320Brinell, The high capper matrix supporting itis approximately 145 Brinell, The hard grainsprovide wear resistance and help reduce fric-tion. The softer matrix allows surface defer-

marion to distribute stress. A simple modelwould be to picture marble (delta phase)imbedded in clay (matrix).

Alternate gear materials may increase cer-tain properties, but loses in others will tendto make them unsuitable for general use. Forspecial applications bronze alloys other thantin bronze may perform better. Gear materi-als, such as cast iron, plastic, and even steel,have worked very welJ in certain applica-tions. Each application must be thoroughlyanalyzed by a. gear engineer before selectingalternate materials.

Worms are generally made from an alloysteel. Steel worms can be divided into hard-ened and non-hardened. Hardened worms aresuperior in most application . When urfacehardness of approximately 58Rc is used, sev-eral benefits are gained. Material strength isincreased, friction is lowered, and wear isreduced. Often a. worm can be reused after thegear has worn out.

Non-hardened refer to the surface beinglower than the typical 58 Re' Non-hardenedworms may actually have a heat treatment tobring up the core hardne s for inc reased strength.In industrial applications, a core hardness of300 Brinell is typical. Non-hardened wormsare useful in applications with low continu-ous power and very high peak or shock loads,The e applications are most often machineadjustments or mechanisms that are infre-quently activated. Heat treating for increasedsurface hardness may be eliminated in lowpower applications to decrease cost. ~fa worm

GeneralizedTheoreticalS·N CurveCycles vs. Stress

Steel

Infinite Ufetor Sleel

Finite Life for BronzeIBronze

Cycles

Fig. 6 - Generalized theoretical S·N curve.

MARCH/APRIL '993 3,9

is used with a cast iron or steel gear.jt shouldbe non-hardened.

Backlash MeasurementBacklash is the measure of the free clear-

ance between the worm and the gear teeth.Measurement is done by locking the wormagainst rotation, setting a dial indicator on agear tooth at the pitch radius, and rocking thegear back and forth. The total. indicator read-ing is the measurement of backlash. Lockingthe gear and measuring worm rotation doesnot measure backlash. In an assembled unitwhere the gear teeth are not readily acces-sible, backlash can be approximated by plac-ing the indicator on any convenient point thatis fixed to the gear, such as a shaft keyway orcoupI.ing. This measurement must be multi-plied by the ratio of the gear pitch radius tothe measurement radius. Note that if the e-lected point is on the radius smaller than thepitch radius a multiplication of measurementerror will occur.

Backlash =(Measurement) x Gear Pitch Radius

Measurement Radius

LubricationWorm gearing has a high slide-to-roll ratio

when compared to other types of gearing.Because of a high sliding component, it reliesheavily on the generation of an oil film be-tween the worm and gear. The oil film pro-duces an effect similar to what happens whena speeding car hits a rain puddle. The car tirehas a tendency to float on a wedge of water.In a car this is called hydroplaning: in gear itis called elasto-hydrodynamic lubrication(EHL). This is a simplistic description withother modes of lubrication coming into play,depending on conditions, bUI it gives thegeneral idea.

For EHL to be the only lubrication mode, itmust generate a film thickness greater than thesurface roughness ofthe contacting parts ..Filmthickness is proportional to the sliding velocityand lubricant viscosity and inversely propor-tional to the unit load. High unit loads possibleat the relatively low speed of worm gearingrequires a very high viscosity lubricant. Vis-cositie of over 400 cSt at 40°C are normallyused to prevent premature wear and high con-

,40 ClEAR TECHNOLOGY

------------------~

tact temperatures. Under high loads the filmcan collapse, causing the surfaces to contact,This is called "boundary lubrication ." In thislubrication mode, other properties (i.e., lubric-ity or sIipperiliess) of the lubricant becomemore important than the viscosity. In a wormgear set, a mixture of EHL and boundarylubrication are at work.

A satisfactory lubricant for most averageapplications is a AGMA 7 compounded oil,Low speeds require the higher viscosity ofAGMA 8 compounded oil. Both are petro-leum ba ed mineral oils compounded with3% to 10% fatty oils. These lubricants aresometimes referred to as steam cylinder oils.The compounded oil provides lower frictionand better wear characteristics than a: traigbtmineral oil. At the high pressures and tem-perature in the contact area, a chemical reac-tion occurs on the tooth surface, forming aprotective skin.

Extreme pressure oils (EP oils) are anothertype of lubricant that uses a surface actingchemistry. Most EP oils lise sulfur, phospho-rus, and/or chlorine additives, and are de-signed to work in steel-an-steel applications.When these oils are used with bronze underhigh temperature and pressure, conditions com-mon ill the me h contact, the chemical reac-tion can go awry. The surface of the bronzecan begin to flake off, causing massive wear,and intergranular stress corrosion call. cause theteeth to break. There are EP oils designed foruse with bronze that use a different additivepackage. and in certain applications a standardEP oi] may work very wen. When selecting aEP oil for bronze gearing make sure it wascarefully reviewed.

Synthetic lubricants are aliso very com-mon. They are mote viscosity-temperaturestable than mineral oils. This allows one lubri-cant to provide adequate service over a broadertemperature range, They have longer servicelife. reducing the number of oil changes re-quired. They reduce wear and friction, in-creasing gearbox Iife ..Efficiency increase of20% of the lost power are possible. Undersevere conditions properly selected syntheticoils are outstanding. Many companies havefound cost advantages using the more expen-sive synthetic oil for normal applications .•