engranajes de precision

8/8/2019 Engranajes de Precision

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326 Gear Train Design and Synthesis

Straight knurl

Figure 7-28 Press-fit gear-to-shaft assembly.

diameter tolerances can be achieved by providing a straight knurl,in Fig. 7-28. However, precise control of concentricity is then lost.

Shrink Fit. This is a special press fit in which the "forcing" is aby substituting temperature effect. The shaft is cooled and/or theheated, and assembly is made with a shrink fit obtained ontemperature equilibrium. This method allows assembly of largerference fits and results in increased torque capacity. However,straining is a danger because of the negatio'n of force in makingassembly and the loss of feel for the generated powerful forces.Mechanical Lock (Fig. 7-29). There are miscellaneous, psimple mechanical locking means such as staking, pegging, rivand spinning. All are relatively simple and inexpensive. Goodcentricity is established by close-fitting a reference mounting diCementing Compounds. A number of reliable cements haveavailable for bonding metals, and metals to plastics. Epoxy resinstrade-named items such as Locktite (made by American Sealantsoffer economical means for f astening elements when other methodsunsuitable because of thin sections and small diameters. Certainpounds, such as Locktite, can be nondestructively unbonded,they are not recommended when disassembly is a normal expThe major disadvantages are that they are less reliable thanicallocks, and there is danger of gear contamination during andapplication of the compound. This means of fastening is no tmended for precision gears.

Molded Assembly (Fig. 7-30). High-production assembly ofgears and shafts can be accomplished by a molding operation in

Gear Mountings and Fastenings 327teeth are simultaneously formed with the blank. With proper toolthe shaft can be positioned while the gear is either die cast ored to it with plastic. Since concentricity and squareness are in theof several thousandths of an inch, the method is not suitable for

,cvH,ion gearing. This objection is overcome if the molding does no tthe teeth bu t leaves them to a later generating operation.

Molding of small gears to shafts can be a simple all-plastic blank-to-arrangement as pictured in Fig. 7-30a. Because nonmetillics havelarge coefficients of expansion and low moduli of elasticity,arger proportion of metal is desired for quality gears requiring plas

tooth material. This is accomplished with a large metallic hub asFig.7-30b.

(a )

(e)

Spun-overmaterial

(b)

(d)7-29 Permanent mechanical lock of gear to shaft: (a) staked gear to

(b) pegging or "dutchman" .,assembly, (e) riveted assembly, (d) spinningbly.


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IiIi

328

c..:::

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+" +"


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330 Gear Train Design and Synthesis

(a)

(b)Figure 7-31 Uear ami bearing arrangements: (a) inhoardgear an d plain cylindrical shaft, (b) outhoard gear an dstepped shaft.

offset by increased fabrication cost and less flexibility in assemblydisassembly.7-13 Bearing Arrangement

:VIost gears are inboard-mounted between bearings, as in l


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332

1Ts

Gear Train Design and SynthesisRange of gear displacement

/ from ideal positionr - 'I-TI IBearing 2 I l - lI I

- = - : - = - : ~ : - = ~ = ~ = ~ I f = X ~ -I II I- - JI II I-t--=.-r-III (a) Gear radial displacement due to bearing clearancesII II II " II u IIt: 2St t, =r-------_ = - ~ - - ____- : I ~ - - - - - - - - -

III

LL nvelope of max. radial displacement(b) Same-direction bearing forces and shaft displacement

1


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,l

334 Gear Train Design and SynthesisEnvelope of eccentric shaftr---------- Icenterlinesfore =0 to 360 /_J-__

I d --t__ / /' 1 "i leal f l - - - // / ,I centerlme I L I e2 \I \ I I l e 2 I e \. ~ . - - - + I \p...-r; I -1/ . _ .--l--._-- ._ - I e

e I // \ I1 1- 1" / \ I//J/-1:..:I- \\ \ eg ;'///'1 / / " e /// ", 1 /"......----_/

m(Mounting dist.)--I >I(Bearing spread)Figure 7-33 General case of bearings with unequal eccentricities and randomphase angle O.

Fig. 7-33-has gear eccentricity according to the expression

egwhere

1 ; ' (mL)2 mL cos ex'\) el" + -Z- - 2elL = V ~ 1 2 + e22 - 2ele2 cos e

. -1 (e2 sin e)x = S in ---LEqual bearing eccentricities are most frequent, and analysis of equa

tion 7-20 indicates a cyclic minimum gear eccentricity versus phangle for mounting location midway between bearings. lVlaximumeccentricities occur for inboard mounting adjacent to the bearings.outboard mounting, eccentricit y is increasingly magnifiedwith'ing overhang. From this we can draw the following conclusions.

1. Outboard-mounted gears will probably magnify radial playeccentricity, th e exact increase depending upon th e length ofoverhang.2. Inboard mounting will probably demagnify eccentricity sincewill be maximum only if the eccentricities are phased alike inbearings.3. I f there is a quality difference betwee n paired bearings, th ebearing (less eccentric ity and play) should be installed nearest th e4. For best precision inboard mounting of gears is preferred.outboard mounting is used, the gear should be located as closepossible to the bearing.

Bearings 3355. When making error analyses of the type described in Chapter 5,magnifying effects of cantilevered gears are not to be overlooked.

Bearingsis in print on th e subject of bearings, and the objective here is

to highlight those features that particularly relate to precisiontrain design. We shall limit the discussion to sleeve and ball bearwhich are the prevalent types of precision gear train bearings.

Bearings. These are simple arrangements in which a shaft orrotates in a sleeve of bearing material separated by whatever

an t film is present. I t is an inexpensive bearing, offering goodtricity, close radial-play control, and high resistance to vibra

and shock. The main advantage is that there is no inner-race bear-eccentricity, which is the problem with ball bearings. The limitain comparison to ball bearings, are

The coefficient of friction is an order of magnitude greater thanof ball bearings.Compatibility of the shaft and th e bearing material is veryThe finish requirements 011 shafts ar e stringent for reliable

e.Differential expansion of bearing and shaft because of temperavariation must be entirely accounted for by clearance; thisa difficult requirement on minimum radial-clearance designs.Loss of lubricant increases friction severely and greatly increasesof failure.Bearing squareness, shaft alignment, and parallelism are critical.,saligned shaft causes serious reduction in performance because th eis squeezed out; it also results in extremely high unit presbecause of the essentially point contacts at th e bearing edges.spite of th e above-mentioned limitations, sleeve bearings can beadvantageously in gear trains to provide close radial control free

tricity.Bearings. These are more widely used in precision gear trains,because of th e sleeve-bearing shortcomings mentioned above,because of convenience and flexibility. Although a ball bearing

more expensive than a sleeve bearing, it is inexpensive inf precision. High-quality ball bearings are available because of. ation and vast production volumes.bearings, in comparison to sleeve bearings, offer several imporadvantages. These are elimination of material combination prob-


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336 Gear Train Design and Synthesislems, reliable performance with low friction; retentionlubricant for a longer period, and the ability to absorb radialwithout failure. A unique problem with ball bearings inhigh-precision gear trains is brinelling effects. In a very precisesensitive train, brinelled bearings cause a small restoring ortorque action, which appears as gear train position error.

In addition, most bearings exhibit a similar characteristic ofIn a precision train creep occurs when gears stop rotating,small bearing deflection and shear lubricant forces tend to roll backrotating bearing race. It is as if th e rolling balls have a material wbuilding before them which presses the balls back upon relaxationthe driving torque. Th e extent of this position error source is depupon driving force, load, and degree of ball and racewayThis phenomenon becomes apparent in ultraprecision trainshave sensitivities in the range of creep magnitudes.

Limitations of ball bearings are their low resistance to shockvibration, their need for delicate care in assembly and servicing,inherent rotating race eccentricity.

The ball-bearing industry has standardized various bearingeters. For gear train design pertinent items are specified byclassifications, presented in Table . ~ - 4 . Most directly affectingperformance are toleranees on inner- and outer-race runout, boreeter, and outside diameter. In application to gear trains, theare divided into the following general quality groupings:

~ a u ABECIABEC3ABEC5ABEC7ABEC9

Gear Train Quality GradesCommercialHigh commercial and low precisionPrecisionHigh precisionUl raprecisionIn addition to the dimensional data of Table 5-4, there are other f

pertinent to bearing performance which are not covered byclass number specification. These are:1. Axial play 7. Lubricant and amount2. Radial play 8. Ball retainer design3. Starting torque 9. Surface finish4. Running torque 10. Smoothne ss of operation5. Load capacity 11. Noise and vibration level6. lVIaterial and heat treatment 12. Life4 "Annular Bearing Engineers' Committee" of the Anti-Friction Bearingfacturers Association (AFBMA).

Bearings 337items will have varying degrees of importance in accordance

the application. Radial and axial play will directly affect gearand th e other items will affect system performance inof load rating, reliability, and life.

though ABEC class 9 bearings represent ultraprecision, specialof even greater precision have been produced. These rangeto .00002-inch tolerances for the parameters listed in Table 5-4.tolerances are, for th e most part, excessive for precision geartions. I t is prudent to use bearing tolerances consistent withquality, and in the present state of th e ar t bearings are ahead of

Fits. A di'fficult problem in precision gear train assembly ismating of bearings with shafts and housings. Although precision

have tolerances on th e order of .0002 inch, assembly allowanceshaft and housing bore tolerances introduce greater variables.. tolerances are used, bu t this requires selection or workinginterferences. Th e recent widespread practice, in th e ball-bearingof providing coded bearings is a great aid to selective

press fits are ideal for bearing-shaft-housing assembly; theyelearance of about .00005 inch. A line-to-line fit, in whichis no measurable allowance or interference, is th e ideal for no, bu t actually requires moderate pressing to overcome out-ofand surface variation factors. An interference of .0001 inch

heavy press. Greater interference, .0002 inch and more, requireslarge forces and deformation that bearing damage is likely. Fo rprecision assemblies it is more important to provide an easy

and disassembly than to eliminate all clearance. Nominalfor various types of fit are summarized in Table 7-8. Th eand interference values are only typical since fits vary withsurface finish, and squareness of th e assembly. As size increases,force is required to strain interfering parts. Similarly, th e finer th efinish, the more force required. Also, for tolerances measured inLluusandths of an inch, th e slightest misalignment and out-ofalters clearance and interference.of engagement is also a problem because a long shaft must

be passed through the bearing. For such cases fits with allowpreferably slip, are necessary. I f the bearing is to have a pressis advisable to relieve the shaft to avoid damage to the bearingover a great length. With standardized shaft diameters use

next larger standard diameter bearing accomplishes this.types of fit given in Table 7-8 occur over a relatively narrow


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338 Gear Train Design and SynthesisTable 7-9 Shaft to Ball-Bearing Fit and Tolerance Guide forQuality Gear Trains

TypicalShaft \ BearingDiameter Bore

Desired ToleranceGear Train Fit Nominal C : ~ o l . ) ( ~ ~ o l . ) ProcedureQuality Type ConditionCommercial Loose . 0002 - .0005 - .0003 Specify .0002minimum allowance andclearance apply tolerances.Precision ISlip 1. 0001 - .0002 - .0002 Set diameters withclearance .0001 overlapassembleselectively.High \Finger \ .00005 \ - .0001 \ -.00015 \Set diametersprecision press clearance .0001 overlap

assembleselectively.Ultra-.. \pressprecIsIOn

\ 0 to .00005 \ - . 00005 \ - .0001 \Set diametersclearance .00005 overlapassembleselectively.

range of diameter variation. Considering that typical shaft andtolerances sum to several ten-thousandths of an inch, it isimpossible to achieve one type of fit by direct dimensioning; pren;o;,control of fits compels selectivity. Th e practice is to segregateinto .00005- or .0001-inch classes (the choice depending upondesired narrowness of fit) and to assemble selectively to providedesired fit. An alternative to selective assembly, especially forlots, is to rework parts to a proper fit during assembly byhoning, and polishing shafts and housing bores. Bearings are neverbe reworked.Shaft-ta-Bearing Fit. For the usual case of rotating shaft, it istant to limit looseness between the shaft and bearing bore to abacklash and diminish dynamic effects at high speeds. A guide ofommended fits and tolerances of mating diameters for varioustrain qualities is given in Table 7-9. To achieve the recommendedan overlap of mating diameters is necessary to allow applicationreasonable tolerances. Selectivity or rework at assembly is then

Bearings 339to achieve precision qualities. Only the less accurate. commercialcan accept any resultant assembly from the full tolerance range.Bearing-ta-H au sing Fit. In the typical case of fixed outer race, th e

is slightly less critical than with the bore to shaft because there islikelihood of bearing outer-race rotation, and a slight clearance is

to accommodate housing bearing squeeze caused by differential. with temperature variation. I t is also more difficult tobearing bores, particularly shouldered designs, to the same tol

and degree of surface finish as shafts. A guide of recommendedand tolerances is given in Table 7-10. Again, some selectivity is"'mtered with the higher-quality casesadial and Axial Play. The ABEC ball-bearing classes do no t conradial play, and designers are compelled to specify th e desired

for control. Bearing manufacturers offer a wide selection ofplay, ranging from .0015 inch loose to a few ten-thousandths

preload. Although zero radial play is attractive from th eof minimum backlash of th e train, it is undesirable because

lMlI.u1l1\;antly increased bearing friction. Typical variation of frictionTable 7-10 Ball-Bearing to Housing Fit and Tolerances Guide for

Quality Gear TrainsTypicalHousing I BearingBore ODDesired ToleranceNominal ( ~ ~ O l . ) ( ~ ~ o l . ) ondition Procedure

.0002 min. + .0008 - .0004 Specify .0002 allow-clearance ance and applytolerances.Loose to \.0001 to +.0005 - .0002 Specify zero allow-slip .0005 ance and assembleclearance selectively..0001 to +.0003 - .0002 Set diameters with.0002 .0001 overlap andclearance assembleselectively.o o .0001 1 +.0001clearance 1 - .000151Set diameters with.0001 overlap andassembleselecti vely.


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340 Gear Train Design and SynthesisTable 7-11 Typical Ball-Bearing Radial-Play Values andTolerance for Various Gear Train Qualities

Quality of Gear TrainCommericalPrecisionHigh precisionUltraprecision

Radial-Play Value and Tolerance.0004 to .0015 0003 to .0007 0002 to .0005 0001 to .0003

with radial play is a rapid friction increase as play is reduced towzero with a severalfold increase at zero and beyond into preloOptimum radial play is from about .0002 to .0005 inch, offeringtively low play for near minimum friction.Ball-bearing radial play is a separate control parameter.values for various quality gear trains are listed in Table 7-11,further values relating size and load are in Table 5-6. I f a radialis not specified, the bearing industry has a practice of supplying

Ul q TRange of values forvarious bearing designs

.0061 VCL 1 1


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342 Gear Train Design and Synthesisticularly helpful because of inevitable assembly departure from idealalignment. The degree of misalignment accommodation is a functionof radial play and is a further reason why some play should be tolerated. Ranges of angular misalignment versus radial play are given inFig. 7-35. Misalignment will consume a portion of the radial and axialplays, thus reducing the bearing's looseness; this reduction can besignificant if the full amounts of play are required for special functions.7-15 Housing Design

Hom;ing design influences fabrication and performance oftrains in terms of its materials, misalignments, and mounting.Materials. Housing materials are almost as extensive as th e gearmaterials covered in Chapter 9. Common materials are cast iron, steel,aluminum alloy, and die-casting alloys. Aluminum predominates inpreci8ion gear trains because of its good machinability and lightness.As with gears, material features that affect housing precision, in addition to the obvious machinability criterion, are rigidity, stability, andthermal expansion.

Rigidity is important both to provide accurate machiningfabrication and, in application, to resist distortion forces inducedassembly and during operation. Stiff materials and proper secmust be balanced against other material features for an optimhousing design.Stabilt'ty refers to maintaining fixed dinJensions with time. Creepand the gradual release of internal stresses can nullify precisionbores, flatness, and squareness. For precision gear trains, stablerials are used along with adequate heat treatment and stabiliprocesses, including natural and artificial aging.Thermal expansion creates backlash and interference problemscan be minimized by using housing and gear materials with compatlcoefficients of thermal expansion. Th e thermal coefficients givenTable 9-16 indicate the magnitude of the problem. Data in thisenables selection of compatible housing and gear materials.

Housing misalignments. Design and specification of th ewith manufacturing tolerances introduces several misalignmentsadversely affect gear function. These are shaft nonparallelism,tilt and shaft end play variation.

Shaft nonparallel sm causes edge face contact, with earlydown, resulting in wear, loss of accurate profile, and backlash.though nonparallelism is a second-order effect, it must be watcto prevent it from becoming excessive. Departure from parallelismmostly due to shaft bearing bores that are independently located

Housing Design 343housing half, thus accumulating variations produced by the indet center distance tolerances in th e mated housing parts. This is

in Fig. 7-36a, where shaft S-2 is misaligned in relation to shafta maximum amount when the shaft bore locations in each housingare at opposite tolerance extremes. The misalignment is either in a

as shown, or more generally results in skewed shafts. Shaft S-1also vary its position because of it s locating tolerances, resulting inCoc."" t o l , , , " ~ ',

~ I , t I.JI 1l JQ

,------t-- --1/ilr--T , - 111S-ll s-2!1 \ Out-of-parallelism-----H angle a(a)~ K J r T I I t , " g l " \1

1QMismatch II jtolerance T ii1< KT ::>11< C ",I

(b)Figure 7-36 Shafting misalignment for housing tolerance:(a) shaft misalignment caused by independent center distancetolerance in each housing half, (b) shaft misalignment causedby housing assembly mismatch.


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344 Gear Train Design and Synthesisdouble misalignment. Th e magnitude is

[Maximum angular misalignment] = IX = sin-1 (71 72)where 71 and 72 are bilateral location tolerances for each shaft,Q is th e housing shaft bearing separation. Fo r ball bearings, Q isprecisely th e spread between ball planes, which is significant forbearing spreads.

Shaft tilt is th e nonperpendicularity of the shafts and housingby misalignment of the shaft bearing hole patterns in eachhalf (Fig. 7 36b). Misalignment is caused by unavoidable tolbuildup in assembling th e housing, either by predowel hole locationin th e process of doweling at assembly.

Fortunately, this type of mismatch is no t as detrimental asof individual hole locations because all th e bores in each housingshift together, causing shaft out-of-squareness bu t not nonparWithin the train th e gears will function correctly except for a minand usually negligible decrease in center distance, which is

t:,.G = G(l - cos 8)where . - 18 = Sill Q

I t should be realized that shaft tilt also occurs along with noallelism, as just defined. However, its center distance variationare then within th e established tolerance range, whereas the shaftcaused by mismatch of the housing halves is independent and intion to shaft llonparallelism.Since llonparallelism and tilt are functions of housing bearingbearing location tolerances, and housing misalignment tolerance,can be a trade-off for optimum design. As a guide, Table 7-12 listsmissible values for various gear qualities. I t is obvious fromgeometry that tolerances can be relaxed for increased housingsion Q, bu t this is a nonlinear function, and tolerances rapidlyfor small bearing spreads. To control misalignment, housing boresbe line-bored, thus assuring a high degree of shaft alignment.smaller the dimension Q, which fortunately is small when alignmentmost critical, the more suitable this fabrication process.

A fabrication compromise that partially controls shaft Ull : : i l : tUg , l l l l l l J lis to make housing halves in stacked pairs if they are flat plates.assures identical hole patterns in th e housing mates, leavinghousing assembly misalignment as source of error.

Housing DesignI'" L >1

Out-of-[ parallelismt -1 I t(a) .1Q

II _.1r _ I(b )

Figure 7-37 Housing variations affecting shaft end play: (a) out-ofparallelism caused by variation in housing spacer Q, (b) out-of-flatness Qvariation

345

Shaft end play variation results when th e housing halves are assemout-of-parallel, or the housing walls are out-of-flat as in Fig. 7-37.

ted variations in shaft end play can lead to binding or toolooseness. Generally, variations are small and, for spur gears,serious, providing there is no binding. However, bevel, worm, an dcal meshes are measurably affected, and this is an important back-

source. Guiding tolerance values for nonparallelism and flatnessgiven in Table 7-12.Enclosed versus Open Housing. An enclosed housing design com

envelopes t.he gear train, with only the input and output shaftsThis housing is preferred for precision trains, since it pro

complete protection against contamination, environmental corcontacts, unwarranted tampering, accidental injury, and sealing

the lubricant.Open housings are used when minimum weight is important. In this. one or more sides of th e gear box remain uncovered, and bearing

may be supported on cast spokes or struts, or the bearing platesbe "swiss cheezed" with lightening holes. Besides saving weight,design offers easy access for assembly, maintenance, and phasing


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346 Gear Train Design and SynthesisTable 7-12 Housing Design Tolerances*

Shaft Non- Iparallelism Shaft Tilt Housing Out-(per inch (per inch of-Parallelismof shaft of shaft (per inch ofGear Train bearing bearing housingQuality spacing Q) spacing Q) length L)

Commercial .005 .005 .0020 per inch; .0020.010 totalPrecision .002 .003 .0010 per inch; .0010.005 totalHigh precision I .001 .0015 .0007 per inch; .0005.003 totalUltraprecision .0005 .0010 .0005 per inch; .0003.002 total* Maximum permissible values.

of gears. Ofte n a compromise of the two approaches can be used,the housing open on all or most ends and enclosed wit h separate lighsheet metal covers to provide minimum protection.

Mounting of gear boxes is often for special purposes, and theremyriad designs. I t is important that the mounting be rigid and pto prevent distortion of the housing. This means that mountingmust be held to a flatness and squareness consistent with good maCIllU..,ing practice, and deformation must be avoided in assembly.7 16 Mesh Alignment

This "term" refers to the relative axial positions ofmated gears.requirements range from noncritical for spurs and helicals tofor bevel and worm meshes. In all cases, appropriate alignmentbe specified for all meshes.

Spur and helical pairs are expected to be almost ideally aligned,in Fig. 7-38a. This is no t difficult, particularly if the width of the .is 25 per cent greater than that of the gear, which is the usualHowever, there are many other instances when relatively narrowof equal face width are paired, with the possibility of mismatch asFig. 7-38b. Excessive loss of engagement, particularly narrow gears, ccause increased surface stresses, and if design values are significantl:yexceeded, can result in premature wear and failure. Mesh alignment

Mesh Alignment

;=-=--

(a) (b)Figure 7-38 Spur and helical gear face meshmisalignments: (a) ideal alignment, (b) mismatched face alignment.

347

t upon assembly tolerance buildups or the care given by the. I t is proper practice to specify allowable maximum misGuiding values for controlling mesh alignment are given in7-13.

alignment of bevel gear meshes is critical in comparison tosince this directly effects backlash and proper conjugate action.drawings should specify gear locations from shaft centers,Fig. 7-39. For closer control the practice is to specify location ofbevel by a dimension with tolerance, and to adjust the otherwithin a specified maximum backlash. For bevel Irears the

Tolerance Values for Spur and Helical 111,Mating Gearor PinionFace Width

same as matesame as matesame as matesame as mate

Maximum Gear Face MismatchTolerance20 per cent but no greater than i inch20 per cent15 per eent10 per cent but no less than .004 inch

gear pairs in which one mate is significantly wider than the other, themust be 100 per cent.


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348 Gear Train Design and SynthesisMounting distance I MDt ,.1for proper mesh , c

alignment \

IPitch a p e x ~ ___ -+--+

IRS

Mounting distancefor proper meshalignment

Figure 7-39 Bevel mesh alignment. An alternate procedure is to specify pinion MD as reference (no tolerance)and to adjust pinion axially to a specified backlash forthe pair. '

Table 7-14 Axial Location Tolerances for Bevel and Worm JleshesBevel Mesh Worm Mesh

Tolerance onTolerance on Wormgear Regili-

Registering Surface tering Surface toGear Quality to Apex Worm Center

Commercial ,002 .003Precision .0005 .001High precision .00025 .0005

Cleanliness, Care, ReliabilityMounting distance MDtfor proper mesh ') I EO ... 1alignment

RSc: Q)Q)

C , . ) ~ . Q) en

. . . . . l . . - . ! . - -L

Wormgearcentral planeFigure 7-40 Worm mesh alignment on fixed('enter distanee.

349

of alignment is related to gear quality and backl ash specific a-Table 7-14 offers guiding tolerances.alignment of worm meshes is critical because the line contactbe di:::;rupted, causing point contact, and true c o n j u g a ~ e actionbe lost. The critical alignment (Fig. 7-40) is the ce,nter of thewith the wormgear's central'plane. Again, p e r m i ~ s i b l e deviationfunction of gear quality, and values are given in Table 7-14.

is paramount to precision gear trains. The special effortto the design of precision gearing is to be matched with suit-perations and handling in fabrication, inspection, assembly, andTolerances may be so close that they are impracticalair-temperature control and cleaning. Consequently, gearsousings are cleaned and treated with great care and patience to

them of acceptable quality, and this effort becomes useless unlessassembly, test, and use in the field are equally cautious.


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350 Gear Train Design and SynthesisThe precision gear is easily subject to damage both as a \;Ul1 l11Ull t>U

and in assembly and therefore warrants special handling andSubassembly and assembly design should include protectiveagainst misplaced tools, bench stacking, and droppage. Inpackaging, requiring a screwdriver or other tool to be snakedprecision gear teeth in order to assemble or phase an item, is ament to the preservation of quality.

Gear train cleanliness and care help directly in maintainingability. Random early gear train failure is often attributed totamination or damage suffered during assembly and test phases.7-18 Design Subtleties

Gear Rework. There is a misconception that finished gears canreworked to alter th e bore size or decrease face width. This practicepossible with commercial and subprecision quality gears bu t isacceptable for precision gears. A reboring operation is likely to .duce concentricity errors, and altering the face width risksthin gears and introducing tooth burrs. Although, with propereven a high-precision gear may be modified without degradation, itbetter practice to avoid subjecting quality gears to this risk forresults are neither reliable nor economical.Lightening Holes. The practice of resorting to a pattern of lighholes ill gear faces for reducing inertia and weight, as in Fig.should be carefully scrutinized. The relatively small decrease inand weight is often offset by increased machining cost and risk ofblank distortion.Fo r typical hole pattern designs (Fig. 7-41), ratio plots of l I lUl l l t : ' l l iof inertia with lightening holes to full gears show that, at best,is reduced by only about one-third. Although these patterns areguides, they do typify most designs. Each hole pattern has antageous range of pitch diameters because of the scale factor effectthe design. Th e simple six-hole design, type I, is best for smalland is a reasonable compromise design for a wide range of sizes.and shaft inertias must be added for all assembly total, whichdevalues the effect of lightening holes. Saving weight by meanslightening holes is slightly more productive than inertia impas shown by the weight ratio curves of Fig. 7-41; again, eachhas an advantageous range of size.In any particular application th e practicality of lightening holes isrightful subject of value engineering, since generally inertia canreduced by only ;)0 to 40 per cent an d weight by 40 to 50 perMore profitable gains can be made by other means, without'

Design Subtleties

1-1 dt::: Q I~ : : :

f- ; : : : I ~ ci ~ I ! . O c:iII II II II

"Tj'" CG'". - - - - - . - - - - - - r - - - - ~ - - _ r 1 ~ 1 1 - r - r - - ' 1 ' 1 - , - - - - , , 9

II II 1

--i- I 1 -i -l


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352 Gear Train Design and Synthesisfabrication costs. Fo r example, a material change from steel to aluminum alloy offers a 2.5 reduction factor. Careful examination of facewidth may offer a safe reduction, or a thin web design carried as closeas possible to the root diameter may reduce weight and inertia.In-Line Centers. Improved backlash performance can be obtained ifthe gear center layout follows a rectangular coordinate path rathan random angular arrangement. Referring to Fig. 5-2, lines ofcenters paralleling a coordinate axis bring one tolerance into centerdistance variation, whereas the random angle line of centers is a function of two. Since most fabrication machines utilize coordinate inputsan in-line design eases fabrication.

Face Widths. There is a subtle advantage to unequal faces inand ultraprecision meshes. Deburring is a nasty operation which,best, leaves doubt about the exact quality of the involute profilethe outer face edges. Round-off is no concern, bu t undetected upsetfoldover is detrimental. To decrease the risk, one gear sh'ould bethan the other. Pinions are normally made wider, which alsotheir more sensitive profiles from becoming degra ded by the deproblems. REFERENCES1. G. W. Michalec an d Daniel S. Blohm, "Operating Pressure Angle of

Spur Pinions," Machine Design, April 23, 1964.2. John G. Truxal, Control Engine ering Handbook, McGraw-Hill, New York, 1Chapter 13, pp. 13-5 to 13-21.

Strength, Durability, andRelia bility

Introductiongear can fail to provide its intended service because of any of thefailures: breakage, deformation (elastic, permanent, andflow), wear, surface fatigue, and chemical attack. The last item,al attack, is a function of the material, finish, and lubricant.

proper selections have been made considering the environour concern is with the other four failures.

ting the capacity of a gear begins with an assessment of toothstrength, which is fundamental to transmitting load without

or excessive deflection. This is a function of material, geoform, stress factors, and dynamic loading. However, an affirma,valuation does no t necessarily establish confidence in a designbeam strength by itself is no measure of wear.

rating is essentially the fatigue and wear criteria of theoth surface. I t is the ability to resist the various surface failuresscoring, and scuffing. Durability is evaluated in terms of surtresses, which are defined by system dynamics, profile errors,combination, and lubrication. Calculations are a combination

plus a great amount of empirically derived procedures andDespite the very sophisticated appearance of the many equa-this subject involves considerable "art of doing" rather than

and scientific rigor.ty is the confidence that can be placed in the strength andof a design. I t is a relat ively new engineering discipline thatwith military equipment requirements, which forced th eof new techniques for reliability analysis and prediction.

ethod of failure analysis, and makes it possible to predict thedistribution of failures with operating time and conditions.

brought engineering rigor to predicting performance which wasconsidered in terms of factors of safety. Applied to gear trains,attempt to rate degradation of performance throughout thelife of the equipment. I t s another means of gaging the attain-

engranajes de precision

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