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Home , Bevel gear, Crown gear, Gear, Spiral bevel gear

_------liGEARiFUINID,AMlENTAILS------_ The Basics of' Spiral Bevel

Dr. He.rma,nn J. Stadtfe!ld

This article also ,app,eBTS derived from a straightrack as Chapter , in the' with straight tooth profile. A particular , in the ,G/e'asoRCorpolation pub- rack with constant center dis- lication ..Alvanced .Bevel tance to the rack, requires Gear Techn%.g,,. " involute flank surfaces. A shaping tool with the shape of Gearing Principles in a rack can a gear with Cylindrical and Straight a perfect involute flank form, Bevel Gears Figure ] shows a cylindrical The purpose of gears is to gear rolling in a rack. transmit motion and To understand the bevel from one shaft to another. That gear tooth geometry, one normally bas to might first observe the case of occur with a constant ratio, the straight bevel gears. If the lowest possible disturbances generating rack used to derive and the highest possible effi- the cylindrical gear involute is f,igurll 2-- Brrangemenl In be:vel gear sets.

ciency. Tooth profile. length bent in 8. horizontal plane into tion point of the and which causes 8. straight lead and shape are derived from a circular shape, it results in a gear shafts. and an oetoid profile on the those requirements. crown gear, which is used to As a mental exercise. the generated teeth. The octoid With cylindrical gears, it is derive the flank form of bevel crown gear should consist of a basically is the ana- easier to understand that the pinion and gear. In. the case of very thin material like alu- log of an involute. The octoid involute profile provides a. straight bevel gears. the CroWD minum foil, Inthat case, it is provides a constant ratio and constant ratio and is insensi- gear or generating gear can be possible for all three elements makes the gears insensitive to tive to center distance dis- placed between the pinion and to be in mesh at the same time. displacements perpendicular placement. The generating gear assembly. Its center is Figure 2 shows how the to the pitch line. principle of an involute is located exactly at the intersec- pinion is located at the back- ircular utting Tools and side of the crown gear and Spiral Bevel Gears meshes with the "negative A face cutter comes with teeth," while the ring gear is many blades to increase pro- placed at the front side of the ductivity ..It generates a curved crown gear and meshes with tooth shape. whic'h provides the "posjtive teeth." If such an arrangement is possible. then the kinematic condi- tions of the bevel gear set are fulfilled, which means the pin- ion and gear can mesh with Dr. Hermann J. Sta.dtfeld Is vice president of research &; each other, too. development witn The Gleason A single profile of the gen- Works. a leading manufacturer of erating gear generates a gear bevel and cylindrical gear malll4- facturing equipment. He IIO.swrit- on its one side and the mating tell /lIImeroll. articles 011'he theory member on its other side. The of gearillg and on practical aspects figurie l---Cylind'rical gear generatingl prine·ple. profile and lead are straight. of gear nurmt/acllIring. w .. w.powerrransmission.com .• www.gearrecl1norogy.com • GEAR TECHNOLO v • JANUARYIFEBRUARY 2001 31 ••• _ GEARFUNDA~ENITAlS, •••• _ 20 increased face contact ratio" ling gear into the pinion. The REilSHAUER tooth rigidity and adjUst...a~i1ity.. I pinion slot produced in that CiNC , to load-dependent deflections. I way has two defects. First, the A'RE REAIDY In the case of'a single index i profile will not allow rolling TOWOR,K face method. the tooth I between pinion and generating FOR YOU! lead function is circular. as the I gear (compare to the rack and blade in the cutter performs a I cylindrical gear tooth in , while the Figure 1). Second, the pinion generating gear rests in a.fixed slot does not have the proper angular position. depth along the face width. As

The toolh profiling be- !" soon as the teeth have II spiral tweenthecutter and the gener- i angle and the slot inclines to' ating gear does [lot require any I an angle on an axial plane. the The Crown Train with its remarkable expenence in g.ears of the generating gear, ! teeth wind around the work production has developed a CNC gear inspection machinafor: The virtual generating gear is ! gear body. ]n a. fixed angular • quick, easy and affordable sarvice formed by the cutter head in II I position, just the heel section, • Check cylindrical gears. in,lead, pitch and involute profile non-generatlng process. In : for lex.ample,is cut to the prop- • Module between O.5mm and 16.00mm (1.6 to SOD?) Fjgure 1, the rotating blades in • Outside' diameter betwesl110.00mm and 420.00mm (.4' to 116.5') I er depth. PRICE: $ 120,OOO.OO-FOB Crown included three days of tJ;aining: (he cutter head can be under- The roll motion rotates the stood to represent one tooth of virtual generating gear and the

Request information: the generating gear. worlcgear with the proper Call: +390307156530 As explained earlier, the ratio while they are engaged Fax: .. 39 030 7059035 generating gear is the bevel (similar to the linear motion of Ililltp:llwww.crown.l1 [email protected] gear equivalent of the straight the rack, Figure I,in conjunc- rack for generating a cylindri- tion with the gear rotation). CIRCi.'E122 cal gear toolll. Therefore. it is! Since thegenerating gear is

understandable that the gener- 'I; just virtual and doesn't physi- ating gear tooth profile is a . cally exist, the cutter that sim- mirror image oftheblade pro- ulates one tooth of the gener- file (it is not an involute or sting gear has to rotate around oetoid). the generating gear axis. ~Our engineers are fully conversant with gear shapingl and hob- If a pinion blank without r With this rotarion (mil bing applications. rhey can also supply necessary gages and teeth ispositioned in front of I motion), the cutler blades master gears whether spur or helical. We feel that we have a the generating gear and then . work: their way from the heel vary good in depth ,knowledge of gear product jon and tooling, and have all ANSIIA.GMA specifications on hand Includlngl for- moved towards the cutter, the I to the toe and generate the eign specifications such as DIN (German), JIIS (Japanese), BS blades will cut the same trape- proper oetoidal profile along (British) and others. Remember too, that we not only supply I carbide nebs but carbiele snaper cutters and master gears for zoldal profile of thegenerat- i the entiTle face width. The slart v.ery spe.Cial apPlica.nons, w.e invite' y.o.uto call and discuss your looling requirements with us. 'We don'. lake a week Illlquote; one'or twOI days would be normal :andfew Ihours Inol UTIUISUal... A SINGLE PRORLE OF THE GENERAnNG GEAR GENERATES A GEAR ON ITS ONE SIDE AND THE MAnNG MEMBER ON ITS OTHER SIDE. THE PROFILE AND LEAD ARE STRAIGHT. WHICH CAUSES A STRAIGHT LEAD AND AN OCTOID PROFILE ON THE GENERATED TEETH. THE OCTOID BASICAUY IS THE BEVEL GEAR AdJlISlabl'el HOlling IReamers: ANALOG OF AN INVOLUTE. THE OCTOID PROVIDES

CFlARIER, Skiving A CONSTANT RAnO AND MAKES THE GEARS tNOOSJ1'lIES we Hobs 1650 Sycamore AvenlJe. Bdhemia., NY nn6 INSENSITIVE TO DISPLACEMENTS 1-631-567-1'000· Fax: 1-6311·561-1355 Visit us on' the Web at: www.park:erlnd.cQm or E·Mail: [email protected] PERPENDICULAR TO THE PITCH UNE. 180 32 JANUARYI'FEB.I'lUAAY 2001 • GEAR ' www.goarlechnology.oom '. www.powe·r!tIl",mlssIOIl.com _------'GEAR IFUlNDA'MENTALS, _ roll position is normally on the bevel gear set have different side of the tooth with the big lengths. The bottom of figure 5 diameter (heel), The roll shows the movement of the motion ends when the profile contact from heel top to we generating "arrives" at the root. The very short contact opposite side of'the face width length increases from the (toe), beginning of the roll towards That procedure was for the center of'the face width and one slot. To reduces as the roll. approaches machine the next slot, the cut- the exit at the we end. ter withdraws, and the work Th.e contact lines between indexesone pitch. The spiral pinion and generating gear are angle is the inclination angle identical to the contact lines of the curved tooth tangent to between cutter blades and pin- the radius vector from the ion flanks, intersection point of pinion Single Index Process-> and. gear axis (see Figure 4)1, Face Milling Because of the curved shape [0 a single index process, of the tooth length, different just. one slot is cut ala time. points along the face width for the non-generated mem- have different spiral angles, ber only, the cutter rotates and The nominal spiral angl.e of is fed into the work gear to the Figure 3--tircular cuttingl tool andvirtuall !gene~atiDg:!liear. the or pinion full depth. After reaching the is the angle measured from the full depth, the cutter with- center of the tooth, draws and the work indexes It is possible to use a bevel one pitch to the next desired generating gear that is identi- slot position (Figure 6, right cal to the ring gear. The pinion side). The process repeats is in that case generated by until all slots have been rolling with the bevel generat- machined, The resulting flank ing gear, and the gear is man- ! lead function is a circular arc. ufactured simply by plunging j Machining a generated the cutter to fun depth without I member is done by plunging Figure4-Definition of spira'il angle. rolling (non-generated fonn. I. at the heel roll position first. cutting). After plunging, the roll PATH 'OF CONTACT A stra:igbt tooth bevel gear I motion begins, and generat- sethas contact lines that are j ing of the flanks from heel to parallel to the pitch line! toe occurs. The flank lead (Figure 5, top). The first con- I function for a face milled, tact between a generating gear i generated gear is a circular tooth and a pinion tooth. starts, j arc that is wound around a I for example, in the root and ! conical surface. moves daring the rotation of I The manufacturing of a the two mating members j face milled bevel gear pair is along the path of contact possible in a five-cut process ! PATH 'OF CONTACT straight up to the top. The con- 1 or in a completing process, The five-cut process consists tact lines represent the I"" momentary contact between of tbe following five indepen- the two flanks in mesh, . dent operations: TOE With a spiral bevel gear set, ! l. Gear roughing (alternate

the contact lines are inclined .,1 roughing blades), relative to,the pitch line orien- 2. Gear finishing (alternate SPIRAL. ANGLE .,35" tation, Unlike the contact lines I finishing blades), of the straight bevel. gear set, i 1. Pinion roughing (alternate HEel the contact lines of the spiral ~ roughing blades), Figur,e S-Contact lines for differenh,pir I angles .. www.pOWlJrrrllnsm/uion"com • www.gurrechn%gy.com • GEAR TECHNOLOGY· JANUARY/FEBRUARY 2001 33 ___ .IGf~RfUNDAMENTALS II. _

Cominuous IlndexIng Single Indexing

,G8·0UND ,GEARS - Ten or Te'nThousand For sma'll to medium quantities 01 spurs or hsllcals that have to ~igur~ '&-Kinematic ,principle of continuous :indexing VS. siDgl'a meet dcse-tnlerance AGMAor DIN specs, our Reishauer grinders indeXing. and M&M gea1analysis systems are the perfect combination. For Long runs, we offer the unique Uebherr CBN grinding process with full SPG quality control and documentation. So whether your needs are for ten or tens of thousands, we invite you to join the growing: list of INSCO customers who rely on us for consistent quality, reasonable costs, and reliable delivery.

IPHONE: 97,8-448-6368 FAX-= '978~448-5155, . WEB: inscocorp.'com 412 Majn Street, Groton, Massachusetts 01450 rnscoOflPORAT/ON G ISO 90011 Registered

CIRCLE 162

o 2 TImeS l[mIIt]1

Figure 7-Cycle diagram for generating a fac·e hobbed Ipinion .. 4, Pillion finishing convex ! between the [lumber or work ('.mnerbl a.es d OlllllYnly) , an·d ':;':" gear teeth and the.nUnlucf '-- 0f . 5. Pinion finishing concave cutter head blade groups (outer blades only). I (starts). The resulting flank A completing process uses I lead function is aaepicycloid, two combined operations: j The effective cutting direction 1. Gear roughingaadfinishing I,ofthe blades tin the cutter head (alternate ['Qughing- ! is not perpendicular to the cut-

finishing blades) and I" ter radius vector Oike in the Pinion reughing and finis- single indexing process). The ing (alternate roughing- j blades are moved in the cutter finishing blades), I bead tangentiaUy to an offset Continuous Indexing ! position to accommodate the Process-face ! correct orientation with A continuous cutting ~ respect to the cutting motion process consists of continuous I vector, The pitch poi~ts on the and a feed motion ~ cutting edge ofinner and outer only. While an outer and an blade have an identical radius. inner blade move through a The right slot width is slot of the work gear, the work lacldeved with the angular dis- gear is rotating in the opposite tance between the outer blade direction. The relation of the (first) and the following inner cutter rpm and the work rota- blade. The left portion of tion is equivalent to the ratio , Figure 6 shows the kinematic 34 JANUARY/FEBRUARY 2001 • GEAR TECHNOLOGY· www.glU!rtechn(Ji(J(Jy.com • www.powfl'rlrsnsmiss/on.com _----'GEAR IFUNID.A_MENTALS _ relationship and the orienta- l N is the number of cutter starts tion of the blades relative to ; times the number of gear cutter and cutting motion. I teeth. N is equivalent to as Balancing ~f the~ooth I many ring gear revolutions as thicknesses between pinion I the cutter has starts. IModel G"32-11 and gear can only be realized For a generated pinion, a ! IHigh Production by different radii of inner and roll motion follows 1iheplung- ! 'Gear Hobber outer blade pitch points. since I ing cycle in. the center roll $159_ the spacing between the! position (the cutter doesnot 32" Diameter blades is given by the cutter ! cut the full depth yet). The roll - I 111" ,or 19" face motioD after plunging moves head design and therefore i".! (7/((1 It • "f: . remains consiaat, the cutting action to the heel; J7SS aoou our zero mferesf finanCIng: While one blade group I both pl.unging and rolling to (Iile shown in figure 6) is I heel is part of the mugh.ing moving through one slot, the I cycle. At the heel.roll position, Model GS1'(J..3HS work rotates in the opposite I the cutter advances to the full High Precision direction. such that the next ! depth. position, the cutter rpm GearShaper $64,795 blade group enters the next I increases loa finishing surface 10" Diameter slot. That way, all tile slots speed, and a slow roll motion I! around the work gear ate cut l from heel to toe follows. atabout the same time. The When. arri.ving at the toe "end I Visit our web, lite: www.basicma.chinelools.com feed motion to feed the cutter ! roll position), all teeth. of the Email wolt r. basrcmactunotoots COI11 to the full depth position is ~,! generated work gear or pinion "So I(. Tetephone i323) 9337191 therefore slower than in the are finished (see Figure 7). g]'.;( '( )It P<)I.( '" I' E I) Fax i323) 933.7~87 1 I{« ) ( .I" p a Box 36276. Los Angeles. CA 90036 single index. process. I Heat Treatment of A nOll-generated wo.rk:gear ! Bevel Gears CIRCLE 155 is finished wnen the full depth. i Heat treatment follows the position is reached. To get the I soft cutting operation. T,ne highest possible spacing aceu- ! generally used low carbon ---- I ra.cy,a dwell time is applied to' ! steel has to be carburized on th.e non-generated member. I the surface, by case hardening The aim of the dwell motion is I for example, The heat treat- toaHow each blade to move I ment is finished with tile once more to each slot, which ! quenching operation that pro- takes N slots m pass by, where I vides a s-urface hardness in the

• Precision carburized gears, housings and gearbox assemblies • Newllowllne production • Supplier to leading: aerospace mSJlufactuJers • Tolerances to AGMA Class 12 • Design assistance For more Information, oontact: available, __ 2 A,ero ,Gear Iinc. 1050 01)' HIURei., WlrulJor, CT 116095 CERTIFIED Tel: (860)1 68&-0888 IS DO Fax: (B80~ 285-85114 emall:·[email protected] • ·www.aerogear.com

CIRCLE 148 W..... pOWtUI'/M.smjl5Slon.com· .. ",w.f/ssrlschnolof/y.com • ,G,EAR TECHNOLOGY'· JANUARY/FEBRUARV 2001 35, SiPII:RAIL :BIE,VIE,IL GiEAIRS (Transmiss,ioos)

Figure I-Lapping o'a beve'llgear set Spiral & Straight Bevel"Gear ,Manufacturing~. Commercial to aircrLft quality gearing" Spur~ belicaJ, spUnedshafis,intema'i & 'Bldernal. sha,ved &: !ground gears. Spiral beve'I'grinding. Midwest TrLhsmissions & IReducers. ISO compliant

MIDWEST 'GEA_R CONT~CT: &.TODlINC. CRAIG III. ROSS 12024 E. INine Mile Road (810) 754-11923: War,ren. IMI 48011!1' FAX (8101 754.8926

'Figure,9-Grinding oI a bevel pinion. range of 60 to 63 Rc 1 most cases, is shaped like a (Rockwell C}. The pinion may ! long shaft that loses its be 3 Rc harder than the ring I straightness (radial run-out). gear to equalize the wear a:nd l In addition to the blank reduce the risk of scoring. The I body distortions, heat treating core material stays softer and I causes a distortion of the indi- more ductile, with a hardness i vidual teeth ..The spiral. angle in the range of 30 to 40 Rc, I changes.jhe flank length cur- The distortions from. heat i vature is reduced and the pres- Feather hydraulic treatment are critical to the I sure angle changes. To arbors can be final. hard finishing operation. ~achleve the best results, atten- manufactured with The kind of heat treatment ! tion has to be paid to process- runout as low as facility [salt bath, furnace or ing and handling of the parts 2 microns. The c'lamping I sleeves are replaoeable. This continuous furnace), as well] through the furnace. Quench- tooling is suitable for measuring', as the differences between the I ing the ring gears with a testing, balancing, gear grinding charges of blank material, has ~ quench press assures good and other applications. a significant influence on the ~ flatness of the heat-treated \0, ... oxcIu>Ivo _ T_ ~ Ii:xJlink Engineering 01' K6n1J1 mIm _ gear distortion. The gear, ring gears, for example...... -. <11._ 2870' Wilderness Place i Hi;ikIif1g Dt\l~ R....~ for t\I;t ~; Boulder. CO 80301 ·~·o.-.g·o-"Sho1'*>V which is mostly shaped like a ; HardF.inibing ef -= PH 303.938.8510 I o.r HobblngI' Our :Shavlng I, loQ! MI'!!dIng ,~ 'TMtI---.IlIiI ~ LD. ~ O.D. Grind!lng: FAX. 303.938.8512 ri.ng,loses its flatness (it gets a ! Bevel Gears "~"'IIImIng' -.. face run-out) via the harden- 1 The final machining opera- 'CIRCLE 178 ing procedure. The pinion, in j tion after heat treatment 36, JANUARY/FEBRUARY 2001 " GEAR TE.C'HNOlOGY " www.gsartschn%gy.com .,. www.powertransmisslon.com ______--GEAIR FUN'DAMEINrfAlS,•••••••••••• _

shouldprov.ide a good surface Another finishing option is Ii finish and remove flank dis- grinding of bevel gears, which I tortions. The most common is limited to face milled (sin- process used is lapping. gle index) bevel gears. The Pinion and gear are brought grinding envelops a sin- into mesh and rolled under gle side or an alternate com- . root tooth bearing li.ght torque. To provide an pleting cutter (Figure 9). i ----- heell ~-~-. tOIl' abrasive action. a mixture of ; Today's technology does not ! I oil and silicon carbide is I allow the use of a grinding i Irotary transmission poured between the [,eetil! tool ill a continuous indexing I (Figure 8). A relative move- I process. The advantage of] (!!IF SIJ...... -....-t - grinding is the manufacturing : ment of pillion and gear along ["",i theiraxes and a movement i:n of an accurate flank surface I Figure 1o--Tooth cont .ct analysis r,esult of 8 conjugl!1:e, bevell ge r wuha predetermined ropogra- ' sel ~~~t t:~;e~:n c~:ta::eaa~:~ I phy. The process allows the possible use of the same cut- applied to pinion andlor gear .. constantly repealed produc- , ting machine. That makes the The ease-off tOP.ography i moves from toe to heel and i"",.; back numerous times. non of equal parts. Building in ! investment in machines and defined ill the ring gear coor- The lapping process. pairs is not necessary, ! tools a minimum. dinate system, regardless of Lapped pairs used in vehi- ! Some Bevel 'Gear where the corrections were des require an oil change after i Convenfon done (pinion. gear or both). the first 1,000 miles because i The expression "bevel Protuberance is a profile ~~~~;§~§~Iof abrasive particles intro- i gears" is used as a general relief in the root area of the duced to the tooth surfaces. I description for straight and I flank, which prevents flank

~:m::~le ise~:n~~i!~ :e:~ I"" during lapping. A further i spiral bevel gears as well as damage resulting from "dig- different flank sections and advantage of grinding over i hypoid gear sets. lf the axes of ' ging in" of the mating tooth'

varies from set to set. since the lapping is that such an oil I. the pinion and gear do n.ot top edge. Protuberance is real- pinion and gear are used as change is unnecessary with intersect but have a distance in ized with a cutting blade mod- tools to bard finish each other. ground spiral bevel gears. space, the gear set is called a ification. This is the reason why lapped A process between lapping ! bypoid gear set. The name is Localized Tooth CODtact sets have to be built as a pair; and grinding with respect to ! derived from the hyperbolic I When bevel gear sets 3X,e lapped and gears are surface speed and relative ! s~ap~.ofth~ "pitch cones." For I cut according to the crown not interchangeable. motion is honing. HOlling tri- ! simplification, the blanks ar,e ; ge or generating gear princi- The lapping surface struc- als on bevel gears have been I still manufactured with II con- i ple, the result is a ,co.njugate ture is mot oriented in the done, but they haven't been ! ical shape, I pair of gears. onjugate direction of the contact lines, proven succe sful, I The convex gear flank rolll . means pinion and gear have 8 thus providing a good hydro- Skiving is a hard cutting I with the concave pinion flank. line conta.ctin each angular dynamic oil fib between the process. A [001 material such I This pair of flanks is called the position. While rctating the contact areas. The lapping as carbide or boron carboai- ! "drive side." The direction of gear in mesh, the contact line structure also tends to deliver tride is used on the cutting ! rotation where those flanks moves from heel top to toe side bands in a noise frequen- edge. The cutting machine ! contact the pinion drives is root. The motion transmission. cy analysis, which makes tl:te setup is identical to that For I called the drive direction, The happens in each rcll position gear set appear to roll. more soft machining. The blade j drive side direction is always with precisely the same con- quietly. point is wider than I used in to drive the stant ratio, Roll testing is done During the lapping process, the one For sofi:clltting, such j forward. The reverse ill specially designed bevel a pinion and a gear are always that a. n.OOS- uniform I direction is subsequently gear test machines. If 8. mark- machined and finished at the stock removal per flank takes 1 called the coast side (vehicle ing compound (paint) is same time. The time to lap a place. Skiving delivers a high ! rolls downhill, foot is off the brushed onto the flanks of the pair is equal 10or shorter than qllality part accuracy and a i gas pedal .., drive the ring gear member. a rolling in the time to machine one mem- fine surfacefinish, Skiving is j ). In some cases, the mesh under light torque makes ber using another finishing applied to small batches of 1 coast. side is used to drive the the contact area visible. In the method. Therefore. lapping is mostly larger gear sets. The j vehicle. but it is sti II called the case of a. c.onjugate pair, the often caJiled the most. 'econom- advantage of skiving is the use I coast side. contactarea is spread out over ical bevelgeu finishing of the same cutter head "only ! Ease-off is the pre entation the entire active flank, That is process. with different blades) and the! of flank form corrections the official definition. of the ...... po.... "'.n·.ml •• ton.com .,...... "'.lIurl.cl'lnorOIlY.com • GEAR TECHINOLOGY • J...'NUARY/FEBRU ....RY Z001 31 _------GEAR FUND'A'M:ENTALSI _

~ENGTHCROWNING

Ease-Oft IEase-'Ofl Ease-Oft

I

I foe Heel

Toothl Contact Tooth contact Tooth Contact

-

-. 0 .i.> e-;:-: - ik

Motion Gra,phl Motion IGr:aph lX figure 11'-Tooth ,contactanalpis of pnJfil'lIlcrowning, raDom ,crowning and'flanlc: (Wist

contact area. It is the summa-I octoidal profileund curved! To achieve II suitable flank ~ bet stress and gear deflec- tien of aU contact lines during lead function are filtered out, i contact,today's flank conec- tions ..O the complete roll of one pair Therefore the ease-off is a ! tions mostly consist of three of teeth, "flat" zero topography for I elements, shown in Figure l 1. Refer,e.DCe;t Conjugate bevel. gear pairs conjugate gears, The tooth ! Profile crowning ,(Figure 11, I. Stadtfeld, HJ. HandbookofB'eve.1 are not suitabl.e for operation contact is shown below the i left) is the result of at blade and Hypoid Gears; Calculation, Manufacturing and Optimizatiml'. under load and. deflections, ease-off Tooth orientation is I profile curvature. Length :It.oohester Institu!e of TcclmoLogy, Misalignment causes a high indicated with "heel. toe and ! crowniQg (Figure 11,center) Rochester, NY, 1993. stress concentration 00 the I root." TIlle coast and drive! can be achieved by modifica- tooth edges. To prevent those sides show a. full contact, cov-! tiOD of the cutter radius or by a J stress c.oncentrations, a i ering the entire active working! tilted cutter head in conjuae- i crowning in face width and i area of the flanks. The lower j tion w:ithlblade angle modifi- I profit.e direction is applied to diagram in Figure m is the cation, Flank twist (Figure II, ! nearly aU bevel pillions. The trans:mission error. Conjugate right) is a kinematic effect I amount of crowning has a pairs roll kinematically exact-resulting fmm a. higher order I relationship to the expected Iy with each other; That roll is mcdufation of the roll ratio I contact stress and deflections. .reflected by points on graphs . (modified roU) or cutter head j Toana.lyze tooth contact that match the abscissas of the i tilt in conjunction with a i and crowning, pro- diagramS ..Each point of those 1 machine root angle change. I ~ms for tooth contact anaIY-l; graphs hasa zero value (ZG- j The three mentioned flank ! SIS (TeA) were deveJoped. direction), so they cannot be i modiflcatiens be com- i Figure 10 shows the TeA distinguished from the base i billed, such that the desirable : result of a conjugate bevel grid ..The base grid and graph I contact .length and width, pa.th gear set TIlle top section of are identical and ,drawn on top i of contact direction and traas- FigUre ]0 represents a.graplltic of each other. That character- I mission variation magnitude of the ease-off; The ease-off izes a conjugate pair of gear! are realized ..The TCA charac- represents. the sum of'the flank flanks. TIIIetransmissioll graph ! teristics '(contact pattern. and 1 corrections, regardless of lalw.ay~ displays the ~otion ;1 transmission variati.on), are whether they were donein the I variation of three adjacent 1 chosen to 8U,;,t the gear set for pinion or gear member, The! pairs of teeth. ! the expected amount of con-

38· JANUARY/FEBRUARY2001 •. GEA!R TECHNOLOGY· www.gsllrrlll7lm0/olly.com • www.powlJrtrllflsmlssion .com