_------------liGEARiFUINID,AMlENTAILS------------_ The Basics of' Spiral Bevel Gears 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 gear, rolling 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 machine 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 torque To understand the bevel from one shaft to another. That gear tooth geometry, one transmission 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--Crown gear Brrangemenl In be:vel gear sets. ciency. Tooth profile. length bent in 8. horizontal plane into tion point of the pinion 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 bevel gear 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 coupling 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 MACHINES, 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 milling 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 circular motion, 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 Power Train with its remarkable expenence in g.ears rotation 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. CIRCLE 180 32 JANUARYI'FEB.I'lUAAY 2001 • GEAR TECHNOLOGY' 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 machining 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 spiral bevel gear 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.