Transcription of Back to Basics - Gear Design
1 BACKTOBASICS. GearDesignNational Broach and Machine Division ,ofLear Siegler, gear can be defined as a toothed wheel which, whenmeshed with another toothed wheel with similar configura-tion, will transmit rotation from one shaft to upon the type and accuracy of motion desired,the gears and the profiles of the gear teeth can be of almostany come in all shapes and sizes from square to circular,elliptical to conical and from as small as a pinhead to aslargeasahouse.
2 They are used to provide positive transmis-sion of both motion and power. Most generally, gear teethare equally spaced around the periphery of the original gear teeth were wooden pegs driven into theperiphery of wooden wheels and driven by other woodenwheels of similar construction ..As man's progress in the useof gears, and the form of the gear teeth changed to suit contacting sides or profiles of the teethchanged in shape until eventually they became parts ofregular curves which were easily obtain correct tooth action, (constant instantaneousrelative motion between two engaging gears)
3 ,the commonnormal of the curves of thetwoteeth in mesh must passthrough the common point,orpoint of contact, of the pitchcircles of the two wheels,Fig. 1-1. The common normal to apair of tooth curves is the line along which the normalpressure between 'the teeth is exerted. It is not necessarily astraight line. Profiles of gear teeth may be any type or typesof curves, provided that they satisfy the law of contact justdefined. However, manufacturingconsiderationslimit theprofiles to simple curves belonging to the circle group, orthose which can be readily generated or cut, as withgear cutters on standard milling machines.
4 Because of inherent good properties and easy reproduc-ibility, the family of cycloid curves was adopted early (1674)and used extensively for gear tooth profiles. The "~---,,----::-~COMMON NORMALOF TOOTH CURVES--FIG. l"l-Forconstant instantaneousrelative motion between two engag-inggears, the common normal of thecurves of the two 'teeth in mesh mustpass through the commonpoint,or point of contact, of the pitch circles ofthetwo Tec'hnologyFig.
5 1-2- The common normal of cycloidal gears which variesfrom a maximum inclination with respect to the common tangent at thepitch point to coincidence with the direction of this tangent. For cycloidalgears rotating as shown here. the arcB'Pis theArcofApproach,and theall;PA,theArc of ] of cydoidal gearsisacurve, Fig. 1-2, which is not ofa fixed direction, but varies from. a maximum inclinationwith respect to the common tangent at the pitch point tocoincidence with the direction of this tangent.
6 Cydoidalgears roll with the direction of this tangent. Cycloidal gearsroll with conjugate tooth action providing constant powerwith uninterrupted rotary motion ..One disadvantage of thistype of gear is that the center distance between mates mustbe held to fairly close tolerances, otherwise mating gearswill not perform involute curve was first recommended for gear toothprofiles in the year 1694 but was not commonly used until150 years later.
7 The curve is generated by the end of a tautline as it is unwound from the circumference of a circle, Fig ..1~3. Thecirclefrom which the line is unwound is commonly,-////////.>/.-";"--//.E,\\\"\\I I I/"\ \ II /,./, \ \ I II /,\ \ II{ ,-~, Involute tooth form used for virtually all gearing todayisgenerated by the end ofa tautlineas it is unwound from the circumference'0 a circle. The circle from which the line is unwound is theBase 4 ON READER REPLY CA'RDB-I_][-4-The common normal of involute gear teethisa straightIineAB'.}
8 Known as the' "base circle". The common normal of involutegear teeth is a straight line (AB, in ).Gears of this'typesatisfy all the requirements for smonthvaccureteandcontinuous motion. Gears with involute tooth profile arevery flexible in both geometric modificati ..on and centerdistance been many other types of gear tooth forms,some related to the involute curve, One particular type ofrecent interest isthe"circular arc" gear {where the profile isan arc from }.
9 Pirst proposed country by Ernest Wildhaber in 'the 1920's, the circulararc gear was recently introduced by the Russians as the"Novikov" tooth form .. These profiles are not this tooth form depend upon helical overlappingof the teeth in order to roll continuously. This can and doescreate face width size and end thrust problems,At the present time, except for clock and watch gears, theinvolute curve is almost exclusively used for gear tooth pro-files,Therefore,exceptfor an occasional comment, thefollowing discussionwillcover some 'of the basic elementsand modificationsused in the Design of involute toothform primary purpose of gears is to transmit motion and atthe same time.
10 Multiply either torque or speed, Torque is afunction of the horsepower and speed of the power an indication of the power transmitted through a driv-ing shaft and from it the gear tooth loads are ealculated. Theloads applied to gear trains can vary from practicallyFig. 11-5-Ratios of the gear 'teeth in this hypothetical hoist drive would de-penduponweight (~to, belifted andtorque(navailable from the to several. tons or more. Gears, properly designedand meshed.))
