【正文】 ect gear design does not limit fillet shape definition. One possibility is to describethe fillet profile as a trace of the top part of themating gear tooth (with corresponding minimumradial clearance) (Refs. 4 and 5). Application offinite element analysis allows for forming the fillet profiles to balance and minimize bendingstresses.Extreme Parameters of Involute GearsPoint A(tangent point of isograms εα= andαw= max) of the area of existence describes gearswith the maximum achievable operating pressureangle. There is no such limit for helical gearsbecause a lack of the transverse contact ratio (εα) is pensated by the axial contact ratio εβ.A sample of a helical gear with high operatingpressure angle (Ref. 6) is shown in Figure 8. InFigure 5, the point B (intersection point of interference isograms αp1= 0H11034 and αp2= 0H11034) of thearea of existence describes the gears with themaximum achievable transverse contact ratio.Table 5 presents maximum values for operatingpressure angle αwA(Point Aof the area of existence) and transverse contact ratio εαB(Point B ofthe area of existence) for gear pairs with differentnumbers of teeth and the proportional top landFigure 10—Spur gears with minimum number of teeth: a) z1= 5, z2= 5, αw=, εα= 。 6c, at point C ofFigure 5 (αwmax= 176。pressure angle is shown inFigure 1. The zone shown contains all gear binations that can be produced using this particular generating rack. Its area is limited by the minimum contact ratio for spur gears εα= (isogram A), the sharp tip of the pinion (isogram B),and the tipfillet interference (isograms C and D).The undercut isograms E and F put additionallimitations on the zone area. Other available gearbinations exist outside the zone borders, butin order to realize them, the generating rack parameters would have to be changed. In other words,a range of possible gear binations is limitedby the cutting tool (generating rack) parametersand the machine tool setup (xshift).Direct gear design is the way to obtain all possible gear binations by analyzing their properties without using any of the generating processparameters. Those parameters can be definedTable 1Drawing Specification Generating Process Parameter Gear ParameterNumber of Teeth XStandard Normal Pitch XNormal Pressure Angle XStandard Pitch Diameter XHelix Angle XHand of Helix XHelix Lead XBase Diameter XForm Diameter XRoot Diameter XOutside Diameter XTooth Thickness on Standard Pitch Diameter XAddendum XWhole Depth XTable 2ParameterNumber of teeth (given)Proportional top land thicknesses (given)Center distance, in. (given)Proportional base tooth thicknesses (chosen from area of existence)Profile angle in the involute intersection point, deg.Profile angles on outside diameters, deg.Operating pressure angle, deg.Transverse contact ratio Profile angles in the bottom contact points, deg. Base diameters, in. Base pitch, in.Operating pitch, in.Operating pitch diameters, in.Operating tooth thicknesses, in.Outside diameters, in.Outside diameter tooth thicknesses, in.Symbolz1z2ma1ma2awmb1mb2ν1ν2αa1αa2αwεa αp1αp2db1db2pbpwdw1dw2Sw1Sw2da1da2Sa1Sa2Equation(4a)(5a)(10)(12)(13)(14)(11a)db2= db1? u(3)(7)(8)(9)(2a)(5b)Value1428after the gear design is pletely finished. There were attempts to use the base circle as afoundation for the involute gear theory, separating the gear analysis from the gear generatingprocess. Professor . Vulgakov developed thesocalled theory of generalized parameters forinvolute gears (Ref. 2). . Colbourne (Ref. 3)described an alternative definition of the involutewithout using the generating rack. The selfgenerating method “gear forms gear” was proposedfor plastic molded gears (Refs. 4 and 5).According to this method, the top land of thetooth of one of the gears forms the fillet of themating gear and vice versa. At a glance, it lookssimilar to a gear shaping or gear rolling process,but the fact that both gears are described withoutthe generating rack parameters makes a difference in their geometry and characteristics.Involute Tooth ParametersAn involute tooth is formed by two involutesunwound from the base circle db, outside circlediameter daand fillet (Ref. 2) (see Fig. 2). Unlessotherwise stated, the following equations are correct for spur gears and for helical gears in thetransverse section (the section perpendicular tothe axis of the gear). Equation numbers withalphabetic modifiers are given for use in thenumeric examples listed in Tables 2, 3 and 4.The profile angle in the intersection point ofthe two involutes (tip angle) isν = acos(db/d?)where d?is the sharp tip circle diameter.The profile angle on the outside diameter daisαa= acos(db/da) da= db/cos(αa) The base pitch ispb= π ? db/zwhere z is the number of teeth.The proportional base tooth thickness ismb= Sb/pb= z ? inv(ν)/π inv(ν) = π ? mb/zwhere Sbis the base thickness.The proportional top