【文章內容簡介】 r generation. However, an overpositiveshifted modification may result in the appear ance of pointed teeth. Pointed teeth are generated when the right and leftside involute tooth profiles intersect on or below the addendum circle of the gear. Further, the pointed teeth are usually generated on the two major axis of an elliptical gear. If a profile index is defined to prevent pointed teeth generation on the two major axis of an elliptical gear, then no other pointed tooth will be generated for all elliptical gear profiles. Thus, the puter program developed here can calculate and provide proper design parameters for the designed elliptical gears to avoid tooth undercutting and pointed teeth. 2. Mathematical model of the elliptical gear surfaces Shaper cutters are used to generate elliptical gears, and the profiles of shaper cutters are the same as those of spur gears. Hence, the mathematical model of the shaper cutter is the same as that of the spur gear, which is generated from rack cutters. A plete elliptical gear tooth profile consists of three surface regions, . the working region, the fillet and the bottom land. Therefore, the profile parameters of a shaper cutter can be represented by the parameters of a rack cutter. Fig. 1 shows three regions of a rack cutter 2p including the working region, the fillet and the top land, used for shaper cutter and elliptical gear generations. When the shaper cutter creates the elliptical gear in a cutting mechanism, its center rotates along the Zcaxis and translates along the Xc and Ycaxes, performing a pure roll without sliding on the pitch ellipse, and the gear blank is rotated about its geometric center 01 as in Fig. 2. . Working region of shaper cutter profile Fig. 1 presents the design of the normal section of rack cutter 2p, where regions 3 and 4 are the left and rightside working regions, regions 2and 5 are the left and rightside fillets, and regions 1 and 6 are the left and rightside top lands. Meanwhile, parameter 163。p = M0 M1 is a design parameter, expressing the distance measured from the initial point M0 to an arbitrary point M1 in the working region. The three dimensional rack cutter profile can be obtained by translating its normal section, presented in Fig. 1, along the Zraxis with a displacement parameter Up. Therefore, by applying the theory of gearing, the mathematical model of the working region of the shaper cutter can be represented in the coordinate system Sc (Xc , Yc , Zc ) by the following equation (Litvin, 1989): Fig. 1. Normal section of a rack cutter 2p for generating the driving shaper cutter. Fig. 2. Kinematic relationship between the shaper cutter and the generated gear. where A0 is the design parameter used to determine the addendum of the shaper, B0 the tooth width of the shaper, rs the pitch radius of the shaper, cc the generated angle of the shaper and i/in the pressure angle as shown in Fig. 1. In Eq. (1), the upper sign indicates the rightside shaper surface while the lower sign represents the leftside shaper surface. The normal vector of the working region of the shaper cutter surface can be obtained as follows: . Locus of the shaper cutter Fig. 2displays the kinematic relationship bet