In the blank design of spiral bevel and hypoid gears, the face cone is defined as an imaginary cone tangent to the tops of the teeth. Traditionally, the face cone element or generatrix is a straight line. On the other hand, the tooth root lines, which are traced by the blade tips, are normally not straight lines. As a result, the tooth top geometry generally does not fit the mating member’s real root shape, providing an uneven tooth root-tip clearance; additionally, in some cases root-tip interference between the tooth tip and the root tooth surfaces of the mating gear members may be observed. To address this issue, this paper describes a method of determining an optimized face cone element for spiral bevel and hypoid gears. The method is based on the incorporation of calculation of tooth surface and root geometries, the conjugate relationship of the mating gear members, the ease-off topography, and the tooth contact analysis. The resulting face cone element may not be a straight line but generally an optimized curve that, in addition, to avoidance of the interference, offers maximized contact ratio and even tooth root-tip clearance. Manufacturing of bevel gear blanks with a curved face cone element can be implemented by using computer numerically controlled machines.

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