Bevel and hypoid gears commonly have a parabolic motion error which is the result of circular crowning on the surface of the teeth in tooth profile and length direction. The crowning is required in order to allow for load affected deflections in the gearbox housing, the bearings and shafts and the gears themselves. Those deflections are a magnitude larger than in cylindrical gear transmissions which is related to the angular shaft orientation and the often cantilever style pinion support. Bevel gear sets without crowning are conjugate, which means they transmit the rotation of a driving pinion precisely with the ratio given by the division of the number of gear teeth by the number of pinion teeth. Traditional flank form corrections in bevel and hypoid gears and today also in cylindrical gears use dominating second order modifications. A combination of circular length and profile crowning is shown in the Ease-Off in Figure 1. In bevel and hypoid gears, the crowning is partially applied to the pinion and partially to the gear. In cylindrical gears it is common practice to manufacture one of the two members without any modification and apply the entire crowning in the second member (Ref.1).
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