Three interrelated mathematical models are developed to determine the size and shape of a helical gear tooth. These models are combined into a design procedure to produce a compact high load capacity helical gear set. The profile geometry is based on synthesis and consists of two differential equations concerning conjugate profiles and the Hertz contact pressure. This is merged with a bending strength model based on the moment image method. This merger is accomplished by adjusting the pitch line tooth thickness and the profile curvature. A balanced design is reached where the three load capacities are equal or where the weakest tooth in bending is made as wide as possible. This makes the most efficient use of the given pitch line space. A third model, consisting of a search routine, is placed around the capacity models. Its purpose is to select values for the variables describing the tooth contact area which provides the maximum capacity for the gear set. These variables are needed in the boundary conditions for the profile model and to determine the tooth height for bending strength calculations. A comparison is made with the 20 deg involute system. The synthesized gears show twice the load capacity of an equivalent sized involute gear set for softer materials. This is reduced to a 50 percent improvement for the harder steels.

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