Fast modeling of conjugate gear tooth profiles using discrete presentation by involute segments

This paper introduces the method of the discretization of the gear tooth flank in involute segments for the determination of conjugate gear tooth profiles. Instead of following a point-to-point analytical approach to the problem of determining the path of contact and the geometry of the generating rack and the mating wheel, the actual tooth flank is considered to be composed of infinitesimal local involutes and therefore a closed solution can be achieved. Due to its simplicity, the method is faster than the standard theory of gearing and this is particularly useful in problems requiring iterative calculations of the tooth geometry such as gear optimization. The method is implemented on modified involute as well as loboid gears used in lobe pumps and it is verified against existing theories.