Mathematical models of hobs for conjugate-curve gears having three contact points

Conjugate-curve gears are the gears which are point contact and the locus curves of the contact points are conjugate curves. The contact pattern of the conjugate-curve gear tooth surfaces are convex to concave, which reduces the contact stress of the tooth surfaces due to the small value of the relative curvature radius at the contact point. The tubular tooth surfaces of the conjugate-curve gears have one pair of conjugate curves. To decrease the running-in time and increase the load capacity, the conjugate-curve gears having three pairs of conjugate curves are designed. The contact stress of the tooth surfaces having three contact points is much smaller than that of the tubular tooth surfaces in the computer contact analysis. For the further study of the performance of the conjugate-curves gears having three contact points, hobs are considered to manufacture the gears. Two mismatched rack cutters having three contact points are applied for the design of hobs. The working edge in the normal section profile of the rack cutter for the hob generating the pinion is a circular arc and the working edges in the normal section of the rack cutter for the hob generating the gear are two parabolic curves that are tangent to the convex circular arc. By applying the designed rack cutter profiles, the principle of coordinate transformation, the differential geometry theory, and the theory of gearing, mathematical models of the hobs are established. To verify the proposed tooth profile and the hobs, the experimental cutting trials and the load capacity test are carried out. The final accuracy of the gear satisfies the design requirements. The results demonstrate the feasible of the proposed design method.