Calculation of Curvatures is not just for scientific curiosity but, much much more importantly, for applications. Majority of gear failures in the field and in test are surface failure including scoring and pitting, or mixture of the two. Both are closely related to surface curvatures, or more precisely, relative curvatures of the two mating surfaces (Hertz theory and Elasto-Hydro Dynamic lubrication). DDS can calculate first, second and n-order derivatives along the wires on the tooth surface mesh. Below are some calculation results for spiral bevel gears.

Novikov spiral bevel gear tooth surface curvatures in U-direction (along the tooth). Red color shows the area with the smallest radius.

 

Novikov gear tooth surface curvatures >>