Theoretical peculiarities regarding the definition and representation of the rolling surfaces

This paper presents the matrix-vector calculus of the rolling surfaces of a bevel worm gear with inverted conicity. By this gear the worm gear is situated on the inner side of the crown taper. It is to remark that in this case both rolling surfaces cannot be tangent. Keeping the worm’s rolling surface conical, it is necessary to calculate the profile of the crown’s rolling surface that becomes a hyperboloid. Using a numerical approach, the best approximating cone of the crown wheel’s rolling surface will be calculated.