Involute (ZI) type worm gear set

grabcad

z1=3 z2=60 mn=0.75 alphan=20° gamma= 7.81667°RH x1=0 ratio=20.Worm normals computed as of a helical gear with beta= 82.183333°.Contact points and flank points are computed according to the Law of Conjugate Action.Blueish surfaces are the contact surfaces LH & RH.Remark: you can extract surface normal vectors from existing CAD models of the teeth. These normal vectors are of poor accuracy in comparision with computed ones (cross products of the tangent vectors obtained by partial derivation of the surface in respect to its parameters).The normals for this model are computed, not extracted from the worm model. Therefore the contact and flank surfaces are quite exact. The root is a fitted radius fillet, the generated fillet is possible but tedious.