Induced curvature of common roller surface of spiral bevel gear meshing

When two surfaces s (1) and S (2) are completely conjugate, their relative curvature at the contact point is called induced curvature.

According to the surface meshing conditions, the surface s (2) is completely determined by the equation of the surface s (1) and the relative motion between the two motion coordinate systems, so their induced curvature at the contact position is also completely determined by the relative motion between the surface s (1) and the two motion coordinate systems. Using the second equation of the differential equations of the relative differential method, we can get:

Since N1 = N2, n can be used to represent the common normal vector of the two surfaces at the contact point, and the differential relationship of the normal vector along the common roller direction can be obtained by substituting the above formula for simplification:

Differential the meshing equation v12n = 0 to obtain:

Of which:

After substituting them into the formula, let:


The formula can then be rewritten as:

Thus, the expression of DT can be obtained as: