An efficient approximate profiling method for the rack gear tool

This paper presents a simplified algorithm for the profiling of the rack gear tool to generate the active profile associated with rolling centrodes. The algorithm is based on the enveloping surfaces principles and reduces the computational problem by proposing an approximate representation of tool’s profile using only three or four points on the profile to be generated by using Bezier representations of the surfaces. The algorithm computes the coefficients of a Bezier substitution polynomial instead of computing hundreds of points on the active profile. This simplifies the solution methodology and requires only a limited number of points along the profile to be generated. The algorithm is computationally efficient and can also be used in the case when the active profile to be generated is physically measured at a few points. Examples include mill tools, splined shafts, and gears.