Mathematical simulation of a profile cutter for processing parts of a cylindrical gear

Various types of cutters (spherical, toroidal, etc.) are used for processing surfaces of transmission gear parts. The cost of a special forming tool is somewhat higher than that of such cutters. However, the increase in the cost pays a significant reduction in time necessary for processing parts. The paper presents mathematical simulation of a profile cutter (as a surface of revolution) for processing parts of a cylindrical transmission gear with an eccentrically cycloidal gearing (EC-gearing). In part 1 this problem is solved for the input part. The surface of the cutter is constructed as a family of circles with increasing radii in planes perpendicular to the axis of the cutter, the centres lying on this axis. We have obtained an equation for the family of curves, which are cross sections of the tooth surface of the gear by these planes. It is these curves that must be touched by circles forming the surface of the profile cutter. The requirement of the circles touching the curves of the family leads to a system of equations which allows finding the radii of the circles depending on the height of the cross section rise. The solution to this system is found analytically, which eventually leads to one equation for one unknown. The root of this transcendental equation is found numerically. A similar scheme is used in part 2 to find the equation of the profile cutter's surface for the output part. A computer program has been made aiming to specify the radii of the cutter's circular cross-sections for a given set of displacements along the axis of rotation. The work provided substantial assistance in manufacturing EC-engagement parts for gears of various types.

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