High-order involute modified noncircular bevel gears

Noncircular bevel gears (NBGs) is a kind of spatial transmission mechanism which can be used to transmit the motion and power between two intersecting axes with a variable transmission ratio and according to a suitable motion program. Given that the pitch curve and tooth profile curve of NBGs are spherical curve rather than plane curve, the research methods on NBGs is complicated than bevel gears as well as plane noncircular gears. In this paper, the pitch curve equations of NBGs are obtained for any order and in any configuration during their pure rolling based on the spherical polar coordinate system. The relationship of least teeth number avoiding undercutting and the pitch curve curvature of NBGs is analyzed. Being directed against high-order involute NBGs drive, a kind of varying-coefficient-profile-shift-modification method has been presented. The equations of the modified addendum and dedendum curves are implemented in MATLAB. The algorithm for generating tooth profile of NBGs by the hypothetical involute modified shaper cutter under UG platform is proposed and some significant examples are included. The 3D models and prototype of a pair of conjugate high-order involute modified NBGs are demonstrated to verify the correctness of this modification method.