Computerized design, simulation of meshing, and stress analysis of curvilinear cylindrical gears based on the active design of the meshing line function

The computerized design of curvilinear cylindrical gears based on the active design of the meshing line function is presented. The parametric equations of their meshing line functions are based on a parabola to control the curvilinear shape of the teeth along the face width of the gears. Different numbers of control points and different combinations of curves, including parabolic curves, circular arcs, and involutes, smoothly connected with each other at the control points are chosen to form the active tooth profile. The meshing performance, mechanical behavior, and influence of the parameters of combined curves are studied in terms of the contact patterns, variation of the maximum stresses and loaded functions of transmission errors and compared to two types of curvilinear cylindrical gear drives generated by face-milling cutters as a reference. The investigated curvilinear gear drives with five control points show lower maximum contact and bending stresses as well as lower peak-to-peak level of loaded transmission errors compared to other cases of curvilinear gear drives.