Cutting Teeth of Non-involute Gears of the Cylinder–Conical Internal Transmission of Internal Gearing

The paper deals with a cylinder–conical internal gearing consisting of an involute cylindrical wheel with internal teeth and a cone-shaped (according to the form of the workpiece) non-involute gear, the axis of which is at the angle to the wheel axis. With the use of these gearings, it is possible to create eccentric planetary transmissions with two inclined satellites which implement large gear ratios (in the power drives 90–500) and having high load capacity with relatively simple design. In their characteristics, they are comparable with harmonic gear, but more reliable. However, non-involute gear teeth have a complex barrel-shaped, getting them theoretically accurate surface difficult. Cutting teeth of the considered gear can be carried out with a sufficient practical accuracy in the machine gearing of the workpiece and the tooth-carving hob as it moves along a certain curvilinear trajectory. The dependencies for determining the trajectory of the axis of the milling cutter when cutting teeth of a non-involute gear of the cylinder–conical transmission of internal gearing are obtained. The movement of the milling cutter along a curved path can be realized in CNC tooth milling machines. In the paper, the example of calculation of a trajectory of motion of the axis of the cutters for cutting the teeth of a crown pinion planetary reducer with internal, helical-bevel gearing is shown. The research results were used in the design and manufacture of planetary gearboxes for various purposes.