Research on equaling design and machining method of roughing allowances of a dual-cone enveloping toroidal worm

method and high-efficiency machining method for the consistency rough machining allowance of the toroidal worm are not perfect, which is not conducive to improving the grinding efficiency and quality of the toroidal worm. Aiming at the design and processing of the toroidal worm roughing allowance, this paper studies the design method of the toroidal worm roughing allowance surface, and proposes a machining method of the allowance surface used in an ordinary CNC lathe. First, according to the forming principle of the dual-cone enveloping toroidal worm, the helical surfaces of the multi-thread toroidal worm with a given throat tooth thickness are established. Then, each point on the helical surface is rotated by an allowance angle around the axis of the worm, and the mathematical model of the roughing allowance surface is established by setting the arc length of each point rotation equally. The designed allowance surface is discretized into a series of helical lines, and a series of helical lines are discretized into points. The cone helical line interpolation is used between two adjacent points for turning the allowance surface based on an ordinary CNC lathe. Based on the axial indexing method, different helical lines can be machined by adjusting the starting points X and Z of the tool when processing helical surfaces at different positions. Through research, the allowance equalization and rough machining of the variable-lead enveloping helical surface are realized, which provides a new method for the processing of complex and special-shaped helical surfaces.