A Designing and Generating Method for Grinding Relief Surfaces of a Dual-Cone Double-Enveloping Hourglass Worm Gear Hob

Land widths and relief angles of a dual-cone double-enveloping hourglass worm gear hob are important factors that influence the life and the hobbing performance of the hob. Both of them are obtained by generating relief surfaces of the hob. Due to the reason that all teeth of this type of hob have different profiles with each other, all of the relief surfaces are difficult to generate for keeping all cutting teeth with uniformed relief angles and uniformed land widths. For the purpose that land widths and relief angles could be machined precisely, this paper puts forward a designing and generating method for grinding the relief surfaces. The relief surfaces are ground using the same double-cone grinding wheel as grinding the helical surfaces of the worm. Based on the theory of gearing, the mathematical model for grinding relief surfaces is built. Motion parameters when grinding the different points of the land edges on different teeth of the hob are solved. A generating simulation is built by putting those motion parameters into a four-axis hourglass worm-grinding machine. The results of the simulation show that the relief surfaces can be ground continuously and the land widths and the relief angles meet the requirements.