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.
All of the cutting edges on an hourglass worm gear hob have different shapes and spiral angles. If the spiral angles are small, straight flutes are typically adopted. However, for hobs with multiple threads, the absolute values of the negative rake angles on one side of the cutting teeth will greatly affect the cutting performance of the hob if straight flutes are still used. Therefore, spiral flutes are typically adopted to solve this problem. However, no method to determine the spiral flute of an hourglass worm gear hob has been proposed until now. Based on the curved surface generating theory and the hourglass worm forming principle, a method for generating the spiral flute of the planar double enveloping hourglass worm gear hob is proposed in this paper. A mathematical model was built to generate the spiral flute. The rake angles of all cutting teeth of the hob are calculated. The laws of the rake angles of the cutting teeth for four hobs with different threads from one to four threads were analyzed when straight flutes and spiral flutes are adopted. The laws between the value of the negative rake angles of the hob with four threads and the transmission ratio were studied. The most appropriate transmission ratio for generating the spiral flute was obtained. The machining of the spiral flutes was simulated using a virtual manufacturing system, and the results verify the correctness of the method.
Cutting teeth of a dual-cone double enveloping hourglass worm wheel hob retain land surfaces with a certain width to increase the service life of the hob because this kind of hob cannot be re-sharpened. The land widths from the top to the root of all of the cutting teeth should be uniform so that all of them have the same cutting performance. However, the accuracy and the uniformity of the land width of the land surface of hob with spiral rake faces have not been studied till now. To solve this problem, this paper puts forward a method for designing the land surfaces of the hob with spiral rake faces and studies the accuracy and the uniformity. The spiral rake faces of the teeth of the hob are generated by a cylindrical surface. The offset surfaces of the spiral rake faces are obtained by offsetting the spiral rake faces along their normal vector directions with the offsetting distance equal to the land width. The rake faces and the offsetting surfaces intersect with the helical surfaces so the cutting edges and the land edges can be gotten, respectively. The land width of each cutting tooth is the distance between its cutting edge and its land edge. The results of a numerical example show that the calculated land widths on the pitch torus decrease firstly and then increase from one end to another end along the axial direction. The difference of the calculated land widths between the top and the root is larger at side teeth than that at middle teeth. The calculated land widths are slightly larger than the given one and all the calculated land widths change within a small range that can be ignored. Therefore, the method can keep the accuracy and the uniformity.
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