A Method to Generate the Spiral Flutes of an Hourglass Worm Gear Hob

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.