Optimization Design of the Toroidal Worm Wheel Hob for Robotic Joint with Worm Gear Pair Transmission

To improve the transmission efficiency of the toroidal worm gear pairs in robotic joints and to enhance the accuracy of the toroidal worm wheel hob in cutting worm wheels, a method is proposed that involves using cylindrical forming surface milling to create helical grooves on the front face of the toroidal worm wheel hob. Based on the principle of gear meshing, a mathematical model is established for the development of the helical grooves on the front face of the toroidal worm wheel hob using a cylindrical generating surface. The model uses planar second envelopment for the toroidal worm wheel. Additionally, formulas are provided for calculating the rake angles on both sides of the cutting edges in the indexing ring plane. The analysis of the obtained rake angle values reveals that when machining helical chip clearance grooves for variable transmission ratio toroidal worm wheel hobs, the rake angles on both sides of the hob are within ±0.25°. Compared to machining helical chip clearance grooves for fixed transmission ratio toroidal worm wheel hobs, there is a noticeable decrease in the absolute value of the rake angles on both sides of the cutting edges, leading to a significant improvement in cutting conditions. Simulation machining of the helical grooves for the toroidal worm wheel hob was carried out, and the rake angle was measured within the simulation software. The measurement results align with the calculated results, validating the correctness of the method presented in this paper.