Mathematical model and tooth surfaces of recess action worm gears with double-depth teeth

In this study, the surface equations of recess action (RA) worm gears with double-depth teeth, generated by a ZN worm-type hob cutter, are proposed. Based on the generation mechanism and the theory of gearing, a mathematical model of a series of worm gears, semi RA, full RA and standard proportional tooth types, with double-depth teeth is developed as the function of design parameters of the ZN worm-type hob cutter. According to the derived tooth surface equations, computer graphs of a series of worm gears with double-depth teeth are plotted. Tooth surface variations of the generated RA worm gears due to the varying pitch line, pressure angle and tooth height of the hob cutter are also investigated.

► Mathematical model of the RA worm gear with double-depth teeth is developed.
► Pitch circle and throat circle of the full RA worm gear are identical.
► Transverse chordal tooth thickness is calculated.