THE UNDERCUTTING OF HOBBED SPUR GEAR TEETH

A general method is presented for the determination of the minimum number of teeth that can be cut in a spur gear without undercutting by a rounded-tooth tip hob. The minimum number of teeth to produce undercutting was investigated for three trochoid/tooth-profile relations: (1) trochoid tangent to the involute profile at the base circle, (2) trochoid tangent to a straight portion of the tooth flank, and (3) trochoid intersecting the involute profile at the base circle. A set of figures representing the variation of the amount of undercutting versus the number of teeth, radius of hob-tooth tip, hob addendum, cutting pressure angle, and the corresponding derivatives are included for a typical gear.