Mathematical Model of the ZN-Type Worm Gear set with a Non-ninety-degree Crossing Angle and Undercutting Analysis of Worm Wheel Tooth Surfaces

A mathematical model of the ZN-type worm gear set with a non-ninety-degree crossing angle is developed based on the theory of gearing. The worm wheel is generated by a worm-type hob cutter, which is identical to the ZN-type worm. Based on the developed mathematical model of the worm gear set, a three-dimensional computer-aided graph of the ZN-type worm gear set with a non-ninety-degree crossing angle is presented. Tooth undercutting of the worm wheel is also investigated. Besides, undercutting lines of the worm wheel tooth surfaces are calculated and plotted. It is found that tooth undercutting is easier to occur at the middle region of the worm wheel tooth surface. In addition, pressure angle and crossing angle of the worm gear set play very important roles on the tooth undercutting.