Helix Error Testing and Tracing on Planar Enveloping Hourglass Worm Tooth Surface

In order to improve the manufacture precision of planar enveloping hourglass worm tooth surface, a method for the helix error testing, tracing, and correction was proposed. Based on the theory of differential geometry and gear meshing, mathematical models for the tooth surface, the hourglass helix, and the hourglass helix with manufacturing errors were established for the planar enveloping hourglass worm. The principle of probe radius compensation and the method of error assessment were analyzed. In addition, the helix error of the prototype tooth surface was tested using the developed hourglass worm detector, and the error tracing was analyzed by the genetic algorithm. The prototype tooth surface was then amended and manufactured based on the results of error tracing. The results show that through the error tracing and error correction, the helix error of the prototype tooth surface was reduced from 0.140 to 0.025 mm.