Study on the tooth profile and meshing equation of the anti-backlash double-roller enveloping hourglass worm with errors

The mismatched errors of the anti-backlash double-roller enveloping hourglass worm (ADEHW) plays a very critical role on its performance, but the influence of errors on ADEHW are rarely reported in available literatures, and the most important thing that we concerned is how to acquire the meshing equation and generate the tooth profile of ADEHW involving errors. Therefore, the new anti-backlash double-roller enveloping hourglass worm tooth profile equation which involved the grinding wheel radius, angular position error of the worm wheel axis, the centre distance errors and the shaft angle was established for the first time in order to study the effects of worm parameters on the worm tooth profile by using the theories of differential geometry and gear meshing. A new method to acquire the contact line of worm was presented by using the corresponding computer program and dichotomy. The real tooth surface was acquired based on the Pro/E software using the contact helix line equation and the three-dimension (3D) geological modeling of the Anti-backlash double-roller enveloping hourglass worm was established. The results obtained show that the formula established of worm tooth profile is important to analysis the characters of gearing mesh and parameter.