To eliminate the backlash and improve the precision and efficiency of enveloping worm, by analyzing the shortcomings in the existing non-backlash worm gear sets,non-parallel double-roller enveloping hourglass worm gearing was proposed based on the research of non-backlash double-roller enveloping hourglass worm gearing.Two rows of rollers were assigned to misplace and there was a certain defection angle between the roller axis and the radial.The working principle was introduced. According to the theories of differential geometry and space engagement theory, the dynamic and static coordinate system based on worm gear pair and the moving coordinate system based on the contacting point were established. The tooth surface equations of worm and contacting line equations of worm gear were deduced. The formulas of meshing limit function, induced normal curvature, lubrication angle and rotation angle of the non-parallel double-roller enveloping hourglass worm gearing were derived by means of the theory of differential geometry. The simulation was conducted using MATLAB software,c2,Rand γ, which impacted the engagement performance of this transmission, were analyzed. The numerical example showed that c2 should not be more than 10 cm,Rshould be controlled within 8 to 15 cm, and should be controlled within 28° to 50°, for effectively improving the meshing performance of the non-parallel double-roller enveloping hourglass worm gearing.
