Calculation and analysis of contact ratio of helical curve-face gear pair

Helical curve-face gear pair is a new type of gear pair consisting of a helical non-circular gear and a helical curve-face gear, which can transfer the movement of variable transmission ratio between intersecting axes. According to the spatial gear engagement theory and the spatial coordinate transformation theory, the transformation matrix of helical curve-face gear pair and the unit normal of helical cutter are deduced. Based on the meshing theory, the meshing equation of helical curve-face gear pair is built. Equations of instantaneous contact ratio of helical curve-face gear pair are proposed by transforming helical curve-face gear pair into helical non-circular rack and pinion. Besides, the influences of basic parameters of helical cutter and helical curve-face gear pair on contact ratio are analyzed. The tooth surface coordinate data of helical curve-face gear pair is obtained by using the gear measuring center, and the comparison findings between experimental and theoretical results are the experiment data basically agree with the theoretical calculation value, and error is within 5%, so the calculation method of contact ratio is verified.