Study on the design and the shaping of the pitch surface of a multi-lobed non-circular bevel gear

In order to extend the type of multi-lobed non-circular bevel gear, some curves such as an Archimedes spiral, a quadratic curve and a Pascal curve are applied to the design of the pitch surface of a multi-lobed non-circular bevel gear. With the aim of studying the design defects of a multi-lobed non-circular bevel gear which has a pitch surface with a concave cusp or a convex cusp, a novel pitch-surface-shaping method is presented to shape the concave cusp or the convex cusp of the pitch surface of a multi-lobed non-circular bevel gear. A section of the pitch surface of the cutter is used to replace the concave or convex pitch surface of the multi-lobed non-circular bevel gear by using the above shaping method. Mathematical models of the pitch surface with multi-stage space curves for a multi-lobed non-circular bevel gear are established. Numerical examples demonstrate that the shaping method is beneficial for improving the machining quality of the teeth profile as well as the transmission performance of a multi-lobed non-circular bevel gear.