Investigation on the generation of bevel gear by disk tool with curved tooth surface of trapezoidal tooth profile

A bevel gear pair with curved tooth surface is widely used for power transmission of intersecting shafts. The bevel gear pair with curved tooth surface has higher load bearing capacity than straight bevel gears, longer line length, quieter, center distance assembly error, and does not change the speed ratio. This paper proposes a disk cutter with curved tooth surface of trapezoidal tooth profile to generate a bevel gear pair. One continuously distributed a trapezoidal tooth profile with curved tooth surface on a disc into an imaginary disc cutter to generate a bevel gear pair with curved tooth surface. This method has never appeared in the literature. Therefore, a mathematical model of a disc cutter with curved tooth surface of trapezoidal tooth profile was established and used to generate the mathematical model of the bevel gear pair via the theory of gearing. Through the undercutting analysis, explore the undercutting conditions of the proposed disc cutter and determine the parameter size limit. Based on tooth contact analysis (TCA), the transmission error and the contact pattern of the bevel gear pair with curvilinear teeth is calculated under the assembly error of the bevel gear. The advantage of the proposed disc cutter is that the transmission error of the parabolic type without modification of the tooth surface of the bevel gear pair can be obtained.