Since the coincidence degree and the transmission error amplitude at the transition of high-speed and heavy-duty spiral bevel gears are mainly affected by the second-order contact parameters, and the three second-order contact parameters are independent of each other, based on the local synthesis method and TCA, LTCA technology, the tooth surface with high coincidence degree and low amplitude at the meshing transition is designed, and the following multi-objective optimization design model is established:
Optimization variables

Objective function

Constraint condition

Where, η, m’21, δ It is the three second-order contact parameters of the tooth surface of high-speed and heavy-duty spiral bevel gears.