Nonlinear correction of hypoid gear machine tool parameters by duplex helical method

To reduce the vibration noise of hypoid gear pairs machined using the duplex helical method (DHM), the machine tool machining parameters of hypoid gears were nonlinearly correction using the active design method. By presetting the second-order parabolic-shaped transmission error curve, a Levenberg-Marquard (L-M) algorithm with a double dogleg step trust domain strategy is proposed, compared to the Gauss-Newton (G-N) method. With the optimization objective of minimizing the square of the deviation of the two tooth flanks, the simultaneous optimization of the flank deviation and transmission error on both sides of the pinion gear has been realized. With the concave-convex tooth deviation reduced by 52.7 % and 70.15 %, the transmission error values differed from the preset values by 0.25″ and 0.2″, respectively. A numerical example and finite element simulations were used to validate the effectiveness of the suggested strategy.