Tooth Surface Error Correction Methodologies for Spiral Bevel and Hypoid Gears Generated by Duplex Helical Method

In order to eliminate the tooth surface errors and ensure precision of spiral bevel and hypoid gears generated by the duplex helical method, two new methodologies for the format gears and the generated gear or the pinion manufactured by the duplex helical method are proposed. Firstly, the cutting characteristics of this method is analyzed, both mathematical models for the format gear and the generated gear or the pinion generated by the duplex helical are established, one includes 8 machine settings, the other one includes up to 40 universal motion coefficients. Furthermore, the tooth surface errors of the grid points are represented by up to 6th order polynomials, then Constraint Least Square Method for determining the appropriate changes of the corrective machine settings is proposed to minimize the tooth flank form errors. Finally, new tooth flank form error correction software for spiral bevel and hypoid gears has been developed and a hypoid gear set generated by the duplex helical method is used as an example to validate the effectiveness of the software. The results reveal that the flexibility and efficiency of the tooth flank form error correction for both format gear and pinion generated by duplex helical method are greatly improved. In addition, the new approach can also be applied to the tooth flank form error correction of bevel and hypoid gears generated by other process methods.