Curvature synthesis for face-milling spiral bevel gears with high-order transmission errors

  • Jianjun YangEmail author
  • Bingyang Wei
  • Hua Zhang
  • Zhenghong Shi
  • Jubo Li
  • Teik C. Lim
Technical Paper


A modification methodology based on curvature synthesis for face-milling spiral bevel gears is proposed in this paper. This scheme includes the calculation of machine-tool settings and determination of the instantaneous modified roll ratio based on different predesigned high-order transmission error (TE) curves. Firstly, the principal curvatures and directions of ease-off pinion surface at mean contact point are carried out based on the fully conjugate pinion surface. The machine-tool settings of the pinion can be determined to meet with the meshing conditions between the cradle and the pinion. Then, compared with the parabolic TE, the amplitudes of loaded TE under a series of pinion torque for fourth-order and sixth-order TE are decreased based on the results of loaded tooth contact analysis. Finally, an example is provided to verify the proposed method. The parabolic, fourth-order and sixth-order transmission error curves are used to illustrate how to obtain the modified roll curve.


Curvature synthesis Relative principal curvature High-order transmission error Modified roll ratio Spiral bevel gears 



The authors would like to express their appreciation to the financial assistance from the National Natural Science Foundation of China (No. 51875174) and Key Scientific and Technological Project of Henan Province (Nos. 192102210057, 182102210287, 182102210042, and 172102210037).


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Copyright information

© The Brazilian Society of Mechanical Sciences and Engineering 2019

Authors and Affiliations

  • Jianjun Yang
    • 1
    Email author
  • Bingyang Wei
    • 1
  • Hua Zhang
    • 1
  • Zhenghong Shi
    • 2
  • Jubo Li
    • 1
  • Teik C. Lim
    • 2
  1. 1.School of Mechanical and Electronic EngineeringHenan University of Science and TechnologyLuoyangPeople’s Republic of China
  2. 2.Vibro-Acoustics and Sound Quality Research Laboratory, Department of Mechanical and Materials EngineeringUniversity of CincinnatiCincinnatiUSA

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