To address the stability issues in face gear transmission and to achieve more balanced contact and load distribution, this study investigates the tooth surface geometry and meshing characteristics of non-orthogonal offset face gears. First, coordinate systems for the gear pairs are established, and the tool equation, meshing equation, and tooth surface equation are derived. Then, the effects of parameters such as pressure angle and module on the theoretical inner radius, outer radius, and face width are analyzed. Based on this, a tooth surface modification method is proposed, and the modification parameters are optimized. Furthermore, the influences of shaft angle and offset distance on the amplitude of transmission error and the maximum contact stress are examined, followed by an evaluation of edge contact behavior after modification. The results show that proper modification significantly improves edge contact performance. Within certain ranges of modification amounts and load conditions, the modified gears effectively reduce the transmission error amplitude and maximum contact stress, thereby enhancing the stability and reliability of gear transmission.
ChuXZengHWangY, et al. Research on tooth surface design and side milling machining method of ruled line face gear. Int J Adv Manuf Technol2023; 124: 511–526. https://doi.org/10.1007/s00170-022-10537-0
3.
WangYSuGChuX, et al. A finishing method for the continuous generation of spur face gears with shaving cutters. Int J Mech Sci2021; 190: 106020. https://doi.org/10.1016/j.ijmecsci.2020.106020
4.
ChenHLiQJiaC. Research on the design and meshing performance analysis of face gear face gear meshing nutation reducers. Mathematics2025; 13(3): 476. https://www.mdpi.com/2227-7390/13/3/476
5.
WangLGaoYZhangJ. Study on the dynamic load sharing characteristics of nutation face gear transmission. Discov Appl Sci2025; 7(2): 111. https://doi.org/10.1007/s42452-025-06494-4
6.
JiaCLiBXuJ. A novel tooth modification methodology for improving the load-bearing capacity of non-orthogonal helical face gears. Machines2023; 11(12): 1077. https://doi.org/10.3390/machines11121077
7.
TangJYLiuYP. Loaded multi-tooth contact analysis and calculation for contact stress of face-gear drive with spur involute pinion. J Central South Univ2013; 20(2): 354–362. https://doi.org/10.1007/s11771-013-1495-x
8.
WangSHuBWuZ, et al. A comprehensive optimization model of tooth surface parameters for the minimization of contact tress of helical face gears by considering the avoidance of edge contact. Mathematics2022; 10(17): 3102.
ZhuoSZhouYTangZ, et al. A novel topological modification method for the pinion of the face gears with large contact areas. J Phys Conf Ser2025; 3080(1): 012040. https://doi.org/10.1088/1742-6596/3080/1/012040
15.
HanZYJiangCDengXZ. Research on machining nonorthogonal face gears by power skiving with tooth flank modification based on a six-axis machine tool. Int J Adv Manuf Technol2022; 121(3–4): 2735–2746. https://doi.org/10.1007/s00170-022-09427-2
16.
WangLSunLZhaoN, et al. An efficient semi-analytical loaded tooth contact analysis method for modified face-gear drive using Rayleigh–Ritz approach. Meccanica2025; 60(9): 3027–3045. https://doi.org/10.1007/s11012-025-02041-y
FuXHuangYFangZ, et al. Dynamic load sharing characteristics of a dual-branch transmission system with offset nonorthogonal spur face gear pairs. J Mech Sci Technol2021; 35(7): 2793–2808. https://doi.org/10.1007/s12206-021-0603-3
PauTDKorkaZINedelcuD, et al. Assessing the meshing for windage power loss simulations of an orthogonal face gear. Machines2025; 13(5): 341. https://doi.org/10.3390/machines13050341
23.
TangZZhouYTangJ. An ease-off based tooth contact analysis method for measured face gear flanks. Appl Sci2025; 15(17): 9336. https://doi.org/10.3390/app15179336
24.
FuXZhangCXuH, et al. Static load sharing performance of non-orthogonal and offset helical face gear dual-branch drivetrain. Adv Mech Eng2025; 17(1): 1–11. https://doi.org/10.1177/16878132241310064
25.
MoSZhangYTangW, et al. Design methods and stress analysis of asymmetric offset face-gear transmission. Proc Inst Mech Eng C J Mech Eng Sci2022; 236(14): 7814–7828. https://doi.org/10.1177/09544062221079169
LiZFanJZhuR. Construction of tooth modeling solutions of face gear drives with an involute pinion. Iran J Sci Technol Trans Mech Eng2018; 42(1): 35–39. https://doi.org/10.1007/s40997-017-0074-4
