Geometric Design Methodology and Meshing Behavior Controlling Technology for the Hypoid Gears with Obtuse Crossed Shaft Angle

doi:10.3901/JME.260410

Abstract

Abstract: In response to the demand for hypoid gears with obtuse crossed angles in helicopter transmissions, a geometric design and contact behavior control method is proposed. By establishing an obtuse crossed shaft angle hypoid gear pitch cone tangential contact model based on the three fundamental geometric relationships in space, different selection rules for gear tooth taper methods are proposed, forming a geometric design method for both inner and outer cones forms of obtuse crossed hypoid gears. Closed diagrams of boundary design parameter selections for both inner and outer cones are presented. Utilizing a local synthesis method that considers the avoidance of tooth surface defects, a comprehensive control method for the contact behavior of the obtuse crossed shaft angle hypoid gears is introduced. By employing digital tooth flank modeling techniques, an accurate meshing model of this type of gear transmission is obtained. Through tooth contact analysis and load tooth contact analysis to simulate the tooth contact behavior. Additionally, a testing machine is developed for the hypoid gear pair, allowing for adjustable shaft angles and offset distances to conduct rolling imprint tests, yielding consistent results that mutually validate each other.

Key words: obtuse crossed shaft angle, hypoid gear, geometric design, meshing behavior controlling

CLC Number:

TH132

PANG Jingwei, LIU Siyuan, HE Wenjun, SONG Chaosheng. Geometric Design Methodology and Meshing Behavior Controlling Technology for the Hypoid Gears with Obtuse Crossed Shaft Angle[J]. Journal of Mechanical Engineering, 2026, 62(9): 131-144.

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http://www.cjmenet.com.cn/EN/Y2026/V62/I9/131

References

[1] LEI D，RONG K，SONG B，et al. Digital twin modeling for tooth surface grinding considering low-risk transmission performance of non-orthogonal aviation spiral bevel gears[J]. ISA Transactions，2021，128(Part B)：646-663.
[2] STEWART A，WILDHABER E. Design，production and application of the hypoid rear-axle gear[R]. SAE Tech.，1926.
[3] FAN Qi. Computerized modeling and simulation of spiral bevel and hypoid gears manufactured by gleason face hobbing process[J]. ASME J. Mech.，2006，128(6)：1315-1327.
[4] IGNACIO G，ALFONSO F. An exact system of generation for face-milled hypoid gears with uniform depth taper：Application to hypoid gear drives with high gear ratio[J]. Mechanism and Machine Theory，2024，196：105629.
[5] ARTONI A，GABICCINI M，GUIGGIANI M，et al. Multi-objective ease-off optimization of hypoid gears for their efficiency[J]. ASME J. Mech.，2011，133(12)：121007.
[6] LIU Siyuan，ZHU Caichao，SONG Chaosheng，et al. Investigation on the influence of work holding equipment errors on contact characteristics of face-hobbed hypoid gear[J]. Mechanism and Machine Theory，2019，138：95-111.
[7] 李聚波，王永强，魏冰阳，等. 曲面综合高减比准双曲面齿轮加工参数计算与接触仿真[J]. 机械工程学报，2022，58(13)：282-289. LI Jubo，WANG Yongqiang，WEI Bingyang，et al. Calculation of machining parameters and contact simulation of high reduction hypoid gear on surface synthesis[J]. Journal of Mechanical Engineering，2022，58(13)：282-289.
[8] 王星，方宗德，王磊，等. 刀倾全展成准双曲面齿轮的切齿设计[J]. 哈尔滨工业大学学报，2016，48(7)：163-168. WANG Xing，FANG Zongde，WANG Lei，et al. Machine-tool setting design for HGT hypoid gear drives[J]. Journal of harbin institute of technology，2016，48(7)：163-168.
[9] 梁成成，宋朝省，朱才朝，等. 基于刀具法向基准的奥利康准双曲面齿轮精确建模与验证[J]. 重庆大学学报，2020，43(2)：1-11. LIANG Chengcheng，SONG Chaosheng，ZHU Caichao，et al. Accurate modeling and verification of Oerlikon hypoid gears based on tool normal benchmark[J]. Journal of Chongqing University，2020，43(2)：1-11.
[10] PENG Shandong，DING Han，TANG Jinyuan，et al. Collaborative machine tool settings compensation considering both tooth flank geometrical and physical performances for spiral bevel and hypoid gears[J]. Journal of Manufacturing Processes，2020，54：169-179.
[11] DING Han，TANG Jinyuan. Six sigma robust multi-objective optimization modification of machine-tool settings for hypoid gears by considering both geometric and physical performances[J]. Applied Soft Computing，2018，70：550-561.
[12] DOONER D B，SEIREG A A. The kinematic geometry of gearing：A concurrent engineering approach[M]. London：John Wiley，1995.
[13] STADTFELD H J. Hypoloid gears with small shaft angles and zero-to-large offsets[J]. Gear Technology，2009(11)：58-66.
[14] YANG Xingyu，SONG Chaosheng，ZHU Caichao，et al. Computational study on machine settings for face-milled hypoid gears with low shaft angles[J]. Journal of Mechanical Design，2020，142(11)：113402.
[15] LIU Siyuan ，ZHU Caichao，ALFONSO F，et al. Computerized approach for design and generation of face-milled non-generated hypoid gears with low shaft angle[J]. Mechanism and Machine Theory，2021，155：104084.
[16] LIU Siyuan，ZHU Caichao，ALFONSO F，et al. Computerized determination of the qualified region of main design parameters of face-milled hypoid gears with low shaft angle[J]. Mechanism and Machine Theory，2021，159：104259.
[17] LIU Siyuan，ZHU Caichao，SONG Chaosheng，et al. Compensation of errors of alignment and contact pattern repositioning in hypoid gears with low crossing shaft angle[J]. Meccanica，2021，56：2861-2875.
[18] DOONER D B. On evolutoids and spatial involutoids to define hypoid flank geometry[J]. Mechanism and Machine Theory，2021，156：104150.
[19] ANSI/AGMA. ISO 23509-B17 Design Manual for Bevel Gears[S]. AGMA，Alexandria，VA，2017.
[20] LITVIN F L，GUTMAN Y. Methods of synthesis and analysis for hypoid gear-drives of formate and helixform-part 1. Calculations for machine settings for member gear manufacture of the formate and helix form hypoid gears[J]. Mech. Des.，1981，103：83-88.
[21] LITVIN F L，ALFONSO F. Gear geometry and applied theory[M]. New York：Cambridge University Press，2004.