Numerical Calculation Method for Loaded Tooth Contact Analysis of Face Gear Pair with Localized Line Contact

doi:10.3901/JME.260341

Abstract

Abstract: To improve the load performance of face gear pair and prevent edge contact during meshing, a localized line contact modification method is proposed, and a high efficiency load contact analysis model is developed based on the influence coefficient method. First, the standard tooth surface is digitally discretized using tooth surface contact lines, and modification amounts are superimposed on discrete nodes along the contact line and a predetermined contact path to construct a geometric model of the face gear pair with localized line contact characteristics. Second, a mesh model of the face gear pair is developed from the geometric model, and a tooth surface force-displacement response matrix is established based on the influence coefficient method. The contact stress and load distribution on the face gear tooth surface are numerically calculated using deformation compatibility equations and moment equilibrium conditions. Finally, the effectiveness of the localized line contact modification method and the accuracy of the numerical calculation model for loaded contact analysis are validated. The results demonstrate that the predetermined contact path agrees well with the simulated contact path, and the contact stress computed by the proposed numerical method shows good agreement in magnitude and distribution with the Abaqus results while achieving significantly higher computational efficiency. Compared with point contact, the localized line contact effectively reduces the contact stress on the tooth surface and eliminates edge contact.

Key words: face gear, modification method, meshing performance, loaded tooth contact analysis, numerical method

CLC Number:

TH114

HE Kun, LI Ronghao, LI Guolong, CAO Bing, DU Yanbin. Numerical Calculation Method for Loaded Tooth Contact Analysis of Face Gear Pair with Localized Line Contact[J]. Journal of Mechanical Engineering, 2026, 62(11): 215-226.

Add to citation manager EndNote|Reference Manager|ProCite|BibTeX|RefWorks

URL: http://www.cjmenet.com.cn/EN/10.3901/JME.260341

http://www.cjmenet.com.cn/EN/Y2026/V62/I11/215

References

[1] ZHU L Y，SHI J F，GOU X F. Modeling and dynamics analyzing of a torsional-bending-pendular face-gear drive system considering multi-state engagements[J]. Mechanism and Machine Theory，2020，149：103790.
[2] 莫帅，岳宗享，冯志友，等. 面齿轮分汇流系统动力学均载特性研究[J]. 华中科技大学学报：自然科学版，2020(2)：6. MO Shuai，YUE Zongxiang，FENG Zhiyou，et al. Analytical investigation on load sharing characteristics for face gear split flow system[J]. Journal of Huazhong University of Science and Technology：Natural Science Edition，2020(2)：6.
[3] HANDSCHUH R F，LEWICKI D G，BOSSLER R B. Experimental testing of prototype face gears for helicopter transmissions[J]. Proceedings of the Institution of Mechanical Engineers，Part G：Journal of Aerospace Engineering，1994，208(2)：129-136.
[4] ZSCHIPPANG H，WEIKERT A，KUCUK S，et al. Face-gear drive：Geometry generation and tooth contact analysis[J]. Mechanism and Machine Theory，2019，142：103576.
[5] LI S. Effects of machining errors，assembly errors and tooth modifications on loading capacity，load-sharing ratio and transmission error of a pair of spur gears[J]. Mechanism and Machine Theory，2007，42(6)：698-726.
[6] LITVIN F L，ZHANG Y，WANG J C，et al. Design and geometry of face-gear drives[J]. Journal of Mechanical Design，1992，114(4)：642-647.
[7] TSAY M F，FONG Z H. Novel profile modification methodology for moulded face-gear drives[J]. Proceedings of the Institution of Mechanical Engineers，Part C：Journal of Mechanical Engineering Science，2007，221(6)：715-725.
[8] FU X Z，FANG Z D，PENG X L，et al. Computerized design and optimization of tooth modifications on pinions for face gear drives[J]. Arabian Journal for Science and Engineering，2019，44(2) ：1097-1108.
[9] 何沁怡，郭辉，阮宇航，等. 高阶分段拓扑修形面齿轮副啮合性能研究[J]. 机械强度，2025，1-9. HE Qinyi，GUO Hui，RUAN Yuhang，et al. Research on meshing performance of high-order segmented topologymodification in face gear pair[J]. Journal of Mechanical Strength，2025，1：1-9.
[10] PENG X L，HU X W，FANG Z D. Active design of face gear drive for modifying ease off topology flank[J]. Journal of Aerospace Power，2014(5)：1216-1222.
[11] 周如传，赵宁，李旺，等. 锥形面齿轮副的几何展成及轮齿接触分析[J]. 机械工程学报，2020，56(7)：86-95. ZHOU Ruchuan，ZHAO Ning，LI Wang，et al. Generation，TCA and stress analysis of the face gear drive with a tapered involute pinion[J]. Journal of Mechanical Engineering，2020，56(7)：86-95.
[12] 付学中，方宗德，李建华，等. 面齿轮副小轮拓扑修形设计及啮合性能分析[J]. 哈尔滨工程大学学报，2016，37(9)：1281-1286. FU Xuezhong，FANG Zongde，LI Jianhua，et al. Design of topological shape modification of auxiliary pinion of face gears and analysis of meshing performance[J]. Journal of Harbin Engineering University，2016，37(9)：1281-1286.
[13] WANG Y，SU G，LIU D，et al. A hobbing method for spur face gears with bidirectional modification[J]. The International Journal of Advanced Manufacturing Technology，2022，119(1)：275-286.
[14] LIU Wenzheng，ZHU Rupeng，ZHOU Wenguang，et al. Calculation and analysis of TVMS considering profile shifts and surface wear evolution process of spur gear[J]. Chinese Journal of Mechanical Engineering，2024，37(1)：1-15.
[15] LITVIN F L，CHEN J，LU J，et al. Application of finite element analysis for determination of load share，real contact ratio，precision of motion，and stress analysis[J]. The American Society of Mechanical Engineers，1996，118(4)：561-567.
[16] LITVIN F L，NAVA A，FAN Q，et al. New geometry of face worm gear drives with conical and cylindrical worms：generation，simulation of meshing，and stress analysis[J]. Computer Methods in Applied Mechanics & Engineering，2002，191(27-28)：3035-3054.
[17] ZHANG Y，FANG Z. Analysis of tooth contact and load distribution of helical gears with crossed axes[J]. Mechanism and Machine Theory，1999，34(1)：41-57.
[18] 李政民卿，朱如鹏. 面齿轮传动的承载接触分析[J]. 南京航空航天大学学报，2010，42(2)：219-223. LI Zhengminqing，ZHU Rupeng. Load tooth contact analysis on face gear driver[J]. Transactions of Nanjing University of Aeronautics and Astronautics，2010，42(2)：219-223.
[19] CAO B，ALESSANDRO F，LI G，et al. A computerized method of contact pressure and load distribution for crossed beveloid gears[J]. Mechanism and Machine Theory，2022，175，104943.
[20] PEDRERO J I，VALLEJO I I，PLEGUEZUELOS M. Calculation of tooth bending strength and surface durability of high transverse contact ratio spur and helical gear drives[J]. Journal of Mechanical Design，2007，129(1)：69-74.
[21] YE S Y，TSAI S J. A computerized method for loaded tooth contact analysis of high-contact-ratio spur gears with or without flank modification considering tip corner contact and shaft misalignment[J]. Mechanism and Machine Theory，2016，97：190-214.
[22] HOU X，FANG Z，ZHANG X，et al. Static contact analysis of spiral bevel gear based on modified VFIFE (vector form intrinsic finite element) method[J]. Applied Mathematical Modelling，2018，60：192-207.
[23] TANG Jinyuan，LIU Yanping. Loaded multi-tooth contact analysis and calculation for contact stress of face-gear drive with spur involute pinion[J]. Journal of Central South University，2013，20(2)：354-362.
[24] 唐进元，刘艳平. 直齿面齿轮加载啮合有限元仿真分析[J]. 机械工程学报，2012，48(5)：124-131. TANG Jinyuan，LIU Yanping. Loaded meshing simulation of face-gear drive with spur involute pinion based on finite element analysis[J]. Journal of Mechanical Engineering，2012，48(5)：124-131.
[25] YANG Shiping，JI Yixing，MO Yulin，et al. Effects of prestressing of the ring gear in interference fit on flexural fatigue strength of tooth root[J]. Chinese Journal of Mechanical Engineering，2019，32(4)：71.
[26] SHUTING L I. Gear contact model and loaded tooth contact analysis of a three-dimensional，thin-rimmed gear[J]. Journal of Mechanical Design，2002，124(3)：511-517.
[27] HUGHES T J R，COHEN M，HAROUN M. Reduced and selective integration techniques in the finite element analysis of plates[J]. Nuclear Engineering and Design，1978，46(1)：203-222.