Active Tooth Surface Design and Performance Optimization of High Reduction Ratio Hypoid Gears

doi:10.12141/j.issn.1000-565X.240586

Abstract

Abstract:

To enhance the comprehensive transmission performance of hypoid gears with high reduction ratios, this paper proposed a design method for significantly inclined contact lines based on active tooth surface design techno-logy. Firstly, multiple tooth surface imprints with varying degrees of contact line inclination were preset, with specified values for the semi-major axis of the contact ellipse and the length of the contact trace. The pinion conjugate tooth surface was then modified with a parabolic shape to achieve a tooth surface that meets the preset parameters. Subsequently, by integrating Tooth Contact Analysis (TCA) and Load Tooth Contact Analysis (LTCA) techniques, the amplitude of transmission error (ATE), amplitude of loaded transmission error (ALTE), tooth surface load distribution, root bending stress amplitude, and tooth surface flash temperature amplitude were obtained for each tooth surface. The influence of variations in contact trace length on these performance parameters was then analyzed. Finally, a target modified tooth surface was selected, and its comprehensive performance was analyzed and compared with that of the original tooth surface. A case study demonstrates that for a hypoid gear pair with a gear ratio of 5∶75, under conditions of highly inclined contact trace on the tooth surface, a longer contact trace length leads to lower contact stress, as well as reduced root bending stress and flash temperature on the tooth surface. The target tooth surface exhibits weakened edge contact, a 12.0% reduction in maximum root bending stress, more uniform contact stress distribution, and a 6.3% decrease in peak flash temperature. As a result, the scuffing load-carrying capacity is enhanced. Overall, the modified target tooth surface exhibits superior contact performance, better load-carrying capacity, and significantly enhanced comprehensive transmission performance.

Key words: high reduction ratio hypoid gear, active design, modification, load tooth contact analysis, loaded transmission, tooth flash temperature

CLC Number:

TH132.41

JI Shuting, LI Jiahao, ZHANG Yueming. Active Tooth Surface Design and Performance Optimization of High Reduction Ratio Hypoid Gears[J]. Journal of South China University of Technology(Natural Science Edition), 2025, 53(9): 106-116.

Figures/Tables 19

Fig.1

Fig.2

Fig.3

Table 1

Fig.4

Table 2

Fig.5

Fig.6

Fig.7

Table 3

Fig.8

Fig.9

Fig.10

Fig.11

Fig.12

Fig.13

Fig.14

Fig.15

Fig.16

References 21

[1]	LI G， WANG Z， KUBO A ．Error-sensitivity analysis for hypoid gears using a real tooth surface contact model ［J］．Proceedings of the Institution of Mechanical Engineers，Part C：Journal of Mechanical Engineering Science，2017，231（3）：507-521.
[2]	古德万，魏冰阳，任明辉，等．Ease-off修形高减速比准双曲面齿轮接触仿真与动态性能试验［J］．机械传动，2023，47（5）：128-133，142.
	GU Dewan， WEI Bingyang， REN Minghui，et al ．Contact simulation and dynamic performance test of ease-off modified high reduction hypoid gears［J］．Journal of Mechanical Transmission，2023，47（5）：128-133，142.
[3]	SHIH Y P， FONG Z H ．Flank modification methodo-logy for face-hobbing hypoid gears based on ease-off topo-graphy［J］．Journal of Mechanical Design，2007，129（12）：1294-1302.
[4]	SHIH Y P ．A novel ease-off flank modification methodo-logy for spiral bevel and hypoid gears［J］．Mechanism and Machine Theory，2010，45（8）：1108-1124.
[5]	MU Y， XIU F， HE X ．An ease-off tooth surface redesign for spiral bevel gears considering misalignment under actual working conditions［J］．Transactions of the Canadian Society for Mechanical Engineering，2023，47（4）：618-625.
[6]	聂少武，邓静，邓效忠，等．弧齿锥齿轮齿面拓扑修形及加工参数计算［J］．航空动力学报，2017，32（8）：2009-2016.
	NIE Shaowu， DENG Jing， DENG Xiaozhong，et al ．Tooth surface topology modification and processing parameters calculation for spiral bevel gears［J］．Journal of Aerospace Power，2017，32（8）：2009-2016.
[7]	聂少武，蒋闯，邓效忠，等．Ease-off拓扑修正的准双曲面齿轮齿面修形方法［J］．中国机械工程，2019，30（22）：2709-2715，2740.
	NIE Shaowu， JIANG Chuang， DENG Xiaozhong，et al ．Flank modification method of hypoid gears with Ease-off topology correction［J］．China Mechanical Enginee-ring，2019，30（22）：2709-2715，2740.
[8]	CHEN P， WANG S， LI F，et al ．A direct preset method for solving ease-off tooth surface of spiral bevel gear［J］．Mechanism and Machine Theory，2023，179：105123/1-18.
[9]	杜进辅，方宗德，张永振，等．摆线齿准双曲面齿轮齿面主动设计［J］．国防科技大学学报，2015，37（6）：167-174.
	DU Jinfu， FANG Zongde， ZHANG Yongzhen，et al ．Active tooth surface design of cycloid hypoid gears［J］．Journal of National University of Defense Technology，2015，37（6）：167-174.
[10]	彭先龙，韩飞燕，乔心州，等．斜齿面齿轮传动齿面主动修形与边缘接触分析［J］．计算机集成制造系统，2020，26（11）：3040-3048.
	PENG Xianlong， HAN Feiyan， QIAO Xinzhou，et al ．Tooth surface active modification and edge contact analysis for face gear drives with helical pinion［J］．Computer Integrated Manufacturing Systems，2020，26（11）：3040-3048.
[11]	蒋进科，方宗德，刘钊．Ease-off拓扑修形准双曲面齿轮齿面多目标优化设计方法［J］．西安交通大学学报，2019，53（6）：44-53.
	JIANG Jinke， FANG Zongde， LIU Zhao ．Design of multi-objective tooth optimization for hypoid gear with ease-off topological modification［J］．Journal of Xi’ an Jiaotong University，2019，53（6）：44-53.
[12]	吴骁，史文库，郭年程，等．基于Ease off的准双曲面齿轮多目标优化［J］．吉林大学学报（工学版），2024，54（1）：76-85.
	WU Xiao， SHI Wenku， GUO Niancheng，et al ．Multi-objective optimization of hypoid gears based on Ease off［J］．Journal of Jilin University（Engineering and Technology Edition），2024，54（1）：76-85.
[13]	WANG Q， ZHOU C， GUI L，et al ．Optimization of the loaded contact pattern of spiral bevel and hypoid gears based on a kriging model［J］．Mechanism and Machine Theory，2018，122：432-449.
[14]	王笑乐．准双曲面齿轮副啮合性能优化与非线性动力学特性研究［D］．合肥：合肥工业大学，2020.
[15]	肖扬，王三民，李飞，等．Blok闪温法的改进及在弧齿锥齿轮齿面温度预测中的应用［J］．航空动力学报，2024，39（11）：423-431.
	XIAO Yang， WANG Sanmin， LI Fei，et al ．Improvement of Blok flash temperature method and its application in prediction of tooth surface temperature of spiral bevel gears［J］．Journal of Aerospace Power，2024，39（11）：423-431.
[16]	刘玄，方宗德，赵宁，等．人字齿轮小轮轴向窜动的多目标复合修形优化［J］．西安交通大学学报，2021，55（1）：118-126.
	LIU Xuan， FANG Zongde， ZHAO Ning，et al ．Multi-objective compound modification optimization of pinion axial floating for the double helical gears［J］．Journal of Xi’ an Jiaotong University，2021，55（1）：118-126.
[17]	唐进元，聂金安，王智全．螺旋锥齿轮HFT法加工的反调修正方法［J］．中南大学学报（自然科学版），2012，43（6）：2142-2419.
	TANG Jin-yuan， NIE Jin-an， WANG Zhi-quan ．Reverse correction of spiral bevel gear HFT method［J］．Journal of Central South University （Science and Technology），2012，43（6）：2142-2149.
[18]	ARTONI A， GABICCINI M， KOLIVAND M ．Ease-off based compensation of tooth surface deviations for spiral bevel and hypoid gears：only the pinion needs corrections［J］．Mechanism and Machine Theory，2013，61（3）：84-101.
[19]	董学朱．摆线齿锥齿轮与准双曲面齿轮设计和制造［M］．北京：机械工业出版社，2003.
[20]	崔慧军，杨宏斌，魏冰阳．准双曲面齿轮弯曲应力的计算［J］．机械设计与制造，2008（1）：39-40.
	CUI Hui-jun， YANG Hong-bin， WEI Bing-yang ．The computation of hypoid gear bending stress［J］．Mechanical Design and Manufacturing，2008（1）：39-40.
[21]	谷建功，方宗德，扶碧波，等．混合弹流润滑下弧齿锥齿轮齿面闪温研究［J］．航空动力学报，2010，25（12）：2846-2850.
	GU Jian-gong， FANG Zong-de， FU Bi-bo，et al ．Study on surface flash temperature for spiral bevel gears under condition of mixed elasto-hydrodynamic lubrication［J］．Journal of Aerospace Power，2010，25（12）：2846-2850.

齿轮副	轴交角/（°）	偏置距/mm	齿数	中点节锥距/mm	节锥角/（°）	面锥角/（°）	根锥角/（°）	顶点到交叉点的距离/mm			螺旋角/（°）	齿顶高/mm	齿根高/mm	齿宽/mm
齿轮副	轴交角/（°）	偏置距/mm	齿数	中点节锥距/mm	节锥角/（°）	面锥角/（°）	根锥角/（°）	节锥	面锥	根锥	螺旋角/（°）	齿顶高/mm	齿根高/mm	齿宽/mm
大轮	90	27	75	69.862	74.15	81.978	81.221	2.883	2.765	1.677	27.269	0.275	9.510	11.200
小轮	90	27	5	51.930	14.10	7.960	6.852	12.210	3.036	16.820	50.110	2.712	0.769	13.892