Tooth Flank Optimization Design of Hypoid Gear with Low Installation Error Sensitivity

doi:10.12141/j.issn.1000-565X.250079

Abstract

Abstract:

Regarding problems such as the contact characteristics being extremely sensitive to installation error and generating vibration and noise caused by improper parameters design of hypoid gears, this paper proposed an optimized design method for gear aimed at reducing sensitivity to installation error. Firstly, it proposed a tooth flank contact characteristics evaluation model considering the installation error, including the variation of contact area, the offset of contact trace center value, and the variation of the conversion point amplitude of the transmission error curve. Then, it proposed a NURBS surface fitting method with reduced parameters and carried out tooth flank contact analysis. The mapping relationships among the installation error, the preset control parameters of tooth flank, the machining parameters of tooth flank and the contact characteristic parameters were established. Continuing, this study elucidated the influence patterns of installation error on tooth flank contact characteristics. It established a comprehensive sensitivity model for individual contact characteristic parameter relative to installation error. Finally, with the lowest sensitivity as the optimization goal, the genetic algorithm was used to optimize the design of the preset parameters of the tooth flank. Taking two typical operation condition as an example, through the comparative analysis of the meshing characteristics before and after optimization, it is found that the sensitivity of the optimized tooth flank contact area, the center point coordinates of the contact trace and the variation of the transmission error to the installation error are reduced. The tooth flank optimization design method proposed in this paper can effectively solve the problem that the tooth flank contact characteristics are extremely sensitive to the installation error, and reduce the vibration and noise in the transmission.

Key words: hypoid gear, zone of action, non-uniform rational B-spline, installation error, optimization design

CLC Number:

TH132.41

JI Shuting, ZHAI Zixuan, ZHANG Yueming, YUAN Erhao, BIAN Xinyi, ZHANG Qing. Tooth Flank Optimization Design of Hypoid Gear with Low Installation Error Sensitivity[J]. Journal of South China University of Technology(Natural Science Edition), 2025, 53(10): 97-108.

Figures/Tables 18

Fig.1

Fig.2

Fig.3

Fig.4

Fig.5

Fig.6

Fig.7

Fig.8

Fig.9

Fig.10

Fig.11

Fig.12

Table 1

Table 2

Fig.13

Fig.14

Fig.15

Table 3

References 21

[1]	王星，方宗德，牟彦铭，等．HGT 准双曲面齿轮承载传动误差的优化设计［J］．振动与冲击，2017，36（8）：34-40.
	WANG Xing， FANG Zongde， MOU Yanming，et al ．Optimization design of loaded transmission error for HGT hypoid gear drives［J］．Journal of Vibration and Shock，2017，36（8）：34-40.
[2]	王星．HGT准双曲面齿轮的齿面设计及啮合特性分析［D］．西安：西北工业大学，2016.
[3]	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.
[4]	莫易敏，莫仁杰，李其明，等．基于真实齿面的准双曲面齿轮传动误差研究［J］．机械传动，2022，46（1）：19-26.
	MO Yimin， MO Renjie， LI Qiming，et al ．Research on transmission error of hypoid gear based on real tooth surface［J］．Journal of Mechanical Transmission，2022，46（1）：19-26.
[5]	GUO W，MOA S， YANG Y，et al ．Optimization of cutter blade profile for face-hobbed spiral bevel gears［J］．The International Journal of Advanced Manufacturing Technology，2016，85（1）：209-216.
[6]	WANG X， LU J， YANG S ．Sensitivity analysis and optimization design of hypoid gears’ contact pattern to misalignments［J］．Journal of Zhejiang University-Science A （Applied Physics & Engineering），2019，20（6）：411-430.
[7]	ZHUO Y B， XIANG X Y， ZHOU X J，et al ．A method for the global optimization of the tooth contact pattern and transmission error of spiral bevel and hypoid gears［J］．Journal of Zhejiang University-Science A （Applied Physics & Engineering），2017，18（5）：377-392.
[8]	VIVET M， MUNDO D， TAMAROZZI T，et al ．An analytical model for accurate and numerically efficient tooth contact analysis under load，applied to face-milled spiral bevel gears［J］．Mechanism and Machine Theory，2018，130：137-156.
[9]	蔡香伟，方宗德，候祥颖．考虑安装错位的弧齿锥齿轮小轮齿面再设计［J］．哈尔滨工业大学学报，2015，47（5）：57-62.
	CAI Xiangwei， FANG Zongde， HOU Xiangying ．Redesign of pinion surface for spiral bevel gears with misalignment［J］．Journal of Harbin Institute of Technology，2015，47（5）：57-62.
[10]	SIMON V ．Computer simulation of tooth contact analysis of mismatched spiral bevel gears［J］．Mechanism and Machine Theory，2007，42（3）：365-381.
[11]	唐进元，雷国伟，杜晋，等．螺旋锥齿轮安装误差敏感性与容差性研究［J］．航空动力学报，2009，24（8）：1878-1885.
	TANG Jinyuan， LEI Guowei， DU Jin，et al ．Research on alignment error sensitivity and tolerance limit analysis of spiral bevel gears［J］．Journal of Aerospace Power，2009，24（8）：1878-1885.
[12]	LITVIN F L， FUENTES A ．齿轮几何与应用原理［M］．北京：机械工业出版社，2023.
[13]	DING H， ZHOU Y， TANG J，et al ．A novel operation approach to determine initial contact point for tooth contact analysis with errors of spiral bevel and hypoid gears［J］．Mechanism and Machine Theory，2017，109：155-170.
[14]	刘国政，史文库，陈志勇．考虑安装误差的准双曲面齿轮传动误差有限元分析［J］．吉林大学学报（工学版），2018，48（4）：984-989.
	LIU Guozheng， SHI Wenku， CHEN Zhiyong ．Finite element analysis of transmission error for hypoid gears considering installation error［J］．Journal of Jilin University （Engineering and Technology Edition），2018，48（4）：984-989.
[15]	唐进元，聂金安．含过渡曲面的准双曲面齿轮精确三维几何建模方法［J］．机械科学与技术，2010，29（3）：358-363，368.
	TANG Jinyuan， NIE Jin’an ．A method for accurate modeling of a hypoid gear with fillet［J］．Mechanical Science and Technology for Aerospace Engineering，2010，29（3）：358-363，368.
[16]	刘光磊，张瑞庭，赵宁，等．安装误差对航空弧齿锥齿轮传动误差曲线的影响分析［J］．航空发动机，2012，38（2）：32-35.
	LIU Guang-lei， ZHANG Rui-ting， ZHAO Ning，et al ．Effect of installation error on transmission error curve for aero spiral bevel gears［J］．Aeroengine，2012，38（2）：32-35.
[17]	严宏志，邓辰，胡志安，等．双重螺旋法切齿参数对螺旋锥齿轮啮合特性的影响［J］．现代制造工程，2019，41（2）：70-77.
	YAN Hongzhi， DENG Chen， HU Zhian，et al ．Effect of duplex helical method cutting parameters on spiral bevel gears meshing characteristic［J］．Modern Manufacturing Engineering，2019，41（2）：70-77.
[18]	SIMON V V ．Optimization of face-hobbed hypoid gears［J］．Mechanism and Machine Theory，2014，77：164-181.
[19]	Assembling Bevel Gears：［S］
[20]	HASHEMIAN A， HOSSEINI S F ．An integrated fitting and fairing approach for object reconstruction using smooth NURBS curves and surfaces［J］．Computers & Mathematics with Applications，2018，76（7）：1555-1575.
[21]	SIMON V ．Computer simulation of tooth contact analysis of mismatched spiral bevel gears［J］．Mechanism & Machine Theory，2007，42（3）：365-381

齿面参数和加工参数	大轮凸面	小轮凹面
轴交角Σ/（°）	90
偏置距E/mm	44.450
中点节锥距R/mm	75.97	118.50
刀尖半径r_p/mm	90.91	91.55
刀转角α_r/（°）	0	357.97
刀倾角α_t/（°）	0	22.06
径向刀位S_r1/mm	102.98	99.21
角向刀位q/（°）	62.02	86.35
床位X_b1/mm	0	7.76
垂直轮位E₁/mm	0	39.33
轴向轮位X_g1/mm	-2.94	-0.282
安装角γ₁/（°）	65.68	-6.56

工况	ΔX_g/mm	ΔZ_p/mm	ΔE/mm	ΔΣ /（°）
1	0.1	0.1	0.1	0.1
2	-0.1	-0.1	-0.1	-0.1

工况	有无安装误差	S_cp/mm²	x_cp/mm	y_cp/mm	T_E/arcsec
工况1 优化前	无	52.92	19.53	7.01	24.98
工况1 优化前	有	37.74（-29%）	19.92（+2%）	9.53（+36%）	39.84（+59%）
工况1 优化后	无	72.15	19.87	7.13	41.06
工况1 优化后	有	60.87（-16%）	18.72（-6%）	9.20（+29%）	40.40（-2%）
工况2 优化前	无	52.92	19.53	7.01	24.98
工况2 优化前	有	40.86（-23%）	18.83（-4%）	4.86（-31%）	56.56（+126%）
工况2 优化后	无	70.29	19.48	6.90	39.36
工况2 优化后	有	60.09（-14%）	19.73（+1%）	5.22（-24%）	47.58（+21%）