Full Text:   <5384>

Summary:  <1951>

CLC number: TH122

On-line Access: 2017-05-03

Received: 2016-03-14

Revision Accepted: 2016-08-31

Crosschecked: 2017-04-11

Cited: 0

Clicked: 4873

Citations:  Bibtex RefMan EndNote GB/T7714

 ORCID:

Yao-bin Zhuo

http://orcid.org/0000-0002-0954-9740

Xiao-jun Zhou

http://orcid.org/0000-0003-2565-1398

-   Go to

Article info.
Open peer comments

Journal of Zhejiang University SCIENCE A 2017 Vol.18 No.5 P.377-392

http://doi.org/10.1631/jzus.A1600240


A method for the global optimization of the tooth contact pattern and transmission error of spiral bevel and hypoid gears


Author(s):  Yao-bin Zhuo, Xue-yan Xiang, Xiao-jun Zhou, Hao-liang Lv, Guo-yang Teng

Affiliation(s):  College of Engineering and Design, Lishui University, Lishui 323000, China; more

Corresponding email(s):   zhuoyaobin@163.com

Key Words:  Spiral bevel gear, Tooth contacts, Transmission error, Optimal design, Genetic algorithm, Finite element analysis


Yao-bin Zhuo, Xue-yan Xiang, Xiao-jun Zhou, Hao-liang Lv, Guo-yang Teng. 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, 2017, 18(5): 377-392.

@article{title="A method for the global optimization of the tooth contact pattern and transmission error of spiral bevel and hypoid gears",
author="Yao-bin Zhuo, Xue-yan Xiang, Xiao-jun Zhou, Hao-liang Lv, Guo-yang Teng",
journal="Journal of Zhejiang University Science A",
volume="18",
number="5",
pages="377-392",
year="2017",
publisher="Zhejiang University Press & Springer",
doi="10.1631/jzus.A1600240"
}

%0 Journal Article
%T A method for the global optimization of the tooth contact pattern and transmission error of spiral bevel and hypoid gears
%A Yao-bin Zhuo
%A Xue-yan Xiang
%A Xiao-jun Zhou
%A Hao-liang Lv
%A Guo-yang Teng
%J Journal of Zhejiang University SCIENCE A
%V 18
%N 5
%P 377-392
%@ 1673-565X
%D 2017
%I Zhejiang University Press & Springer
%DOI 10.1631/jzus.A1600240

TY - JOUR
T1 - A method for the global optimization of the tooth contact pattern and transmission error of spiral bevel and hypoid gears
A1 - Yao-bin Zhuo
A1 - Xue-yan Xiang
A1 - Xiao-jun Zhou
A1 - Hao-liang Lv
A1 - Guo-yang Teng
J0 - Journal of Zhejiang University Science A
VL - 18
IS - 5
SP - 377
EP - 392
%@ 1673-565X
Y1 - 2017
PB - Zhejiang University Press & Springer
ER -
DOI - 10.1631/jzus.A1600240


Abstract: 
In this paper, we present a method for the global optimization of the tooth contact pattern and transmission error of spiral bevel and hypoid gears, which includes three optimization objectives, three control parameters, and a complex-constrain genetic algorithm solving method. A new set of fundamental equations for pitch cone parameters of hypoid gear drives are established, as well as the relationships between pitch cone and curvature parameters. Based on this theory, three control parameters are selected to determine the pinion tooth surface. A hypoid gear drive is chosen for case studies. The results verify that the optimization methodology can achieve the expected optimization objectives and has good convergence. Correlations between optimization objectives and control parameters are discussed. Furthermore, a finite element model of a simplified hypoid gear drive system is established and its quasi-static meshing characteristics analyzed. The results again confirm the correctness of the optimization method. The effects of torque load on the contact pattern and transmission error are discussed. The results provide a theoretical reference for geometric calculations, quasi-static analysis, and optimal design of spiral bevel and hypoid gears.

This paper covers a proposal of a global optimization methodology of the tooth contact pattern and transmission error of spiral bevel and hypoid gears.

一种螺旋锥齿轮齿面接触区和传动误差的全局优化方法

目的:传统的齿面接触分析技术存在调整参数繁多、控制目标不明确和不包含传动误差优化等缺陷。本文旨在提出一种齿面接触区和传动误差的全局优化设计方法,以得到满足齿轮传动性能要求的小轮产形轮节锥参数及机床调整参数。
创新点:1. 提出了新的确定各节锥参数之间几何关系的计算公式,并建立了节锥参数与曲率参数的相关公式;2. 提出以齿面接触区长半轴、接触线方向角和传动误差曲线交点纵坐标为优化目标,以齿面法曲率和短程挠率为控制参数,以复合形法约束处理的遗传算法为求解途径的齿面接触特性全局优化设计方法。
方法:1. 分析常见齿面接触区和传动误差曲线的缺陷及其原因(图1);2. 提出全局优化目标(图2),进行节锥参数和曲率参数分析,从而确定控制参数(图3~6),建立优化方程并进行求解算法分析(图7和8),然后进行实例计算分析(图9和10);3. 建立齿轮副传动系统有限元分析模型,验证优化方法的正确性(图11~13)。
结论:1.优化设计的实例分析表明,优化目标、控制参数和优化算法具有良好的匹配性;2. 通过优化目标与控制参数的相关性分析,得出了控制参数的影响特征;3. 通过有限元分析验证,优化设计结果达到了预期的齿轮传动性能指标。

关键词:螺旋锥齿轮;齿面接触;传动误差;优化设计;遗传算法;有限元分析

Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article

Reference

[1]Achtmann, J., Bär, G., 2004. Optimized bearing ellipses of hypoid gears. Journal of Mechanical Design, 125(4):739-745.

[2]Argyris, J., Fuentes, A., Litvin, F.L., 2002. Computerized integrated approach for design and stress analysis of spiral bevel gears. Computer Methods in Applied Mechanics and Engineering, 191(11-12):1057-1095.

[3]Artoni, A., Bracci, A., Gabiccini, M., et al., 2008. Optimization of the loaded contact pattern in hypoid gears by automatic topography modification. Journal of Mechanical Design, 131(1):011008.

[4]Artoni, A., Kolivand, M., Kahraman, A., 2009. An ease-off based optimization of the loaded transmission error of hypoid gears. Journal of Mechanical Design, 132(1):011010.

[5]Guo, W., Mao, S., Yang, Y., et al., 2016. Optimization of cutter blade profile for face-hobbed spiral bevel gears. The International Journal of Advanced Manufacturing Technology, 85(1):209-216.

[6]Litvin, F.L., Fuentes, A., 2004. Gear Geometry and Applied Theory (2nd Edition). Cambridge University Press, Cambridge, UK, p.627.

[7]Litvin, F.L., Wang, A.G., Handschuh, R.F., 1998. Computerized generation and simulation of meshing and contact of spiral bevel gears with improved geometry. Computer Methods in Applied Mechanics and Engineering, 158(1-2):35-64.

[8]Litvin, F.L., Fuentes, A., Fan, Q., et al., 2002. Computerized design, simulation of meshing, and contact and stress analysis of face-milled formate generated spiral bevel gears. Mechanism and Machine Theory, 37(5):441-459.

[9]Litvin, F.L., Fuentes, A., Hayasaka, K., 2006. Design, manufacture, stress analysis, and experimental tests of low-noise high endurance spiral bevel gears. Mechanism and Machine Theory, 41(1):83-118.

[10]Mermoz, E., Astoul, J., Sartor, M., et al., 2013. A new methodology to optimize spiral bevel gear topography. CIRP Annals — Manufacturing Technology, 62(1):119-122.

[11]Shtipelman, B.A., 1978. Design and Manufacture of Hypoid Gears. John Wiley & Sons, New York, USA.

[12]Simon, V.V., 2009a. Design and manufacture of spiral bevel gears with reduced transmission error. Journal of Mechanical Design, 131(4):041007.

[13]Simon, V.V., 2009b. Head-cutter for optimal tooth modifications in spiral bevel gears. Mechanism and Machine Theory, 44(7):1420-1435.

[14]Simon, V.V., 2013. Design of face-hobbed spiral bevel gears with reduced maximum tooth contact pressure and transmission errors. Chinese Journal of Aeronautics, 26(3):777-790.

[15]Simon, V.V., 2014. Optimization of face-hobbed hypoid gears. Mechanism and Machine Theory, 77:164-181.

[16]Vogel, O., Griewank, A., Bär, G., 2002. Direct gear tooth contact analysis for hypoid bevel gears. Computer Methods in Applied Mechanics and Engineering, 191(36):3965-3982.

[17]Wu, X.T., 2009. Gear Engagement Principle (2nd Edition). Xi’an Jiaotong University Press, Xi’an, China (in Chinese).

[18]Zeng, T., 1989. Spiral Bevel Gear Design and Processing. Harbin Institute of Technology Press, Harbin, China (in Chinese).

[19]Zhang, T.T., Huang, W., Wang, Z.G., et al., 2016. A study of airfoil parameterization, modeling, and optimization based on the computational fluid dynamics method. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 17(8):632-645.

[20]Zhuo, Y., Zhou, X., 2015. Dynamic characteristic analysis of high-speed spherical ball bearing. Journal of Mechanical Engineering, 51(5):37-46 (in Chinese).

Open peer comments: Debate/Discuss/Question/Opinion

<1>

Please provide your name, email address and a comment





Journal of Zhejiang University-SCIENCE, 38 Zheda Road, Hangzhou 310027, China
Tel: +86-571-87952783; E-mail: cjzhang@zju.edu.cn
Copyright © 2000 - 2024 Journal of Zhejiang University-SCIENCE