Full Text:   <327>

Summary:  <136>

CLC number: TH132.41

On-line Access: 2019-06-05

Received: 2019-01-20

Revision Accepted: 2019-05-03

Crosschecked: 2019-05-20

Cited: 0

Clicked: 1868

Citations:  Bibtex RefMan EndNote GB/T7714

 ORCID:

Xiao-le Wang

https://orcid.org/0000-0002-3516-3366

-   Go to

Article info.
Open peer comments

Journal of Zhejiang University SCIENCE A 2019 Vol.20 No.6 P.411-430

10.1631/jzus.A1900021


Sensitivity analysis and optimization design of hypoid gears’ contact pattern to misalignments


Author(s):  Xiao-le Wang, Jian-wei Lu, Shi-qin Yang

Affiliation(s):  School of Automotive and Transportation Engineering, Hefei University of Technology, Hefei 230009, China; more

Corresponding email(s):   jwlu75@hfut.edu.cn

Key Words:  Hypoid gear, Misalignment, Tooth contact analysis (TCA), Sensitivity analysis, Multi-population genetic algorithm (MPGA), Multi-objective optimization


Xiao-le Wang, Jian-wei Lu, Shi-qin Yang. Sensitivity analysis and optimization design of hypoid gears’ contact pattern to misalignments[J]. Journal of Zhejiang University Science A, 2019, 20(6): 411-430.

@article{title="Sensitivity analysis and optimization design of hypoid gears’ contact pattern to misalignments",
author="Xiao-le Wang, Jian-wei Lu, Shi-qin Yang",
journal="Journal of Zhejiang University Science A",
volume="20",
number="6",
pages="411-430",
year="2019",
publisher="Zhejiang University Press & Springer",
doi="10.1631/jzus.A1900021"
}

%0 Journal Article
%T Sensitivity analysis and optimization design of hypoid gears’ contact pattern to misalignments
%A Xiao-le Wang
%A Jian-wei Lu
%A Shi-qin Yang
%J Journal of Zhejiang University SCIENCE A
%V 20
%N 6
%P 411-430
%@ 1673-565X
%D 2019
%I Zhejiang University Press & Springer
%DOI 10.1631/jzus.A1900021

TY - JOUR
T1 - Sensitivity analysis and optimization design of hypoid gears’ contact pattern to misalignments
A1 - Xiao-le Wang
A1 - Jian-wei Lu
A1 - Shi-qin Yang
J0 - Journal of Zhejiang University Science A
VL - 20
IS - 6
SP - 411
EP - 430
%@ 1673-565X
Y1 - 2019
PB - Zhejiang University Press & Springer
ER -
DOI - 10.1631/jzus.A1900021


Abstract: 
Accurate evaluation of the misalignment sensitivity of hypoid gears is a significant foundation for analysis of its dynamics and for the calculation of machining parameters. A tooth contact analysis (TCA) methodology considering four kinds of misalignments is presented to calculate the contact pattern and transmission error. A sensitivity model of contact pattern to misalignments is established to investigate the effects of different alignment errors on meshing performance. By parameterizing the contact pattern, the influences of offset error, angular error, and the axial error of pinion and gear on the direction, shape, and position features of contact pattern are studied. Coefficients of four evaluation indexes to different misalignments are defined respectively, and the minimum sum of the weighted coefficients is utilized to establish a multi-objective comprehensive sensitivity model. Three curvatures of the pitch cone of the pinion are taken as the control variables, and a global selection space is then built within the reasonable range of those curvatures. An improved multi-population genetic algorithm (MPGA) is used to find the optimal set of curvatures to achieve the minimum synthetic sensitivity. TCA results indicate that the offset error and angular error have the greatest influence on the contact pattern. By adopting this methodology appropriately, the sensitivity of the contact pattern to misalignments can be reduced. The contributions of this paper can be summarized as: (1) an accurate parameterized measurement model of the contact pattern; (2) a comprehensive sensitivity model of the contact pattern to misalignments; (3) an optimization framework consisting of a calculation model of the machining parameters, a TCA model considering misalignments, and a misalignment sensitivity evaluation model.

This paper presents an optimization methodology for determining profile modification based on contact pattern and transmission error. This process is for unloaded contact conditions.

准双曲面齿轮接触印痕对安装误差的敏感性分析与优化设计

目的:准双曲面齿轮副在实际装配过程中不可避免地存在安装误差. 本文旨在建立考虑多种安装误差的准双曲面齿轮啮合模型,对齿轮副啮合印痕特征(齿面分布位置、大小和方向)进行参数化建模,精确评价印痕对安装误差的敏感性,以及研究降低接触性能对安装误差的敏感度的方法,为准双曲面齿轮副的加工和安装提供理论依据.
创新点:1. 对准双曲面齿轮齿面接触印痕进行精确的参数化建模; 2. 建立考虑轴交角误差、偏置距误差以及大小轮轴向误差的齿轮副啮合分析模型; 3. 建立准双曲面齿轮副安装误差敏感度综合评价模型; 4. 通过优化齿轮加工参数,在齿轮副设计环节实现齿轮副安装误差敏感度的降低.
方法:1. 对准双曲面齿轮副安装误差和齿面接触印痕进行参数化建模,推导出表示接触印痕大小、方向和齿面分布位置的解析表达式(公式(1)~(3)); 2. 建立考虑4种安装误差的准双曲面齿轮副啮合分析模型(公式(4)~(11)),得到不同安装误差对啮合印痕的影响(图5~7); 3. 建立准双曲面齿轮副安装误差综合敏感度优化模型(公式(15)),并基于改进的多种群遗传算法(图14)实现齿轮副安装误差敏感性的降低(图8).
结论:1. 四种安装误差对准双曲面齿轮啮合质量的影响程度不同; 其中轴交角误差的影响最大,其次是偏置距误差,而大小轮的轴向安装误差的影响最小,因此安装齿轮副必须注重轴交角及偏置距的安装精度. 2. 通过降低齿轮副安装误差综合敏感度,可在一定程度上降低系统对装配误差的敏感性; 在齿轮副设计环节加入安装误差敏感度分析,优化机床加工参数,对装配后的啮合质量控制具有积极意义. 3. 考虑安装误差的轮齿接触分析模型能够得到不同安装误差对啮合印痕及传动误差的影响规律,是一种对失配状态下的准双曲面齿轮副进行无载啮合分析的有效工具.

关键词:准双曲面齿轮; 失配; 轮齿接触分析; 敏感性分析; 多种群遗传算法; 多目标优化

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

Reference

[1]Achtmann J, Bär H, 2003. Optimized bearing ellipses of hypoid gears. Journal of Mechanical Design, 125(4):739-745.

[2]ANSI-AGMA, 2005. Design Manual for Bevel Gears, ANSI/ AGMA 2005-D03. National Standards of America, USA.

[3]ANSI-AGMA, 2008. Assembling Bevel Gears, ANSI/AGMA 2008-C01. National Standards of America, USA.

[4]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.

[5]Baxter ML, Spear GM, 1961. Effect of misalignment on tooth action of bevel and hypoid gears. ASME Design Conference, ASME 61-MD-20.

[6]Bracci A, Gabiccini M, Artoni A, et al., 2009. Geometric contact pattern estimation for gear drives. Computer Methods in Applied Mechanics and Engineering, 198(17-20):1563-1571.

[7]Deng XZ, Wei BY, 2012. The New Methodology of the Bevel Gear’s Design. Science Press, Beijing, China (in Chinese).

[8]Ding H, Zhou YS, Tang JY, et al., 2016. A novel operation approach to determine initial contact point for tooth contact analysis with errors of spiral bevel and hypoid gears. Mechanism and Machine Theory, 109:155-170.

[9]Elisaus V, Mohammadpour M, Theodossiades S, et al., 2017. Effect of teeth micro-geometrical form modification on contact kinematics and efficiency of high performance transmissions. Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-body Dynamics, 231(3):538-555.

[10]Fan Q, 2011. Optimization of face cone element for spiral bevel and hypoid gears. Journal of Mechanical Design, 133(9):091002.

[11]Fan Q, Wilcox L, 2007. New developments in tooth contact analysis (TCA) and loaded TCA for spiral bevel and hypoid gear drives. Gear Technology, 24(3):26-35.

[12]Gabiccini M, Bracci A, Guiggiani M, 2010. Robust optimization of the loaded contact pattern in hypoid gears with uncertain misalignments. Journal of Mechanical Design, 132(4):041010.

[13]Guo WC, Mao SM, Yang Y, et al., 2016. Optimization of cutter blade profile for face-hobbed spiral bevel gears. The International Journal of Advanced Manufacturing Technology, 85(1-4):209-216.

[14]Hotait MA, Kahraman A, Nishino T, 2011. An investigation of root stresses of hypoid gears with misalignments. Journal of Mechanical Design, 133(7):071006.

[15]Kolivand M, Kahraman A, 2009. A load distribution model for hypoid gears using ease-off topography and shell theory. Mechanism and Machine Theory, 44(10):1848-1865.

[16]Litvin FL, Fuentes A, 2004. Gear Geometry and Applied Theory (2nd Edition). Cambridge University Press, New York, USA.

[17]Litvin FL, Tsung WJ, Lee HT, 1987. Generation of Spiral Bevel Gears with Conjugate Tooth Surfaces and Tooth Contact Analysis. NASA Contractor Report No. 4088, National Aeronautics and Space Administration, USA.

[18]Litvin FL, Zhang Y, Handschuh RF, 1991. Local Synthesis and Tooth Contact Analysis of Face-milled Spiral Bevel Gears. NASA Contractor Report No. 4342, National Aeronautics and Space Administration, USA.

[19]Litvin FL, Chen JS, Sep TM, et al., 1995. Computerized simulation of transmission errors and shift of bearing contact for face-milled hypoid gear drive. Journal of Mechanical Design, 117(2A):262-268.

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

[21]Mohammadpour M, Theodossiades S, Rahnejat H, et al., 2014. Transmission efficiency and noise, vibration and harshness refinement of differential hypoid gear pairs. Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-body Dynamics, 228(1):19-33.

[22]Pourvaziri H, Naderi B, 2014. A hybrid multi-population genetic algorithm for the dynamic facility layout problem. Applied Soft Computing, 24:457-469.

[23]Simon V, 1996. Tooth contact analysis of mismatched hypoid gears. American Society of Mechanical Engineers, Design Engineering Division (Publication) DE, 88:789-797.

[24]Simon V, 1998. The influence of misalignments on mesh performances of hypoid gears. Mechanism and Machine Theory, 33(8):1277-1291.

[25]Simon V, 2008. Machine-tool settings to reduce the sensitivity of spiral bevel gears to tooth errors and misalignments. Journal of Mechanical Design, 130(8):082603.

[26]Simon VV, 2014. Optimal tooth modifications in face-hobbed spiral bevel gears to reduce the influence of misalignments on elastohydrodynamic lubrication. Journal of Mechanical Design, 136(7):071007.

[27]Stadtfeld HJ, 1993. Handbook of Bevel and Hypoid Gears. Gleason Works, Rochester Institute of Technology, New York, USA.

[28]The Gleason Works, 1971. Method for Designing Hypoid Gear Blanks. The Gleason Works, Rochester, USA.

[29]Vivet M, Mundo D, Tamarozzi T, et al., 2018. An analytical model for accurate and numerically efficient tooth contact analysis under load, applied to face-milled spiral bevel gears. Mechanism and Machine Theory, 130:137-156.

[30]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.

[31]Wang P, Zhang YD, Wan M, 2016. Global synthesis for face milled spiral bevel gears with zero transmission errors. Journal of Mechanical Design, 138(3):033302.

[32]Wang Q, Zhou C, Gui LJ, et al., 2018. Optimization of the loaded contact pattern of spiral bevel and hypoid gears based on a Kriging model. Mechanism and Machine Theory, 122:432-449.

[33]Wang XC, Ghosh SK, 1994. Advanced Theories of Hypoid Gears. Elsevier, Amsterdam, The Netherlands.

[34]Wu XT, 2009. Gear Engagement Principle (2nd Edition). Xi’an Jiaotong University Press, Xi’an, China (in Chinese).

[35]Xu H, Kahraman A, 2007. Prediction of friction-related power losses of hypoid gear pairs. Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-body Dynamics, 221(3):387-400.

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

[37]Zhuo YB, Xiang XY, Zhou XJ, et al., 2017. A method for the global optimization of the tooth contact pattern and transmission error of spiral bevel and hypoid gears. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 18(5):377-392.

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 - Journal of Zhejiang University-SCIENCE