Please wait a minute...
 首页  期刊介绍 期刊订阅 联系我们 横山亮次奖 百年刊庆
 
最新录用  |  预出版  |  当期目录  |  过刊浏览  |  阅读排行  |  下载排行  |  引用排行  |  横山亮次奖  |  百年刊庆
清华大学学报(自然科学版)  2018, Vol. 58 Issue (6): 529-538    DOI: 10.16511/j.cnki.qhdxxb.2018.22.023
  机械工程 本期目录 | 过刊浏览 | 高级检索 |
螺旋锥齿轮齿面加载性能多目标优化
王琪, 周驰, 桂良进, 范子杰
清华大学 汽车工程系, 汽车安全与节能国家重点实验室, 北京 100084
Multi-objective optimization of loaded spiral bevel and hypoid gears
WANG Qi, ZHOU Chi, GUI Liangjin, FAN Zijie
State Key Laboratory of Automotive Safety and Energy, Department of Automotive Engineering, Tsinghua University, Beijing 100084, China
全文: PDF(12344 KB)  
输出: BibTeX | EndNote (RIS)      
摘要 针对螺旋锥齿轮齿面设计需进行多次试算的问题,提出了齿面加载性能多目标优化问题数学模型的建立及求解方法。建立了包含最大接触应力、加载传动误差、加载接触区范围和齿根弯曲应力的齿面加载性能多目标优化问题的数学模型;建立了考虑齿根弯曲应力计算的加载接触分析模型,用于计算优化问题中的目标函数和约束函数;采用Kriging代理模型结合多目标遗传算法对该优化问题进行求解;通过对驱动桥螺旋锥齿轮副进行多目标优化,实现了接触区完全位于理想接触区且无边缘接触,最大接触应力降低11.7%,加载传动误差降低27.9%,大小轮最大齿根弯曲应力分别降低2.0%和12.6%。通过对优化后的齿面进行驱动桥加载接触印迹台架试验,对接触区进行了验证,结果显示优化得到的接触区与试验结果吻合良好,验证了优化方法的可行性和正确性。
服务
把本文推荐给朋友
加入引用管理器
E-mail Alert
RSS
作者相关文章
王琪
周驰
桂良进
范子杰
关键词 螺旋锥齿轮齿面优化齿面加载接触分析加载接触性能    
Abstract:The loaded stresses in the tooth flank of spiral bevel and hypoid gears were optimized without a trial-and-error procedure in a multi-objective optimization model. The multi-objective optimization model was developed considering the maximum contact pressure, load transmission error, load contact pattern and the maximum bending stress. A semi-analytical loaded tooth contact analysis model for the root bending stress was developed to calculate the objectives and constraints. Kriging surrogate models of the objectives and constraints together with a multi-objective genetic algorithm were used to solve the optimization model. The model was then used to optimize a spiral bevel gear pair for a drive axle. The loaded contact pattern was completely in the ideal zone with the maximum contact pressure decreased by 11.7%, the loaded transmission error decreased by 27.9% and the maximum bending stresses in the wheel and pinion decreased by 2.0% and 12.6%. The optimal design was installed in a drive axle for loaded contact tests that showed that the actual loaded contact pattern coincided well with the predicted loaded contact pattern, which verified the accuracy of the optimization approach.
Key wordsspiral bevel and hypoid gear    tooth flank optimization    loaded tooth contact analysis    loaded contact performance
收稿日期: 2017-11-24      出版日期: 2018-06-21
基金资助:清华大学校企合作项目(20152000879);清华大学汽车安全与节能国家重点实验室重点项目(ZZ2013-014)
通讯作者: 范子杰,教授,E-mail:zjfan@tsinghua.edu.cn     E-mail: zjfan@tsinghua.edu.cn
引用本文:   
王琪, 周驰, 桂良进, 范子杰. 螺旋锥齿轮齿面加载性能多目标优化[J]. 清华大学学报(自然科学版), 2018, 58(6): 529-538.
WANG Qi, ZHOU Chi, GUI Liangjin, FAN Zijie. Multi-objective optimization of loaded spiral bevel and hypoid gears. Journal of Tsinghua University(Science and Technology), 2018, 58(6): 529-538.
链接本文:  
http://jst.tsinghuajournals.com/CN/10.16511/j.cnki.qhdxxb.2018.22.023  或          http://jst.tsinghuajournals.com/CN/Y2018/V58/I6/529
  图1 小轮投影面内接触迹线示意图
  图2 螺旋锥齿轮错位量示意图
  图3 小轮修形面示意图
  图4 (网络版彩图)加载接触区域示意图
  图5 (网络版彩图)半解析 LTCA计算流程图
  图6 求解多目标优化问题流程图
  表1 螺旋锥齿轮设计参数表
  表2 运行工况齿轮错位量
  图7 (网络版彩图)原始设计加载性能
  图8 目标函数 EI值变化曲线
  图9 优化问题的 Pareto解集
  表3 G1 解优化设计变量对应的小轮凹面加工参数
  表4 解G1 目标函数与约束函数代理模型 计算值与 LTCA计算值对比
  表5 优化后 Pareto解集中G1 解与原始设计的 计算结果对比
  图10 (网络版彩图)解G1 优化设计的加载性能
  图11 优化设计得到的加载传动误差曲线与 未优化时的对比
  图12 (网络版彩图)螺旋锥齿轮驱动桥 加载接触印迹台架试验流程
  图13 (网络版彩图)驱动桥加载接触印迹试验台架
  图14 (网络版彩图)优化后 LTCA分析 与试验得到的接触区对比
[1] LITVIN F L. Gear geometry and applied theory[M]. Englewood Cliffs, USA:Prentice-Hall, 1994.
[2] SHIH Y P. A novel ease-off flank modification methodology for spiral bevel and hypoid gears[J]. Mechanism and Machine Theory, 2010, 45(8):1108-1124.
[3] 曹雪梅, 邓效忠, 聂少武. 基于共轭齿面修正的航空弧齿锥齿轮高阶传动误差齿面拓扑结构设计[J]. 航空动力学报, 2015, 30(1):195-200. CAO X M, DENG X Z, NIE S W. Ease-off flank topography design for aviation spiral bevel gears with higher-order transmission errors by modification of conjugate flank[J]. Journal of Aerospace Power, 2015, 30(1):195-200. (in Chinese)
[4] ACHTMANN J, BAÄR G. Optimized bearing ellipses of hypoid gears[J]. Journal of Mechanical Design, 2004, 125(4):739-745.
[5] 田行斌, 方宗德. 弧齿锥齿轮加工参数的全局优化设计[J]. 航空动力学报, 2000, 15(1):75-77. TIAN X B, FANG Z D. Overall optimization on machine-tool settings of spiral bevel gears[J]. Journal of Aerospace Power, 2000, 15(1):75-77. (in Chinese)
[6] 周彦伟, 方宗德, 邓效忠. 航空弧齿锥齿轮齿面接触应力计算与优化[J]. 航空动力学报, 2002, 17(3):373-376. ZHOU Y W, FANG Z D, DENG X Z. Calculation and optimization for tooth contact stress of spiral bevel gears[J]. Journal of Aerospace Power, 2002, 17(3):373-376. (in Chinese)
[7] 张金良, 李少华, 方宗德, 等. 准双曲面齿轮的齿面优化设计[J]. 机械科学与技术, 2007, 26(3):366-368. ZHANG J L, LI S H, FANG Z D, et al. Hypoid gear machining parameter optimization[J]. Mechanical Science and Technology, 2007, 26(3):366-368. (in Chinese)
[8] 刘光磊, 樊红卫, 谷霁红, 等. 弧齿锥齿轮传动误差曲线优化的半变性法[J]. 航空动力学报, 2010, 25(8):1888-1893. LIU G L, FAN H W, GU J H, et al. Half-modified roll for the optimization of transmission error function of spiral bevel gears[J]. Journal of Aerospace Power, 2010, 25(8):1888-1893. (in Chinese)
[9] 刘光磊, 刘则良. 弧齿锥齿轮传动误差曲线的双层优化法[J]. 农业机械学报, 2012, 43(7):223-227, 222. LIU G L, LIU Z L. Dual-layer optimization for transmission errors of spiral bevel gears[J]. Transactions of the Chinese Society for Agricultural Machinery, 2012, 43(7):223-227, 222. (in Chinese)
[10] SIMON V. Optimal machine tool setting for hypoid gears improving load distribution[J]. Journal of Mechanical Design, 2001, 123(4):577-582.
[11] SIMON V. Design of face-hobbed spiral bevel gears with reduced maximum tooth contact pressure and transmission errors[J]. Chinese Journal of Aeronautics, 2013, 26(3):777-790.
[12] ARTONI A, BRACCI A, GABICCINI M, et al. Optimization of the loaded contact pattern in hypoid gears by automatic topography modification[J]. Journal of Mechanical Design, 2008, 131(1):011008.
[13] GABICCINI M, BRACCI A, GUIGGIANI M. Robust optimization of the loaded contact pattern in hypoid gears with uncertain misalignments[J]. Journal of Mechanical Design, 2010, 132(4):041010.
[14] ARTONI A, KOLIVAND M, KAHRAMAN A. An ease-off based optimization of the loaded transmission error of hypoid gears[J]. Journal of Mechanical Design, 2009, 132(1):011010.
[15] ARTONI A, GABICCINI M, GUIGGIANI M, et al. Multi-objective ease-off optimization of hypoid gears for their efficiency, noise and durability performances[C]//Proceedings of the International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. Washington DC, USA:ASME, 2011:DETC2011-47715.
[16] 王琪, 周驰, 桂良进, 等. 准双曲面齿轮LTCA弯曲变形约束方法[J]. 航空动力学报, 2017, 32(11):2800-2807. WANG Q, ZHOU C, GUI L J, et al. Constraint method of calculating tooth bending deformation of hypoid gears in LTCA[J]. Journal of Aerospace Power, 2017, 32(11):2800-2807. (in Chinese)
[17] WILCOX L E, CHIMNER T D, NOWELL G C. Improved finite element model for calculating stresses in bevel and hypoid gear teeth[R]. Alexandria, USA:AGMA, 1997.
[18] HOTAIT M A, KAHRAMAN A, NISHINO T. An investigation of root stresses of hypoid gears with misalignments[J]. Journal of Mechanical Design, 2011, 133(7):071006.
[19] 周驰, 彭钱磊, 丁炜琦, 等. 汽车驱动桥主减速器支承刚度的有限元分析[J]. 汽车工程, 2016, 38(8):981-988. ZHOU C, PENG Q L, DING W Q, et al. Finite element analysis on the support stiffness of final drive in vehicle drive axle[J]. Automotive Engineering, 2016, 38(8):981-988. (in Chinese)
[20] GOSSELIN C, NONAKA T, SHIONO Y, et al. Identification of the machine settings of real hypoid gear tooth surfaces[J]. Journal of Mechanical Design, 1998, 120(3):429-440.
[21] LIN C Y, TSAY C B, FONG Z H. Computer-aided manufacturing of spiral bevel and hypoid gears with minimum surface-deviation[J]. Mechanism and Machine Theory, 1998, 33(6):785-803.
[22] ARTONI A, GABICCINI M, GUIGGIANI M. Nonlinear identification of machine settings for flank form modifications in hypoid gears[J]. Journal of Mechanical Design, 2008, 130(11):112602.
[23] GIUNTA A A, WATSON L T. A comparison of approximation modeling techniques:Polynomial versus interpolating model[R]. Blacksburg, USA:AIAA, 1998.
[24] JONES D R, SCHONLAU M, WELCH W J. Efficient global optimization of expensive black-box functions[J]. Journal of Global Optimization, 1998, 13(4):455-492.
[25] DEB K, PRATAP A, AGARWAL S, et al. A fast and elitist multiobjective genetic algorithm:NSGA-Ⅱ[J]. IEEE Transactions on Evolutionary Computation, 2002, 6(2):182-197.
[26] JEONG S, OBAYASHI S. Efficient global optimization (EGO) for multi-objective problem and data mining[C]//Proceedings of 2005 IEEE Congress on Evolutionary Computation. Edinburgh, UK:IEEE, 2005, 3:2138-2145.
No related articles found!
Viewed
Full text


Abstract

Cited

  Shared   
  Discussed   
版权所有 © 《清华大学学报(自然科学版)》编辑部
本系统由北京玛格泰克科技发展有限公司设计开发 技术支持:support@magtech.com.cn