摘要(英) |
The purpose of this study is to analyze the meshing characteristics of harmonic drives (HD) with involute profile and double-circular-arc profile. Firstly, the 2-D mathematical model of flexsplines (FS) with involute tooth profile and double-circular-arc profile were developed by using respective rack cutter based on the theory of gearing. Then the engaging circular spline (CS) with conjugate tooth profile of FS was derived based on the enveloping theory and kinematic model of HD. Additionally, a mesh generation program was developed to discretize the FS based on the 2-D mathematical model. Furthermore, 2-D FEA was conducted to explore the engagement movement of the FS, the torsional stiffness, transmission ratio, fillet stress and contact stress of the FS during meshing process and the engaged area of teeth of the HD under various conditions. In this study, an optimization method was adopted in the parametric design of 2-D tooth profile. The optimization aims to achieve the maximum torsional stiffness, and the constraints are that the stress is smaller than the fatigue limit of the FS material and no interference between the teeth of FS and CS is presented. An 2-D tooth profile optimization processing combining c++, finite element analysis and optimization algorithm was successfully performed. Moreover, a preliminary 3-D FEA was conducted to explore the torsional stiffness and the engaged area of teeth of the HD under two conditions, such as HD with lead crowning or HD without lead crowning by adding in axial parameters, including cup length, tooth width and so on. Finaly, The results from 2-D FEA and 3-D FEA were compared and discussed. The proposed methodology in this study paved the way for future investigations of 3-D FEA and 3-D optimization.
keywords:harmonic drive, torsional stiffness, engaged area of teeth, involute tooth profile, double-circular-arc profile, finite element analysis, optimization
|
參考文獻 |
[1] 網路資料,http://www.gelufu.com/article_read_976.html
[2] 沈允文,葉慶泰,“諧波齒輪傳動的理論和設計”,北京:機械工業出版社,1985。
[3] 網路資料,https://kknews.cc/zh-mo/tech/ev92a4.html
[4] C. W. Musser, “Strain Wave Gearing,” U.S. Patent, No.2906143, Sept. 29, 1959.
[5] Harmonic Drive LLC. (2015), “Cup Type Component Sets & Housed Units,” available at: http://www.harmonicdrive.net/_hd/content/documents/CSF-CSG.pdf (accessed 05 July 2016).
[6] 程廷瑋,“諧波齒輪運動分析”,國立成功大學,碩士論文,民國104年6月。
[7] 陳毅恆,“諧波齒輪傳動系統有限元素分析”,國立交通大學,碩士論文,民國102年7月。
[8] 梁鈺麟,“雙圓弧齒型諧波齒輪之共軛性質探討”,國立台北科技大學,碩士論文,民國104年7月。
[9] 彭啟綱,“諧波齒輪傳動系統之結構分析”,逢甲大學,碩士論文,民國103年6月。
[10] 王培郁,蔡昕儒,“禮帽型諧波齒輪之柔輪幾何設計與分析”,中國機械工程學會第三十三屆全國學術研討會,論文編號#1177,民國105年12月。
[11] 傅銘田,“諧波齒輪動態響應”,國立中山大學,碩士論文,民國89年6月。
[12] Y. Kiyosawa, N. Takizawa, T. Oukura and Y. Yamamoto, “Cup-Type Harmonic Drive Having a Short, Flexible Cup Member,” U.S. Patent, No.5269202, Dec. 14, 1993.
[13] 曹廷駒,“動力諧波齒輪傳動的共軛運動分析”,華北水利水電學院學報,第一期,1982。
[14] 曹廷駒,陳光志,“諧波齒輪的瞬時嚙合研究”,武漢水利電力學院學報,第四期,1983。
[15] 樂可錫,傅西玲,“擺線諧波齒輪傳動”,中國學術期刊電子雜誌出版社,1991。
[16] 盧其輝,梁醫,范元勳,王華坤,“基於諧波齒輪嚙合仿真的齒形干涉研究”,系統仿真學報,第21卷,第19期, 第6317-6320頁,2009。
[17] 李克美,尹儀方,陳仕賢,“一種漸開線齒廓三維修形的諧波傳動裝置”,中國專利,CN200610127982.6,2006。
[18] 劉鄧輝,邢靜忠,陳曉霞,“漸開線諧波齒輪空間齒廓設計與仿真分析”,計算機集成製造系統,第21卷,第3期,第709-715頁,2015。
[19] 王家序,周祥祥,李俊陽,肖科,周廣武,“杯形柔輪諧波齒輪三維雙圓弧齒廓設計”,浙江大學學報,第50卷,第4期,第616-624頁,2016。
[20] O. Kayabasi and F. Erzincanli, “Shape Optimization of Tooth Profile of a Flexspline for a Harmonic Drive Element Modelling,” Materials and Design, Vol. 23, pp. 441-447, 2007.
[21] W. Ostapski and I. Mukha, “Stress State Analysis of Harmonic Drive Elements by FEM,” Bulletin of the Polish Academy of Sciences Technical Sciences, Vol. 55, No. 1, 2007.
[22] F-E Rhéaume, H. Champliaud and Z. Liu, “Understanding and Modelling the Torsional Stiffness of Harmonic Drives through Finite-Element Method,” Journal of Mechanical Engineering Science, Vol. 223, pp. 515-524, 2009.
[23] X. Chen, Y. Liu, J. Xing, S. Lin and M. Ma, “A Novel Method Based on Mechanical Analysis for the Stretch of the Neutral Line of Flexspline Cup of a Harmonic Drive,” Mechanism and Machine Theory, Vol. 76, pp. 1-19, 2014.
[24] S. Li, “Diaphragm Stress Analysis and Fatigue Strength Evaluation of the Flex-Spline, a Very Thin-Walled Spur Gear Used in the Strain Wave Gearing,” Mechanism and Machine Theory, Vol. 104, pp. 1-16, 2016.
[25] L. M. Hsia, “The Analysis and Design of Harmonic Gear Drive,” Proceedings of the IEEE International Conference on Systems, Man, and Cybernetics, pp. 616-619, 1988.
[26] H. S. Jeon and S. H. Oh, “A Study on Stress and Vibration Analysis of a Steel and Hybrid Flexspline for Harmonic Drive,” Composite Structures, Vol. 47, pp. 827-833, 1999.
[27] Q. Xiao, X. Han and H. Jia, “Dynamic Optimum Design and Analysis of Cam Wave Generator for Harmonic Gear Drive,” Proceeding of the IEEE International Conference on Information and Automation, pp. 315-319, 2011.
[28] T. Tjahjowidodo, F. Al-Bender and H. Van Brussel, “Theoretical Modelling and Experimental Identification of Nonlinear Torsional Behavior in Harmonic Drives,” Mechatronics, Vol. 23, pp. 497-504, 2013.
[29] C. Zou, T. Tao, G. Jiang, X. Mei and J. Wu, “A Harmonic Drive Model considering Geometry and Internal Interaction,” Journal of Mechanical Engineering Science, 2015. (Published online before print, doi: 10.1177/0954406215621097)
[30] F. L. Litvin and A. Fuentes, “Gear Geometry and Applied Theory, 2nd ed.,” Cambridge University Press, New York, 2004.
[31] K. Kondo and J. Takada, “Study on Tooth Profiles of the Harmonic Drive,” Journal of Machine Design, Vol. 112, pp. 131-137, 1990.
[32] S. Ishikawa, “Tooth Profile of Spline of Strain Wave Gearing,” U.S. Patent, No.4823638, Apr. 25, 1989.
[33] S. Y. Chen, “SmartDO Tutorial Manual,” 2013.
[34] 周衛東,“漸開線諧波齒輪傳動齒廓參數優化及動態仿真”,大連理工大學,碩士論文,民國97年6月。 |