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System No. U0002-0708201410010300
Title (in Chinese) 有限元素密合接觸分析
Title (in English) Finite Element Analysis of Conforming Contacts
Other Title
Institution 淡江大學
Department (in Chinese) 機械與機電工程學系碩士班
Department (in English) Department of Mechanical and Electro-Mechanical Engineering
Other Division
Other Division Name
Other Department/Institution
Academic Year 102
Semester 2
PublicationYear 103
Author's name (in Chinese) 呂宗穎
Author's name(in English) Zong-Ying Lu
Student ID 601370264
Degree 碩士
Language Traditional Chinese
Other Language
Date of Oral Defense 2014-07-09
Pagination 76page
Committee Member advisor - Chao-Hwa Liu
co-chair - 陳正光
co-chair - 王銀添
Keyword (inChinese) 接觸分析
有限元素法
密合接觸
Keyword (in English) Contact analysis
Finite element analysis
Conforming contacts
Other Keywords
Subject
Abstract (in Chinese)
本論文探討圓柱的密合接觸問題,並利用套裝軟體ANSYS進行有限元素接觸分析。首先針對非密合接觸部分,目的是與解析解比較結果。結果包括球與平面及圓柱與平面的接觸分析,並與赫氏接觸的解析解比較;以及正向力與側向力同時作用時圓柱與平面的摩擦接觸,分析結果與Mindlin的解析結果進行比較。
本論文所分析的密合接觸包含三個部分,第一部分是分析圓柱與不同半徑曲面之密合無摩擦接觸,分析結果分別與赫氏接觸及Persson的結果相互比對。第二部分為材料相異圓柱間的密合摩擦接觸,在給定不同的彈性係數與蒲松比時,密合圓柱受到的接觸壓力與接觸區域大小。第三部分分析密合圓柱即將轉動時所受到的力矩與摩擦應力。
Abstract (in English)
Conforming contact of cylinders is treated in this thesis. Finite element analysis is performed using ANSYS. Results are first compared to known analytical solutions in nonconforming contacts, which include the Hertz solutions for normal contacts between two cylinders and between two spheres, and Mindlin’s solutions for sliding contact. A favorable mesh is chosen from the comparisons for further analysis.
Then three cases of conforming contact are dealt with. The first case is conforming contact between a cylinder and a concave surface with different radii. Results are compared to Hertz solutions and to solutions obtained by Persson. The second case is the frictional contact between two conforming cylinders with different elastic constants. Contact pressure and contact region size for different values of elastic constants are obtained. The third case is the analysis to obtain torque and friction stress when a cylinder is about to rotate on a conforming surface.
Other Abstract
Table of Content (with Page Number)
目錄 
中文摘要----------------I
英文摘要----------------II
目錄------------------III
圖目錄------------------V
第一章 緒論	1
1.1 研究動機與文獻回顧	1
第二章 有限元素分析	4
2.1 有限元素分析簡介	4
2.2 座標與位移的內插	5
2.3 位移與應變關係式	9
2.4 應變與應力關係式	11
2.5 平衡方程式	12
第三章 接觸分析	14
3.1 接觸分析簡介	14
3.2 接觸方式與設定接觸元素	14
3.3 接觸分析後處理	15
第四章 接觸範例	16
4.1 球與平面之正向無摩擦接觸	16
4.2 圓柱與平面之正向無摩擦接觸	22
4.3 圓柱與平面之側向摩擦接觸	27
第五章 結果與討論	40
5.1 圓柱與不同半徑曲面之密合無摩擦接觸	40
5.2 密合正向接觸-與赫氏接觸比較	50
5.3 密合正向接觸-與Persson比較	54
5.4 相異材料密合圓柱之摩擦接觸	61
5.5 即將轉動之密合圓柱	69
第六章 結論	73
參考文獻	75
 
圖目錄
圖1	將梯形物件分割成有限個元素	 4
圖2	平面8節點元素	         6
圖3	在- η座標系的平面8節點元素	 6
圖4	圓球(或圓柱)與平面接觸示意圖	19
圖5	圓球與平面接觸,平均長度為6.5mm網格圖	20
圖6	圓球與平面接觸壓力分布圖	21
圖7	圓柱與平面接觸,平均長度為20mm網格圖	25
圖8	圓柱與平面接觸,4種網格接觸壓力分布圖	26
圖9 	圓柱平面接觸並加入Fx與t	30
圖10	t作用在圓柱上x座標500mm及-500mm	31
圖11	t作用在圓柱上緣x座標255.72mm及-255.72mm	32
圖12	t作用在圓柱上緣x座標19.878mm及-19.878mm	33
圖13	圓柱與平面整體網格圖	34
圖14	t作用在圓柱上x座標500及-500摩擦應力分布	35
圖15	t作用在圓柱上x座標255.72及-255.72摩擦應力分布	36
圖16	t作用在圓柱上x座標19.878及-19.878摩擦應力分布	37
圖17	圓柱接近完全滑動時的摩擦應力分布圖	38
圖18	圓柱完全滑動時的摩擦應力分布圖	39
圖19	圓柱與曲面接觸示意圖	41
圖20	R2為-900mm之網格	42
圖21	R2為−750mm之網格	43
圖22	R2為−550mm之網格	44
圖23	R2為−900mm之接觸壓力分布圖	47
圖24	R2為−750mm之接觸壓力分布圖	48
圖25	R2為−550mm之接觸壓力分布圖	49
圖26	P為50kN/mm時的接觸壓力分布圖	52
圖27	P為1500kN/mm時的接觸壓力分布圖	53
圖28	圓柱密合接觸,接觸壓力與接觸區示意圖	56
圖29	α為14.52度時的接觸壓力分布	57
圖30	α為29.16度時的接觸壓力分布	58
圖31	α為44.66度時的接觸壓力分布	59
圖32	α為60.59度時的接觸壓力分布	60
圖33	E1=E2=210 GPa,摩擦應力分布	64
圖34	E1=140 GPa,E2=210 GPa,摩擦應力分布	65
圖35	E1=105 GPa,E2=210 GPa,摩擦應力分布	66
圖36	E1=92.316 GPa,E2=235.904 GPa,摩擦應力分布	67
圖37	E1=100 GPa,E2=279.382 GPa,摩擦應力分布	68
圖38	圓柱密合接觸承受力矩	70
圖39	圓柱密合接觸網格圖	71
圖40	即將滑動之密合圓柱,摩擦應力分布	72
References
[1]	徐正陽,束縛條件用在二維彈性體摩擦接觸問題的有限元素分析,淡江大學機械工程研究所碩士學位論文,1998。
[2]	王樂榮,以有限元素多點拘束條件分析二維滾動接觸,淡江大學機械與機電工程學系碩士學位論文,2003。
[3]	林毅弘,三維靜態接觸下之切線應力分析,淡江大學機械與機電工程學系碩士學位論文,2004。
[4]	蔡岸祺,以有限元素多點拘束條件分析二維異材質滾動接觸問題,淡江大學機械與機電工程學系碩士學位論文,2004。
[5]	洪明智,以有限元素多點拘束條件分析共形滾動接觸,淡江大學機械與機電工程學系,2007。
[6]	Carter, F.W. “ On the Action of a Locomotive Driving Wheel ”, Royal Society, 1926.
[7]	Persson, A. “ On the Stress Distribution of Cylindrical Elastic Bodies in Contact ”,Chalmers Technical University, Goteborg, 1964.
[8]	Solodovnikov, V.N. “Solution of the contact problem for a pin-loaded plate ”, Journal of Applied Mechanics and Technical Physics, v38, n1, 1997.
[9]	Liu, S & Chen, W. “ Two-dimensional numerical analyses of double conforming contact with effect of curvature ”, Interna-tional Journal of Solid and Structures, v49, n11-12, p1365-1374, 2012.
[10]	Vollebregt, E. & Segal, G. “ Solving conformal wheel-rail rolling contact problems ”, Vehicle System Dynamics, v52, n SUPPL. 1, p455-468, 2014.
[11]	Recuero, A.M. & Shabana, A.A. “ A simple procedure for the solution of three-dimensional wheel/rail conformal contact problem ”, Journal of Computational and Nonlinear Dynamics, v9, n3 , 2014.
[12]	Johnson, K. L. “ Contact Mechanics ”, Cambridge University Press, UK, 1985.
[13]	Mindlin, R.D. “ Compliance of elastic bodies in contact ”, Trans. ASME, Series E, Journal of Applied Mechanics, 1949.
[14]	Dundurs, J. & Lee, M.S. “ Stress concentration at a sharp edge in contact problems ”, Journal of Elasticity, 1972.
[15]	Chandrupatla, T.R. & Belegundu, A.D. “ Introduction to Finite Elements in Engineering”, 4th ed., Pearson Education, 2012.
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