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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
Keyword (in English) Contact analysis
Finite element analysis
Conforming contacts
Other Keywords
Abstract (in Chinese)
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)
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
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