有限元素密合接觸分析

Finite Element Analysis of Conforming Contacts

呂宗穎(Zong-Ying Lu)

指導教授 ： 劉昭華

淡江大學/工學院/機械與機電工程學系碩士班/碩士(2014年)

https://doi.org/10.6846/TKU.2014.00199

摘要

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。

關鍵字

接觸分析 ； 有限元素法 ； 密合接觸

並列摘要

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.

並列關鍵字

Contact analysis ； Finite element analysis ； Conforming contacts

參考文獻

[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.