具橢圓粗度形貌表面之面積增長與摩擦力的碎形分析

Fractal Analysis of the Junction Growth and Friction Coefficient for Elliptical Roughness Topography

陳群岳(Chun-Yueh Chen)

指導教授 ： 洪政豪

國立虎尾科技大學/工程學院/機械與機電工程研究所/碩士(2012年)

https://doi.org/10.6827/NFU.2012.00231

摘要

材料加工後表面粗度波峰各方向的曲率半徑經常不一樣，故以非等向之橢圓波峰為基礎的分析遠比球體波峰假設更接近真實的粗糙表面。又兩元件在相互運動時會產生接觸面積增長現象，也是影響元件磨潤性質的主要因子之一，本文利用碎形特性探討兩相對運動所產生出的面積增長與摩擦變化情形，並且考慮參數橢圓率、表面能與材料參數在相互運動時對表面磨潤性能的影響。分析結果可顯示各的參數，對於摩擦係數的影響關係：
1.改變摩擦係數的最主要因素為，碎形粗度參數G與黏附功?a*，摩擦係數會隨著?a*的增加而增加，會隨著G的增加而減少。
2.摩擦係數最大值在D的落點會隨著負荷增加而增加，且會隨著G增加而減少，也會隨著?a*增加而增加。
3.在D=1.25，?a*=1×10-10時，在G=1×10-9至G=1×10-11無論橢圓率大小，摩擦係數都會隨著負荷減少而減少，且在P*=1×10-7得到摩擦係數最值，然而摩擦係數會隨著負荷增加而增加。
4.摩擦係數都會隨著D的增加而增加至D=1.45至1.6左右，然而會隨著D的增加而減少，所以摩擦係數最低值會在D=1.1~1.25或1.8~1.9；在本文研究範圍內，G=1×10-9 、?a*=1×10-10至1×10-11與G=1×10-10 、?a*=1×10-10的地方，摩擦係數最低值會在D=1.1~1.25，隨著?a*增加與G減少，摩擦係數最低值會移動至D=1.8~1.9的地方。可依照需求來設計表面形貌。

關鍵字

碎形 ； 碎形維數 ； 碎形粗度參數 ； 黏附效應 ； 橢圓率

並列摘要

Curvatures of surface irregularities of an object are different after smoothing. Thus, an analysis based on non-homogeneous, oval peak is better in understanding the true irregularities of the object comparison with that based on spherical peak. Junction of two objects may grow when a relative movement between them exists. The increased contact area is one of the factors affecting tribology. This thesis is directed to junction growth and friction change when a relative movement of objects exists when fractal is under consideration. Oval curvature of parameters and tribology change due to surface irregularities and material parameters when a relative movement of objects exists are also addressed.
The following factors affect friction coefficients of different parameters based on my analysis:
Factors affecting friction coefficient changes include fractal roughness parameter G and adhesion ?a* in which the friction coefficient increases as ?a* increases and decreases as G increases.
Maximum friction coefficient occurs at D when friction coefficient gradually increases as load increases. Friction coefficient decreases as G increases and increases as ?a* increases.
Minimum friction coefficient occurs at D =1.25 when G is between 1×10-9 and 1×10-10 and ?a* is 1×10-11 (or specifically G is 1×10-9 and ?a* is 1×10-10). Minimum friction coefficient occurs when D = 1.9 in other conditions. Maximum friction coefficients of all parameters occur when D is between 1.45 and 1.6. Thus, object contour can be designed based on applications.

並列關鍵字

fractal ； fractal dimension ； fractal roughness parameter ； adhesion effect ； elliptical rate

參考文獻

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