滑動過程中粗糙表面之波?個數與接觸溫度及應力關係之分析研究

Analysis of Sliding Contact Temperature and Stress with the Number of Contact Peaks of Rough Surface

許沛文(Pei-Wen Hsu)

指導教授 ： 陳新郁

共同指導教授 ： 洪政豪(Jeng-Haur Horng)

國立虎尾科技大學/工程學院/機械與機電工程研究所/碩士(2014年)

https://doi.org/10.6827/NFU.2014.00081

摘要

從微觀角度觀察元件表面，發現表面充滿著高低不等之波?與波谷。在相對運動的過程中，表面會因為相互之磨擦而造成表面溫度上升。因此兩表面之間的波?與波谷接觸對於材料之表面接觸溫度、應力及應變有非常大之影響。過去粗糙表面之接觸溫度分析，大都以一個波?在承受壓力下進行分析，較少用多波?之實際表面進行分析。

本論文主要使用ANSYS有限元素軟體建立粗糙表面滑塊，並給予不同之負載、移動速度、表面粗糙度、熱傳導係數以及粗糙表面接觸波?個數等參數，探討滑塊在不同粗糙表面接觸波?個數下，其表面接觸溫度、應力與應變之變化，也透過培克萊特數的熱源分布建立預測方程式。由分析結果顯示：(一)影響最大溫升參數的主要因素為壓力以及滑塊滑動速度，隨著這兩種因素之數值的增加，其最大溫升參數有明顯增加的趨勢，但熱傳導係數與上述影響因素相反，熱傳導係數越小則最大溫升參數越高，而當表面粗糙度越大時，其最大溫升參數僅略微增加。(二)不同接觸波?個數的比較部分，主要透過各接觸波?個數之最大溫升數值比較其差異值。在相同壓力與速度下，當接觸波?個數愈多其接觸溫度會逐漸減少。研究發現，九個波?已足夠分析粗糙度表面溫度參數。(三) 應力與應變部分，當接觸波?同時承受壓力以及進行滑動的過程中，最大等效應力與等效應變值隨著壓力與滑塊滑動速度的改變而增加，且最大等效應力與最大等效應變會發生在接觸波?的接觸區域，也就是接觸區域之邊緣。 (四)數值迴歸分析部分，主要比較有限元素法分析結果以及使用數值迴歸結果相互比較其誤差性，並建立一預測方程式探討表面接觸波?個數等對於表面接觸溫度之影響，此研究結果可以做為在製作元件表面時重要的依據。其預測公式如下：

(1) Pe > 5的回歸方程式
最小誤差值為0.001%，最大誤差值為26.03 %，標準誤差29.29。若將誤差過大的資料移除並重新再迴歸，其誤差值會小於10 % 以內。

(2) 0.1 < Pe < 5的回歸方程式
最小誤差值為0.042 %，最大誤差值為9.19 %，標準誤差4.706。

(3) Pe < 0.1的回歸方程式
最小誤差值為0.021 %，最大誤差值為6.34 %，標準誤差0.77。

關鍵字

接觸溫度 ； 接觸波?個數 ； 最大等效應力 ； 數值迴歸

並列摘要

Observing component surface from micro point of view, we can find that the surface is full of uneven peaks and valleys. In the process of relative motion, the surface temperature will rise due to friction. Therefore, the contact between peaks and valleys on both surfaces has great influence on surface contact temperature, stress and strain. The past experiments generally analyzed the condition that one peak was under loads, and only a few experiments analyzed the conditions that multiple Peaks were under loads.

This paper mainly uses ANSYS, finite element software, to establish rough surface slider and give different loads, movement speeds, surface roughness, thermal conductivity and the quantity of rough surface contact peaks, to discuss change of surface contact temperature, stress and strain of sliders in different quantities of rough surface contact peaks, as well as thermal source distribution of Peclet number to establish prediction equation. The analysis results show: (1) the main factors affecting maximum temperature rise parameter are pressure and slidng speed; with increase of the two factors, the maximum temperature rise parameter has obvious increasing tread, but thermal conductivity is on the contrary, namely, the smaller thermal conductivity brings higher maximum temperature rise parameter, when the surface roughness is bigger, its maxium temperature rise strategy slightly increases. (2) For comparison part of different quantities of contact peaks, it compares difference mainly through maximum temperature rise value of quantities of contact peaks. In the same pressure and speed, the more contact peaks will generate less contact temperature. This research finds that 9 peaks are enough to analyze roughness surface temperatue parameters. (3) For stress and strain, when the contact peaks are under pressure at the same time and pushing the slider, the maxium equivalent stress and equivalent strain value increase as sliding speed changes, and the maxium equivalent stress and the maximum equivalent strain will generate contact area in contact peaks, namely, edge of the contact area. (4) For numerical regression analysis, it mainly compares finite element analysis result and uses numerical regression analysis result to compare its difference, as well as establishes prediction formula to discuss influence of quantity of surface contact peaks on surface contact temperature. The research result can be regarded as important basis for manufacturing component surface. Its prediction formula is as follows:

(1) Regression equiation for Pe > 5
The minimum error is 0.001%, the maximum error is 26.03 %, standard deviation is 29.29. If the data with bigger errors is removed and regressed, its error value will be within 10 %.

(2) Regression equiation for 0.1 < Pe < 5
The minimum error is 0.042 %, the maximum error is 9.19 %, and standard deviation is 4.706.

(3) Regression equiation of Pe < 0.1
The minimum error is 0.021 %, the maximum error is 6.34 %, and standard deviation is 0.77.

並列關鍵字

Contact Temperature ； Number of Peaks ； Real Contact Area ； Numerical Regression

參考文獻

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[5] H. A. Francis, 1971, “Interfacial temperature distribution within a sliding Hertzian contact”, ASLE Transactions, vol.14, pp. 41–54.

[6] M. A. Tanvir, 1980, “Temperature rise due to slip between wheel and rail—an analytical solution for hertzian contact”, Wear, vol.61, pp.295–308.