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博碩士論文 etd-0728103-115946 詳細資訊
Title page for etd-0728103-115946
論文名稱
Title
以逆解法計算彈液動潤滑問題之壓力及黏度特性
Inverse Approach for Evaluating Pressure and Viscosity in Elastohydrodynamic Lubrication Problems
系所名稱
Department
畢業學年期
Year, semester
語文別
Language
學位類別
Degree
頁數
Number of pages
182
研究生
Author
指導教授
Advisor
召集委員
Convenor
口試委員
Advisory Committee
口試日期
Date of Exam
2003-07-18
繳交日期
Date of Submission
2003-07-28
關鍵字
Keywords
黏度、彈液動潤滑、逆解法
inverse approach, viscosity, EHL
統計
Statistics
本論文已被瀏覽 5696 次,被下載 1969
The thesis/dissertation has been browsed 5696 times, has been downloaded 1969 times.
中文摘要
中 文 摘 要

本文提出一個新穎性的逆解法來分析彈液動潤滑(EHL)問題,首先,利用有限差分法將彈性變形方程式及負荷平衡方程式離散化,並加以重新排列成一個矩陣式,再將欲求之壓力分佈值表示成一個函數矩陣式代入上述矩陣式,藉由最小均方根誤差法可直接解出未知係數值。只需使用少數的量測點即可克服傳統逆解法所造成壓力擾動的現象,快速且準確的求出一平滑的壓力曲線,再將其代入雷諾方程式,並運用最小均方根誤差法即可求得潤滑劑的最佳壓力-黏度指數值。此逆解法已解析線接觸、點接觸、純擠壓彈液動潤滑問題及彈液動薄膜潤滑(EHTFL)問題。
本文亦針對油膜厚度、負荷、彈性模數、常壓黏度和平均速度誤差對黏度計算的影響進行討論。結果顯示負荷、彈性模數的量測誤差影響較大,而常壓黏度與平均速度值影響較小,其中以油膜厚度量測誤差在計算黏度時扮演最重要的角色。當油膜厚度有量測誤差時,使用本文所提之彈液動潤滑逆解法仍可得到準確的壓力-黏度指數值,誤差值比傳統彈液動潤滑逆解法所得的壓力-黏度指數值來得小,使用本文所提之彈液動潤滑逆解法比傳統彈液動潤滑逆解法可容許較大的量測誤差值,此值可容許的範圍會增加3-10倍。
本文也運用吸附層模式,將油膜分為三層加以處理,各層的潤滑劑為可壓縮,壓黏,推導出修正的雷諾方程式以計算彈液動薄膜潤滑問題。探討彈液動薄膜潤滑與傳統彈液動潤滑之差異處,並找出影響彈液動薄膜潤滑的重要參數。結果顯示,運用此模式可合理的計算出彈液動薄膜潤滑狀態下的油膜厚度值及黏度值。吸附層厚度及黏度值對接觸區的潤滑特性會有顯著影響。再使用本文所發展的逆解法,求出在薄膜潤滑狀態下接觸區的壓力分佈值、壓力-黏度指數值、吸附層厚度值和吸附層黏度值。
本文採用自行開發的彈液動潤滑試驗機及光學干涉設備,觀測在點接觸彈液動潤滑,穩態及純擠壓狀態下油膜厚度分佈情形,並配合本文發展的彈液動潤滑逆解法來求出接觸區的壓力分佈值,進而求得潤滑劑的壓力-黏度指數值。結果顯示,逆解法所求得之壓力-黏度指數值比實驗值高,其誤差值皆在7﹪以內。當最小油膜厚度值低於30nm之條件下,使用本文發展的彈液動薄膜潤滑逆解法,可降低壓力-黏度指數值與實驗值的誤差。



Abstract
Abstract

This paper proposes a novel approach to analyze the inverse problems of elastohydrodynamic lubrication (EHL). First, a finite-difference method is employed to discretize the elastic deformation and the force balance equations. The discretizing equations can be rearranged into a matrix form. The pressure distribution can be expressed in an appropriate function and then substituting it into the matrix form. The least-squares error method is adopted to find the undetermined coefficients, which generates a smooth pressure distribution based upon a small number of measuring points on the film thickness map and overcomes the problems of pressure fluctuations obtained from the traditional methods. The apparent viscosity can be solved from the Reynolds equations by using the least-squares method to predict the optimum value of the pressure-viscosity index ( ). The proposed method is applied to analyze four kinds of the inverse problems, namely, EHL of line contacts, EHL of point contacts, pure squeeze EHL motion of circular contacts, and elastohydrodynamic thin film lubrication (EHTFL).
This paper discusses the effects of the implemented errors on the predicted value of apparent viscosity. The errors are implemented at the film thickness, the load, the effective elastic modulus, the viscosity at ambient pressure, and the mean velocity. Results show that the implemented errors in load and effective elastic modulus have a significant influence on the accuracy of the results, but the errors in average velocity and in the viscosity at ambient pressure do not have a significant effect. In these implemented errors, the resolution of the film thickness measurement plays the most important role in determining the accuracy of the apparent viscosity. Even when errors in the film thickness measurements are deliberately introduced, the inverse approach still provides a satisfactory value of the pressure-viscosity index. The resulting apparent viscosity errors are much smaller than those generated when using the traditional inverse method. The inverse approach can allow higher measurement error than traditional inverse method, and the allowable resolution range can be increased to about 3-10 times.
Base on the viscous adsorption theory, the modified Reynolds equation is derived for EHTFL. In this theory, the film thickness between lubricated surfaces is simplified as three fixed layers across the film, and the viscosity and the density of lubricant vary with pressure in each layer. The difference between classical EHL and EHTFL is investigated to find the important parameters of EHTFL. Results show that the proposed model can reasonably calculate the film thickness and the viscosity under EHTFL. Adsorbent layer thickness and viscosity significantly influence the lubrication characteristics of the contact conjunction. The inverse approach is developed to evaluate the pressure of contact region, pressure-viscosity index ( ) of oil film, and the film thickness and viscosity of adsorbent layer under EHTFL.
This paper also uses a self-development EHL tester with the optical interferometry equipment to observe the EHL film thickness map of circular contacts under the steady state and the pure squeeze motion. The inverse approach can be used to estimate the pressure distribution on a film thickness map obtained from optical EHL tester. By using this pressure distribution, the estimated pressure-viscosity index can be obtained. Result shows that the inverse approach predicts a larger value of the pressure-viscosity index than the actual value. The error between the actual and the estimated values of is less than 7 percent. When the minimum film thickness is less than 30 nm, the inverse approach based on EHTFL theory can reduce the error between the actual and the estimated values of .



目次 Table of Contents
總目錄
總目錄 i
圖目錄 v
表目錄 x
符號說明 xi
論文摘要(中文) xiv
論文摘要(英文) xvi
第一章 緒論
1-1研究動機與背景 1
1-2文獻回顧 3
1-3本論文之研究目的 9
1-4本論文架構 11
第二章 彈液動潤滑理論
2-1簡介 14
2-2接觸幾何形狀 15
2-3雷諾方程式 16
2-4膜油厚度方程式 19
2-4-1線接觸 20
2-4-2點接觸 21
2-5負荷平衡方程式 22
2-6潤滑劑的黏度與密度 23
第三章線接觸彈液動潤滑逆解法問題分析
3-1簡介 29
3-2線接觸彈液動潤滑數學模式 30
3-3線接觸彈液動潤滑逆解法 32
3-3-1壓力與黏度計算 32
3-3-2逆解法求壓力與黏度 34
3-4結果與討論 36
3-4-1直接解 36
3-4-2直接逆解法求壓力 37
3-4-3逆解法求壓力 38
3-4-4逆解法求黏度 40
3-4-5誤差效應對逆解法之影響 41
3-5結論 42
第四章點接觸彈液動潤滑逆解法問題分析
4-1簡介 57
4-2點接觸彈液動潤滑數學模式 58
4-3點接觸彈液動潤滑逆解法 59
4-3-1壓力與黏度計算 59
4-3-2逆解法求壓力與黏度 61
4-4結果與討論 63
4-4-1直接解 63
4-4-2直接逆解法求壓力 64
4-4-3逆解法求壓力 65
4-4-4直接逆解法求黏度 70
4-4-5逆解法求黏度 71
4-4-6油膜量測配合逆解法求 值 73
4-5結論 74
第五章點接觸純擠壓彈液動潤滑逆解法問題分析
5-1簡介 91
5-2點接觸純擠壓彈液動潤滑直接解 93
5-3純擠壓彈液動潤滑逆解法 97
5-3-1壓力與黏度計算 97
5-3-2逆解法求壓力與黏度 98
5-4結果與討論 100
5-4-1直接解-在三種操作條件下的油膜厚度
變化情況 100
5-4-2直接逆解法 104
5-4-3逆解法求壓力分佈 105
5-4-4逆解法求黏度 106
5-4-5油膜量測值配合逆解法求 值 107
5-5結論 108
第六章點接觸彈液動薄膜潤滑逆解法問題分析
6-1簡介 125
6-2點接觸彈液動薄膜潤滑數學模式 129
6-3點接觸彈液動薄膜潤滑表面力數學模式 132
6-4薄膜 、 及 值計算 133
6-5結果與討論 135
6-5-1直接解 135
6-5-2直接逆解法求壓力 141
6-5-3逆解法求壓力 141
6-5-4逆解法求 、 及 值 144
6-5-5油膜量測值配合逆解法求 、 及 值 145
6-6結論 146
第七章總論與展望
7-1總論 167
7-2未來展望 170
參考文獻 172
作者簡介 182
研究著作目錄 183
參考文獻 References
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