臺灣博碩士論文加值系統

根據Stokes微連體理論和Christensen隨機模式，本研究主要目的乃是理論性探討偶應力流體和表面粗糙度模式之複合效應對軸承系統操作性能的影響。為了同時考慮軸承表面粗糙度和因潤滑液添加極性懸浮劑所造成偶應力效應，吾人將先推導出廣義隨機非牛頓雷諾型方程式，並應用於計算軸承系統的定常態軸承特性和短頸軸承近似模式的平衡點。根據線性微擾法理論，系統的八個油膜剛性係數和阻尼係數及振動時判斷系統穩定與否的門檻速率(threshold speed)條件將可決定。
根據研究所得結果，偶應力流體和表面粗糙度模式之複合效應對軸承系統操作性能的影響是顯著而不可忽略的。相對於牛頓流體和軸承表面光滑的情形而言，偶應力效應可提升潤滑液流體的薄膜壓力、改善系統的負載能力和降低摩擦係數，此種情形在高偏心率比時尤甚。表面粗糙度效應對軸承特性的影響在長頸軸承近似模式時非常顯著，且一維橫向和縱向粗糙度對軸承性能的影響，其趨勢恰好相反。根據研究結果，短頸模式和長頸模式粗糙度效應發生反轉的臨界值在軸承長度-直徑比為1.1時。
由短頸軸承近似模式的線性穩定定分析知，當軸承系統存在偶應力效應和加工表面為縱向粗糙度時，將會增加系統剛性係數KXX, KXY 和 KYX 及阻尼係數的CXX數值，而這將導致系統有較高的穩定門檻速率。然而，若和光滑軸承表面受偶應力效應作用的情形比較，一維橫向粗糙度模式將會降低系統的門檻速率。

According to the Stokes microcontinuum theorem and the Christensen’s stochastic model, the main objective of this paper is to theoretically predict the combined influences of couple stresses and surface roughness on the lubrication performance of journal-bearing systems. To take account of both the presence of surface roughness of bearings and the couple stress effect due to the lubricant containing the polar suspensions, the generalized stochastic non-Newtonian Reynolds-type equation is derived and applied to evaluate the equilibrium solution of a short journal bearing. By using the linear theory, the eight oil-film stiffness and damping coefficients as well as the vibration stability boundary were determined.
According to the results obtained, the combined effects of couple stress and surface roughness on the characteristics of journal-bearing systems are apparently and can not be negligible. Comparing to the Newtonian-lubricant smooth-bearing case, the couple stress effects can raise the film pressure of the lubricant fluid, improve the load-carrying capacity and reduce the friction parameter, especially at high eccentricity ratio. The surface roughness effect is dominant in long bearing approximation and the influence of transverse or longitudinal roughness to the journal bearing is in reversed trend. In general, the critical value of length–to– diameter ratio is 1.1.
As for the linear stability analysis of short journal-bearing system, the presence of couple stress together with the longitudinal roughness provides an increase in the values of stiffness coefficients KXX, KXY and KYX as well as the damping coefficient CXX. In addition, this couple stress results in a higher stability threshold speed. Whereas, when compared to the smooth bearing lubricated with couple stress fluid, a decrease in the threshold speed is found in the case of transverse roughness.

目 錄
中文摘要 I
ABSTRACT II
誌謝 III
表目錄 VII
圖目錄 VII
符號說明 X
第一章 緒 論 1
1-1研究動機與背景 1
1-2文獻回顧 3
1-3研究目的及方法 9
1-4本文架構 10
1-4-1第一章 緒論 10
1-4-2第二章 短頸軸承理論分析與結果討論 11
1-4-3第三章 長頸軸承理論分析與結果討論 11
1-4-4第四章 有限長頸軸承理論分析與結果討論 11
1-4-5第五章 短頸軸承穩定度理論分析與結果討論 12
1-4-6第六章 結論與未來展望 12
第二章 短頸軸承 13
2-1理論分析 13
2-1-1 非牛頓流體雷諾型方程式 15
2-1-2 非牛頓流體廣義隨機雷諾型方程式 16
2-1-3 短頸軸承近似模式 19
2-1-4 軸承定常態性能 20
2-1-4-1荷重能力 和姿態角 20
2-1-4-2摩擦係數F R/C 21
2-2結果與討論 23
第三章 長頸軸承 30
3-1理論分析 30
3-1-1 非牛頓流體雷諾型方程式 31
3-1-2 非牛頓流體廣義隨機雷諾型方程式 32
3-1-3 壓力分佈與零壓力梯度角 35
3-1-4 軸承定常態性能 36
3-1-4-1荷重能力 和姿態角 36
3-1-4-2摩擦係數F R/C 37
3-2結果與討論 38
第四章 有限長頸軸承 47
4-1理論分析 47
4-1-1 非牛頓流體雷諾型方程式 48
4-1-2 非牛頓流體廣義隨機雷諾型方程式 48
4-1-3 數值分析 52
4-1-4 軸承定常態性能 54
4-1-4-1荷重能力 和姿態角 54
4-1-4-2摩擦係數 55
4-2結果與討論 56
第五章 短頸軸承穩定度理論分析 66
5-1理論分析 66
5-1-1 薄膜壓力和作用力(FILM PRESSURE AND FORCE) 69
5-1-2 運動方程式(EQUATIONS OF MOTION) 70
5-1-3軸承特性(BEARING CHARACTERISTICS) 72
5-1-3-1平衡點(EQUILIBRIUM POINTS) 72
5-1-3-2 動態特性(DYNAMIC CHARACTERISTICS) 73
5-2結果與討論 74
第六章 結論與未來展望 86
6-1短頸軸承結論 86
6-2長頸軸承結論 86
6-3有限長頸軸承結論 87
6-4短頸軸承穩定度分析結論 88
6-5 未來展望 88
參考文獻 91
附錄A 動態係數的推導 100

VII
表目錄
表5-1 具一維橫向粗糙度軸承的定常態操作性能----------------------------------- 78
表5-2 具一維縱向粗糙度軸承的定常態操作性能----------------------------------- 79
圖目錄
圖2-1 頸軸承之物理機制圖---------------------------------------------------------------- 25
圖2-2 在* z =0, l =0.25, e =0.6 時，不同* l 和L 下，壓力* p 和q 之關係------- 25
圖2-3 在q = o 120 , l =0.25,e =0.6 時，壓力* p 和* z 之關係---------------------------- 26
圖2-4 不同的L 和* l 時，荷重能力* W 相對於e 之關係---------------------------- 26
圖2-5 l =0.25，不同的e 及l 時，荷重能力* W 相對於* l 之關係------------- 27
圖2-6 l =0.25,不同的L 和* l 時，姿態角y 相對於e 之關係-------------------- 27
圖2-7 l =0.25,不同的L 和e 時，姿態角y 相對於* l 之關係-------------------- 28
圖2-8 l =0.25,不同的L 和* l 時，摩擦係數C R f / 相對於e 之關係----------- 28
圖2-9 圖l =0.25,不同的L 和e 時，摩擦係數C R f / 相對於* l 之關係--------- 29
圖3-1 長頸軸承之物理機制圖------------------------------------------------------------- 41
圖3-2 e =0.4 時，不同* l 和L 下，壓力* p 和q 之關係------------------------------- 41
圖3-3 * l =0.6 時，不同e 和L 下，壓力* p 和q 之關係------------------------------- 42
圖3-4 不同* l 和L 下零壓力梯度角2 q 和e 之關係---------------------------------- 42
圖3-5 不同e 和L 下，零壓力梯度角2 q 和* l 之關係--------------------------------- 43
圖3-6 不同* l 和L 下， * W 和e 之關係----------------------------------------------- 43
圖3-7 不同e 和L 下， * W 和* l 之關係----------------------------------------------- 44
VIII
圖3-8 不同* l 和L 下，y 對e 之關係------------------------------------------------- 44
圖3-9 不同e 和L 下，y 對* l 之關係---------------------------------------------------- 45
圖3-10 不同* l 和L 下， C R f / 對e 之關係-------------------------------------------- 45
圖3-11 不同e 和L 下， C R f / 對* l 之關係-------------------------------------------- 46
圖4-1 長頸軸承之物理機制圖------------------------------------------------------------- 59
圖4-2 油膜格點切割說明------------------------------------------------------------------- 59
圖4-3 2 . 0 , 4 . 0 = L = e 時，軸承內潤滑液油膜分佈----------------------------------- 60
圖4-4 e =0.4, * l =0.3 時，短頸、有限長和長頸三種軸承在中央平面處壓力
P* 和圓周座標q 關係之比較圖--------------------------------------------------- 61
圖4-5 在不同e 和L 參數值時，負重能力* W 和* l 之關係-------------------------- 61
圖4-6 在不同e 和L 參數值時，負重能力* W 和l 之關係-------------------------- 62
圖4-7 在不同* l 和L 參數值時， * W 和l 之關係--------------------------------------- 62
圖4-8 在不同e 和L 參數值時，姿態角y 隨* l 變化之曲線-------------------------- 63
圖4-9 在不同* l 和L 參數值時，姿態角y 隨* l 變化之曲線------------------------- 63
圖4-10 在不同* l 和L 參數值時，姿態角y 隨* l 變化之曲線------------------------ 64
圖4-11 在不同e 和L 參數值時，摩擦係數C R f / 和* l 之函數關係--------------- 64
圖4-12 在不同e 和L 參數值時，摩擦係數C R f / 和* l 之函數關係-------------- 65
圖4-13 在不同* l 和L 參數值時，摩擦係數C R f / 和* l 之函數關係-------------- 65
圖5-1 短頸軸承之物理機制與粗糙度模式示意圖------------------------------------ 80
圖5-2 不同粗糙度模式，定常態薄膜作用力分量( *
s
Fe - )和*
s
Fj 與偏心率比s e 之關係----80
圖5-3 不同粗糙度模式，定常態偏心率比s e 與蘇馬費數Sm 之關係--------------- 81
圖5-4 不同粗糙度模式，定常態姿態角s j 與偏心率比s e 之關係------------------- 81
IX
圖5-5 不同粗糙度模式，剛性係數KXX 和KXY 與定常態偏心率比s e 之關係--- 82
圖5-6 不同粗糙度模式，剛性係數KYX 和KYY 與定常態偏心率比s e 之關係---- 82
圖5-7 不同粗糙度模式，阻尼係數CXX 和CXY 與定常態偏心率比s e 之關係--- 83
圖5-8 不同粗糙度模式，阻尼係數CYX 和CYY 與定常態偏心率比s e 之關係---- 83
圖5-9 不同粗糙度模式，穩定門檻速率cr w 與定常態偏心率比s e 之關係--------- 84
圖5-10 不同粗糙度模式，穩定門檻速率cr w 與偶應力參數* l 之關係-------------- 84
圖5-11 不同粗糙度模式，穩定門檻速率cr w 與粗糙度參數L 之關係-------------- 85

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