平面四桿機(jī)構(gòu) 畢業(yè)設(shè)計,平面四桿機(jī)構(gòu),畢業(yè)設(shè)計,平面,機(jī)構(gòu) 第7屆ICFDM2006 設(shè)計制造業(yè)前沿國際會議議項 2006年6月19-22日，中國，廣州 第25-30頁 ICE關(guān)于低環(huán)境壓力對軸承的影響的研究 馮凱 、張岫云 和 郝欣 潤滑和軸承理論學(xué)院 西安交通大學(xué) 西安710049, 中國 摘要：低環(huán)境壓力對主要軸承和 I.C發(fā)動機(jī)大端軸承的影響是基于單缸柴油發(fā)動機(jī)調(diào)查的。 首先，通過使用來自AVL公司名為“EXCITE Designer”的商業(yè)軟件，單缸發(fā)動機(jī)模型建立了起來 。之后, 做一系列的實驗來得到在不同的環(huán)境壓力之下的氣缸氣壓。 當(dāng)發(fā)動機(jī)模型視氣壓為加載的載荷時,主軸承和大端軸承的偏心率和摩擦損失利用實驗驗證的結(jié)果計算出來。 計算結(jié)果表明, 隨著環(huán)境壓力的下降，主軸承和大端軸承的加載變化, 在它們的摩擦損失略微減少的時候，偏心率有規(guī)律地變化。 關(guān)鍵詞: I.C發(fā)動機(jī); 低環(huán)境壓力 ; 軸承載荷 ; 偏心率 ; 摩擦損失 1.介紹 中國西部大部分是高海拔高原。 隨海拔高度增加，氣壓和空氣密度下降, 吸進(jìn)發(fā)動機(jī)的空氣減少以及可燃混合氣體變得過于密集，以致燃燒過程變得糟糕，發(fā)動機(jī)的動態(tài)行為劇烈地惡化[1] 。在這種工作條件下,主要軸承和軸瓦性能都將會為下降的氣壓所影響。因此，對發(fā)動機(jī)主要軸承和大端軸承在西部低壓力環(huán)境的工作狀況的研究對設(shè)計、產(chǎn)品和該類發(fā)動機(jī)維護(hù)有重要的指導(dǎo)意義。 目前,雖然不同海拔高度下的發(fā)動機(jī)燃燒過程和動力學(xué)影響的研究文件是在國內(nèi)和國外很常見的[2][3] ， 但是還沒有低氣壓對發(fā)動機(jī)軸承影響的系統(tǒng)的研究作品出現(xiàn)。在本論文中, 考慮氣壓影響的單缸發(fā)動機(jī)模型建立了起來。不同環(huán)境壓力和不同轉(zhuǎn)速作為模型的輸入載荷條件，利用在此情況下實驗測得的燃燒氣壓，借助于AVL公司出品的商務(wù)軟件“EXCITE Designer”，可以算出主要軸承和軸瓦隨不同環(huán)境壓力和不同轉(zhuǎn)速的工作狀態(tài)的變化，而結(jié)果可以通過慣性中心實驗場加以比較和校核。 2. 低氣壓的處理方法 高原低氣壓力對發(fā)動機(jī)軸承性能的影響主要來自發(fā)動機(jī)動力學(xué)性能的惡化。 在本文中, 一個西部環(huán)境模擬發(fā)動機(jī)測試裝置用來模擬高原低氣壓并且測量低氣壓對發(fā)動機(jī)的影響。 模擬低氣壓環(huán)境的核心技術(shù)是如何模擬并且校正壓力發(fā)動機(jī)進(jìn)氣壓力[4]. 這個測試系統(tǒng)不對排氣壓力和曲柄室中的壓力進(jìn)行模擬, 但這些工作將會稍后完成。 在實驗中, 測量了不同進(jìn)氣壓力對氣缸內(nèi)壓力的影響，壓力值也加載于以下建立的模型，并且低壓對發(fā)動機(jī)軸承性能的影響也計算出來了 測試裝置結(jié)構(gòu)如圖1 所示。 透過控制發(fā)動機(jī)進(jìn)氣壓力, 模擬容器能模擬在不同的環(huán)境氣壓下發(fā)動機(jī)的工作情況。 然后，通過安裝在氣缸里的高壓和高溫壓力傳感器，測量在發(fā)動機(jī)氣缸內(nèi)的壓力。 由于實驗條件限制,主要軸承的偏心率不能直接地測量, 飛輪的軸心軌跡用渦流感應(yīng)器測量, 并且它的偏心率計算出來取代主要軸承的偏心率以使計算模型有效。 各種各樣的因素影響到氣缸里的燃?xì)鈮毫?，其中環(huán)境氣壓，轉(zhuǎn)速和載荷是特別重要的。視發(fā)動機(jī)運轉(zhuǎn)不加載（發(fā)動機(jī)主要運行克服摩擦）來測量在不同轉(zhuǎn)速和不同環(huán)境壓力下的氣缸內(nèi)壓力。 圖2顯示了以1000R/M轉(zhuǎn)速不同環(huán)境下的氣缸內(nèi)壓力 3. 低氣壓對發(fā)動機(jī)軸承受力影響 3.1 活塞桿系統(tǒng)得受力分析 為簡化模型，假設(shè)活塞針和曲柄旋轉(zhuǎn)軸總是處于活塞的中心線上。以下發(fā)動機(jī)活塞桿的受力分析如圖3所示。氣缸內(nèi)壓力Fz分解到軸承上. 圖3 活塞桿受力分析和慣性力分析 Fz是氣缸內(nèi)燃?xì)鈿鈮?，模型的輸入載荷; FT和 FR是作用于副大端軸承的力，F(xiàn)z ,Fs 是作用于主要軸承的力. 3.2 活塞桿的慣性力分析慮在內(nèi)： 1）沿曲柄半徑方向的旋轉(zhuǎn)慣性力 在本文中，如圖3所示兩種慣性力考 2）沿活塞中心軸方向的第一和第二相互作用力 以坐標(biāo)軸分解： 通過發(fā)動機(jī)活塞桿的受力分析，氣缸內(nèi)燃?xì)鈮毫Ψ纸鉃橹饕S承和一致大端軸承，同時由活塞桿系統(tǒng)引起的慣性力。主要軸承和一致大端軸承上的加載力可以由這兩種力的組合推得。 3.3 軸承載荷計算結(jié)果和分析 （a）1000r/m轉(zhuǎn)速下主要軸承載荷（以下類推） (b) 1800r/m Main Bearing Load (c)2200r/m Main Bearing Load (d)1000r/m Concord Big End Bearing Load (e) 1800r/m Concord Big End Bearing Load 圖5所示隨著環(huán)境壓力下降，主要軸承和一致大端軸承的載荷在爆炸沖程時期急劇減少，而在其他沖程輕微變化。讀入并分析主要軸承和一致大端軸承在爆炸沖程時期的載荷，結(jié)果如表1所示。 表1 主要軸承和一致大端軸承在不同環(huán)境壓力和轉(zhuǎn)速下，在爆炸沖程時期的載荷分析 Main Bearing(主要軸承) Environment Pressure (kPa)（環(huán)境壓力） 97 80 60 1000 r/m Bearing Load (kN) （軸承載荷） 16000 13500 11000 Decrease Percent（下降百分比） (relative to 97kPa) （相比97 kPa） 15.6 31.3 1800 r/m Bearing Load (kN) 14000 10000 4500 Decrease Percent 28.6 67.8 2200 r/m Bearing Load (kN) 9000 5000 3000 Decrease Percent 44.4 66.7 Concord Big End Bearing（一致大端軸承） Environment Pressure (kPa) 97 80 60 1000 r/m Bearing Load (kN) 32500 27500 22500 Decrease Percent 15.4 30.8 1800 r/m Bearing Load (kN) 28000 20000 10000 Decrease Percent 28.6 64.3 2200 r/m Bearing Load (kN) 20000 11500 8000 Decrease Percent 42.5 60.0 表1顯示，主要軸承和一致大端軸承的載荷將會在任何轉(zhuǎn)速下隨著環(huán)境壓力下降而下降。氣壓越低，載荷下降得越多。隨著發(fā)動機(jī)轉(zhuǎn)速的上升，主要軸承和一致大端軸承的爆炸載荷增加量下降得更加劇烈。換言之，轉(zhuǎn)速越高，主要軸承和一致大端軸承的爆炸載荷對環(huán)境壓力越敏感。這種情況的原因是，隨著發(fā)動機(jī)轉(zhuǎn)速上升，氣缸內(nèi)氣壓下降量增加，然后軸承載荷急劇下降。進(jìn)一步得說，隨著轉(zhuǎn)速上升，慣性力增加，但軸承載荷受牽連影響而減少。 然而，當(dāng)轉(zhuǎn)速上升到1800r/m ，氣壓下降到60kPa ，主要軸承和一致大端軸承的爆炸載荷下降量并不隨轉(zhuǎn)速上升而變化。意味著轉(zhuǎn)速上升到某個程度，環(huán)境壓力足夠低，環(huán)境壓力對爆炸過程中的軸承載荷的影響在任何轉(zhuǎn)速下，幾乎是一樣的。這是因為當(dāng)環(huán)境壓力下降到某個程度時，轉(zhuǎn)速上升，氣壓對氣缸內(nèi)燃燒影響下降，同時氣缸內(nèi)壓力相當(dāng)?shù)馗?，慣性力的影響很小，所以相當(dāng)程度上軸承載荷保持不變。 圖5 (c) (f) 顯示，在轉(zhuǎn)速2200r/m下，主要軸承和一致大端軸承與曲柄角度相關(guān)的載荷變化。圖中顯示，這兩個軸承載荷的升降，在發(fā)動機(jī)整個工作過程中，并不與環(huán)境氣壓的減少一致，但是因沖程而異。這種現(xiàn)象可解釋如下：在發(fā)動機(jī)整個工作過程中，氣缸內(nèi)氣壓（公式（1）—（4）中Fz）特別是燃燒過程中的燃?xì)鈮毫﹄S著環(huán)境壓力下降而下降，所以主要軸承和一致大端軸承的載荷整個來看下降。在曲柄角度在300～360和 -360～-300 之間是的增加是因為，活塞此時處于排氣沖程的后半部分，以及吸氣沖程的前半部分，氣缸與環(huán)境交換空氣；在此，沿Z軸負(fù)方向慣性力Fz比沿Z軸正方向慣性力小，意味著合力是沿Z軸正方向的，隨Fz減小，合力反而增加，所以軸承載荷將會增加。 4. 低氣壓對發(fā)動機(jī)軸承偏心率的影響 4.1 Reynolds'方程的建立及偏心率的解決 發(fā)動機(jī)Reynolds’方程可以表述為： 在此， D是軸承軸瓦的參數(shù)，BR是軸瓦的寬度，ε是偏心率， η 是發(fā)動機(jī)汽油的動力粘度，δ是最小角速度，ω是軸心轉(zhuǎn)速。π是汽油薄膜壓力，t是時間坐標(biāo)，φ 和 z是尺寸坐標(biāo)。 分別分析軸承偏心率的增減過程，不同偏心率協(xié)同因素和恒定轉(zhuǎn)速的關(guān)系可以如下所示： （公式略） 式中：B=δS－γS 0≤︱B︱≤90° 在計算中應(yīng)用了Butenschoen 方法，數(shù)字 SOD 和SOV 可以在參考[5]中找到，Runge-Kutta方法用來解決重復(fù)循環(huán)的偏心率。 4.2 軸承偏心率的計算機(jī)運算結(jié)果及分析 圖6 主要軸承和一致大端軸承在不同環(huán)境壓力下的偏心率 圖形6 (a) (d)顯示，當(dāng)發(fā)動機(jī)轉(zhuǎn)速在1000r/m以下時，兩個軸承的偏心形狀都發(fā)生收縮；圖形6 (b) (e) 顯示，當(dāng)發(fā)動機(jī)轉(zhuǎn)速為1800r/m時，兩個軸承的偏心形狀都發(fā)生膨脹，主要軸承的偏向方向改變；圖形6(c) (f) 顯示，當(dāng)轉(zhuǎn)速為 時，兩個軸承的偏心形狀都發(fā)生膨脹。我們可以從以上數(shù)據(jù)下結(jié)論，當(dāng)發(fā)動機(jī)轉(zhuǎn)速較低時，兩個軸承的偏心形狀隨著環(huán)境氣壓的下降都發(fā)生收縮，軸承的輪滑條件得以改善，軸承工作更加穩(wěn)定；當(dāng)轉(zhuǎn)速較高時，這兩個軸承的偏心形狀反而膨脹，輪滑條件惡化，軸承工作不穩(wěn)定。以特定轉(zhuǎn)速，偏心率的偏差方向可能也隨環(huán)境氣壓下降而變化。燃?xì)鈮毫蛽u桿的往復(fù)運動慣性力的合力決定軸承承載。當(dāng)軸承轉(zhuǎn)速較低時，往復(fù)運動慣性力較小，發(fā)動機(jī)軸承的主要承載是由氣缸內(nèi)燃?xì)鈮毫σ鸬模ㄟ@也是軸承偏心偏向軸心一邊 的原因）。正因如此，環(huán)境壓力的下降導(dǎo)致了氣缸內(nèi)壓力的下降，于是軸承偏心收縮。但是當(dāng)發(fā)動機(jī)轉(zhuǎn)速較高時，搖桿的往復(fù)運動慣性力增加，并且可能在轉(zhuǎn)速足夠高時在特殊的曲柄角度超過氣缸內(nèi)燃?xì)鈮毫?。此時，當(dāng)環(huán)境壓力的下降導(dǎo)致氣缸內(nèi)壓力的下降，軸承偏心的偏斜也會改變。 隨著發(fā)動機(jī)轉(zhuǎn)速持續(xù)上升，搖桿的往復(fù)運動慣性力在一個較大的曲柄角度超過氣缸內(nèi)壓力。 結(jié)果，軸承承載是往復(fù)運動慣性力減去氣缸內(nèi)燃?xì)鈮毫Φ慕Y(jié)果。當(dāng)環(huán)境空氣壓力導(dǎo)致氣缸內(nèi)壓力下降時，軸承承載增加，偏心率增加。 5. 低氣壓對發(fā)動機(jī)軸承摩擦功率損失的影響 5.1 摩擦功率損失的計算[5] 如果軸承軸和軸瓦沒有直接的關(guān)系，摩擦功率損失大部分是由發(fā)動機(jī)汽油粘性的剪切力引起的。本文中，只考慮到部分摩擦功率損失。 The friction coefficient μ (α ) is: （摩擦因素μ (α )為：） 5.2 軸承摩擦功率損失的計算結(jié)果及分析 圖7 主要軸承和一致大端軸承在不同環(huán)境空氣壓力下的摩擦功率損失 圖形7指出，發(fā)動機(jī)汽油粘性引起的主要軸承和一致大端軸承的功率損失隨著還擊空氣壓力的下降而略微減少。這是因為當(dāng)環(huán)境空氣壓力下降，汽油粘度隨氣壓上升減少時，軸承承載整體下降，因此汽油粘性引起的剪切力也略微減少，這樣摩擦功率損失減少。進(jìn)一步地說，圖形中顯示，環(huán)境壓力在爆炸沖程間對摩擦功率損失相當(dāng)?shù)刂匾?。這也是因為在那時軸承承載的下降更加的嚴(yán)重。 6. 實驗證明 在“西部環(huán)境實驗發(fā)動機(jī)測試裝置” 頂上，裝有位移傳感器，可以用來測試飛輪慣性中心及計算其偏心，并且可以用這來取代主要軸承的偏心率以驗證計算機(jī)模型。 圖8 主要軸承偏心率 因為實驗條件的限制，主要軸承的偏心率不能直接測得，所以試驗測得是飛輪的偏心率。因為曲柄連桿是彈性的，將會在發(fā)動機(jī)箱體內(nèi)，主要軸承和飛輪的偏心的壓力下彎曲和扭曲，這些因素是在活塞桿的不同段，是明顯不同的。但是在它們之間應(yīng)該有一些共同特征；運動狀態(tài)應(yīng)該一樣，且慣性中心軌跡應(yīng)該類似。這主要是因為主要軸承和飛輪都是在曲柄連桿上，它們之間的距離不長，所以曲柄桿的彎曲和扭曲是有限的，偏心形狀在某種程度上相似。進(jìn)一步地說，因為它們都是在曲柄桿上，都有相同的承載，偏心的變化趨勢應(yīng)該是相同的。本文中，對通過實驗測得的飛輪上的偏心率和主要軸承的計算偏心率加以比較來驗證計算模型。 如圖8 所示，從兩幅圖片的形狀和注明的點的順序來看，它們以圖形9所示的方向從A，B，C…H的方向輪流運動。比較圖8(a) ,圖8 (b)中的點A，G和H有一點向右偏移，而點F微向上偏。這主要是曲柄桿的扭曲所引起的。通過以上兩幅圖形的分析比較，我們可以看到，兩種偏心的運動規(guī)律是連續(xù)的，并且它們的形狀某種程度上相似。所以我們可以下結(jié)論說，計算結(jié)果通過實驗證明是正確的，可信的。 7. 結(jié)論 本文中，建立了單缸發(fā)動機(jī)模型，其考慮了低氣壓對主要軸承和一致大端軸承的影響，并通過了試驗驗證?？傊l(fā)動機(jī)轉(zhuǎn)速越高，主要軸承和一致大端軸承的爆炸承載受環(huán)境空氣壓力的影響越敏感。但是當(dāng)環(huán)境空氣壓力下降到某一個程度，它對高轉(zhuǎn)速發(fā)動機(jī)的主要軸承和一致大端軸承的爆炸承載的影響不再存在；環(huán)境空氣壓力對發(fā)動機(jī)主要軸承和一致大端軸承的爆炸承載的影響是同樣程度的。隨著環(huán)境空氣壓力的下降，主要軸承和一致大端軸承的偏心有規(guī)律地變化。當(dāng)轉(zhuǎn)速較低時，偏心的形狀收縮且軸承的工作更加穩(wěn)定；當(dāng)轉(zhuǎn)速較高時，偏心的形狀反而膨脹，且軸承工作不穩(wěn)定。主要軸承和一致大端軸承的摩擦功率損失隨著空氣壓力的下降而略微減少。 鳴謝 本課題的研究得到中國自然科學(xué)基金會的支持。ID50375115 參考： [1] Liu Rui lin, Liu Hong wei, Qin De. An Experimental Study on Performance of Turbocharged Diesel Engines at High Altitude (Low Air Pressure). Transactions of Csice, 2003 [2] Liu Yong-hong, Ren Gong-chang, Zhang You-yun. The Virtual Simulation Modeling and Analysis for I.C. Engine Based on WEC. Acta Simulata Systematica Sinica, 2004 [3] Liu Yong-hong. Influence of Environment Factors of Western China on Dynamics of Piston-Crankshaft System in Internal-Combustion Engine. Xi’an: Xi’an Jiaotong University, 2005 [4] SHEN Li zhong, Shen Ying gang, BI Yu hua. Combustion Process of Naturally Aspirated and Supercharged Diesel Engines at Regions with Different Altitude. Transactions of Csice，2000，11 [5] AVL, Excite Designer Version 6.0 Excite Designer Theory, 2003 [6] Wen Shizhu, Huang Ping. The Theory of Tribology. Beijing: Tsinghua University Press, 2002. 10~11 聯(lián)絡(luò)信息: 張岫云 教授 西安交通大學(xué) 潤滑和軸承理論學(xué)院, N0.28 陜西省西安市咸寧西部路 郵編：710049 中華人民共和國。 電話:029-82669159 傳真:029-82668552 電子郵箱:yyzhang1@mail.xjtu.edu.cn 馮凱 碩士研究生 西安交通大學(xué) 軸承和潤滑理論學(xué)院, N0.28 陜西省西安市咸寧西部路 郵編：710049 中華人民共和國。 電話:029-82678594 傳真:029-82668552 電子郵箱:fengkai@tlbi.xjtu.edu.cn Proceedings of the 7th ICFDM2006 International Conference on Frontiers of Design and Manufacturing June 19-22, 2006, Guangzhou, China Pages 25-30 25 STUDY OF THE INFLUENCE THE INFLUENCE OF LOW ENVIRONMENT PRESSURE ON THE BEARING In ICE Feng Kai, Zhang Youyun and Xin Hao Theory of Lubrication and Bearing Institute, Xi’an Jiaotong University, Xi’an 710049, China Abstract: The influence of low environment pressure on the main bearing and big end bearing of I.C. engine was investigated based on a one-cylinder diesel engine. Firstly, a model of one-cylinder engine was set up, by the use of the commercial software EXCITE Designer from AVL company. Then, a series of experiments were done to gain the gas pressure in cylinder under different environment pressure. When the model of the engine considered the gas pressure as load, the applied load, eccentricity ratio and friction loss of the main bearing and the big end one were calculated, with the results validated by the experiments. The calculation results show that, with the decrease in environment pressure, the applied load of main bearing and big end one change, and the eccentricity ratio vary regularly, while their friction loss decrease a little. KeyWords: I.C. Engine; Low Environment Pressure; Bearing Load; Eccentricity Ratio; Friction Loss 1. Introduction Most of western China is high altitude plateau. As the increase of altitude, the air pressure and air density decrease, the air draw into the engine reduces and the combustible mixed gas becomes too dense ， so the combustion process becomes worse and dynamic behavior of the engine deteriorate significantly [1] . Under this working condition, the performance of both the main bearing and concord bearing will be affected by the drop of air pressure. So the research on the working condition of engine main bearing and concord bearing under western low pressure environment has important guiding significance for the design, manufacture and maintenance of engines working under western environment. At present, research documents on engine combustion process and dynamics influence at different altitude are usual at home and abroad [2][3] , but no systematic research work on the influence of low air pressure to the engine bearing appears. In this paper, single cylinder engine model considered the influence of air pressure is constructed. Using the combustion gas pressure measured through experiment under different environment pressure and different rotate speed as the input loading condition of the model, the change of the working condition of main bearing and concord bearing along with the environment air pressure under different rotate speed is calculated with business software EXCITE Designer of AVL Company, and the result is compared and validated with the experimental locus of journal center. 2. The Processing Method of low Air Pressure The influence of plateau low air pressure to the performance of engine bearing mainly comes from the deterioration of the engine dynamic behavior. In this paper, a western environment simulation engine test rig is used to simulate plateau low air pressure and measure the influence of low air pressure to the engine. The key technology of simulating low air pressure environment is how to simulate and adjust the intake pressure of the engine [4] . The exhaust pressure and the pressure in the crank shaft case are not simulated in this test system, and these works will be done later on. In the experiment, the influence of different intake pressure on the pressure in the cylinder is measured and the pressure value is loaded to the model constructed below, and then the influence of low pressure on the performance of engine bearing is worked out. The structure of the test rig is showed in fig. 1. Through the control of engine intake pressure, the simulation case can simulate the working condition of the engine under different environment air pressure. Then the pressure in the cylinder of the engine is measured by the high pressure and high temperature pressure sensor implemented in the cylinder. Due to the restriction of experimental condition, the eccentricity of the main bearing can not be measured directly, so the locus of journal center of the flywheel is measured with vortex sensor, and its eccentricity is worked out to replace that of the main bearing to validate the computational model. There are various factors which affect the combustion gas pressure in the cylinder, among which environment air pressure, rotate speed and load are especially important. Consider to run the engine with no load (the engine mainly do work to overcome friction) and measure Fig. 1 View of the Simulation Test Rig * Sponsored by National Natural Science foundation of China 26 the pressure in the cylinder under different rotate speed and different environment pressure. Fig.2 shows the pressure in the cylinder under different environment air pressure at 1000r/m. 3． The Influence of low Air Pressure on the Load of Engine Bearings 3.1 Force analysis of the piston-shafting system In order to simplify the model, it is assumed that the piston pin and rotate axis of the crank shaft are all on the central line of the piston. Then the force analysis of the engine piston-shafting is showed in fig.3. The gas pressure in the cylinder F Z is disassembled to the bearing. Fig.3 Piston-Shafting Force Analysis and Inertial Force Analysis 22 11 cos 1sin SS Z Z FF F F β λ ψ ′ ==? =? ? (1) 22 sin tan 1sin NN Z Z FF F F λψ β λ ψ ? ′ == =? ?? (2) () 2 22 sincos cos cos 1sin RZ Z FF F λψψβ ψ β λψ ?+ =? =? ? ?? ?? ?? ?? (3) () 22 sin sin cos sin cos 1sin RZ Z FF F ψβ λ ψ ψ ψ β λψ +?? =? =? + ?? ?? ?? ?? (4) F Z is the combustion gas pressure in the cylinder, the input load of the model; F T and F R are the forces applied on the concord big end bearing; FZ and FS are the force applied on the main bearing. 3.2 Inertial force analysis of the piston-shafting In this paper, two kinds of inertial force are considered as shown in fig.3 1) Rotate inertial force along the crank shaft radial direction 2) 1 st and 2nd order reciprocal inertial force along the piston central axis direction Disassemble to coordinate system: ( ) 0 2 01 0 cos cos cos 2 Zr Fr m mA mAωψ ψ ψ=? ? ? ? + ? ? + ? ? +K (5) 2 sin ry Fr mω ψ=? ? ? (6) Through force analysis of piston-shafting of the engine, combustion gas pressure in the cylinder is disassembled to the main bearing and concord big end bearing, at the same time the inertial force caused by the movement of the piston-shafting system. The load force on the main bearing and concord big end bearing can be derived from the combination of these two kinds of force. 3.3 Calculation result and analysis of bearing load Fig.2 Gas Pressure in the Cylinder under Different Environment Pressure at 1000r/m (a) 1000r/m Main Bearing Load (b) 1800r/m Main Bearing Load (d) 1000r/m Concord Big End Bearing Load (c) 2200r/m Main Bearing Load 27 Fig.5 Main Bearing and Concord Big End Bearing under Different Rotate Speed and Different Environment Pressure Fig.5 shows that as the environment air pressure decreases, the load of main bearing and the concord big end bearing significantly reduces during the deflagration stroke, and slightly changes during other strokes. Read in and analysis the load of the main bearing and concord big end bearing during the deflagration stroke, the results are showed in form 1: Form 1 Analysis of the Load of Main Bearing and Concord Big End Bearing during Deflagration Stroke under Different Environment Pressure and Different Rotate Speed Main Bearing Environment Pressure (kPa) 97 80 60 Bearing Load (kN) 16000 13500 110001000 r/m Decrease Percent (relative to 97kPa) 15.6 31.3 Bearing Load (kN) 14000 10000 4500 1800 r/m Decrease Percent 28.6 67.8 Bearing Load (kN) 9000 5000 3000 2200 r/m Decrease Percent 44.4 66.7 Concord Big End Bearing Environment Pressure (kPa) 97 80 60 Bearing Load (kN) 32500 27500 225001000 r/m Decrease Percent 15.4 30.8 Bearing Load (kN) 28000 20000 100001800 r/m Decrease Percent 28.6 64.3 Bearing Load (kN) 20000 11500 8000 2200 r/m Decrease Percent 42.5 60.0 It shows in form 1 that the load of the main bearing and concord big end bearing will decreases along with the reduce of environment air pressure at any speed. The lower the air pressure, the more significant the load decreases. As the rise of engine rotate speed, the decrease of the deflagration load of the main bearing and the concord big end bearing augment becomes more significant. In another word, the higher the engine rotate speed, the more sensitive the deflagration load of the main bearing and concord big end bearing is to the environment air pressure. The reason of this situation is that as the engine rotate speed rises, the decrease of the pressure in the cylinder increases, then the load of the bearing reduces significantly. Further more, as the rotate speed rises, the inertial force augment, but the load of the bearing reduces under the combinational influence. However, when the rotate speed rises to 1800r/m and the air pressure drops to 60kPa, the decrease of the deflagration load of the main bearing and concord big end bearing do not change along with the rise of the engine rotate speed. It means that when the rotate speed rise to a certain extent, and the environment air pressure is low enough, the influence of the environment air pressure to the load of the bearing in deflagration process is almost the same at different rotate speed. This is because when the environment air pressure decrease to a certain extent, and the rotate speed is upper, the influence of the air pressure to the combustion in the cylinder decreases, at the same time the pressure in the cylinder is pretty high, and the effect of the inertial force is minor, so the bearing load keeps unchanged to a large extent. Fig.5(c) (f) shows the change of the load of the main bearing and concord big end bearing in relation to the crank angle at the rotate speed of 2200r/m. It shows in the figure that the decrease or increase of the load of the two bearing is not congruously along with the diminishment of the environment air pressure in the whole working process of the engine, but differ in different strokes. This phenomenon can be explained as follows: In the whole working process of the engine, the air pressure in the cylinder (F Z in formula (1)-(4)) especially the combustion gas pressure in the deflagration process decreases along with the decrease of the environment air pressure, so the load of the main bearing and concord big end bearing decreases as a whole. The increase of bearing load when the crank angle is between 300～ 360 and -360～ -300 is because the piston is in the latter half of exhaust stroke and the first half of air intake stroke at that time, and the cylinder is exchanging air with the environment; here the inertial force along the negative direction of z axis F Z is smaller than that along the positive direction of z axis, it means that the resultant force is along the positive direction of z axis, as F Z diminish, the resultant force will augment on the contrary, so the bearing load will increase. 4． The influence of low Air Pressure to the Eccentricity of the Engine Bearing 4.1 The establish of Reynolds' equation and the solving of the eccentricity The Reynolds’ equation of the engine bearing can be expressed as [5] : () () () () () 2 33 ** 1 cos 1 cos 22 6sin sin cos D BR z dd dt dz ππ εφ εφ φφφ εδ ε ε φδ φδ φδ ωω ?????? ?? +++ ???? ???? =? ? + ? ? ? (7) In which D is the diameter of the bearing bush, BR is the width of the bearing bush, ε is the eccentricity, η (e) 1800r/m Concord Big End Bearing Load (f) 2200r/m Concord Big End Bearing Load 28 is the dynamic viscosity of the engine oil, δ is the minimum gap angular velocity, ω is the rotate speed of the journal. π is the oil film pressure, t is the time coordinate, φ and z are dimensional coordinate. Analyze the increase and decrease process of the bearing eccentricity respectively, the relation of the differential coefficient of eccentricity and the journal rotate speed can be expressed as below: () 2 Psin cos tan / , V B B So BR D BR D ψ ε ηβε ? ? ?? ?? ?? null null nullnullnull ＝ (8) () 2 * sin sin / , D PB So BR D BR D ψ ω η βε = ?? ?? ?? null null nullnullnull (9) In which B=δ S －γ S 0≤︱ B︱≤ 90° In the calculation Butenschoen method is used, and Sommerfeld number S OD and S OV can be find in reference [5], then Runge-Kutta method is used to solve the eccentricity through loop iteration. 4.2 Computing result and analysis of the bearing eccentricity Fig.6 Eccentricity of the Main Bearing and Concord Big End Bearing under Different Environment Air Pressure. Fig.6 (a) (d) show that when the engine rotate speed is under 1000r/m, both of the eccentricity shape of the two bearing shrink; fig.6 (b) (e) show that when the speed is 1800r/m, both of the eccentricity shape expand, and the deviation direction of the main bearing changed; and fig.6 (c) (f) show that when the rotate speed is 2200r/m, both of the eccentricity of the two bearing expand. We can conclude from the above figures that when the engine rotate speed is lower, the eccentricity shape of the main bearing and concord big end bearing shrink as the decrease of the environment air pressure, the lubrication condition of the bearing is improved and the bearing works more stable; when the rotate speed is higher, the eccentricity shape of the two bearing expand on the (a) 1000r/m Main Bearing Eccentricity (b) 1800r/m Main Bearing Eccentricity (c) 2200r/m Main Bearing Eccentricity (d) 1000r/m Concord Big End Bearing Eccentricity (e) 1800r/m Concord Big End Bearing Eccentricity (f) 2200r/m Concord Big End Bearing Eccentricity 29 contrary, the lubrication condition deteriorate and the bearing works unstable. At specific rotate speed, the deviation of the eccentricity may also change as the environment air pressure decreases. The load of the bearing is determined by the resultant force of the combustion gas pressure and the reciprocating inertial force of the shafting. When the rotate speed is lower, the reciprocator inertial force is lesser, and the main load of the engine bearing is caused by the combustion gas pressure in the cylinder (this is also the reason why the bearing eccentricity deflect to one side of the axis center). For this reason, the decrease of the environment air pressure causes the decrease of the pressure in the cylinder, thus the bearing eccentricity shrink. But when the engine rotate speed is higher, the reciprocating inertial force of the shafting increases and may at specific crank angle exceeds the combustion gas pressure in the cylinder if rotate speed is high enough. This makes the shape of the bearing eccentricity deflect to another side of the shaft center. At this time, when the decrease of environment air pressure causes the decrease of the pressure in the cylinder, the deflection of the bearing eccentricity also changes. As the engine rotate speed keeps on increasing, the reciprocating inertial force of the shafting exceeds the pressure in the cylinder in a bigger range of the crank angle. As a result, the bearing load is the result of the reciprocating inertial force minus the combustion gas pressure in the cylinder. When the decrease of the environment air pressure causes the decrease of the pressure in the cylinder, the load of the bearing increases and the eccentricity augments. 5. The influence of low Air Pressure to the Friction Power loss of Engine Bearing 5.1 The calculation of the friction power loss [5] If there is no direct contact between the bearing journal and bush, most of the friction power loss is caused by the shearing force of the engine oil viscosity. In this paper, only this part of friction power loss is considered. The friction coefficient ()μ α is: () () 4 sin 21 D So μα π ε β ψ ε =+ ?? (10) () () 2 * D D F So BR D αψ α η ω ? = ??? (11) Then the friction power loss is: () () () 2 4 * 0 42 Z FD BR D PSod π ηω μα α ωαα πψ ψ ??? =?? ? ∫ (12) 5.2 Calculation result and analysis of friction power loss of the bearing Fig.7 Friction Power Loss of the Main Bearing and Concord Big End Bearing under Different Environment Air Pressure It is figured out in Fig.7 that the power loss of the main bearing and concord big end bearing caused by the engine oil viscosity minish slightly along with the decrease of the environment air pressure. This is because the bearing load decrease as a whole when environment air pressure decreases, and the oil viscosity also reduces along with the increase of pressure [6] , thus the shearing force caused by the oil viscosity also decrease slightly, so the friction power loss reduces. Furthermore, it is shown in the fig that the influence of environment pressure to the friction power loss is relatively more significant during the deflagration stroke. This is also because the decrease of the bearing load is more severe at that time. 6. Experimental Verification Measure the locus of journal center of the flywheel with vertex displacement sensor on the “Western environment engine test rig” and calculate its eccentric, and then use it instead of the eccentricity of the main bearing to verify the computational model. (a) 2200r/m Main Bearing Friction Power Loss (a) 2200r/m,97kPa Calculated Eccentricity of the Main Bearing (b) 2200r/m,97kPa Eccentricity at the Fly Wheel Measured Through Experiment (b) 2200r/m Concord Big End Bearing Friction Power Loss 30 Fig 8 Eccentricity of Main Bearing Because of the restriction of experimental condition, the eccentricity of the main bearing can not be measured directly, so the eccentricity measured in the experiment is that of the flywheel. Because the crank shaft is flexible and will bend and distort under the stress of the concord and the engine cabinet, the eccentricity of the main bearing and the flywheel, which are at different section of the crank shaft, is apparently different. But there should be some common characteristics between them; the movement condition should be the same, and the locus of journal center should be similar. This is mainly because the main bearing and the flywheel are both on the crank shaft and the distance between them is not long, so the bend and distortion of the crank shaft is limited, thus the eccentricity shape is similar to some extent. Furthermore, because they are both on the crank shaft, and both have the same load, the change trend of the eccentricity should be the same. In this paper, the eccentricity at the flywheel measured through experiment and the calculated eccentricity of the main bearing are compared to verify the computational model. Fig.9 The movement condition of the eccentricity As shown in fig.8, it can be seen from the shape of the two graphics and the order of the marked point that both of them are moving according to the direction in fig.9 from A to B, C …H in turn. Compared to fig.8 (a), point A, G and H in fig.8 (b) deflect a little to the right, and point F deflects slightly up. This is mainly caused by the distortion of the crank shaft. Through the analysis and comparison of the two figure above, we can see that the movement rule of the two eccentricity are consistent, and the shape of them are similar to some extent. So we can come to the conclusion that the computational result is verified correct and credible through experiment. 7. Conclusion In this paper, single cylinder engine model considered the influence of low air pressure to the main bearing and concord big end bearing is constructed and verified through experiment. Generally, the higher the rotate speed of the engine