曲柄滑塊機(jī)構(gòu)基于連桿-滑塊間隙流體潤滑的動態(tài)分析雷戈瑞.丹尼爾,凱迪.凱文機(jī)械設(shè)計部,坎皮納斯大學(xué),機(jī)械工程學(xué)院,郵件信箱 6122,13083-970 坎皮納斯,SP ,巴西摘要傳統(tǒng)的曲柄滑塊連桿機(jī)構(gòu)廣泛的應(yīng)用于機(jī)械系統(tǒng)中。軸承在機(jī)械中的使用特別作用在于減小摩擦,主要用于特殊條件的潤滑,如曲柄滑塊的鉸鏈連接。這類軸承屬于一類交替旋轉(zhuǎn)運(yùn)動的軸承??紤]到曲柄滑塊系統(tǒng)的動力學(xué)與軸承潤滑現(xiàn)象是相互作用的,本文為這種特殊問題提供了一種數(shù)學(xué)模型。兩種數(shù)學(xué)模型被使用與動態(tài)系統(tǒng)的分析。第一種模型(Eksergian 的運(yùn)動方程),假設(shè),連桿一端與軸承表面接觸時代表系統(tǒng),在這種情況下,連桿的行為與剛性軸承相同(無間隙)。第二種模型(拉格朗日方法),當(dāng)連桿一端在以在滑塊的間隙中為潤滑方式時,則代表系統(tǒng),在這種情況下,在關(guān)系到連桿滑塊移動,則呈現(xiàn)出多自由度問題。流體動力潤滑的數(shù)學(xué)模型介紹了獲得系統(tǒng)動態(tài)行為中更為現(xiàn)實的結(jié)果。1.介紹在眾多功能中潤滑系統(tǒng)是評價機(jī)械最佳性能的一個至關(guān)重要的因素,例如,潤滑和保護(hù)部件,減少摩擦,清洗和冷卻的內(nèi)部機(jī)制。本系統(tǒng)的操作需要適當(dāng)?shù)男?zhǔn)。因此,過多或者潤滑不足會影響機(jī)器的動態(tài)行為,會嚴(yán)重?fù)p害所設(shè)計的機(jī)構(gòu)。許多機(jī)器的機(jī)構(gòu),包含了大量的流體動壓軸承,而軸承連桿-滑塊聯(lián)合尤為重要,因為這是一個新的流體動力軸承,被稱為流體動力軸承交替運(yùn)動。不同于傳統(tǒng)的動壓軸承,這種軸承不是一個完整的旋轉(zhuǎn)。因此,隨著近來來日益增長的需要,研究這一特定類型的流體動力軸承和機(jī)器的動態(tài)行為的影響。目前為止,大多數(shù)關(guān)于滑塊連接的鉸鏈的流體動力軸承正在被研究所所研究著。事實上,該研究所已開發(fā)和建造的設(shè)備來研究摩擦潤滑滑塊銷軸承超過 15 年。比如,Takiguchi [ 1 ]等人研究一種浮式活塞在汽油動力汽車引擎上采用旋轉(zhuǎn)運(yùn)動。三年后,他 [ 2 ]開發(fā)一個測量的設(shè)備,確定在連桿 –滑塊聯(lián)合的基礎(chǔ)上測得的摩擦力的流體動力軸承的潤滑狀態(tài)。在另一項研究中,在武藏技術(shù)研究所進(jìn)行,有 Suhara 等人 [ 3 ]檢查潤滑條件下軸承的滑銷的汽油發(fā)動的汽車發(fā)動機(jī),作為考慮的參數(shù)分析的長度,內(nèi)徑和活塞銷的材料。最近,張等人 [ 4 ]開發(fā)的工具,探討在活塞銷軸承磨損。2005,利吉爾、拉戈分析了活塞銷軸承的行為。一年后,這些作者 [ 7 ]表達(dá)餓了連桿 –活塞接頭在四沖程發(fā)動機(jī)軸承運(yùn)行的總的看法,強(qiáng)調(diào)在軸承供油。如前所述,流體動壓軸承的往復(fù)運(yùn)動的滑塊曲柄機(jī)構(gòu)一部分。因此,這一機(jī)制可靠的的數(shù)學(xué)模型必須考慮連桿 –滑塊聯(lián)合軸承的行為。由于曲柄滑塊機(jī)構(gòu)的廣泛應(yīng)用,許多研究都集中在設(shè)計的數(shù)學(xué)模型,分析了機(jī)械系統(tǒng)的動力學(xué)行為。施瓦布,梅嘉德,梅耶爾 [ 8 ]比較了滑塊曲柄連桿機(jī)構(gòu)的動力學(xué)行為,考慮到不同的連桿 –滑塊聯(lián)合模型如耗散赫茲接觸模型,影響模型和動壓軸承模型在上述工作,在考慮連桿彈性與剛性構(gòu)件的同時,作者還比較了動態(tài)行為的機(jī)制。那些作者所獲得的結(jié)果表明,連桿的假設(shè)為彈性元件,以及在關(guān)節(jié)的潤滑條件,往往顯著降低振動機(jī)構(gòu)的動態(tài)響應(yīng)。弗洛雷斯等人 [ 9 ]分析了曲柄滑塊連桿機(jī)構(gòu)的動態(tài)行為建模,連桿 –滑塊聯(lián)合作為一個干接點無摩擦,干摩擦接觸和混合模型考慮了小偏心率和高偏心率的摩擦接觸的流體動力潤滑。他們的研究結(jié)果表明,由于在動態(tài)響應(yīng)的振蕩幅度,干接觸摩擦模型比干接觸模型無摩擦更現(xiàn)實的。對于混合模型,他們獲得的結(jié)果顯示最小的振蕩的動態(tài)響應(yīng),但在文獻(xiàn)中沒有結(jié)果能支持這一觀察。此后不久,弗洛雷斯等人 [ 10 ]分析了滑塊曲柄機(jī)構(gòu)考慮 –干接觸影響的動力學(xué),在連桿 –滑塊摩擦和流體動力潤滑鉸鏈。得到的結(jié)果與干接觸模型無摩擦表現(xiàn)出較高的振蕩機(jī)構(gòu)的動態(tài)響應(yīng),使該模型比摩擦干接觸模型不現(xiàn)實。當(dāng)軸承模型被認(rèn)為是,結(jié)果是那些與理想的滑塊曲柄機(jī)構(gòu)鉸鏈獲得非相似。erkaya,su ,uzmay [ 11 ]進(jìn)行了運(yùn)動學(xué)和動力學(xué)的一個改進(jìn)的滑塊曲柄機(jī)構(gòu)和一個額外的 –偏心連桿之間的連桿和曲柄銷。他們將滑塊曲柄機(jī)構(gòu)開發(fā)得到的結(jié)果進(jìn)行了評價,同時與常規(guī)滑塊曲柄機(jī)構(gòu)比較。這種比較表明,雖然傳統(tǒng)的和改進(jìn)的滑塊曲柄機(jī)構(gòu)的行程和缸內(nèi)氣體壓力的改性機(jī)理相同,具有比常規(guī)的機(jī)制更高的扭矩輸出。khemili 和 Romdhane[ 12 ]分析了平面柔性滑塊曲柄含間隙機(jī)構(gòu)的動力學(xué)行為,進(jìn)行仿真和實驗測試,比較利用亞當(dāng)斯軟件模擬的數(shù)值實驗結(jié)果。他們發(fā)現(xiàn),間隙的存在影響了系統(tǒng)的動態(tài)響應(yīng),和耦合器的靈活性作為機(jī)制的懸掛系統(tǒng)。 estupi? 和 santos[ 13 ]建立一個線性往復(fù)壓縮機(jī)的數(shù)學(xué)型。他們檢查了機(jī)械系統(tǒng)的動態(tài)行為,考慮到基于多體動力學(xué)的機(jī)械部件的動力學(xué)(剛性部件)和有限元法(彈性元件)。他們還評估了流體動力軸承的影響,描述在鉸鏈處用雷諾茲方程的流體動力。他們的研究結(jié)果顯示,得到當(dāng)活塞接近上死點,由于傾斜振蕩的曲柄的軌道的非線性行為的增加是最大力和最小油膜厚度,這是由曲柄銷的長度的影響。這項工作涉及的滑塊曲柄機(jī)構(gòu)和軸承的流體動力潤滑條件在滑塊連桿鉸鏈處的動態(tài)行為分析。為此,分析是基于兩個不同的模型,其應(yīng)用程序依賴于潤滑條件(偏心值)的軸承。第一個模型(1DOF)認(rèn)為,連桿 –滑塊聯(lián)合作為一種理想的聯(lián)合應(yīng)用時,連桿的一端與軸承表面接觸 [ 14 ]。第二個模型(3DOF)時,連桿一端的滑塊潤滑孔的間隙。在這種情況下,在關(guān)系到連桿滑塊,表征問題的多個自由度,通過流體的流體動力潤滑連桿和滑塊之間發(fā)生的相互作用。因此,解決的辦法是從一個由滑塊曲柄機(jī)構(gòu) –理想鉸鏈與連接桿 –滑塊聯(lián)合軸承滑塊曲柄機(jī)構(gòu)的模型的混合模型得到的。因此,在這種分析的一個重要參數(shù)是考慮最小油膜厚度在流體動力潤滑。根據(jù)弗洛雷斯 [ 9 ],高偏心率(低最小油膜厚度),壓力使表面的彈性變形,這可以是相同的順序作為潤滑油膜厚度。這些情況與那些在流體動力潤滑獲得一個更現(xiàn)實的分析,可以基于彈流潤滑理論。因為這個原因,這項工作被認(rèn)為是最小油膜厚度超過 10%的徑向間隙的流體動力潤滑狀態(tài),這代表 0.9 的偏心率。從混合模型得出的曲柄滑塊機(jī)構(gòu)的動態(tài)響應(yīng)與從常規(guī)的模型相比(理想滑塊曲柄機(jī)構(gòu)鉸鏈)。此外,在軸承的壓力分布一個周期期間獲得的潤滑條件。它強(qiáng)調(diào)的是,通過與 Bannwart [ 12 ]合作以前開發(fā)相比,作者在目前的工作中使用的流體動力學(xué)模型更為重要。2.方法在這項工作中,一個平面曲柄滑塊機(jī)構(gòu)模型,被用來確定其動態(tài)行為。然而,滑液壓動壓軸承被認(rèn)為是在連桿滑塊的一個鉸鏈,代替?zhèn)鹘y(tǒng)的曲柄滑塊機(jī)構(gòu) –。這種假設(shè)認(rèn)為這樣當(dāng)軸承不考慮間隙時,銷不局限于只有一個方向的運(yùn)動。本節(jié)描述的混合模型(自由度)的平面曲柄滑塊機(jī)構(gòu),考慮連桿 –滑塊聯(lián)合滑動軸承,這是用來分析在潤滑條件下的動態(tài)行為。該數(shù)學(xué)模型用于分析接觸狀況的動態(tài)行為是傳統(tǒng)的滑塊曲柄機(jī)構(gòu)(1 自由度),是 Doughty [ 14 ]提出的。2.1 平面曲柄滑塊機(jī)構(gòu)的運(yùn)動學(xué)分析平面曲柄滑塊機(jī)構(gòu)的運(yùn)動學(xué)研發(fā)考慮了圖 1 中的方案。圖 1a 顯示了平面滑塊曲柄機(jī)構(gòu)和圖 1b 描繪了自由體圖的連桿銷和滑塊孔。R 是曲柄的長度,L 是連接桿的長度,Q 是曲軸的角位移,一個是連桿的角位移,XP 和 YP 是連桿銷線性位移,XPT 和 YPT 是滑塊的直線位移, FXP 和 FYP 是分別在 x 和 y 方向上的流體動力。圖 1c 顯示的是連接的平面滑塊曲柄機(jī)構(gòu)桿液壓動壓軸承軸承。OH 是中心的軸承,OP 是連桿銷中心,RH 是軸承的半徑,RP 是連桿銷半徑,E 是偏心的,hmix 是最小油膜厚度,hmax 是最大油膜厚度。此外,偏心率(ε)之間的偏心率(E)和徑向間隙(CR),在徑向游隙的軸承半徑和連桿銷半徑之間的差異根據(jù)這個數(shù)字,滑塊的銷的位置可以被表示為公式 1 所示: Xp = R:cos(q)+ L:cos(A) (1)Yp = R:sin(q)?L:sin (A) :公式 1 對連桿銷,速度和加速度的派生公式,得到: 圖 1.平面滑塊曲柄機(jī)構(gòu),(a)普通視圖,(b)擴(kuò)展視圖,(C)的流體動力軸承在[ KP ]是的滑塊銷速度系數(shù)矩陣,和[LqP]和[LAP]是滑塊的銷的速度系數(shù)的偏導(dǎo)數(shù)矩陣,定義為:2.2. 對曲柄連桿系統(tǒng) –質(zhì)心運(yùn)動學(xué)分析這種分析的目的是確定的組件的質(zhì)量中心的動態(tài)行為,使它找到一個滑塊曲柄機(jī)構(gòu) [ 14 ]的運(yùn)動方程。圖 2a 和 b 顯示的分別是曲柄連桿與曲柄質(zhì)心桿子系統(tǒng)和連桿。Upm 和 VPM 是曲軸的質(zhì)量中心的坐標(biāo)參考系統(tǒng)(PM)在位于曲柄(UM,VM),UPb 和 VPb 是質(zhì)心坐標(biāo)(PB)的參考系統(tǒng)位于連桿(UB,VB),XPM 和 YPM 的曲軸的質(zhì)量中心直線位移(PM)在慣性參考系統(tǒng)(X,Y)和 XPB 和有排搏是連桿的質(zhì)心線位移(PB)在慣性參考系統(tǒng)(X,Y)。根據(jù)圖 2a,曲柄的質(zhì)量中心位置可以被描述為:速度可寫式的派生形式(4)為:考慮在圖 2b 的方案,得到同樣的連桿質(zhì)心位移和速度。圖 2.曲柄連桿系統(tǒng)(a)對曲軸質(zhì)量中心子系統(tǒng),(b)在質(zhì)量上的連桿中心子系統(tǒng)為了確定曲柄連桿系統(tǒng)的動態(tài)行為,線性和角的這個子系統(tǒng)的所有組件的速度必須分開 [ 14 ]。這些速度是需要確定的動能(旋轉(zhuǎn)和平移)的子系統(tǒng),因此,采用拉格朗日方法得到的運(yùn)動方程。因此,根據(jù)公式 7 和公式 9,它可能是寫:在[KC]代表曲柄連桿系統(tǒng)的廣義速度系數(shù)矩陣。導(dǎo)出[KC]相對獨立的變量 Q 和,有:在[LQ]和[LA]是廣義速度系數(shù)的偏導(dǎo)數(shù)矩陣。最后,分別考慮到 MM,MB,IM E IB 曲柄連桿質(zhì)量,質(zhì)量,轉(zhuǎn)動慣量和曲柄連桿轉(zhuǎn)動慣量,質(zhì)量矩陣可以得到:2.3.在曲柄連桿系統(tǒng)的廣義力通過虛功的概念,得到了廣義的激振力,在這里提出的混合模型的情況下,由于流體動力潤滑在連桿銷 –滑塊間隙應(yīng)用于耗散粘滯力。根據(jù)強(qiáng) [ 14 ],廣義力可確定使用廣義速度系數(shù)矩陣的連接點,在外力施加的條件下。因此,廣義力是由公式 14 給出了:由于液壓動力施加在滑動鉸鏈(FXP 和 FYP)中,導(dǎo)致廣義力發(fā)生。在這項工作中,液壓動力是由滑動軸承的潤滑模型確定的振蕩運(yùn)動,通過邦瓦特 [ 13 ]的提議。2.4.的曲柄連桿系統(tǒng)的動能和勢能曲柄連桿系統(tǒng)動能的質(zhì)量矩陣和廣義速度系數(shù)矩陣的確定,根據(jù)式 15:圖 3 顯示考慮到這些組件的質(zhì)量中心,子系統(tǒng)由曲柄、連桿組成。根據(jù)圖 3A,潛在的能量可以寫成:3.結(jié)果本研究的目的是確定模型的適用性。計算機(jī)模擬在 FORTRAN?執(zhí)行,允許在流體動力軸承的潤滑狀態(tài)分析。圖 4 中的圖表明求解過程在動態(tài)分析中的應(yīng)用。首先,在軸承的流體動力分析的初始條件。連桿銷和滑塊加速度的確定和液壓動力計算。因此,對初始條件求解運(yùn)動方程,并與加速度的水動力進(jìn)行了評價。因此,連桿的銷和滑塊的位移和速度計算到下一個時間步長(T +ΔT)。在確定了新的速度和位移,銷軸承偏心必須驗證。如果偏心率小于 0.9 時,該銷是在潤滑條件下。在這種情況下,新的液壓力計算,先后對銷和滑塊的加速度的重新確定。在流體動力潤滑條件下,考慮在第 2.7 節(jié)潤滑模型,對系統(tǒng)的動態(tài)行為進(jìn)行評估,。然而,當(dāng)滑塊銷超過閾值(偏心 ε= 0.9),它被認(rèn)為是與軸承的表面接觸。在這種情況下,它是假定系統(tǒng)的動態(tài)行為是由傳統(tǒng)的滑塊曲柄機(jī)構(gòu)的,在連桿 –滑塊聯(lián)合沒有間隙。因此,滑塊的曲柄連桿機(jī)構(gòu) –常規(guī)模型應(yīng)用到一個反向運(yùn)動發(fā)生在滑塊。在滑塊的反向運(yùn)動后,滑塊銷葉片軸承表面,改變潤滑條件。至于運(yùn)動微分方程的分辨率,傳統(tǒng)的模型并不復(fù)雜,因此可以解決比較快(在 2 GHz 處理器,3 GB RAM 的計算機(jī)系統(tǒng) 10 分鐘)。然而,由于高數(shù)值剛度的潤滑條件下的運(yùn)動方程是高度復(fù)雜的。因此,一個特定的數(shù)值積分方法必須根據(jù)這些方程的特征選擇。在這項工作中,對 3 自由度的解決方案?;旌夏P褪峭ㄟ^使用一個僵硬的初始值問題的積分多步法的發(fā)現(xiàn),rowmap 方法 [ 8 ]。然而,盡管這種方法的效率,對微分方程的解還需要計算成本高(約 48 小時,在 2 GHz 處理器,3 GB RAM 的計算機(jī)系統(tǒng))。列于表 1 和表 2 參數(shù)分別表示軸承的幾何形狀和 –滑塊曲柄機(jī)構(gòu)。從傳統(tǒng)的內(nèi)燃發(fā)動機(jī),得到了這些參數(shù)。表 3 給出的初始條件,在計算機(jī)模擬中考慮并與文獻(xiàn)一致,在操作過程中發(fā)現(xiàn)了一些實驗值。仿真我們開始考慮在表 1 和表 2 給出的物理參數(shù),初始條件列于表 3 和 20μM 軸承徑向間隙?;瑝K的曲柄連桿機(jī)構(gòu)的動力學(xué)與連桿軸承滑塊鉸鏈的分析在這項工作中的計算機(jī)模擬,考慮流體動力潤滑的閾值條件。因此,流體動力潤滑條件下高達(dá) 0.9 的偏心率是極低的膜的厚度,這是流體動力潤滑不充分的條件。因此,最大限度的模擬偏心率的值是 0.9,這表明銷在假設(shè)是接觸支承面上不是液壓動力條件。圖 5a 和 b 分別顯示在第一和第二圈獲得的軌道。如圖 5a 表示,銷的初始偏心率是 0.6。當(dāng)運(yùn)動開始,銷向左移動直到超過偏心極限,之后它可能仍然在與軸承表面接觸到滑塊的運(yùn)動倒置。在這種情況下,即,當(dāng)銷與軸承的接觸面,動力學(xué)是基于傳統(tǒng)的滑塊曲柄機(jī)構(gòu)的 [ 14 ]的數(shù)學(xué)模型分析。當(dāng)運(yùn)動倒置,銷從軸承表面的軸承上的區(qū)域。表一流體動力軸承的參數(shù)。參數(shù)和單位 符號 數(shù)值動水軸承半徑[m]軸的半徑(連桿銷)[m]水動力軸承寬度[m]徑向間隙[μm]絕對粘度[Pa.s]質(zhì)量密度[kg/m3] 表二曲柄滑塊機(jī)構(gòu)的參數(shù)參數(shù)和單位 符號 數(shù)值曲柄的長度[m]連桿長度[m]曲柄慣性[kg.m]連桿慣性[kg.m]曲柄質(zhì)量[kg]連桿質(zhì)量[kg]滑塊質(zhì)量[kg]曲軸質(zhì)量中心在軸的位置[m]曲軸中心在軸虛擬機(jī)中的位置[m]該連接在軸 UB 桿質(zhì)心位置[m]該連接在軸的 VB 桿質(zhì)心位置[m]表三采用計算機(jī)模擬的初始條件。初始條件和裝置 符號 模擬 1 模擬 2 模擬 3曲柄的角位置[rad]曲柄角速度[rad/s]連桿的角位置[rad]連桿角速度[rad/s]滑塊的直線位置[m]滑塊的線性速度[m] 接近表面的軸承,銷和滑塊推向相反的方向上的流體動力,使它們相對于彼此移動。這使得銷回到軸承的下部區(qū)域,再次超過偏心極限。銷并保持與表面接觸到底圈。在第二圈,活塞銷的動態(tài)行為類似于第一圈。圖 6 說明了曲軸的動態(tài)行為??梢钥闯?,曲柄的速度和加速度的兩個系統(tǒng),即是相似的,滑動軸承滑塊曲柄機(jī)構(gòu)(3 自由度)和常規(guī)滑塊曲柄機(jī)構(gòu)(1 自由度)。然而,請注意,速度和加速度都傾向于作為一個在 3 自由度模型的時間函數(shù)的兩個應(yīng)用模型之間的過渡的增加。圖 5.軌道滑塊的聯(lián)合模擬, (a)第一圈,(b)第二圈圖 6 曲柄分析模擬 (a)角速度,角加速度(b)圖 7.連桿分析模擬 (a)角位移、角速度(b)當(dāng)銷超過偏心極限,最后重點分析了在水動力條件的 1 自由度的初始條件。傳統(tǒng)的機(jī)制(接觸)。因此,在這一點上的運(yùn)動,是由上述自由度模型給定初始條件的動態(tài)行為描述。因此,在混合模型與傳統(tǒng)的過渡,輸入的速度不同,給出了兩種模型在 t = 0 的初始條件。因此,主要作用是在模型的每個過渡曲柄的角速度的增大,這是相對于 1 自由度位移的傳統(tǒng)的模型??梢钥吹皆趫D 6 b,曲軸的角加速度小斷層與傳統(tǒng)的模型。雖然曲柄不能直接連接到水動力軸承,這些不再生產(chǎn)的動態(tài)響應(yīng)是由銷在潤滑條件。相同的行為由施瓦布報道,Meijaard 和 Meijers[8]。根據(jù) Schwab[8],與液壓動力軸承的動態(tài)行為曲柄滑塊機(jī)構(gòu)在曲柄滑塊聯(lián)合常規(guī)機(jī)制類似,所代表的動態(tài)響應(yīng)的平滑曲線。然而,反應(yīng)略有不同,只有當(dāng)銷進(jìn)入軸承。這穿越涉及高速度和期刊中心,因此, 它增加了高峰。圖 7 描述了連桿的位移和速度。注意連桿的位移、速度和軸承滑塊曲柄機(jī)構(gòu)(3 自由度)和常規(guī) –滑塊曲柄機(jī)構(gòu)( 1 自由度)是相似的。圖 8 所示,滑塊的動態(tài)行為的兩個系統(tǒng)是相似的(1DOF 和 3 自由度)。圖 9 顯示了連桿的角加速度和滑塊的直線加速。注意連桿和滑塊的加速度與軸承滑塊曲柄機(jī)構(gòu)達(dá)到(3 自由度)類似于傳統(tǒng)的滑塊曲柄機(jī)構(gòu)實現(xiàn)加速度(1自由度)。然而,在與軸承表明振蕩由于在流體動力潤滑條件的鉸鏈行為的滑塊曲柄機(jī)構(gòu)達(dá)到加速度。圖 8.滑塊分析模擬 (a)線性位移、(b)線性速度圖 9.在模擬加速度分析 ,(a)連桿加速度, (b)滑塊加速度如圖 9 顯示,在潤滑時更重要的是在滑塊的加速度和連桿軸承的原因引起不連續(xù),因為這些組件的交互。當(dāng)銷是不是在潤滑條件下,它被認(rèn)為是接觸支承面。的數(shù)學(xué)模型,用來分析在接觸條件的動態(tài)行為是傳統(tǒng)的滑塊曲柄機(jī)構(gòu)模型。因此,機(jī)構(gòu)的動態(tài)行為是傳統(tǒng)。4.結(jié)論這項工作涉及的滑塊曲柄機(jī)構(gòu)和在潤滑條件下滑塊鉸鏈的動態(tài)行為分析。為此,考慮連桿滑塊鉸鏈的流體動力軸承,建立一個曲柄滑塊連桿機(jī)構(gòu)的數(shù)學(xué)模型,。在這項工作中,數(shù)學(xué)模型的計算機(jī)模擬了連 –滑塊鉸鏈銷的動態(tài)行為。結(jié)果表明,在操作過程中進(jìn)行的銷兩個條件。在某些時刻銷進(jìn)行流體動力潤滑條件和別人是在與軸承的表面接觸。數(shù)值結(jié)果表明,不論初始條件軸承參數(shù)多少,銷斷裂的油膜,進(jìn)入與軸承的表面接觸,如前所述的規(guī)定,達(dá)到一個高的偏心銷,使油膜壓力甚至分裂它。這種行為表明,彈流潤滑模型的混合模型接觸條件的使用(3 DOF。)可能更適合本文的分析,在這種情況下,直接接觸可以防止甚至當(dāng)銷不動壓潤滑。然而,評估的動態(tài)響應(yīng)和壓力分布潤滑時,所提出的混合模型可以應(yīng)用。的彈流模型的實現(xiàn)需要從流體的混合模型彈流狀態(tài)過渡的進(jìn)一步研究。對于軸承的徑向間隙,可以得出結(jié)論,在徑向間隙的增加會導(dǎo)致油膜厚度隨之增加,降低水動力和促進(jìn)與軸承表面引腳的接觸。相反,在初始角速度的增加導(dǎo)致的流體動力作用于銷增加,因為這些力量的初始角速度成正比。這些較強(qiáng)的液壓動力增加銷的軸承表面的距離,防止觸碰這面。連桿滑塊鉸鏈?zhǔn)窍鄬?fù)雜的流體動力軸承由于使用的兩種流體動力潤滑和滑塊曲柄機(jī)構(gòu) –模型的非線性方程組 –滑塊曲柄機(jī)構(gòu)問題的解決方案。這組方程提出了高數(shù)值的剛度,使數(shù)值積分方法在微分方程的成功解決問題的一個重要因素的選擇。致謝作者希望感謝 FAPESP,CAPES 和 CNPQ 提供的資金支持這項工作的。參考文獻(xiàn)[ 1 ] M. Takiguchi, M. Oguri, T. Someya,,旋轉(zhuǎn)在汽油發(fā)動機(jī)活塞銷的運(yùn)動研究,SAE 論文 938142,底特律,美國,1993.[ 2 ]M. Takiguchi, K. Nagasawa, T. Suhara, M. Hiruma,摩擦小端連接一個汽車發(fā)動機(jī)連桿軸承潤滑特性,秋天技術(shù)會議 ASME 2 卷(1996)1 –6。T. Suhara, S. Ato, M. Takiguchi, S. Furuhama,,本文對古浜莊,活塞銷座軸承的汽車發(fā)動機(jī)的摩擦與潤滑特性,SAE 論文 970840,底特律,美國,1997。[ 4 ]C. Zhang, H.S. Cehng, L. Qiu, K.W. Knipstein, J. Bolyard,,活塞銷/行為劃傷孔軸承的混合潤滑,部分。1,實驗研究,賽寶反。46 卷(2004)193–199。。[ 5 ]C. Zhang, H.S. Cehng, J.O. Wang,活塞銷/行為劃傷孔軸承的混合潤滑,部分。2,實驗研究,賽寶。反。47 卷(2004)149 –156。丹尼爾的學(xué)生,,機(jī)械原理 46(2011)1434 –14521451[ 6 ] J.L. Ligier, P. Ragot,活塞 –銷:磨損和旋轉(zhuǎn)運(yùn)動,SAE 紙 2005-01-1651,美國,底特律,2005。[ 7 ] J.L. Ligier, P. Ragot,小端連桿潤滑, SAE 紙 2006-01-1101,美國,底特律,2006。[ 8 ] A.L. Schwab, J.P. Meijaard, P. Meijers,在剛性和彈性力學(xué)系統(tǒng)的動態(tài)分析的旋轉(zhuǎn)關(guān)節(jié)間隙模型的比較,機(jī)械原理(9)37(2002)895 –913。[ 9 ] P. Flores, J. Ambrosio, J.P. Claro,潤滑關(guān)節(jié)的平面多體機(jī)械系統(tǒng)的動態(tài)分析,多體系統(tǒng)動力學(xué) 12 卷(2004)47 –74。[ 10 ] P. Flores, J. 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The use of hydrodynamic bearings in the mechanism joints is of particular interest in reducing friction, mainly in special conditions of lubrication such as the connecting rod–slider joint. This bearing belongs to a class of bearings with alternating rotational motion. This paper proposes a mathematical model for this particular problem, considering the dynamics of the slider-connecting rod–crank system interacting with the lubrication phenomenon in bearings with alternating motion. Two models were used to analyze the dynamics of the system. The first model (by Eksergian Equation of Motion) represents the system when the connecting rod end is in contact with the bearing surface, assuming, in this condition, the same behavior as that of rigid bearings (without clearance). The second model (by Lagrange Method) represents the system when the connecting rod end is in the hydrodynamic lubrication mode in the slider bore clearance. In this condition, the slider moves in relation to the connecting rod, presenting a problem of multi-degrees-of-freedom. The mathematic model of hydrodynamic lubricationwas introduced to obtain more realistic results of the system's dynamic behavior.1. IntroductionThe lubrication system is a crucial element in the optimal performance of machines in general in view of its numerous functions, e.g., lubricating and protecting components, reducing friction, and cleaning and cooling internal mechanisms. The operation of this system requires proper calibration. Therefore, excessive or insufficient lubrication influences the dynamic behavior of the machine and can seriously damage the mechanisms involved. The mechanisms of many machines contain numerous hydrodynamic bearings, but the hydrodynamic bearing of the connecting rod–slider joint is particularly important because it is part of a new class of hydrodynamic bearing called a Hydrodynamic Bearing with Alternating Motion. Unlike traditional hydrodynamic bearings, this type of hydrodynamic bearing does not make a complete rotation. Therefore, recent years have seen a growing need to study the behavior of this specific type of hydrodynamic bearing and its influence on the dynamic behavior of the machine. Most of the research into the hydrodynamic bearing of the connecting rod–slider joint has so far been conducted by the Musashi Institute of Technology. In fact, this institute has developed and constructed devices to investigate lubrication and friction in the hydrodynamic bearing of slider pins for more than 15 years. Takiguchi et al. [1], for example, studied the rotating motion of a floating piston pin applied in gasoline-powered automotive engines. Three years later, Takiguchi et al. [2]developed a measuring device that determines the status of lubrication in the hydrodynamic bearing of the connecting rod–slider joint based on measured friction force. In another study conducted at the Musashi Institute of Technology, Suhara et al. [3]examined lubrication conditions in the hydrodynamic bearing of the slider pin of gasoline-powered automotive engines, considering as parameters of analysis the length, internal diameter and material of the piston pin. More recently, Zhang et al. [4,5]developed tools to investigate wear in hydrodynamic bearings of the piston pin. In 2005, Ligier and Ragot [6]analyzed the behavior of the hydrodynamic bearing of the piston pin. The following year, these authors [7] presented a general view of the operation of the hydrodynamic bearing of the connecting rod–piston joint in four-stroke engines, emphasizing the oil feed in the bearing.As mentioned earlier, hydrodynamic bearings with alternating motion are part of slider–crank mechanisms. Hence, a reliable mathematical model of this mechanism must take into account the behavior of the bearing in the connecting rod–slider joint. Owing to the wide application of the slider–crank mechanism, many studies have focused on devising a mathematical model and analyzing the dynamic behavior of this mechanical system. Schwab, Meijaard and Meijers [8]compared the dynamic behavior of the slider–crank mechanism, considering different connecting rod–slider joint models such as a Hertz contact model with dissipation, an impact modeland a hydrodynamic bearing model. In the aforementioned work, the authors also compared the dynamic behavior of the mechanism considering the connecting rod as an elastic and rigid component. The results obtained by those authors show that the assumption of a connecting rod as an elastic component, as well as the lubrication condition in the joint, tends to significantly decrease the vibrations in the dynamic response of the mechanism. Flores et al. [9] analyzed the dynamic behavior of the slider–crank mechanism, modeling the connecting rod–slider joint as a dry contact without friction, a dry contact with friction and as a hybrid model which considershydrodynamic lubrication for small eccentricity and dry contact with friction for high eccentricity. Their results show that the dry contact model with friction is more realistic than the dry contact model without friction, due to the magnitude of the oscillations in the dynamic response. As for the hybrid model, the results they obtained showed the smallest oscillation in the dynamic response, but there are no results in the literature that can support this observation. Soon thereafter, Flores et al. [10]analyzed the dynamics of the slider–crank mechanism considering the effects of dry contact, friction and hydrodynamic lubrication on the connecting rod–sliderjoint. The results obtained with the dry contact model without friction showed high oscillations in the dynamic response of the mechanism, making this model less realistic than the dry contact model with friction. When the model with hydrodynamic bearing was considered, the results were very similar to those obtained in the slider–crank mechanism with ideal joints. Erkaya, Su and Uzmay [11]analyzed the kinematics and dynamics of a modified slider–crank mechanism with an additional eccentric link between the connecting rod and crank pin. The results they obtained with the slider–crank mechanism they developed were evaluated and compared to that of a conventional slider–crank mechanism. This comparison indicated that although the conventional and modified slider–crank mechanisms have the same stroke and the same gas pressure in the cylinder, the modified mechanism has a higher torque output than the conventional mechanism. Khemili and Romdhane [12]analyzed the dynamic behavior of a planar flexible slider–crank mechanism with clearance, performing simulated and experimental tests and comparing the experimental results withthe numerical results of the simulations using ADAMS software. They found that the presence of clearance affects the dynamic response of the system, and that the coupler's flexibility acts as a suspension system in the mechanism. Estupi?an and Santos [13] developed a mathematical model for a linear reciprocating compressor. They checked the dynamic behavior of the mechanical system, considering the dynamics of the mechanical components based on multibody dynamics (rigid components) and the finite element method (flexible components). They also evaluated the influence of the hydrodynamic bearing, describing the hydrodynamic forces in the joints using the Reynolds equation. Their results showed that maximum forces and minimum film thickness are obtained when the piston is close to the top dead center and that the nonlinear behavior of the orbits increases due to the tilting oscillations of the crank, which are influenced by the length of the crank pin.This work involves an analysis of the dynamic behavior of the slider–crank mechanism and the hydrodynamic lubrication condition of the bearing in the connecting rod–slider joint. For this reason, the analysis is based on two different models, whose application depends on the lubrication conditions (eccentricity value) of the bearing. The first model (1dof) considers the connecting rod–slider joint as an ideal joint and is applied when the connecting rod end is in contact with the bearing surface [14]. The second model (3dof) is applied when the connecting rod end is in hydrodynamic lubrication in the slider bore clearance. In this condition, the slider moves in relation to the connecting rod, characterizing a problem of multiple degrees of freedom in which the interaction between the connecting rod and the slider occurs through the hydrodynamic forces of the lubricant fluid. Therefore, the solution is obtained from a hybrid model composed of a model of the slider–crank mechanism with ideal joints and a model of the slider–crank mechanism with hydrodynamic bearing in the connecting rod–slider joint.Thus, an important parameter in this analysis is the minimum oil film thickness considered in the hydrodynamic lubrication. According to Flores [9], for high eccentricity (low minimum oil film thickness), the pressure causes elastic deformation of the surfaces, which can be of the same order as the lubricant film thickness. These circumstances differ from those obtained in hydrodynamic lubrication and a more realistic analysis can be made based on the theory of elastohydrodynamic lubrication. For this reason, this work considered the hydrodynamic lubrication condition for a minimum oil film thickness exceeding 10% of the radial clearance, which represents an eccentricity ratio of 0.9.The dynamic responses of the slider–crank mechanism obtained from the hybrid model are compared with those obtained from the conventional model (slider–crank mechanism with ideal joints). Moreover, the pressure distribution in the bearing isobtained during one period of lubrication condition. It is important to emphasize that the hydrodynamic model used in the present work was developed previously by the authors in cooperation with Bannwart [12].2. MethodologyIn this work, a planar slider–crank mechanism was modeled in order to determine its dynamic behavior. However, instead of the conventional slider–crank mechanism, a hydrodynamic bearing was considered in the connecting rod–slider joint. Thisassumption considers that the pin is not restricted to only one direction of motion, which is the case when the bearing is considered without clearance.This section describes the hybrid mathematical model (3DOF) of the planar slider–crank mechanism considering a hydrodynamic bearing in the connecting rod–slider joint, which is used to analyze the dynamic behavior in the lubricationcondition. The mathematical model used to analyze the dynamic behavior in the contact condition was the conventional slider–crank mechanis