【正文】 se starts in the higher pressure than the pure cavitation process mainly in turbulent shear layers, which occur in scenario V. Therefore, the vapor pressure might be adjusted to design the overlap area by Eq. (16) if there exists substantial trapped and dissolved air in the fluid. The laminar leakages through the clearances aforementioned are a tradeoff in the design. It is demonstrated that the more leakage from the pump case to piston may relieve cavitation , the more leakage may degrade the pump efficiency in the discharge ports. In some design cases, the maximum timing angles can be determined by Eq. (17)to not have both simultaneous overlapping and highly low pressure at the TDC and BDC. While the piston rotates to have the zero displacement, the minimum overlap area can be determined by Eq. 18 , which may assist the piston not to have the large pressure undershoots during flow intake. 6 Conclusions The valve plate design is a critical issue in addressing the cavitation or aeration phenomena in the piston pump. This study uses the control volume method to analyze the flow, pressure, and leakages within one piston bore related to the valve plate timings. If the overlap area developed by barrel kidneys and valve plate ports is not properly designed, no sufficient flow replenishes the rise volume by the rotating movement. Therefore, the piston pressure may drop below the saturated vapor pressure of the liquid and air ingress to form the vapor bubbles. To control the damaging cavitations, the optimization approach is used to detect the lowest pressure constricted by valve plate timings. The analytical limitation of the overlap area needs to be satisfied to remain the pressure to not have large undershoots so that the system can be largely enhanced on cavitation/aeration issues. In this study, the dynamics of the piston control volume is developed by using several assumptions such as constant discharge coefficients and laminar leakages. The discharge coefficient is practically nonlinear based on the geometrics, flow number, etc. Leakage clearances of the control volume may not keep the constant height and width as well in practice due to vibrations and dynamical ripples. All these issues are plicated and very empirical and need further consideration in the future. The results presented in this paper can be more accurate in estimating the cavitations with these extensive studies. Nomenclature 0( ), ( )AA??? the total overlap area between valve plate ports and barrel kidneys 2()mm Ap = piston section area 2()mm A, B, C= constants A= offset between the pistonslipper joint and surface of the swash plate 2()mm dC = orifice discharge coefficient e= offset between the swash plate pivot and the shaft centerline of the pump 2()mm kh = the height of the clearance 2()mm kL = the passage length of the clearance 2()mm M= mass of the fluid within a single piston (kg) N= number of pistons n = piston and slipper counter ,pp = fluid pressure and pressure drop (bar) Pc= the case pressure of the pump (bar) Pd= pump discharge pressure (bar) Pi = pump intake pressure (bar) Pn = fluid pressure within the nth piston bore (bar) Pvp = the vapor pressure of the hydraulic fluid(bar) qn, qLn, qTn = the instantaneous flow rate of each piston (l/min) R = piston pitch radius 2()mm r = piston radius (mm) t=time (s) V= volume 3()mm wk = the width of the clearance (mm) x,x˙= piston displacement and velocity along the shaft axis (m, m/s) x y z?? =Cartesian coordinates with an origin on the shaft centerline x y z? ? ??? = Cartesian coordinates with an origin on swash plate pivot ,??=swash plate angle and velocity (rad, rad/s) ? = fluid bulk modulus (bar) ,BT??= timing angle of valve plates at the BDC and TDC (rad) ? = the open angle of the barrel kidney(rad) ? = fluid density(kg?m3) ,?? = angular position and velocity of the rotating kit (rad, rad/s) ? =absolute viscosity(Cp) 0,??= coefficients related to the pressure drop 外文中文翻譯： 在軸向柱塞泵氣蝕問題的分析 本 論 文討論和分析了一個(gè) 柱塞 孔與配流盤 限制在軸向柱塞泵的控制量 設(shè)計(jì) 。 關(guān)鍵詞：空 蝕 ，優(yōu)化， 配流盤 ， 負(fù)脈沖壓力 1 介紹 在水壓機(jī)等液壓元件中，空穴或氣穴意味著，在低壓區(qū)液壓液體會(huì)出有空腔或氣泡形成以及崩潰在高壓地區(qū)，這將導(dǎo)致噪聲，振動(dòng)，這將會(huì)降低效率。 在液壓機(jī)設(shè)計(jì)中的氣蝕現(xiàn)象 ，許多研究成果已取得一定的成果 。 其中包括 流體勢(shì)效應(yīng)和 氣蝕在氣缸內(nèi) 高速度和高負(fù)荷條件 的預(yù)測(cè) 。 Dular et al 開發(fā)了一 套 專 業(yè) 系統(tǒng) 用它來 監(jiān)測(cè)和控制的液壓機(jī)械和調(diào)查 氣 蝕的可能性 通過使用 運(yùn)用計(jì)算流體 動(dòng)力學(xué) (CFD)工具。 一個(gè)新的空蝕裝置 ,稱為漩渦汽蝕生成器 ,介紹了各種侵蝕情況 。 一種改進(jìn)的模型 已經(jīng)被提出 且 實(shí)驗(yàn)驗(yàn)證了 其 結(jié)果。 然而 ,這項(xiàng)研究的目的是 修改配流盤的設(shè)計(jì)來防止氣 蝕造成侵蝕蒸汽或空氣泡沫崩潰的墻壁上的軸向泵組件。 在這種情況下，軸偏移 e的設(shè)計(jì) 對(duì) 降低成本 是十分重要的 。 配流盤吸排油窗口的幾何形狀以及瞬時(shí)相對(duì)缸體腰形窗口的位置通常被稱為配流盤的時(shí)間效應(yīng) 。 正是由于它的存在，使柱塞泵的容積效率大大的降低。在每個(gè)柱塞空中，其瞬時(shí)質(zhì)量計(jì)算式為 nM = ? nV (3) 對(duì)上式求導(dǎo)可得 nnnd M d Vd Vd t d t d t? ??? (4) 根據(jù)連續(xù)性方程，控制體積的質(zhì)量率為 n ndM qdt ?? (5) 其中 nq 為一個(gè)柱塞空中的瞬時(shí)流量 從體積彈性模量的定義 可知 ， ndPddt dt???? (6) 其中， Pn是 柱塞孔內(nèi) 的瞬時(shí)壓力。如果是一個(gè)閉區(qū)間上連續(xù)函數(shù)， 其 最大值和最小值 必然 存在。因此，讓 方程 （ 10） 的左邊 等于零 ，可得： ta n( ) c os( ) 0n p nq A R ? ? ??? (11) 因此，柱塞泵吸油窗口的壓力不能太低，否則易產(chǎn)生汽蝕現(xiàn)象。 2 ( ) 2 ( )( ) ( )i n d nT n d i d dp p P pq c A c A???????? (14) 其中 Pi和 分別為柱塞泵吸排油窗口的壓力 和 ()iA? ， ()dA? 分別為 每缸體腰形窗口 和 配流盤吸排油窗口 單獨(dú)的瞬時(shí)之間 的重疊面積。此時(shí)柱塞泵非常容易發(fā)生汽蝕，為阻止此類現(xiàn)象的發(fā)生，總的重疊量的面積 ()A? 設(shè)計(jì)應(yīng)滿足 30ta n ( ) c o s( ) ( )12() 2 ( )K I V kkP n v p ckI kd i v phA r p pLAc p p?? ? ?? ??????? ??(16) 其中 0()A? 的 最小面積 為 0()A? = 0( ) ( )idAA? ? ?? 0? 的定義為： 0 /d v p i v pp p p p? ? ? ? 蒸氣壓的壓力下，液體蒸發(fā)成氣態(tài)形式。 當(dāng)柱塞經(jīng)過配流盤吸油口時(shí)，壓力變化依賴于余弦函數(shù)式 （ 10）。 那么 整體的重疊區(qū)域，可以得出有一個(gè)設(shè)計(jì)上的 極限 。 事實(shí) 上，空氣釋放開始在更高的壓力主要集中在純剪切湍流層蝕過程中，發(fā)生在場(chǎng)景五。然而 ， 越 多的泄漏，可能會(huì)降低泵的效率 在排油窗口 。如果重疊區(qū)域由 缸體腰形窗口 和 配流盤 的 開口 開發(fā)設(shè)計(jì)不當(dāng)， 就不會(huì)有 足夠的流量 來 補(bǔ)充 由于 旋轉(zhuǎn)運(yùn)動(dòng) 引起的空間 。 在這項(xiàng)研究中， 柱塞 控制量的動(dòng)態(tài)開發(fā)利用 恒定的流量 系數(shù)和層滲漏等幾個(gè)假設(shè)。