【正文】 v phA r p pLAc p p???? ?????? ?? (18) where 0(0)A is the minimum overlap area of 0(0) (0)iAA? . To prevent the low piston pressure building bubbles, the vapor pressure is considered as the lower limitation for the pressure settings in Eq. (16). The overall of overlap areas then can be derived to have a design limitation. The limitation is determined by the leakage conditions, vapor pressure, rotating speed, etc. It indicates that the higher the pumping speed, the more severe cavitation may happen, and then the designs need more overlap area to let flow in the piston bore. On the other side, the low vapor pressure of the hydraulic fluid is preferred to reduce the opportunities to reach the cavitation conditions. As a result, only the vapor pressure of the pure fluid is considered in Eqs. (16)–(18). In fact, air release 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 柱塞 孔與配流盤 限制在軸向柱塞泵的控制量 設(shè)計 。真空 是由柱塞的運動量 引起的，需要由流動補償，否則，低氣壓可能導(dǎo)致的氣蝕和曝氣。 配流盤 幾何的研究，可以優(yōu)化一些分析性的限制，以防止蒸氣壓以下的 柱塞 壓力。 配流盤 的端口和 缸體腰形窗口 之間重疊的地方， 設(shè)計時 要考慮的空蝕和曝氣。 關(guān)鍵詞：空 蝕 ，優(yōu)化， 配流盤 ， 負脈沖壓力 1 介紹 在水壓機等液壓元件中，空穴或氣穴意味著，在低壓區(qū)液壓液體會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，這將會降低效率?？瘴g對泵的使用是極為不利的，這是因為倒塌形成的沖擊波可能像炸彈一樣足以損 壞元件。當(dāng)其壓力過低或溫度過高時，液壓油會蒸發(fā)。 在實踐中，許多方法大多用于處理這些問題，比如：（ 1）提高油箱中的液位高度，（ 2 油箱加壓 ，（ 3）提高泵的進口壓力，（ 4）降低 泵內(nèi)流體的溫度 ，（ 5） 特意 設(shè)計的 柱塞 泵本身 ，對其結(jié)構(gòu)進行優(yōu)化設(shè)計 。 在液壓機設(shè)計中的氣蝕現(xiàn)象 ，許多研究成果已取得一定的成果 。在柱塞泵中， 氣蝕 主要可以分為 兩種類型： 一是與困油 現(xiàn)象有關(guān)（ 這種現(xiàn)象 可通過適當(dāng)?shù)脑O(shè)計 配流盤來阻止困油現(xiàn)象的發(fā)生 ） 和 所觀察到的層上收縮或擴大 后的流動通道 (由于旋轉(zhuǎn)設(shè)計所造成的 )。在這項研究中處理氣 蝕和測量氣缸壓力之間的關(guān)系 。 Edge and Darling 報道了關(guān)于 軸向柱塞泵內(nèi)的氣缸壓力的實驗研究。 其中包括 流體勢效應(yīng)和 氣蝕在氣缸內(nèi) 高速度和高負荷條件 的預(yù)測 。 另一項研究 概述了液壓流體影響進氣條件和汽蝕潛力 的觀點 。 它表明 ,物理屬性 (如蒸汽 壓力、粘度、密度和體積彈性模量 )對 適當(dāng)?shù)卦u估影響潤滑和 氣 蝕是至關(guān)重要的。 一個 相似 的 氣蝕 模型