基于UG的軸向柱塞泵設(shè)計(jì)

62頁 18000字?jǐn)?shù)+論文說明書+任務(wù)書+8張CAD圖紙【詳情如下】

基于UG的軸向柱塞泵設(shè)計(jì)開題報(bào)告.doc

基于UG的軸向柱塞泵設(shè)計(jì)論文.doc

外文翻譯--利用被困體積提高軸向柱塞泵的容積效率.doc

奇數(shù)柱塞泵瞬時(shí)流量圖.dwg

柱塞受力圖.dwg

柱塞泵三維仿真.swf

柱塞泵任務(wù)書.doc

柱塞腔通油孔圖.dwg

柱塞運(yùn)動(dòng)特征圖.dwg

軸向柱塞泵裝配圖.dwg

零件圖傳動(dòng)軸.dwg

零件圖滑靴.dwg

零件圖配油盤.dwg

摘要

軸向柱塞泵是向液壓系統(tǒng)提供一定流量和壓力的油液的動(dòng)力元件,它是每個(gè)液壓系統(tǒng)中不可缺少的核心元件,合理的選擇液壓泵對于液壓系統(tǒng)的能耗﹑提高系統(tǒng)的效率﹑降低噪聲﹑改善工作性能和保證系統(tǒng)的可靠工作都十分重要

本設(shè)計(jì)對軸向柱塞泵進(jìn)行了分析,主要分析了軸向柱塞泵的分類,對其中的結(jié)構(gòu),例如,柱塞的結(jié)構(gòu)型式﹑滑靴結(jié)構(gòu)型式﹑配油盤結(jié)構(gòu)型式等進(jìn)行了分析和設(shè)計(jì),還包括它們的受力分析與計(jì)算.還有對缸體的材料選用以及校核很關(guān)鍵;最后對變量機(jī)構(gòu)分類型式也進(jìn)行了詳細(xì)的分析,比較了它們的優(yōu)點(diǎn)和缺點(diǎn).該設(shè)計(jì)最后對軸向柱塞泵的優(yōu)缺點(diǎn)進(jìn)行了整體的分析,對今后的發(fā)展也進(jìn)行了展望.

關(guān)鍵詞: 柱塞泵,液壓系統(tǒng),結(jié)構(gòu)型式,今后發(fā)展.

Abstract

Liquid's pressing a pump is the motive component of oil liquid which presses system to provide certain discharge and pressure toward the liquid, it is each core component that the liquid presses the indispensability in the system, reasonable of choice liquid's pressing a pump can consume a ﹑ exaltation the efficiency ﹑ of the system to lower a Zao voice ﹑ an improvement work function and assurance system for liquid pressing system of of dependable work all very important

This design filled a pump to carry on toward the pillar to the stalk analytical, mainly analyzed stalk to fill the classification of pump toward the pillar, as to it's win of structure, for example, the pillar fill of the ﹑ slippery Xue structure pattern ﹑ of the structure pattern went together with the oil dish structure pattern's etc. to carry on analysis and design, also include their is analyze by dint with calculation.The material which still has a body to the urn chooses in order to and school pit very key;Finally measure an organization classification towards change, the pattern also carried on detailed analysis and compared their advantage and weakness.That design end filled the merit and shortcoming of pump to carry on whole analysis toward the pillar to the stalk and also carried on an outlook to aftertime's development.

Keyword: The pillar fills a pump, the liquid presses system, structure pattern, will develop from now on.

目   錄

摘 要…………………………………………………………………………………………… Ⅰ

ABSTRACT Ⅱ

緒論……………………………………………………………………………………………4

1軸向柱塞泵工作原理與性能參數(shù)……………………………………………… 6

1.1軸向柱塞泵工作原理……………………………………………………………… 6

1.2軸向柱塞泵主要性能參數(shù)………………………………………………………… 6

1.2.3排量﹑流量與容積效率……………………………………………………………… 7

    1.2.2扭矩與機(jī)械效率 8

    1.2.3功率與效率…………………………………………………………………………… 9

2 軸向柱塞泵運(yùn)動(dòng)學(xué)及流量品質(zhì)分析………………………………………… 10

2.1柱塞運(yùn)動(dòng)學(xué)分析…………………………………………………………………………10

2.1.1柱塞行程S…………………………………………………………………………… 11

2.1.2柱塞運(yùn)動(dòng)速度分析v………………………………………………………………… 12

2.1.3柱塞運(yùn)動(dòng)加速度a…………………………………………………………………… 13

2.2滑靴運(yùn)動(dòng)分析…………………………………………………………………………… 14

2.3瞬時(shí)流量及脈動(dòng)品質(zhì)分析……………………………………………………………… 15

    2.3.1脈動(dòng)頻率…………………………………………………………………… 15

2.3.2脈動(dòng)率…………………………………………………………………………………16

3 柱塞受力分析與設(shè)計(jì)………………………………………………………………………17

3.1柱塞受力分析……………………………………………………………………………17

3.1.1柱塞底部的液壓力 …………………………………………………………………17

3.1.2柱塞慣性力……………………………………………………………………………18

    3.1.3離心反力 ……………………………………………………………………………18

3.1.4斜盤反力N…………………………………………………………………………… 19

3.1.5柱塞與柱塞腔壁之間的接觸應(yīng)力 和 ………………………………………… 20

3.1.6摩擦力 和 ………………………………………………………………………20

3.2柱塞設(shè)計(jì)………………………………………………………………………………… 21

3.2.1柱塞結(jié)構(gòu)型式…………………………………………………………………………22

3.2.2柱塞結(jié)構(gòu)尺寸設(shè)計(jì)……………………………………………………………………23

3.2.3柱塞摩擦副比壓P﹑比功 驗(yàn)算……………………………………………………23

4滑靴受力分析與設(shè)計(jì)………………………………………………………………………25

4.1滑靴受力分析…………………………………………………………………………… 25

4.1.1分離力…………………………………………………………………………………26

4.1.2壓緊力 ………………………………………………………………………………27

4.1.3力平衡方程式…………………………………………………………………………27

4.2滑靴設(shè)計(jì)………………………………………………………………………………… 28

4.2.1剩余壓緊力法…………………………………………………………………………28

4.3滑靴結(jié)構(gòu)型式與結(jié)構(gòu)尺寸設(shè)計(jì)…………………………………………………………29

4.3.1滑靴結(jié)構(gòu)型式…………………………………………………………………………29

4.3.2結(jié)構(gòu)尺寸設(shè)計(jì)………………………………………………………………………  31

5 配油盤受力分析與設(shè)計(jì)………………………………………………………………… 32

5.1配油盤受力分析………………………………………………………………………… 32

5.1.1壓緊力 ………………………………………………………………………………33

    5.1.2分離力 …………………………………………………………………………… 34

5.2配油盤設(shè)計(jì)……………………………………………………………………………… 35

5.2.1過渡區(qū)設(shè)計(jì)……………………………………………………………………………35

    5.2.2配油盤主要尺寸確定…………………………………………………………………37

5.2.3驗(yàn)算比壓p﹑比功pv………………………………………………………………… 38

6 缸體受力分析與設(shè)計(jì)………………………………………………………………………40

   6.1缸體的穩(wěn)定性……………………………………………………………………………40

   6.2缸體主要結(jié)構(gòu)尺寸的確定………………………………………………………………40

    6.2.1通油孔分布圓半徑 和面積F…………………………………………………… 40

    6.2.2缸體內(nèi)﹑外直徑 ﹑ 的確定…………………………………………………… 42

6.2.3缸體高度H…………………………………………………………………………… 43

7柱塞回程機(jī)構(gòu)設(shè)計(jì)…………………………………………………………………………44

8 斜盤力矩分析……………………………………………………………………………… 46

8.1柱塞液壓力矩 ……………………………………………………………………… 46

8.2過渡區(qū)閉死液壓力矩……………………………………………………………………46

    8.2.1具有對稱正重迭型配油盤……………………………………………………………46

    8.2.2零重迭型配油盤………………………………………………………………………47

8.2.3帶卸荷槽非對稱正重迭型配油盤……………………………………………………47

   8.3回程盤中心預(yù)壓彈簧力矩 ………………………………………………………… 48

8.4滑靴偏轉(zhuǎn)時(shí)的摩擦力矩 …………………………………………………………… 48

8.5柱塞慣性力矩 ……………………………………………………………………… 48

   8.6柱塞與柱塞腔的摩擦力矩 …………………………………………………………49

   8.7斜盤支承摩擦力矩 …………………………………………………………………49

 8.8斜盤與回程盤回轉(zhuǎn)的轉(zhuǎn)動(dòng)慣性力矩 ………………………………………………50

   8.9斜盤自重力矩 ………………………………………………………………………50

9 變量機(jī)構(gòu)……………………………………………………………………………………51

   9.1手動(dòng)變量機(jī)構(gòu)……………………………………………………………………………51

9.2手動(dòng)伺服變量機(jī)構(gòu)………………………………………………………………………53

   9.3恒功率變量機(jī)構(gòu)…………………………………………………………………………55

   9.4恒流量變量機(jī)構(gòu)…………………………………………………………………………56

結(jié)論…………………………………………………………………………………………… 57

參考文獻(xiàn)………………………………………………………………………………………58

致謝…………………………………………………………………………………………… 59

緒論

隨著工業(yè)技術(shù)的不斷發(fā)展，液壓傳動(dòng)也越來越廣，而作為液壓傳動(dòng)系統(tǒng)心臟的液壓泵就顯得更加重要了。在容積式液壓泵中，惟有柱塞泵是實(shí)現(xiàn)高壓﹑高速化﹑大流量的一種最理想的結(jié)構(gòu)，在相同功率情況下，徑向往塞泵的徑向尺寸大、徑向力也大，常用于大扭炬、低轉(zhuǎn)速工況，做為按壓馬達(dá)使用。而軸向柱塞泵結(jié)構(gòu)緊湊，徑向尺寸小，轉(zhuǎn)動(dòng)慣量小，故轉(zhuǎn)速較高；另外，軸向柱塞泵易于變量，能用多種方式自動(dòng)調(diào)節(jié)流量，流量大。由于上述特點(diǎn)，軸向柱塞泵被廣泛使用于工程機(jī)械、起重運(yùn)輸、冶金、船舶等多種領(lǐng)域。航空上，普遍用于飛機(jī)液壓系統(tǒng)、操縱系統(tǒng)及航空發(fā)動(dòng)機(jī)燃油系統(tǒng)中。是飛機(jī)上所用的液壓泵中最主要的一種型式。

本設(shè)計(jì)對柱塞泵的結(jié)構(gòu)作了詳細(xì)的研究，在柱塞泵中有閥配流﹑軸配流﹑端面配流三種配流方式。這些配流方式被廣泛應(yīng)用于柱塞泵中，并對柱塞泵的高壓﹑高速化起到了不可估量的作用?？梢哉f沒有這些這些配流方式，就沒有柱塞泵。但是，由于這些配流方式在柱塞泵中的單一使用，也給柱塞泵帶來了一定的不足。設(shè)計(jì)中對軸向柱塞泵結(jié)構(gòu)中的滑靴作了介紹，滑靴一般分為三種形式；對缸體的尺寸﹑結(jié)構(gòu)等也作了設(shè)計(jì)；對柱塞的回程結(jié)構(gòu)也有介紹。

柱塞式液壓泵是靠柱塞在柱塞腔內(nèi)的往復(fù)運(yùn)動(dòng)，改變柱塞腔容積實(shí)現(xiàn)吸油和排油的。是容積式液壓泵的一種。柱塞式液壓泵由于其主要零件柱塞和缸休均為圓柱形，加工方便配合精度高，密封性能好，工作壓力高而得到廣泛的應(yīng)用。

    柱塞式液壓泵種類繁多，前者柱塞平行于缸體軸線，沿軸向按柱塞運(yùn)動(dòng)形式可分為軸向柱塞式和徑向往塞式兩大類運(yùn)動(dòng)，后者柱塞垂直于配油軸，沿徑向運(yùn)動(dòng)。這兩類泵既可做為液壓泵用，也可做為液壓馬達(dá)用。

泵的內(nèi)在特性是指包括產(chǎn)品性能、零部件質(zhì)量、整機(jī)裝配質(zhì)量、外觀質(zhì)量等在內(nèi)的產(chǎn)品固有特性，或者簡稱之為品質(zhì)。在這一點(diǎn)上，是目前許多泵生產(chǎn)廠商所關(guān)注的也是努力在提高、改進(jìn)的方面。而實(shí)際上，我們可以發(fā)現(xiàn)，有許多的產(chǎn)品在工廠檢測符合發(fā)至使用單位運(yùn)行后，往往達(dá)不到工廠出廠檢測的效果，發(fā)生諸如過載、噪聲增大，使用達(dá)不到要求或壽命降低等等方面的問題；而泵在實(shí)際當(dāng)中所處的運(yùn)行點(diǎn)或運(yùn)行特征，我們稱之為泵的外在特性或系統(tǒng)特性。

    正如科學(xué)技術(shù)的發(fā)展一樣，現(xiàn)階段科技領(lǐng)域中交叉學(xué)科、邊緣學(xué)科越來越豐富，跨學(xué)科的共同研究是十分普遍的事情，作為泵產(chǎn)品的技術(shù)發(fā)展亦是如此。以屏蔽式泵為例，取消泵的軸封問題，必須從電機(jī)結(jié)構(gòu)開始，單局限于泵本身是沒有辦法實(shí)現(xiàn)的；解決泵的噪聲問題，除解決泵的流態(tài)和振動(dòng)外，同時(shí)需要解決電機(jī)風(fēng)葉的噪聲和電磁場的噪聲；提高潛水泵的可靠性，必須在潛水電機(jī)內(nèi)加設(shè)諸如泄漏保護(hù)、過載保護(hù)等措施；提高泵的運(yùn)行效率，須借助于控制技術(shù)的運(yùn)用等等。這些無一不說明要發(fā)展泵技術(shù)水平，必須從配套的電機(jī)、控制技術(shù)等方面同時(shí)著手，綜合考慮，最大限度地提升機(jī)電一體化綜合水平。

柱

1  直軸式軸向柱塞泵工作原理與性能參數(shù)

1．1直軸式軸向柱塞泵工作原理

直軸式軸向柱塞泵主要結(jié)構(gòu)如圖1.1所示。柱塞的頭部安裝有滑靴，滑靴底面始終貼著斜盤平面運(yùn)動(dòng)。當(dāng)缸體帶動(dòng)柱塞旋轉(zhuǎn)時(shí)，由于斜盤平面相對缸體平面（xoy面）存在一傾斜角 ，迫使柱塞在柱塞腔內(nèi)作直線往復(fù)運(yùn)動(dòng)。如果缸體按圖示n方向旋轉(zhuǎn)，在 ～ 范圍內(nèi)，柱塞由下死點(diǎn)(對應(yīng) 位置)開始不斷伸出，柱塞腔容積不斷增大，直至上死點(diǎn)(對應(yīng) 位置)止。在這過程中，柱塞腔剛好與配油盤吸油窗相通，油液被吸人柱塞腔內(nèi)，這是吸油過程。隨著缸體繼續(xù)旋轉(zhuǎn)，在 ～ 范圍內(nèi)，柱塞在斜盤約束下由上死點(diǎn)開始不斷進(jìn)入腔內(nèi)，柱塞腔容積不斷減小，直至下孔點(diǎn)止。在這過程中，柱塞腔剛好與配油盤排油窗相通，油液通過排油窗排出。這就是排油過程。由此可見，缸體每轉(zhuǎn)一跳各個(gè)往塞有半周吸油、半周排油。如果缸體不斷旋轉(zhuǎn)，泵便連續(xù)地吸油和排油。

圖中恒流量變量機(jī)構(gòu)由帶有節(jié)流閥的雙邊控制閥(恒流量閥)和差動(dòng)變量缸組成。控制閥C端預(yù)壓彈簧調(diào)定后，節(jié)流閥兩側(cè)壓力差在控制閥閥芯上產(chǎn)生的液壓力與彈簧力相平衡，閥芯處于中垃，斜盤傾角固定在某一角度，泵輸出流量為調(diào)定值。

當(dāng)泵轉(zhuǎn)速增加時(shí)，輸出流量也相應(yīng)增加。由于節(jié)流器面積不變，則節(jié)流器兩端壓力差 增大，推動(dòng)控制閥閥芯左移，帶動(dòng)變量活塞左移，斜盤傾角減小，流量城少，直至恢復(fù)到調(diào)定值。此時(shí)，閥芯上液壓力與彈簧力重新平衡閥芯處于中位，斜盤傾角穩(wěn)定，泵輸出流量為恒定值。反之，當(dāng)泵轉(zhuǎn)速減小后，輸出流量減少。類似的分析可知，斜盤傾角會增加，流量也隨之增加，仍保持為一恒定值。

  圖9.5(b)為變量特性曲線。 為保持調(diào)定流量 的最低穩(wěn)定轉(zhuǎn)速。從圖中可以看出，從 以上，泵輸出流量不隨轉(zhuǎn)速變化而改變，始終保持恒定值。

恒流量變星泵用于對液壓執(zhí)行機(jī)構(gòu)要求速度恒定的設(shè)備中。例如，機(jī)床、運(yùn)輸機(jī)械等液壓系統(tǒng)。但是恒流量變量泵恒定流星的精度不高，誤差較大，這也限制了它的應(yīng)用。

結(jié)論

液壓泵是向液壓系統(tǒng)提供一定流量和壓力的油液的動(dòng)力元件,它是每個(gè)液壓系統(tǒng)中不可缺少的核心元件,合理的選擇液壓泵對于液壓系統(tǒng)的能耗﹑提高系統(tǒng)的效率﹑降低噪聲﹑改善工作性能和保證系統(tǒng)的可靠工作都十分重要.

    選擇液壓泵的原則是:根據(jù)主機(jī)工況﹑功率大小和系統(tǒng)對工作性能的要求,首先確定液壓泵的類型,然后按系統(tǒng)所要求的壓力﹑流量大小確定其規(guī)格型號.

一般來說,由于各類液壓泵各自突出的特點(diǎn),其結(jié)構(gòu)﹑功用和運(yùn)轉(zhuǎn)方式各不相同,因此應(yīng)根據(jù)不同的使用場合選擇合適的液壓泵.一般在機(jī)床液壓系統(tǒng)中,往往選用雙作用葉片泵和限壓式變量葉片泵;而在筑路機(jī)械﹑港口機(jī)械以及小型工程機(jī)械中,往往選擇抗污染能力比較強(qiáng)的齒輪泵;在負(fù)載大﹑功率大的場合往往選擇柱塞泵.

正如科學(xué)技術(shù)的發(fā)展一樣，現(xiàn)階段科技領(lǐng)域中交叉學(xué)科、邊緣學(xué)科越來越豐富，跨學(xué)科的共同研究是十分普遍的事情，作為泵產(chǎn)品的技術(shù)發(fā)展亦是如此。以屏蔽式泵為例，取消泵的軸封問題，必須從電機(jī)結(jié)構(gòu)開始，單局限于泵本身是沒有辦法實(shí)現(xiàn)的；解決泵的噪聲問題，除解決泵的流態(tài)和振動(dòng)外，同時(shí)需要解決電機(jī)風(fēng)葉的噪聲和電磁場的噪聲；提高潛水泵的可靠性，必須在潛水電機(jī)內(nèi)加設(shè)諸如泄漏保護(hù)、過載保護(hù)等措施；提高泵的運(yùn)行效率，須借助于控制技術(shù)的運(yùn)用等等。這些無一不說明要發(fā)展泵技術(shù)水平，必須從配套的電機(jī)、控制技術(shù)等方面同時(shí)著手，綜合考慮，最大限度地提升機(jī)電一體化綜合水平。

參 考 文 獻(xiàn)

〔1〕李培滋﹑王占林主編.《飛機(jī)液壓傳動(dòng)與伺服控制》（上冊）.國防工業(yè)出版社.1989

〔2〕曾祥榮﹑葉文柄﹑吳沛容編著.《液壓傳動(dòng)》.國防工業(yè)出版社.1980

〔3〕何存興主編.《液壓元件》.機(jī)械工業(yè)出版社.1982

〔4〕張赤誠等編.《液壓傳動(dòng)》.地質(zhì)出版社.1986

〔5〕齊任賢主編.《液壓傳動(dòng)和液力傳動(dòng)》.冶金工業(yè)出版社.1981

〔6〕上海煤礦機(jī)械研究所編.《液壓傳動(dòng)設(shè)計(jì)手冊》.上海人民出版社.1976

〔7〕（日）市川常雄著.雞西煤礦機(jī)器廠譯.《液壓技術(shù)基本理論》.煤炭工業(yè)出版社.1975

〔8〕（美）H﹒E﹒梅里特著.陳燕慶譯.《液壓控制系統(tǒng)》.科學(xué)出版社.1979

〔9〕成大先主編.《機(jī)械設(shè)計(jì)手冊》.化學(xué)工業(yè)出版社.2004

〔10〕聞德生著.《開路式柱塞泵》.航空工業(yè)出版社.1998

〔11〕吉林工業(yè)大學(xué)等校編.《工程機(jī)械液壓與液力傳動(dòng)》.機(jī)械工業(yè)出版社.1978

〔12〕AD 811166.1981.

〔13〕馬玉貴、馬治武主編.《新編液壓件使用與維修技術(shù)大》.中國建材工業(yè)出版社.1998

〔14〕左健民主編. 《液壓與氣壓傳動(dòng)》.機(jī)械工業(yè)出版社.1999

〔15〕文懷興主編.《泵的排量設(shè)計(jì)工況及優(yōu)化設(shè)計(jì)》. 北京.機(jī)械工業(yè)出版社.2005

〔16〕成大先主編.《機(jī)械設(shè)計(jì)圖冊》.化學(xué)工業(yè)出版社.2000

〔17〕沙毅 聞建龍主編.《泵與風(fēng)機(jī)》.中國科學(xué)技術(shù)大學(xué)出版社.2005

〔18〕陳允中 曹占文 黃紅梅 鄧國強(qiáng)等譯.《泵手冊》.中國石化出版社.2003

〔19〕路甬祥主編.《液壓氣動(dòng)技術(shù)手冊》.北京.機(jī)械工業(yè)出版社.2002

〔20〕張耀宸.《機(jī)械加工設(shè)計(jì)手冊》.北京.航空工業(yè)出版社,1987

致   謝

論文是在講師的悉心指導(dǎo)下完成的，在我即將完成學(xué)士學(xué)位學(xué)習(xí)之際，衷心感謝老師們給我提供了良好的學(xué)習(xí)條件、科研環(huán)境和全面鍛煉的機(jī)會以及在生活、學(xué)習(xí)上給予的關(guān)心和幫助。各位老師不僅以其淵博的學(xué)識、創(chuàng)造性的思維方式、嚴(yán)謹(jǐn)?shù)闹螌W(xué)風(fēng)范、高度的責(zé)任感使作者在學(xué)術(shù)上受益匪淺、而且言傳身教，以其高尚的人格和坦蕩寬廣的胸懷教導(dǎo)了我做人的道理。值此論文完成之際，瑾向張勇老師以及全系各位老師表示最衷心的感謝，并致以崇高的敬意！在課題的研究和論文撰寫過程中，得到了學(xué)院老師的大力支持，在此對你們表示衷心的感謝。

畢業(yè)設(shè)計(jì)(論文)外文資料翻譯系　　部： 機(jī)械工程系 專 業(yè)： 機(jī)械工程及自動(dòng)化 姓 名： 學(xué) 號： 外文出處： ASME J.Dyn.Syst.,Meas.,Control 107,246–251 Bull.JSME 9,No.34,305–313 附 件： 1.外文資料翻譯譯文；2.外文原文。附件 1：外文資料翻譯譯文利用被困體積提高軸向柱塞泵的容積效率 研究分析結(jié)果顯示，標(biāo)準(zhǔn)配流盤設(shè)計(jì)因?yàn)橛胁皇芸刂频嘏蛎浐蛪嚎s的流體發(fā)生經(jīng)過插槽本身而產(chǎn)生一種容積損失。通過去除這些插槽同時(shí)采用被困容積式，真正起到改善柱塞泵的容積效率的結(jié)果。雖然目的并不在于研究適合所有柱塞泵的理想配流盤設(shè)計(jì)，但是該報(bào)告的確在被困容積的應(yīng)用方面提供了理論依據(jù)，并且也對解決配流盤的整體設(shè)計(jì)中的問題進(jìn)行了進(jìn)一步的探索。柱塞泵的工作和受力在這一節(jié)中，推導(dǎo)出了和軸向柱塞泵操縱效率有關(guān)的方程。注意：這里的效率在通篇中僅指和流體壓縮損失有關(guān)的效率。這次分析由泵的單一柱塞的機(jī)械和液壓力圖表展開。利用該圖表，分析計(jì)算了作用在柱塞上的機(jī)械力和作用在泵排油區(qū)一液體單元的液壓力。通過輸出功率和輸入功率的比值，推導(dǎo)出了泵的瞬時(shí)功率的表達(dá)式。該表達(dá)式表明，為了計(jì)算泵的效率，必須考慮到必須的動(dòng)力學(xué)、柱塞腔內(nèi)的壓力和流入流出柱塞腔的體積。這些數(shù)值來源于本文接下來的章節(jié)中。N 個(gè)柱塞 X 周正方向的力 Fn。這個(gè)力是由于斜盤對滑靴的反作用力而使柱塞擠入。同理，在柱塞排油的一腔流體上也作用了一壓力 Pn。該壓力驅(qū)使流體流出腔體或被認(rèn)為是流體的排出力。把輸入的機(jī)械力 Fn 轉(zhuǎn)換為輸出的液壓力 Pn，是該柱塞泵的工作的基礎(chǔ)。液壓力容積流量說明瞬時(shí)流線從第 n 個(gè)腔流出混入泵的排油腔。用 Q0 表示泵的眾多容積流量網(wǎng)合成系統(tǒng)的排油。每個(gè)柱塞腔的壓力是各不相同的，但是泵排油區(qū)一條流線上的壓力是一個(gè)常數(shù) Pd。液壓系統(tǒng)排油區(qū)的壓力為 P0。在以下的分析中，我們來考慮一個(gè)流體單元。這個(gè)單元是封閉的從而可以代表第 n 個(gè)柱塞腔到系統(tǒng)排油區(qū)的流線。液壓力(Pn Po)An 作用于此單元，這里 Pn 是第 n 個(gè)柱塞腔的壓力，Po 是系統(tǒng)排油腔的壓力，An 是代表著從第 n 個(gè)柱塞腔流出的流線的流體單元的瞬時(shí)橫截面。被困體積柱塞泵的設(shè)計(jì)。圖 5 是修飾后的配流盤的圖解，它省去了最頂點(diǎn)和最底點(diǎn)的卸荷槽。(intake port:吸入口 discharge port:排出口 kidney-shaped flow passage from a single piston chamber: 從單個(gè)柱塞腔引出來的腎臟形狀的流道)和圖 4 同理，圖 5 同樣給出了從單個(gè)柱塞腔引出來的腎臟形狀的流道配合著配流盤上的弓形門狀幾何體。當(dāng)流道向 位置移動(dòng)是，事實(shí)上流道逐漸被此區(qū)域內(nèi)的門狀幾何體所阻斷。當(dāng)柱塞腔正好位于頂死點(diǎn)時(shí)，柱塞腔是關(guān)閉的沒有流體的流進(jìn)和流出。如圖 5 所示，當(dāng)柱塞向配流盤吸油區(qū)移動(dòng)時(shí)這種封閉的情況依然存在。在這種封閉的狀況下，柱塞腔內(nèi)的流體被困住，所以叫做被困容積泵的設(shè)計(jì)。封閉區(qū)域的角度尺寸用 表示。在這種設(shè)計(jì)中，壓力的轉(zhuǎn)變并不是靠配流盤上的卸荷槽來實(shí)現(xiàn)的，而是單獨(dú)靠受控體積在柱塞腔內(nèi)的體積膨脹來完成的。當(dāng)穿過封閉區(qū)時(shí)，柱塞腔立刻與吸油區(qū)聯(lián)通，流體從泵的吸油區(qū)流入柱塞腔。當(dāng)柱塞腔靠近最底線時(shí)，也會有同樣的狀況。在此區(qū)域內(nèi)柱塞從吸油區(qū)移動(dòng)到排油區(qū)，其封閉的角度尺寸用 .表示。在這個(gè)位置，壓力的轉(zhuǎn)變由柱塞腔內(nèi)受控體積的壓縮來完成。（ 圖 6 piston pressures:活塞壓強(qiáng) equation:方程式 angular position:有角的位置）（piston discharge flows:活塞流體流動(dòng)）圖 5 也在事實(shí)上考慮了柱塞泵中單一個(gè)柱塞腔的四個(gè)不同的區(qū)域的壓力和流動(dòng)分析?？偨Y(jié)圖 6 用這種泵的設(shè)計(jì)理論作為知道思想，把壓力方程（27）和壓力方程(36)做了比較。同樣的道理，把流體流動(dòng)方程（28）和（37 ）做對比，我們還能得到圖 7。如圖 6 所示，被困體積泵的設(shè)計(jì)中壓力轉(zhuǎn)變相對于標(biāo)準(zhǔn)柱塞泵的設(shè)計(jì)中的壓力轉(zhuǎn)變而言，有很大程度的滯后。從圖 7 可以看出，在配流盤壓力轉(zhuǎn)變區(qū)域內(nèi)，標(biāo)準(zhǔn)柱塞泵設(shè)計(jì)中的容積流動(dòng)受到了很大的阻力。這種流體流動(dòng)的阻力是由于在柱塞腔的最低點(diǎn)和最頂點(diǎn)流體受到了不受控制的膨脹和壓縮而造成的。在最低點(diǎn)附近的不受控制的壓縮對柱塞泵產(chǎn)生了很不利的功率損失。討論因?yàn)橐郧暗慕Y(jié)果都是隨時(shí)間變化的，為了出個(gè)方法解決這個(gè)問題，我們必須為每次壓力轉(zhuǎn)變的操作而設(shè)計(jì)一種新的配流盤的設(shè)計(jì)理念。圖 8 顯示了隨著壓力操縱的改變，柱塞泵配流盤的設(shè)計(jì)也跟著改變，同時(shí)附表給出了基本柱塞泵參數(shù)的變化。方程（40）和方程（43）分別描述了普通柱塞泵設(shè)計(jì)和被困體積柱塞泵設(shè)計(jì)的功率損失。用附錄中的參數(shù)，我們把這些方程描述在了圖 9 中。就如圖 9所示，相對于被困體積泵設(shè)計(jì)的功率損失而言，普通泵設(shè)計(jì)的功率損失要大。這種結(jié)果可以用配流盤上的插槽來解釋。讀者也許會記得，這些插槽分擔(dān)了部分流體容積的流動(dòng)，用來協(xié)調(diào)在最底部和最頂部壓力躍遷的變化的。在最底線那里，當(dāng)柱塞進(jìn)入排油口時(shí)，流體經(jīng)過配流盤上的插槽進(jìn)入柱塞腔內(nèi)直到柱塞腔內(nèi)的壓力等于柱塞泵排油區(qū)的壓力。為了使得這些壓力相等，柱塞腔內(nèi)的流體受到了壓縮，結(jié)果，一部分能量加到了柱塞腔的體積上。在最頂部，配流盤上的插槽是用來緩解在最底部被壓縮的流體體積的。這種流體的緩解或者說是流體的膨脹導(dǎo)致通過插槽的流體流動(dòng)釋放了儲存在流體中的能量。這些被釋放出來的能量因?yàn)橹梦涂诘膲毫κ且粋€(gè)恒定的壓力源而永遠(yuǎn)也不能收回。另一方面，被困體積柱塞泵的設(shè)計(jì)中不用為了在最底部和最頂部得到平穩(wěn)的壓力轉(zhuǎn)變而開設(shè)插槽，所以流體中的能量不會以某種耗費(fèi)能量的方式被儲存和釋放掉。（圖 8 改變門狀幾何面積作為壓力轉(zhuǎn)變的操作）(圖 9 功率損失方程式)在被困體積的情況下，在最底線部位能量由于柱塞腔體積自身的機(jī)械變化而自動(dòng)的補(bǔ)充到流體上。同樣的道理，從流體中釋放出來的能量也因?yàn)橹蝗莘e體積的改變而被自動(dòng)的吸收。（圖 10 容積效率方程式）但是，在這兩種設(shè)計(jì)中能量都在柱塞泵的排油區(qū)和被考慮等于柱塞泵的吸油區(qū)的壓力的液壓系統(tǒng)的艙室的交界面上有了損失。這中能量損失在方程（43）中被計(jì)算到了總的能量損失中，產(chǎn)生它的原因就在與當(dāng)流體在經(jīng)過柱塞泵排油區(qū)和液壓系統(tǒng)艙室時(shí)，不受控制的膨脹造成的。方程（41）和方程（44）分別描述了普通柱塞泵設(shè)計(jì)和被困柱塞泵設(shè)計(jì)中的容積效率。利用附錄中的參數(shù)，這兩個(gè)方程被描述在了圖 10 中。如圖 10 所以，被困體積柱塞泵的設(shè)計(jì)比普通柱塞泵的設(shè)計(jì)更有效。造成這樣的結(jié)果再一次說明了兩種設(shè)計(jì)中不同的能量損失特征。按照柱塞泵的設(shè)計(jì)和操縱壓力，這種效率的提高可以達(dá)到 5%。從分析結(jié)果中可以得到，Vo提高了，使用被困體積設(shè)計(jì)柱塞泵的優(yōu)勢更加明顯。結(jié)論這篇報(bào)告試圖說明一臺柱塞泵的功率損失和效率可以通過改變配流盤通道的幾何尺寸來得到提高。特別是，這次研究對比了具有恒定面積卸荷槽的配流盤設(shè)計(jì)和在卸荷槽位置改用被困體積的流體壓縮的容積損失。在這次研究中，帶有卸荷槽的配流盤因?yàn)榱黧w通過最底部和最頂部是的不受控制的膨脹而產(chǎn)生了損失。另一方面，具有被困體積設(shè)計(jì)的配流盤設(shè)計(jì)可以吸收流體從壓縮到釋放時(shí)的能量。所以，被困體積柱塞泵設(shè)計(jì)比應(yīng)用了卸荷槽的普通柱塞泵設(shè)計(jì)更為有效。附錄專業(yè)名詞和術(shù)語Ab,t 配流盤最頂部和最底部卸荷槽的恒定面積An 包含第 n 個(gè)柱塞流線的流體單元的橫截面積Ap 單個(gè)柱塞的有效壓力面積Cd 柱塞腔外泄系數(shù)Fn 作用在第 n 個(gè)柱塞 x 軸方向的機(jī)械力M p 單個(gè)柱塞的質(zhì)量N 柱塞泵中的柱塞數(shù)目n’ 瞬時(shí)連接到泵的排油區(qū)的柱塞的數(shù)目n 柱塞編號Pb 單個(gè)柱塞腔外的界限壓力Pd 泵的排油壓力Pt 泵的吸入壓力Pn 第 n 個(gè)柱塞腔的流體壓力Po 液壓系統(tǒng)排油區(qū)的流體壓力Qn 流出第 n 個(gè)柱塞腔容積流動(dòng)速率Qo 流入液壓系統(tǒng)的容積流動(dòng)速率r 柱塞節(jié)圓半徑sn 沿著第 n 個(gè)柱塞腔流線的坐標(biāo)t 時(shí)間無標(biāo)注尺寸的柱塞體積V~Vb,t 頂部和底部的柱塞腔的體積Vn 第 n 個(gè)柱塞腔的瞬時(shí)體積Vo 單個(gè)柱塞腔的名義體積W 一般意義上的功Xn 第 n 個(gè)柱塞滑靴球連接在 x 軸上的位置α 旋轉(zhuǎn)斜盤的角度β 流體體積模數(shù)配流盤底部頂部卸荷槽的弧度值bt?η 柱塞泵的效率θ 第 n 個(gè)柱塞的角度位置K 一般性的流動(dòng)效率 配流盤底部頂部被困體積的弧度值bt?П 一般性的功率代號ρ 流體密度Ψ 腎型孔的角度尺寸ω 泵的旋轉(zhuǎn)角速度附件 2：外文原文The exploitation surrounds a physical volume exaltation stalk to fill the capacity efficiency of pump toward the pillarIn the analytical result of this paper, it may be shown that the standard valve-platedesign introduces a volumetric loss whichmay be accounted for by the uncontrolledexpansion andcompression of the fluid that occurs through the slots themselves.Byeliminating these slots, and utilizing a trapped volume design,it may be shown thatimprovements in theoperating efficiencycan be achieved. Though this paper does notclaim to providethe ideal valve-plate design for all pump applications, it doesprovide thetheoretical reason for utilizing trapped volumes andlends general insight into the overallproblem of valve-plate design.Pump Work and PowerIn this section, the equations that govern the operatingefficiency of the axial-piston pump are derived. Note:throughout this research, the word efficiency will refer only to theefficiency that is associated with the compressibility losses of thefluid. This analysis begins by examining a diagram of mechanicaland fluid conditions that exist within the pump for a single piston.Using this diagram, the mechanical work that is exerted on thepiston, and the hydraulic work that is exerted on a fluid columnwithin the discharge chamber of the pump, are considered. Bytaking the ratio of output power to input power, an instantaneousexpression for the efficiency of the pump is derived. Fromthisexpression, it is shown that the kinematics of the piston, the pressurewithin the piston chamber, and the volumetric flow in and outof the piston chamber must be determined for the purposes ofevaluating the efficiency of the pump. These quantities are derivedinsubsequentsections of this paper.a diagram of mechanical and fluid conditionsthat exist for a single piston as it operates within the pump. In thisfigure, it is shown that the nth piston is acted upon by a force, Fn ,which is shown to drive the piston in the positive x-direction. Thisforce is the input to the piston which is generated by the slipper’sreaction against the swash plate. Similarly, the fluid at the dischargeof the piston chamber is acted upon by the pressure withinthe nth piston chamber itself, Pn . This pressure tends to force thefluid out of the chamber and may be considered as the forcinginput to the fluid. Theprocess ofconverting the mechanical input,Fn , to a hydraulic input, Pn , is the fundamental operating task ofthe pump.Hydraulic Power. however, the bottom piston is shown to be the nth piston whichimplies that the number of pistons within the pump is generalized.the diagram of volumetric flow illustrates the instantaneousstreamline of flow that is ejected from the nth pistonchamberinto the discharge chamber of the pump. The net volumetricflow from the pump discharge-chamber into the hydraulicsystem discharge-chamber is given by Qo . the diagramof fluid pressure illustrates that the pressure within each pistonchamber is generally different; but, that the fluid pressure alongthe streamlines within the pump discharge-chamber is essentiallya constant which is given by, Pd . The pressure within the dischargechamber of the hydraulic system is given by the constantpressure, Po .In the analysis which follows, a column of fluid within thedischarge chamber of the pump will be considered. This columnof fluid will be chosen so that it will contain the streamlines offlow from the nth piston chamber to the discharge chamber of thehydraulic system. The hydraulic force exerted on this column offluid is given by, (Pn2Po)An , where Pn is the pressure withinthe nth piston chamber, Po is the pressure within the dischargechamber of the hydraulic system, and An is the instantaneouscross-sectional area of the column of fluid which contains thestreamlines of flow from the nth piston chamber.Trapped-Volume Pump Design. Figure 5 shows a schematicof a modified valve-plate which has eliminated the slots near topand bottom dead-centers. Similar to Fig. 4, Fig. 5 shows a kidneyshapedflow passage from a single piston chamber which matchesthe arcuate porting geometry of the valve plate. As this flow passagemoves toward u n5p/2, the actual flow passage is graduallycut off due to the terminating port-geometry of the valve plate inthis region. When the piston reaches this point, the piston chamberis completely closed off and flow cannot be discharged or receivedby the piston chamber. As shown in Fig. 5, the closedportingcondition continues to exist as the piston moves towardthe intake port of the valve plate. In this closed-porting condition,the fluid within the piston chamber is trapped and thus it is calleda trapped-volume pump design. The angular distance of thisclosed porting is given by the dimension, z t . With this design, thepressure transition is accomplished, not by valve-plate slotting,but by the controlled volumetric expansion of the piston chamberalone. Once the piston chamber crosses the closed-porting zone, itquickly opens up to the intake port and begins to receive fluidfrom the intake side of the pump. A similar set of conditionsexists when the piston chamber is near bottom dead center whenu n53p/2. In this region, the piston is moving from the intakeport into the discharge port and the angular dimension of theclosed-porting zone is given by, z b . In this location, the pressuretransition is accomplished by the controlled volumetric compressionof the piston chamber.Again, the valve plate shown in Fig. 5 provides, essentially,four different regions to be considered in the pressure and flowanalysis for a single piston-chamber within the pump. Table 2 Trapped-volume value slate regionsRegion Angular Position Pressure Conditions Flow ConditionsThe pressure within the piston chamber is at dischargepressure.The discharge flow is equal to the displacement of theThe pressure within the piston chamber is betweenintake pressure and discharge pressure.The valve-plate porting is closed off and the dischargeflow is zeroThe pressure within the piston chamber is at intakepressure.The intake flow is equal to the displacement of the piston.The pressure within the piston chamber is betweenintake pressure and discharge pressure.The valve-plate porting is closed off and the intake flowis zero.Within Regions 1 and 3, the pressure is approximated as a constant,either Pd or Pi , and the volumetric flow rate is given by thenegative of the volumetric time rate-of-change of the piston chamberitself, 2V˙ n5Apr tan(a)v cos(un). In Regions 2 and 4, thepressure is changing as a function of u n and therefore some analysisis required to approximate the pressure characteristics withinthese regions.In Region 2 of the valve plate, the porting is closed off andvolumetric flow in and out of the piston chamber is no longerpossible. In this case, the time rate-of-change of the fluid pressurewithin the nth piston chamber is given bydPndt52bVndVndt, (29)where Vn is the instantaneous volume of the nth piston chamber.By eliminating dt from the denominator of both sides of this equation,the following separable differential-equation with its appropriatebounds of integration may be writtenEPdPndPn52b EVtVn 1VndVn , (30)where Vt is the volume in the nth piston chamber when u n5p/2. The solution to this equation is given byPn5Pd2b lnSVnVt D'Pd2b SVnVt21 D, (31)where Vn is given in Eq. ~16! and Vt5Vo2Apr tan(a). Usingthese results yields the following simplified expression for thepressure within the nth piston chamber as the piston passesthrough Region 2 of the valve plate:Pn5Pd2b S12sin~u n!V?21 D, (32)where V? 5Vo /Apr tan(a). Note: V? is always greater than unity.Within Region 2 of the valve plate Qn50. To insure that theclosed-porting zone on the valve plate is designed sufficiently, itis important to note that when u n5p/21z t , the pressure withinthe piston chamber should equal the intake pressure, Pi . Thismeans that the closed-porting zone on the valve-plate has effectivelyfacilitated a full pressure transition from the discharge pressure,Pd , to the intake pressure Pi . By setting Pn equal to Pi ,and u n equal to p/21z t , Eq. ~32! may be solved to determine theproper length of the closed-porting zone on the valve-plate. Thisresult is given byz t5cos21S12Pd2Pib~V?21! D. (33)Similar analysis can be done for Region 4 where the pressuretransition being achieved is between the intake pressure, Pi , andthe discharge pressure, Pd . In this region, the pressure within thenth piston chamber is given byPn5Pi1b S11sin~u n!V?11 D. (34)Again, within Region 4 of the valve plate, Qn50. It can be shownthat the appropriate closed-porting length in Region 4 is given byz b5cos21S12Pd2Pib~V?11! D. (35)To summarize the approximate pressure results of this section,the following piecewise equation is presented for the instantaneouspressure within the nth piston chamber:Pn5| Pd z b2p2,u n,p2Pd2b S12sin~u n!V?21 D p2,u n,p21z tPip21z t,u n,3p2Pi1b S11sin~u n!V?11 D 3p2,u n,3p21z b.(36)The approximate volumetric flow results of this section may besummarized using the following piecewise equation for the instantaneousdischarge-flow from the nth piston chamber:Qn5|Apr tan~a !v cos~u n! z b2p2,u n,p20p2,u n,p21z tApr tan~a !v cos~u n!p21z t,u n,3p203p2,u n,3p21z b.(37)Summary. Using the pump design information in the Appendix,Fig. 6 has been generated for the purpose of comparing thepressure equations ~27! and ~36!. Similarly, Fig. 7 has been generatedfor the purpose of comparing the flow equations ~28!and~37!. As shown in Fig. 6, the pressure transition of the trappedvolumedesign significantly lags the pressure transition of thestandard design. From Fig. 7, it can be seen that the volumetricflow of the standard design experiences significant spikes in thetransition regions of the valve plate. The flow spikes of the standarddesign result from the uncontrolled expansion and compressionof the fluid at top and bottom dead centers. At bottom deadcenter, the uncontrolled compression of the fluid causes an undesirablepower loss for the pump.Standard Pump Design. Substituting the results of Eqs.~13!, ~27!, and ~28! into Eqs. ~10! and ~12! yields the followingresults for the output and input power of the standard pumpdesign:P ˉout5PidealHcos2Sj b2 D2DPb~V?11!4 J,(38)P ˉin5PidealH12cos~j t!j t2 112cos~j b!jb 2 2DPb~V?21!4 J,where the ideal power transmission of the pump is given byPideal5NAprv tan~a !DPp. (39)In these equations, DP5Pd2Pi . Subtracting the output powerfrom the input power yields the power loss of the standard pumpdesign. This result is given byP ˉloss5PidealH12cos~j t!j t2 112cos~j b!jb 2 2cos2Sj b2 D1DPb12J.(40)The efficiency of the standard pump design is given byh5P ˉoutP ˉin5Hcos2Sj b2 D2DPb~V?11!4 JH12cos~j t!j t2 112cos~j b!jb 2 2DPb~V?21!4 J . (41) Trapped-Volume Pump Design. Substituting the results ofEqs. ~13!, ~36!, and ~37! into Eqs. ~10! and ~12! yields the followingresults for the output and input power of the trapped-volumepump design:P ˉout5PidealH12DPb~V?11!2 J, P ˉ in5PidealH12DPbV?2 J.(42)Subtracting the output power from the input power yields thepower loss of the trapped-volume pump design. This result isgiven byP ˉloss5PidealHDPb12J. (43)The efficiency of the trapped-volume pump design is given byh5P ˉoutP ˉin5121 S2bDP2V? D. (44)Journal of Dynamic Systems, Measurement, and Control DiscussionTo make plots of the previous results as they vary with pressure,a new valve plate needs to be designed for each operatingpressure. Figure 8 illustrates the changing valve-plate designs asthey vary with operating pressure for the basic pump parametersgiven in the Appendix.Equations ~40! and ~43! describe the power losses of the standarddesign and the trapped-volume design respectively. Theseequations are plotted in Fig. 9 using the parameters given in theAppendix. As shown in Fig. 9, the power losses are greater for thestandard design as compared to the trapped-volume design.Thisfact may be explained by the slots on the valve plate. The readerwill recall that the slots are used to provide a flow passage whichaccommodates the pressure transitions at top and bottom deadcenters. At bottom dead center, when the piston is entering thedischarge port, fluid flows through the valve-plate slot into thepiston chamber until the fluid pressure within the piston chamberis equal to that of the fluid pressure in the discharge port of thepump. In order to make these pressures equal, the fluid in thepiston chamber needed to be compressed; and, as a result, energywas added to the piston-chamber volume. At top dead center, thevalve-plate slot is used to decompress the fluid that was compressedat bottom dead center. This decompression or expansionof the fluid results in a flow through the slot which releases thestored energy in the fluid. This released energy is never recoveredsince the intake port of the pump is modeled as a constant pressuresource of fluid. On the other hand, the trapped-volume pumpdesign does not utilize slots for achieving a smooth pressure transitionat top and bottom dead centers; and, as a result, the energyin the fluid is not added or released in an uncontrollable fashionthat dissipates energy. In the trapped-volume case, the energyadded to the fluid at bottom dead center is added mechanicallythrough the volume change of the piston chamber itself. Similarly,at top dead center, the energy released from the fluid is recoveredmechanically since it is achieved through the volumetric changeof the piston chamber as well. In both design cases, however,energy is lost at the interface between the pump discharge chamberand the hydraulic system chamber which is considered to be atthe same pressure as the intake port of the pump. This energy lossamounts to the total energy loss shown in Eq. ~43! and is due tothe uncontrolled expansion of the fluid as it crosses the boundarybetween the pump discharge-chamber and the hydraulic systemchamber.Equations ~41! and ~44! describe the volumetric efficiency ofthe standard design and the trapped-volume design, respectively.These equations are plotted in Fig. 10 using the parameters givenin the Appendix. As shown in Fig. 10, the trapped-volume designis more efficient than the standard design. Again, this is due to thedifferences in power-loss characteristics of these two designs.This efficiency improvement can be as high as 5 percent dependingupon the pump design and the operating pressure. It can beshown from the analytical results of this study that, as Vo increases,the advantages of using a trapped-volume design becomemore apparent.ConclusionThis paper has attempted to show that the power loss and efficiencyof a pump can be altered by changing the porting geometryof the valve plate. In particular, this research has compared thevolumetric losses due to fluid compression between valve-platedesigns that have constant-area slots and ones that utilize trappedvolumeregions in the place of slots. In this research, it has beenshown that valve plates with slots generate losses that result fromthe uncontrolled expansion of fluid which occurs through the slotsat top and bottom dead centers. On the other hand, valve platesthat are designed with trapped-volume regions can mechanicallyrecover the energy change that occurs from compressing and decompressingthe fluid. As a result, trapped-volume designs aremore efficient than the standard pump designs which utilize slotson the valve plate.AppendixAb,t 5 16.0E206 m2Ap 5 789.2E206 m2Cd 5 0.62N 5 9Pd 5 35.0E106 PaPi 5 5.0E106 Par 5 67.3E203 mVo 5 43.6E206 m3a 5 0.244 radb 5 1.2E109 Par 5 850 kg/m3v 5 188.5 rad/sNomenclatureAb,t 5 constant slot areas on the valve plate at bottom and topdead centersAn 5 cross sectional area of the fluid column containing thestreamlines of flow from the nth piston chamberAp 5 pressurized area of a single pistonCd 5 discharge coefficient of a piston chamberFn 5 mechanical force exerted on the nth piston in thex-directionMp 5 mass of a single pi