| | |
| | | 液压缸有多种形式。按照结构特点,它可分为活塞式、柱塞式和摆动式三大类;按作用方式,它又可分为单作用式和双作用式两种。单作用式液压缸只能使活塞(或柱塞)做单方向运动,即液压油液只通向液压缸的一腔,而反方向运动则必须依靠外力(如弹簧力或自重等)来实现;双作用式液压缸,在两个方向上的运动都由液压油液的推动来实现。 |
| | | </p> |
| | | <p class="titleQuot-1">5.1.1 活塞式液压缸</p> |
| | | <p class="content">活塞式液压缸可分为双杆式和单杆式两种结构形式。其固定方式有缸筒固定和活塞杆固定两种。</p> |
| | | <p class="content"> |
| | | 活塞式液压缸可分为双杆式和单杆式两种结构形式。其固定方式有缸筒固定和活塞杆固定两种。 |
| | | </p> |
| | | <p class="poemtitle-l">1.双杆活塞式液压缸</p> |
| | | <p class="content"> |
| | | 图5.1所示为双杆活塞式液压缸示意图,图5.1(a)所示为缸筒固定式结构,液压缸的左腔进油,推动活塞向右运动,右腔回油;反之,活塞反向运动。其运动范围约等于活塞有效行程l的3倍,一般用于中小型设备。图5.1(b)所示为活塞杆固定式结构,液压缸的左腔进油,推动缸体向左运动,右腔回油;反之,缸体反向移动。其运动范围约等于缸筒有效行程l的2倍,因此常用于大中型设备中。实际上液压缸的运动范围还要考虑活塞和缸盖等结构尺寸所占用的空间。其特点是在活塞两侧都有活塞杆伸出。 |
| | |
| | | <img src="../../assets/images/Figure-0001-02.jpg" style="width:80%" alt="" active="true" /> |
| | | <p class="center img">图5.1 双杆活塞式液压缸示意图</p> |
| | | </div> |
| | | <p class="content">当两侧活塞杆直径相同、供油压力和流量不变时,活塞(或缸筒)在两个方向上的运动速度v和推力F都相等,即</p> |
| | | <p class="center"><math display="0"> |
| | | <p class="content"> |
| | | 当两侧活塞杆直径相同、供油压力和流量不变时,活塞(或缸筒)在两个方向上的运动速度v和推力F都相等,即 |
| | | </p> |
| | | <p class="center"> |
| | | <math display="0"> |
| | | <mi>v</mi> |
| | | <mn>=</mn> |
| | | <mfrac> |
| | |
| | | <mn>v</mn> |
| | | </mrow> |
| | | </msub> |
| | | </math></p> |
| | | </math> |
| | | </p> |
| | | <p class="right-info">(5.1)</p> |
| | | |
| | | <div class="t-right mb-20 mt-20"> |
| | | <img src="../../assets/images/Figure-0001-03.jpg" style="width:65%" alt="" active="true" /> |
| | | </div> |
| | | </div> |
| | | </div> |
| | | </div> |
| | |
| | | </ul> |
| | | <div class="bodystyle"> |
| | | <div class="t-right mb-10 mt-20"> |
| | | <p class="center"><i>F</i> |
| | | <mn>=</mn><i>A</i> |
| | | <mn>(</mn><i>p</i><span class="sub">1</span>-<i>p</i><span |
| | | class="sub">2</span>)<i>η</i><span class="sub">m</span>=<math display="0"> |
| | | <p class="center"> |
| | | <math display="0"> |
| | | <mi>F</mi> |
| | | <mn>=</mn> |
| | | <mi>A</mi> |
| | | <mn>(</mn> |
| | | <msub> |
| | | <mi>p</mi> |
| | | <mrow> |
| | | <mo>1</mo> |
| | | </mrow> |
| | | </msub> |
| | | <mn>-</mn> |
| | | <msub> |
| | | <mi>p</mi> |
| | | <mrow> |
| | | <mo>2</mo> |
| | | </mrow> |
| | | </msub> |
| | | <mn>)</mn> |
| | | <msub> |
| | | <mi>η</mi> |
| | | <mrow> |
| | | <mi>m</mi> |
| | | </mrow> |
| | | </msub> |
| | | <mn>=</mn> |
| | | <mfrac> |
| | | <mn>π</mn> |
| | | <mn>4</mn> |
| | | <mi>π</mi> |
| | | <mrow> |
| | | <mo>4</mo> |
| | | </mrow> |
| | | </mfrac> |
| | | </math>(<i>D</i><span class="super">2</span>-<i>d</i><span |
| | | class="super">2</span>)(<i>p</i><span class="sub">1</span>-<i>p</i><span |
| | | class="sub">2</span>)<i>η</i><span class="sub">m</span> |
| | | <mn>(</mn> |
| | | <msup> |
| | | <mi>D</mi> |
| | | <mrow> |
| | | <mo>1</mo> |
| | | </mrow> |
| | | </msup> |
| | | <mn>-</mn> |
| | | <msup> |
| | | <mi>d</mi> |
| | | <mrow> |
| | | <mo>2</mo> |
| | | </mrow> |
| | | </msup> |
| | | <mn>)</mn> |
| | | <mn>(</mn> |
| | | <msub> |
| | | <mi>p</mi> |
| | | <mrow> |
| | | <mo>1</mo> |
| | | </mrow> |
| | | </msub> |
| | | <mn>-</mn> |
| | | <msub> |
| | | <mi>p</mi> |
| | | <mrow> |
| | | <mo>2</mo> |
| | | </mrow> |
| | | </msub> |
| | | <mn>)</mn> |
| | | <msub> |
| | | <mi>η</mi> |
| | | <mrow> |
| | | <mi>m</mi> |
| | | </mrow> |
| | | </msub> |
| | | </math> |
| | | </p> |
| | | <p class="right-info">(5.2)</p> |
| | | </div> |
| | | <p class="left">式中 q——进入液压缸的流量(m<span class="super">3</span>/s);</p> |
| | | <p class="content"> A——活塞有效作用面积(m<span class="super">2</span>);</p> |
| | | <p class="content"> η<span class="sub">V</span>——液压缸的容积效率;</p> |
| | | <p class="content"> D——活塞直径(即缸筒直径)(m);</p> |
| | | <p class="content"> d——活塞杆直径(m);</p> |
| | | <p class="content"> p<span class="sub">1</span>——进油压力(Pa);</p> |
| | | <p class="content"> p<span class="sub">2</span>——回油压力(Pa);</p> |
| | | <p class="content"> η<span class="sub">m</span>——液压缸的机械效率。</p> |
| | | <p class="content"><span class="bold">【例5.1】</span> 某液压传动系统执行元件为双杆活塞式液压缸,液压缸的工作压力p=3.5 MPa,活塞直径D=9 |
| | | cm,活塞杆直径d=4 cm,工作进给速度v=1.52 cm/s,求液压缸能克服多大的阻力?液压缸所需流量为多少? |
| | | <p class="left"> |
| | | 式中 <math display="0"> |
| | | <mi>q</mi> |
| | | </math>——进入液压缸的流量(m<span class="super">3</span>/s); |
| | | </p> |
| | | <p class="content td-3"> |
| | | <math display="0"> |
| | | <mi>A</mi> |
| | | </math>——活塞有效作用面积(m<span class="super">2</span>); |
| | | </p> |
| | | <p class="content td-3"> |
| | | <math display="0"> |
| | | <msub> |
| | | <mi>η</mi> |
| | | <mrow> |
| | | <mi>v</mi> |
| | | </mrow> |
| | | </msub> |
| | | </math> |
| | | ——液压缸的容积效率; |
| | | </p> |
| | | <p class="content td-3"> |
| | | <math display="0"> |
| | | <msub> |
| | | <mi>D</mi> |
| | | </msub> |
| | | </math>——活塞直径(即缸筒直径)(m); |
| | | </p> |
| | | <p class="content td-3"> |
| | | <math display="0"> |
| | | <msub> |
| | | <mi>d</mi> |
| | | </msub> |
| | | </math>——活塞杆直径(m); |
| | | </p> |
| | | <p class="content td-3"> |
| | | <math display="0"> |
| | | <msub> |
| | | <mi>p</mi> |
| | | <mrow> |
| | | <mi>1</mi> |
| | | </mrow> |
| | | </msub> |
| | | </math>——进油压力(Pa); |
| | | </p> |
| | | <p class="content td-3"> |
| | | <math display="0"> |
| | | <msub> |
| | | <mi>p</mi> |
| | | <mrow> |
| | | <mi>2</mi> |
| | | </mrow> |
| | | </msub> |
| | | </math>——回油压力(Pa); |
| | | </p> |
| | | <p class="content td-3"> |
| | | <math display="0"> |
| | | <msub> |
| | | <mi>η</mi> |
| | | <mrow> |
| | | <mi>m</mi> |
| | | </mrow> |
| | | </msub> |
| | | </math>——液压缸的机械效率。 |
| | | </p> |
| | | <p class="content"> |
| | | <span class="bold">【例5.1】</span> 某液压传动系统执行元件为双杆活塞式液压缸,液压缸的工作压力 <math display="0"> |
| | | <msub> |
| | | <mi>p</mi> |
| | | </msub> |
| | | </math> =3.5 |
| | | MPa,活塞直径 <math display="0"> |
| | | <msub> |
| | | <mi>D</mi> |
| | | </msub> |
| | | </math> =9 cm,活塞杆直径 <math display="0"> |
| | | <msub> |
| | | <mi>d</mi> |
| | | </msub> |
| | | </math> =4 cm,工作进给速度 <math display="0"> |
| | | <msub> |
| | | <mi>v</mi> |
| | | </msub> |
| | | </math> =1.52 cm/s,求液压缸能克服多大的阻力?液压缸所需流量为多少? |
| | | <span class="btn-box" @click="showAnswerOne = !showAnswerOne" title="查看答案"> |
| | | <svg xmlns="http://www.w3.org/2000/svg" width="20.501" height="20.501" |
| | | viewBox="0 0 20.501 20.501"> |
| | |
| | | </span> |
| | | </p> |
| | | <div v-if="showAnswerOne"> |
| | | <p class="content"><span class="bold">解</span> (1)活塞的有效作用面积</p> |
| | | <p class="center"> |
| | | <img class="img-c" src="../../assets/images/Figure-0002-02.jpg" alt=""> |
| | | <p class="content"> |
| | | <span class="bold">解</span> (1)活塞的有效作用面积 |
| | | </p> |
| | | <p class="center"><math display="0"> |
| | | <mi>A</mi> |
| | | <mn>=</mn> |
| | | <mfrac> |
| | | <mi>π</mi> |
| | | <mrow> |
| | | <mo>4</mo> |
| | | </mrow> |
| | | </mfrac> |
| | | <mn>(</mn> |
| | | <msup> |
| | | <mi>D</mi> |
| | | <mrow> |
| | | <mo>2</mo> |
| | | </mrow> |
| | | </msup> |
| | | <mn>-</mn> |
| | | <msup> |
| | | <mi>d</mi> |
| | | <mrow> |
| | | <mo>2</mo> |
| | | </mrow> |
| | | </msup> |
| | | <mn>)</mn> |
| | | <mn>=</mn> |
| | | <mfrac> |
| | | <mi>π</mi> |
| | | <mrow> |
| | | <mo>4</mo> |
| | | </mrow> |
| | | </mfrac> |
| | | <mn>(</mn> |
| | | <msup> |
| | | <mo>9</mo> |
| | | <mrow> |
| | | <mo>2</mo> |
| | | </mrow> |
| | | </msup> |
| | | <mn>-</mn> |
| | | <msup> |
| | | <mo>4</mo> |
| | | <mrow> |
| | | <mo>2</mo> |
| | | </mrow> |
| | | </msup> |
| | | <mn>)</mn> |
| | | <msup> |
| | | <mi>cm</mi> |
| | | <mrow> |
| | | <mo>2</mo> |
| | | </mrow> |
| | | </msup> |
| | | <mn>=</mn> |
| | | <mo>51.03</mo> |
| | | <msup> |
| | | <mi>cm</mi> |
| | | <mrow> |
| | | <mo>2</mo> |
| | | </mrow> |
| | | </msup> |
| | | </math></p> |
| | | |
| | | <p class="content">(2)液压缸能克服的最大阻力</p> |
| | | <p class="center"> |
| | | <img class="img-c" src="../../assets/images/Figure-0002-02.jpg" alt=""> |
| | | </p> |
| | | <p class="center"><math display="0"> |
| | | <mi>F</mi> |
| | | <mn>=</mn> |
| | | <mi>p</mi> |
| | | <mi>A</mi> |
| | | <mn>=</mn> |
| | | <mo>3.5</mo> |
| | | <mn>×</mn> |
| | | <msup> |
| | | <mo>10</mo> |
| | | <mrow> |
| | | <mo>6</mo> |
| | | </mrow> |
| | | </msup> |
| | | <mn>×</mn> |
| | | <mo>51.03</mo> |
| | | <mn>×</mn> |
| | | <msup> |
| | | <mo>10</mo> |
| | | <mrow> |
| | | <mo>-4</mo> |
| | | </mrow> |
| | | </msup> |
| | | <mn>(</mn> |
| | | <mo>N</mo> |
| | | <mn>)</mn> |
| | | <mn>=</mn> |
| | | <mo>17.86</mo> |
| | | <mn>(</mn> |
| | | <mo>kN</mo> |
| | | <mn>)</mn> |
| | | </math></p> |
| | | |
| | | <p class="content">(3)液压缸所需流量</p> |
| | | <div class="center"> |
| | | <img class="img-c" src="../../assets/images/Figure-0002-02.jpg" alt=""> |
| | | <p class="content">答:液压缸能克服的阻力是17.86 kN,液压缸所需流量是4.65 L/min。</p> |
| | | <p class="content">这种液压缸常用于要求往返运动速度相同的场合,如液压磨床等。</p> |
| | | <p class="center"><math display="0"> |
| | | <mi>q</mi> |
| | | <mn>=</mn> |
| | | <mi>v</mi> |
| | | <mi>A</mi> |
| | | <mn>=</mn> |
| | | <mo>1.52</mo> |
| | | <mn>×</mn> |
| | | <mo>60</mo> |
| | | <mn>×</mn> |
| | | <mo>51.03</mo> |
| | | <mn>×</mn> |
| | | <mn>=</mn> |
| | | <mo>4653.94</mo> |
| | | <mn>(</mn> |
| | | <msup> |
| | | <mn>cm</mn> |
| | | <mrow> |
| | | <mn>3</mn> |
| | | </mrow> |
| | | </msup> |
| | | <mn>/</mn> |
| | | <mn>min</mn> |
| | | <mn>)</mn> |
| | | <mn>=</mn> |
| | | <mo>4.65</mo> |
| | | <mn>(</mn> |
| | | <mn>L</mn> |
| | | <mn>/</mn> |
| | | <mn>min</mn> |
| | | <mn>)</mn> |
| | | </math></p> |
| | | |
| | | <p class="content"> |
| | | 答:液压缸能克服的阻力是17.86 kN,液压缸所需流量是4.65 L/min。 |
| | | </p> |
| | | <p class="content"> |
| | | 这种液压缸常用于要求往返运动速度相同的场合,如液压磨床等。 |
| | | </p> |
| | | </div> |
| | | </div> |
| | | |
| | | |
| | | <p class="poemtitle-l">2.单杆活塞式液压缸</p> |
| | | <p class="content"> |
| | | 图5.2所示为双作用单杆活塞式液压缸图形符号和实物图。液压缸的一端有活塞杆伸出,在另一端没有活塞杆伸出,这样使液压缸两腔有效作用面积不等,当向液压缸两腔分别供油,且压力和流量都不变时,活塞在两个方向上的运动速度和推力都不相等。当在无杆腔进油且有杆腔回油时(图5.2(a)),活塞的运动速度v<span |
| | | class="sub">1</span>和推力F<span class="sub">1</span>分别为 |
| | | 图5.2所示为双作用单杆活塞式液压缸图形符号和实物图。液压缸的一端有活塞杆伸出,在另一端没有活塞杆伸出,这样使液压缸两腔有效作用面积不等,当向液压缸两腔分别供油,且压力和流量都不变时,活塞在两个方向上的运动速度和推力都不相等。当在无杆腔进油且有杆腔回油时(图5.2(a)),活塞的运动速度<math |
| | | display="0"> |
| | | <msub> |
| | | <mi>v</mi> |
| | | <mrow> |
| | | <mi>1</mi> |
| | | </mrow> |
| | | </msub> |
| | | </math>和推力<math display="0"> |
| | | <msub> |
| | | <mi>F</mi> |
| | | <mrow> |
| | | <mi>1</mi> |
| | | </mrow> |
| | | </msub> |
| | | </math>分别为 |
| | | <span class="btn-box" @click="showAnswerTwo = !showAnswerTwo" title="查看答案"> |
| | | <svg xmlns="http://www.w3.org/2000/svg" width="20.501" height="20.501" |
| | | viewBox="0 0 20.501 20.501"> |
| | | <path class="a" |
| | | d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z" |
| | | transform="translate(-3327.144 15329)" /> |
| | | </svg> |
| | | </span> |
| | | </p> |
| | | <p class="content">当在有杆腔进油且无杆腔回油时(图5.2(b)),活塞的运动速度v<span class="sub">2</span>和推力F<span |
| | | class="sub">2</span>分别为</p> |
| | | <p class="left">式中 q——进入液压缸的流量(m<span class="super">3</span>/s);</p> |
| | | <div v-if="showAnswerTwo"> |
| | | <p class="center mb-10 mt-10"><math display="0"> |
| | | <msub> |
| | | <mi>v</mi> |
| | | <mrow> |
| | | <mo>1</mo> |
| | | </mrow> |
| | | </msub> |
| | | <mn>=</mn> |
| | | <mfrac> |
| | | <mi>q</mi> |
| | | <mrow> |
| | | <msub> |
| | | <mi>A</mi> |
| | | <mrow> |
| | | <mo>1</mo> |
| | | </mrow> |
| | | </msub> |
| | | </mrow> |
| | | </mfrac> |
| | | <msub> |
| | | <mi>η</mi> |
| | | <mrow> |
| | | <mn>v</mn> |
| | | </mrow> |
| | | </msub> |
| | | <mn>=</mn> |
| | | <mfrac> |
| | | <mrow> |
| | | <mn>4</mn> |
| | | <mi>q</mi> |
| | | </mrow> |
| | | <mrow> |
| | | <mn>π</mn> |
| | | <msup> |
| | | <mi>D</mi> |
| | | <mrow> |
| | | <mo>2</mo> |
| | | </mrow> |
| | | </msup> |
| | | </mrow> |
| | | </mfrac> |
| | | <msub> |
| | | <mi>η</mi> |
| | | <mrow> |
| | | <mn>v</mn> |
| | | </mrow> |
| | | </msub> |
| | | <mn>(</mn> |
| | | <mn>m</mn> |
| | | <mn>/</mn> |
| | | <mn>s</mn> |
| | | <mn>)</mn> |
| | | </math> |
| | | </p> |
| | | <p class="right-info">(5.3)</p> |
| | | <p class="center mb-10 mt-10"><math display="0"> |
| | | <msub> |
| | | <mi>F</mi> |
| | | <mrow> |
| | | <mn>1</mn> |
| | | </mrow> |
| | | </msub> |
| | | <mn>=</mn> |
| | | <mn>(</mn> |
| | | <msub> |
| | | <mi>p</mi> |
| | | <mrow> |
| | | <mn>1</mn> |
| | | </mrow> |
| | | </msub> |
| | | <msub> |
| | | <mi>A</mi> |
| | | <mrow> |
| | | <mn>1</mn> |
| | | </mrow> |
| | | </msub> |
| | | <mn>-</mn> |
| | | <msub> |
| | | <mi>p</mi> |
| | | <mrow> |
| | | <mn>2</mn> |
| | | </mrow> |
| | | </msub> |
| | | <msub> |
| | | <mi>A</mi> |
| | | <mrow> |
| | | <mn>2</mn> |
| | | </mrow> |
| | | </msub> |
| | | <mn>)</mn> |
| | | <msub> |
| | | <mi>η</mi> |
| | | <mrow> |
| | | <mi>m</mi> |
| | | </mrow> |
| | | </msub> |
| | | <mn>=</mn> |
| | | <mo data-mjx-texclass="OPEN">[</mo> |
| | | <mfrac> |
| | | <mn>π</mn> |
| | | <mn>4</mn> |
| | | </mfrac> |
| | | <msup> |
| | | <mi>D</mi> |
| | | <mrow> |
| | | <mn>2</mn> |
| | | </mrow> |
| | | </msup> |
| | | <msub> |
| | | <mi>p</mi> |
| | | <mrow> |
| | | <mn>1</mn> |
| | | </mrow> |
| | | </msub> |
| | | <mn>-</mn> |
| | | <mfrac> |
| | | <mn>π</mn> |
| | | <mn>4</mn> |
| | | </mfrac> |
| | | <mn>(</mn> |
| | | <msup> |
| | | <mi>D</mi> |
| | | <mrow> |
| | | <mn>2</mn> |
| | | </mrow> |
| | | </msup> |
| | | <mn>-</mn> |
| | | <msup> |
| | | <mi>d</mi> |
| | | <mrow> |
| | | <mn>2</mn> |
| | | </mrow> |
| | | </msup> |
| | | <mn>)</mn> |
| | | <msub> |
| | | <mi>p</mi> |
| | | <mrow> |
| | | <mn>2</mn> |
| | | </mrow> |
| | | </msub> |
| | | <mo data-mjx-texclass="CLOSE">]</mo> |
| | | <msub> |
| | | <mi>η</mi> |
| | | <mrow> |
| | | <mi>m</mi> |
| | | </mrow> |
| | | </msub> |
| | | <mn>=</mn> |
| | | <mo data-mjx-texclass="OPEN">[</mo> |
| | | <mfrac> |
| | | <mn>π</mn> |
| | | <mn>4</mn> |
| | | </mfrac> |
| | | <msup> |
| | | <mi>D</mi> |
| | | <mrow> |
| | | <mn>2</mn> |
| | | </mrow> |
| | | </msup> |
| | | <mn>(</mn> |
| | | <msub> |
| | | <mi>p</mi> |
| | | <mrow> |
| | | <mn>1</mn> |
| | | </mrow> |
| | | </msub> |
| | | <mn>-</mn> |
| | | <msub> |
| | | <mi>p</mi> |
| | | <mrow> |
| | | <mn>2</mn> |
| | | </mrow> |
| | | </msub> |
| | | <mn>)</mn> |
| | | <mn>=</mn> |
| | | <mfrac> |
| | | <mn>π</mn> |
| | | <mn>4</mn> |
| | | </mfrac> |
| | | <msup> |
| | | <mi>D</mi> |
| | | <mrow> |
| | | <mn>2</mn> |
| | | </mrow> |
| | | </msup> |
| | | <msub> |
| | | <mi>p</mi> |
| | | <mrow> |
| | | <mn>2</mn> |
| | | </mrow> |
| | | </msub> |
| | | <mo data-mjx-texclass="CLOSE">]</mo> |
| | | <msub> |
| | | <mi>η</mi> |
| | | <mi>m</mi> |
| | | </msub> |
| | | <mn>(</mn> |
| | | <mn>N</mn> |
| | | <mn>)</mn> |
| | | </math></p> |
| | | <p class="right-info">(5.4)</p> |
| | | <p class="content"> |
| | | 当在有杆腔进油且无杆腔回油时(图5.2(b)),活塞的运动速度<math display="0"> |
| | | <msub> |
| | | <mi>v</mi> |
| | | <mrow> |
| | | <mi>2</mi> |
| | | </mrow> |
| | | </msub> |
| | | </math>和推力<math display="0"> |
| | | <msub> |
| | | <mi>F</mi> |
| | | <mrow> |
| | | <mi>2</mi> |
| | | </mrow> |
| | | </msub> |
| | | </math>分别为 |
| | | </p> |
| | | <p class="center mb-10 mt-10"><math display="0"> |
| | | <msub> |
| | | <mi>v</mi> |
| | | <mrow> |
| | | <mo>2</mo> |
| | | </mrow> |
| | | </msub> |
| | | <mn>=</mn> |
| | | <mfrac> |
| | | <mi>q</mi> |
| | | <mrow> |
| | | <msub> |
| | | <mi>A</mi> |
| | | <mrow> |
| | | <mo>2</mo> |
| | | </mrow> |
| | | </msub> |
| | | </mrow> |
| | | </mfrac> |
| | | <msub> |
| | | <mi>η</mi> |
| | | <mrow> |
| | | <mn>v</mn> |
| | | </mrow> |
| | | </msub> |
| | | <mn>=</mn> |
| | | <mfrac> |
| | | <mrow> |
| | | <mn>4</mn> |
| | | <mi>q</mi> |
| | | </mrow> |
| | | <mrow> |
| | | <mn>π</mn> |
| | | <mn>(</mn> |
| | | <msup> |
| | | <mi>D</mi> |
| | | <mrow> |
| | | <mo>2</mo> |
| | | </mrow> |
| | | </msup> |
| | | <mn>-</mn> |
| | | <msup> |
| | | <mi>d</mi> |
| | | <mrow> |
| | | <mo>2</mo> |
| | | </mrow> |
| | | </msup> |
| | | <mn>)</mn> |
| | | </mrow> |
| | | </mfrac> |
| | | <msub> |
| | | <mi>η</mi> |
| | | <mrow> |
| | | <mn>v</mn> |
| | | </mrow> |
| | | </msub> |
| | | <mn>(</mn> |
| | | <mn>m</mn> |
| | | <mn>/</mn> |
| | | <mn>s</mn> |
| | | <mn>)</mn> |
| | | </math></p> |
| | | <p class="right-info">(5.5)</p> |
| | | <p class="center mb-10 mt-10"><math display="0"> |
| | | <msub> |
| | | <mi>F</mi> |
| | | <mrow> |
| | | <mn>2</mn> |
| | | </mrow> |
| | | </msub> |
| | | <mn>=</mn> |
| | | <mn>(</mn> |
| | | <msub> |
| | | <mi>p</mi> |
| | | <mrow> |
| | | <mn>1</mn> |
| | | </mrow> |
| | | </msub> |
| | | <msub> |
| | | <mi>A</mi> |
| | | <mrow> |
| | | <mn>2</mn> |
| | | </mrow> |
| | | </msub> |
| | | <mn>-</mn> |
| | | <msub> |
| | | <mi>p</mi> |
| | | <mrow> |
| | | <mn>2</mn> |
| | | </mrow> |
| | | </msub> |
| | | <msub> |
| | | <mi>A</mi> |
| | | <mrow> |
| | | <mn>1</mn> |
| | | </mrow> |
| | | </msub> |
| | | <mn>)</mn> |
| | | <msub> |
| | | <mi>η</mi> |
| | | <mrow> |
| | | <mi>m</mi> |
| | | </mrow> |
| | | </msub> |
| | | <mn>=</mn> |
| | | <mo data-mjx-texclass="OPEN">[</mo> |
| | | <mfrac> |
| | | <mn>π</mn> |
| | | <mn>4</mn> |
| | | </mfrac> |
| | | <mn>(</mn> |
| | | <msup> |
| | | <mi>D</mi> |
| | | <mrow> |
| | | <mn>2</mn> |
| | | </mrow> |
| | | </msup> |
| | | <mn>-</mn> |
| | | <msup> |
| | | <mi>d</mi> |
| | | <mrow> |
| | | <mn>2</mn> |
| | | </mrow> |
| | | </msup> |
| | | <mn>)</mn> |
| | | <msub> |
| | | <mi>p</mi> |
| | | <mrow> |
| | | <mn>1</mn> |
| | | </mrow> |
| | | </msub> |
| | | <mn>-</mn> |
| | | <mfrac> |
| | | <mn>π</mn> |
| | | <mn>4</mn> |
| | | </mfrac> |
| | | <msup> |
| | | <mi>D</mi> |
| | | <mrow> |
| | | <mn>2</mn> |
| | | </mrow> |
| | | </msup> |
| | | <msub> |
| | | <mi>p</mi> |
| | | <mrow> |
| | | <mn>2</mn> |
| | | </mrow> |
| | | </msub> |
| | | <mo data-mjx-texclass="CLOSE">]</mo> |
| | | <msub> |
| | | <mi>η</mi> |
| | | <mrow> |
| | | <mi>m</mi> |
| | | </mrow> |
| | | </msub> |
| | | <mn>=</mn> |
| | | <mo data-mjx-texclass="OPEN">[</mo> |
| | | <mfrac> |
| | | <mn>π</mn> |
| | | <mn>4</mn> |
| | | </mfrac> |
| | | <msup> |
| | | <mi>D</mi> |
| | | <mrow> |
| | | <mn>2</mn> |
| | | </mrow> |
| | | </msup> |
| | | <mn>(</mn> |
| | | <msub> |
| | | <mi>p</mi> |
| | | <mrow> |
| | | <mn>1</mn> |
| | | </mrow> |
| | | </msub> |
| | | <mn>-</mn> |
| | | <msub> |
| | | <mi>p</mi> |
| | | <mrow> |
| | | <mn>2</mn> |
| | | </mrow> |
| | | </msub> |
| | | <mn>)</mn> |
| | | <mn>=</mn> |
| | | <mfrac> |
| | | <mn>π</mn> |
| | | <mn>4</mn> |
| | | </mfrac> |
| | | <msup> |
| | | <mi>d</mi> |
| | | <mrow> |
| | | <mn>2</mn> |
| | | </mrow> |
| | | </msup> |
| | | <msub> |
| | | <mi>p</mi> |
| | | <mrow> |
| | | <mn>1</mn> |
| | | </mrow> |
| | | </msub> |
| | | <mo data-mjx-texclass="CLOSE">]</mo> |
| | | <msub> |
| | | <mi>η</mi> |
| | | <mi>m</mi> |
| | | </msub> |
| | | <mn>(</mn> |
| | | <mn>N</mn> |
| | | <mn>)</mn> |
| | | </math></p> |
| | | <p class="right-info">(5.6)</p> |
| | | <p class="left"> |
| | | 式中 <math display="0"> |
| | | <msub> |
| | | <mi>q</mi> |
| | | </msub> |
| | | </math>——进入液压缸的流量(m<span class="super">3</span>/s); |
| | | </p> |
| | | </div> |
| | | |
| | | </div> |
| | | </div> |
| | | </div> |
| | |
| | | <li class="headerText">液 压 传 动</li> |
| | | </ul> |
| | | <div class="bodystyle"> |
| | | <p class="content"> A<span class="sub">1</span>——无杆腔的活塞有效作用面积(m<span class="super">2</span>);</p> |
| | | <p class="content"> D——活塞直径(即缸筒直径)(m);</p> |
| | | <p class="content"> η<span class="sub">V</span>——液压缸的容积效率;</p> |
| | | <p class="content"> p<span class="sub">1</span>——进油压力(Pa);</p> |
| | | <p class="content"> p<span class="sub">2</span>——回油压力(Pa);</p> |
| | | <p class="content"> A<span class="sub">2</span>——有杆腔的活塞有效作用面积(m<span class="super">2</span>);</p> |
| | | <p class="content td-3"> |
| | | <math display="0"> |
| | | <msub> |
| | | <mi>A</mi> |
| | | <mrow> |
| | | <mi>1</mi> |
| | | </mrow> |
| | | </msub> |
| | | </math>——无杆腔的活塞有效作用面积(m<span class="super">2</span>); |
| | | </p> |
| | | <p class="content"><math display="0"> |
| | | <msub> |
| | | <mi>D</mi> |
| | | </msub> |
| | | </math>——活塞直径(即缸筒直径)(m);</p> |
| | | <p class="content"> |
| | | <math display="0"> |
| | | <msub> |
| | | <mi>η</mi> |
| | | <mrow> |
| | | <mi>v</mi> |
| | | </mrow> |
| | | </msub> |
| | | </math>——液压缸的容积效率; |
| | | </p> |
| | | <p class="content"> <math display="0"> |
| | | <msub> |
| | | <mi>p</mi> |
| | | <mrow> |
| | | <mi>1</mi> |
| | | </mrow> |
| | | </msub> |
| | | </math>——进油压力(Pa);</p> |
| | | <p class="content"> <math display="0"> |
| | | <msub> |
| | | <mi>p</mi> |
| | | <mrow> |
| | | <mi>2</mi> |
| | | </mrow> |
| | | </msub> |
| | | </math>——回油压力(Pa);</p> |
| | | <p class="content"> |
| | | A<span class="sub">2</span>——有杆腔的活塞有效作用面积(m<span class="super">2</span>); |
| | | </p> |
| | | <p class="content"> d——活塞杆直径(m);</p> |
| | | <p class="content"> η<span class="sub">m</span>——液压缸的机械效率。</p> |
| | | <p class="content"> |
| | | η<span class="sub">m</span>——液压缸的机械效率。 |
| | | </p> |
| | | <div class="fl jc-sb al-fe openImgBox"> |
| | | <div> |
| | | <img class="w80" src="../../assets//images/Figure-0003-01-01.png" alt=""> |
| | | <img class="w80" src="../../assets//images/Figure-0003-01-01.png" alt="" /> |
| | | </div> |
| | | <div> |
| | | <img class="w80" src="../../assets//images/Figure-0003-01-02.png" alt=""> |
| | | <img class="w80" src="../../assets//images/Figure-0003-01-02.png" alt="" /> |
| | | </div> |
| | | <div> |
| | | <img class="w80" src="../../assets//images/Figure-0003-01-03.png" alt=""> |
| | | <img class="w80" src="../../assets//images/Figure-0003-01-03.png" alt="" /> |
| | | </div> |
| | | </div> |
| | | <!-- 轮播图 --> |
| | |
| | | <div class="swiper-button-prev"></div> |
| | | </div> |
| | | </div> |
| | | <p class="img"> |
| | | 图5.2 双作用单杆活塞式液压缸图形符号和实物图 |
| | | </p> |
| | | <p class="content">比较上述各式,由于面积A<span class="sub">1</span>>A<span class="sub">2</span>,所以速度v<span |
| | | <p class="img">图5.2 双作用单杆活塞式液压缸图形符号和实物图</p> |
| | | <p class="content"> |
| | | 比较上述各式,由于面积A<span class="sub">1</span>>A<span class="sub">2</span>,所以速度v<span |
| | | class="sub">1</span><v<span class="sub">2</span>,输出力F<span class="sub">1</span>>F<span |
| | | class="sub">2</span>。</p> |
| | | <p class="content">由式(5.3)和式(5.5)得液压缸往复运动时的速度比为</p> |
| | | class="sub">2</span>。 |
| | | </p> |
| | | <p class="content"> |
| | | 由式(5.3)和式(5.5)得液压缸往复运动时的速度比为 |
| | | </p> |
| | | <div class="img-rights w200"> |
| | | <img src="../../assets/images/Figure-0003-03.jpg" alt=""> |
| | | <img src="../../assets/images/Figure-0003-03.jpg" alt="" /> |
| | | <p class="img">图5.3 差动连接液压缸连接方式</p> |
| | | </div> |
| | | <span> |
| | | <p class="content">式(5.7)表明,当活塞杆直径愈小时,两腔分别进液压油,活塞的运动速度比愈接近于1,在两个方向上的速度差值就愈小。</p> |
| | | <p class="content"> |
| | | 式(5.7)表明,当活塞杆直径愈小时,两腔分别进液压油,活塞的运动速度比愈接近于1,在两个方向上的速度差值就愈小。 |
| | | </p> |
| | | <p class="content"> |
| | | 当单杆活塞式液压缸两腔同时通入液压油时,如图5.3所示,由于无杆腔受力面积大于有杆腔的受力面积,使得活塞向右的作用力大于向左的作用力,因此活塞杆做伸出运动,并将有杆腔的液压油挤出,流进无杆腔,加快了活塞杆的伸出速度,单杆活塞式液压缸的这种连接方式称为差动连接。 |
| | | </p> |
| | | </span> |
| | | <p class="content">当单杆活塞式液压缸差动连接时,有杆腔排出流量q′=v<span class="sub">3</span>A<span |
| | | class="sub">2</span>进入无杆腔,根据流量连接性方程,则有</p> |
| | | <p class="center">v<span class="sub">3</span>A<span class="sub">1</span>=q+v<span |
| | | class="sub">3</span>A<span class="sub">2</span></p> |
| | | <p class="content">在考虑了液压缸的容积效率η<span class="sub">V</span>(注意:这里仅有外泄漏)后,活塞杆的伸出速度v<span |
| | | class="sub">3</span>为</p> |
| | | <p class="content"> |
| | | 当单杆活塞式液压缸差动连接时,有杆腔排出流量q′=v<span class="sub">3</span>A<span |
| | | class="sub">2</span>进入无杆腔,根据流量连接性方程,则有 |
| | | </p> |
| | | <p class="center"> |
| | | v<span class="sub">3</span>A<span class="sub">1</span>=q+v<span class="sub">3</span>A<span |
| | | class="sub">2</span> |
| | | </p> |
| | | <p class="content"> |
| | | 在考虑了液压缸的容积效率η<span class="sub">V</span>(注意:这里仅有外泄漏)后,活塞杆的伸出速度v<span class="sub">3</span>为 |
| | | </p> |
| | | |
| | | <p class="center">v<span class="sub">3</span>=<math display="0"> |
| | | <p class="center"> |
| | | v<span class="sub">3</span>=<math display="0"> |
| | | <mfrac> |
| | | <mn>q</mn> |
| | | <mn> |
| | |
| | | </msup> |
| | | </mn> |
| | | </mfrac> |
| | | </math>η<span class="sub">v</span></p> |
| | | </math>η<span class="sub">v</span> |
| | | </p> |
| | | <p class="right-info">(5.8)</p> |
| | | <p class="content">欲使差动连接液压缸的往复运动速度相等,即v<span class="sub">3</span>=v<span |
| | | <p class="content"> |
| | | 欲使差动连接液压缸的往复运动速度相等,即v<span class="sub">3</span>=v<span |
| | | class="sub">2</span>,则由式(5.5)和式(5.8)可得D=d<math display="0"> |
| | | <msqrt> |
| | | <mn>2</mn> |
| | |
| | | <li>·83·</li> |
| | | </ul> |
| | | <div class="bodystyle"> |
| | | <p class="content">单杆活塞式液压缸差动连接在忽略两腔液压油流动和其他压力损失的情况下,压力p<span class="sub">2</span>≈p<span |
| | | <p class="content"> |
| | | 单杆活塞式液压缸差动连接在忽略两腔液压油流动和其他压力损失的情况下,压力p<span class="sub">2</span>≈p<span |
| | | class="sub">1</span>,同时考虑到机械效率η<span class="sub">m</span>,这时活塞的推力F<span |
| | | class="sub">3</span>为</p> |
| | | class="sub">3</span>为 |
| | | </p> |
| | | |
| | | <p class="center">F<span class="sub">3</span>=[p<span class="sub">1</span>A<span |
| | | class="sub">1</span>-p<span class="sub">2</span>A<span class="sub">2</span>]η<span |
| | | class="sub">m</span>=[<math display="0"> |
| | | <p class="center"> |
| | | F<span class="sub">3</span>=[p<span class="sub">1</span>A<span class="sub">1</span>-p<span |
| | | class="sub">2</span>A<span class="sub">2</span>]η<span class="sub">m</span>=[<math |
| | | display="0"> |
| | | <mfrac> |
| | | <mn>π</mn> |
| | | <mn>4</mn> |
| | |
| | | <mn>π</mn> |
| | | <mn>4</mn> |
| | | </mfrac> |
| | | </math>d<span class="super">2</span>p<span class="sub">1</span>η<span class="sub">m</span></p> |
| | | </math>d<span class="super">2</span>p<span class="sub">1</span>η<span class="sub">m</span> |
| | | </p> |
| | | <p class="right-info">(5.9)</p> |
| | | |
| | | <p class="content"> |
| | | 由式(5.8)和式(5.9)可知,单杆活塞式液压缸差动连接时液压缸实际的有效作用面积是活塞杆的横截面积。与非差动连接的单杆活塞式液压缸无杆腔进油工况相比,在输入液压油压力和流量都不变的条件下,活塞杆伸出速度较大而推力较小。实际应用中,液压传动系统常通过控制阀来改变单杆活塞缸的油路连接,使它有不同的工作方式,从而获得快进(差动连接)→工进(无杆腔进油)→快退(有杆腔进油)的工作循环。差动连接是在不增大液压泵规格和功率的情况下,实现系统快速运动的有效方法。它的应用常见于组合机床和各类专用机床中。 |
| | | </p> |
| | | <p class="content">单杆活塞式液压缸往复运动范围是有效行程l的2倍,其结构紧凑,应用广泛。</p> |
| | | <p class="content"><span class="bold">【例5.2】</span> 已知单杆活塞式液压缸的缸筒内径D=100 mm,活塞杆直径d=70 |
| | | mm,进入液压缸的流量q=25 L/min,压力p<span class="sub">1</span>=2 MPa,非差动连接时,p<span |
| | | <p class="content"> |
| | | 单杆活塞式液压缸往复运动范围是有效行程l的2倍,其结构紧凑,应用广泛。 |
| | | </p> |
| | | <p class="content"> |
| | | <span class="bold">【例5.2】</span> 已知单杆活塞式液压缸的缸筒内径D=100 mm,活塞杆直径d=70 |
| | | mm,进入液压缸的流量q=25 L/min,压力p<span class="sub">1</span>=2 |
| | | MPa,非差动连接时,p<span |
| | | class="sub">2</span>=0。如果不考虑损失(容积效率和机械效率为1),求如图5.2(a)、(b)和图5.3所示的活塞杆固定的三种情况下,液压缸可推动的负载和运动速度各是多少?并给出运动方向。 |
| | | <span class="btn-box" @click="showAnswerTwo = !showAnswerTwo" title="查看答案"> |
| | | <svg xmlns="http://www.w3.org/2000/svg" width="20.501" height="20.501" |
| | |
| | | </span> |
| | | </p> |
| | | <div v-if="showAnswerTwo"> |
| | | <p class="content"><span class="bold">解</span> (1)在图5.2(a)中的液压缸无杆腔进压力油,回油腔压力p<span |
| | | class="sub">2</span>为0。</p> |
| | | <p class="content"> |
| | | <span class="bold">解</span> (1)在图5.2(a)中的液压缸无杆腔进压力油,回油腔压力p<span class="sub">2</span>为0。 |
| | | </p> |
| | | <p class="content">根据公式(5.4),可得推动的负载为</p> |
| | | |
| | | |
| | | |
| | | |
| | | <p class="content">根据公式(5.3),可得缸筒的运动速度为</p> |
| | | <p class="content">答:液压缸可推动的负载是15 700 N,运动速度是0.053 m/s,这时缸筒运动方向向左。</p> |
| | | <p class="content">(2)图5.2(b)中的液压缸为有杆腔进压力油,回油腔压力p<span class="sub">2</span>为0。根据公式(5.6),可得推动的负载为 |
| | | <p class="content"> |
| | | 答:液压缸可推动的负载是15 700 N,运动速度是0.053 |
| | | m/s,这时缸筒运动方向向左。 |
| | | </p> |
| | | <p class="content"> |
| | | (2)图5.2(b)中的液压缸为有杆腔进压力油,回油腔压力p<span class="sub">2</span>为0。根据公式(5.6),可得推动的负载为 |
| | | </p> |
| | | <p class="content">根据公式(5.5),可得缸筒的运动速度为</p> |
| | | <p class="content">答:液压缸可推动的负载是8 007 N,运动速度是0.104 m/s,这时缸筒运动方向向右。</p> |
| | | <p class="content">(3)图5.3中的液压缸为差动连接,根据公式(5.9),可得推动的负载为</p> |
| | | |
| | | <p class="content"> |
| | | 答:液压缸可推动的负载是8 007 N,运动速度是0.104 |
| | | m/s,这时缸筒运动方向向右。 |
| | | </p> |
| | | <p class="content"> |
| | | (3)图5.3中的液压缸为差动连接,根据公式(5.9),可得推动的负载为 |
| | | </p> |
| | | </div> |
| | | </div> |
| | | </div> |
| | |
| | | <div class="bodystyle"> |
| | | <div v-if="showAnswerTwo"> |
| | | <p class="content">根据公式(5.8),可得缸筒的运动速度为</p> |
| | | <p class="content">答:液压缸可推动的负载是7 693 N,运动速度是0.108 m/s,这时缸筒运动方向向左。</p> |
| | | </div> |
| | | <p class="content"><span class="bold">【例5.3】</span> 在单出杆活塞式液压缸中,已知缸筒内径D=125 mm,活塞杆直径 d=70 |
| | | mm,液压缸大腔进油,活塞运动的速度为v=0.1 m/s,求进入液压缸的流量q<span class="sub">1</span>和排出液压缸的流量q<span |
| | | class="sub">2</span>各有多少? |
| | | <p class="content"> |
| | | 答:液压缸可推动的负载是7 693 N,运动速度是0.108 |
| | | m/s,这时缸筒运动方向向左。 |
| | | </p> |
| | | |
| | | </div> |
| | | <p class="content"> |
| | | <span class="bold">【例5.3】</span> 在单出杆活塞式液压缸中,已知缸筒内径D=125 mm,活塞杆直径 d=70 |
| | | mm,液压缸大腔进油,活塞运动的速度为v=0.1 |
| | | m/s,求进入液压缸的流量q<span class="sub">1</span>和排出液压缸的流量q<span class="sub">2</span>各有多少? |
| | | </p> |
| | | </div> |
| | | </div> |
| | | </div> |
| | |
| | | <li class="headerText">第 5 章 液  压  缸</li> |
| | | <li>·85·</li> |
| | | </ul> |
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| | | </div> |
| | | </div> |
| | | <!-- 86页 --> |
| | |
| | | <li>·86·</li> |
| | | <li class="headerText">液 压 传 动</li> |
| | | </ul> |
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| | | </div> |
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| | | <li class="headerText">第 5 章 液  压  缸</li> |
| | | <li>·87·</li> |
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| | | <!-- 88页 --> |
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| | | <li>·88·</li> |
| | | <li class="headerText">液 压 传 动</li> |
| | | </ul> |
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| | | <li class="headerText">第 5 章 液  压  缸</li> |
| | | <li>·89·</li> |
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| | | <div class="bodystyle"> |
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| | | <!-- 90页 --> |
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| | | <li>·90·</li> |
| | | <li class="headerText">液 压 传 动</li> |
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| | | <!-- 91页 --> |
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| | | <li class="headerText">第 5 章 液  压  缸</li> |
| | | <li>·91·</li> |
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| | | <div class="bodystyle"> |
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| | | </div> |
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| | | <!-- 92页 --> |
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| | | <li>·92·</li> |
| | | <li class="headerText">液 压 传 动</li> |
| | | </ul> |
| | | <div class="bodystyle"> |
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| | | <!-- 93页 --> |
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| | | <li class="headerText">第 5 章 液  压  缸</li> |
| | | <li>·93·</li> |
| | | </ul> |
| | | <div class="bodystyle"> |
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| | | <div class="bodystyle"></div> |
| | | </div> |
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| | | <!-- 94页 --> |
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| | | <li>·94·</li> |
| | | <li class="headerText">液 压 传 动</li> |
| | | </ul> |
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| | | <li class="headerText">第 5 章 液  压  缸</li> |
| | | <li>·95·</li> |
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| | | <li>·96·</li> |
| | | <li class="headerText">液 压 传 动</li> |
| | | </ul> |
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| | | <li class="headerText">第 5 章 液  压  缸</li> |
| | | <li>·97·</li> |
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