直動式減壓閥設計.docx

浙江大學2011-2012學年秋冬學期氣動電子技術課程設計題 目 直動式減壓閥特性曲線分析 姓名與學號 林嘉穎 3090100768 指導教師 陶國良 年級與專業(yè) 機械電子工程0902 所在學院 機械工程學系 一 主要參數(shù)及工作原理如圖,直動式減壓閥由主閥芯1,膜片2,彈簧3,調(diào)節(jié)手柄4,主閥體5組成.其中P1為氣源壓力P2為減壓輸出壓力Fs彈簧預緊壓力A為膜片的面積。當P2*Fs時，主閥芯上移，主閥口關閉，使P2逐漸下降。如果是卸壓型直動式減壓器，在主閥芯和彈簧之間(3)裝上小型溢流閥，當P2*AFs時，膜片上移，頂開活塞，氣體便從膜片上方溢流出去。二 方案設計根據(jù)相關參數(shù)使用solidworks對減壓閥進行尺寸設計,再使用matlab及excel對數(shù)據(jù)進行仿真與分析.根據(jù)相關資料，使用solidworks設計尺寸如下：進氣口直徑D1=20mm出氣口直徑D2=20mm 溢流口工作直徑d1=11mm d2=14mm膜片接觸面積設計 Error! Main Document Only.膜片與出氣缸中氣體接觸面積的直徑 d=80mm主閥芯下表面圓直徑為d3=21mm，閥體直徑為d4=20mm。主閥芯直徑為d5=8mm。溢流口設計 Error! Main Document Only.如下表，選擇進口壓力最高1.6MPa，則出口壓力為0.11.0MPa設彈簧最大伸長量為12mm（P1小于特定壓力時，主閥芯全開，此時8mm處恰好在交界口處。當P1大于特定壓力時，理想狀態(tài)是P2保持不變。主閥芯恰好封緊，上升12mm）彈簧彈性系數(shù)k將在后續(xù)中求得。氣體設為標準狀態(tài)。溫度273.15K（0），壓力101.325KPaR=8.314410.00026J/(molK）。空氣密度為=1.293kg/m3三 特性曲線3.1 流量特性曲線理想特性曲線如下：減壓閥理想特性曲線 1受力分析：在流量不變時，以膜和主閥芯為分析對象向上的力：P1對主閥芯的力,P對主閥芯的摩擦力.P2對膜的力.(此處壓力均為相對壓力)向下的力:主要為彈簧對膜的壓力.理想狀況下，忽略摩擦力,則有力的平衡方程:P1*d424+P2*(d2-d12)4=k(-x+x0)+ P2*d42420由于主閥芯尾部有一定的錐度，若以與閥體平行線為分界線（如圖）設在p1=p2=0時楔形口處于下方，邊沿與開口平齊，當p1=p2=1.0MPa時，楔形口與開口接觸。此時x=-x+x0=12mm代入P1*d424+P2*(d2-d12)4=k(x)+ P2*(d42-d12)4; d6=(8+x)mm得彈性系數(shù)k=418.879KN/m取k=420KN/m若設分界線以上壓強為P2，分界線以下為P1，為簡化計算過程,設P1的作用力一直為直徑20mm的圓力的平衡方程修正如下：P1*d424+P2*(d2-d12)4=k(x)+ P2*(d42-d12)4P2=kx-P1*d424d2-d124-(d42-d12)4=4*420x-P1*202(802-202)MPax0,12mm當P2P10.5283時流量為：Q=SeP12kk-1*1RT1(P2P1)2k-(P2P1)k+1k k=1.4；P2P10.5283時，Q=SeP1kRT1(1k+1)k+1k-1;Se為截面有效面積，Se=202-8+x24*10-6m2; x0,12mm；由理想狀態(tài)的減壓特性曲線得：當p10.5283。P1=0.5MPa時，首先對P2=kx-P1*d624d2-d124-(d62-d12)4=4*420x*106-P1*8+x2802-8+x2求反函數(shù)。Matlab求反函數(shù)如下： p1=0.5p1 = 0.5000 syms x p2=(4*420*x-p1*pi*(8+12)2)/(pi*802-pi*(8+12)2) p2 = -(200*pi - 1680*x)/(6000*pi) deltax=finverse(p2) deltax = (25*pi*(x + 1/30)/7 其中上式的deltax為x，x為P2。代入Se中，得： Se=pi*(400-(8+deltax)2 )/4 Se = -(pi*(25*pi*(x + 1/30)/7 + 8)2 - 400)/4 其中的x仍為P2,單位為MPa。Se單位為mm2再通過Q=SeP12kk-1*1RT1(P2P1)2k-(P2P1)k+1k k=1.4；求Q. k=1.4; R=8.31441; T=273.15;Q=(2*k/(k-1)*R*T)*(x/p1 )(2/k)-(x/p1 )(k+1)/k)(1/2)*Se*p1 Q = -(pi*(3553572156649665*(2*x)(10/7)/1152921504606846976 - (3553572156649665*(2*x)(12/7)/1152921504606846976)(1/2)*(25*pi*(x + 1/30)/7 + 8)2 - 400)/8由于用matlab不能求出Q的反函數(shù),因此應用插值的方法,以彈簧伸長量為中間變量,從而求出Q和P2的關系,通過EXCEL來進行插值法描點.設P1=0.5MPa時,編寫如下兩段matlab程序:for i=5.9:0.01:6 p1=0.5; p2=(4*420*i-p1*pi*(8+12)2)/(pi*802-pi*(8+12)2); x=p2; Q =-(pi*(3553572156649665*(2*x)(10/7)/1152921504606846976 - (3553572156649665*(2*x)(12/7)/1152921504606846976)(1/2)*(25*pi*(x + 1/30)/7 + 8)2 - 400)/8; fprintf(%12.8fn,Q)fprintf(%12.8fn,x)endfor i=4:0.1:5.9 p1=0.5; p2=(4*420*i-p1*pi*(8+12)2)/(pi*802-pi*(8+12)2); x=p2; Q =-(pi*(3553572156649665*(2*x)(10/7)/1152921504606846976 - (3553572156649665*(2*x)(12/7)/1152921504606846976)(1/2)*(25*pi*(x + 1/30)/7 + 8)2 - 400)/8; fprintf(%12.8fn,Q)fprintf(%12.8fn,x)end經(jīng)過整理得 流量Q出口壓力P2流量Q出口壓力P2流量Q出口壓力P21.399171660.323173741.016028240.41230050.274414650.493405871.371048210.332086420.963251250.42121320.255099490.494297131.340798750.340999090.906919050.43012590.234228780.49518841.308401170.349911770.846504870.43903850.211342810.496079671.273820390.358824450.78125760.44795120.185698670.496970941.237005880.367737120.710057620.45686390.15594240.49786221.197888230.37664980.631127220.46577660.119030040.498753471.156374670.385562480.541362410.47468930.063518630.499644741.112342690.394475150.434421170.483601900.500536011.065631290.403387830.292482130.492514600.50142728用excel得圖線為: 同理,分別計算當入口壓力P1=0.8MPa,1MPa,0.2MPa時的曲線，（其中Q的特性曲線因為P1的變化而變化，需要通過以下程序段計算每一次Q的函數(shù)式：p1=0.2; syms x p2=(4*420*x-p1*pi*(8+12)2)/(pi*802-pi*(8+12)2); deltax=finverse(p2); Se=pi*(400-(8+deltax)2 )/4; R=8.31441;k=1.4;T=273.15; Q=(2*k/(k-1)*R*T)*(x/p1 )(2/k)-(x/p1 )(k+1)/k)(1/2)*Se*p1P1=0.5MPAP1=0.8MPAP1=1MPAP1=0.2MPA流量Q出口壓力P2流量Q出口壓力P2流量Q出口壓力P2流量Q出口壓力P21.399171660.323173741.392936630.583923061.399272750.68196250.7075010.100535231.371048210.332086421.371927060.58837941.376947020.686418840.7064020.104991571.340798750.340999091.350740060.592835741.354535850.690875180.7037520.109447911.308401170.349911771.329378580.597292071.332044050.695331520.6995520.113904241.273820390.358824451.307845470.601748411.309476480.699787860.6937950.118360581.237005880.367737121.286143510.606204751.286838080.70424420.6864650.122816921.197888230.37664981.264275380.610661091.264133810.708700530.6775320.127273261.156374670.385562481.242243650.615117431.241368710.713156870.6669590.13172961.112342690.394475151.220050770.619573771.218547860.717613210.6546910.136185941.065631290.403387831.197699060.62403011.195676420.722069550.6406590.140642271.016028240.412300511.175190690.628486441.172759620.726525890.6247730.145098610.963251250.421213181.152527690.632942781.149802730.730982230.6069180.149554950.906919050.430125861.129711890.637399121.126811110.735438560.5869480.154011290.846504870.439038541.10674490.641855461.103790210.73989490.5646730.158467630.78125760.447951211.083628150.64631181.080745520.744351240.5398420.162923970.710057620.456863891.060362760.650768131.057682650.748807580.5121250.16738030.631127220.465776571.036949610.655224471.034607270.753263920.4810640.171836640.541362410.474689251.013389210.659680811.011525150.757720260.4460080.176292980.434421170.483601920.989681720.664137150.988442140.76217660.4059730.180749320.292482130.49251460.965826880.668593490.965364220.766632930.3593580.185205660.274414650.493405870.941823940.673049830.942297430.771089270.3032110.1896620.255099490.494297130.917671580.677506170.919247940.775545610.2307670.194118330.234228780.49518840.893367860.68196250.896222040.780001950.1145860.198574670.211342810.496079670.868910090.686418840.873226120.7844582900.203031010.185698670.496970940.844294720.690875180.85026670.7889146300.207487350.15594240.49786220.819517210.695331520.827350440.793370960.119030040.498753470.794571840.699787860.804484120.79782730.063518630.499644740.76945150.70424420.781674680.8022836400.500536010.744147440.708700530.758929210.8067399800.501427280.718648960.713156870.736254940.811196320.6929430.717613210.71365930.815652660.667013650.722069550.691149880.820108990.64084150.726525890.668734460.824565330.614402830.730982230.646421030.829021670.587668530.735438560.624217780.833478010.560602690.73989490.602133140.837934350.533160610.744351240.580175770.842390690.505286210.748807580.558354590.846847020.476908140.753263920.53667880.851303360.447934390.757720260.515157890.85575970.418243920.76217660.493801650.860216040.387673750.766632930.472620230.864672380.355997720.771089270.451624140.869128720.322889340.775545610.430824250.873585060.287851660.780001950.41023190.878041390.250069310.784458290.389858860.882497730.208042810.788914630.369717410.886954070.158413990.793370960.349820370.891410410.089264020.79782730.330181160.8958667500.802283640.310813850.9003230900.806739980.291733250.9047794200.811196320.272954960.9092357600.815652660.254495470.913692100.820108990.236372270.9181484400.824565330.2186040.9226047800.829021670.201210520.9270611200.833478010.184213210.9315174500.837934350.167635070.935973790.151501060.940430130.13583840.944886470.120677030.949342810.106050090.953799150.091994680.958255480.07855280.962711820.065772650.967168160.053710540.97162450.042433670.976080840.032024560.980537180.02258840.984993520.014266650.989449850.007264640.993906193.2 壓力特性曲線由上述公式，約去中間變量x，matlab公式為：syms p1 syms p2 deltax=pi*(75*p2-5*p1)/21; Se=pi*(400-(8+deltax)2 )/4; R=8.31441;k=1.4;T=273.15; Q=(2*k/(k-1)*R*T)*(p2/p1 )(2/k)-(p2/p1 )(k+1)/k)(1/2)*Se*p1Q = -(pi*p1*(3553572156649665*(p2/p1)(10/7)/1152921504606846976 - (3553572156649665*(p2/p1)(12/7)/1152921504606846976)(1/2)*(pi*(5*p1 - 75*p2)/21 - 8)2 - 400)/4由于Q=SeP12kk-1*1RT1(P2P1)2k-(P2P1)k+1k過于復雜，直接用matlab解不出P2的值。由理想特性曲線及老師上課筆記得P2P11.設P2P1=0.85，代入上式，得Q的簡化表達式。因此由matlab算法，設Q=1dm3/s,有 p2=solve(1=-(pi*p1*(3553572156649665*(0.85)(10/7)/1152921504606846976 - (3553572156649665*(0.85)(12/7)/1152921504606846976)(1/2)*(pi*(5*p1 - 75*x)/21 - 8)2 - 400)/4) p2 = (1.0*10(-67)*(4.8026710038503888982870641436426*1066*(- 4.6588965684808449721090220054471*10(-34)*p14 + 9.9655774465618838997905594373673*10(-33)*p13 + 13.775603498253215348712157917925*p12 - 4.164349376412757690974805339266*p1)(1/2) - 7.1301414505169110424459925990886*1066*p1 + 6.6666666666666666666666666666667*1065*p12)/p1 -(1.0*10(-67)*(7.1301414505169110424459925990886*1066*p1 + 4.8026710038503888982870641436426*1066*(- 4.6588965684808449721090220054471*10(-34)*p14 + 9.9655774465618838997905594373673*10(-33)*p13 + 13.775603498253215348712157917925*p12 - 4.164349376412757690974805339266*p1)(1/2) - 6.6666666666666666666666666666667*1065*p12)/p1 對結果進行簡化： p=simplify(p2) p = 0.066666666666666666666666666666667*p1 + (0.48026710038503888982870641436426*(- 4.6588965684808449721090220054471*10(-34)*p14 + 9.9655774465618838997905594373673*10(-33)*p13 + 13.775603498253215348712157917925*p12 - 4.164349376412757690974805339266*p1)(1/2)/p1 - 0.71301414505169110424459925990886 0.066666666666666666666666666666667*p1 - (0.48026710038503888982870641436426*(- 4.6588965684808449721090220054471*10(-34)*p14 + 9.9655774465618838997905594373673*10(-33)*p13 + 13.775603498253215348712157917925*p12 - 4.164349376412757690974805339266*p1)(1/2)/p1 - 0.71301414505169110424459925990886取P20的值，得出P2與P1的關系for p1=0.4:0.05:2 p2=0.066666666666666666666666666666667*p1 + (0.48026710038503888982870641436426*(- 4.6588965684808449721090220054471*10(-34)*p14 + 9.9655774465618838997905594373673*10(-33)*p13 + 13.775603498253215348712157917925*p12 - 4.164349376412757690974805339266*p1)(1/2)/p1 - 0.71301414505169110424459925990886;fprintf(%12.8fn,p2)end 由此得P2的值：同理，分別解出Q=0.4,0.8,1.2時P1與P2的關系，得：（單位均為MPa）P1Q=0.4的P2Q=0.8的P2Q=1.2的P2Q=1的P20.05-0.70968081-0.7096808-0.7096808-0.709680810.1-0.70634748-0.7063475-0.7063475-0.706347480.15-0.703014150.08184749-0.7030142-0.703014150.2-0.699680810.42119559-0.6996808-0.699680810.25-0.374287120.58450286-0.6963475-0.696347480.30.091847490.68420045-0.6930142-0.693014150.350.301240770.75242839-0.6896808-0.031616310.40.434528930.80257768-0.14244520.194616090.450.529345520.841329690.101847490.338216420.50.601169530.872416140.254209030.441195590.550.657928230.898092740.363710850.519899360.60.704200450.919806050.447862260.582590090.650.742847550.938527620.515282650.634039790.70.775761720.954934620.570908460.677244950.750.804249470.969513780.61783620.714200450.80.829244340.982624040.658132160.746293790.850.851432390.994535990.693239140.774523610.90.8