直动式减压阀设计.docx

浙江大学2011-2012学年秋冬学期气动电子技术课程设计题 目 直动式减压阀特性曲线分析 姓名与学号 林嘉颖 3090100768 指导教师 陶国良 年级与专业 机械电子工程0902 所在学院 机械工程学系 一 主要参数及工作原理如图,直动式减压阀由主阀芯1,膜片2,弹簧3,调节手柄4,主阀体5组成.其中P1为气源压力P2为减压输出压力Fs弹簧预紧压力A为膜片的面积。当P2*Fs时，主阀芯上移，主阀口关闭，使P2逐渐下降。如果是卸压型直动式减压器，在主阀芯和弹簧之间(3)装上小型溢流阀，当P2*AFs时，膜片上移，顶开活塞，气体便从膜片上方溢流出去。二 方案设计根据相关参数使用solidworks对减压阀进行尺寸设计,再使用matlab及excel对数据进行仿真与分析.根据相关资料，使用solidworks设计尺寸如下：进气口直径D1=20mm出气口直径D2=20mm 溢流口工作直径d1=11mm d2=14mm膜片接触面积设计 Error! Main Document Only.膜片与出气缸中气体接触面积的直径 d=80mm主阀芯下表面圆直径为d3=21mm，阀体直径为d4=20mm。主阀芯直径为d5=8mm。溢流口设计 Error! Main Document Only.如下表，选择进口压力最高1.6MPa，则出口压力为0.11.0MPa设弹簧最大伸长量为12mm（P1小于特定压力时，主阀芯全开，此时8mm处恰好在交界口处。当P1大于特定压力时，理想状态是P2保持不变。主阀芯恰好封紧，上升12mm）弹簧弹性系数k将在后续中求得。气体设为标准状态。温度273.15K（0），压力101.325KPaR=8.314410.00026J/(molK）。空气密度为=1.293kg/m3三 特性曲线3.1 流量特性曲线理想特性曲线如下：减压阀理想特性曲线 1受力分析：在流量不变时，以膜和主阀芯为分析对象向上的力：P1对主阀芯的力,P对主阀芯的摩擦力.P2对膜的力.(此处压力均为相对压力)向下的力:主要为弹簧对膜的压力.理想状况下，忽略摩擦力,则有力的平衡方程:P1*d424+P2*(d2-d12)4=k(-x+x0)+ P2*d42420由于主阀芯尾部有一定的锥度，若以与阀体平行线为分界线（如图）设在p1=p2=0时楔形口处于下方，边沿与开口平齐，当p1=p2=1.0MPa时，楔形口与开口接触。此时x=-x+x0=12mm代入P1*d424+P2*(d2-d12)4=k(x)+ P2*(d42-d12)4; d6=(8+x)mm得弹性系数k=418.879KN/m取k=420KN/m若设分界线以上压强为P2，分界线以下为P1，为简化计算过程,设P1的作用力一直为直径20mm的圆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当P2P10.5283时流量为：Q=SeP12kk-1*1RT1(P2P1)2k-(P2P1)k+1k k=1.4；P2P10.5283时，Q=SeP1kRT1(1k+1)k+1k-1;Se为截面有效面积，Se=202-8+x24*10-6m2; x0,12mm；由理想状态的减压特性曲线得：当p10.5283。P1=0.5MPa时，首先对P2=kx-P1*d624d2-d124-(d62-d12)4=4*420x*106-P1*8+x2802-8+x2求反函数。Matlab求反函数如下： 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为x，x为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仍为P2,单位为MPa。Se单位为mm2再通过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的反函数,因此应用插值的方法,以弹簧伸长量为中间变量,从而求出Q和P2的关系,通过EXCEL来进行插值法描点.设P1=0.5MPa时,编写如下两段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经过整理得 流量Q出口压力P2流量Q出口压力P2流量Q出口压力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得图线为: 同理,分别计算当入口压力P1=0.8MPa,1MPa,0.2MPa时的曲线，（其中Q的特性曲线因为P1的变化而变化，需要通过以下程序段计算每一次Q的函数式：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出口压力P2流量Q出口压力P2流量Q出口压力P2流量Q出口压力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 压力特性曲线由上述公式，约去中间变量x，matlab公式为：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过于复杂，直接用matlab解不出P2的值。由理想特性曲线及老师上课笔记得P2P11.设P2P1=0.85，代入上式，得Q的简化表达式。因此由matlab算法，设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 对结果进行简化： 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与P1的关系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，分别解出Q=0.4,0.8,1.2时P1与P2的关系，得：（单位均为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