活塞式壓縮機設計說明

1、活塞式壓縮機的設計說明姓名：班級：學號：指導老師:1.題目:復算19WY-9/150型氫氮氣壓縮機在目前操作條件下的各級壓力、排氣溫度、排氣量、功率,作出計算示功圖、切向力圖、活塞力圖、標明最大活塞力與切向力,核算配用電機功率是否適當150型氫氨氣壓縮機簡介19WY-9/150型氫氮氣壓縮機是我省投產(chǎn)3000噸小型化肥廠的氮氫氣壓縮機,二列之間為飛輪,由電機通過三角皮帶拖動.壓縮機為臥式、兩列、門型、四線壓縮.原料半水煤氣經(jīng)脫硫后進入I級,經(jīng)I級壓縮后送去變換、水洗、碳化,碳化后為碳化氣.碳化氣返回II級、III、IV級壓縮后去洗銅、合成.019WT-9/150JE縮機示意圖3.目前操作條件與

2、有關數(shù)據(jù)1操作條件：吸氣壓力：絕排氣壓力：絕I級出口與II級進口壓力差為P=吸氣溫度:級IIIIIIIVTs(C)30354040I級進口相對濕度=1(2)氣體組成組分NbH2COCOC2ArCH半水煤氣碳化氣(3)有關數(shù)據(jù)：活塞行程：S=310mm活塞桿直徑d=60mm轉(zhuǎn)速：n=209rpm,連桿長度l=700mmI、IV列超前II、III列90度往復運動件重量：IIV列210.9kg;IIIII列193.7kg級IIIIIIIV直彳全D34021013565相對余隙抽氣系數(shù)1飛輪矩GD為,配用電機額定功率：155kw.設計計算一.計算各級的行程容積.I級：&4(d2D4d2d2)S(0.3

3、4220.06520.062)0.310.05439m3II級:VS24(2D2D3)S(0.210.1352)0.310.01704m3III級：VS34(d20.00356m3IV級：d2)S71(0.13520.062)0.31VS4D2s0.06520.310.00103m計算各級名義壓力和名義壓力比0.15MPaPd416MPa21%1Ps242Ts122飛1%20.150.054393080.4867MPa0.01704303Pcl10.090.5767MPaPS3區(qū)1乂1飛3飛1乂30.150.054383130.003563032.3673MPaPd3Ps、1Ts4Ts1440

4、.150.054393138.1822MPaPd10.57670.150.001033.8453032Pd22.3673Ps20.48673Pd38.18222.3673Ps3&4Pd4168.1822Ps44.8643.4561.955三排氣溫度1.絕熱指數(shù)計算首先需算出各氣體的絕熱指數(shù),查?活塞式壓縮機?附表1常用氣體物理性質(zhì)得:各氣體絕熱指數(shù)組分N2H2CO2COO2ArCH4絕熱指數(shù)注：表中所列的氣體絕熱指數(shù)為t0：CP1.013105pa時的參數(shù),但對于理想氣體絕熱指數(shù)的大小與溫度的關系不大,顧可不考慮溫度的影響,可把k看做是常數(shù)1混合氣體的k值計算式為：-一-0對于半水煤氣來說有k

5、1kj110.210.390.120.260,0050.0045k-1-40=1+1741=I+二,*40.+140=7.168=70.0105+1.32-1k=同理對碳化氣有:10.2370.7090.0050.0290.0030005k-1-140=1+1741F+f-31二,+40.+；40+68K0.012+1.32-1k=所ki=1.3898ks=ka=k41.40612計算排氣溫度口k1k1由式TdTs哈產(chǎn)Ts尸可得Ps1.38981kl1Td1飛15H3033.845解898k21Td2Ts22k2k313Td3Ts33k31.406113084.8641.40611.40611

6、3133.4561.4061442.07K486.37K447.81Kk411.40611Td43464k3131.9551.4061379.87K級次吸氣溫度排氣溫度壓力比Ts(K)Td(K)I303II308III313IV313四第一次精度計算1各級容積系數(shù)根據(jù)?過程流體機械?表1.19491.30461.35740.86440.64570.76110.9389f1.5bar910.5(k11)Ps24.867barm210.75(k21)F323.673barm310.88(k31)Ps481.822barm4k41.4061對于理想氣體,容積系數(shù)1入v11a1(1m11)1m2入v2

7、1a2(21)1,m,、入v31oc3(31)1入v4114n1)2-1計算膨脹指數(shù)m得：10.5(1.38981)10.75(1.40611)10.88(1.40611)1入v1a(m1)11-0.065(3.8441.19491)11-0.15(4.8641.30461)11-0.16(3.4561.35741)11-0.1(1.9551.40611)C1由B2計算工況系數(shù)C和精度B入V1VS1C至獸.3Ps1Tsi因CminCmaxC1Xv1S10.86440.054390.04701ps2飛1入v2、,0.48673030.6457絲-s1-v2乂20.017040.03946ps1T

8、2N20.153080.89C3Ps3Ts1入v32.3673303Ps1ps4Ps1CminCmax0.153130.76110.003560.890.046510乂4N48.18223030.153130.93890.001030.890.057380.039460.690.970.05738精度不達標進行第一次復算1.計算各級進出口壓力由式psiPsi(1CiG計算各級壓力Ps1Ps10.15MPaPs21,2ps2(1f)C20.50.4867(10.047010.039460.5333MPaPs31,2ps3(1CiC30.52.3673(10.047010.046512.3800M

9、PaPs42ps4(1C1)c40.58.1822(10.047010.057387.4428MPaPd1Ps20.090.6233MPaPd2Ps33800MPaPd3Ps47.4428MPaPd4Pd416MPa2計算各級壓力比1Pd10.62334.155Psi0.1582Pd22.38004.4628旦20.53333Pd37.44283.1272旦32.38004Pd4162.1497Ps47.44283確定膨脹系數(shù)根據(jù)?過程流體機械?表2-1計算膨脹指數(shù)m得:旦1ml玲2m2艮3m3玲4m41.5bar10.5(k11)15. 333bar1 0.75(k21)123.800bar

10、10.88(k31)174.428bark4m41.40610.5(1.38981)0.75(1.40611)0.88(1.40611)1.19491.30461.357414計算容積系數(shù)11)入v1、v2Xv3入v411oci(&im1)11a2(e2m21)113(e3m31)11a4(e4m41)11-0.065(4.1551.194911-0.15(4.46281.304611-0.16(3.12721.357411-0.1(2.14971.40611)1)1)1)0.85090.67790.78940.92765計算工況系數(shù)C和精度BC1入vMl,C魯單處JB警psisi4CmaxC

11、i入v1%10.85090.054390.04628_ps2ISl入v20.53333030.6779_._一八C2三衛(wèi)_v420.017040.04540ps1TS2W20.153080.89cPs3Q入v32.38003030.7894C3金衛(wèi)上乂3-0.003560.048503ps11s3科30.153130.89ps41sl入v47.44283030.9276C4理之二4-0.001030.05156ps1飛4科40.153130.89CminC20.04540B-mn-0.880.97CmaxC40.05156精度/、達標進行第二次復算六第二次復算重復第一次復算步驟,列出計算結(jié)果如

12、卜表級IIIIIIIV進氣壓力psi排氣壓力pdi16壓力比容積系數(shù)vi工況常數(shù)C精度b,八修正排氣溫度Td1由式石飛(Pd)ki1TsiMk1k21Td2飛22k2k1k飛,可得1.389813034.18871.3898452.81K1.406113084.24521.4061467.62Kk31Td3飛33k3Td4k41Ts44k41.406113133.01461.4061430.48K1.406113132.32251.4061399.24K級次吸氣溫度排氣溫度壓力比Ts(K)Td(K)I303II308III313IV313九排氣量計算1 容積系數(shù)入v10.8495入v20.69

13、57入v30.7993入v40.91792 確定壓力系數(shù)對于第一級,壓力系數(shù)可取為,故取P10.97;p對于其余各級,壓力系數(shù)可取為1,故取p2p3p40.99;3 確定溫度系數(shù)根據(jù)各級壓力比,查?過程流體機械?圖2-12可得：14.1887/4.2452匕3.0146入t10.94入t20.94入t30.95442.3225入口0.954 確定泄露系數(shù)對于泄露系數(shù)的選取,有如下規(guī)那么：對于不嚴密,延遲關閉的閥門：vv0.010.04;對于單作用式氣缸的活塞環(huán)：vr0.010.05;對于雙作用式氣缸的活塞環(huán)：vr0.0030.015;對于填料vpi(0.00050.0010)j,j為級次.泄露

14、系數(shù)計算表級次IIIIIIIV氣閥IIIIIIIV活塞環(huán)IIIIIIIV填料IIIIIIIV總相對泄漏量泄露系數(shù)5綜上并且將結(jié)果列表如下級次行程容積%容積系數(shù)N壓力系數(shù)為溫度系數(shù)Ai泄露系數(shù)不轉(zhuǎn)速n(r/min)I209IIIIIIV6 計算排氣量由式qviVi%i%入i4n,并代入上表數(shù)據(jù)可得qvi8.5153m3/minqv22.2310m3/min3.qv30.5309m/minqv40.1767m3/min十計算功率并核算電機功率是否適當1計算各級指示功率和總指示功率計算相對壓力損失根據(jù)各級進排氣壓力,查?過程流體機械?圖2-14可得:ps10.15MPa,8sl6.4%;pd10.6

15、283MPa,8dl9.6%ps20.5383MPa,Ss2Ps32.2852MPa,以34.4%;pd22.2852MPa,8d26.6%ps46.889MPa,Ss42%;pd416MPa,Sd43.8%2.6%;pd36.889MPa,Sd34.8%S018sl8dl16.0%802s2d211.0%沁3叁337.4%804(5s4,d45.8%計算實際循環(huán)指示功率ni1由公式Nid卻MW4式尸1取門1-0,97klN1d嗎1600.064)0.150.84950.054391.38980.971.38980.97-11.38980.97-14.1887(10.16)1.38980.97

16、1103293.36kW2092d茄(10.044)0.53830.69571.406114.2452(10.11)1.406111030.01704248.34kWN3d20960(13.0146(10.026)2.28521.406110.074)1.40610.79930.00356N4d20960(12.3225(10.02)6.8891.406110.058)1.40611.40611.406111.40611.406111103158.69kW0.91790.001031.40611.406111103104.74kW總指示功率NdN1dN2dN3dN4d805.13kW2計算軸功

17、率取機械效率m0.88那么軸功率Nd805.13N-914.92kWrim0.883計算驅(qū)動機功率取傳動效率c0.97那么驅(qū)動機功率N914.9270.97943.22kW考慮到實際運行當中壓縮時機受到載荷波動,氣體泄漏等因素影響,會引起功率的增加,驅(qū)動機因留有515%的儲藏功率,故所選用壓縮機的功率為990.38kW-1084.70kW,取壓縮機功率為1100kW而配用電機額定功率為155kW,故不適當.十示功圖繪制示功圖及壓力指示圖是壓縮機循環(huán)過程在P-V圖上的表示,從圖中可反映出循環(huán)的功耗.在作示功圖時,可將膨脹變壓和壓縮變壓過程可看做是絕熱膨脹和壓縮過程,其體積和壓力之間存在著關系式：

18、pVkC,C為常數(shù).對于I,II,III,IV級汽缸,具相關參數(shù)列表如下:級次IIIIIIIV行程容積Vsi相對余隙容積i余隙容積VciiVsi容積系數(shù)viVs1viVsi絕熱指數(shù)kTiV1VcVsVV2于V3VcV4VcVsVs1利用Matlab畫出示功圖,圖及程序如下:第一級： x1=:; y1=; x2=:; y2=*A*x2A; x3=:;y3=;x4=:;y4=*A.*x4.A;Plot(x1,y1,x2,y2,x3,y3,x4,y4)0.807060504030201QG.01002d03004005QQ8第二級： x1=:; y1=; x2=:; y2=*A*x2A; x3=:;

19、 y3=; x4=:;y4=*A.*x4.A;Plot(x1,y1,x2,y2,x3,y3,x4,y4)24噴應010400060004O1001700U00WC01BQQ?第三級： x1=:; y1= x2=:; y2=*A*x2A;x3=:; y3=; x4=:;y4=*A.*x4.A;Plot(x1,y1,x2,y2,x3,y3,x4,y4)第四級:y1=;x2=:;y2=*A*x2A;x3=:;y3=16;x4=:;y4=16*A.*x4.A;plot(x1,y1,x2,y2,x3,y3,x4,y4)X伯十一綜合活塞力的計算綜合活塞力為活塞中的氣體力、往復慣性力和往復摩擦力的代數(shù)和1氣

20、體力計算確定蓋側(cè)面積AGi和軸側(cè)面積AziAG1AZ1AG2AZ2AG3AZ3九_2小D12九d27D2(D24D4)d2)22-(0.3420.0652)22-(0.3420.062)44.2120.03464m2d2)7(0.2120.1352)0.08747m20.08796m20.02032m2d2)-(0.135240.052)0.01149m2AG4D40.00332m24AZ40活塞運動分析活塞的位移公式為：xr(1cos)-(1.12sin2)2,活塞的加速度為：ar(coscos2)式中:1557000.2214,6022096021.89rad/s+90o其中I-IV列運動

21、的角度為,II-III列為,且以II-III列為例,那么蓋側(cè)對應于氣缸容積的活塞當量位移：xGir(1cos)(112sin2)軸側(cè)對應于氣缸容積的活塞當量位移：xZir(1cos)1(1、.12sin2)計算任意過程中的某處壓力,.一,與、k膨脹過程：PpiPd()scX吸氣過程：Pxi壓縮過程:排氣過程:PyiPpiPsPsPd其中余隙容積的當量行程I-IV列氣體力計算蓋側(cè)氣體力計算膨脹過程：AG1,Sc1Pd1(ScT-Sc4k,AG4Pd4(4)4Sc4x40.087470.62831030.0033216103(3100.0651551cos03100.13100.0654.5161

22、(1,10.04903sin2.)1.389854.957(5.6461cos0(3100.115510.13cose4.5161(1)1.406110.04903sin20)53.124.516110.04903sin0.2)1.38982e5.7161cos4.5161.10.04903sin)14061kN2吸氣過程:(AG1ps1AG4ps4)(0.087470.151030.003326.7728103)35.61kN壓縮過程:AG1Sc1Ps1#Sc1s一)AG4xiPs4(Sc4Sc4x4)k40.087470.151033100.0653100.003326.889103(31

23、00.0651551cos04.5161(13100.1310)1.389810.04903sin2.)13.12122.871(3100.11551-374.5161(11)1.406120.04903sin20)2.13(5.6461-cosl4.51611-0.04903sin2e)1.3898()5.7161cos04.516110.04903sin2.kN排氣過程：F(AG1Pd1AG4108.0774kNPd4)(0.087470.62831030.0033216103)軸側(cè)氣體力計算壓縮過程:FAZ1ps)k10.087960.15103Ps4(c4-)k4Sc4x4(3100.

24、06515513100.06531013.194(-3.3861cos94.5161(12.13)1.3898,10.04903sin2.)排氣過程:FAZ1pd1AZ455.27kN膨脹過程:FAZ1pd1(o汩Sc1cos0Pd4_)k1x10.087960.6283103(3100.065155155.27(吸氣過程FAziPsi13.19kN4.5161.10.04903sin)1.3898kN280.08796AZ4Pd4(0.6283103Sc4)k4Sc4x43100.065cos94.5161(110.04903sin%)1.38980.133.3861cos94.5161,1

25、)1.3898kN0.04903sin%AZ4ps40.087960.15103列氣體力計算AG3pd3(S.3SC3蓋側(cè)氣體力計算膨脹過程:F(Ag2Pd2(c2一)k2Sc2x2(0.034642.2852103(3100.15155(13100.15cosa4.5161(1)1.40612,10.04903sina)79.16(0.3)1.4061kN5.8161cosa4.516110.04903sin2a吸氣過程F(Ag2Ps2Ag3Ps3)0.034640.535410318.55kN壓縮過程S2skoSr3sk.F(Ag2Ps2(2產(chǎn)Ag3Ps3(3尸Sc2x2Sc3x3(0.0

26、34640.5383103(3100.15310)1.40613100.15155(1cosa4.5161(110.04903sin%)18.65(2.3)1.4061kN5.8161cosa4.5161.10.04903sin2a排氣過程：F(Ag2Pd2Ag3Pd3)0.034642.285210379.16kN軸側(cè)氣體力計算壓縮過程：FAz2Ps2(Sc2士)k2X2AZ3Ps3(Sc3Sc3sk3)3X30.020320.5383103(3100.1515513100.153102cos4.5161(1,10.04903sin2)1.4061)0.011492.2852103(3100

27、.1615513100.16310cos4.5161(1)1.40612,10.04903sin2)10.94(-3.2161cos2.304.516110.04903sin2)1.406126.262.323.1961cos24.516110.04903sin2)1.4061kN排氣過程FAZ2pd2AZ3Pd30.020322.28521030.011496.889103125.58kN膨脹過程:FAZ2pd2(空2ST-)k2X2AZ3pd3(Sc30.020322.2852103(3100.151551cos3100.150.011496.889103(3100.161551cos4.

28、5161(1.10.04903sin23100.164.5161(1)1.4061)1.406120.04903sin2)0.346,44(-3.2161cos4.5161.10,04903sin2)1.406179,14(-3.1961cos0.324.516110.04903sin2)1.4061kN吸氣過程：FAZ2ps2AZ3ps30.020320.53831030.011492.285210337.20kN2往復慣性力的計算叫1210.9kg,叫2193.7kg對I-IV列F|s1ms1r送cosO入cos26)2109Q155(20927t,cosO0.2214Gos2n60151

29、5cosO0221400sz)kN其中一階往復慣性力:I2,20927t、2.66cos0Finsira2cosO210.90.155()cosO=15二階往復慣性力：II2.F1ms1r3cos2=0.2214210.90.155(2092冗60)2cos23=cos20對II-III列FIs2ms2r/cos入cos2)1937.155(生薩)c0sQ2214cos2)1438cos02214cos2)kN階往復慣性力:f2ms1ra2cose193.70.155,2092兀2()cos60.38cos二階往復慣性力：f2Ims1r32cos2,2092兀、2=0.2214193.70.1

30、55()2cos260=cos2由于一四列超前二三列90,所以8二3+90一階往復慣性力合力：FIs=F1I+f2=門；W上二階往復慣性力合力：F2F1+f2I=cos2cos23往復摩擦力的計算1Pi(1)為壓縮機的機取Ffs0.65；40,式中Pi為第i列指示功率；m械效率；s為活塞行程,n為壓縮機轉(zhuǎn)速對I-IV列(Nid0.65一、,1N4d-刀mns/301)1(293.36104.74)(1)0.655882090.31/3016.34kN對II-III列(N2d0.651N3d)(1)4mns/30(248.340.651158.69)(-1)0.882090.31/3016.71

31、kN十二活塞力圖的繪制1)由以上的計算結(jié)果,利用matlab繪制I-IV列活塞力圖及程序如下:蓋側(cè)活塞力程序及Matlab圖：a1=0二；b1=-./(a1).*.*(sin(a1).A2).A(1./2).A+./(a1).*.*(sin(a1).A2).A(1./2)A;a2=:pi;b2=;a3=pi:;b3=-./(a3).*.*(sin(a3).A2).A(1./2).A+./(a3).*.*(sin(a3).A2).A(1./2).a;a4=:2.*pi;b4=;Plot(a1,b1,a2,b2,a3,b3,a4,b4)蓋側(cè)活塞力軸測活塞力Matlab程序及Matlab圖： a1=

32、0:;b1=./+cos(a1)+.*.*(sin(a1).A2).A.A;a2=:pi;b2=;a3=pi:;b3=./+cos(a3)+.*.*(sin(a3)A2)AA;a4=:2.*pi;b4=;Plot(a1,b1,a2,b2,a3,b3,a4,b4)軸測氣體力圖摩擦力和往復慣性力Matlab程序及Matlab圖：對I-IV列 a1=0:2.*pi;b1=;a2=0:2.*pi;b2=.*(cos(a2)+.*cos(2.*a2);plot(a1,b1,a2,b2)摩擦力和往復慣性力圖綜合活塞力的matlab程序及matlab圖： a1=0:;b1=-./(a1).*.*(sin(a

33、1)A2)A(1./2)A+./(a1)*(sin(a1)A2)A(1./2)A+./+cos(a1)+.*.*(sin(a1)A2)AA+;a2=:;b2=+./+cos(a2)+.*.*(sin(a2).A2).A.A+.*(cos(a2)+.*cos(2.*a2)+;a3=:pi;b3=+.*(cos(a3)+.*cos(2.*a3)+;a4=pi:;b4=-./(a4).*.*(sin(a4).A2).A(1./2).A+./(a4).*.*(sin(a4).A2).A(1./2).a+./+cos(a4)+.*.*(sin(a4).A2).A.A+.*(cos(a4)+.*cos(2

34、.*a4)+;a5=:;b5=-./(a5).*.*(sin(a5).A2).A(1./2).A+./(a5).*.*(sin(a5).A2).A(1./2).A+.*(cos(a5)+.*cos(2.*a5)+;a6=:2.*pi;b6=+.*(cos(a6)+.*cos(2.*a6)+;Plot(a1,b1,a2,b2,a3,b3,a4,b4,a5,b5,a6,b6)綜合活塞力圖綜合活塞力的最大值約在弧度的位置,其大小約為25kN2)由以上的計算結(jié)果,利用matlab繪制II-III列活塞力圖及程序如下:蓋側(cè)活塞力程序及Matlab圖：a1=0:;b1=.*./(a1).*.*(sin(a

35、1)A2)A)A;a2=:pi;b2=;a3=pi:;b3=.*./(a3).*.*(sin(a3)A2)A)A;a4=:2.*pi;b4=;Plot(a1,b1,a2,b2,a3,b3,a4,b4)蓋側(cè)活塞力軸測活塞力Matlab程序及Matlab圖:a1=0:;b1=.*./+cos(a1)+.*.*(sin(a1).A2).A).A+.*./+cos(a1)+.*.*(sin(a1)A2)A)A.a2=:pi;b2=;a3=pi:;b3=.*./+cos(a3)+.*(sin(a3)A2)A)A+.*./+cos(a3)+.*(sin(a3)A2)A)A.a4=:2.*pi;b4=;Pl

36、ot(a1,b1,a2,b2,a3,b3,a4,b4)軸測氣體力圖摩擦力和往復慣性力Matlab程序及Matlab圖:a1=0:2.*pi;b1=;a2=0:2.*pi;b2=.*(sin(a2)+.*cos(2.*a2);plot(a1,b1,a2,b2)摩擦力和往復慣性力圖綜合活塞力的matlab程序及matlab圖：a1=0:;b1=.*./(a1).*(sin(a1)A2)A)A+.*./+cos(a1)+.*.*(sin(a1)A2).A)A+.*./+cos(a1)+.*(sin(a1)A2)A)A+.*(sin(a2)+.*cos(2.*a2);a2=:;b2=+.*./+cos

37、(a1)+.*.*(sin(a1).A2).A).A+.*./+cos(a1)+.*.*(sin(a1).A2).A).A+.*(sin(a2)+.*cos(2.*a2);a3=:pi;b3=+.*(sin(a3)+.*cos(2.*a3);a4=pi:;b4=.*./(a4).*.*(sin(a4).A2).A).A+.*./+cos(a4)+.*.*(sin(a4).A2).A).A+.*./+cos(a4)+.*.*(sin(a4).A2).A).A+.*(sin(a4)+.*cos(2.*a4);a5=:;b5=.*./(a5).*.*(sin(a5).A2).A).A+.*(sin(

38、a5)+.*cos(2.*a5);a6=:2.*pi;b6=+.*(sin(a5)+.*cos(2.*a5);Plot(a1,b1,a2,b2,a3,b3,a4,b4,a5,b5,a6,b6)綜合活塞力圖綜合活塞力的最大值約在弧度的位置,其大小約為135kN=十三、切向力計算及切向力圖的繪制由?化工機器?P72公式得切向力的公式為：TFpK3式中:K3=sinsin2+2.1. 2sin2Fp為列的綜合活塞力,T為切向力由以上公式和已算得的綜合活塞力,使用Matlab容易得I、IV列的切向力圖：a1=0:;b1=(-./(a1).*.*(sin(a1)A2)A(1./2)A+./(a1)*(s

39、in(a1)A2)A(1./2)A+./+cos(a1)+.*.*(sin(a1)A2)AA+.*(sin(a1)+.*sin(2.*a1)./(2.*.*(sin(a1)A2)A)；a2=:;b2=+./+cos(a2)+.*.*(sin(a2).A2).A.A+.*(cos(a2)+.*cos(2.*a2)+.*(sin(a2)+.*sin(2.*a2)./(2.*.*(sin(a2).A2).A)；a3=:pi;b3=+.*(cos(a3)+.*cos(2.*a3)+.*(sin(a3)+.*sin(2.*a3)./(2.*.*(sin(a3).A2).A)；a4=pi:;b4=(-./(a4).*.*(sin(a4)A2)A(1./2)A+./(a4)*(sin(a4)A2)A(1./2).A+./+cos(a4)+.*.*(sin(a4).A2).A.A+.*(cos(a4)+.*cos(2.*a4)+.*(sin(a4)