凸极同步发电机电磁计算程序

凸极同步发电机电磁计算程序额定数据及主要尺寸1.额定功率：PN75kW2.额定电压：UN400V3.额定转速：nN1500r/min4.额定频率：fN50Hz5.额定功率因数cos0.86.相数：m=37.额定相电流（星形连接）：PN75103INA135.3A3UNcos34000.8极数：120fN120502p=4nN1500定子铁芯外径：Dl=430mm定子铁芯内径：Dil=300mmDl在凸极同步电机中，1.42Dil极距：Dil3002pmm235.62mm4圆周速度：v2fN250235.62m/s23.562m/s10001000定子铁芯总长度：lt=300mm定子铁芯净长度：lFet=KFet(lt-nkbk)=0.92×(300-0)mm=276mm式中，nk为通风道数；bk为通风道宽度；KFet为定子铁芯叠压系数，本设计中定子铁芯采纳0.5mm厚热轧硅钢片，取KFet=0.92磁极铁芯总长度：lm=300mm磁极铁芯净长度：lFem=KFemlm=0.95×300mm=285mm式中，KFem=0.95~0.97(1~1.5mm厚钢板)铁芯计算长度：有径向通风道时，liltnkbk'式中，bk'为通风道宽度无径向通风道时lilt2，定转子铁芯长度相等时li1(ltlm)，定转子铁芯长度不等时2本设计为无径向通风道且定转子长度相等时，故lilt230021.1302.2mm最吝啬隙：K0KcA103Bδ(0.25~0.30)0.527.563235.62103mm0.7151.04~1.25mm按标准取1.1mm式中，K0为半经验系数，K00.25~0.30；Kc为饱和短路比，对自励恒压发电机可取Kc0.5；A=27.563A/mm为定子线负荷，Bδ0.715T为气隙磁密，下文均会计算最大气隙：m1.21.21.1mm1.32mm定子绕组每极每相槽数：q=4定子（虚）槽数：Z12pmq43448绕组节距：y1=10绕组节距比：y110=5mq346绕组短距系数（基波）：Kpsin()sin(5)0.9659262绕组分布系数（基波）：sinsin2m60.9577Kdqsin4sin2mq24绕组系数（基波）：KdpKdKp0.95770.96590.925并联支路数：a=2每槽导体数：Ns=8并绕导线根数：Nt=3每相串连导体数：NsZ1848N364ma2槽满率：取Sf=75%槽面积（梨形槽）：初定槽形尺寸：bs0=3mm，hs0=1mm，hs1=1.5mm，hs2=11mm，齿靴角=30bs1ts1bt119.962118.3962mm9mm式中，ts119.962mm为定子齿距，bt111mm为定子齿宽度，下文均会计算Rsbs1hs218091805.2mm，槽楔厚h=2.5mm2tan211tanZ148As2Rsbs1(hs1hs2h)Rs22225.29(12.52.5)5.2222139.47mm2槽绝缘占面积：AiCi[2(hs1hs2)(2)Rsbs1]0.3[212.5(2)5.29]mm218.22mm2式中，Ci=0.3mm为单边槽绝缘厚度则槽有效面积：AsefAsAi139.4718.22121.25mm2导线直径：AsefSf121.2575%d31.95mmNtNs8查表取铜对应的标称线规QZ得：漆包线最大外径d=1.93mm，导线dc=1.81mm定子导线截面积：qa=2.573mm2定子绕组电密：IN135.3A/mm28.76A/mm2ja232.573aNtqa线负荷：mNIN364135.3AA/mm27.563A/mmDil300发热参数：AAja275.638.76A2cm-1mm22414.5A2cm-1mm2j磁路计算38.定子铁芯拼片：nt26（应为偶数或分子为偶数的最简分数）p62式中，n为每片重叠数；为每层叠片的重叠片数；为极对数。定子齿距：Dil30019.635mmtsmmZ148[Dil2(hs0hs1)][3002(11.5)]mm19.962mmts1Z148[Dil2(hs0hs1hs2)][3002(11.511)]21.402mmts2Z148mm[Dil2(hs0hs1hs2)][3002(11.511)]ts133mm20.224mmZ148340.定子齿宽度：tsBδ19.6350.715mm8.976~11.738mmbt1KFeBts0.92(1.20~1.60)式中，KFet为铁芯叠压系数，取0.92Bts为定子齿，取1.30~1.70T取bt1=11mmbt2ts22Rs21.40225.22110.96mm定子齿计算宽度：btsbtmax2btmin11210.96mm10.973mm33定子槽深：hs=hs0+hs1+hs2+Rs=1+1.5+11+5.2=18.7mm（合用圆底槽）定子齿计算高度：hts'hs1hs2Rs1.5115.214.23mm（合用圆底槽）33定子轭高度：DlDilhs430300hjs218.746.3mm2定子轭计算高度：'hjsRs46.35.2（合用圆底槽）hjs348.03mm3定子轭磁路长度：ljs(Dlh'js)(43048.03)mm=150.00mm4p8极靴宽度：bp(Dil2m)sinp1802p(30021.32)sin(0.716180)mm4159.73mm式中，p为极弧系数，下文会计算磁极偏爱距：H(m)(Dilm)(Dil2[(Dil)m)cos1]22(1.321.1)(3001.321.1)[(3001.1)(300mm21.32)cos32.49]221.39mm式中，1arcsinbparcsin159.7332.492m2Dil3001.3249.极靴圆弧半径：RpDilH3001.391.1147.51mm22极靴边沿高度：hp'2.5mm极靴中心高度：hp(Dilhp')(Dilm)cos1223002.51.1)(300(1.32)cos32.492225.99mm初取漏磁系数：'1101101.11.0467235.62磁极宽度：1061.04670.03564106bmlFemBmmm84.45mm2851.55磁极中心高度：hm1(DilDjr)hp1(300155)25.991.145.41mm22磁极侧高度：'Djr(1cos2)45.41155cos33.01)57.92mmhmhm2(12式中，2arcsinbmarcsin84.4533.01Djr15556.转子轭内径：Dir=90mm57.转子轭外径：Djr=155mm58.转子轭高度：hjrDjrDir15590mm32.5mm22转子轭计算高度：hjr'hjr1Dir32.519047.5mm(合用于转子轭直接套在轴上)i660.转子轭磁路长度：ljr(Djrhjr')(15547.5)mm42.215mm4p8转子轭轴向长度：lr292mm磁极与轭间残隙：2(lm8)102(3008)102mm0.09mm300300实质极弧系数：2Rparcsinbp159.732147.51arcsin2Rp2147.510.716p180253.62180气隙比：m1.321.21.1最吝啬隙比极距：1.10.00467235.62基波磁场幅度系数：A1B11.0836（查中小型电机设计手册）三次谐波磁场幅度系数：1(A3B30.6)0.04855（查中小型电机设计手册）磁场分布系数：fd2(13)2(1.0860.04855)0.70033磁场波形系数：11.0836fb1.09462fd20.70070.直轴电枢反应磁场幅度系数：Ad1AdBd0.9156（查中小型电机设计手册）71.交轴电枢反应磁场幅度系数：Aq1AqBq0.46（查中小型电机设计手册）电枢磁动势直轴折算系数：KadAd10.91560.845011.083673.电枢磁动势交轴折算系数：KaqAq10.460.42451.0836174.定子卡氏系数：Kδ1ts(4.440.75bs0)ts(4.440.75bs0)bs0219.635(4.441.10.753)19.635(4.441.10.753)321.0687（合用于半闭嘴或半张口槽，本设计为半张口槽）阻尼笼卡氏系数：td(4.440.75bd)Kδ20.75bd)bd2td(4.4417.12(4.441.10.752)17.12(4.441.10.752)221.0380式中，td17.12mm为阻尼槽距，对于q=整数的槽绕组，td应吻合以下关系：0.8tstd0.9tsbd=2mm为阻尼槽口宽度卡氏系数：KδKδ1Kδ21.06871.0380=1.1093空载每极总磁通：UN400/3Wb0.03564Wb2fbfKdpN21.0946500.9256478.气隙磁密最大值：Bδ1060.03564106T0.715Tlifd235.62302.20.779.定子视在齿磁密Bts'tsliBδ19.635302.20.715T1.40TbtslFet10.973276BtsBts'1.40T当Bts'1.8T时，对付Bts'进行修正；当Bts'1.8T时，BtsBts'。齿磁密修正系数：对平行齿(ts1ts)2KFb(etbt1)t2KnKFe(tbt1b)t2ts1KFebtts对平行槽3KnKFebtts定子轭磁密：Bjs1060.035641062hjs'lFet248.03T1.3442T276气隙磁压降：Fδ0.8KδBδ1030.81.11.10930.715103A697.972A定子齿磁压降：'FtshtsHts14.230.673A9.577A84.定子轭磁压降：FjsljsHjs150.000.538960.4134A33.421A式中，Hjs对应于Bjs，查磁化曲线知Hjs0.53896A/mm为轭部磁路长度因数，查表知0.4134气隙、定子齿、轭磁压降之和：FδtjFδFtsFjs697.9729.57733.421740.970A计算漏磁几何尺寸：1arctanbmarctan84.4524.20Djr2hmhm'245.4115557.922arctanbparctan159.7332.752hmhp'245.41Djr1552.5ambm2(Djrhm)2sin(1801)2p84.452(15545.41)2sin(4524.20)mm77.23mmapbp2(Djr2hmhp')2sin(1802)2p159.732(155245.412.5)2sin(4532.75)mm62.65mmhpm1(2hphp')1(225.992.5)mm18.16mm33磁极压板厚：d'6mm磁极压板宽：b'86mm磁极计算长度：lm'lm2d'30026312mm极靴漏磁导：p5lmhpm1097.32hlg(1bp)109appmap2530018.161097.3218.16lg(1159.73)10962.6562.6525.2777107H极身漏磁导：m2.5lm'hm'1093.66hm'lg(1bm)109amam22.531257.921093.6657.92lg(184.45)10977.2377.2326.7702107H磁极漏磁导：1.1(pm)1.1(5.27776.7702)107H1.3253106H93.每极漏磁通：σFδtj1.3253106740.970Wb9.820104Wb94.漏磁系数：1σ19.8201.0276356.4与'之差应小于5%，不然应重新假设'再计算'1.04671.0276100%1.82%5%'100%1.0467故假设成立95.磁极磁通：mσ3.5641020.09821020.03662Wb磁极极身截面积：SmlFembm2d'b'28584.452686251.00cm2极身磁密：Bmm1040.03662104T1.4590TSm251.00转子轭磁密：Bjrm1060.03662106T=1.3201T2hjr'lr247.5292残隙处磁密：Bδ2m1060.03662106T1.4454Tlmbm30084.45100.极身磁压降：FmhmHm45.411.82650A82.941A式中，Hm对应Bm，查磁化曲线得Hm1.82650A/mm101.转子轭磁压降：FjrljrHjr42.2151.67050A70.520A式中，Hjr对应Bjr，查磁化曲线得Hjr1.67050A/mm102.残隙磁压降：Fδ20.82Bδ21030.80.091.4454103A104.069A103.空载每极磁压降：Ff0FδtjFmFjrFδ2740.97082.94170.520104.069998.500A稳态参数104.定子线圈尺寸：carcsinbs12Rs(2~4)ts1ts2925.2(2~4)arcsin19.96221.40231.16~34.45取c32y[Dil2(hs0hs1)hs2Rs]2p[3002(11.5)115.2]564210.225mmlFy210.225123.946mm2cos2cos32clElFsinc123.946sin32mm65.68mmlBlt2lD300220340mm式中，lD为线圈伸出铁芯直线长度，取lD=20mm105.线圈半匝均匀长度：lcalB2lF3402123.946587.892mm106.定子绕组相电阻：Ra(75oC)75oClcaNaNtqa1030(1Cut)lcaNaNtqa1030.0164(14.310375)587.89264232.5731030.0529式中，Cu4.3103C1为电阻温度系数；温度为t时导体资料的电阻率：t0(1t)式中，0为导体资料0C时的电阻率，0Cu0.0164mm2/m107.定子槽比漏磁导：s341(hs02hs1)97Lbs0bs0bs116351121.59576(60.56（合用圆底槽）433)1691.0179式中，L为下部单位漏磁导，查表得L0.56108.定子绕组端部比漏磁导：0.3m1)0.33235.6250.3350e(3(31)li302.26109.谐波比漏磁导：m23235.622Kdp0.925h12Kδmq121.11.10930.286834（合用于有阻尼绕组的状况）110.每相漏抗：0.79fliN22Xsseh2p100100100q0.7950302.26421.017920.33500.2868410010010040.09386111.漏抗标幺值：Xs*XsIN0.09386135.30.055UN400/3112.相电阻标幺值：R*oRoIN0.0529135.30.0310a(75C)a(75C)UN400/3113.每极电枢反应磁动势：Fa0.45mINNKdp0.453135.3640.9252703.29A2p4A114.电枢反应直轴折算磁动势：FadKadFa0.84502703.29A2284.28A115.电枢反应交轴折算磁动势：FaqKaqFa0.42452703.29A1147.55A116.直轴电枢反应电抗标幺值：XadFad2284.28FδFδ22.8481697.972104.069117.交轴电枢反应电抗标幺值：XaqFaq1147.551.4308FδFδ2673.244103.968118.直轴同步电抗标幺值：XdXad*Xs*2.84810.0552.9031119.交轴同步电抗标幺值：XqXaq*Xs*1.43080.0551.4858120.短路比：KcFf0998.500Fad0.43712284.28121.内功率因数角：=arctansinXq*0.61.4858R*arctan68.28cosoC)0.80.0310a(75122.额定功角：68.2836.8731.41额定负载时励磁磁动势和励磁绕组123.额定负载时内电动势标幺值：Ei*1Ra(75*oC)cosXs*sinj(Xs*cosRa(75*oC)sin)W2Q21.05811.38式中，W1R*ocosXs*sin10.03100.80.0550.61.0578a(75C)QXs*cosR*osin0.0550.80.03100.60.0254a(75C)Q0.02541.38arctanarctanW1.0578124.额定工况时磁路计算：NEi*1.05810.03564Wb0.03771WbBδNEi*Bδ1.05810.715T0.7565TBtsN'Ei*Bts'1.05811.40T1.4813T式中，BtsN'1.80T，故BB'1.4813TtsNtsNBjsNEi*Bjs1.05811.3442T1.4223TFδNEi*Fδ1.0581697.972A738.524AFtsNhts'HtsN14.230.94207A13.406A式中，HtsN对应BtsN，查磁化曲线得HtsN0.94207A/mmFjsNljsHjsNN150.000.738130.3666A40.590A式中，HjsN对应BjsN，查磁化曲线得HjsN0.73813A/mm0.366为6额定工况时轭部磁路长度因数FδtjNFδNFtsNFjsN738.52413.40640.590792.520AσNFδtjN1.3253106792.520Wb1.0503103WbN1σNN11.05031.027937.71mNNσN3.7711020.105031023.8760102WbBmNmN43.87601021041.5442TSm10251.00TBjrNmN1063.8760102106T1.3973T2hjr'lr247.5292Bδ2NmN1063.8760102106T1.5299Tlmbm30084.45FjrNljrHjrN42.2152.07380A87.545A式中，HjrN对应BjrN，查磁化曲线得HjrN2.07380A/mmFmNhmHmN45.412.95140A134.023A式中，HmN对应BmN，查磁化曲线得HmN2.95140A/mmFδ2N0.82Bδ2N1030.80.091.5299103A110.153A125.额定负载时每极磁压降：FEi1.1(FδtjNFjrNFmNFδ2N)1.1(792.52087.545134.023110.153)A1236.665A126.额定负载时励磁磁动势：Fad22Fadsin(FfN1.05FEi1)FEiFEi2284.28022284.280sin(36.871.051236.665121.38)A1236.6651236.6653360.765A127.励磁绕组每极匝数：Wf=136128.额定励磁电流：FfN3360.76524.712AIfN136AWf129.空载励磁电流：If0Ff0998.500A7.342AWf136130.励磁绕组线规（漆包扁线）：ab1.68mm3.80mm131.励磁绕组导线截面积：qf6.17mm2132.第n层线圈均匀匝长度：lfn2QmWm(rm2n12b)式中，Qm=82mm，为线圈框架直线宽度；Wm=300mm，为线圈框架直线长度；rm=5mm，为框架圆角半径；b=3.80mm，为导线长边尺寸133.励磁绕组均匀匝长度：nflfn11467.0866lcfcm84.3168cmWf136励磁绕组每极136匝，4层，每层34匝，式中，nf为第n层线圈的匝数。134.励磁绕组电阻：2pCu(75oＣ)WflcfRf(75oC)100qf40.02168913684.31681006.171.6124135.励磁绕组电密：jfIfN24.712A/mm24.0052A/mm2qf6.17136.额定励磁电压：UfNIfNRf(120oC)0.61.15IfNRf(75oC)0.6（合用于有刷发电机）1.1524.7121.61240.646.4225V式中，0.6V为电刷压降；对于B级绝缘的励磁绕组，Rf(120oC)1.15Rf(75oC)137.空载励磁电压：Uf0If0Rf(25oC)0.67.3421.35030.610.5138V（合用于有刷发电机）式中，0.6V为电刷压降阻尼绕组设计138.每极阻尼条数：nd=4139.每极定子绕组截面积：SamqNtNsqa34382.573mm2741.024mm2140.每根阻尼条截面积：SdkSa0.2741.024mm237.051mm2nd4式中，k为系数，当阻尼条采纳紫铜时k=0.2141.阻尼条直径：dy1.13Sd1.1337.051mm6.8783mm取dy=7mmdd(1.05~1.1)dy1.057mm7.35mm142.阻尼条节距：tdpdd2cnd10.716235.627.35255mm4117.12mm对于q为整数的槽绕组，td应吻合以下关系：0.8tstd0.9ts式中，c=55mm为极靴边沿处的齿宽，c应大于5mm143.阻尼齿的最大磁密：BdBδNtdli0.756517.12302.2T1.4056TtdddlFem17.127.35285144.端环尺寸：本设计中，取高度ay14mm，厚度by6mmay2dyay14mmby0.75dy即by5.25mmayby(0.4~0.6)ndSdayby88.9224mm2消耗与效率145.定子齿钢片重：GtZ1lFethts'bts7.71064827614.2310.9737.7106kg15.9284kg146.定子轭钢片重：Gjs(Dlhjs')hjs'lFet7.7106(43048.03)48.032767.7106kg122.4874kg147.资料单位消耗：P2.20W/kg10/50148.齿部单位消耗：ptP10/50BtsN22.201.48132W/kg4.8273W/kg149.轭部单位消耗：pjsPB22jsN2.201.4223W/kg4.4505W/kg10/50150.定子铁消耗：pFeKtptGtKjspjsGjs4.827315.92841.54.4505122.4874971.4776W式中，Kt、Kjs为经验系数。当PN100kVA时，t，js=1.5；当K=2KcosPN100kVA时，Kt=1.7，Kjs=1.3cos151.磁极单位表面消耗：Z1nN322pbmKbm10000(B0ts)3481500210000437.6351W/m22W/m2(0.171419.635)2式中，B0为齿谐波磁通密度最大值。B00KδBδN0.20431.10930.7565T0.1714T01111110.20432222bs01311.122Kbm为表面消耗系数，与资料厚度及加工工艺有关，叠片磁极，钢片厚度1mm时，Kbm=2；叠片磁极，钢片厚度1.5mm是，Kbm=2.6；叠片磁极，硅钢片厚度0.5mm时，表面切削加工，Kbm=1.7；叠片磁极，硅钢片厚度0.5mm时，表面不切削加工，Kbm=0.7。152.磁极表面消耗：pFeb2pplmpbm10640.716235.62300437.6351106W88.5969W153.定子绕组铜消耗：pCu1mIN2Ra(x)3135.320.0529W2905.1765W式中，E、B级绝缘，Ra(x)Ra(75oC)；F、H级绝缘，Ra(x)Ra(115oC)154.励磁消耗：IfN2Rf(x)0.6IfNpCuff24.71221.61240.624.7120.871147.1928W式中，f0.87为励磁系统效率；W（合用于有刷发电机）Rf(x)155.机械消耗：Rf(75oC)E、B级绝缘Rf(115oC)F、H级绝缘3lmpmec0.82pv1034019023.56233000.84103W40190821.8457W156.附带消耗：padKPN10375000W1125Wcos0.0120.80.015PN75kW式中，K0.01275kWPN200kW0.010PN200kW157.总消耗：ppFepFebpCu1pCufpmecpad971.477688.59692905.17651147.1928821.845711257059.2895W158.效率：PN100%7500091.40%PN100%p750007059.2895瞬态参数和时间常数159.励磁绕组漏抗标幺值：Xfs*6.4Kad2lifsFa1094Kad1Xad*6.40.84502302.20.67162703.2910940.845012.84810.035640.2865式中，fs为励磁绕组比漏磁导fshm'hpm2hm'0.5bm3amap4lm57.9218.16257.920.584.45377.2362.6543000.6716160.励磁绕组电抗标幺值：Xf*Xfs*Xad*0.28652.84813.1346161.阻尼绕组直轴电抗标幺值：Xds*7.9Falids7.92703.29302.21.61010.0729nd10940.03564109式中，ds为阻尼绕组比漏磁导ds0.623hd0.06ndbdli0.6231.6235.6220.064302.21.6101式中，hd=1.6mm162.阻尼绕组横轴电抗标幺值：Xqs*0.75Xds*0.750.07290.0547（合用于全阻尼绕组）163.直轴瞬态电抗标幺值：Xd'*Xs*Xad*Xfs*0.0552.84810.28650.3153Xf*3.1346164.交轴瞬态电抗标幺值：Xq'*Xq*1.4858165.直轴超瞬态电抗标幺值：Xd''*Xs*1111Xad*Xfs*Xds*0.05511112.84810.28650.07290.05695166.交轴超瞬态电抗标幺值：Xq''*Xs*1110.055110.10771Xaq*Xqs*1.43080.0547167.励磁绕组电阻标幺值：Rf*44Kad2lcfFa106fqfWf440.8450284.31682703.29106506.171360.035640.00479168.励磁绕组时间常数：Td0Xf*3.1346s2.083s2fRf*2500.00479169.瞬变电流时间常数：'*Td'Xd*Td00.31532.083s0.226sXd2.9031170.超瞬变电流时间常数：Td''1Td'10.226s0.0283s88171.负序电抗：X2*Xd''*Xq''*0.056950.10770.07832172.直流重量时间常数：TaX2*0.078320.00804sfR*250s20.0310a(75C)173.空载励磁连续短路电流倍数：fk0Kc0.4371174.额定励磁连续短路电流倍数：fkNFfN3360.765Fad1.472284.28175.冲击短路电流倍数：fy1.891.89Xd''*33.190.05695176.整步功率：Pr57.3PN57.37531.41kW/rad149.69kW/rad0.9140有效资料177.定子绕组铜重：GCu11.05(lZNtNq)8.9106ca1sa1.05(587.89248382.573)8.9106kg16.2843kg178.励磁绕组铜重：GCuf1.05(lcfWf2pqf)8.91061.05(843.16813646.17)8.9106kg26.4471kg179.定子硅钢片重：GFe(Dl2Dil2)lFet7.71064(43023002)2767.7106kg4158.4003kg