三相异步电动机电磁计算

三相电机额定电压U=380V，f=50HZ,机座号Y132，输出P2=8KW，p=4极型号：Y132M输出功率：PN=8KW相数：m1=3接法：相电压：Uφ=380V功电流：Iw=P2×103m1UΦ=8×1033×380=7.018A极对数：p=2定子槽数：Z1=36转子槽数：Z2=32定子每极每相槽数：Qp1=Z12pm1=362×2×3=3定子外径：D1=21cm定子内径：Di1=13.6cm气隙长度：δ=0.4mm转子外径：D2=13.52cm13.6-0.04*2=13.52cm转子内径：Di2=4.8cm定子槽型：半闭口圆底槽定子槽尺寸：bo1=0.35cmb1=0.67cmho1=0.08cmR1=0.44cmh12=1.45cm转子槽形：梯形槽转子槽尺寸：bo2=0.1cmbr1=0.55cmbr2=0.3cmho2=0.05cmhr12=2.3cm极距：τ=πDi12p=3.1415×13.64=10.681cm定子齿距：t1=πDi1Z1=3.1415×13.636=1.187cm转子齿距：t2=πD2Z2=3.1415×13.5232=1.327cm气隙长度：δ=0.04cm转子斜槽距：bsk=t1=1.187cm铁芯长度：l=16cm铁芯有效长度：无径向通风道：lef=l+2δ=16.08cm净铁芯长：无径向通风道：lFe=KFel=0.95*16=15.2cmKFe=0.95（不涂漆）绕组型式：单层交叉式并联支路数：a1=1节距：1-9,2-10,11-18每槽导线数：由后面计算的数据根据公式计算为：每极磁通φ1=0.00784wb波幅系数：KA=1.46绕组系数：Kdp1=0.96每相串联有效导线数：Nφ1Kdp1=Kz'U1×10-2KAφ1×50f1=1.21×380×10-21.46×0.00784×5050=401.70K’z取1.21每相串联导线数：Nφ1=Nφ1Kdp1Kdp1=401.700.96=418每槽导线数：N1‘=41812=34.83取整数：N1=35线规：导线并饶根数与截面积之积（式中的值由其后的公式算得）：N1’A1'=I1a1J1=9.16271×5.19=1.7655mm2由此可通过查 表 关于同志近三年现实表现材料材料类招标技术评分表图表与交易pdf视力表打印pdf用图表说话 pdf 知线规为：2-1.06（N-φ）每根导线截面积：Acl=0.00882cm2槽有效面积：Ae=As-Ai=1.1444cm2As=2R+bs12×hs'-h+πR22Ai=Ci(2hs12+πR)Ci-绝缘厚度h-槽楔厚度Ci=0.08mm槽满率：ks=Ns1Ncld2Ae×100%=2×35×0.0131.1444=79.5%d-绝缘导线外径d=1.14mm每相串联导线数：Nφ1=Z1Ns1ma1=35×363=420绕组分布系数：Kd1=sinα2q1q1sinα2=0.96q1=Z12pm=364×3=3α=2pπZ1=2×2×180°36=20°绕组短距系数：Kp1=sin(β×90°)=1β=ymq1绕组系数：Kdp1=Kd1Kp1=0.96二．磁路计算每极磁通：∅1=KEU∅2.22fN∅1Kdp1=0.00784Wb=380×0.9232.22×50×420×0.96KE=0.923KE范围0.85-0.95定子齿截面积:At1=bt1lFeZ12p=76.05cm2转子齿截面积：At2=bt2lFeZ22p=75.95cm2bt1,bt2-定，转子齿宽定子轭部截面积：Aj1=hj'lFe=1.877×15.2=28.53cm2hj'=D1-Di12-hs+13R=3.7-0.08+1.45+0.44+0.443=1.877转子轭部截面积：Aj2=hj2'lFe=30.65cm2hj2'=D2-Di22-hR-23dk=2.016因无通风孔dk=0空气隙面积：Aδ=τlef=10.681×16.08=171.8cm2波幅系数：KA=1.46KS=1.276KA由饱和系数KS查得，开始计算时先假定KS定子齿磁密：Bt1=KA∅1At1×104=1.46×0.0078476.05×104=1.505T转子齿磁密：Bt2=KA∅1At2×104=1.46×0.0078475.95×104=1.507T定子轭磁密：Bj1=12×∅1Aj1×104=12×0.0078428.53×104=1.37T转子轭磁密：Bj2=12×∅1Aj2×104=12×0.0078430.65×104=1.28T气隙磁密：Bδ=KA∅1Aδ×104=1.46×0.00784171.8×104=0.666T定子齿磁场强度：HT1=20.58A/cm（查表硅钢片磁化曲线）转子齿磁场强度：Ht2=20.79A/cm（查表硅钢片磁化曲线）定子轭磁场强度：Hj1=11.44A/cm（查表硅钢片磁化曲线）转子轭磁场强度：Hj2=8.43A/cm（查表硅钢片磁化曲线）定子齿磁路计算长度：hT1'=hs1+hs2+R3=1.597cm转子齿磁路计算长度：hT2'=hR1+hR2=2.3cm定子轭磁路计算长度：lj1'=πDi1-hj1'4p=7.51cm转子轭部磁路计算长度：lj2'=πDi2+hj2'4p=2.67cm气隙磁路计算长度：δe=δKc1Kc2=0.4×1.308×1.031÷10=0.05393cmKc1=t1t1-r1δKc2=t2t2-r2δt-齿距b0-槽口宽定子齿磁位降：Ft1=Ht1×ht1'=32.86A转子齿磁位降：Ft2=Ht2×ht2'=47.81A定子轭部磁位降：Fj1=C1Hj1lj1'=43.31AC1=0.504定子轭部磁路校正系数转子轭部磁位降：Fj2=C2Hj2lj2'=9.23AC2=0.41转子轭部磁路校正系数气隙磁位降：Fδ=0.8Bδδe×104=0.8×0.666×0.05393×104=287.34A饱和系数：Ks=Ft1+Ft2+FδFδ=32.86+47.81+287.34287.34=1.28与38项比对总磁位降：F=Ft1+Ft2+Fj1+Fj2+Fδ=32.86+47.81+43.31+9.23+287.34=420.55A励磁电流：Im=4.44pFmN∅1Kdp1=4.44×2×420.553×420×0.96=3.087A励磁电流标幺值：Im*=ImIw=3.0877.018=0.4399励磁电抗标幺值：Xm*=1Im*=10.4399=2.2732三．参数计算线圈平均半匝长度：lc1=le+2d+lE'=31.22cmd=1.5cm(直线部分伸出长)lE'=kτck对2,4极取0.58τc-平均节距τc=10.54cm线圈端部平均长度：lE=2lE'+d=15.22cm线圈端部轴向投影长度：fd=lE'sinα=3.77cm阻抗折算系数：Kz=m1N∅1Kdp12m2N∅2Kdp22=15241式中：对笼型转子m2=Z2，N∅2=1，Kdp2=1定子相电阻：R1=ρ1N∅1lc1a1Nc1Ac1=1.61Ωρ1-导线电阻率标幺值：R1*=R1IwU∅=0.0297转子导条电阻：RB=KzKBρBlBAB=1.1407Ω式中：KB=1.04(对铸铝转子)ρB-导条电阻率lB=16cm(转子导条长度)AB=0.965cm2(每根导条截面积)标幺值：RB*=RB×I2U∅=1.1407×7.018380=0.0211转子端环电阻：RR=KzρRZzDR2πp2AR=0.3467ΩρR-端环电阻系数DR-端环平均直径（10.7cm）AR-端环截面积（2.6cm2）标幺值：RR*=RRIwU∅=0.3467×7.018380=0.006转子电阻标幺值：R2*=RB*+RR*=0.0211+0.006=0.0271漏抗系数：Cx=0.4π2flefN∅12pq1IwU∅×10-5=0.4×3.14152×50×16.08×42022×37.018380×10-8=0.01723定子槽漏磁导：λs1=KU1λU1+Kc1λc1=1.2431KU1=1Kc1=1λU1=0.4097λc1=0.8334定子槽漏抗：Xs1*=lσ1lefλc1Cx=1616.08×0.8334×0.01723=0.01429lσ1=l1(对无径向通风道)定子谐波漏磁导：λd1=0.0129对60°相带整数槽绕组，且23≤β≤1λd1=π218×5q12+1-14cq1+23c2-14c3q13q12-Kdp12式中:c-短距槽数，c=8q1(1-p)定子谐波漏抗：xd1*=m1q1τπ2δefKsλd1Cx=1.8243×0.01723=0.03143定子端部漏磁导：λE1=0.67(lE-0.64τc)=5.6778定子端部漏抗：XE1*=q1lefλE1Cx=316.08×5.6778×0.01723=0.01825定子漏抗标幺值：X1*=Xs1*+Xd1*+XE1*=0.01429+0.03142+0.01825=0.06397转子槽漏磁导：λs2=λU2+λc2=2.1754λU2=hR0b02=0.5(槽上部漏磁导)λL2=1.6754(槽下部漏磁导)转子槽漏抗：Xs2*=lσ2lefKdp12Z1Z2λs2Cx=0.03862=2.2413×0.01723lσ2=l2转子谐波漏磁导：对笼型转子：λd2=1kZ2p±12=0.013K=1，2,3转子谐波漏抗：Xd2*=m1q1τKdp12π2δefKsλd2Cx=1.6757×0.01723=0.02887转子端部漏磁导：λE2=0.757lB-l21.13+DR2p=2.025(对笼型转子)转子端部漏抗：XE2*=q1lefKdp12λE2Cx=0.3478×0.01723=0.00599转子斜槽漏抗：Xsk*=0.5bskt22Xd2*=0.5×1.1871.3272×0.02887=0.01155转子漏抗标幺值：X2*=Xs2*+Xd2*+XE2*+Xsk*=0.08503运行总漏抗：X*=X1*+X2*=0.06397+0.08503=0.149四．运行性能计算满载电流有功分量：Ip*=1η=10.88=1.136设η=0.88η-效率满载电抗电流：Ix*=σ1X*Ip*21+σ1X*Ip*2=1.0281×0.149×1.1362×1+1.0281×0.149×1.1362=0.2037式中：σ1=1+Im*X1*=1+0.4399×0.06397=1.0281满载电流无功分量：IQ*=Im*+Ix*=0.4399+0.2037=0.6436满载电动势比值：KE=1-Ip*R1*+IQ*X1*=1-1.136×0.0297+0.6436×0.06397=0.925与32项进行比对定子电流：I1*=Ip*2+IQ*2=1.1362+0.64362=1.3056I1=I1*Iw=1.3056×7.018=9.1627A转子导条电流：I2*=Ip*2+Ix*2=1.1362+0.20372=1.154I2=I2*IwK1=1.154×7.018×37.8=306.13AK1-电流折算系数K1=m1N∅1Kdp1Z2=3×420×0.9632=37.8转子端环电流：IR=Z22πpI2=322×3.1415×2×306.13=779.58A定子电密：J1=I1a1Nc1Ac1×102=9.16271×1.76423=5.19A/mm2线负荷：A1=m1Z∅1I1πDi1=3×420×9.16273.1415×13.6=270.22Acm热负荷：AJ1=A1J1=1402.44转子导条电密：JB=I2AB×102=306.130.965×102=3.17A/mm2转子端环电密：JR=IRAR×102=779.582.6×100=2.998A/mm2空载电动势比值：KE0=1-Im*X1*=1-0.4399×0.06397=0.9719空载定子齿磁密：Bt10=KE0KEBt1=0.97190.925×1.505=1.5813T空载定子轭磁密：Bj10=KE0KEBj1=0.97190.925×1.37=1.4395T定子齿单位铁损耗：pt1由Bt10查表得44.02×10-3W/cm3定子轭单位铁损耗：pj1由Bj10查表的36.7×10-3W/cm3定子齿体积：Vt1=2pAt1ht1'=485.68cm3定子轭体积：Vj1=4pAj1lj1'=1713.73cm3铁损耗：PFe=k1pt1Vt1+k2pj1Vj1对半闭口槽：k1=2.5,k2=2PFe=2.5×44.02×485.68+2×36.7×1713.73×10-3=179.24W标幺值：PFe*=PFePN×103=0.0224基本铁耗：PFe1*=pt1Vt1+pj1Vj1PN×103=44.02×10-3×485.68+36.7×10-3×1713.738000=0.01053定子电阻损耗：Pcu1*=I1*2R1*=1.30562×0.0297=0.0506Pcu1=Pcu1*PN×103=0.0506×8000=404.8W转子电阻损耗：Pcu2*=I2*2R2*=1.1542×0.0271=0.0361Pcu2=Pcu2*PN×103=288.8W风摩损耗：Pfv*参考试验值确定为0.01Pfv=Pfv*PN×103=0.01×8000=80W杂散损耗：Ps*对铸铝转子可取0.02Ps=Ps*PN×103=0.02×8000=160W总损耗：P*=Pcu1*+Pcu2*+PFe*+Pfv*+Ps*=0.0506+0.0361+0.0224+0.01+0.02=0.1391输入功率：P1*=1+P*=1.1391满载效率：η=1-P*P1*=1-0.13911.1391=0.878η-η'η=0.878-0.880.878=-0.0023>-0.005与88项假定值比对功率因数：cosφ=1I1*η=11.3056×0.878=0.872满载转差率：SN=Pcu2*Pem*=0.03611.07797=0.0335Pem*-气隙电磁功率Pem*=P1*-Pcu1*-PFe1*=1.07797额定转速：nN=60f1-SNp=60×50×1-0.03352=1449.75r/min最大转矩倍数：Tmax*=1-SN2×R1*+R1*2+X*2=1-0.03352×0.0297+0.02972+0.1492=2.66五．起动性能计算Ist=2.5~3.5Tmax*×Iw=61.8A起动时槽磁动势：Fst=0.707IstN∅1a1×KV1+Kdp1Kd1Z1Z2KE0=3071.09A虚拟磁密：BL=Fst×10-41.6δβc=5.0241TβL=0.64+2.5δt1+t2=0.955起动漏磁饱和系数：Kas=0.418定子槽口宽增大：∆b01=t1-b011-kas=0.4874转子槽口宽增大：∆b02=t2-b021-kas=0.7141定子槽上部漏磁导减少：∆λU1=hr0-0.58hr1b01∆b01∆b01+1.5b01=0.1836转子槽上部漏磁导减少：∆λU2=hR0b02∆b02∆b02+b02=0.4397起动定子槽漏磁导：λs1st=KU1λU1-∆λU1+Kc1λc1=1.0596起动定子槽漏抗标幺值：Xs1st*=λs1stλs1Xs1*=1.05961.2431×0.01429=0.01218起动定子谐波漏抗标幺值：Xd1st*=kasXd1*=0.01218定子起动漏抗标幺值：X1st*=Xs1st*+Xd1st*+XE1*=0.01218+0.01313+0.01825=0.04356挤流转子导条相对高度：ε=2πhBbBbsfρB×109=1.551hB-转子导条高度（cm）bRbS-转子导条宽与槽宽之比，对铸铝转子为1ρB-转子导条电阻率hB=2.35cm导条电阻等效高度：hρR=hBφεka=2.351.45×1=1.621槽漏抗等效高度：hρx=hBψεka=2.35×0.78×1=1.833挤流电阻增大系数：KR=1+aφ2ε1+a2φε-1=1.308a=b1b2挤流漏抗减少系数：Kx=b21+a2ψεbpx1+a'2Kr1'Kr1=0.888a'=b1bpxbpx=b1+b2⋯⋯b1ψ(ε)起动转子槽下部漏磁导：λL2st=KxλL2=KX×2h1b0+b1+λL=1.4875λL=4β(1+α)2kτ1起动转子槽漏磁导：λs2st=λU2-∆λU2+λL2st=1.5478起动转子槽漏抗标幺值：Xs2st*=λs2stλs2×Xs2*=0.0275起动转子谐波漏抗标幺值：Xd2st*=kasXd2*=0.01207起动转子斜槽漏抗标幺值：Xskst*=kasXsk*=0.0048转子起动漏抗标幺值：X2st*=Xs2st*+Xd2st*+XE2*+Xskst*=0.05036起动总漏抗标幺值：Xst*=X1st*+X2st*=0.04356+0.05036=0.09392RBst*=kRlef-NV2b02lB+lB-lf-NV2b02lB×RB*=0.0276转子起动电阻标幺值：R2st*=RBst*+RR*=0.0276+0.006=0.0336起动总电阻标幺值：Rst*=R1*+R2st*=0.0297+0.0336=0.0633起动总阻抗：Zst*=Rst*2+Xst*2=0.1133起动电流：Ist=IKwZst*=7.0180.1133=61.94A61.94-61.861.94=0.0023<0.005起动电流倍数：Ist*=61.949.1627=6.76起动转矩倍数：Tst*=R2st*Zst*21-SN=0.03360.11332×1-0.0335=2.53相带槽号磁极AZBXCYN1,S135,36,12,3,45,6,78,9,1011,12,1314,15,16N2,S217,18,1920,21,2223,24,2526,27,2829,30,3132,33,34