直流电机计算

1、主要技术指标[1]额定电压UN12V[2]额定电流IN2.2A[3]额定转速nN13000RPM[4]输出功率PN10W2、主要尺寸确定2、主要尺寸确定[5]电枢外径D=(6.1*108*P'/(αδABδnNλkp))1/3厘米[6]D=1.99(cm)选用2.04(cm)A--线负荷，对于连续工作状态取60~80安/厘米式中A--取60安/厘米Bδ--气隙磁密，铝镍钴一般取0.33~0.45特选铁氧体磁钢Y20Bδ=（0.7~0.85）*3550铁氧体Bδ=（0.7~0.85）BrBδ--取2800Gsαδ--极弧系数，一般取0.6~0.75；αδ--取0.72λ--lt2/De2,lt2为电枢铁心长度，一般λ取0.7~1.5。λ--取0.8kp--短矩系数kp=sin(y1π/2τ)kp--取0.951η--效率η=PN/UNIN效率η=0.38P'--视在功率P'=(1+2*η)pN/3η视在功率P'=15.47W[6]电枢计算长度lδ[6]电枢计算长度lδ=1.63(cm)lδ=λD（厘米）3、定子尺寸3、定子尺寸[7]机壳外径Dj1[7]机壳外径Dj1Dj1=（1.4~1.7）D（厘米）Dj1=2.856~3.468(cm)Dj1应与标准外径符合，或Dj1值由用户给出。取Dj1=3.26(cm)[8]机壳厚度Δj1查表或自定[8]机壳厚度Δj1取0.08(cm)[9]气隙δ取0.015~0.06厘米,p=1及铁氧体电机取最大值[9]气隙δ选取δ=0.06(cm)[10]磁钢外径DMe=Dj1-2Δj1（厘米）[10]磁钢外径DMe=3.1(cm)[11]磁钢内径DMi=D+2δ（厘米）[9]磁钢内径DMi=2.16(cm)[12]电枢铁心长度l2[12]电枢铁心长度l2=1.45(cm)对铁氧体磁铁l2=lδ-l0对铝镍钴磁铁l2lδ端部气隙等效长度取l0=0.18(cm)[13]磁铁轴向长度l1[13]磁铁轴向长度l1取1.85(cm)对铁氧体磁铁l1lδ对铝镍钴磁铁l1=l2=lδ[14]磁铁径向高度hm[14]磁铁径向高度hmhm=(DMe-DMi)/2（厘米）hm=0.47(cm)对铁氧体磁铁hm应在下述范围：hm范围0.36~0.48hm=(6~8)δ（厘米）[15]磁铁截面积SM[15]磁铁截面积SM环形铝镍钴磁铁瓦形铁氧体SM=（DMe-DMi）l1/2p（厘米2）SM=αδπ（DMi+hm）l1/2p=5.50（CM2）瓦形铁氧体磁铁SM=αδπ（DMi+hm）l1/2p（厘米2）其中极对数p=1环形铁氧体磁铁SM=αδπ（D+hm）lδ/2p（厘米2）[16]瓦形铁氧体磁铁弧度角β[16]瓦形铁氧体磁铁弧度角ββ=αδ180°/pβ=129.6°4、电枢冲片尺寸[17]槽数Z[17]槽数ZZ=（2~4）DZ=4.08~8.16=3~13取Z=5通常选用奇数槽[18]槽形[18]槽形选半梨形槽、平行齿的槽形。一般选梨形平行齿或半梨形平行齿槽形，在容量极小的电机中也有采用圆形槽的。[19]冲片材料[19]冲片材料根据性能、经济要求选用。片厚为0.35或0.5毫米。选50W600，厚0.5mm[20]槽距t2[20]槽距t2t2=πD/Z（厘米）t2=1.282(cm)[21]极距τ[21]极距ττ=πD/2p（厘米）或τ=Z/2p槽τ=3.204(cm)或τ=2.5[22]齿宽bt2[22]齿宽bt2bt2=Bδt2lδ/kFeBt2l2（厘米）bt2=0.247~0.323(cm)式中Bt2=13000~17000（Gs）取bt2=0.26(cm)kFe--查表2-6取0.96[23]轭高hj2[23]轭高hj2hj2=αδτlδBδ/2kFeBj2l2（厘米）hj2=0.252~0.315(cm)式中Bj2=12000~15000（Gs）考虑到1/4转轴直径可导磁，因为转子冲片直接压装到转轴上，可认为1/4转轴取hj2=0.21(cm)直径导磁。[24]冲片内径d0[24]冲片内径d0冲片直接压装到转轴上,轴伸端直径应符合标准。内径d0取0.3(cm)[25]齿高ht2[25]齿高ht2ht2=(D-D4)/2+r2ht2=0.66(cm)式中D4、r2参考[18]中的图形位置。式中D4=1.12(cm)r2=0.2(cm)[26]槽口宽b02[26]槽口宽b02b02（厘米）b02=0.34(cm)[27]槽口高h02[27]槽口高h02h02（厘米）h02=0.1(cm)[28]槽面积SS[28]槽面积SS计算出SS=0.272(cm2)5、磁路计算[29]气隙系数kδ[29]气隙系数kδ对半闭口槽kδ=t2(5δ+b02)/(t2(5δ+b02)-b02b02)对铁氧体磁钢kδ=[1/(2ln(1+0.5b02*/(δ*+hm*))+(1-b02*)/(δ*+hm*))-hm*]/δ*kδ=1.306式中δ*=δ/t2δ*=0.0468b02*=b02/t2b02*=0.2653hm*=hm/t2hm*=0.2515hm=hm(D-δ)/μr(D+hm)hm=0.3224μr取1.15[30]气隙磁密Bδ[30]气隙磁密BδBδ=φδ/αδτlδ（Gs）Bδ=0.266φδ（Gs）[31]气隙磁压降Fδ[31]气隙磁压降FδFδ=1.6kδδBδ(安)Fδ=0.1254Bδ(A)[32]齿磁密Bt2[32]齿磁密Bt2Bt2=t2lδBδ/bt2l2kFe（Gs）Bt2=5.771903Bδ（Gs）[33]齿磁场强度Ht2[33]齿磁场强度Ht2Ht2（安/厘米）Ht2（A/cm）查磁化曲线[34]齿磁压降Ft2[34]齿磁压降Ft2Ft2=2ht2Ht2（安）Ft2=1.32Ht2(A)[35]转子轭磁密Bj2[35]转子轭磁密Bj2Bj2=φδ/2kFeht2'l2（Gs）Bj2=1.449296φδ（Gs）式中hj2'--考虑1/4d0后的转子铁心轭高hj2'=hj2+1/8d0（厘米）hj2'=0.2475(cm)[36]转子轭磁场强度Hj2[36]转子轭磁场强度Hj2Hj2（安/厘米）Hj2（A/cm）查磁化曲线[37]转子轭磁压降Fj2[37]转子轭磁压降Fj2Fj2=lj2Hj2（安）Fj2=0.801106Hj2(A)式中lj2=π(D4-d2-hj2)/2p（厘米）式中lj2=0.801106(cm)[38]定子轭磁密Bj1[38]定子轭磁密Bj1Bj1=σφδ/2Δj1lj（Gs）Bj1=2.003205φδ（Gs）式中σ--磁铁漏磁系数，1.1~1.3取σ=1.25lj--机壳轴向长（厘米）lj=3.9(cm)[39]定子轭磁场强度Hj1[39]定子轭磁场强度Hj1Hj1（安/厘米）Hj1（A/cm）查磁化曲线[40]定子轭磁压降Fj1[40]定子轭磁压降Fj1Fj1=Lj1Hj1（安）Fj1=4.995132Hj1(A)式中Lj1=π(Dj1-Δj1)/2p（厘米）式中Lj1=4.995132(cm)[41]外磁路总磁压降F0[41]外磁路总磁压降F0F0=Fδ+Fj1+Fj2+Ft1（安）F0=Fδ+Fj1+Fj2+Ft1(A)[42]空载特性计算[42]空载特性计算见下表见下表(Mx)φδ600065007000750080008500900095001000010500110009200(Gs)Bδ=φδ/αδτlδ1593.491726.2781859.071991.862124.6522572390.2312523.02132655.8122788.62921.42443.347(A)Fδ=1.6kδδBδ199.769216.4164233.064249.711266.359283299.6535316.30094332.9484349.596366.24306.3125(Gs)Bt2=t2lδBδ/bt2l2kFe9197.459963.90710730.411496.812263.31303013796.1814562.63315329.0916095.51686214102.76(A/cm)Ht22.32.723.263.8957.110.2417.23251.29612.8(A)Ft2=2ht2Ht23.0363.59044.30325.13486.69.37213.516822.70442.2467.584126.7216.896(Gs)Bj2=φδ/2kFeht2'l28695.779420.42110145.110869.711594.41231913043.6613768.30814492.9615217.61594213333.52(A/cm)Hj22.112.452.843.343.965.27.110.2416.0829.8488(A)Fj2=lj2Hj21.690331.962712.275142.675693.172384.1665.6878538.203326712.8817923.87338.4536.408849(Gs)Bj1=σφδ/2Δj1lj12019.213020.8314022.41502416025.61702718028.8519030.44920032.0521033.72203518429.49(A/cm)Hj18.259.916.626.2365885124177240328100(A)Fj1=Lj1Hj141.209849.4518182.9192130.872179.825289.7424.5862619.39641884.13841198.831638.4499.5132(A)F0=Fδ+Fj1+Fj2+Ft2245.705271.4214322.561388.394455.956586.3743.4444966.604681272.2091639.882169.8829.1306(Mx)φm=σφδ75008125875093751000010625112501187512500131251375011500-245.71-271.421-322.56-388.39-455.96-586-743.444-966.6047-1272.21-1639.9-2170-829.131[43]磁铁平均磁路长LM[43]磁铁平均磁路长LM瓦形和环形铁氧体磁铁LM=0.94(cm)LM=2hm=DMe-EMi（厘米）环形铝镍钴磁铁LM=π(DMe+DMi)(1-αδ/2)/4p（厘米）带轭铁磁极极靴的铝镍钴磁铁LM=π(DMe+DMi)/4p-bM（厘米）式中bM--软铁磁极之身宽[44]去磁曲线0-188-376-564-752-940-1128-1316-1504-1692-1880Bm(Gs)355031952840248521301775142010657103550Hm(Oe)02505007501000125015001750200022502500φm=SMBm(Mx)19534.817581.2915627.813674.311720.997677813.9065860.42973906.9531953.480Fm=0.8LMHm(A)018837656475294011281316150416921880[45]磁铁工作图[45]磁铁工作图见下图见下图求出空载工作点工作点为：φm，Fmφm=11500(Mx)求出气隙磁通量Fm=829.1306(A)φδ=φm/σ(Mx)φδ=9200(Mx)0500010000150002000025000-2500-2000-1500-1000-5000φmFm6、电枢绕组计算6、电枢绕组计算[46]计算电势初算Ei'[46]计算电势初算Ei'Ei'=(1+2η)UN/3(伏）Ei'=7.030303(V)[47]电枢绕组总导体数N’[47]电枢绕组总导体数N’N'=60aEi'*108/pnNkpφδN'=370.841支路对数