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1、 汽车主减速器传动比优化某轻型货车，车有关数据如下：发动机的最低转速nmin600r/min， 最高转速nmax=4000r/min。 总质量3650kg；车轮半径0.367m；传动系机械效率nT0.85；滚动阻力系数f0.013；空气阻力系数*迎风面积CDA2.77m2；飞轮转动惯量If0.218kg.m2；二前轮转动惯量Iw11.798kg.m2;轴距L=3.2m;质心至前轴距离（满载）a=1.947m；质心高（满载）hg=0.9m；四后轮转动惯量Iw23.598kg.m2；T=-19.313+295.27*(n/1000)-165.44*(n/1000).2+40.874*(n/1000
2、).3-3.8445*(n/1000).4;怠速油耗Qid0.299mL/s（怠速转速400r/min）。负荷特性曲线拟合公式为：b=B0+B1*Pe+B2*Pe.2+B3*Pe.3+B4*Pe.4.N/(r/min)B0B1B2B3B48151326.8-416.4672.379-5.86290.1776812071354.7-303.9836.657-2.05530.04307216141284.4-189.751452.4-0.511840.006816420121122.9-121.597.0035-0.185170.001855526031141.0-98.8934.4763-0.0
3、910770.0006890630061051.2-73.7142.8593-0.051380.0003503234031233.9-84.4782.9788-0.0474490.0002823038041129.7-45.2910.71113-0.00075215-0.0000385681档2档3档4档5档变速器传动比5.064.0163.091.711计算1计算加速时间Matlab程序：n=600:1:4000; m=3650; g=9.8; G=m*g;r=0.367; i0=5.089;nT=0.85; f=0.013;CdA=2.77; Iw1=1.798; Iw2=3.598; I
4、w=Iw1+Iw2; If=0.218;a=1.947; hg=0.9; L=3.2;Ttq=-19.313+295.27*n/1000-165.44*(n/1000).2+40.874*(n/1000).3-3.8445*(n/1000).4;%以2挡加速时间计算u(1)=0.377*r*600/i0/4.016;dt=0.01;w=1;t(1)=0;ig=4.016;while(u(w)=0.377*4000*r/4.016/i0) ig=3.09; end if(u(w+1)=0.377*4000*r/3.09/i0) ig=1.71; end if(u(w+1)=0.377*4000*
5、r/1.71/i0) ig=1; end t(w+1)=(w+1)*dt; w=w+1;endfigure;plot(t,u);axis(0 80 0 100);title(2挡原地起步加速时间曲线);xlabel(时间t/s),ylabel(车速u/(km/h);x1,y1=ginput(1);disp(加速到70km/h的时间);disp(x1); 以加速到70公里的时间作为加速时间。io5.0895.445.856.016.17加速时间24.055324.239624.055323.871023.68662计算六工况百公里油耗%等速百公里油耗n=600:1:4000; m=3650; g
6、=9.8; G=m*g;r=0.367; i0=5.089;nT=0.85; f=0.013;CdA=2.77;n1=815,1207,1614,2012,2603,3006,3403,3804;b0=1326.8,1354.7,1284.4,1122.9,1141.0,1051.2,1233.9,1129.7;b1=-416.46,-303.98,-189.75,-121.59,-98.893,-73.714,-84.478,-45.291 ;b2=72.379,36.657,14.524,7.0035,4.4763,2.8593,2.9788,0.71113;b3=-5.8629,-2.0
7、553,-0.51184,-0.18517,-0.091077,-0.05138,-0.047449,-0.00075215;b4=0.17768,0.043072,0.0068164,0.0018555,0.00068906,0.00035032,0.00028230,-0.000038568;B0=spline(n1,b0,n); B1=spline(n1,b1,n); B2=spline(n1,b2,n); B3=spline(n1,b3,n); B4=spline(n1,b4,n);pg=7;ig=1.00; Ua=0.377*r*n/ig/i0; Pf=G*f*Ua/3600; Pw
8、=CdA*Ua.3/76140; P=(Pf+Pw)/nT; b=B0+B1.*P+B2.*P.2+B3.*P.3+B4.*P.4; Q=P.*b./(1.02*Ua*pg); Iw1=1.798; Iw2=3.598; Iw=Iw1+Iw2; If=0.218;pg=7;Ff=G*f; ua1=25,40,50;Fw=CdA*ua1.2/21.15;Pa=(Ff+Fw).*ua1/3600/nT;b=spline(P,b,Pa);s=50,250,250;Q1=s.*Pa.*b./(102*ua1*pg);disp(Q1);Q1=Q1(1)+Q1(2)+Q1(3);%匀加速行驶的油耗%第一段
9、ua=25:1:40;a=0.25;q=1+Iw/(m*r2)+If*ig2*i02*nT/(m*r2);Pa=(G*f*ua/3600+CdA*ua.3/76140+q*m*ua.*a/3600)/nT;n=ua*ig*i0/0.377/r;B0=spline(n1,b0,n); B1=spline(n1,b1,n); B2=spline(n1,b2,n); B3=spline(n1,b3,n); B4=spline(n1,b4,n);b=B0+B1.*Pa+B2.*Pa.2+B3.*Pa.3+B4.*Pa.4;b=spline(Pa,b,Pa);Qs=Pa.*b/(367.1*pg);t=
10、1/(3.6*a);Q21=0;for n=1:15Q21=Q21+(Qs(n)+Qs(n+1)*t/2;enddisp(Q21);%第二段ua=40:1:50;a=0.20;q=1+Iw/(m*r2)+If*ig2*i02*nT/(m*r2);Pa=(G*f*ua/3600+CdA*ua.3/76140+q*m*ua.*a/3600)/nT;n=ua*ig*i0/0.377/r;B0=spline(n1,b0,n); B1=spline(n1,b1,n); B2=spline(n1,b2,n); B3=spline(n1,b3,n); B4=spline(n1,b4,n);b=B0+B1.*
11、Pa+B2.*Pa.2+B3.*Pa.3+B4.*Pa.4;b=spline(Pa,b,Pa);Qs=Pa.*b/(367.1*pg);t=1/(3.6*a);Q22=0;for n=1:10Q22=Q22+(Qs(n)+Qs(n+1)*t/2;enddisp(Q22);Q2=Q21+Q22;%匀减速行驶的油耗Qid=0.299;t3=19.3;Q3=Qid*t3;disp(Q3);%总油耗s=1075;Q=(Q1+Q2+Q3)*100/1075;disp(Q);io5.0895.445.856.016.17Q(L)13.000613.408613.739913.853513.96823. 绘
12、制燃油经济性-加速时间曲线Q= 13.0006 13.4086 13.7399 13.8535 13.9682;t= 24.0553 24.2396 24.0553 23.8710 23.6866;plot(Q,t,+r);hold on q1=linspace(Q(1),Q(5),100); t1=spline(Q,t,q1); %三次样条插值plot(q1,t1); %绘制燃油经济性-加速时间曲线title(燃油经济性加速时间曲线);xlabel(百公里油耗/(L/100km);ylabel(加速时间/s);gtext(i0=5.089),gtext(i0=5.44),gtext(i0=5
13、.85),gtext(i0=6.01),gtext(i0=6.17);4. 计算最高车速n=600:1:4000; r=0.367; i0=5.089; nT=0.85; f=0.013;m=3650; g=9.8; G=m*g; CdA=2.77; a=1.947; hg=0.9; L=3.2; If=0.218;Ttq=-19.313+295.27*n/1000-165.44*(n/1000).2+40.874*(n/1000).3-3.8445*(n/1000).4;%驱动力行驶阻力平衡图for ig=5.06,4.016,3.09,1.71,1 Ua=0.377*r*n/ig/i0;
14、Ft=Ttq*ig*i0*nT/r; plot(Ua,Ft); hold on;endFf=G*f;ua=0:0.1:max(Ua);Fw=CdA*ua.2/21.15;plot(ua,(Ff+Fw); title(驱动力-行驶阻力平衡图); xlabel(Ua/(km/h);ylabel(Ft/N);i05.0895.445.856.016.17umax102.4102.1100.299.297.95.绘制i0-umax曲线（求最高车速约束条件下临界i0值）i0=5.089 5.44 5.85 6.01 6.17;umax=102.4 102.1 100.2 99.2 97.9;plot(i
15、0,umax,+r);hold on i01=linspace(i0(1),i0(5); umax1=spline(i0,umax,i01); plot(i01,umax1); title(i0-umax曲线);xlabel(i0);ylabel(最高车速km/h);x,y=ginput(1);disp(临界i0=);disp(x);%根据最高车速约束条件，求临界i0值gtext(i0=5.089),gtext(i0=5.44),gtext(i0=5.85),gtext(i0=6.01),gtext(i0=6.17);临界i0=5.8855 最高车速大于100km/h. 所以io取5.089
16、5.44 5.856. 绘制i0-t图（求加速时间约束下临界i0值）i0=5.089 5.44 5.85 6.01 6.17;t= 24.0553 24.2396 24.0553 23.8710 25.6866;plot(i0,t,+r);hold on ；i01=linspace(i0(1),i0(5); umax1=spline(i0,t,i01); plot(i01,umax1); title(i0-t曲线);xlabel(i0);ylabel(加速时间s);zoom on;x,y=ginput(1);zoom off;disp(临界i0=);disp(x); gtext(i0=5.08
17、9),gtext(i0=5.44),gtext(i0=5.85),gtext(i0=6.01),gtext(i0=6.17);加速时间不超过25s 所以io可以取5.089 5.44 5.85 6.01 7最大爬坡度计算n=600:1:4000; r=0.367; i0=5.089; eff=0.85; f=0.013;m=3650; g=9.8; G=m*g; CdA=2.77; a=1.947; hg=0.9; L=3.2; If=0.218;Ttq=-19.313+295.27*n/1000-165.44*(n/1000).2+40.874*(n/1000).3-3.8445*(n/10
18、00).4;ig=5.06 4.016 3.09 1.71 1;Ft1=Ttq*ig(1)*i0*nT/r; ua1=0.377*r*n/ig(1)/i0;Ff=G*f; Fw1=CdA*ua1.2/21.15;Fz1=Ff+Fw1; Fi1=Ft1-Fz1; imax=100*tan(asin(max(Fi1/G);disp(汽车最大爬坡度=); disp(imax); disp(%);i05.0895.445.856.016.17i(%)28.973131.274134.013335.1017 36.2011绘制i0-i曲线（求最大爬坡度约束下i0)i0=5.089 5.44 5.85 6
19、.01 6.17;i=28.9731 31.2741 34.0133 35.1017 36.2011;plot(i0,i,+r); hold on i01=linspace(i0(1),i0(5),100); i1=spline(i0,i,i01); plot(i01,i1); title(i0-imax曲线);xlabel(i0);ylabel(imax(%);x,y=ginput(1);disp(临界i0=);disp(x); gtext(i0=5.089),gtext(i0=5.44),gtext(i0=5.85),gtext(i0=6.01),gtext(i0=6.17); 最大的爬坡
20、度大于32%，因此io大于5.55,io可取5.85 6.01 6.17。 8最高档动力因数校核一最大转矩计算n=600:1:4000;Tq=-19.313+295.27*(n/1000)-165.44*(n/1000).2+40.874*(n/1000).3-3.8445*(n/1000).4; plot(n,Tq);hold on;title(n-Tq曲线);xlabel(转速n r/min);ylabel(转矩Tq n*m);max_Tq,nn = max(Tq);disp(最大值:);disp(max_Tq);disp(对应的 n 的值:);disp(n(nn);最大转矩 174.96
21、67 最大转矩的转速 2041二校核最高档的动力因数Tmax=174.9667;n=2041;CdA=2.77;nT=0.85;ig=1;r=0.367;m=3650;g=9.8;G=m*g;i0=5.44 5.85;F=Tmax*i0*ig*nT/r;uat=0.377*n*r./(i0*ig);Fw=CdA*uat.*uat/21.15;D0max=(F-Fw)/GD0max = 0.0518 0.05779优化结果总结传动比i05.44（原传动比）5.85（优化后传动比）最高车速(km/h)102.1 100.2加速时间(s)24.239624.0553最大爬坡度(%)31.274134.0133最高档动力因数0.0518 0.0577百公里油耗(L/100km)13.4086 13.7399综上所诉优化后的传动比最高车速和加速时间指标较原来的传动比稍差，但最大爬坡度和最高档的动力因素较原传动比要好。