汽車主減速器傳動(dòng)比優(yōu)化某輕型貨車，車有關(guān)數(shù)據(jù)如下：發(fā)動(dòng)機(jī)的最低轉(zhuǎn)速nmin600r/min， 最高轉(zhuǎn)速nmax=4000r/min。 總質(zhì)量3650kg；車輪半徑0.367m；傳動(dòng)系機(jī)械效率nT0.85；滾動(dòng)阻力系數(shù)f0.013；空氣阻力系數(shù)*迎風(fēng)面積CDA2.77m2；飛輪轉(zhuǎn)動(dòng)慣量If0.218kg.m2；二前輪轉(zhuǎn)動(dòng)慣量Iw11.798kg.m2;軸距L=3.2m;質(zhì)心至前軸距離（滿載）a=1.947m；質(zhì)心高（滿載）hg=0.9m；四后輪轉(zhuǎn)動(dòng)慣量Iw23.598kg.m2；T=-19.313+295.27*(n/1000)-165.44*(n/1000).2+40.874*(n/1000).3-3.8445*(n/1000).4;怠速油耗Qid0.299mL/s（怠速轉(zhuǎn)速400r/min）。負(fù)荷特性曲線擬合公式為：b=B0+B1*Pe+B2*Pe.2+B3*Pe.3+B4*Pe.4.N/(r/min)B0B1B2B3B48151326.8-416.4672.379-5.86290.1776812071354.7-303.9836.657-2.05530.04307216141284.4-189.751452.4-0.511840.006816420121122.9-121.597.0035-0.185170.001855526031141.0-98.8934.4763-0.0910770.0006890630061051.2-73.7142.8593-0.051380.0003503234031233.9-84.4782.9788-0.0474490.0002823038041129.7-45.2910.71113-0.00075215-0.0000385681檔2檔3檔4檔5檔變速器傳動(dòng)比5.064.0163.091.711計(jì)算1計(jì)算加速時(shí)間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; Iw=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擋加速時(shí)間計(jì)算u(1)=0.377*r*600/i0/4.016;dt=0.01;w=1;t(1)=0;ig=4.016;while(u(w)<99.08) n(w)=u(w)*ig*i0/0.377/r;Ttq(w)=-19.313+295.27*n(w)/1000-165.44*(n(w)/1000)2+40.874*(n(w)/1000)3-3.8445*(n(w)/1000)4; Ft(w)=Ttq(w)*ig*i0*nT/r; Ff=G*f; Fw(w)=CdA*u(w)2/21.15; q=1+Iw/(m*r2)+If*ig2*i02*nT/(m*r2); a(w)=3.6*(Ft(w)-(Ff+Fw(w)/q/m; u(w+1)=u(w)+a(w)*dt; if(u(w+1)>=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*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擋原地起步加速時(shí)間曲線);xlabel(時(shí)間t/s),ylabel(車速u/(km/h);x1,y1=ginput(1);disp(加速到70km/h的時(shí)間);disp(x1); 以加速到70公里的時(shí)間作為加速時(shí)間。io5.0895.445.856.016.17加速時(shí)間24.055324.239624.055323.871023.68662計(jì)算六工況百公里油耗%等速百公里油耗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;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,-2.0553,-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=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);%勻加速行駛的油耗%第一段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=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.*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;%勻減速行駛的油耗Qid=0.299;t3=19.3;Q3=Qid*t3;disp(Q3);%總油耗s=1075;Q=(Q1+Q2+Q3)*100/1075;disp(Q);io5.0895.445.856.016.17Q(L)13.000613.408613.739913.853513.96823. 繪制燃油經(jīng)濟(jì)性-加速時(shí)間曲線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); %三次樣條插值plot(q1,t1); %繪制燃油經(jīng)濟(jì)性-加速時(shí)間曲線title(燃油經(jīng)濟(jì)性加速時(shí)間曲線);xlabel(百公里油耗/(L/100km);ylabel(加速時(shí)間/s);gtext(i0=5.089),gtext(i0=5.44),gtext(i0=5.85),gtext(i0=6.01),gtext(i0=6.17);4. 計(jì)算最高車速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;%驅(qū)動(dòng)力行駛阻力平衡圖for ig=5.06,4.016,3.09,1.71,1 Ua=0.377*r*n/ig/i0; 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(驅(qū)動(dòng)力-行駛阻力平衡圖); xlabel(Ua/(km/h);ylabel(Ft/N);i05.0895.445.856.016.17umax102.4102.1100.299.297.95.繪制i0-umax曲線（求最高車速約束條件下臨界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(i0,umax,+r);hold on i01=linspace(i0(1),i0(5); umax1=spline(i0,umax,i01); plot(i01,umax1); title(i0-umax曲線);xlabel(i0);ylabel(最高車速km/h);x,y=ginput(1);disp(臨界i0=);disp(x);%根據(jù)最高車速約束條件，求臨界i0值gtext(i0=5.089),gtext(i0=5.44),gtext(i0=5.85),gtext(i0=6.01),gtext(i0=6.17);臨界i0=5.8855 最高車速大于100km/h. 所以io取5.089 5.44 5.856. 繪制i0-t圖（求加速時(shí)間約束下臨界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曲線);xlabel(i0);ylabel(加速時(shí)間s);zoom on;x,y=ginput(1);zoom off;disp(臨界i0=);disp(x); gtext(i0=5.089),gtext(i0=5.44),gtext(i0=5.85),gtext(i0=6.01),gtext(i0=6.17);加速時(shí)間不超過25s 所以io可以取5.089 5.44 5.85 6.01 7最大爬坡度計(jì)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/1000).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(汽車最大爬坡度=); disp(imax); disp(%);i05.0895.445.856.016.17i(%)28.973131.274134.013335.1017 36.2011繪制i0-i曲線（求最大爬坡度約束下i0)i0=5.089 5.44 5.85 6.01 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曲線);xlabel(i0);ylabel(imax(%);x,y=ginput(1);disp(臨界i0=);disp(x); gtext(i0=5.089),gtext(i0=5.44),gtext(i0=5.85),gtext(i0=6.01),gtext(i0=6.17); 最大的爬坡度大于32%，因此io大于5.55,io可取5.85 6.01 6.17。 8最高檔動(dòng)力因數(shù)校核一最大轉(zhuǎn)矩計(jì)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曲線);xlabel(轉(zhuǎn)速n r/min);ylabel(轉(zhuǎn)矩Tq n*m);max_Tq,nn = max(Tq);disp(最大值:);disp(max_Tq);disp(對(duì)應(yīng)的 n 的值:);disp(n(nn);最大轉(zhuǎn)矩 174.9667 最大轉(zhuǎn)矩的轉(zhuǎn)速 2041二校核最高檔的動(dòng)力因數(shù)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優(yōu)化結(jié)果總結(jié)傳動(dòng)比i05.44（原傳動(dòng)比）5.85（優(yōu)化后傳動(dòng)比）最高車速(km/h)102.1 100.2加速時(shí)間(s)24.239624.0553最大爬坡度(%)31.274134.0133最高檔動(dòng)力因數(shù)0.0518 0.0577百公里油耗(L/100km)13.4086 13.7399綜上所訴優(yōu)化后的傳動(dòng)比最高車速和加速時(shí)間指標(biāo)較原來的傳動(dòng)比稍差，但最大爬坡度和最高檔的動(dòng)力因素較原傳動(dòng)比要好。