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1、 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nmin＝600r/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nT＝0.85；滾動(dòng)阻力系數(shù)f＝0.013； 空氣阻力系數(shù)*迎風(fēng)面積CDA＝2.77m2； 飛輪轉(zhuǎn)動(dòng)慣量If＝0.218kg.m2；二前輪轉(zhuǎn)動(dòng)慣量Iw1＝1.798kg.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Iw2＝3.598kg.m2；

2、 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Qid＝0.299mL/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) B0 B1 B2 B3 B4 815 1326.8 -416.46 72.379 -5.8629 0.17768 1207 1354.7 -303.98 36.657 -2.0553 0.0430

3、72 1614 1284.4 -189.75 1452.4 -0.51184 0.0068164 2012 1122.9 -121.59 7.0035 -0.18517 0.0018555 2603 1141.0 -98.893 4.4763 -0.091077 0.00068906 3006 1051.2 -73.714 2.8593 -0.05138 0.00035032 3403 1233.9 -84.478 2.9788 -0.047449 0.00028230 3804 1129.7 -45.291 0.71113

4、 -0.00075215 -0.000038568 1檔 2檔 3檔 4檔 5檔 變速器傳動(dòng)比 5.06 4.016 3.09 1.71 1 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/1

5、000-165.44*(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*

6、nT/r; Ff=G*f; Fw(w)=CdA*u(w)^2/21.15; q=1+Iw/(m*r^2)+If*ig^2*i0^2*nT/(m*r^2); 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+

7、1)>=0.377*4000*r/1.71/i0) ig=1; end t(w+1)=(w+1)*dt; w=w+1; end figure;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。 io 5.089 5.44 5.85 6.01 6.17 加速時(shí)間 2

8、4.0553 24.2396 24.0553 23.8710 23.6866 2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,-

9、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); B

10、1=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

11、.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*r^2)+If*ig^2*i0^2*nT/(m*r^2); Pa=(G*f*ua/3600+CdA*ua.^3/76140

12、+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=1:15 Q21=Q21+(Qs(n)+Qs(n+1))*t/2; end d

13、isp(Q21); %第二段 ua=40:1:50; a=0.20; q=1+Iw/(m*r^2)+If*ig^2*i0^2*nT/(m*r^2); 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

14、=spline(Pa,b,Pa); Qs=Pa.*b/(367.1*pg); t=1/(3.6*a); Q22=0; for n=1:10 Q22=Q22+(Qs(n)+Qs(n+1))*t/2; end disp(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); io 5.089 5.44 5.85 6.01 6.17 Q(L) 13.0006 13.408

15、6 13.7399 13.8535 13.9682 3. 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/

16、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).

17、^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; end Ff=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); i0 5.089 5.44 5.85 6

18、.01 6.17 umax 102.4 102.1 100.2 99.2 97.9 5.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

19、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 5.85 6. 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 2

20、4.0553 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(i

21、0=6.17); 加速時(shí)間不超過(guò)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.

22、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(%); i0 5.089 5.44 5.85 6.01 6.17 i(%) 28.9731 31.2741 34.0133 35.1017 36.2011 繪制i0-i曲線（求最大爬坡度約束下i0) i0

23、=[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),g

24、text(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*

25、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)/G D0max = 0.0518 0.0577 9優(yōu)化結(jié)果總結(jié) 傳動(dòng)比i0 5.44（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) 24.2396 24.0553 最大爬坡度(%) 31.2741 34.0133 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(lái)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。