汽车理论--习题1.3.doc

1) “汽车驱动力-行驶阻力平衡图”、“汽车行驶加速度曲线”、“汽车加速度倒数曲线”、“汽车爬坡度图”分析如下：利用MATLAB编程如下:ig=5.56,2.769,1.644,1.00,0.793; %变速器传动比i0=5.83; %主减速器传动比r=0.367; %车轮半径h=0.85; %传动系机械效率 cda=2.77; %空气阻力系数*迎风面积m=3880; %汽车总质量Iw1=1.798; %二前论转动惯量Iw2=3.598; %四后轮转动惯量 I=0.218; %飞轮转动惯量g=9.8; %重力加速度for j=1:5 for n=600:100:4000; ua(j,n)=(0.377*r*n)/(ig(j)*i0); c=n/1000; tq=-19.313+295.27*c-165.44*c.2+40.874*c.3-3.8445*c.4; %发动机转矩 Ft(j,n)=tq*ig(j)*i0*h/r; %汽车驱动力 f(j,n)=cda*ua(j,n)*ua(j,n)/21.15+494.3; %汽车行驶阻力 s(j)=1+(Iw1+Iw2)/(m*r.2)+(I*ig(j).2*i0.2*h)/(m*r.2); %汽车旋转质量换算系数 a(j,n)=(Ft(j,n)-f(j,n)/(s(j)*m) %汽车加速度 b(j,n)=1/a(j,n); D(j,n)=asin(Ft(j,n)-f(j,n)/(3800*g); %坡度角 i(j,n)=tan(D(j,n)*100 %坡度值 Pe(j,n)=Ft(j,n)*ua(j,n)/3600 %汽车功率 endendsubplot(2,2,1)k=600:100:4000plot(ua(1,k),Ft(1,k),ua(2,k),Ft(2,k),ua(3,k),Ft(3,k),ua(4,k),Ft(4,k),. ua(5,k),Ft(5,k),ua(1,k),f(1,k),ua(2,k),f(2,k),ua(5,k),f(5,k);title(汽车驱动力-行驶阻力平衡图)xlabel(ua/(km*h-1); ylabel(F/N);text(26, 12000,Ft1,HorizontalAlignment, right);text(36, 6450,Ft2,HorizontalAlignment, right);text(56, 3900,Ft3,HorizontalAlignment, right);text(66, 2500,Ft4,HorizontalAlignment, right);text(66, 1800,Ft5,HorizontalAlignment, right);text(100, 1400,Ff+Fw,HorizontalAlignment, right);subplot(2,2,2)k=600:100:4000plot(ua(1,k),a(1,k),ua(2,k),a(2,k),ua(3,k),a(3,k),ua(4,k),a(4,k),ua(5,k),a(5,k);title(汽车行驶加速度曲线)xlabel(ua/(km*h-1); ylabel(a/m*s-2) ;axis(0,120,-0.5,2.5);text(14, 2,1,HorizontalAlignment, right);text(20, 1.2,2,HorizontalAlignment, right);text(30, 0.7,3,HorizontalAlignment, right);text(50, 0.5,4,HorizontalAlignment, right);text(60, 0.15,5,HorizontalAlignment, right);subplot(2,2,3)k=600:100:4000plot(ua(1,k),b(1,k);hold onplot(ua(2,k),b(2,k),ua(3,k),b(3,k),ua(4,k),b(4,k),ua(5,k),b(5,k);title(汽车加速度倒数曲线)xlabel(ua(km/h); ylabel(1/a);axis(0,100,0,15);subplot(2,2,4)m=600:100:4000imax=max(i(1,m);plot(ua(1,m),i(1,m);hold onplot(ua(2,m),i(2,m),ua(3,m),i(3,m),ua(4,m),i(4,m),ua(5,m),i(5,m);ua=0:1:12;plot(ua,imax);title(汽车爬坡度图)xlabel(ua/(km*h-1); ylabel(i/(%) axis(0,120,-5,40);text(14, 32,1,HorizontalAlignment, right);text(23, 14,2,HorizontalAlignment, right);text(30,7,3,HorizontalAlignment, right);text(50,5,4,HorizontalAlignment, right);text(65, 0.3,5,HorizontalAlignment, right);text(25, 36,imax,HorizontalAlignment, right);grid off画出图形如下：2） “汽车功率平衡图”分析：利用MATLAB编程如下:ma=3880;%汽车的总质量g=9.81;%重力加速度r=0.367;%汽车车轮半径nt=0.85;%传动系机械效率f=0.013;%滚动阻力系数CdA=2.77;%空气阻力系数X迎风面积i0=5.83;%主减速器传动比If=0.218;%飞轮转动惯量Iw1=1.798;%二前轮转动惯量Iw2=3.598;%四后轮转动惯量%绘制变速器处于一档时汽车的驱动力曲线G=ma*g;ig=5.56,2.769,1.644,1.00,0.793; for j=1:5 for n=600:100:4000; ua(j,n)=(0.377*r*n)/(ig(j)*i0); c=n/1000; tq=-19.313+295.27*c-165.44*c.2+40.874*c.3-3.8445*c.4; %发动机转矩 Ft(j,n)=tq*ig(j)*i0*nt/r; %汽车驱动力 Pe(j,n)=Ft(j,n)*ua(j,n)/3600 %汽车功率 endendk=600:100:4000Pemax=max(Pe(1,k);plot(ua(1,k),Pe(1,k);hold on;plot(ua(2,k),Pe(2,k),ua(3,k),Pe(3,k),ua(4,k),Pe(4,k),ua(5,k),Pe(5,k);ua=0:0.1:110;Pf=G*f*ua/3600;Pw=CdA*ua.3/76140;Pz=(Pf+Pw)/nt;plot(ua,Pz,m,LineWidth,2);plot(ua,Pemax,k,LineWidth,2);title(汽车功率平衡图)xlabel(ua(km/h); ylabel(P/kw);text(10, 48,档位1,HorizontalAlignment, right);text(38, 48,档位2,HorizontalAlignment, right);text(54, 43.5,档位3,HorizontalAlignment, right);text(66, 35.5,档位4,HorizontalAlignment, right);text(66, 28,档位5,HorizontalAlignment, right);text(54, 57,Pemax,HorizontalAlignment, right);text(99, 57,(Pf+Pw)/nt,HorizontalAlignment, right);画出图形如下：3）由于滚动阻力系数为常数,用MATLAB画图命令可知: x =0:0.001:1plot(x,0.013)axis(0,1,0,0.05)title(滚动阻力系数与驱动力系数)xlabel(驱动力系数); ylabel(f)4）汽车最高车速分析: 由汽车驱动力-行驶阻力平衡图可知:汽车在处于5档时,Ft5 曲线与Ff+Fw曲线的交点便是Umax.根据这个原理,利用MATLAB编写程序解得Ft5=Ff+Fw,从而求的Umax:计算程序如下:%5d档变速器传动比ig5=0.793;%主减速器传动比i0=5.83; %车轮半径r=0.367; %传动系机械效率h=0.85; %空气阻力系数*迎风面积cda=2.77; %汽车动力Ft=(-19.313+295.27*c-165.44*c.2+40.874*c.3-3.8445*c.4)*ig5*i0*h/r;%汽车行驶阻力f=cda*ua*ua/21.15+494.3; format shorty=sym(-19.313+295.27*c-165.44*c2+40.874*c3-3.8445*c4)*0.793*5.83*0.85/0.367)-(2.77*(0.377*0.367*1000*c)/(0.793*5.83)2/21.15+494.3)c=solve(y)ua=(0.377*0.367*1000*c)/(0.793*5.83)解得:ua=99.08 故 Umax=99.08km/h5）汽车最大爬坡度及对应的附着率分析: 由汽车的爬坡度曲线分析可知汽车在1档的时候有最大的爬坡度.因为:汽车在一档的驱动力为:Ft1=Ttq*ig1*i0*h/r=75.075*Ttq=-1449.9.+5193.38*ua-681.72*ua2+39.46*ua3-0.87*ua4 行使阻力为: f=Ff+Fw=m*g*f+1/2*CdA*P*Ur2=1.698*ua2+494.3利用MATLAB编写计算程序如下:%1d档变速器传动比ig1=5.56;%主减速器传动比i0=5.83; %车轮半径r=0.367; %传动系机械效率h=0.85; %空气阻力系数*迎风面积cda=2.77; %汽车动力Ft=(-19.313+295.27*c-165.44*c.2+40.874*c.3-3.8445*c.4)*ig5*i0*h/r;%汽车行驶阻力f=cda*ua*ua/21.15+494.3; a=sym(asin(-1944.23+5193.38*ua-683.42*ua2+39.46*ua3-.87*ua4)/(3880*9.8)i=tan(a)uamax=solve(diff(i)syms uaamax=subs(a,ua,uamax(1)imax=tan(amax)imax=subs(imax,amax,amax)求得: imax =0.35 由于该车为后轮驱动,而上坡时可忽略空气阻力,滚动阻力和加速阻力,于是可得: C=imax/(a/L+hg*imax/L)=0.3485/(1.947/3.2+0.9*0.3485/3.2) =0.48故克服最大爬坡度所对应的附着率为0.48利用MATLAB编写画图程序如下:nmin=600;%发动机的最低速度nmax=4000;%发动机最高速度n=nmin:1:nmax;%发动机转速变化向量me=2000;%汽车的装载质量m0=1880;%汽车的整车整备质量ma=3880;%汽车的总质量g=9.81;%重力加速度r=0.367;%汽车车轮半径nt=0.85;%传动系机械效率f=0.013;%滚动阻力系数CdA=2.77;%空气阻力系数X迎风面积i0=5.83;%主减速器传动比If=0.218;%飞轮转动惯量Iw1=1.798;%二前轮转动惯量Iw2=3.598;%四后轮转动惯量ig1=5.56;%变速器一档传动比ig2=2.769;%变速器二档传动比ig3=1.644;%变速器三档传动比ig4=1;%变速器四档传动比ig5=0.793;%变速器五档传动比L=3.2;e=1.947;hg=0.9;%发动机使用外特性曲线公式Ttq=-19.313+295.27*(n/1000)-165.44*(n/1000).2+40.874*(n/1000).3-3.8445*(n/1000).4;%绘制变速器处于一档时汽车的驱动力曲线G=ma*g;Ff=G*f;ua1=0.377*r*n/(ig1*i0);%此时发动机转速对应的车速Ft1=Ttq*ig1*i0*nt/r;%汽车驱动力的计算F1=Ft1/G/sqrt(f*f+1);d=asin(F1);p=atan(f);y=d-p;i=tan(y);imax=max(i);Cq2=tan(y)*L/(e+hg*tan(y)+f;plot(ua1,imax);%绘制曲线命令hold on;plot(ua1,Cq2);title(汽车最大爬坡度及相应的附着率图);xlabel(ua(km/h);ylabel(imax及相应的附着率Cq2);gtext(imax=0.35,HorizontalAlignment, right);gtext(Cq2=0.48,HorizontalAlignment, right);axis(0,20,0.1,0.6);画出图形如下：附着率分析:1)汽车处于五档高速行驶时的附着率分析：利用MATLAB编写画图程序如下:ma=3880;%汽车的总质量g=9.81;%重力加速度r=0.367;%汽车车轮半径nt=0.85;%传动系机械效率f=0.013;%滚动阻力系数CdA=2.77;%空气阻力系数X迎风面积i0=5.83;%主减速器传动比If=0.218;%飞轮转动惯量Iw1=1.798;%二前轮转动惯量Iw2=3.598;%四后轮转动惯量L=3.2;e=1.947;hg=0.9;G=ma*g;Ff=G*f;ig=5.56,2.769,1.644,1.00,0.793; Cr1=0;for j=1:5 for n=600:100:4000; ua(j,n)=(0.377*r*n)/(ig(j)*i0); c=n/1000; tq=-19.313+295.27*c-165.44*c.2+40.874*c.3-3.8445*c.4; %发动机转矩 s(j)=1+(Iw1+Iw2)/(ma*r.2)+(If*ig(j).2*i0.2*nt)/(ma*r.2); %汽车旋转质量换算系数 C1(j,n)=(e*G/L)*f+CdA*ua(j,n)*ua(j,n)/21.15; C2(j,n)=e*G/L-2.8296*Cr1*ua(j,n)*ua(j,n); Cq2(j,n)=C1(j,n)/C2(j,n); endendk=600:100:4000plot(ua(5,k),Cq2(5,k);hold on;Cr2=0.15;for j=1:5 for n=600:100:4000; ua(j,n)=(0.377*r*n)/(ig(j)*i0); c=n/1000; tq=-19.313+295.27*c-165.44*c.2+40.874*c.3-3.8445*c.4; %发动机转矩 s(j)=1+(Iw1+Iw2)/(ma*r.2)+(If*ig(j).2*i0.2*nt)/(ma*r.2); %汽车旋转质量换算系数 C1(j,n)=(e*G/L)*f+CdA*ua(j,n)*ua(j,n)/21.15; C2(j,n)=e*G/L-2.8296*Cr2*ua(j,n)*ua(j,n); Cq2(j,n)=C1(j,n)/C2(j,n); endendk=600:100:4000plot(ua(5,k),Cq2(5,k);Cr3=0.28;for j=1:5 for n=600:100:4000; ua(j,n)=(0.377*r*n)/(ig(j)*i0); c=n/1000; tq=-19.313+295.27*c-165.44*c.2+40.874*c.3-3.8445*c.4; %发动机转矩 s(j)=1+(Iw1+Iw2)/(ma*r.2)+(If*ig(j).2*i0.2*nt)/(ma*r.2); %汽车旋转质量换算系数 C1(j,n)=(e*G/L)*f+CdA*ua(j,n)*ua(j,n)/21.15; C2(j,n)=e*G/L-2.8296*Cr3*ua(j,n)*ua(j,n); Cq2(j,n)=C1(j,n)/C2(j,n); endendk=600:100:4000plot(ua(5,k),Cq2(5,k);title(汽车处于五档高速行驶时的附着率图)xlabel(ua(km/h); ylabel(Cq2);gtext(Cr=0,HorizontalAlignment, right);gtext(Cr=0.15,HorizontalAlignment, right);gtext(Cr=0.28,HorizontalAlignment, right);axis(0,125,0,0.2);画出图形如下：2)汽车全力加速行驶时的附着率分析：利用MATLAB编写画图程序如下:ma=3880;%汽车的总质量g=9.81;%重力加速度r=0.367;%汽车车轮半径nt=0.85;%传动系机械效率f=0.013;%滚动阻力系数CdA=2.77;%空气阻力系数X迎风面积i0=5.83;%主减速器传动比If=0.218;%飞轮转动惯量Iw1=1.798;%二前轮转动惯量Iw2=3.598;%四后轮转动惯量L=3.2;e=1.947;hg=0.9;G=ma*g;Ff=G*f;ig=5.56,2.769,1.644,1.00,0.793; for j=1:5 for n=600:100:4000; ua(j,n)=(0.377*r*n)/(ig(j)*i0); c=n/1000; tq=-19.313+295.27*c-165.44*c.2+40.874*c.3-3.8445*c.4; %发动机转矩 Ft(j,n)=tq*ig(j)*i0*nt/r; %汽车驱动力 Fz(j,n)=CdA*ua(j,n)*ua(j,n)/21.15+Ff; %汽车行驶阻力 s(j)=1+(Iw1+Iw2)/(ma*r.2)+(If*ig(j).2*i0.2*nt)/(ma*r.2); %汽车旋转质量换算系数 a(j,n)=(Ft(j,n)-Fz(j,n)/(s(j)*ma) %汽车加速度 O(j,n)=asin(Ft(j,n)-Fz(j,n)/(ma*g); %坡度角 i(j,n)=tan(O(j,n); %坡度值 C1(j,n)=L*a(j,n); C2(j,n)=e*g+hg*a(j,n); Cq2(j,n)=C1(j,n)/C2(j,n); endendk=600:100:4000plot(ua(1,k),Cq2(1,k);hold on;plot(ua(2,k),Cq2(2,k),ua(3,k),Cq2(3,k),ua(4,k),Cq2(4,k),ua(5,k),Cq2(5,k);ua=0:0.1:115;q=0.6;plot(ua,q);title(汽车全力加速行驶时的附着率图)xlabel(ua(km/h); ylabel(Cq2);text(12, 0.28,1,HorizontalAlignment, right);text(23, 0.2,2,HorizontalAlignment, right);text(40, 0.15,3,HorizontalAlignment, right);text(60, 0.07,4,HorizontalAlignment, right);text(60, 0.02,5,HorizontalAlignment, right);text(55, 0.62,q,HorizontalAlignment, right);axis(0,120,0,0.7);画出图形如下：结果分析:由“汽车全力加速行驶时的附着率图”可知，汽车驱动轮的附着率Cq2=q,其中q为汽车的附着系数，其值为0.6。所以汽车在全力加速行驶时可发挥其全部性能。3)汽车全力爬坡行驶时的附着率分析：利用MATLAB编写画图程序如下:ma=3880;%汽车的总质量g=9.81;%重力加速度r=0.367;%汽车车轮半径nt=0.85;%传动系机械效率f=0.013;%滚动阻力系数CdA=2.77;%空气阻力系数X迎风面积i0=5.83;%主减速器传动比If=0.218;%飞轮转动惯量Iw1=1.798;%二前轮转动惯量Iw2=3.598;%四后轮转动惯量L=3.2;e=1.947;hg=0.9;G=ma*g;Ff=G*f;ig=5.56,2.769,1.644,1.00,0.793; for j=1:5 for n=600:100:4000; ua(j,n)=(0.377*r*n)/(ig(j)*i0); c=n/1000; tq=-19.313+295.27*c-165.44*c.2+40.874*c.3-3.8445*c.4; %发动机转矩 Ft(j,n)=tq*ig(j)*i0*nt/r; %汽车驱动力 Fz(j,n)=CdA*ua(j,n)*ua(j,n)/21.15+Ff; %汽车行驶阻力 s(j)=1+(Iw1+Iw2)/(ma*r.2)+(If*ig(j).2*i0.2*nt)/(ma*r.2); %汽车旋转质量换算系数 a(j,n)=(Ft(j,n)-Fz(j,n)/(s(j)*ma) %汽车加速度 O(j,n)=asin(Ft(j,n)-Fz(j,n)/(ma*g); %坡度角 i(j,n)=tan(O(j,n); %坡度值 C1(j,n)=L*g*sin(O(j,n); C2(j,n)=e*g*cos(O(j,n)+hg*g*sin(O(j,n); Cq2(j,n)=C1(j,n)/C2(j,n); endendk=600:100:4000plot(ua(1,k),Cq2(1,k);hold on;plot(ua(2,k),Cq2(2,k),ua(3,k),Cq2(3,k),ua(4,k),Cq2(4,k),ua(5,k),Cq2(5,k);ua=0:0.1:115;q=0.6;plot(ua,q);title(汽车全力爬坡行驶时的附着率图)xlabel(ua(km/h); ylabel(Cq2);text(12, 0.45,1,HorizontalAlignment, right);text(23, 0.21,2,HorizontalAlignment, right);text(40, 0.15,3,HorizontalAlignment, right);text(60, 0.08,4,HorizontalAlignment, right);text(60, 0.02,5,HorizontalAlignment, right);text(55, 0.62,q,HorizontalAlignment, right);axis(0,120,0,0.7);画出图形如下：结果分析:由“汽车全力爬坡行驶时的附着率图”可知，汽车驱动轮的附着率Cq2=q,其中q为汽车的附着系数，其值为0.6。所以汽车在全力加速行驶时可发挥其全部性能。4)汽车加速、上坡行驶时的附着率分析：利用MATLAB编写画图程序如下:ma=3880;%汽车的总质量g=9.81;%重力加速度r=0.367;%汽车车轮半径nt=0.85;%传动系机械效率f=0.013;%滚动阻力系数CdA=2.77;%空气阻力系数X迎风面积i0=5.83;%主减速器传动比If=0.218;%飞轮转动惯量Iw1=1.798;%二前轮转动惯量Iw2=3.598;%四后轮转动惯量L=3.2;e=1.947;hg=0.9;G=ma*g;Ff=G*f;ig=5.56,2.769,1.644,1.00,0