汽车理论课后习题Matlab程序

1.3确定一轻型货车的动力性能〔货车可装用4挡或5挡变速器，任选其中的一种进行整车性能计算〕：1〕绘制汽车驱动力与行驶阻力平衡图。2〕求汽车最高车速，最大爬坡度及克服该坡度时相应的附着率。3〕绘制汽车行驶加速度倒数曲线，用图解积分法求汽车用2档起步加速行驶至70km/h的车速－时间曲线，或者用计算机求汽车用2档起步加速行驶至70km/h的加速时间。轻型货车的有关数据：汽油发动机使用外特性的Tq-n曲线的拟合公式为式中，Tq为发动机转矩〔N•m〕;n为发动机转速〔r/min〕。发动机的最低转速nmin=600r/min,最高转速nmax=4000r/min。装载质量2000kg整车整备质量1800kg总质量3880kg车轮半径0.367m传动系机械效率ηt=0.85滚动阻力系数f=0.013空气阻力系数×迎风面积CDA=2.77m主减速器传动比i0=5.83飞轮转动惯量If=0.218kg•m2二前轮转动惯量Iw1=1.798kg•m2四后轮转动惯量Iw2=3.598kg•m2变速器传动比ig(数据如下表)Ⅰ档Ⅱ档Ⅲ档Ⅳ档Ⅴ档四档变速器6.093.091.711.00-五档变速器5.562.7691.6441.000.793轴距L=3.2m质心至前轴距离〔满载〕a=1.974m质心高〔满载〕hg=0.9m解：Matlab程序：(1)求汽车驱动力与行驶阻力平衡图和汽车最高车速程序：n=[600:10:4000];Tq=-19.313+295.27*(n/1000)-165.44*(n/1000).^2+40.874*(n/1000).^3-3.8445*(n/1000).^4;m=3880;g=9.8;nmin=600;nmax=4000;G=m*g;ig=[5.562.7691.6441.000.793];nT=0.85;r=0.367;f=0.013;CDA=2.77;i0=5.83;L=3.2;a=1.947;hg=0.9;If=0.218;Iw1=1.798;Iw2=3.598;Ft1=Tq*ig(1)*i0*nT/r;Ft2=Tq*ig(2)*i0*nT/r;Ft3=Tq*ig(3)*i0*nT/r;Ft4=Tq*ig(4)*i0*nT/r;Ft5=Tq*ig(5)*i0*nT/r;ua1=0.377*r*n/ig(1)/i0;ua2=0.377*r*n/ig(2)/i0;ua3=0.377*r*n/ig(3)/i0;ua4=0.377*r*n/ig(4)/i0;ua5=0.377*r*n/ig(5)/i0;ua=[0:5:120];Ff=G*f;Fw=CDA*ua.^2/21.15;Fz=Ff+Fw;plot(ua1,Ft1,ua2,Ft2,ua3,Ft3,ua4,Ft4,ua5,Ft5,ua,Fz);title('驱动力-行驶阻力平衡图');xlabel('ua(km/s)');ylabel('Ft(N)');gtext('Ft1'),gtext('Ft2'),gtext('Ft3'),gtext('Ft4'),gtext('Ft5'),gtext('Ff+Fw');zoomon;[x,y]=ginput(1);zoomoff;disp('汽车最高车速=');disp(x);disp('km/h');汽车最高车速=99.3006km/h(2)求汽车最大爬坡度程序：n=[600:10:4000];Tq=-19.313+295.27*(n/1000)-165.44*(n/1000).^2+40.874*(n/1000).^3-3.8445*(n/1000).^4;m=3880;g=9.8;nmin=600;nmax=4000;G=m*g;ig=[5.562.7691.6441.000.793];nT=0.85;r=0.367;f=0.013;CDA=2.77;i0=5.83;L=3.2;a=1.947;hg=0.9;If=0.218;Iw1=1.798;Iw2=3.598;Ft1=Tq*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;Zoomon;imax=100*tan(asin(max(Fi1/G)));disp('汽车最大爬坡度=');disp(imax);disp('%');汽车最大爬坡度=35.2197%(3)求最大爬坡度相应的附着率和求汽车行驶加速度倒数曲线程序：clearn=[600:10:4000];Tq=-19.313+295.27*(n/1000)-165.44*(n/1000).^2+40.874*(n/1000).^3-3.8445*(n/1000).^4;m=3880;g=9.8;nmin=600;nmax=4000;G=m*g;ig=[5.562.7691.6441.000.793];nT=0.85;r=0.367;f=0.013;CDA=2.77;i0=5.83;L=3.2;a=1.947;hg=0.9;If=0.218;Iw1=1.798;Iw2=3.598;Ft1=Tq*ig(1)*i0*nT/r;Ft2=Tq*ig(2)*i0*nT/r;Ft3=Tq*ig(3)*i0*nT/r;Ft4=Tq*ig(4)*i0*nT/r;Ft5=Tq*ig(5)*i0*nT/r;ua1=0.377*r*n/ig(1)/i0;ua2=0.377*r*n/ig(2)/i0;ua3=0.377*r*n/ig(3)/i0;ua4=0.377*r*n/ig(4)/i0;ua5=0.377*r*n/ig(5)/i0;Fw1=CDA*ua1.^2/21.15;Fw2=CDA*ua2.^2/21.15;Fw3=CDA*ua3.^2/21.15;Fw4=CDA*ua4.^2/21.15;Fw5=CDA*ua5.^2/21.15;Ff=G*f;deta1=1+(Iw1+Iw2)/(m*r^2)+(If*ig(1)^2*i0^2*nT)/(m*r^2);deta2=1+(Iw1+Iw2)/(m*r^2)+(If*ig(2)^2*i0^2*nT)/(m*r^2);deta3=1+(Iw1+Iw2)/(m*r^2)+(If*ig(3)^2*i0^2*nT)/(m*r^2);deta4=1+(Iw1+Iw2)/(m*r^2)+(If*ig(4)^2*i0^2*nT)/(m*r^2);deta5=1+(Iw1+Iw2)/(m*r^2)+(If*ig(5)^2*i0^2*nT)/(m*r^2);a1=(Ft1-Ff-Fw1)/(deta1*m);ad1=1./a1;a2=(Ft2-Ff-Fw2)/(deta2*m);ad2=1./a2;a3=(Ft3-Ff-Fw3)/(deta3*m);ad3=1./a3;a4=(Ft4-Ff-Fw4)/(deta4*m);ad4=1./a4;a5=(Ft5-Ff-Fw5)/(deta5*m);ad5=1./a5;plot(ua1,ad1,ua2,ad2,ua3,ad3,ua4,ad4,ua5,ad5);axis([099010]);title('汽车的加速度倒数曲线');xlabel('ua(km/h)');ylabel('1/a');gtext('1/a1');gtext('1/a2');gtext('1/a3');gtext('1/a4');gtext('1/a5');a=max(a1);af=asin(max(Ft1-Ff-Fw1)/G);C=tan(af)/(a/L+hg*tan(af)/L);disp('假设后轮驱动，最大爬坡度相应的附着率=');disp(C);假设后轮驱动，最大爬坡度相应的附着率=0.4219(4)>>clearnT=0.85;r=0.367;f=0.013;CDA=2.77;i0=5.83;If=0.218;Iw1=1.798;Iw2=3.598;L=3.2;a=1.947;hg=0.9;m=3880;g=9.8;G=m*g;ig=[5.562.7691.6441.000.793];nmin=600;nmax=4000;u1=0.377*r*nmin./ig/i0;u2=0.377*r*nmax./ig/i0;deta=0*ig;fori=1:5deta(i)=1+(Iw1+Iw2)/(m*r^2)+(If*(ig(i))^2*i0^2*nT)/(m*r^2);endua=[6:0.01:99];N=length(ua);n=0;Tq=0;Ft=0;inv_a=0*ua;delta=0*ua;Ff=G*f;Fw=CDA*ua.^2/21.15;fori=1:Nk=i;ifua(i)<=u2(2)n=ua(i)*(ig(2)*i0/r)/0.377;Tq=-19.313+295.27*(n/1000)-165.44*(n/1000)^2+40.874*(n/1000)^3-3.8445*(n/1000)^4;Ft=Tq*ig(2)*i0*nT/r;inv_a(i)=(deta(2)*m)/(Ft-Ff-Fw(i));delta(i)=0.01*inv_a(i)/3.6;elseifua(i)<=u2(3)n=ua(i)*(ig(3)*i0/r)/0.377;Tq=-19.313+295.27*(n/1000)-165.44*(n/1000)^2+40.874*(n/1000)^3-3.8445*(n/1000)^4;Ft=Tq*ig(3)*i0*nT/r;inv_a(i)=(deta(3)*m)/(Ft-Ff-Fw(i));delta(i)=0.01*inv_a(i)/3.6;elseifua(i)<=u2(4)n=ua(i)*(ig(4)*i0/r)/0.377;Tq=-19.313+295.27*(n/1000)-165.44*(n/1000)^2+40.874*(n/1000)^3-3.8445*(n/1000)^4;Ft=Tq*ig(4)*i0*nT/r;inv_a(i)=(deta(4)*m)/(Ft-Ff-Fw(i));delta(i)=0.01*inv_a(i)/3.6;elsen=ua(i)*(ig(5)*i0/r)/0.377;Tq=-19.313+295.27*(n/1000)-165.44*(n/1000)^2+40.874*(n/1000)^3-3.8445*(n/1000)^4;Ft=Tq*ig(5)*i0*nT/r;inv_a(i)=(deta(5)*m)/(Ft-Ff-Fw(i));delta(i)=0.01*inv_a(i)/3.6;enda=delta(1:k);t(i)=sum(a);endplot(t,ua);axis([0800100]);title('汽车2档原地起步换挡加速时间曲线');xlabel('时间t〔s〕');ylabel('速度ua〔km/h〕');>>ginputans=25.822370.073725.746770.0737所以汽车2档原地起步换挡加速行驶至70km/h的加速时间约为25.8s2.7货车装用汽油发动机的负荷特性与万有特性。负荷特性曲线的拟合公式为：其中，b为燃油消耗率[g/(kW•h)]；Pe为发动机净功率〔kW〕；拟合式中的系数随转速n变化。怠速油耗〔怠速转速400r/min〕。计算与绘制题1.3中货车的1〕汽车功率平衡图。2〕最高档与次高档的等速百公里油耗曲线。或利用计算机求货车按JB3352-83规定的六工况循环行驶的百公里油耗。计算中确定燃油消耗值b时，假设发动机转速与负荷特性中给定的转速不相等，可由相邻转速的两根曲线用插值法求得。解：Matlab程序：汽车功率平衡图程序：clearn=[600:10:4000];Tq=-19.313+295.27*(n/1000)-165.44*(n/1000).^2+40.874*(n/1000).^3-3.8445*(n/1000).^4;m=3880;g=9.8;G=m*g;ig=[5.562.7691.6441.000.793];nT=0.85;r=0.367;f=0.013;CDA=2.77;i0=5.83;L=3.2;a=1.947;hg=0.9;If=0.218;Iw1=1.798;Iw2=3.598;ua1=0.377*r*n/ig(1)/i0;ua2=0.377*r*n/ig(2)/i0;ua3=0.377*r*n/ig(3)/i0;ua4=0.377*r*n/ig(4)/i0;ua5=0.377*r*n/ig(5)/i0;Pe1=Tq.*ig(1)*i0.*ua1./(3600*r);Pe2=Tq.*ig(2)*i0.*ua2./(3600*r);Pe3=Tq.*ig(3)*i0.*ua3./(3600*r);Pe4=Tq.*ig(4)*i0.*ua4./(3600*r);Pe5=Tq.*ig(5)*i0.*ua5./(3600*r);ua=[0:0.35:119];Ff=G*f;Fw=CDA*ua.^2/21.15;Pf=Ff*ua/3600;Pw=Fw.*ua/3600;Pe0=(Pf+Pw)./nT;Pe=max(Pe1);plot(ua1,Pe1,ua2,Pe2,ua3,Pe3,ua4,Pe4,ua5,Pe5,ua,Pe0,ua,Pe);axis([01190100]);title('汽车功率平衡图');xlabel('ua(km/h)');ylabel('Pe(kw)');gtext('1'),gtext('2'),gtext('3'),gtext('4'),gtext('5'),gtext('(Pf+Pw)/et'),gtext('Pe');〔2〕最高档与次高档的等速百公里油耗曲线程序：clearn=600:1:4000;m=3880;g=9.8;G=m*g;ig=[5.562.7691.6441.000.793];nT=0.85;r=0.367;f=0.013;CDA=2.77;i0=5.83;L=3.2;a=1.947;hg=0.9;If=0.218;Iw1=1.798;Iw2=3.598;n0=[8151207161420122603300634033804];B00=[1326.81354.71284.41122.91141.01051.21233.91129.7];B10=[-416.46-303.98-189.75-121.59-98.893-73.714-84.478-45.291];B20=[72.37936.65714.5247.00354.47632.85932.97880.71113];B30=[-5.8629-2.0553-0.51184-0.18517-0.091077-0.05138-0.047449-0.00075215];B40=[0.177680.0430720.00681640.00185550.000689060.000350320.00028230-0.000038568];B0=spline(n0,B00,n);B1=spline(n0,B10,n);B2=spline(n0,B20,n);B3=spline(n0,B30,n);B4=spline(n0,B40,n);Ff=G*f;ua4=0.377*r*n/ig(4)/i0;ua5=0.377*r*n/ig(5)/i0;Fz4=Ff+CDA*(ua4.^2)/21.15;Fz5=Ff+CDA*(ua5.^2)/21.15;Pe4=Fz4.*ua4./(nT*3.6*1000);Pe5=Fz5.*ua5./(nT*3.6*1000);fori=1:1:3401b4(i)=B0(i)+B1(i)*Pe4(i)+B2(i)*Pe4(i).^2+B3(i)*Pe4(i).^3+B4(i)*Pe4(i).^4;b5(i)=B0(i)+B1(i)*Pe5(i)+B2(i)*Pe5(i).^2+B3(i)*Pe5(i).^3+B4(i)*Pe5(i).^4;endpg=7.0;Q4=Pe4.*b4./(1.02.*ua4.*pg);Q5=Pe5.*b5./(1.02.*ua5.*pg);plot(ua4,Q4,ua5,Q5);axis([01001030]);title('最高档与次高档等速百公里油耗曲线');xlabel('ua(km/h)');ylabel('百公里油耗〔L/100km〕');gtext('4'),gtext('5');3.1改变1.3题中轻型货车的主减速器传动比，做出为5.17、5.43、5.83、6.17、6.33时的燃油经济性—加速时间曲线，讨论不同值对汽车性能的影响。解：Matlab程序：主程序：i0=[5.17,5.43,5.83,6.17,6.33];%输入主传动比的数据fori=1:1:5y(i)=jiasushijian(i0(i));%求加速时间endy;fori=1:1:5b(i)=youhao(i0(i));%求对应i0的六工况百公里油耗endb;plot(b,y,'+r')holdonb1=linspace(b(1),b(5),100);y1=spline(b,y,b1);%三次样条插值plot(b1,y1);%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=5.17'),gtext('i0=5.43'),gtext('i0=5.83'),gtext('i0=6.17'),gtext('i0=6.33');子程序：(1)functiony=jiasushijian(i0)%求加速时间的处理函数n1=linspace(0,5000);%先求各个档位的驱动力nmax=4000;nmin=600;r=0.367;yita=0.85;CDA=2.77;f=0.013;G=(3880)*9.8;ig=[6.09,3.09,1.71,1.00];%i0=5.83fori=1:1:4%i为档数uamax(i)=chesu(nmax,r,ig(i),i0);%计算各个档位的最大速度与最小速度uamin(i)=chesu(nmin,r,ig(i),i0);ua(i,:)=linspace(uamin(i),uamax(i),100);n(i,:)=zhuansu(ua(i,:),r,ig(i),i0);%计算各个档位的转速范围Ttq(i,:)=zhuanju(n(i,:));%求出各档位的转矩范围Ft(i,:)=qudongli(Ttq(i,:),ig(i),i0,yita,r);%求出驱动力F(i,:)=f*G+CDA*(ua(i,:).^2)/21.15;%求出滚动阻力和空气阻力的和delta(i,:)=1+(1.798+3.598+0.218*(ig(i)^2)*(i0^2)*yita)/(3880*r^2);%求转动质量换算系数a(i,:)=1./(delta(i,:).*3880./(Ft(i,:)-F(i,:)));%求出加速度F2(i,:)=Ft(i,:)-F(i,:);end%下面分各个档位进行积分，求出加速时间temp1(1,:)=ua(2,:)/3.6;temp1(2,:)=1./a(2,:);n1=1;forj1=1:1:100ifua(3,j1)>max(ua(2,:))&&ua(3,j1)<=70temp2(1,n1)=ua(3,j1)/3.6;temp2(2,n1)=1./a(3,j1);n1=n1+1;endendn2=1;forj1=1:1:100ifua(4,j1)>max(ua(3,:))&&ua(4,j1)<=70;temp3(1,n2)=ua(4,j1)/3.6;temp3(2,n2)=1./a(4,j1);n2=n2+1;endendy=temp1(1,1)*temp1(2,1)+qiuji(temp1(1,:),temp1(2,:))+qiuji(temp2(1,:),temp2(2,:))+qiuji(temp3(1,:),temp3(2,:));end(2)functionua=chesu(n,r,ig,i0);%由转速计算车速ua=0.377*r.*n/(ig*i0);(3)functionn=zhuansu(ua,r,ig,i0);%求转速n=ig*i0.*ua./(0.377*r);end(4)functiony=zhuanju(n);%求转矩函数y=-19.313+295.27.*(n./1000)-165.44.*(n./1000).^2+40.874.*(n./1000).^3-3.8445.*(n./1000).^4;(5)functiony=qudongli(Ttq,ig,i0,yita,r);%求驱动力函数y=(ig*i0*yita.*Ttq)/r;end(6)functionp=qiuji(x0,y0)%求积分函数n0=size(x0);n=n0(2);x=linspace(x0(1),x0(n),200) ; y=spline(x0,y0,x); %插值 %figure;plot(x,y);p=trapz(x,y) ;end(7)%求不同i0下的六工况油耗functionb=youhao(i0);globalfGCDAyitamrIfIw1Iw2pgB0B1B2B3B4n%声明全局变量ig=[6.09,3.09,1.71,1.00];r=0.367;yita=0.85;CDA=2.77;f=0.013;%i0=5.83;G=(3880)*9.8;If=0.218;Iw1=1.798;Iw2=3.598;m=3880;%汽车的根本参数设定n0=[8151207161420122603300634033804];B00=[1326.81354.71284.41122.91141.01051.21233.91129.7];B10=[-416.46-303.98-189.75-121.59-98.893-73.714-84.478-45.291];B20=[72.37936.65714.5247.00354.47632.85932.97880.71113];B30=[-5.8629-2.0553-0.51184-0.18517-0.091077-0.05138-0.047449-0.00075215];B40=[0.177680.0430720.00681640.00185550.000689060.000350320.00028230-0.000038568];n=600:1:4000;B0=spline(n0,B00,n);B1=spline(n0,B10,n);B2=spline(n0,B20,n);%使用三次样条插值，保证曲线的光滑连续B3=spline(n0,B30,n);B4=spline(n0,B40,n);ua4=0.377*r.*n./(i0*ig(4));%求出发动机转速范围内对应的III、IV档车速F4=f*G+CDA*(ua4.^2)/21.15;%求出滚动阻力和空气阻力的和P_fw4=F4.*ua4./(yita*3.6*1000);%求出阻力功率fori=1:1:3401%用拟合公式求出各个燃油消耗率b4(i)=B0(i)+B1(i)*P_fw4(i)+B2(i)*(P_fw4(i))^2+B3(i)*(P_fw4(i))^3+B4(i)*(P_fw4(i))^4;endpg=7.06;%汽油的重度取7.06N/Lua4_m=[25,40,50];%匀速阶段的车速s_m=[50,250,250];%每段匀速走过的距离b4_m=spline(ua4,b4,ua4_m);%插值得出对应速度的燃油消耗率F4_m=f*G+CDA*(ua4_m.^2)/21.15;%车速对应的阻力P_fw4_m=F4_m.*ua4_m./(yita*3.6*1000);%发动机功率Q4_m=P_fw4_m.*b4_m.*s_m./(102.*ua4_m.*pg);Q4_a1=jiasu(40,25,ig(4),0.25,ua4,i0);Q4_a2=jiasu(50,40,ig(4),0.2,ua4,i0);Qid=0.299;tid=19.3;s=1075;Q_i=Qid*tid;%求出减速阶段的燃油消耗量Q4all=(sum(Q4_m)+Q4_a1+Q4_a2+Q_i)*100/s;%IV档六工况百公里燃油消耗量b=Q4all;(8)加速阶段处理函数functionq=jiasu(umax,umin,ig,a,ua0,i0);globalfGCDAyitamrIfIw1Iw2pgB0B1B2B3B4n;%i0;ua1=umin:1:umax;%把速度范围以1km/h为间隔进行划分delta=1+(Iw1+Iw2)/(m*r^2)+(If*ig^2*i0^2*yita)/(m*r^2);P0=(G*f.*ua0./3600+CDA.*ua0.^3/76140+(delta*m.*ua0/3600)*a)/yita;P=(G*f.*ua1/3600+CDA.*ua1.^3/76140+(delta*m.*ua1/3600)*a)/yita;dt=1/(3.6*a);%速度每增加1km/h所需要的时间fori=1:1:3401%重新利用拟合公式求出b与ua的关系b0(i)=B0(i)+B1(i)*P0(i)+B2(i)*(P0(i))^2+B3(i)*(P0(i))^3+B4(i)*(P0(i))^4;endb1=interp1(ua0,b0,ua1);%插值出各个速度节点的燃油消耗率Qt=P.*b1./(367.1.*pg);%求出各个速度节点的燃油消耗率i1=size(Qt);i=i1(2);Qt1=Qt(2:i-1);q=(Qt(1)+Qt(i))*dt./2+sum(Qt1)*dt;%求该加速阶段的燃油消耗量4.3一中型货车装有前后制动器分开的双管路制动系，其有关参数如下：载荷质量〔kg〕质心高hg/m轴距L/m质心至前轴距离a/m制动力分配系数β空载40800.8453.9502.1000.38满载92901.1703.9502.9500.38计算并绘制利用附着系数曲线和制动效率曲线求行驶车速Ua＝30km/h，在＝0.80路面上车轮不抱死的制动距离。计算时取制动系反响时间＝0.02s，制动减速度上升时间＝0.02s。求制动系前部管路损坏时汽车的制动距离s，制动系后部管路损坏时汽车的制动距离。解：Matlab程序：求利用附着系数曲线和制动效率曲线程序：cleark=4080;hgk=0.845;Lk=3.950;ak=2.10;betak=0.38;bk=Lk-ak;%空载时的参数mm=9290;hgm=1.170;Lm=3.950;am=2.950;betam=0.38;bm=Lm-am;%满载时的参数z=0:0.01:1.0;figure(1);fai=z;fai_fk=betak*z*Lk./(bk+z*hgk);%空载时前轴的φffai_fm=betam*z*Lm./(bm+z*hgm);%满载时前轴的φffai_rk=(1-betak)*z*Lk./(ak-z*hgk);%空载时后轴的φrfai_rm=(1-betam)*z*Lm./(am-z*hgm);%满载时后轴的φrplot(z,fai_fk,'b--',z,fai_fm,'r',z,fai_rk,'b--',z,fai_rm,'r',z,fai,'k');title('利用附着系数与制动强度的关系曲线');xlabel('制动强度(z/g)');ylabel('利用附着系数φ');gtext('φr(空载)'),gtext('φr(满载)'),gtext('φ=z'),gtext('φf(空载)'),gtext('φf(满载)');figure(2);Efk=z./fai_fk*100;%空载时前轴的制动效率Efm=z./fai_fm*100;Erk=z./fai_rk*100;Erm=z./fai_rm*100;plot(fai_fk,Efk,'b',fai_fm,Efm,'r',fai_rk,Erk,'b',fai_rm,Erm,'r');axis([010100]);title('前.后制动效率曲线');xlabel('附着系数φ');ylabel('制动效率%');gtext('Ef'),gtext('Er'),gtext('Er'),gtext('满载'),gtext('空载');问和(3)问程序：clearmk=4080;hgk=0.845;Lk=3.950;ak=2.10;betak=0.38;bk=Lk-ak;%空载时的参数mm=9290;hgm=1.170;Lm=3.950;am=2.950;betam=0.38;bm=Lm-am;%满载时的参数z=0:0.01:1;fai_fk=betak*z*Lk./(bk+z*hgk);%空载时前轴的φffai_fm=betam*z*Lm./(bm+z*hgm);%满载时前轴的φffai_rk=(1-betak)*z*Lk./(ak-z*hgk);%空载时后轴的φrfai_rm=(1-betam)*z*Lm./(am-z*hgm);%满载时后轴的φrEfk=z./fai_fk*100;%空载时前轴的制动效率Efm=z./fai_fm*100;Erk=z./fai_rk*100;Erm=z./fai_rm*100;t1=0.02;t2=0.02;ua0=30;fai=0.80;g=9.8;ak1=Erk(81)*g*fai/100;am1=Erm(81)*g*fai/100;Sk1=(t1+t2/2)*ua0/3.6+ua0^2/(25.92*ak1);%制动距离Sm1=(t1+t2/2)*ua0/3.6+ua0^2/(25.92*am1);disp('空载时，汽车制动距离Sk1=');disp(Sk1);disp('满载时，汽车制动距离Sm1=');disp(Sm1);ak2=fai*g*ak/(Lk+fai*hgk);am2=fai*g*am/(Lm+fai*hgm);ak3=fai*g*bk/(Lk-fai*hgk);am3=fai*g*bm/(Lk-fai*hgm);Sk2=(t1+t2/2)*ua0/3.6+ua0^2/(25.92*ak2);%制动距离Sm2=(t1+t2/2)*ua0/3.6+ua0^2/(25.92*am2);Sk3=(t1+t2/2)*ua0/3.6+ua0^2/(25.92*ak3);Sm3=(t1+t2/2)*ua0/3.6+ua0^2/(25.92*am3);disp('空载时，前制动器损坏，汽车制动距离Sk2=');disp(Sk2);disp('满载时，前制动器损坏，汽车制动距离Sm2=');disp(Sm2);disp('空载时，后制动器损坏，汽车制动距离Sk3=');disp(Sk3);disp('满载时，后制动器损坏，汽车制动距离Sm3=');disp(Sm3);空载时，汽车制动距离Sk1=7.8668满载时，汽车制动距离Sm1=5.6354空载时，前制动器损坏，汽车制动距离Sk2=10.0061满载时，前制动器损坏，汽车制动距离Sm2=7.5854空载时，后制动器损坏，汽车制动距离Sk3=8.0879满载时，后制动器损坏，汽车制动距离Sm3=13.59865.11二自由度轿车模型的有关参数如下：总质量m=1818.2绕Oz轴转动惯量轴距L=3.048质心至前轴距离a=1.463质心至后轴距离b=1.585前轮总侧偏刚度k1=-62618N/rad后轮总侧偏刚度k2=-110185N/rad转向系总传动比i=20试求：稳定性因数K、特征车速uch。稳态横摆角速度增益曲线、车速u=22.35m/s时的转向灵敏度。静态储藏系数S.M.，侧向加速度为0.4g时的前、后轮侧偏角绝对值之差与转弯半径的比值R/R0(R0=15m)。车速u=30.56m/s时，瞬态响应的横摆角速度波动的固有〔圆〕频率、阻尼比、反响时间与峰值反响时间解：Matlab程序：m=1818.2;Iz=3885;L=3.048;a=1.463;b=1.585;k1=-62618;k2=-110185;i=20;g=9.8;R0=15;u1=30.56;K=m*(a/k2-b/k1)/L^2;Uch=(1/K)^(1/2);%特征车速disp('稳定性因数(s^2/m^2)K=');disp(K);disp('特征车速(m/s)Uch=');disp(Uch);u=0:0.05:30;S=u./(L*(1+K*u.^2));%稳态横摆角速度增益plot(u,S);title('汽车稳态横摆角速度增益曲线');xlabel('车速u(m/s)');ylabel('稳态横摆角速度增益');disp('u=22.35m/s时，转向灵敏度为');disp(S(448));SM=k2/(k1+k2)-a/L;ay=0.4*g;A=K*ay*L;B=L/R0;R=L/(B-A);C=R/R0;%转弯半径比disp('静态储藏系数S.M.=');disp(SM);disp('侧向加速度为0.4g时前、后轮侧偏角绝对值之差(rad)a1-a2=');disp(A);disp('侧向加速度为0.4g时转弯半径比值R/R0=');disp(C);W0=L/u1*(k1*k2/(m*Iz)*(1+K*u1^2))^(1/2);%固有〔圆〕频率D=(-m*(k1*a^2+k2*b^2)-Iz*(k1+k2))/(2*L*(m*Iz*k1*k2*(1+K*u1^2))^(1/2));%阻尼比t=atan((1-D^2)^(1/2)/(-m*u1*a*W0/(L*k2)-D))/(W0*(1-D^2)^(1/2));%反响时间E=atan((1-D^2)^(1/2)/D)/(W0*(1-D^2)^(1/2))+t;%峰值反响时间disp('车速u=30.56m/s时的瞬态响应参数分别为：');disp('横摆角速度波动的固有(圆)频率(rad)为');disp(W0);disp('阻尼比为');disp(D);disp('反响时间(s)为');disp(t);disp('峰值反响时间(s)为');disp(E);稳定性因数(s^2/m^2)K=0.0024特征车速(m/s)Uch=20.6053u=22.35m/s时，转向灵敏度为3.3690静态储藏系数S.M.=0.1576侧向加速度为0.4g时前、后轮侧偏角绝对值之差(rad)a1-a2=0.0281侧向加速度为0.4g时转弯半径比值R/R0=1.1608车速u=30.56m/s时的瞬态响应参数分别为：横摆角速度波动的固有(圆)频率(rad)为5.5758阻尼比为0.5892反响时间(s)为0.1811峰值反响时间(s)为0.38996.5车身-车轮双质量系统参数：。“人体-座椅”系统参数：。车速，路面不平度系数，参考空间频率n0=0.1m-1。计算时频率步长，计算频率点数。计算并画出幅频特性、、和均方根值谱、、谱图。进一步计算值改变“人体-座椅”系统参数：。分析值随的变化。分别改变车身-车轮双质量系统参数：，。绘制三个响应量均方根值随以上四个系统参数变化的曲线。解：Matlab程序(1)问yps=0.25;%阻尼比ζgama=9;%刚度比γmu=10;%质量比μfs=3;ypss=0.25;g=9.8;a0=10^(-6);f0=1.5;ua=20;Gqn0=2.56*10^(-8);n0=0.1;detaf=0.2;N=180;f=detaf*[0:N];lamta=f/f0;lamtas=f/fs;Wf=0*f;deta=((1-lamta.^2).*(1+gama-1/mu*lamta.^2)-1).^2+4*yps^2*lamta.^2.*(gama-(1/mu+1)*lamta.^2).^2;z1_q=gama*sqrt(((1-lamta.^2).^2+4*yps^2*lamta.^2)./deta);z2_z1=sqrt((1+4*yps^2*lamta.^2)./((1-lamta.^2).^2+4*yps^2*lamta.^2));p_z2=sqrt((1+(2*ypss*lamtas).^2)./((1-lamtas.^2).^2+(2*ypss*lamtas).^2));z2_q=gama*sqrt((1+4*yps^2*lamta.^2)./deta);p_q=p_z2.*z2_q;jfg_Gqddf=4*pi^2*sqrt(Gqn0*n0^2*ua)*f;jfg_Gzdd1f=z1_q.*jfg_Gqddf;jfg_Gzdd2f=z2_q.*jfg_Gqddf;jfg_Gaf=p_q.*jfg_Gqddf;sigmaqdd=sqrt(trapz(f,jfg_Gqddf.^2));%路面不平度加速度均方根值sigmazdd1=sqrt(trapz(f,jfg_Gzdd1f.^2));%车轮加速度均方根值sigmazdd2=sqrt(trapz(f,jfg_Gzdd2f.^2));%车身加速度均方根值sigmaa=sqrt(trapz(f,jfg_Gaf.^2));%人体加速度均方根值fori=1:(N+1)iff(i)<=2Wf(i)=0.5;elseiff(i)<=4Wf(i)=f(i)/4;elseiff(i)<=12.5Wf(i)=1;elseWf(i)=12.5/f(i);endendkk=Wf.^2.*jfg_Gaf.^2;aw=sqrt(trapz(f,kk));%加权加速度均方根值Law=20*log10(aw/a0);%加权振级disp('路面不平度加速度均方根值为');disp(sigmaqdd);disp('车轮加速度均方根值为');disp(sigmazdd1);disp('车身加速度均方根值为');disp(sigmazdd2);disp('人体加速度均方根值为');disp(sigmaa);disp('加权加速度均方根值为');disp(aw);disp('加权振级');disp(Law);figure(1)plot(f,z1_q),title('幅频特性|z1/q|,(f=1.5Hz,ζ=0.25,γ=9,μ=10)'),xlabel('激振频率f/Hz'),ylabel('|z1/q|');figure(2)plot(f,z2_z1),title('幅频特性|z2/z1|,(f=1.5Hz,ζ=0.25,γ=9,μ=10)'),xlabel('激振频率f/Hz'),ylabel('|z2/z1|');figure(3)plot(f,p_z2),title('幅频特性|p/z2|,(fs=1.5Hz,ζs=0.25)'),xlabel('激振频率f/Hz'),ylabel('|p/z2|');figure(4)plot(f,jfg_Gzdd1f),title('车轮加速度均方根值√Gz1(f)谱图'),xlabel('激振频率f/Hz'),ylabel('√Gz1(f)');figure(5)plot(f,jfg_Gzdd2f),title('车身加速度均方根值√Gz2(f)谱图'),xlabel('激振频率f/Hz'),ylabel('√Gz2(f)');figure(6)plot(f,jfg_Gaf),title('人体加速度均方根值√Ga(f)谱图'),xlabel('激振频率f/Hz'),ylabel('√Ga(f)');路面不平度加速度均方根值为0.3523车轮加速度均方根值为0.2391车身加速度均方根值为0.0168人体加速度均方根值为0.0161加权加速度均方根值为0.0100加权振级80.0291(2)问程序1：cleargama=9;%刚度比γmu=10;%质量比μf0=1.5;g=9.8;a0=10^(-6);ua=20;Gqn0=2.56*10^(-8);n0=0.1;detaf=0.2;N=180;f=detaf*[0:N];lamta=f/f0;Wf=0*f;fori=1:(N+1)iff(i)<=2Wf(i)=0.5;elseiff(i)<=4Wf(i)=f(i)/4;elseiff(i)<=12.5Wf(i)=1;elseWf(i)=12.5/f(i);endendfs=3;ypss=0.25;ypss0=[0.125:0.005:0.5];a=0*ypss0;La=0*ypss0;M=length(ypss0);fori=1:Myps=ypss0(i);lamtas=f/fs;deta=((1-lamta.^2).*(1+gama-1/mu*lamta.^2)-1).^2+4*yps^2*lamta.^2.*(gama-(1/mu+1)*lamta.^2).^2;p_z2=sqrt((1+(2*ypss*lamtas).^2)./((1-lamtas.^2).^2+(2*ypss*lamtas).^2));z2_q=gama*sqrt((1+4*yps^2*lamta.^2)./deta);p_q=p_z2.*z2_q;jfg_Gqddf=4*pi^2*sqrt(Gqn0*n0^2*ua)*f;jfg_Gaf=p_q.*jfg_Gqddf;kk=Wf.^2.*jfg_Gaf.^2;aw(i)=sqrt(trapz(f,kk));endLaw=20*log10(aw/a0);figure(1)plot(ypss0,aw);title('aw随ζs的变化'),xlabel('“人体—座椅”系统的阻尼比ζs'),ylabel('aw/m*s^-2');figure(2)plot(ypss0,Law);title('Law随ζs的变化'),xlabel('“人体—座椅”系统的阻尼比ζs'),ylabel('Law/dB');程序2：clearyps=0.25;%阻尼比ζgama=9;%刚度比γmu=10;%质量比μf0=1.5;g=9.8;a0=10^(-6);ua=20;Gqn0=2.56*10^(-8);n0=0.1;detaf=0.2;N=180;f=detaf*[0:N];lamta=f/f0;Wf=0*f;fori=1:(N+1)iff(i)<=2Wf(i)=0.5;elseiff(i)<=4Wf(i)=f(i)/4;elseiff(i)<=12.5Wf(i)=1;elseWf(i)=12.5/f(i);endendypss=0.25;fs=[1.5:0.025:6];M=length(fs);fori=1:Mfs0=fs(i);lamtas=f/fs0;deta=((1-lamta.^2).*(1+gama-1/mu*lamta.^2)-1).^2+4*yps^2*lamta.^2.*(gama-(1/mu+1)*lamta.^2).^2;p_z2=sqrt((1+(2*ypss*lamtas).^2)./((1-lamtas.^2).^2+(2*ypss*lamtas).^2));z2_q=gama*sqrt((1+4*yps^2*lamta.^2)./deta);p_q=p_z2.*z2_q;jfg_Gqddf=4*pi^2*sqrt(Gqn0*n0^2*ua)*f;jfg_Gaf=p_q.*jfg_Gqddf;kk=Wf.^2.*jfg_Gaf.^2;aw(i)=sqrt(trapz(f,kk));endLaw=20*log10(aw/a0);figure(3)plot(fs,aw);title('aw随fs的变化'),xlabel('“人体—座椅”系统的固有频率fs'),ylabel('aw/m*s^-2');figure(4)plot(fs,Law);title('Law随fs的变化'),xlabel('“人体—座椅”系统的固有频率fs'),ylabel('Law/dB');〔3〕问程序1：clearfigure(1)fs=3;yps_s=0.25;g=9.8;ua=20;Gqn0=2.56*10^(-8);n0=0.1;detaf=0.2;N=180;f0=1.5;yps=0.25;gama=9;mu=10;ff0=[0.25:0.05:3];sigmaz2=0*ff0;sigmafd=0*ff0;sigmaFd_G=0*ff0;M=length(ff0);fori=1:Mf0=ff0(i);f=detaf*[0:N];lamta=f/f0;lamtas=f/fs;deta=((1-lamta.^2).*(1+gama-1/mu*lamta.^2)-1).^2+4*yps^2*lamta.^2.*(gama-(1/mu+1)*lamta.^2).^2;z2_qdot=2*pi*f*gama.*sqrt((1+4*yps^2*lamta.^2)./deta);fd_qdot=gama*lamta.^2./(2*pi*f+eps)./sqrt(deta);Fd_Gqdot=2*pi*f*gama/g.*sqrt(((lamta.^2/(mu+1)-1).^2+4*yps^2*lamta.^2)./deta);Gq_dotf=4*pi^2*Gqn0*n0^2*ua;Gz2f=(z2_qdot).^2*Gq_dotf;Gfd_qf=(fd_qdot).^2*Gq_dotf;GFd_Gf=(Fd_Gqdot).^2*Gq_dotf;sigmaz2(i)=sqrt(trapz(f,Gz2f));sigmafd(i)=sqrt(trapz(f,Gfd_qf));sigmaFd_G(i)=sqrt(trapz(f,GFd_Gf));iff0==1.5sgmz2=sigmaz2(i);sgmfd=sigmafd(i);sgmFd_G=sigmaFd_G(i);endendsz2=20*log10(sigmaz2/sgmz2);sfd=20*log10(sigmafd/sgmfd);sFd_G=20*log10(sigmaFd_G/sgmFd_G);plot(ff0,sz2,'r-',ff0,sfd,'b-.',ff0,sFd_G,'k--');axis([0.253-2515]);title('三个响应量均方根值随f0变化的曲线'),xlabel('车身局部固有频率f0/Hz'),ylabel('σz2/dB,σfd/dB,σFd/G/dB');程序2：clearfigure(2)fs=3;yps_s=0.25;g=9.8;ua=20;Gqn0=2.56*10^(-8);n0=0.1;detaf=0.2;N=180;f0=1.5;yps=0.25;gama=9;mu=10;c=(0.5-0.125)/180;yps0=[0.125:c:0.5];sigmaz2=0*yps0;sigmafd=0*yps0;sigmaFd_G=0*yps0;M=length(yps0);fori=1:Myps=yps0(i);f=detaf*[0:N];lamta=f/f0;lamtas=f/fs;deta=((1-lamta.^2).*(1+gama-1/mu*lamta.^2)-1).^2+4*yps^2*lamta.^2.*(gama-(1/mu+1)*lamta.^2).^2;z2_qdot=2*pi*f*gama.*sqrt((1+4*yps^2*lamta.^2)./deta);fd_qdot=gama*lamta.^2./(2*pi*f+eps)./sqrt(deta);Fd_Gqdot=2*pi*f*gama/g.*sqrt(((lamta.^2/(mu+1)-1).^2+4*yps^2*lamta.^2)./deta);Gq_dotf=4*pi^2*Gqn0*n0^2*ua;Gz2f=(z2_qdot).^2*Gq_dotf;Gfd_qf=(fd_qdot).^2*Gq_dotf;GFd_Gf=(Fd_Gqdot).^2*Gq_dotf;sigmaz2(i)=sqrt(trapz(f,Gz2f));sigmafd(i)=sqrt(trapz(f,Gfd_qf));sigmaFd_G(i)=sqrt(trapz(f,GFd_Gf));ifyps==0.25sgmz2=sigmaz2(i);sgmfd=sigmafd(i);sgmFd_G=sigmaFd_G(i);