Car Theoretical Dynamics Simulation-MATLAB

introduction

Automobile dynamics refers to the average driving speed that can be achieved by the longitudinal external force on the car when the car is running straight on a good road. The evaluation indexes of automobile dynamic performance mainly include the maximum speed of the automobile, the acceleration time and the maximum climbing gradient.

1. Vehicle dynamics simulation parameters

1. Basic car parameters:

Total car mass m/kg	Coefficient of rolling resistance $f$	Air resistance coefficient $C_D$	Windward frontal area A/ $m^2$	Rolling radius r/ $m$	Rotating mass conversion factor $d$	Transmission efficiency ${the}_t$	Gear ratio of final drive $i_0$	The transmission ratio ig i_g of each gear of the transmission$i_g$
936	0.012	0.3	1.75	0.272	1.03+0.04*$i_g$	0.9	4.388	[3.416,1.894,1.280,1.000,0.757]

2. Engine speed and torque data:

Minimum speed: 800 r/min; maximum speed: 6800r/min.
The known speed and torque data are as follows:

Speed/(r/min)	1000	1500	2000	2500	3000	3500	4000	4500	5000
Torque/N • m	78.6	83.0	85.0	86. 6	87. 1	85.9	84.7	82.5	80. 5

Using the speed and torque data in the above table, write the engine torque and speed relationship curve fitting program in MATLAB as follows:

n=[1000,1500,2000,2500,3000,3500,4000,4500,5000];
T=[78.6,83.0,85.0,86.6,87.1,85.9,84.7,82.5,80.5];
cftool；

After the program runs,

use the drop-down menus of "X data" and "Y data" in 1 to read the speed data n and torque data T; select the polynomial function, and select the fitting times to be 3 in 2, and the fitting graph window displays The fitting curve diagram shows the parameters p1/p2/p3 of the fitting formula in 3, and the relationship between the engine torque and the speed is obtained according to the parameters:

Ttq=(2.714e-10)*n.^3-(4.255e-06)*n.^2+0.01756*n+65.07

Note: If this formula is known, it can be directly used in dynamic simulation without re-fitting.

2. Driving Force-Driving Resistance Balance Diagram

1. Driving force-traveling resistance balance diagram

1.1 MATLAB program

n=800:10:6800;
Ttq=(2.714e-10)*n.^3-(4.255e-06)*n.^2+0.01756*n+65.07;
m=936;%质量
r=0.272;%滚动半径
nt=0.9;%传动效率
CD=0.3;%空气阻力系数
A=1.75;%迎风面积
f=0.012;%滚动阻力系数
i0=4.388;%主减速器传动比
ig=[3.416,1.894,1.28,1.00,0.757];%变速器各档传动比
g=9.8;%重力加速度
%汽车的基本参数
Ft1=Ttq*ig(1)*i0*nt/r;
Ft2=Ttq*ig(2)*i0*nt/r;
Ft3=Ttq*ig(3)*i0*nt/r;
Ft4=Ttq*ig(4)*i0*nt/r;
Ft5=Ttq*ig(5)*i0*nt/r;
%各档位的驱动力
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;
%各档位的速度与转速之间的关系
ua=0:5:220;
Ff=m*g*f;%滚动阻力
Fw=CD*A*ua.^2/21.25;%空气阻力
Fx=Ff+Fw;%行驶阻力
plot(ua1,Ft1,ua2,Ft2,ua3,Ft3,ua4,Ft4,ua5,Ft5,ua,Fx);
text(35,4100,'Ft1');
text(55,2400,'Ft2');
text(100,1600,'Ft3');
text(135,1300,'Ft4');
text(200,950,'Ft5');
text(175,1200,'Ft+Fw');
xlabel('车速/（km/h）');
ylabel('汽车驱动力/N,行驶阻力/N');
%驱动力-行驶阻力平衡图
Fw5=CD*A*ua5.^2/21.25;
Fx2=Ff+Fw5;
k=find(abs(Ft5-Fx2)<1.5);
uamax=ua5(k);
fprintf('最高车速Vmax = %.2f km/h\n',uamax);
%根据驱动力-行驶阻力平衡图可知驱动力曲线与行驶阻力曲线有交点，交点所对应的车速就是最高车速。

Maximum vehicle speed $V_{max}=173.49km/h$

1.2 Running results

Maximum vehicle speed $V_{max}=173.49km/h$

2. Acceleration curves of each gear

2.1 MATLAB program

n=800:10:6800;
Ttq=(2.714e-10)*n.^3-(4.255e-06)*n.^2+0.01756*n+65.07;
m=936;%质量
r=0.272;%滚动半径
nt=0.9;%传动效率
CD=0.3;%空气阻力系数
A=1.75;%迎风面积
f=0.012;%滚动阻力系数
i0=4.388;%主减速器传动比
ig=[3.416,1.894,1.28,1.00,0.757];%变速器各档传动比
g=9.8;%重力加速度
Ft1=Ttq*ig(1)*i0*nt/r;
Ft2=Ttq*ig(2)*i0*nt/r;
Ft3=Ttq*ig(3)*i0*nt/r;
Ft4=Ttq*ig(4)*i0*nt/r;
Ft5=Ttq*ig(5)*i0*nt/r;
%各档位的驱动力
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;
%各档位的速度与转速之间的关系
Fw1=CD*A*ua1.^2/21.25;
Fw2=CD*A*ua2.^2/21.25;
Fw3=CD*A*ua3.^2/21.25;
Fw4=CD*A*ua4.^2/21.25;
Fw5=CD*A*ua5.^2/21.25;
%各档位的迎风阻力
Ff=m*g*f;
dt1=1.03+0.04*ig(1);
dt2=1.03+0.04*ig(2);
dt3=1.03+0.04*ig(3);
dt4=1.03+0.04*ig(4);
dt5=1.03+0.04*ig(5);
%各档位的旋转质量换算系数
a1=(Ft1-Ff-Fw1)/dt1/m;
a2=(Ft2-Ff-Fw2)/dt2/m;
a3=(Ft3-Ff-Fw3)/dt3/m;
a4=(Ft4-Ff-Fw4)/dt4/m;
a5=(Ft5-Ff-Fw5)/dt5/m;
%各档位的加速度
plot(ua1,a1,ua2,a2,ua3,a3,ua4,a4,ua5,a5);
text(35,3.7,'一档');
text(55,2.2,'二档');
text(85,1.4,'三档');
text(130,0.8,'四档');
text(165,0.3,'五档');
ylim([0 4]);
xlabel('车速/（km/h）');
ylabel('加速度/(m/s^2)');
%加速度曲线图
k=max(a1);
amax=k;
fprintf('最大加速度amax = %.2f m/s^2\n',amax);
%由加速度曲线图可知一档时有最大加速度

2.2 Running results

Maximum acceleration $a_{max}=3.83m/s^2$

3. Climbing curves of each gear

3.1 MATLAB program

n=800:10:6800;
Ttq=(2.714e-10)*n.^3-(4.255e-06)*n.^2+0.01756*n+65.07;
m=936;%质量
r=0.272;%滚动半径
nt=0.9;%传动效率
CD=0.3;%空气阻力系数
A=1.75;%迎风面积
f=0.012;%滚动阻力系数
i0=4.388;%主减速器传动比
ig=[3.416,1.894,1.28,1.00,0.757];%变速器各档传动比
g=9.8;%重力加速度
Ft1=Ttq*ig(1)*i0*nt/r;
Ft2=Ttq*ig(2)*i0*nt/r;
Ft3=Ttq*ig(3)*i0*nt/r;
Ft4=Ttq*ig(4)*i0*nt/r;
Ft5=Ttq*ig(5)*i0*nt/r;
%各档位的驱动力
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;
%各档位的速度与转速之间的关系
Fw1=CD*A*ua1.^2/21.25;
Fw2=CD*A*ua2.^2/21.25;
Fw3=CD*A*ua3.^2/21.25;
Fw4=CD*A*ua4.^2/21.25;
Fw5=CD*A*ua5.^2/21.25;
%各档位的迎风阻力
Ff=m*g*f;
i1=asin((Ft1-Ff-Fw1)/m/g);
i2=asin((Ft2-Ff-Fw2)/m/g);
i3=asin((Ft3-Ff-Fw3)/m/g);
i4=asin((Ft4-Ff-Fw4)/m/g);
i5=asin((Ft5-Ff-Fw5)/m/g);
%各档位的爬坡度
plot(ua1,i1,ua2,i2,ua3,i3,ua4,i4,ua5,i5);
text(35,0.45,'一档');
text(55,0.25,'二档');
text(90,0.16,'三档');
text(130,0.09,'四档');
text(165,0.03,'五档');
ylim([0 0.5]);
xlabel('车速/（km/h）');
ylabel('爬坡度');
%爬坡度曲线图
k=max(i1);
imax=k;
anglemax=imax*45;
fprintf('最大爬坡度imax = %.2f\n',imax);
fprintf('最大坡度角anglemax = %.2f°\n',anglemax);
%由爬坡度曲线图可知一档时有最大爬坡度和最大坡度角

3.2 Running Results

Maximum gradeability $i_{max}=0.47$
maximum slope angle$angl{e}_{max}=21.33°$

3. Dynamic characteristic diagram

1. Dynamic characteristic diagram

1.1 MATLAB program

n=800:10:6800;
Ttq=(2.714e-10)*n.^3-(4.255e-06)*n.^2+0.01756*n+65.07;
m=936;%质量
r=0.272;%滚动半径
nt=0.9;%传动效率
CD=0.3;%空气阻力系数
A=1.75;%迎风面积
i0=4.388;%主减速器传动比
ig=[3.416,1.894,1.28,1.00,0.757];%变速器各档传动比
g=9.8;%重力加速度
Ft1=Ttq*ig(1)*i0*nt/r;
Ft2=Ttq*ig(2)*i0*nt/r;
Ft3=Ttq*ig(3)*i0*nt/r;
Ft4=Ttq*ig(4)*i0*nt/r;
Ft5=Ttq*ig(5)*i0*nt/r;
%各档位的驱动力
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;
%各档位的速度与转速之间的关系
ua=0:5:220;
Fw1=CD*A*ua1.^2/21.25;
Fw2=CD*A*ua2.^2/21.25;
Fw3=CD*A*ua3.^2/21.25;
Fw4=CD*A*ua4.^2/21.25;
Fw5=CD*A*ua5.^2/21.25;
%各档位的迎风阻力
D1=(Ft1-Fw1)/m/g;
D2=(Ft2-Fw2)/m/g;
D3=(Ft3-Fw3)/m/g;
D4=(Ft4-Fw4)/m/g;
D5=(Ft5-Fw5)/m/g;
%各档位的动力因数
c=1.2;%良好沥青路面
f0=0.008;%范围：0.0072～0.0120以上
f1=0.00025;%范围：0.00025～0.00280
f4=0.002;%范围：0.00065～0.002以上
f=c*(f0+f1*(ua/100)+f4*(ua/100).^4);%良好道路上轿车轮胎的滚动阻力系数
plot(ua1,D1,ua2,D2,ua3,D3,ua4,D4,ua5,D5,ua,f);
text(35,0.45,'一档');
text(68,0.25,'二档');
text(104,0.15,'三档');
text(144,0.09,'四档');
text(180,0.02,'五档');
text(60,0.03,'f');
ylim([0 0.5]);
xlabel('速度/（km/h）');
ylabel('动力因数');
%动力特性图
f5=c*(f0+f1*(ua5/100)+f4*(ua5/100).^4);
k=find(abs(D5-f5)<0.0002);
uamax=ua5(k);
fprintf('最高车速Vmax = %.2f km/h\n',uamax);
%由动力特性图可知五档时有最高车速值

1.2 Running results

Maximum vehicle speed $V_{max}=160.53km/h$

2. Acceleration curves of each gear

2.1 MATLAB program

n=800:10:6800;
Ttq=(2.714e-10)*n.^3-(4.255e-06)*n.^2+0.01756*n+65.07;
m=936;%质量
r=0.272;%滚动半径
nt=0.9;%传动效率
CD=0.3;%空气阻力系数
A=1.75;%迎风面积
i0=4.388;%主减速器传动比
ig=[3.416,1.894,1.28,1.00,0.757];%变速器各档传动比
g=9.8;%重力加速度
Ft1=Ttq*ig(1)*i0*nt/r;
Ft2=Ttq*ig(2)*i0*nt/r;
Ft3=Ttq*ig(3)*i0*nt/r;
Ft4=Ttq*ig(4)*i0*nt/r;
Ft5=Ttq*ig(5)*i0*nt/r;
%各档位的驱动力
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;
%各档位的速度与转速之间的关系
ua=0:5:220;
Fw1=CD*A*ua1.^2/21.25;
Fw2=CD*A*ua2.^2/21.25;
Fw3=CD*A*ua3.^2/21.25;
Fw4=CD*A*ua4.^2/21.25;
Fw5=CD*A*ua5.^2/21.25;
%各档位的迎风阻力
D1=(Ft1-Fw1)/m/g;
D2=(Ft2-Fw2)/m/g;
D3=(Ft3-Fw3)/m/g;
D4=(Ft4-Fw4)/m/g;
D5=(Ft5-Fw5)/m/g;
%各档位的动力因数
c=1.2;%良好沥青路面
f0=0.008;%范围：0.0072～0.0120以上
f1=0.00025;%范围：0.00025～0.00280
f4=0.002;%范围：0.00065～0.002以上
f=c*(f0+f1*(ua/100)+f4*(ua/100).^4);%良好道路上轿车轮胎的滚动阻力系数
f21=c*(f0+f1*(ua1/100)+f4*(ua1/100).^4);
f22=c*(f0+f1*(ua2/100)+f4*(ua2/100).^4);
f23=c*(f0+f1*(ua3/100)+f4*(ua3/100).^4);
f24=c*(f0+f1*(ua4/100)+f4*(ua4/100).^4);
f25=c*(f0+f1*(ua5/100)+f4*(ua5/100).^4);
%各档位的滚动阻力系数
dt1=1.03+0.04*ig(1);
dt2=1.03+0.04*ig(2);
dt3=1.03+0.04*ig(3);
dt4=1.03+0.04*ig(4);
dt5=1.03+0.04*ig(5);
%各档位的旋转质量换算系数
a1=g/dt1*(D1-f21);
a2=g/dt2*(D2-f22);
a3=g/dt3*(D3-f23);
a4=g/dt4*(D4-f24);
a5=g/dt5*(D5-f25);
%各档位的加速度
plot(ua1,a1,ua2,a2,ua3,a3,ua4,a4,ua5,a5);
text(40,3.5,'一档');
text(70,2,'二档');
text(108,1.2,'三档');
text(140,0.6,'四档');
text(160,0.15,'五档');
ylim([0 4]);
xlabel('速度/（km/h）');
ylabel('加速度/（m/s^2）');
%加速度曲线图
k=max(D1-f21);
amax=g/dt1*k;
fprintf('最大加速度amax = %.2f m/s^2\n',amax);
%由加速度曲线图可知一档时有最大加速度

2.2 Running results

Maximum acceleration $a_{max}=3.85m/s^2$

3. Climbing curves of each gear

3.1 MATLAB program

n=800:10:6800;
Ttq=(2.714e-10)*n.^3-(4.255e-06)*n.^2+0.01756*n+65.07;
m=936;%质量
r=0.272;%滚动半径
nt=0.9;%传动效率
CD=0.3;%空气阻力系数
A=1.75;%迎风面积
f=0.012;%滚动阻力系数
i0=4.388;%主减速器传动比
ig=[3.416,1.894,1.28,1.00,0.757];%变速器各档传动比
g=9.8;%重力加速度
Ft1=Ttq*ig(1)*i0*nt/r;
Ft2=Ttq*ig(2)*i0*nt/r;
Ft3=Ttq*ig(3)*i0*nt/r;
Ft4=Ttq*ig(4)*i0*nt/r;
Ft5=Ttq*ig(5)*i0*nt/r;
%各档位的驱动力
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;
%各档位的速度与转速之间的关系
ua=0:5:220;
Fw1=CD*A*ua1.^2/21.25;
Fw2=CD*A*ua2.^2/21.25;
Fw3=CD*A*ua3.^2/21.25;
Fw4=CD*A*ua4.^2/21.25;
Fw5=CD*A*ua5.^2/21.25;
%各档位的迎风阻力
D1=(Ft1-Fw1)/m/g;
D2=(Ft2-Fw2)/m/g;
D3=(Ft3-Fw3)/m/g;
D4=(Ft4-Fw4)/m/g;
D5=(Ft5-Fw5)/m/g;
%各档位的动力因数
i1=D1-f;
i2=D2-f;
i3=D3-f;
i4=D4-f;
i5=D5-f;
%各档位的爬坡度
plot(ua1,i1,ua2,i2,ua3,i3,ua4,i4,ua5,i5);
text(38,0.42,'一档');
text(70,0.23,'二档');
text(106,0.14,'三档');
text(136,0.08,'四档');
text(165,0.03,'五档');
ylim([0 0.5]);
xlabel('速度/（km/h）');
ylabel('爬坡度');
%爬坡度曲线图
k=max(D1);
amax=asin((k-f*sqrt(1-k.^2+f.^2))/(1+f.^2));
imax=tan(amax);
anglemax=imax*45;
fprintf('最大爬坡度imax = %.2f\n',imax);
fprintf('最大坡度角anglemax = %.2f°\n',anglemax);
%由爬坡度曲线图可知一档时有最大爬坡度和最大坡度角

3.2 Running Results

Maximum gradeability $i_{max}=0.52$
maximum slope angle$angl{e}_{max}=23.18°$

4. Power balance diagram

1. Power balance diagram

1.1 MATLAB program

n=800:10:6800;
Ttq=(2.714e-10)*n.^3-(4.255e-06)*n.^2+0.01756*n+65.07;
m=936;%质量
r=0.272;%滚动半径
nt=0.9;%传动效率
CD=0.3;%空气阻力系数
A=1.75;%迎风面积
f=0.012;%滚动阻力系数
i0=4.388;%主减速器传动比
ig=[3.416,1.894,1.28,1.00,0.757];%变速器各档传动比
g=9.8;%重力加速度
Ft1=Ttq*ig(1)*i0*nt/r;
Ft2=Ttq*ig(2)*i0*nt/r;
Ft3=Ttq*ig(3)*i0*nt/r;
Ft4=Ttq*ig(4)*i0*nt/r;
Ft5=Ttq*ig(5)*i0*nt/r;
%各档位的驱动力
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;
%各档位的速度与转速之间的关系
Pe1=Ft1.*ua1/3600;
Pe2=Ft2.*ua2/3600;
Pe3=Ft3.*ua3/3600;
Pe4=Ft4.*ua4/3600;
Pe5=Ft5.*ua5/3600;
%各档位的发动机功率
ua=0:5:220;
Pf=m*g*f*ua/3600;
Pw=CD*A*ua.^3/76140;
Pz=(Pf+Pw)/nt;
%阻力功率
plot(ua1,Pe1,ua2,Pe2,ua3,Pe3,ua4,Pe4,ua5,Pe5,ua,Pz);
text(20,42,'一档');
text(50,42,'二档');
text(80,42,'三档');
text(110,42,'四档');
text(185,42,'五档');
text(120,15,'(Pf+Pw)/ηt');
ylim([0 60]);
xlabel('速度/（km/h）');
ylabel('功率/(kw)');
%功率平衡图
Pf5=m*g*f*ua5/3600;
Pw5=CD*A*ua5.^3/76140;
Pz5=(Pf5+Pw5)/nt;
k=find((Pe5-Pz5)>0&(Pe5-Pz5)<0.1);
uamax=ua5(k);
fprintf('最高车速Vmax = %.2f km/h\n',uamax);
%由功率平衡图可知发动机功率曲线与阻力功率曲线相交处对应的车速为最高车速
%由功率平衡图可知发动机功率曲线与阻力功率曲线相交处对应的车速为最高车速

1.2 Running results

Maximum vehicle speed $V_{max}=164.23km/h$

2. Acceleration curves of each gear

2.1 MATLAB program

n=800:10:6800;
Ttq=(2.714e-10)*n.^3-(4.255e-06)*n.^2+0.01756*n+65.07;
m=936;%质量
r=0.272;%滚动半径
nt=0.9;%传动效率
CD=0.3;%空气阻力系数
A=1.75;%迎风面积
f=0.012;%滚动阻力系数
i0=4.388;%主减速器传动比
ig=[3.416,1.894,1.28,1.00,0.757];%变速器各档传动比
g=9.8;%重力加速度
Ft1=Ttq*ig(1)*i0*nt/r;
Ft2=Ttq*ig(2)*i0*nt/r;
Ft3=Ttq*ig(3)*i0*nt/r;
Ft4=Ttq*ig(4)*i0*nt/r;
Ft5=Ttq*ig(5)*i0*nt/r;
%各档位的驱动力
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;
%各档位的速度与转速之间的关系
ua=0:5:220;
Pe1=Ft1.*ua1/3600;
Pe2=Ft2.*ua2/3600;
Pe3=Ft3.*ua3/3600;
Pe4=Ft4.*ua4/3600;
Pe5=Ft5.*ua5/3600;
%各档位的发动机功率
Pf1=m*g*f*ua1/3600;
Pf2=m*g*f*ua2/3600;
Pf3=m*g*f*ua3/3600;
Pf4=m*g*f*ua4/3600;
Pf5=m*g*f*ua5/3600;
%各档位的滚动阻力功率
Pw1=CD*A*ua1.^3/76140;
Pw2=CD*A*ua2.^3/76140;
Pw3=CD*A*ua3.^3/76140;
Pw4=CD*A*ua4.^3/76140;
Pw5=CD*A*ua5.^3/76140;
%各档位的迎风阻力功率
dt1=1.03+0.04*ig(1);
dt2=1.03+0.04*ig(2);
dt3=1.03+0.04*ig(3);
dt4=1.03+0.04*ig(4);
dt5=1.03+0.04*ig(5);
%各档位的旋转质量换算系数
a1=(Pe1-(Pf1+Pw1)/nt)*3600/m/dt1/ua1;
a2=(Pe2-(Pf2+Pw2)/nt)*3600/m/dt2/ua2;
a3=(Pe3-(Pf3+Pw3)/nt)*3600/m/dt3/ua3;
a4=(Pe4-(Pf4+Pw4)/nt)*3600/m/dt4/ua4;
a5=(Pe5-(Pf5+Pw5)/nt)*3600/m/dt5/ua5;
%各档位的加速度
plot(ua1,a1,'.',ua2,a2,'.',ua3,a3,'.',ua4,a4,'.',ua5,a5,'.');
text(50,3.5,'一档');
text(88,1.9,'二档');
text(128,1.1,'三档');
text(164,0.65,'四档');
text(215,0.1,'五档');
ylim([0 4]);
xlabel('速度/（km/h）');
ylabel('加速度/(m/s^2)');
%加速度曲线图
amax=a1;
fprintf('最大加速度amax = %.2f\n',amax);
%由加速度曲线图可知一档时有最大加速度

2.2 Running results

Maximum acceleration $a_{max}=3.45$

3. Climbing curves of each gear

3.1 MATLAB program

n=800:10:6800;
Ttq=(2.714e-10)*n.^3-(4.255e-06)*n.^2+0.01756*n+65.07;
m=936;%质量
r=0.272;%滚动半径
nt=0.9;%传动效率
CD=0.3;%空气阻力系数
A=1.75;%迎风面积
f=0.012;%滚动阻力系数
i0=4.388;%主减速器传动比
ig=[3.416,1.894,1.28,1.00,0.757];%变速器各档传动比
g=9.8;%重力加速度
Ft1=Ttq*ig(1)*i0*nt/r;
Ft2=Ttq*ig(2)*i0*nt/r;
Ft3=Ttq*ig(3)*i0*nt/r;
Ft4=Ttq*ig(4)*i0*nt/r;
Ft5=Ttq*ig(5)*i0*nt/r;
%各档位的驱动力
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;
%各档位的速度与转速之间的关系
ua=0:5:220;
Pe1=Ft1.*ua1/3600;
Pe2=Ft2.*ua2/3600;
Pe3=Ft3.*ua3/3600;
Pe4=Ft4.*ua4/3600;
Pe5=Ft5.*ua5/3600;
%各档位的发动机功率
Pf1=m*g*f*ua1/3600;
Pf2=m*g*f*ua2/3600;
Pf3=m*g*f*ua3/3600;
Pf4=m*g*f*ua4/3600;
Pf5=m*g*f*ua5/3600;
%各档位的滚动阻力功率
Pw1=CD*A*ua1.^3/76140;
Pw2=CD*A*ua2.^3/76140;
Pw3=CD*A*ua3.^3/76140;
Pw4=CD*A*ua4.^3/76140;
Pw5=CD*A*ua5.^3/76140;
%各档位的迎风阻力功率
i1=(Pe1-(Pf1+Pw1)/nt)*3600/m/g/ua1;
i2=(Pe2-(Pf2+Pw2)/nt)*3600/m/g/ua2;
i3=(Pe3-(Pf3+Pw3)/nt)*3600/m/g/ua3;
i4=(Pe4-(Pf4+Pw4)/nt)*3600/m/g/ua4;
i5=(Pe5-(Pf5+Pw5)/nt)*3600/m/g/ua5;
%各档的爬坡度
plot(ua1,i1,'.',ua2,i2,'.',ua3,i3,'.',ua4,i4,'.',ua5,i5,'.');
text(50,0.41,'一档');
text(87,0.22,'二档');
text(128,0.13,'三档');
text(165,0.07,'四档');
text(215,0.01,'五档');
ylim([0 0.45]);
xlabel('速度/（km/h）');
ylabel('爬坡度');
%爬坡度曲线图
imax=i1;
anglemax=imax*45;
fprintf('最大爬坡度imax = %.2f\n',imax);
fprintf('最大坡度角anglemax = %.2f°\n',anglemax);
%由爬坡度曲线图可知一档时有最大爬坡度和最大坡度角

3.2 Running Results

Maximum climbability $i_{max}=0.41$
maximum slope angle$angl{e}_{max}=18.50°$

Summarize

According to the simulation results, in general, the maximum speed is in the fifth gear; the maximum acceleration (shortest acceleration time) is in the first gear; and the maximum gradient is in the first gear.