汽车主减速器传动比优化.docx
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汽车主减速器传动比优化.docx
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汽车主减速器传动比优化
汽车主减速器传动比优化
某轻型货车,车有关数据如下:
发动机的最低转速nmin=600r/min,
最高转速nmax=4000r/min。
总质量3650kg;
车轮半径0.367m;传动系机械效率nT=0.85;滚动阻力系数f=0.013;
空气阻力系数*迎风面积CDA=2.77m2;
飞轮转动惯量If=0.218kg.m2;二前轮转动惯量Iw1=1.798kg.m2;
轴距L=3.2m;质心至前轴距离(满载)a=1.947m;
质心高(满载)hg=0.9m;
四后轮转动惯量Iw2=3.598kg.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Qid=0.299mL/s(怠速转速400r/min)。
负荷特性曲线拟合公式为:
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
0.043072
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
-0.00075215
-0.000038568
1档
2档
3档
4档
5档
变速器传动比
5.06
4.016
3.09
1.71
1
计算
1计算加速时间
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挡加速时间计算
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*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+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([0800100]);
title('2挡原地起步加速时间曲线');
xlabel('时间t/s'),ylabel('车速u/(km/h)');
[x1,y1]=ginput
(1);disp('加速到70km/h的时间');
disp(x1);
以加速到70公里的时间作为加速时间。
io
5.089
5.44
5.85
6.01
6.17
加速时间
24.0553
24.2396
24.0553
23.8710
23.6866
2计算六工况百公里油耗
%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);
%匀加速行驶的油耗
%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+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;
forn=1:
15
Q21=Q21+(Qs(n)+Qs(n+1))*t/2;
end
disp(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=spline(Pa,b,Pa);
Qs=Pa.*b/(367.1*pg);
t=1/(3.6*a);
Q22=0;
forn=1:
10
Q22=Q22+(Qs(n)+Qs(n+1))*t/2;
end
disp(Q22);
Q2=Q21+Q22;
%匀减速行驶的油耗
Qid=0.299;
t3=19.3;
Q3=Qid*t3;
disp(Q3);
%总油耗
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
13.4086
13.7399
13.8535
13.9682
3.绘制燃油经济性-加速时间曲线
Q=[13.000613.408613.739913.853513.9682];
t=[24.055324.239624.055323.871023.6866];
plot(Q,t,'+r');
holdon
q1=linspace(Q
(1),Q(5),100);
t1=spline(Q,t,q1);%三次样条插值
plot(q1,t1);%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=5.089'),gtext('i0=5.44'),gtext('i0=5.85'),
gtext('i0=6.01'),gtext('i0=6.17');
4.计算最高车速
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;
%驱动力行驶阻力平衡图
forig=[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);
holdon;
end
Ff=G*f;
ua=0:
0.1:
max(Ua);
Fw=CdA*ua.^2/21.15;
plot(ua,(Ff+Fw));title('驱动力-行驶阻力平衡图');xlabel('Ua/(km/h)');ylabel('Ft/N');
i0
5.089
5.44
5.85
6.01
6.17
umax
102.4
102.1
100.2
99.2
97.9
5.绘制i0-umax曲线(求最高车速约束条件下临界i0值)
i0=[5.0895.445.856.016.17];
umax=[102.4102.1100.299.297.9];
plot(i0,umax,'+r');
holdon
i01=linspace(i0
(1),i0(5));
umax1=spline(i0,umax,i01);
plot(i01,umax1);
title('i0-umax曲线');
xlabel('i0');ylabel('最高车速km/h');
[x,y]=ginput
(1);
disp('临界i0=');disp(x);%根据最高车速约束条件,求临界i0值
gtext('i0=5.089'),gtext('i0=5.44'),gtext('i0=5.85'),
gtext('i0=6.01'),gtext('i0=6.17');
临界i0=5.8855最高车速大于100km/h.
所以io取5.0895.445.85
6.绘制i0-t图(求加速时间约束下临界i0值)
i0=[5.0895.445.856.016.17];
t=[24.055324.239624.055323.871025.6866];
plot(i0,t,'+r');
holdon;
i01=linspace(i0
(1),i0(5));
umax1=spline(i0,t,i01);
plot(i01,umax1);
title('i0-t曲线');
xlabel('i0');
ylabel('加速时间s');
zoomon;[x,y]=ginput
(1);zoomoff;
disp('临界i0=');disp(x);
gtext('i0=5.089'),gtext('i0=5.44'),gtext('i0=5.85'),
gtext('i0=6.01'),gtext('i0=6.17');
加速时间不超过25s所以io可以取5.0895.445.856.01
7最大爬坡度计算
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=[5.064.0163.091.711];
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('汽车最大爬坡度=');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
绘制i0-i曲线(求最大爬坡度约束下i0)
i0=[5.0895.445.856.016.17];
i=[28.973131.274134.013335.101736.2011];
plot(i0,i,'+r');
holdon
i01=linspace(i0
(1),i0(5),100);
i1=spline(i0,i,i01);
plot(i01,i1);
title('i0-imax曲线');
xlabel('i0');
ylabel('imax(%)');
[x,y]=ginput
(1);
disp('临界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5.856.016.17。
8最高档动力因数校核
一最大转矩计算
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);
holdon;
title('n-Tq曲线');
xlabel('转速nr/min');
ylabel('转矩Tqn*m');
[max_Tq,nn]=max(Tq);
disp('最大值:
');
disp(max_Tq);
disp('对应的n的值:
');
disp(n(nn));
最大转矩174.9667最大转矩的转速2041
二校核最高档的动力因数
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=[5.445.85];
F=Tmax*i0*ig*nT/r;
uat=0.377*n*r./(i0*ig);
Fw=CdA*uat.*uat/21.15;
D0max=(F-Fw)/G
D0max=
0.05180.0577
9优化结果总结
传动比i0
5.44(原传动比)
5.85(优化后传动比)
最高车速(km/h)
102.1
100.2
加速时间(s)
24.2396
24.0553
最大爬坡度(%)
31.2741
34.0133
最高档动力因数
0.0518
0.0577
百公里油耗(L/100km)
13.4086
13.7399
综上所诉优化后的传动比最高车速和加速时间指标较原来的传动比稍差,但最大爬坡度和最高档的动力因素较原传动比要好。
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