单缸发动机扭矩动力学计算：理论计算&&virtual.lab motion仿真

最新推荐文章于 2023-12-26 16:40:50 发布

lijil168

最新推荐文章于 2023-12-26 16:40:50 发布

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分类专栏：机械 matlab 数学文章标签： virtual.lab motion 动力学发动机

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本文详细解析了单缸发动机曲轴连杆活塞系统的动力学特性，包括活塞受力、连杆惯性力、曲柄销轴承力及发动机转矩等关键参数的计算方法。通过MATLAB编程实现理论计算，并与virtual.labmotion仿真结果对比，验证了计算的准确性。

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一、单缸发动机曲轴连杆活塞系统动力学分析参考：

汽车动力总成系统/（伊朗）贝赫鲁兹.马沙迪，（英）戴维.克罗拉著；

白先旭，刘勇强译。——北京：机械工业出版社，2018.6

（汽车先进技术译丛.汽车创新与开发系列）

书名原文：Vehicle Powertrain Systems

ISBN 978-7-111-60005-3

曲柄连杆机构受力分析

燃烧室压力如下：

X_Column(turn_mn)   Y_Column(deg)   Z_Column(N_m2)
3000   0   1.82E+06
3000   20   3.24E+06
3000   23   3.29E+06
3000   26   3.24E+06
3000   50   2.03E+06
3000   60   1.52E+06
3000   70   1.01E+06
3000   80   8.10E+05
3000   100   6.08E+05
3000   110   5.07E+05
3000   150   3.04E+05
3000   190   1.22E+05
3000   200   6.08E+04
3000   220   0.00E+00
3000   540   0.00E+00
3000   600   1.01E+05
3000   630   2.03E+05
3000   660   4.05E+05
3000   690   9.12E+05
3000   710   1.52E+06
3000   720   1.82E+06

用matlab 编程求解结果如下：

1、活塞受力

2、连杆惯性力

3、连杆惯性力矩

4、曲柄销轴承上的力

5、发动机转矩

二、virtual.lab motion仿真

1、利用PDS建立单缸发动机模型，然后导入到virtual.lab motion中

2、活塞轴向受力（活塞销受力）

3、曲柄销轴承上的力

4、发动机转矩

三、总结：virtual.lab motion 仿真的结果与理论计算的结果几乎完全一致！

计算代码如下：

Example2.3.3-Single cylinder,4 stroke-engine torque
-----input-----
pi=3.141593;
mPiston=4.1;               %kg
mConnectingRod=4.0;        %kg
l=225/1000;                 %m,Connecting rod pin-pin length
lB=63.054/1000;             %m,Connecting rod pin B-CG lengh
R=76/1000;                  %m,Crank radius
Ap=pi*61.5^2;               %mm2,Pistion area
?IC=0.041687-mConnectingRod*lB^2;                  %kg.m2,Connecting rod inertia

-------Pressure in combustion chamber--------
pr[1][21]=[160.31,162.88,140.14,128.16,51.2,35.12,27.01,21.43,15.12,13.35,8.57,4.16,4.04,3.84,3.08,4.02,6.23,12.94,45.18,125.29,160.31]
ca[1][21]=[0,20,23,26,50,60,70,80,100,110,150,190,200,220,540,600,630,660,690,710,720]

i=0;
omega=1900;
omeg=omega*pi/30;
Rl=R/l;       %define ratio R over l
lA=l-lB;

print("转角 活塞气压力 惯性力  合力  连杆惯性力x   y  惯性力矩 曲柄销力x y 发动机力矩 气缸侧压")
while(i<21){
 ang=ca[0][i]*pi/180
 sa=sin(ang);
 ca=cos(ang);
 s2a=sin(2*ang);
 c2a=cos(2*ang);
 beta=asin(Rl*sa);
 ka=ca+Rl*c2a/cos(beta)+Rl^3*s2a^2/cos(beta)^3/4;

 //Piston acceleration:
 aP=R*ka*omeg^2;

 //Connecting rod angular acceleration:
 alpha_c=Rl*omeg^2*sa/cos(beta);

 //Connecting rod GC acceleration:
 k3=lA*sa/l;
 k4=ca+Rl*c2a*lB/cos(beta)/l;
 agx=-R*omeg^2*k3;
 agy=-R*omeg^2*k4;
 ag=sqrt(agx^2+agy^2);

 //Piston pressure force:
 Fp=pr[0][i]*Ap/9.8;

 //Piston inertia force:
 FIP=-mPiston*aP;

 //Resultant piston force:
 FPt=Fp+FIP;

 //Connection rod inertia forces(N):
 FIx=-mConnectingRod*agx;
 FIy=-mConnectingRod*agy;

 //Conneting rod inertia torque(Nm):
 TIG=IC*alpha_c;

 //Crank-pin bearing forces:
 Bx=(-FIP-Fp+lB*FIy/l)*tan(beta)-lA*FIx/l-TIG/l/cos(beta);
 By=Fp+FIP-FIy;

 //Engine torque:
 Te=R*(By*sa-Bx*ca);

 //气缸壁侧压力：
 Fw=-FIx-Bx;
 
 print("%5.1f %8.1f %8.1f %7.1f %7.1f %7.1f %6.2f %7.1f %7.1f %6.1f %7.1f",ca[0][i],Fp,FIP,FPt,FIx,FIy,TIG,Bx,By,Te,Fw)
 i=i+1
}

matlab 代码：

%Example2.3.3-Single cylinder,4 stroke-engine torque
%-----input-----
%pi=3.141593;
mPiston=430/1000;               %kg
mConnectingRod=440/1000;        %kg
l=140/1000;                 %m,Connecting rod pin-pin length
lB=37/1000;             %m,Connecting rod pin B-CG lengh
R=49/1000;                  %m,Crank radius
Ap=5800;               %mm2,Pistion area
IC=0.0015;                  %kg.m2,Connecting rod inertia
 
%-------Pressure in combustion chamber--------
pr=[18,32,32.5,32,20,15,10,8,6,5,3,1.2,0.6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1.0,2.0,4,9,15,18];
crank_angle=[0,20,23,26,50,60,70,80,100,110,150,190,200,220,220,250,280,300,330,360,380,400,440,460,480,500,540,600,630,660,690,710,720];
pr=pr';
crank_angle=crank_angle';

%i=0;
omega=3000;
omeg=omega*pi/30;
Rl=R/l;       %define ratio R over l
lA=l-lB;
 
%print("转角 活塞气压力 惯性力  合力  连杆惯性力x   y  惯性力矩 曲柄销力x y 发动机力矩 气缸侧压")
%while(i<21){
 ang=crank_angle*pi/180;
 sa=sin(ang);
 ca=cos(ang);
 s2a=sin(2*ang);
 c2a=cos(2*ang);
 beta=asin((Rl*sa));
 ka=ca+Rl*c2a./cos(beta)+Rl^3*s2a.^2./cos(beta).^3/4;
 
% //Piston acceleration:
 aP=R*ka*omeg^2;
 
% //Connecting rod angular acceleration:
 alpha_c=Rl*omeg^2*sa./cos(beta);
 
% //Connecting rod GC acceleration:
 k3=lA*sa/l;
 k4=ca+Rl*c2a*lB./cos(beta)/l;
 agx=-R*omeg^2*k3;
 agy=-R*omeg^2*k4;
 ag=sqrt(agx.^2+agy.^2);
 
% //Piston pressure force:
 Fp=pr*Ap/9.8;
 
% //Piston inertia force:
 FIP=-mPiston*aP;
 
% //Resultant piston force:
 FPt=Fp+FIP;
 
% //Connection rod inertia forces(N):
 FIx=-mConnectingRod*agx;
 FIy=-mConnectingRod*agy;
 
% //Conneting rod inertia torque(Nm):
 TIG=IC*alpha_c;
 
% //Crank-pin bearing forces:
 Bx=(-FIP-Fp+lB*FIy/l).*tan(beta)-lA*FIx/l-TIG/l./cos(beta);
 By=Fp+FIP-FIy;
 
% //Engine torque:
 Te=R*(By.*sa-Bx.*ca);
 
% //气缸壁侧压力：
 Fw=-FIx-Bx;
 
 %print("%5.1f %8.1f %8.1f %7.1f %7.1f %7.1f %6.2f %7.1f %7.1f %6.1f %7.1f",ca[0][i],Fp,FIP,FPt,FIx,FIy,TIG,Bx,By,Te,Fw)
 %i=i+1
%}
subplot(2,3,1)
plot(crank_angle,[Fp,FIP,FPt]);%活塞气压力 惯性力  合力
title('活塞气压力 惯性力  合力')
subplot(2,3,2)
plot(crank_angle,[FIx,FIy]);%连杆惯性力x   y
title('连杆惯性力x   y')
subplot(2,3,3)
plot(crank_angle,TIG);%惯性力矩
title('惯性力矩')
subplot(2,3,4)
plot(crank_angle,[Bx,By]);%曲柄销力x y
title('曲柄销力x y')
subplot(2,3,5)
plot(crank_angle,Te);%发动机力矩
title('发动机力矩')
subplot(2,3,6)
plot(crank_angle,Fw);%气缸侧压
title('气缸侧压')