弹性路面
弹性路面
在师弟帮助下,查找了轮胎部分参数,对于查找不到参考数据的先进行假设
参数设定
%% 轮胎参数
pi = 0.58e6; % 额定充气压力pi
pc = 79e6; % 胎体刚度pc
B = 1.097; % 轮胎宽度B
Wf = 52940; % 前轮满载载荷Wf
Wr = 71706; % 后轮满载载荷Wr
R = 3.4788; % 车轮直径R
%% 沙土壤参数
n = 0.45; % 沉陷指数n
kc = 79e3; % 土壤粘聚系数kc
kfai = 2764.9e3; % 土壤内摩擦系数kfai
c = 2.7e3; % 土壤内聚力c
fai = 28.5; % 内摩擦角fai
求解过程
![](https://tsyblog-figure.oss-cn-hangzhou.aliyuncs.com/img/202206241631693.png)
\(F_{g1}\)计算
其中未知量为\(l_1\),\(b_1\),\(z_x\)
- \(l_1\)的确定
- 上式中仅\(l_1\)为未知量,\(z_g(t+l_1/v)\)理解为t时刻\(l_1\)处的的路面不平度
- \(z\)为土壤沉陷量,假设为0.2m
- 通过matlab二分法求解得\(l_1\)
clc
clear
close all
%%
u = 36/3.6; %车速
Gq = 128e-6;
stepsize = 0.1;
time = 200;
noo=0.011; %空间截止频率
f0=2*pi*noo*u; %下截止频率
simout=sim('xuanjiamox1_4_2',0:stepsize:time); %运行simulink模型
zr=simout.zr.Data;
save ('zr.mat',"zr")
%% 轮胎参数
pi = 0.58e6; % 额定充气压力pi
pc = 79e6; % 胎体刚度pc
B = 1.097; % 轮胎宽度B
Wf = 52940; % 前轮满载载荷Wf
Wr = 71706; % 后轮满载载荷Wr
R = 3.4788; % 车轮直径
%% 沙土壤参数
n = 0.45; % 沉陷指数
kc = 79e3; % 土壤粘聚系数
kfai = 2764.9e3; % 土壤内摩擦系数
c = 2.7e3; % 土壤内聚力
fai = 28.5; % 内摩擦角
%%
z = 0.2;
zg = zr;
t =0.1:0.1:100;
for i =1:1000
syms U L; %将区间上下限定为变量
f=@(l1) R-sqrt(R^2-l1^2)-z-zr(i+fix(l1/(0.1*u))); %求给定的函数
U=2;
L=0;
while U-L>1e-10 %设定精度
root=(U+L)/2; %当根的区间大于所给精度时,利用二分法重新规划求根区间
if f(root)==0
break; %r恰好为所求根,直接跳出循环
end
if f(root)*f(U)<0 %用零点存在定理判断根所在的区域
L=root;
else
U=root;
end
end
Root(i)=root;
zx(i) = zr(i);
end
figure(1)
plot(t,Root)
title("l1值")
figure(2)
t1 = 0:0.1:200;
plot(t1,zr)
title("路面不平度位移")
- 得到\(l_1\)值为:
![](https://tsyblog-figure.oss-cn-hangzhou.aliyuncs.com/img/202206251928641.png)
- 根据轮胎型号,查得轮胎宽度\(B = 1.097m\)
- 求得\(b_1 = min(l_1,B)\)
![](https://tsyblog-figure.oss-cn-hangzhou.aliyuncs.com/img/202206251932903.png)
- 求\(z_x\)
其中\(z_g(t+x/v)\)为\(t\)时刻某一点的路面不平度,\(z_0\)为初始沉陷量,\(\delta_0\)为轮胎初始径向变量,\(\delta\)为\(t\)时刻轮胎径向变量,\(z_2\)为车轮跳动量,假设\(z_0\) \(\delta_0\) \(\delta\) \(z_2\) 均为0,则\(z_x = z_g(t+x/v)\).
![](https://tsyblog-figure.oss-cn-hangzhou.aliyuncs.com/img/202206251949371.png)
- 求\(F_{g1}\)
![](https://tsyblog-figure.oss-cn-hangzhou.aliyuncs.com/img/202206252030595.png)
\(F_{g2}\)
-
平均压力计算
满载情况下,车总质量为\(m_总 = 390t\),按前后载荷\(0.3:0.7\),计算得到前悬架大致参数\(m_t = 10750kg\),\(m_s = 52940kg\),单个轮胎的载荷\(F_z = 9.8*(10750+52940) = 624162N\) -
变形量计算
\(F_z/K_t = 624162/3921000 = 0.159m\) -
接地面积计算
通过下图,横坐标为接地面积,纵坐标为变形量,得到大致斜率为0.02275,大致直线方程为\(y = 0.02275x - 297.8\),代入变形量\(y =159\)得,接地面积为\(20079cm^2 = 2m^2\)
![](https://tsyblog-figure.oss-cn-hangzhou.aliyuncs.com/img/202206262053360.jpg)
- 平均压力计算
\(p_0 = F/S = 624162/2 = 312081 N/m^2\)
弹性路面-车辆悬架模型建立
- 参考论文《基于轮胎与地面接触模型的非公路车辆平顺性》
![](https://tsyblog-figure.oss-cn-hangzhou.aliyuncs.com/img/202206262118781.png)
根据上图建立车辆悬架动力学模型,公式如下:
\(m_1\ddot{z_1}+c(\dot{z_1}-\dot{z_2})+k(z_1-z_2) = 0\)
\(m_2\ddot{z_2}+k(z_2-z_1) +k_t(z_2-z_3)+c_t(\dot{z_2}-\dot{z_3}) = 0\)
\(k_t(z_3-z_2)+c_t(\dot{z_3}-\dot{z_2})+(m_1+m_2)g-F_{g1}-F_{g2} = 0\)