Project

vehicle dynamics week 6

KKhaled Ali23 Feb 2021

Question:

How different slip angles (0 deg, 2 deg, 4 deg and 6 deg) influence the force (Fx and Fy) vs slip ratio relationship (sweep from 0 to 60%).

How different slip ratios (0%, 3%, 6% and 9%) influence the force (Fx and Fy) vs slip angle relationship (sweep from 0 to 20 deg).

Use the modified slip approach. Develop your script based on the algorithm we looked at in class. These are your deliverable's:

Plot (use sub-plots) showing the effect of different slip ratios on lateral force vs slip angle relationship (5 points)
Plot showing the effect of different slip ratios on longitudinal force vs slip angle relationship (5 points)
Plot showing the effect of different slip angles on longitudinal force vs slip ratio relationship (10 points)
Plot showing the effect of different slip angles on lateral force vs slip ratio relationship (10 points)
Error free Octave code (5 points) 6. Explanation of the concept using the generated plots (5 points)

Answer:

Matlab code:

clear all

close all

sx_p = 0.09;

alpha_p = 4;

By = 0.27; Cy = 1.2; Dy = 2900; Ey = -1.6; shy = 0; svy = 0;

Bx = 25; Cx = 1.15; Dx = 3200; Ex = -0.4; shx = 0; svx = 0;

sx=[0:0.03:0.09]

alpha=linspace(0,20,100)

for i=1:length(sx)

sx_star=sx(i)/sx_p

for j=1:length(alpha)

alpha_star=alpha(j)/alpha_p

s_star=sqrt((sx_star)^2+(alpha_star)^2)

sx_modified=s_star*sx_p

alpha_modified=s_star*alpha_p

ALPHA_final=alpha_modified+shy

fy(i,j)=(alpha_star/s_star)*(Dy*sin(Cy*atan((By*ALPHA_final-Ey*(By*ALPHA_final-atan(By*ALPHA_final))))))

Fy(i,j)=fy(i,j)+svy

sx_final=sx_modified+shx

fx(i,j)=(sx_star/s_star)*(Dx*sin(Cx*atan((Bx*sx_final-Ex*(Bx*sx_final-atan(Bx*sx_final))))))

Fx(i,j)=fx(i,j)+svx

j=j+1

end

i=i+1

end

figure(1)

subplot(1,2,1)

plot(alpha,Fy)

grid on

subplot(1,2,2)

plot(alpha,Fx)

grid on

alpha1=[0:2:6]

sx1=linspace(0,0.6,100)

for k=1:length(alpha1)

alpha_star1=alpha1(k)/alpha_p

for w=1:length(sx1)

sx_star1=sx1(w)/sx_p

s_star1=sqrt((sx_star1)^2+(alpha_star1)^2)

sx_modified1=s_star1*sx_p

alpha_modified1=s_star1*alpha_p

ALPHA_final1=alpha_modified1+shy

fy1(k,w)=(alpha_star1/s_star1)*(Dy*sin(Cy*atan((By*ALPHA_final1-Ey*(By*ALPHA_final1-atan(By*ALPHA_final1))))))

Fy1(k,w)=fy1(k,w)+svy

sx_final1=sx_modified1+shx

fx1(k,w)=(sx_star1/s_star1)*(Dx*sin(Cx*atan((Bx*sx_final1-Ex*(Bx*sx_final1-atan(Bx*sx_final1))))))

Fx1(k,w)=fx1(k,w)+svx

w=w+1

end

k=k+1

end

figure(2)

subplot(1,2,1)

plot(sx1.*100,Fx1)

grid on

subplot(1,2,2)

plot(sx1.*100,Fy1)

grid on

steps:

-Inputs are declared

-then Slip ratio array specified for 0,0.03,0.06,0.09 slip ratio values

-then Slip angle sweep is made using linspace command from 0 to 20 and 100 values inbetween

-Then a for loop is made with its counter having the same value as the number of elements in the slip ratio array

-Then sx star is calculated using sx star=sx/speak

-Then another for loop is made with its counter having the same value as the number of values in the slip angle array

-The alpha star is calculated using alpha star=alpha/alpha peak

-Then resultant is calculated using s_star=sqrt((sx star)^2+(s peak)^2)

-Then the modified slip is calculated using sx_modified=s _star*s_peak

-Then alpha modified is calculated using alpha_modifiend=s_star*alpha_peak

-Then final alpha is calculated using final_alpha=alpha_modified +shy

-Then lateral force is calculated using fy=(alpha_star/s_star)*(Dy*sin(Cy*tan^-1((By*ALPHA_final-Ey*(By*ALPHA_final-tan^-1(By*ALPHA_final))))))

- Then final lateral force is calculated using F_final=fy+svy

-Then final is sx_final is calculated using sx_final=sx_modified+shx

-then longitudinal force is calculated using fx=(sx_star/s_star)*(Dx*sin(Cx*atan((Bx*sx_final-Ex*(Bx*sx_final-atan(Bx*sx_final))))))

-Then final longitudinal force is calculated using Fx_final=fx+svx

-Then inner loop is increased by one and then ended

-Then the outer loop is increased by one and ended

-Then a figure is constructed using subplot command which has one row and two column s and the first element is plotting the lateral force with slip angle and second elment is the longitudanl force with slip angle plot

- Then Slip ratio array is specified for 0,2,4,6 angle values

-Then Slip ratio sweep is made using linspace command from 0 to 0.6 and 100 values inbetween

-Then a for loop is made with its counter having the same value as the number of elements in the slip angle array

-Then alpha star is calculated using alpha star=alpha/alpha peak

-Then another for loop is made with its counter having the same value as the number of values in the slip ratio array