I need to capture time taken by vehicle when velocity comes to zero after braking application by using following script.
clc
clear
l = 2.5; % wheelbase
ldis = 0.55; % lr/l
lr = ldis*l; % CG distance from the rear axle
lf = l - lr; % CG distance from the front axle
h = 0.55; % CG height of the total vehicle
rw = 0.3; % radius of the wheel
tw = 3; % radius to width ratio of the wheels
Mb = 960; % unsprung mass
Mwr = 20; % mass of rear axle
Mwf = 20; % mass of front axle
M = Mb + (Mwr + Mwf); % total vehicle mass
hb = (M*h - (Mwr + Mwf)*rw)/Mb - rw; % CG height of the vehicle body above the wheel centerw
Iwr = 0.5*Mwr*rw^2; % Moment of Inertia of rear axle
Iwf = 0.5*Mwf*rw^2; % Moment of Inertia of front axle
g = 9.81; % acceleration due to gravity
I = Iwr;
t_in = 1; % Step time
T_in = -306; % Final Value
t_brake = 36; % Step time
mu = 0.3; % coefficient of static friction
Kf_opt = [lr + l*I/(M*rw^2) + mu*(h - 2*I/(M*rw))]/[l*(1 + 2*I/(M*rw^2))];
Kf_app = 0.3;
accRearslip = mu*lf*g./[l*(1 - Kf_app) + mu*h + (I/(M*rw^2))*(l*(1 - 2*Kf_app) - 2*mu*rw)];
accFrontslip = mu*lr*g./[l*Kf_app - mu*h + (I/(M*rw^2))*(l*(2*Kf_app-1) - 2*mu*rw)];
acc_slip = min(abs(accRearslip), abs(accFrontslip));
T_opt = (M*rw^2 + 2*I)*acc_slip/rw;
T_app = 300;
if Kf_app > Kf_opt
T_sat = mu*g*[(rw*M)*(lf/l) + I/rw + mu*M*rw*(rw - h)/l]/[(1 - Kf_app + mu*(rw/l))];
if T_app <= T_opt
acc = rw*T_app/(M*rw^2 + 2*I);
alpha_f = acc/rw;
alpha_r = acc/rw;
Nf = (1/l)*(M*g*lr + M*acc*h + 2*I*acc/rw);
Nr = (1/l)*(M*g*lf - M*acc*h - 2*I*acc/rw);
Ff = (1/rw)*(Kf_app*T_app - I*acc/rw);
Fr = (1/rw)*((1-Kf_app)*T_app - I*acc/rw);
else if T_app <= abs(T_sat)
acc = [(mu*rw*M*g)*(lr/l) + T_app*(1 - Kf_app - mu*rw/l)]/[rw*M + I/rw + mu*M*rw*(h - rw)/l]; %may change
alpha_f = [T_app - (M*rw + (I/rw))*acc]/I;
alpha_r = acc/rw;
Nf = (1/l)*(M*g*lr + M*acc*h + I*alpha_f + I*acc/rw);
Nr = (1/l)*(M*g*lf - M*acc*h - I*alpha_f - I*acc/rw);
Ff = mu*Nf;
Fr = acc*M - Ff;
else
acc = mu*g;
A = [I*(1 - mu*rw/l), -mu*rw*I/l; mu*rw*I/l, I*(1 + mu*rw/l)];
alpha = inv(A)*[mu*rw*M*(acc*h/l - g*lr/l) + Kf_app*T_app; (1 - Kf_app)*T_app - mu*rw*M*(acc*h/l + g*lf/l)]; %may change
alpha_f = alpha(1,1);
alpha_r = alpha(2,1);
Nf = (1/l)*(M*g*lr + M*acc*h + I*alpha_f + I*alpha_r);
Nr = (1/l)*(M*g*lf - M*acc*h - I*alpha_f - I*alpha_r);
Ff = mu*Nf;
Fr = mu*Nr
end
end
else
T_sat = mu*g*[(rw*M)*(lr/l) + I/rw - mu*M*rw*(rw - h)/l]/[Kf_app - mu*(rw/l)];
if T_app <= T_opt
acc = rw*T_app/(M*rw^2 + 2*I);
alpha_f = acc/rw;
alpha_r = acc/rw;
Nf = (1/l)*(M*g*lr + M*acc*h + 2*I*acc/rw);
Nr = (1/l)*(M*g*lf - M*acc*h - 2*I*acc/rw);
Ff = (1/rw)*(Kf_app*T_app - I*acc/rw);
Fr = (1/rw)*((1-Kf_app)*T_app - I*acc/rw);
else if T_app <= abs(T_sat)
acc = [T_app*(Kf_app + mu*rw/l) + (mu*rw*M*g)*(lf/l)]/[rw*M + I/rw - mu*M*rw*(h - rw)/l]; %may change
alpha_f = acc/rw;
alpha_r = [T_app - (M*rw + (I/rw))*acc]/I;
Nf = (1/l)*(M*g*lr + M*acc*h + I*acc/rw + I*alpha_r);
Nr = (1/l)*(M*g*lf - M*acc*h - I*acc/rw - I*alpha_r);
Fr = mu*Nr;
Ff = acc*M - Fr;
else
acc = mu*g;
A = [I*(1 - mu*rw/l), -mu*rw*I/l; mu*rw*I/l, I*(1 + mu*rw/l)];
alpha = inv(A)*[mu*rw*M*(acc*h/l - g*lr/l) + Kf_app*T_app; (1 - Kf_app)*T_app - mu*rw*M*(acc*h/l + g*lf/l)]; %may change
alpha_f = alpha(1,1);
alpha_r = alpha(2,1);
Nf = (1/l)*(M*g*lr + M*acc*h + I*alpha_f + I*alpha_r);
Nr = (1/l)*(M*g*lf - M*acc*h - I*alpha_f - I*alpha_r);
Ff = mu*Nf;
Fr = mu*Nr;
end
end
end
slip_f = (rw*alpha_f - acc)/(rw*alpha_f);
slip_r = (rw*alpha_r - acc)/(rw*alpha_r);
