Vehicle Ride 1
1.Lets first find out the time lag due to the Speed:
Wheelbase = 2.7 mm
Speed = 26.82 mps
Time lag due to speed(t) = Wheelbase/Speed
= 2.7/26.82
= 0.1006 Sec
Front Sprung Mass natural frequency = 1.15 Hz
Front sprung mass time period(Tf) = 1 / 1.15
= 0.869 Sec
For flat tire,
Tr + t = Tf
Tr + 0.1006 = 0.869
Tr = 0.7684 Sec
Rear sprung mass time period(Tr) = 0.7684 Sec
Rear Sprung Mass natural frequency = 1/Tr = 1/0.7684
= 1.3014 Hz
2. Front sprung mass natural frequency at design is 1.15 Hz
3. Front wheel rate(Kwf) = 245 N/mm
Motion ratio = 0.97
Front spring rate = Front wheel rate / (Motion rate)^2
= 245 / (0.97)^2
= 260.38 N/mm
Front spring rate is 260.38 N/mm.
4. Rear wheel rate(Kwf) = 245 N/mm
Motion ratio = 0.85
Rear spring rate = Rear wheel rate / (Motion rate)^2
= 245 / (0.85)^2
= 339.10 N/mm
Rear spring rate is 339.10 N/mm.
5.Calculation for Curb:
Total weight = 1500 Kg
% Front = 60
Front weight = 60% * 1500
= 900 Kg
Weight in front axle single wheel = 900/2
= 450 Kg
Unsprung mass front = 90 Kg
Front unsprung mass in quater car model(Mfus) = 90/2 = 45Kg
Front sprung mass in quater car model(Mfs) = 450-45
= 405 Kg
Rear Weight = 600 Kg
Total rear weight in quater model = 600/2
= 300 Kg
Unsprung mass rear = 60 Kg
Rear unsprung mass in quater car model(Mrus) = 60/2 = 30Kg
Rear sprung mass in quater car model(Mrs) = 300-30
= 270 Kg
Front wheel rate(Kwf) = 245 N/mm
Front spring rate(Ks) = 260.38 N/mm
Front sprung mass in quater car model(Mfs) = 405Kg
Natural Frequency for front sprung mass = `(1/(2*pi))*sqrt((Kwf*Ks)/((Kwf+Ks)*Mfs))`
= `(1/(2*pi))*sqrt((245*260.38)/((245+260.38)*405))`
= 2.8 Hz
Rear wheel rate(Kwr) = 245 N/mm
Rear spring rate(Ks) = 339.1 N/mm
Rear sprung mass in quater car model(Mrs) = 270Kg
Natural Frequency for rear sprung mass = `(1/(2*pi))*sqrt((Kwr*Ks)/((Kwr+Ks)*Mrs))`
= `(1/(2*pi))*sqrt((245*339.1)/((245+339.1)*270))`
= 3.65 Hz
6. Calculation for GVW:
Total weight = 2000 Kg
% Front = 52
Front weight = 52% * 2000
= 1040 Kg
Weight in front axle single wheel = 1040/2
= 520 Kg
Unsprung mass front = 90 Kg
Front unsprung mass in quater car model(Mfus) = 90/2 = 45Kg
Front sprung mass in quater car model(Mfs) = 520-45
= 475 Kg
Rear Weight = 960 Kg
Total rear weight in quater model = 960/2
= 480 Kg
Unsprung mass rear = 60 Kg
Rear unsprung mass in quater car model(Mrus) = 60/2 = 30Kg
Rear sprung mass in quater car model(Mrs) = 480-30
= 450 Kg
Front wheel rate(Kwf) = 245 N/mm
Front spring rate(Ks) = 260.38 N/mm
Front sprung mass in quater car model(Mfs) = 475Kg
Natural Frequency for front sprung mass = `(1/(2*pi))*sqrt((Kwf*Ks)/((Kwf+Ks)*Mfs))`
= `(1/(2*pi))*sqrt((245*260.38)/((245+260.38)*475))`
= 2.6 Hz
Rear wheel rate(Kwr) = 245 N/mm
Rear spring rate(Ks) = 339.1 N/mm
Rear sprung mass in quater car model(Mrs) = 450Kg
Natural Frequency for rear sprung mass = `(1/(2*pi))*sqrt((Kwr*Ks)/((Kwr+Ks)*Mrs))`
= `(1/(2*pi))*sqrt((245*339.1)/((245+339.1)*450))`
= 2.75 Hz
Calculation for Design:
Total weight = 1825 Kg
% Front = 55
Front weight = 55% * 1825
= 1003.75 Kg
Weight in front axle single wheel = 1003.75/2
= 501.875 Kg
Unsprung mass front = 90 Kg
Front unsprung mass in quater car model(Mfus) = 90/2 = 45Kg
Front sprung mass in quater car model(Mfs) = 501.875-45
= 456.875 Kg
Rear Weight = 821.25 Kg
Total rear weight in quater model = 821.25/2
= 410.625 Kg
Unsprung mass rear = 60 Kg
Rear unsprung mass in quater car model(Mrus) = 60/2 = 30Kg
Rear sprung mass in quater car model(Mrs) = 410.625-30
= 380.625 Kg
Front wheel rate(Kwf) = 245 N/mm
Front spring rate(Ks) = 260.38 N/mm
Front sprung mass in quater car model(Mfs) = 456.875Kg
Natural Frequency for front sprung mass = `(1/(2*pi))*sqrt((Kwf*Ks)/((Kwf+Ks)*Mfs))`
= `(1/(2*pi))*sqrt((245*260.38)/((245+260.38)*456.875))`
= 2.64 Hz
Rear wheel rate(Kwr) = 245 N/mm
Rear spring rate(Ks) = 339.1 N/mm
Rear sprung mass in quater car model(Mrs) = 380.625Kg
Natural Frequency for rear sprung mass = `(1/(2*pi))*sqrt((Kwr*Ks)/((Kwr+Ks)*Mrs))`
= `(1/(2*pi))*sqrt((245*339.1)/((245+339.1)*380.625))`
= 3.07 Hz
7. Front unsprung mass in quater car model(Mfus) = 90/2 = 45Kg
Front wheel rate(Kwf) = 245 N/mm
Front spring rate(Ks) = 260.38 N/mm
Front unsprung mass natural frequency at curb = `(1/(2*pi))*sqrt(((Kwf+Ks)/(Mfus))`
= `(1/(2*pi))*sqrt(((245+260.38)/(45)*1000)`
= 16.87 Hz
As the unsprung mass in front axle is equal in all the three cases so the Front Unsprung Mass natural frequency should be equal in all three.
8. Rear unsprung mass in quater car model(Mrus) = 60/2 = 30Kg
Rear wheel rate(Kwr) = 245 N/mm
Rear spring rate(Ks) = 339.1 N/mm
Rear unsprung mass natural frequency at curb = `(1/(2*pi))*sqrt(((Kwr+Ks)/(Mrus))`
= `(1/(2*pi))*sqrt(((245+339.1)/(30))`
= 22.20 Hz
As the unsprung mass in Rear axle is equal in all the three cases so the Front Unsprung Mass natural frequency should be equal in all three.
9. For curb:
Rear/front frquency ratio = 3.65/2.8
= 1.30
For GVW :
Rear/front frquency ratio = 2.75/2.6
= 1.05
For Design:
Rear/front frquency ratio = 3.07/1.16
= 1.16
2.Plot the bump oscillation profile for all three load conditions using the method we developed in class. You can do this in excel. Use e^-t*sin(wt) as a function for the profile.
Matlab Script:
clear all
close all
clc
%frequency front for curb
Ffc=2.8;
%frequency rear for curb
Frc=3.65;
t_wb=0.01;
time= 0:0.01:3;
ct=1;
for t=0:0.01:3
front_amp_curb(ct)= exp(-t)*sin(2*pi*Ffc*t);
rear_amp_curb(ct)= exp(-t)*sin(2*pi*Frc*(t-t_wb));
ct=ct+1;
end
figure(1)
plot(time,front_amp_curb)
hold on
plot(time,rear_amp_curb)
hold off
xlabel('Time')
ylabel('Amplitude')
legend('Front','Rear')
title('Bump Oscillation for Curb')
%frequency front for design
Ffd=2.64;
%frequency rear for design
Frd=3.07;
time= 0:0.01:3;
ct=1;
for t=0:0.01:3
front_amp_design(ct)= exp(-t)*sin(2*pi*Ffd*t);
rear_amp_design(ct)= exp(-t)*sin(2*pi*Frd*(t-t_wb));
ct=ct+1;
end
figure(2)
plot(time,front_amp_design)
hold on
plot(time,rear_amp_design)
hold off
xlabel('Time')
ylabel('Amplitude')
legend('Front','Rear')
title('Bump Oscillation for Design')
%frequency front for GVW
Ffg=2.6;
%frequency rear for GVW
Frg=2.75;
time= 0:0.01:3;
ct=1;
for t=0:0.01:3
front_amp_GVW(ct)= exp(-t)*sin(2*pi*Ffg*t);
rear_amp_GVW(ct)= exp(-t)*sin(2*pi*Frg*(t-t_wb));
ct=ct+1;
end
figure(3)
plot(time,front_amp_GVW)
hold on
plot(time,rear_amp_GVW)
hold off
xlabel('Time')
ylabel('Amplitude')
legend('Front','Rear')
title('Bump Oscillation for GVW')
Result:
The matlab scrpit is attached below: