Damping coefficient determination and Force vs Velocity shock curve

AIM:

1. Calculate the following parameters for front and rear suspension.

(i) Sprung mass critical damping

(ii) Unsprung mass critical damping

(iii) Sprung mass initial damping coefficient

(iv) Unsprung mass initial damping coefficient

(v) Low speed compression damping coefficient

(vi) High speed compression damping coefficient

(vii) Low speed rebound damping coefficient

(viii) High speed rebound damping coefficient

GIVEN DATA:

SOLUTION:

Workflow:

- Find critical damping and damping coefficient

- Find the low speed and high speed compression damping coefficient

- Find the low speed and high speed rebound damping coefficient using the given ratio

Formulae:

Sprung mass critical damping = 2 * sqrt (Ride rate * Sprung mass per corner)

Ride rate = (Wheel rate * Tire rate) / (Wheel rate + Tire rate)

Unsprung mass critical damping = 2 * sqrt [(Wheel rate + Tire rate) * Unsprung mass per corner]

Sprung mass initial damping coefficient = Sprung mass damping ratio * Sprung mass critical damping

Unsprung mass initial damping coefficient = Unsprung mass damping ratio * Unsprung mass critical damping

Low speed compression damping coefficient = Sprung mass initial damping coefficient / 2

High speed compression damping coefficient = Uprung mass initial damping coefficient / 2

Low speed rebound damping coefficient = Rebound/Compression ratio * Low speed compression damping coefficient

High speed rebound damping coefficient = Rebound/Compression ratio * High speed compression damping coefficient

Parameter	Front Shock	Rear Shock	Unit
Sprung mass critical damping (`C_[cs]`)	5781.549486	5631.489539	N/m/sec
Unsprung mass critical damping (`C_[c us]`)	6956.093731	5709.72854	N/m/sec
Sprung mass initial damping coefficient (`C_s`)	4047.08464	3942.042677	N/m/sec
Unsprung mass initial damping coefficient (`C_[us]`)	1391.218746	1141.945708	N/m/sec
Low speed compression damping coefficient (`C_[comp-low]`)	2023.54232	1971.021339	N/m/sec
High speed compression damping coefficient (`C_[comp-high]`)	695.6093731	570.972854	N/m/sec
Low speed rebound damping coefficient (`C_[reb-low]`)	6070.62696	5913.064016	N/m/sec
High speed rebound damping coefficient (`C_[reb-high]`)	2086.828119	1712.918562	N/m/sec

Excel Output:

Excel Link: https://docs.google.com/spreadsheets/d/1o0grqwWKBKO17_VQh7kso6yP9AwlU4q7Fb9kJqgN6fg/edit#gid=0

AIM:

2. Using the information calculated above, come up with a force vs. velocity shock curve for the front and rear suspensions (velocity range = 0 to 500 mm/sec)

SOLUTION:

Formulae:

Below Knee speed (<= 50 mm/sec):

Compression force = Low speed compression damping coefficient * Velocity

Rebound force = - Low speed rebound damping coefficient * Velocity

Above Knee speed (> 50 mm/sec): (n = iteration)

Compression force (n) = Compression force (n-1) + [Velocity (n) - Velocity (n-1)] * High speed compression damping coefficient

Rebound force (n) = Rebound force (n-1) - [Velocity (n) - Velocity (n-1)] * High speed rebound damping coefficient

Front shock:

Code #1:

% Shock curve (Front)

% Inputs:

v = 0:5:500;    % velocity (mm/sec)
Cc_1 = 2023.54232;   % before knee speed - compression
Cc_2 = 695.6093731;    % after knee speed - compression
Cr_1 = 6070.62696;   % before knee speed - rebound
Cr_2 = 2086.828119;   % after knee speed - rebound


% Solution:

i=1;
for ct=1:101    % Divisions in plot
    
    % Compression curve
    if ct <= 10
        Fc(i) = Cc_1*v(i)/1000;   % force upto knee speed
    else
        Fc(i) = Fc(i-1) + Cc_2*(v(i)-v(i-1))/1000;   % force after knee speed
    end
    
    % Rebound curve
    if ct <= 10
        Fr(i) = -Cr_1*v(i)/1000;   % force upto knee speed
    else
        Fr(i) = Fr(i-1) - Cr_2*(v(i)-v(i-1))/1000;   % force after knee speed
    end
    
    i=i+1;
end

 
% Plot:

plot(v,Fc,'linewidth',3)
hold on
plot(v,Fr,'linewidth',3)
plot([0 500],[0 0],'linewidth',3,'linestyle','--','color','k')
xlabel('Velocity (mm/sec)')
ylabel('Force (N)')
title('Shock curve (Front)')
legend('Compression','Rebound')
grid on
hold off

Output #1:

Plot #1:

Rear shock:

Code #2:

% Shock curve (Rear)

% Inputs:

v = 0:5:500;    % velocity (mm/sec)
Cc_1 = 1971.021339;   % before knee speed - compression
Cc_2 = 570.972854;    % after knee speed - compression
Cr_1 = 5913.064016;   % before knee speed - rebound
Cr_2 = 1712.918562;   % after knee speed - rebound


% Solution:

i=1;
for ct=1:101    % Divisions in plot
    
    % Compression curve
    if ct <= 10
        Fc(i) = Cc_1*v(i)/1000;   % force upto knee speed
    else
        Fc(i) = Fc(i-1) + Cc_2*(v(i)-v(i-1))/1000;   % force after knee speed
    end
    
    % Rebound curve
    if ct <= 10
        Fr(i) = -Cr_1*v(i)/1000;   % force upto knee speed
    else
        Fr(i) = Fr(i-1) - Cr_2*(v(i)-v(i-1))/1000;   % force after knee speed
    end
    
    i=i+1;
end

 
% Plot:

plot(v,Fc,'linewidth',3)
hold on
plot(v,Fr,'linewidth',3)
plot([0 500],[0 0],'linewidth',3,'linestyle','--','color','k')
xlabel('Velocity (mm/sec)')
ylabel('Force (N)')
title('Shock curve (Rear)')
legend('Compression','Rebound')
grid on
hold off

Output #2:

Plot #2:

CONCLUSION: From the above results, we can infer that both the compression and rebound forces are high for Front shock as compared to the Rear shock.