Quarter car suspension simulation using SolidThinking Activate

In the previous tutorial we have seen how you can create a 1d model of typical spring damper and simulate it dynamically either by using the differential equations or by transfer function through SolidThinking Activate (or by Simulink).

Here we will see how to simulate a simplified suspension system of a quarter car model.

The system diagram:

System Diagram of Quarter Car Suspension Model
System Diagram of Quarter Car Suspension Model

 

 

Where,

m2 – Sprung mass

m1 – Unsprung mass

k2 – Suspension stiffness

k1 – Wheel stiffness

b2 – Damping coefficient of suspension

x2 – Displacement of sprung mass

x1 – Displacement of unsprung mass

xr – Displacement of road

u1 – Excitation force on unsprung mass

 

Free body diagrams (FBD):

Free Body Diagram of Sprung Mass of Quarter Car Suspension Model
Free Body Diagram of Sprung Mass of Quarter Car Suspension Model

 

Free Body Diagram of UnSprung Mass of Quarter Car Suspension Model
Free Body Diagram of UnSprung Mass of Quarter Car Suspension Model

 

Where,

f1 = k2 * (x2 – x1)

f2 = b2 * (x2’ – x1’)

f3 = k1 * (x1 – r)

 

By applying Newton’s second law of motion:

m2 * x2” = -f1 –f2

  • m2 * x2” = – k2*(x2 –x1) –b*(x2’ – x1’)
  • x2” = (b/m2)*x1’ – (b/m2)*x2’ – (k2/m2)*x2………………………………1

 

m1*x1” = f1 + f2 – f3 –u1

  • m1*x1” = k2*(x2-x1) + b2*(x2’-x1’) – kw(x1 – r) – u1
  • x1” = (b/m1)*x2’ – (b/m2)*x1’ + (k2/m1)*x2 – [(k2 – k1)/m1]*x1 + (kw*r)/m1 – u1/m1 …………2

 

Let’s go to SolidThinking Activate (or Matlab Simulink for that matter). Since I have already explained the basics here, I am avoiding the details.

 

You will end up creating the following model to capture the above two system equations:

1d SolidThinking Activate Model of Quarter Car Suspension
1d SolidThinking Activate Model of Quarter Car Suspension

 

 

1d SolidThinking Activate Model of Quarter Car Suspension - zoomed View
1d SolidThinking Activate Model of Quarter Car Suspension – zoomed View

 

Following input values I have considered for running the simulation:

m1=1;

m2=1.5;

ks=10;

kw=12.5;

b=0.2;

r=0;

And, the initial conditions for the integration blocks are:

x1’(0) = 0.05

x1(0) = 0.15

x2’(0) = 0.03

x2(0) = 0.05

 

For input oscillation, I have considered a step generator of following profile:

Step time – 2

Initial value – 0

Final value – 1

 

And, finally i have run the simulation for 30 sec.

 

To view the required outputs, I have added two main scopes, namely Scope and Scope_1 for viewing the displacements of the unsprung mass and sprung mass respectively.

 

Dynamic displacements of the sprung and unsprung mass are:

 

Quarter Car Suspension - Sprung Mass - Disp vs Time
Quarter Car Suspension – Sprung Mass – Disp vs Time

 

Quarter Car Suspension- Unsprung mass - Disp vs Time
Quarter Car Suspension- Unsprung mass – Disp vs Time

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