Simulink-Week 3 - Challenge

Aim: To create Simulink model for every question and to study the behaviour of spring-mass-damper system by changing its parameters.

Question1: The force on a cutting tool of a shaping machine varies over the length of cut as follows:

Distance (mm) 0 20 40 60 80 100

Force (kN) 60 72 65 53 44 50

Determine the work done as the tool moves through a distance of 100 mm.

Answer: - The total amount of work done can be calculated by the formula:

Where,

W = work done

F = Force acting on the tool

d₁ & d₂ = Initial and final distance travelled by the tool

Simulink Model:

Input parameters:

Question2: Create two array data sets x = [22 3 55.6 9 12 10] and y = [5 31 95 56.3 77 61] from the command window. Create a Simulink model to implement equation z=3x²-5y+18. Store result values using To File block.

Answer:

Initially we define the variables x & y in the base workspace (Command Window)

Simulink Model:

The ‘To File’ block is used to save the model.

Question3: Go to Matlab Help. Type the keyword ‘Mass-Spring-Damper in Simulink and Simscape’.

Open the model and solve the following problems:

1. Derive the governing equation for the model
2. Change the value of mass, damper, and spring for the Simscape model and plot the result. Change the value of Mass x0=2 in the Simulink model and plot the results.
3. Make the response from Simscape and Simulink as two separate displays.

Answer:

Simulink Model:

Derive the governing equation for the model:

Where,

M = mass

K = Spring constant

C = Damper Coefficient

We know that:

`∑F=m.a` ………………… equation 1

Here,

`F_c=c*v`

`F_k=k*x`

Now, considering the sign conventions, (upward negative)

`-F_c-F_k=m*a` ………………… from equation 1

`-c.v-k.x=m*a`

Converting velocity & acceleration into displacement, we get:

`m ( d^2 x)/( dt^2 )= -c dx/dt-k.x`

Multiply throughout by`1/m`

`( d^2 x)/( dt^2 )= -c/m.dx/dt-k/m.x`

This is the final governing equation for this model.

Change the value of mass, damper, and spring for the Simscape model and plot the result. Change the value of Mass x0=2 in the Simulink model and plot the results.

Output:

For x0 = 2:

Make the response from Simscape and Simulink as two separate displays.

Conclusion:

All the questions were completed successfully and the results are shown. The governing equation for spring-mass-damper system was derived successfully.