1. 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.

2. 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.

3. 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.

Grading Policy :

1. Upload the supporting results as images or by any other means
2. Write a detailed report
3. Report attached as an image will lead to zero marks
4. plagiarism is not tolerated
5. upload Simulink files if needed through the google drive, any external links will not be accepted

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:

Repeating Sequence:

RESULT:

The input signal was then integrated using an integrator block and the output was received by the output scope and the answer displayed on the display block was 5780.The output scope plot is as shown be low.

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:

Here in the model common mathematical calculation blocks were used to form the equation. Variables x and y were stored in the Matlab workspace and thereafter were routed in the constant blocks in the initial stage of modelling.

It’s save on workspace

Result

The output value of the function z=3x²-5y+18 is stored in math_function.mat file.

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

Answer:

Simulink Model:

Derive the governing equation for the model:

From the above figure

Xo = initial displacement in body (mm)

M = mass of the body (Kg).

K = stiffness of spring (N/mm).

C = damping co-efficient (N-s/mm).

Arrow indications show forces applying on the body

The second law of newton

∑ F = m. a

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.

OUTPUT :

STUDY - 1 :

Signal Builder is connected with Integrator to make Integral of distance with respect to time (is konwn as displacement) it gives a total area between the path and the boundary.In this case the path is from 0-100(Time) and From (Point 1 - Point 6) is the distance of the boundary from the path. Finally Net Workdone has been calculated.

STUDY - 2:

Input values of x and y is taken from MATLAB which already assigned variables and solving the equation z=3x²-5y+18. Finally Z value displayed in the display block and also same Z values is displayed in the workspace.

STUDY - 3 :

Governing equation of the Mass Spring Damper system is derived successfully. By changing the input value of mass, damper, and spring for the Simscape model & Simulink model obtained that While increasing the damping value, it will reduces the oscillation of the mass and increasing the spring constant it will increases the oscillation of the mass. Damping co-efficient is inversely proportional to the Spring constant.

Conclusion:

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