Week 3

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, displacement as x0=2 in the Simulink model, and plot the results.
3. Make the response from Simscape and Simulink as two separate displays.

NOTE: If you are using Matlab R2021a above versions, kindly convert you to lower or equal to R2021a version and attach it in the submission.

Conversion: Save > Pervoius Version > Choose R2021A or lower version.

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 write a program in MATLAB to calculate the work done by a cutting tool of a shaper in moving 100 mm.
• To compute the value of a function according to the values of arrays x and y typed in command window and use To File block to save the values.
• To analyse the model Mass-Spring –Damper in Simulink and Simscape and the given questions :

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

Governing Equations :-

1. Work done by a Force on a mass when displaced by a distance x is given by the dot product of Force and Displacement vectors given by:

W= F∙d

2.The 2^nd ODE of a Damped Vibrating Systen is given by:

m⋅d2xdt2+b⋅(dxdt)+k⋅x=0m⋅d2xdt2+b⋅(dxdt)+k⋅x=0

where m-Mass of the vibrating system

b-Damping Coefficient

k-Spring Stiffness

x-position,dx-displacement & t- time,dt-change in time

(d2xdt2)−a&(dxdt)−velocity(d2xdt2)-a&(dxdt)-velocity

Body :-

Model 1 :-

Workflow :-

• A repeating sequence input is chosen to show the variation of Force along the length of cut.
• To determine the work done by the tool over a length of 100 mm,an integrator block is used to integrate the Force values wrt their corresponding to displacement values.

Results:-

Model 2 :-

Workflow :-

• In order to form the function z = 3x^2 – 5y + 18 using Simulink blocks,first we need to break this function into three different terms.
• 1^st term 3x^2,can be formed using two constant block using constant 3 and x and further squaring x and lastly multiplying them to get the required term.
• 2^nd term and 3^rd term is obtained using the same above method and atlast summing them up to get the required given equation.
• Results are stored using To File block and can be seen in the MATLAB workspace as z named variable.

Results:-

z values stored using To File block in MATLAB workspace :-

z values :-

Model 3 :-

1.Derivation of governing equation for the model:-

2.Result of the Simscape and Simulink model after changing the value of mass,damper and spring

Plot1:-

Plot 2:-

For seperating the plots into two separate displays,MUX operator should be removed and the input signal is directly given to scope block.