Work done by a cutting tool, Function modeling and Mass-Spring-Damper in Simulink and Simscape.

1 . AIM:

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

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

SIMULINK MODEL:

DESCRIPTION:

Workdone: Work is done when a force that is applied to an object moves that object.

The work is calculated by multiplying the force by the amount of movement of an object.

W = F*d.

where , w = workdone

F = force

d = distance .

Input to repeating sequence: In repeating sequence block the distance values are given as time values and force values are given as output values.

Time values : distance = [ 0 20 40 60 80 100]

Output values : Force = [60 72 65 53 44 50]

Integrator: The integrator block outputs the value of the integral of its input signal with respect to time.

2 . AIM :

To create a Simulink model to implement equation z=3x²-5y+18 and store result values using To File block.

OBJECTIVE :

To 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.

INPUT :

In MATLAB we have created arrays x and y to implement equation z=3x²-5y+18.

SIMULINK MODEL :

Implementing z=3x²-5y+18 equation using simulink model.

For making 3x.^2 we have multiplied x with a square block.

Gain block : The Gain block generates its output by multiplying its input by a specified gain factor. You can enter the gain as a numeric value, or as a variable or expression in the Gain parameter field.

The gain multiplies the input value by a constant value.We have given gain input value as 3.Now, it multiplies by x.^2 and becomes 3x.^2.

Similarly, another gain block is used for 5y.

The value 18 is given to a constant block. Now all these three values are given to a add block.We have changed the inputs of add block to 3 values(+,-,+).

Finally the obtained results are given to a To File block. We have named it as "output".

Inside the "output" file we can see the values of z.

OUTPUT :

Output of z values in workspace.

3 . AIM:

To open the simulink model 'Mass-Spring-Damper in Simulink and Simscape’ 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.

SIMULINK MODEL:

Governing equation for the model :

The governing equation for mass-spring-damper system is

m = mass

b = damping factor

k = spring constant

x = displacement

dx/dt = velocity

dx^2/dt^2 = acceleration

2 . Change the value of x0 = 2 in simulink model:

Values of mass, damper, spring and initial condition (x0)

Result for mass-spring-damper system in simulink model:

Change the values of mass, damper , spring for the simscape model:

Values of mass,damper and spring for the simscape model:

Result for mass-spring-damper system in simscape model: