cutting tool of a shaping machine,implementing equation using simulink and mass-spring-damper

AIM :

to find :

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.

procedure :

• first we give a repeating sequence block to input values
• the corresponding values of distance and force are assigned inside the repeating sequence block
• a scope is acoonected to observe the graph
• now from graph work done can be calculated by fiding the area under the curve.
• to calculate area under the curve we use the intergrator block.
• to observe the workdone we connect a display block .

input parameters for the repeating seqence :

first set of values represent distance and second set of values represent force

\

display from scope :

2) AIM :

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

Procedure :

• first 2 array with vaules X = [22 3 55.6 9 12 10] ; Y = [5 31 95 56.3 77 61]; are created in matlab
• then three constant blocks are made X, Y and constnat block with value 18, the values of x and y are taken from the array created in matlab.
• the constant X is connected to the square block and the square block is connected to the multiply block with value of 3.
• the constant Y is connected to the multiply block with value of 5
• now all the values are connected to add block with symbol + - +
• the add is connected to display block and to file block
• the file name is given inside to file block "result.mat"
• this result will be displayed in the display block for all the values of x , y and the result will get saved in matlab

Simulink model :

result :

3)

AIM:

To open the 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.

Observation :

1)

Mass-Spring-Damper System

Consider now the case of the mass being subjected to a force, f(t), in the
direction of motion.

the net downward force will be

`Mg-T'-D+f(t)`

=`Mg-lamda((e-y))/l-R(dy)/dt+f(t)=-(lamday)/l-R(dy)/dt+f(t).`\

using newtons 2nd law

`M(d^2y)/dt^2+R(dy)/dt+(lamday)/l=f(t)``` or

`M(d^2y)/dt^2+R(dy)/dt+ky=f(t)` , `k=lamda/l`

if its unforced the equationw ill equate to 0.

2) simscape result plot

Damping coefficent =3 n/(m/s)

mass= 1 kg

spring rate = 100 N/m

when the value of Mass x0=2 in the Simulink model

output when x0=1

output when x0=2

3)seperate display for simscape adn simulink