Question

Ball bearings are hardened through a process of heating and then rapid cooling. The temperature of the ball during this process can be estimated using the equation:

T(t) = (ti-to)*e^(-t/T)+to

where ti = initial ball temp = 800 degrees celcius
to = initial oil temp = 40 degrees celcius
   t = time = 0-180 seconds at 1 second intervals
   T = time contraint

Create a graph in matlab showing ball temperature versus time. the graph should have 3 curves for the 3 time contraints entered by the user. the 3 time constrains are:
T = 20, 50, and 80 seconds

Use a while loop to generate the arrays to be plotted, with a stopping condition that the value of temperature for all 3 arrays to be plotted is less than 80 degrees celcius. Include a function that is called from the script to get the time constant from the user, and to verify that it is a value between 20 and 100 inclusive. If not, stay in a loop until the user enters a value between 20 and 100.

The final answer should look like this:

Answer 1

MATLAB SCRIPT :

Code to Copy:

% time interval

t = 0:250;

% initial oil temperature

to = 40;

% initial ball temperature

ti = 800;

% Get the time constant from user

T1 =input('Enter the value of T1: ');

% verify that it is a value between 20 and 100

while ((T1<20)||(T1>100))

    T1 =input('Entered value does not lie between 20 and 100. Reenter the value: ');

end

% Get the time constant from user

T2 =input('Enter the value of T2: ');

% verify that it is a value between 20 and 100

while ((T2<20)||T2>100)

    T2 =input('Entered value does not lie between 20 and 100. Reenter the value: ');

end

% Get the time constant from user

T3=input('Enter the value of T3: ');

% verify that it is a value between 20 and 100

while (T3<20||T3>100)

    T3 =input('Entered value does not lie between 20 and 100. Reenter the value: ');

end

% Initialize the variables

Temp1=0; Temp2=0; Temp3=0;

% verify the stopping the condition that the value of temperature for all 3 arrays to be plotted is less than 80 degrees Celsius

while(((max(Temp1) < 80)&&(max(Temp2) < 80)&&(max(Temp3) < 80)))

      % calculating the ball temperatures

Temp1 = (ti-to).*exp(-t./T1)+to;

Temp2 = (ti-to).*exp(-t./T2)+to;

Temp3 = (ti-to).*exp(-t./T3)+to;

end

% Display the graph

plot(t, Temp1,'r', t, Temp2, 'g', t, Temp3, 'b'), xlabel('time, s'), ylabel ('temperature');

legend('Time constant 1','Time constant 2','Time constant 3');