Brake rotor simulation - Couldn't get results

Hello Everyone, i'm Naveen from Texas. I have a code that simulates dynamic brake rotor temperature. I know the end result and graph. But code doesnt give me the same result. I hope its my mistake and someone can help me out.

Basically, the code simulates a car Accelerating to 60mph at 0.5G and decelerating to 30mph at 1.6G and accelerates to 60mph and repeats to 150 to 300 sec. The temperature curve has to saturate like in the picture.

I have attached the code file and the desired result file.

[darova]

Do you have source formulas? Your origin task

[Naveen Devaraj]

Yes I do have all source formulas. Sharing it in next comment.

[Naveen Devaraj]

Q_brake = ((Weight of the car / number of brake rotors) * (velocity * gees)) / 778

778 - is the unit conversion number

Acceleration, Dx(1) = G's the car pulls * accleration due to gravity

Change in temperature, Dx(2) = Heat input + conductive heat transfer + radiative heat transfer + Conductive heat transfer

Check the pdf for more info.

When you run the code, it will give you two curves. Temperautre curve is at the top and velocity curve at the bottom. I suspect velocity curve to be culprit. It is supposed to do only 30 to 60 and 60 to 30. But it does lot of crazy numbers (84, 71, 66, 41.....). If we get the velocity curve perfect, the temperature curve should be corrected too.

[darova]

Are those values equal?

[darova]

Velocity curve is exactly in between [44 88]

>> V_min = 30*(5280/3600); %minimum speed [ft/s]
>> V_max = 60*(5280/3600); %maximum speed [ft/s]
>> [V_min V_max]
ans =
    44    88

The question: why it doesn't look like

[Naveen Devaraj]

Yes, the values of Thub an d Tinfinite are equal. Thub is the initial temp of hub (75F) and Tinfinite is ambient or envirnoment temperature which is also 75F.

Oh ya 44 and 88 are ft/sec. The curve should be doing 88 to 44 to 88 to and so on for every step. it cant be between the range, it has to be excatly from 88 to 44 and 44 to 88.

Answer 1

[darova]

I set up maxstep

opt = odeset('MaxStep',0.1);
[t,x] = ode45(@DerFun,Tspan,x0,opt);

And now it looks like

[Naveen Devaraj]

Hey Darova, this helped me and the code is solved. It matches the curve in paper. :)

thanks for the time and patience.

Answer 2

[Naveen Devaraj]

Hello guys, Naveen again. I need more help with same code. Now im trying to add actual sense to the code, i have changed some input values. Now, i wanted to change the period, in other words, i want to include coasting or dwell time when the car turns and accelerates.

Old Model- Car accelerates, brakes, accelerates and repeats for 120 seconds.

New model - Car accelerates, brakes, turn, accelerates, brakes, turn and repeat.

Average acceleration takes 6 seconds and Braking takes 1.36 seconds.

I appreciate help in advance

[darova]

How to turn left?

[Naveen Devaraj]

It doesn't matter if the car turns left or right. It turns, meaning that the turning time and accelerating to the Vmax time has to be included into the code (which is 6 seconds).

[Naveen Devaraj]

Can we create a new variable as V_turn = 15*(88/60) and include this condition in If statement?

Like, car accelerates(gees = g_acc), then car decelarates (gees =g_dec), then V_turn for 4 seconds, then car accelerates, repeats.

[darova]

What is the criteria of turning? What should be x(1) (speed)?

[Naveen Devaraj]

While turning constant speed 15mph is maintained.

[darova]

Something like that:

t0 = 0;
%% ...
function Dx = DerFun(t,x)
    if gees < 0 && x(1) < V_min
        gees = 0;
        t0 = t;
    elseif gees > 0 && x(1) > V_max
        gees = G_dec;
    end
    if t-t0 > 4 && gees == 0
        gees = G_acc;
    end
    % ...
end

[Naveen Devaraj]

Thanks for the answer. I dint use it yet. But i figured out a way to do it without the code above. I reduced g_acc value to increase the acceleration time. Let me try using it.

Thanks for the help once again.

Answer 3

[Naveen Devaraj]

Question Number 3:

How do i link data from excel file into the code?

We have specified Vmin and Vmax as 30 and 60 respectively. Now that i have velocity data. Can we link that values to Vmin or Vmax and get the same graph? i know graph will look different but trend is going to be same.

So, trend is same but graph mismatches due to velocity difference. Matlab repeats 30-60-30.. but real time velocity varies.