Lion1996
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Hi there I have been asked to do this question when I am struggling with including part 5 by using matlab or excel. The question has asked the following

Consider the centrifugal clutch above that comprises of four ‘shoes’ symmetrically attached to the ‘spider’. Each shoe with its friction lining has a mass of 275 grams and is attached by means of a linear mechanical spring with a stiffness value of 7.5 kN/m. The coefficient of friction of the material attached to the shoes is 0.35. The centre of mass of each of the shoes is at a radius of 95 mm from the shaft centres in the rest position shown above and has a clearance distance of 9 mm to the outer drum. The outer drum has a wall thickness of 4 mm.

1) What is the diameter of the outer drum?
2) Determine the engagement speed of the centrifugal clutch. You should provide your answer in RPM (revolutions per minute) and rounded to the nearest whole value of RPM.
3) Calculate the radial force acting on the clutch face when the driving shaft is rotating at a speed of 550 RPM.
4) At the driving shaft speed of 550 RPM, what will be the value of torque transmitted to the driven shaft?
5) Using either MatLab or MS Excel, calculate and plot on a suitable graph the transmitted torque at the driven shaft against driving shaft speed, from 450 RPM to 700 RPM in increments of 25 RPM.
6) Undertake the same analysis as in point 5 above but adopt a coefficient of friction of 0.3 and 0.4. Discuss the effect of changing the coefficient of friction of the shoe material on the torque transmitted when comparing the three values of coefficient of friction.
7) For the maximum possible transmitted torque determined from either point 5 or 6 above, and given that the mass of the drum is 750 grams and can be considered as a solid disc, what is the angular acceleration of the drum to achieve the maximum possible torque?
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Callicious
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Scroll down to see full advice.
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Lion1996
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(Original post by Callicious)
For (5) you should have a function of \tau(f) for torque \tau and frequency f. The frequency here is in RPM (I don't do engineering so I'm unsure about the convention.) They've given you a set \{f\} so now you need to calculate the relevant \{\tau\} using the function, then just plot it.

If you were in Python it'd look something like below. Note that you'll need to derive the expression \tau(f) and you'd have done that for (4).
Code:
def torque(frequency):
  t = some_function_of_frequency(frequency)
  return t 
x = [some_list_of_x]
y = [torque(xx) for xx in x]
plt.plot(x,y)
Thanks, could do this via mat lab. 2pi x the value and divide it by 60.
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Lion1996
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(Original post by Lion1996)
Thanks, could do this via mat lab. 2pi x the value and divide it by 60.
(Original post by Callicious)
For (5) you should have a function of \tau(f) for torque \tau and frequency f. The frequency here is in RPM (I don't do engineering so I'm unsure about the convention.) They've given you a set \{f\} so now you need to calculate the relevant \{\tau\} using the function, then just plot it.

If you were in Python it'd look something like below. Note that you'll need to derive the expression \tau(f) and you'd have done that for (4).
Code:
def torque(frequency):
  t = some_function_of_frequency(frequency)
  return t 
x = [some_list_of_x]
y = [torque(xx) for xx in x]
plt.plot(x,y)
I tried entering this and I was getting an error on Matlab.def torque(frequency):
t = some_function_of_frequency(frequency)
return
x = [2.62, 47.12, 73.30,]
y = [torque(XX)for, in]
plt.plot(x,y)

I put the values I had for X in my Y value and when I click run it comes as an error.
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Callicious
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(Original post by Lion1996)
I tried entering this and I was getting an error on Matlab.def torque(frequency):
t = some_function_of_frequency(frequency)
return
x = [2.62, 47.12, 73.30,]
y = [torque(XX)for, in]
plt.plot(x,y)

I put the values I had for X in my Y value and when I click run it comes as an error.
I can't debug your code for you, that's more like something the computer science forum on TSR should be doing (I recommend making a thread there if you're having issues coding something up.)

It's worth noting that what I gave you was closer to pseudocode... "some_function_of_frequency" was a placeholder for the function you use to define torque, working on the value of frequency, etc etc. What I gave isn't a piece of working code.
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Newstudent2021
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(Original post by Lion1996)
Hi there I have been asked to do this question when I am struggling with including part 5 by using matlab or excel. The question has asked the following

Consider the centrifugal clutch above that comprises of four ‘shoes’ symmetrically attached to the ‘spider’. Each shoe with its friction lining has a mass of 275 grams and is attached by means of a linear mechanical spring with a stiffness value of 7.5 kN/m. The coefficient of friction of the material attached to the shoes is 0.35. The centre of mass of each of the shoes is at a radius of 95 mm from the shaft centres in the rest position shown above and has a clearance distance of 9 mm to the outer drum. The outer drum has a wall thickness of 4 mm.

1) What is the diameter of the outer drum?
2) Determine the engagement speed of the centrifugal clutch. You should provide your answer in RPM (revolutions per minute) and rounded to the nearest whole value of RPM.
3) Calculate the radial force acting on the clutch face when the driving shaft is rotating at a speed of 550 RPM.
4) At the driving shaft speed of 550 RPM, what will be the value of torque transmitted to the driven shaft?
5) Using either MatLab or MS Excel, calculate and plot on a suitable graph the transmitted torque at the driven shaft against driving shaft speed, from 450 RPM to 700 RPM in increments of 25 RPM.
6) Undertake the same analysis as in point 5 above but adopt a coefficient of friction of 0.3 and 0.4. Discuss the effect of changing the coefficient of friction of the shoe material on the torque transmitted when comparing the three values of coefficient of friction.
7) For the maximum possible transmitted torque determined from either point 5 or 6 above, and given that the mass of the drum is 750 grams and can be considered as a solid disc, what is the angular acceleration of the drum to achieve the maximum possible torque?
Got the exact same question and don't for the life of me know where to start!
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Phillips_1997
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(Original post by Newstudent2021)
Got the exact same question and don't for the life of me know where to start!
I have same issue, you manage to complete any?
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Newstudent2021
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No sorry assuming you are in UWTSD
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Callicious
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For anyone that comes across this in the future (since this seems to be a hot topic...?) here's a rough guide on how to approach the problem. Not an engineer, though, so my understanding on how this mechanism actually works might be totally off. Hell, I don't even know what the hell a clutch is!

1)
I'm assuming the outer drum is the circular assembly on the RHS (2) image. You know the radial distance from the centre to the CM of the frictional shoes, and you know the clearance on the outside of the shoe. You know the material thickness of the drum. The only missing variable here to finding the total radius of the drum is how thick the shoes are: if you knew that you'd have an answer. They (look) to be around the same thickness as the drum, but yeah, don't hold me to that. Note that you might need the width of the shoes, unless you can ignore it... I don't see anything that implies you can, nor do I see a width, so there might be something I'm missing here, unless they expect you to assume the width based on the "scale" of the diagram.

2)
Engagement speed = the angular velocity of the driving shaft required to get the shoes to engage the drum. The spring needs to extend (from rest) by some length: the length seems to be the clearance distance. Find the force that the spring will exert (this is the centripetal force on the shoes) just at the moment that the shoes contact the drum, and use kx = m\omega^2{r}. The r here will be the radial distance of the CM of the shoes to the centre of the drum, which you are provided, and x the clearance distance. Solving for \omega will give you your angular velocity (you engineers use RPM or whatever else...)


3)
You know that beyond that critical angular velocity from (2) the shoes engage the drum. Any additional spin on the shoes? The drum provides the centripetal force. The amount the springs provide won't change (or at least you're just going to have to assume it doesn't, I'm guessing, unless this is some high-brow engineering stuff I haven't learned in A2.) So, work out the centripetal force needed to maintain this RPM they've given, subtract the force provided by the springs (you know this already from (2)) and you have the answer.

(4)
Torque \vec{\tau} = \vec{r}\times{\vec{F}}. In this case it's all orthogonal: use \tau = rF. You know the radius from the centre of the drum to the (inner) edge of the drum via (1), and you know the force that the shoe is exerting on the (inner) edge of the drum via (3). You know the friction coefficient, too, and thus can find a value for F. Thus you know \tau.

(5)
Just take the formulae you've derived until now, for the love of god I hope you've been working with formulae and not with the individual values, and plot it. If you've done everything in code until now (as you should have: would make the next steps a lot easier and cleaner) it'd help with the next steps.

(6)
Literally change your \mu to the new values they give in your code. Describe what happens.

(7)
"Maximum Possible" is a maximization problem. Maximize your torque equation subject to the bounds they've given you. Once you have maximum possible torque, find the moment of inertia of the drum, then just calculate \ddot{\phi}=\frac{\tau}{I}.


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