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I need help understanding a problem Question
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Posted by: louise16 ®

08/02/2005, 10:51:41
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Hello

I am an A level student studying maths and physics (among other subjects) and I am currently doing work experience for an engineering company. I plan to study engineering (most likely mechanical) at university. I have been set a project to solve a problem which I do not entirely understand. My manager has been fairly nasty about the student who could not solve the problem and I would really like to prove him wrong – I just need some help to understand the problem!

The problem is to find the mass of inertia of a turbocharger. I have to do this by finding the mass of inertia in the polar and diametric (?sp) axes. Am I correct in thinking that the mass of inertia for the turbocharger is the sum of the inertias for the smaller “parts”? I’m not too sure I explained that very well. I am not sure how this problem can be solved. If I can understand more about the problem and how it can be solved, I’ll be in a much better position to actually solve it. Once I get a figure I have to compare this with the actual value that one of the engineers will get from a Pro-Engineer model.

If I haven’t explained this very well, I apologise but I’m still learning!

Thank you, Louise

PS: Incase you are wondering, I am not looking for somebody to solve this for me (I am keen and willing to put in the work), I just need help to understand how I can solve it – thanks again







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Re: I need help understanding a problem
Re: I need help understanding a problem -- louise16 Post Reply Top of thread Forum
Posted by: swearingen ®

08/02/2005, 22:58:08
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There's a fairly simple procedure you can do to get the value of the polar moment of inertia:

1. Mount the turbocharger vertically in such a way that it will spin freely. It must have as little friction as possible.
2. Rig an RPM meter to detect the angular speed. The best case would be to have it connected to a computer that could track RPM vs. time.
3. Wrap a string around the shaft of the turbine being careful not to overlap as you wrap.
4. Run the string over a low-friction pulley mounted with its shaft horizontal.
5. Attach a weight to the end of the string and let it fall.
6. Plot the RPM's vs. time, which will give you angular acceleration.

Go back to your studies, and you will find that you can relate the angular acceleration to the moment of inertia. This should get you fairly close...







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Re: I need help understanding a problem
Re: Re: I need help understanding a problem -- swearingen Post Reply Top of thread Forum
Posted by: louise16 ®

08/03/2005, 05:25:52
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Thanks for your reply. As I htought, I had not made myself very clear (sorry). I have to solve this mathematically - unfortunately, experiments/tests are not allowed. My manager did give me some more information today though. He has devised a computer model which has broken down individual components into smaller "chunks" and I think I'm supposed to find the moment of inertia for all these chunks and add them together to get the total - or am I barking up the wrong tree completely? I seem to be getting very little information out of my mentor and it is very frustrating. I'm not sure if Ive got enough information to solve the problem, or if I'm just stupid!

Louise







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Re: I need help understanding a problem
Re: Re: I need help understanding a problem -- louise16 Post Reply Top of thread Forum
Posted by: zekeman ®

08/03/2005, 10:18:32
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Louise,
First you have to find the moment of inertia of each of the components about their respective centers of mass. Then from the definition of moment of inertia
I=sum of dmij(Rj+rij)^2
where j is the the jth component and rij is the distance from the CM of the the jth mass to the submass dmij.
If you expand and carry out this summation you get
I= sum of dmijRj^2 +2dmijRjrij +dmijrij^2
The last term is the sum of the polar moment of inertias of the j components you mention;the second term vanishes at each of the j components by definition of CM( i.e. sum of dmijrij summed on i =0) and the first term is simply the summation of the individual components about their respective CMs.
You should be able to find this in any dynamics book.






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Re: I need help understanding a problem
Re: Re: I need help understanding a problem -- zekeman Post Reply Top of thread Forum
Posted by: louise16 ®

08/04/2005, 05:53:53
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Thank you Zekeman. Now I get what I'm supposed to do I have a cahnce of proving my manager wrong!

Thanks again

Louise







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