Thomas Kamps Model Jet Engines Typos!

[hendocal]

I'm building a jet engine in the standard micro jet Kamps/Kurtling sort of manner and I've come across a problem.
I have the Thomas Kamps Model Jet Engines (3rd edition) book and it has lots of typos in the equations.... I've figured out what most of them mean but, if you'll excuse the pun, I can't figure out probably the most critical equation, the critical rotational speed equation.
It has this equation for the compressor critical angular velocity:

                                 3 x E  x I
ω = Square root of : ---------------------
                               m x (l+c) x c^2

which is in rad/s so times by 30/pi to get r.p.m.

E=modulus of elasticity of shaft, book says it is 210 x10^-9 for almost all steels
I = (d^4)*Pi/64 where d is the shaft diameter
l = bearing spacing
c = distance from the wheel CG to first bearing
m = wheel mass

There are a few issues.... firstly if I put in the example numbers I get a different answer to the book. Secondly it then says do the same equation respective for the turbine wheel and then use the following equation for the shaft. Only the following equation is just an exact copy of the one for the compressor and turbine. It then lists the variables supposedly used. It lists l, d and rho. Obviously the equation has E, I, m l and c in not l d and rho so that HAS to be wrong. 

To make things worse, my compressor wheel is only 43.9mm in diameter and so, following the compressor map and the correct thrust calculations I have made, it needs to run up to 200,000rpm. From the bits of poking around I have done online it seems that RPMs much higher than 100k are seen as not safe in the model jet engine builders world.

Any advice on correct equations and whether I will be able to get away with such high rotational speeds would be much appreactied!

[racket]

Hi

Your rpm limits will be determined more by the bearings , though there are small microjets that spin >200K , the level of mounting precision is critical and probably a tad outside a homebuilders level .

E in my book is 210 X 10 to the 9th power , not minus 9 .

Have you checked out the GTBA Site for info www.gtba.co.uk/ , they have a huge amount of info available for the small engine homebuilder

Cheers
John

[hendocal]

Dec 27, 2016 19:03:41 GMT -5 racket said:

Hi

Your rpm limits will be determined more by the bearings , though there are small microjets that spin >200K , the level of mounting precision is critical and probably a tad outside a homebuilders level .

E in my book is 210 X 10 to the 9th power , not minus 9 .

Have you checked out the GTBA Site for info www.gtba.co.uk/ , they have a huge amount of info available for the small engine homebuilder

Cheers
John

Thanks, that certainly gets part of my answer a lot closer to what the book is suggesting.

So in the case that the engine was built perfectly, as long as I got high quality bearings rated for over 200K do you think the turbine would cope with the stress?

If anyone could just tell me the correct equations for calculating the critical rotational speed that would be really helpful...

[racket]

Hi

Even with the correct bearings you may not be able to use 200,000, it'll depend on your turb wheel material and temperatures used , also balance will be extremely important

The guys over at the GTBA will have your answers for the critical speeds , you can also try doing a Google search .

Cheers
John

[finiteparts]

Hi,

It sounds like you might be asking something different than what you are calculating. Are you wanting to calculated the stress in the turbine to determine the burst speed? Or are you trying to find the critical rotational speed to try to avoid driving the rotor into resonance at it's natural frequency?
These are two different things...

Chris

[hendocal]

Dec 28, 2016 17:05:32 GMT -5 finiteparts said:

Hi,

It sounds like you might be asking something different than what you are calculating. Are you wanting to calculated the stress in the turbine to determine the burst speed? Or are you trying to find the critical rotational speed to try to avoid driving the rotor into resonance at it's natural frequency?
These are two different things...

Chris

Hi,

You are correct I am trying to do two different things, thanks.
What I am trying to do is calculate the maximum RPM the engine will run at without causing any damage to itself, in other words I really need the turbine stress.

Below is my compressor map. I likely wouldn't run it higher than 190,000. My calculations thus far suggest I can get around 1.5kg of thrust at the point where the 190K speed line crosses the dotted line.



I think that what I need to do is I need to do is reverse engineer the design of the turbine rotor, re-arranging the stress equations into an inequality to calculate what dimensions/material densities I am working with. 


With regards to the GTBA I can't get the website to do very much, do I need to pay the membership fee before I can view any of the forums?

Thanks,
Callum

[racket]

Hi Callum

Yep , you'll need to join the GTBA , for a build like yours it'll be worth the cost as it'll most likely save you from some expensive mistakes

Cheers
John

[hendocal]

My account's just gone through and I found the critical speed equations in seconds!

Thank you John, I shall update my progress once I start construction hopefully later this month.

Callum

[racket]

Hi Callum

Yep , the GTBA is the place for your build :-)

I'll be looking forward to those updates .

Cheers
John

[tranglee]

Dec 27, 2016 19:03:41 GMT -5 racket said:

Hi

Your rpm limits will be determined more by the bearings , though there are small microjets that spin >200K , the level of mounting precision is critical and probably a tad outside a homebuilders level .

E in my book is 210 X 10 to the 9th power , not minus 9 .

Have you checked out the GTBA Site for info www.gtba.co.uk/ , they have a huge amount of info available for the small engine homebuilder

Cheers
John

Can you help me calculate the critical speed of the shaft?

[racket]

We'd need all the dimensions, weights , etc etc