To find the critical speed of a vertical shaft

In summary: Well i tried a harmonic analysis with a crankshaft for a project but couldn't get it to work.If the shaft is constant area, then one needs to find the eigenvalues of: \frac{d^4 y}{dx^4} - B^4 y = 0 Where B^4 = \rho \frac{A}{EI}\omega You would use your "constrains" as the constants of integration (i.e. y(0) = 0) so on and so forth to try and obtain the eigenvalues.
  • #1
vikkispike117
26
0
hi,
i am in great need of help...
i need to determine the critical speed of a vertical shaft using ansys software ...my questions are:

1. which kind of element type should i choose?
2. wiil it be ok if i carry out the analysis without giving any constraints as it is not supported by bearings...it just has a line contact so what kind of boundary constraints am i supposed to give..
pleasezzzzzz help me as soon as possible
 
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  • #2
The question is rather vague, your talk of elements leads me to the conclusion that you are trying to use some sort of FE software.

The natural frequency depends havily on the boundary conditions.
 
  • #3
ya i m using ansys software...i mean that the shaft is not supported by bearings...it just has line contact...so what kind of boundary constraints am i supposed to give
 
  • #4
How is the shaft supported then? Line contact? to what?
 
  • #5
vikkispike117 said:
hi,
i am in great need of help...
i need to determine the critical speed of a vertical shaft using ansys ...my questions are:

1. which kind of element type should i choose?
2. wiil it be ok if i carry out the analysis without giving any constraints.
3.steps involved in determining the critical speed


pleasezzzzzz help me as soon as possible

You're in luck, I happened to catch an ANSYS modal analysis webinar a couple of weeks ago.

1. It depends on what version of ANSYS you have. If you have the new version 12, then you can use almost anything, solid elements included (e.g. 183, etc). With the slightly older (what I'm using) version 11.x, you are restricted to using BEAM elements I believe.

2. Yes, you can carry out the modal analysis with no constraints. In this case, your critical speeds will coincide with the natural frequencies. Sometimes we call this the "free-free" case with no supports.

3. I can't remember exactly the steps, but it's a modal analysis with an incremental omega defined (IIRC). In v12, you can define both rotating and non-rotating geometries, so defining structures and supports can get complex. With v11 I believe that you are restricted to using COMBIN element types for bearing and supports.

The documentation for any type of modal/vibrational analysis is very poor, so I understand your frustration. If all else fails, the ANSYS tech support is pretty helpful though. Try giving them a call.

A simpler approach would be to try and calculate it by hand if the shaft is simple enough, or try a rotordynamics program such as Dyrobes (which we use) which is quite a bit simpler. You can probably ask for a trial version.
 
  • #6
the shaft i am talkin about is called a declamp shaft that is used in a cnc machine to clamp and declamp the tool after an operation. the declamp shaft is loacted inside a spindle cartridge which is driven by a servo motor..the shaft is just supported by a part called sleeve which is connected to the spindle cartridge (here there is a line contact).....
 
  • #7
Interesting stuff minger, I tried a harmonic analysis with a crankshaft for a project but couldn't get it to work. I am on ansys 11 and found the documentation to be poor for more complicated analysis, which is odd as the rest of it is really good.

I get what you mean now vikkispike, that makes some sense :D.
 
  • #8
In your case you'll need to make some assumptions when finding the critical speeds. Your constrains will be the sleeve. Chances are, its constrained in all directions, so you can typically do something like this.

Select the area of the shaft that is attached to the sleeve, then in a cylindrical CS set UX, and UZ to zero. This will restrain the part in the radial and axial directions respectively. Ideally this would be enough to get you started.

For more advanced representation, you could use the COMBIN elements that I mentioned before to represent the stiffness of the sleeve, then attach it to the spindle.

Either way, yes its a PITA right now, but they say that v12 will be much better performing and much better documented.

Also, after a quick Google, I found some more information on calculating the numbere analytically. If the shaft is constant area, then one needs to find the eigenvalues of:
[tex] \frac{d^4 y}{dx^4} - B^4 y = 0 [/tex]
Where
[tex] B^4 = \rho \frac{A}{EI}\omega [/tex]
You would use your "constrains" as the constants of integration (i.e. y(0) = 0) so on and so forth to try and obtain the eigenvalues.

edit: Here is a website that lists some solutions including cantilevered beam
http://www.roymech.co.uk/Useful_Tables/Drive/Shaft_Critical_Speed.html
 
  • #9
I've been reading some papers and most people seem to use MATLAB and do it analytically, with a similar method to the link you gave. COMBIN elemnts are a good idea I never thought of that. I've only ever done static structural analysis, so I am kind of flying blind atm.

This would be for interest only at this point, as I decided that it wasnt strictly necessary for me to complete the work so I've just lumped in the future study section.

ZING! that response probably wasnt for me. but could help anyway :D
 
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  • #10
minger said:
You're in luck, I happened to catch an ANSYS modal analysis webinar a couple of weeks ago.

i am posting the images of the shaft and the sleeve which gets attached to the declamp shaft in the mid portion .this sleeve is attached to the spindle housing which rotates the shaft and at the top of the shaft there is a mass of around 900gms of a part called dublin adaptor...this shaft is held in a vertical position...so what kind of constraints should i give...or shall i do a free free analysis without any constraints...
the main thing is that the shaft is not suported by bearings it just has a line contact it is driven by the sleeve which is inturn connected to the spindle housing...
 

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  • #11
Well the shaft needs to rotate, so don't fix it in that direction, fix it in the other two: axially and radially. Fix in particular the part that slides into the sleeve. Assume the sleeve to be rigid.

I would highly recommend using the link provided and do an analytical solution. Your shaft is essentially pretty "ideal" so the analytically predicted answer should be pretty damn close to the actual one. If your numerical results are not close, then you know that you messed something up.
 
  • #12
minger said:
Well the shaft needs to rotate, so don't fix it in that direction, fix it in the other two: axially and radially. Fix in particular the part that slides into the sleeve. Assume the sleeve to be rigid.

I would highly recommend using the link provided and do an analytical solution. Your shaft is essentially pretty "ideal" so the analytically predicted answer should be pretty damn close to the actual one. If your numerical results are not close, then you know that you messed something up.

In order to determine the analytical solution can i assume it as a cantilever beam with a mass attached at the end....
 
  • #13
Yes.

Apparently I need at least 4 characters to post a message. Please ignore this part of this message.
 
  • #14
The full stop counts as a character :P
 
  • #15
actually my main aim is to determine the failure of the shaft...it fails when it is rotating at 8000rpm...So i think there may be two reasons for the failure of the shaft 1} It may be such that the shaft is rotating near it is natural frequency...and the shaft is subjected to 800kgf load itz an impulse load may be due to that the failure may be occurring...
 
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  • #16
How wide is the range of failures? i.e. is it occurring at 8k and 10k? If so, that's a pretty large range to be critical speed failure. Typically for an undamped system, you're either at the critical speed, which is apparent, or your not.

What do you mean subjected to an 800 kgf (what is kgf?) impulse load? Have you done simple static analysis on this?
 
  • #17
the shaft's operating speed in normal condition is 8000rpm...
1)first i need to check whether the reason of failure is whether the shaft is operating within the critical speed range...
2)MY second part of analysis wil be this one... a impulse load acts on the top of the shaft in order to declamp the tool so the force applied onto the shaft is by a pnuematic cylinder i.e around 800N..
 
  • #18
What do you mean subjected to an 800 kgf (what is kgf?) impulse load? Have you done simple static analysis on this?[/QUOTE]
I wil be carrying out the static analysis after determining the critical speed
 
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  • #19
Well you should be able to pound some hand calcs out pretty quick. Get the critical speed, then do a buckling analysis to make sure you don't have a problem there. The normal compressive stress should be easy enough.
 
  • #20
Does the shaft slide through the adaptor, or is it fixed in the adaptor?

You say it fails when rotating at 8000 rpm. Does it operate at a steady 8000 rpm, or does it operate over a speed range?

Do you have a drawing showing these two parts in position together?
 
  • #21
]

ya i have the assembled drawing of the shaft.Actually i need to determine the critical speed of it because the shaft is failing and i need to determine the cause of it's failure.So my 1st step is whether the shaft is operating within it's critical speed range.I am facing problems when i select the element as beam element 2node 188 i am not able to mesh an error comes.I am able to mesh only if select the element as Solid 45.So can i select the element as solid brick 45...and i need the procedure of determining the critical speed....I am uploadin the photo of how the shaft assembly looks.the adaptor comes at the top and the shaft has only line contact at the middle and is not connected by any other means.
 

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  • #22
Dr.D said:
Does the shaft slide through the adaptor, or is it fixed in the adaptor?

You say it fails when rotating at 8000 rpm. Does it operate at a steady 8000 rpm, or does it operate over a speed range?

Do you have a drawing showing these two parts in position together?

there s a other part called sleeve. the shaft slides inside the sleeve.
 
  • #23
The problem is you are importing a solid model and tring to mesh a beam. A beam mesh is a line, with the CSA and radius of gyration/ 2nd moment area and other stuff inputted as a real constant. To do it as a beam mesh, just draw several horizontal lines (each corresponding to a certain cross section). Mesh then with different real constants.

Where was the shaft failing?
 
  • #24
You say that the shaft slides inside the sleeve. Is it in contact with the sleeve, so that the sleeve constrains the motion, or is the sleeve simply around it but not touching?

What about the matter of steady speed versus operation over a range of speeds?
 
  • #25
To elaborate on what Chris said, you will generate the lines, each representing a cross section. When the cross section changes, start a new line. You will then LMESH to mesh the lines, which will just be more lines basically.

You should be able to LMESH on beam elements. After that, you will define a cross-section. There are pre-defined cross sections such as rectangles and tubes and such. From those, you simply enter length, heights.

If you are doing this in batch, you will says omething like,
Code:
SECTYPE,BEAM,CSOLID !or
SECTYPE,BEAM,ASEC
For circular solid or arbitrary section respectively. You then use SECDATA to describe the geometry of the section. For CSOLID you define:
Code:
SECDATA,radius,number_of_circumferential_divisions,num_radial_divs
For ASEC, you need to define a bunch of stuff, see the SECDATA command reference for more information.
 
  • #26
Can you display the actual cross section that the beam is representing? I know you can do this with shells (show the real thickness) but I can't for the life of me remember how.
 
  • #27
I believe
Code:
/ESHAPE,1
should do it.
 
  • #28
i have drawn the model in ansys and have also meshed it...The shaft isn't supported by any bearings,it just has a sliding support...so what kind of constraints should i give?...IT has a sliding support at two places...so should i constrain UY,UZ,ROTY,ROTZ and keep UX, ROTX free...is this right or i need to change the constraints?

and i need to check whether the solution obtained from ansys is right or not...so which analytical case wil be best suited?
 
  • #29
That sounds ok, could you post a screencap. Those constraints are what I use for a standard bearing (one that doest support thrust).

Also if you are just finding a harmoinic then why are you going to use the FEA, surely its simpler to just use an analytical method. Are you goign to then use the FEA to load the at its critical frequency to test for failure?
 
  • #30
the constraints are what i have mentioned i.e UY,UZ,ROTY,ROTZ and the pther two Ux,ROTx, free...this constraintis at the left extreme end till the other step i have put up the photo...now i am doing a modal analysis for this to find the critical speed ...i got some answers but i need to check whether the answer is correct or not analytically...can u suggest which condition would be suitable...i mean simply supported or cantilever etc...
 

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  • #31
I'd say cantilever over simply supported, as you essentially arent allowing movement.

I'd like to point out that I'm not 100% sure though.
 
  • #32
xxChrisxx said:
I'd say cantilever over simply supported, as you essentially arent allowing movement.

I'd like to point out that I'm not 100% sure though.

the shaft slides while declamping the tool...but sliding takes place when the shaft is not roatating...are u able to get my point...so can i take it as a cantilever only with no mass attached at the end?
 
  • #33
You want to simulate the condition as well as possible. So, your failures occur when your part is rotating at a fixed speed. So, what is happening there? I still am not sure how it's not fixed in the x-direction. It must be fixed in that direction somehow during operation?

Either way, you're going to have a cantilevered beam case and just essentially neglect the fixed part and say that the beam starts where it's not clamped. Don't neglect the mass, that mass at the end of the shaft will be the driving force in the critical speed.

Ya know, if you're just looking a quick estimate, throw me some quick beam numbers (i.e. lengths and diameters) and I'll see if I can spit you out some numbers quickly.
 
  • #34
So my constraints must be Ux,Uy,Uz and ROTy,ROTZ...is it correct



the main aim is to determine the cause of failure of the shaft...so i think that might the shaft is running near the critical speed...there is one more possibility but i wil finish this case first and proceed to the next...

about the declamping i wil xplain 2 u in detail...

the shaft is rotating at a high speed...CNC machine is doing a particular operation(for eg:drilling)...now after the drilling operation,,,,,milling should be done so the tool change must take place...so the spinle stops and the decalmp shaft which is inside the spindle moves down (the declamp shaft moves down due to the application of pressure from above)
now the declamping takes place and the milling tool gets attached to the spindle...




i am trying to explain that the shaft rotates along with the spindle during the operation...
but the shaft is stationary when the declamping(i.e when tool change takes place) is taking place...

Now i think u might be clear about the operation.....
 
  • #35
and about the constraints it's at the left extreme end...
i.e the starting 86.5 mm there is a line contact...
i wil give u the dimenions where it is supposed to be constrained

Ro:13.5 mm

length:86.5 mm
 
<h2>1. What is the purpose of finding the critical speed of a vertical shaft?</h2><p>The critical speed of a vertical shaft is an important factor in determining the stability and safety of rotating machinery. It is the speed at which the shaft begins to vibrate excessively and can lead to failure if not properly addressed.</p><h2>2. How is the critical speed of a vertical shaft calculated?</h2><p>The critical speed of a vertical shaft can be calculated using the formula: Nc = (g x L / 2π) x √(E / ρ), where Nc is the critical speed, g is the acceleration due to gravity, L is the length of the shaft, E is the modulus of elasticity, and ρ is the density of the material.</p><h2>3. What factors can affect the critical speed of a vertical shaft?</h2><p>The critical speed of a vertical shaft can be affected by various factors such as the material and dimensions of the shaft, the type and placement of bearings, and the operating conditions (e.g. temperature, lubrication, load).</p><h2>4. Why is it important to accurately determine the critical speed of a vertical shaft?</h2><p>Determining the critical speed of a vertical shaft is crucial for ensuring the safe and efficient operation of rotating machinery. It helps engineers and designers select appropriate materials and dimensions, as well as identify potential issues that may arise during operation.</p><h2>5. What are the consequences of operating a vertical shaft above its critical speed?</h2><p>Operating a vertical shaft above its critical speed can lead to excessive vibration and potential failure of the shaft and other connected components. This can result in costly downtime, equipment damage, and even safety hazards for workers.</p>

1. What is the purpose of finding the critical speed of a vertical shaft?

The critical speed of a vertical shaft is an important factor in determining the stability and safety of rotating machinery. It is the speed at which the shaft begins to vibrate excessively and can lead to failure if not properly addressed.

2. How is the critical speed of a vertical shaft calculated?

The critical speed of a vertical shaft can be calculated using the formula: Nc = (g x L / 2π) x √(E / ρ), where Nc is the critical speed, g is the acceleration due to gravity, L is the length of the shaft, E is the modulus of elasticity, and ρ is the density of the material.

3. What factors can affect the critical speed of a vertical shaft?

The critical speed of a vertical shaft can be affected by various factors such as the material and dimensions of the shaft, the type and placement of bearings, and the operating conditions (e.g. temperature, lubrication, load).

4. Why is it important to accurately determine the critical speed of a vertical shaft?

Determining the critical speed of a vertical shaft is crucial for ensuring the safe and efficient operation of rotating machinery. It helps engineers and designers select appropriate materials and dimensions, as well as identify potential issues that may arise during operation.

5. What are the consequences of operating a vertical shaft above its critical speed?

Operating a vertical shaft above its critical speed can lead to excessive vibration and potential failure of the shaft and other connected components. This can result in costly downtime, equipment damage, and even safety hazards for workers.

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