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.
  • #36
OK, so based on what you told me I threw the shaft quickly into the rotordynamics program that we use. Here is the geometry
shaft_test_geom.PNG

The coupler on the right, Station 7 is on another "level" in the program, this basically will assume that the coupler is completely rigid. In the real-world it's not, but unless we have a number to put in, that's the best I'm going to be able to do.

The left spring is a bearing, bearing by definition only, I realize this is actually a fit. I have made the bearing very rigid in the lateral directions, essentially cantilevering the rest of the shaft off of it.

Hopefully, the rest of it looks good. The first few mode shapes that the program computes are:
shaft_test_01.PNG

shaft_test_02.PNG

shaft_test_03.PNG

shaft_test_04.PNG

The table of computed critical speeds are:
Code:
           *******   Spin(1)/Whirl Ratio =  1.000    *******

              no     rpm           R/S          Hz

               1    .173939E-01  .182148E-02  .289898E-03
               2    6617.14      692.946      110.286    
               3    23774.2      2489.63      396.237    
               4    54967.9      5756.23      916.132    
               5    117665.      12321.9      1961.09    
               6    186694.      19550.6      3111.57    
               7    546068.      57184.2      9101.14    
               8    631345.      66114.3      10522.4    
               9    .159996E+07  167547.      26666.0    
              10    .244668E+07  256216.      40778.0    
              11    .281101E+07  294368.      46850.1    
              12    .492635E+07  515886.      82105.8    
              13    .685237E+07  717578.      114206.    
              14    .719070E+07  753008.      119845.    
              15    .334042E+08  .349808E+07  556737.    
              16    .504299E+08  .528100E+07  840498.
If you want the data output file, then it's located at:
http://www.eng.utoledo.edu/~mheminge/shaft_test.OU2 The file is open-able in wordpad, it lists the station properties, displacements, energy distributions, etc. Well, hopefully this helps, moreso, hopefully it matches what you tried to compute analytically. If there is any small changes in the inputs, then let me know and I'll try and find time to change it and rerun it.
 
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  • #37
thank u so much ...
ya i wil do it analytically and verify it...
can't u change the constraint from a "all DOf" and making it free to translate along "x-direction" and rotate along "x direction".Is it possible if yes wil it make a huge difference in the solution
 
  • #38
Change what constraint?

In my model, I have not modeled any thrust bearings, so the shaft is able to translate along the x (z in my program) axis. I have only given it stiffness in the x/y directions, which are lateral in this situation.
 
  • #39
oh k den itz right...
 
  • #40
thank u once again

i'll let u knw bout the analytical result...

now the second part comes into picture...
a impulse load acts on the sleeve during declamping i think that the impact load might be causing the shaft 2 fail...can there be other reasons for the shaft failure?
 
  • #41
can you just help me in getting me the trial version of this software...where can i get this one?

can this stuff be done in ansys also?
 
  • #42
To try and get a trial version, contact the creator, I'm sure you can find an email/phone at dyrobes.com Yes, this can all be done in Ansys.
 
  • #43
i had sent a mail to the creator but i haven yet got any reply...but in ansys i have created the model using pipe16element...but i did not get the results as u got it using the dyrobes software...so i m not able to make out in which part i have messed up...i think i might have done mistake with the constraints (OR) in the method used actually there r three methods
1) block lancoz
2)substep
3) reduced
may be i have done mistake in these 2 cases...just can u help me out...
 
  • #44
actually the frequencies in the results start from

27.8hz only...
65hz
100hz...
and keeps increasing
i think the answer which u hav got is right ...i don knw were am i messing up...
 
  • #45
no entiendo nada :P
 
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