Im looking to do some whirling and critical speed analysis on a shaft (at first just a simple cylindrical shaft, then maybe go on to more complex geometries once the simple one is understood). If anyone has any experience of conducting this type of analysis before and could share with me any information it would be greatly appreciated. Id also like to back up any simulation with hand calculations, so any info in that area would also be appreciated.
You need to do a modal analysis. The first natural frequency which excites the shaft laterally corresponds to the critical speed. You just need to convert the Hz to RPM.
Sensitive parameters for the modal analysis would be the end stiffness on the shaft, and the stiffness and mass distribution of the shaft itself of course. If you use beam elements make sure you have at least 10 elements across the free span of the shaft, and I would also suggest that you turn on the complex mass formulation in that case (but not critical, and I don't remember exactly where that is set inb the solver settings - someone else can maybe chime in on that).
Thanks for your reply Kava.
I have been reading up on this topic and found that it is possible to get forward and backward whirling and as a further step to my study I would like to analyse a beam with a mass at the end which could potentially experience this forward and backward whirling, is it possible to analyse these phenomenons in cases where they occur. Also correct me if im wrong but wouldnt whirling be affected by the speed of rotation of the shaft so I was wondering if it would be possible to inlcude a speed dependant analysis.
The backward whirling seems to be an effect that happens when there is a loose fit on the shaft, such that it can be driven opposite the surrounding bearing (kinda like a harmonic drive I think). I'm not sure that applies to a simple shaft, but I've never heard of it before either.
My first instinct is to say that the natural frequency is not going to be sensitive to spin speed, because there is no axial load induced in the shaft. I've just read that the gyroscopic effects can influence the natural frequencies of the shaft. I can believe that but I have no background in it. At any rate, the forward whirl natural frequency seems to increase with shaft speed, so you would be conservative assuming that the static natural frequency is equal to the critical speed.
I'm still curious about reverse whirl though.
You need to run ROTOR DYNAMICS module (this is an add-on module to the Basic package, requires license), in FEMAP go to HELP > NX NASTRAN and open the ROTOR DYNAMICS USER`S GUIDE:
NX Nastran includes a rotor dynamics capability that lets you predict the dynamic behavior of rotating systems. Rotating systems are subject to additional forces not present in non-rotating systems. These additional forces are a function of rotational speed and result in system modal frequencies that vary with the speed of rotation.
In a rotor dynamics analysis, the system’s critical speed is particularly important. The critical speed corresponds to a rotation speed that is equal to the modal frequency. Because the critical speed is the speed at which the system can become unstable, engineers must be able to accurately predict those speeds as well as detect possible resonance problems in an analysis.
With frequency response analyses, the user can predict the steady-state response for different rotor speeds. Asynchronous analysis can be done by keeping the rotor speed constant and varying the excitation frequency. In the synchronous option, the excitation frequency is equal to, or a multiple of the rotor speed. Grid point displacement, velocity and acceleration, element forces and stresses can be recovered as function of rotor speed or excitation frequency.
Transient response in the time domain can be used in order to study the behavior of the rotor when passing a critical speed. Here, the user can define a sweep function of the excitation. In the transient analysis the grid point displacement, velocity and acceleration, element forces and stresses can be calculated as function of time.
Both modal and direct methods can be applied for complex eigenvalues, frequency response and transient response analyses.
Maneuver load analysis is a linear static structural analysis that accounts for inertial loads. The NX Nastran rotor dynamics capabilities allow you to account for gyroscopic forces and forces due to damping of the rotor in a maneuver load analysis.
The following picture is an example of the Campbell diagram generated by ROTOR DYNAMICS module and plotted in FEMAP: