Modern formulas for statics and dynamics: A stress-and-strain approach BY PILKEY AND CHANG is a good source for transfer matrix methods. Walt Pilkey had a set of pregrams.
E. G. Pestel and F. A. Leckie, Matrix Methods in Elasto-Mechanics is great to understand the approach.
Regards,
Bill
I would recommend hiring a professional that allow you to follow what they do, a professional who doesn't use the 4 run method. The 4 run method is very inefficient, and if you have to trim balance you have to start over with another 4 runs.
If something changes, keeping track of phase and...
Burnishing uniformly work hardens the surface, which can help. Some have tried micro-peening for a similar purpose.
Some materials can be come magnetized. Some machining operations can leave the target material non-uniformly magnetized. This requires de-Gaussing.
Hit the target with a...
'If a shaft/rotor is perfectly balanced'
There's the rub, so to speak. This is impossible. Besides, there are other forces to consider.
A perfect circle is unlikely, also. Support asymmetry split the natural frequencies, so do gyroscopic effects. If the x and y dominating natural...
It looks like the extra damping at point locations (bearings) in this case is further constraining the shaft at the bearings, meaning greater strain energy ==> greater natural frequency.
The rigid shaft was to prevent modeshape changes. Different combinations of shaft to bearing stiffness...
For the system you give I believe that damping interacts slightly with the modeshape to give this effect. The attached file runs a case that the modeshape remains almost the same (by forcing the rotor to be rigid), and the case with the flexible rotor.
Regards...
Run the analysis without damping, and you should still see the bifrication of the forward and backward modes. Add damping and see.
Also, you could turn gyroscopics off and see the effect in the modes. I assume you have an overhung rotor for which gyroscopics has a large effect.
Regards,
Bill
The forward whirl frequencies being higher than the undamped forward frequencies does not relate to damping; this is caused by a gyroscopic effect.
Regards,
Bill
The damped natural frequency for a single degree of freedom system is sqrt(1-zeta^2)*undamped frequency, where zeta is the critical damping ratio. So, the damped frequency is lower than the un-damped.
Also, as you approach critical damping the frequency goes to 0. A critically damped (root)...
Have you looked in the turbine manuals? Hopefully, you will have the resources of mechanical and vibration people to assist you.
You mention trip, which makes the monitor have a control function. This gets more serious than if it is just a monitor.
ISO may give some guidance, but you need to...
Rao's (and others) book on rotordynamics talks about this, as I recall.
Gyroscopics, tends to raise the forward 'criticals' and lower the backwards ones. The equations end up with (It-Ip) terms for the cross terms in the equations of motion. The It is the transverse inertia term) - The Ip...
