## Rotordynamics: why does unbalance in rotor only excite forward modes?

## Rotordynamics: why does unbalance in rotor only excite forward modes?

(OP)

I’ve seen many anecdotes in papers that suggest that imbalance forces have a component in the forward direction, or unbalance forces can be considered “forward whirl forces” - but I can’t picture it on a FBD. The unbalance force points out radially (to me) and shouldn’t have a component forward or backward.

Anyone have any light to shed on this?

Any help would be greatly appreciated! Thanks!

Anyone have any light to shed on this?

Any help would be greatly appreciated! Thanks!

## RE: Rotordynamics: why does unbalance in rotor only excite forward modes?

the unbalance force points out radially, yes.... but in which direction?

toward the weight. The weight rotates with the rotor. The direction of the unbalanced force rotates (forward) with the rotor.

So the rotation of the unbalance force vector is forward (seems obvious)

Whether it excites only forward modes...I'm not sure about that.

=====================================

(2B)+(2B)' ?

## RE: Rotordynamics: why does unbalance in rotor only excite forward modes?

Just looking for some further clarification here. I’ve read many papers/texts and they all kind of gloss over this fundamental thing. Or maybe I’m overthinking something that is quite simple.

## RE: Rotordynamics: why does unbalance in rotor only excite forward modes?

F = KX + MX''

(I'm assuming undamped, no gyroscopic effects to make my life simpler)

The centrifugal force due to non-uniform rotor (no whirl) is captured in the F term and depends on spin. This is separate from the system and considered an external excitation.

The centrifugal force associated with whirling of a uniform rotor (no mass non-uniformity) is captured in the MX''. This is part of the system (M) and system response X''

Since the excitation under this model is purely forward, then no matter what kinds of terms we include on the RHS as coefficients of X or its derivatives, the forced solution will be forward. But the natural solution may be reverse.

That's the formulation that I have seen in textbooks. I haven't given a lot of thought to the aspects you mention. You may be right there may be some significant things glossed over even if the assumptions (linearity) are met.

=====================================

(2B)+(2B)' ?

## RE: Rotordynamics: why does unbalance in rotor only excite forward modes?

I do understand that the forcing function (frequency) will drive the steady state response of the equations of motion.

However I am still stuck on spinning vs. whirling, as the external force in an unbalance analysis is - spinning forward -, not necessarily whirling forward. So I’m still a bit confused as to how backward whirl comes about (for instance, what does the unbalance force vector look like during a backward whirl? - the vector really should be the same)..., yet in some cases there will be a backward whirl induced by unbalance and the “forcing function” will be spinning forward, and the “mass*acceleration” will be whirling backward.... can’t get my head around it.

## RE: Rotordynamics: why does unbalance in rotor only excite forward modes?

We assume that 1 ounce at 5" distance from shaft axis is rotating in a 5" radius circle producing a constant centrifugal force, which doesn't change regardless of any rotor whirl/orbit. But in reality that 5" radius circle is pertubed by a few mils as the rotor orbits/whirls. That effect (addition mass acceleration of the unbalance mass due to orbitting/whirling) is clearly neglected in the model I posted. Maybe we can imagine it is negligible since the few mils of pk/pk displacement orbit is much less than the 10" diameter circle path. Then if we start adding bowed rotor things get more complicated as well.

Here's something I can't explain and I think maybe it's the same thing that's bothering you: An overhung disk rotor (with gyroscopic effects) has both forward and reverse modes predicted by modal analysis. And the frequencies of the reverse mode are sometimes observed in the real world during coastdown waterfall plot. It raises a question... what is the exciting those reverse modes during coastdown. By our model I don't think it is unbalance because if we don't have reverse excitation on LHS I don't think we can have reverse response on RHS. Either I am mistaken about my interpretation of the equation, or there is something about the coastdown transient that excites the reverse whirl.

=====================================

(2B)+(2B)' ?

## RE: Rotordynamics: why does unbalance in rotor only excite forward modes?

That contradicts what I surmised from inspection of the matrix equations of motion. I dont' have a good explanation... would have to dig into the math (I'm not THAT curious at the moment).

=====================================

(2B)+(2B)' ?

## RE: Rotordynamics: why does unbalance in rotor only excite forward modes?

Since I can't figure out how to indent for organization, I'm going to set it off in a quote box as follows:

The flaw of my previous logic concerning the matrix equations of motion was that I imagined we could just use a phasor approach, multiplying the force by something like exp(i*(theta-wt)) and exp(i*(theta+wt)) to capture the forward and reverse aspects. But I was really mixing things up.... that's not the way it works. The state vector X includes both x and y components, and the phase relation between these components gives us forwards or backwards rotation sense. I'm sorry that it took me awhile to get there.

=========

By the way, above I am referring to the single rotation sense that we would assign to the single frequency orbit tracing it's path in the x / y plane. Distinct from this, there is a transformation of a given single-frequency orbit or spectrum into forward and reverse components (search for "full spectrum"). That's a completely different take on forward and backward than I'm using.

=====================================

(2B)+(2B)' ?

## RE: Rotordynamics: why does unbalance in rotor only excite forward modes?

I think the way i can rationalize it in my head is as follows:

In absence of bearing support stiffness asymmetry, and nonlinear or cross-coupling forces, the rotor will whirl synchronously in the forward direction, because at the bearings where the shaft is effectively "pinned" it is spinning in the forward direction, which drives the remainder of the shaft in the same direction when travelling off-center.