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Electro-mechanical resonance frequency
4

Electro-mechanical resonance frequency

Electro-mechanical resonance frequency

(OP)
Has anyone got information on Electro-mechanical resonance? I have seen some info about this with servo motors but this concerns a standard AC induction motor. I think that if this resonant frequency coincided with VFD firing frequency or a integer multiple it could cause severe torsional vibration. What do you think? Does anyone check for this potential problem?

RE: Electro-mechanical resonance frequency

Suggestion: Reference:
Electromechanical Resonance
Roubicek, O.   
Dept. of Electr. Syst., Res. Inst. of Electr. Eng., Praha 9-Bechovice;
This paper appears in: Electric Power Applications, IEE Proceedings B [see also IEE Proceedings-Electric Power Applications]

Publication Date: Jul 1990
On page(s): 281-292
Volume: 137,   Issue: 4
ISSN: 0143-7038
References Cited: 24
CODEN: IPPADZ
-------------------------------------------
Abstract:
The symmetric double acting oscillating synchronous linear motor with longitudinal functional air gaps is very well suited to the system synthesis of the electronically controlled drive for working resonant machines used in industrial vibrational techniques. It can be designed for a stroke of up to a few centimetres and a working frequency ranging from about 6 to 70 Hz. What is important in practice is the motor operation in electromechanical resonance with a compensated synchronising (AC) motor circuit and a compensated mechanical load. Then, the operational motor characteristics, derived under the assumption of harmonic oscillations, are functions of real variables. An analysis of these characteristics yields the features of a steady-state motor with harmonic oscillations. Attention is paid to the motor self regulation and the control of the velocity or path amplitude of its oscillations. The theoretical outcome, applicable also for the case of a not fully harmonic motor power supply from a static convertor, is in good agreement with the experimental results obtained from researching motor prototypes of 1 and 5.7 kW

RE: Electro-mechanical resonance frequency

4
From my way of thinking, the resonance is mechancial. It can be lateral or torsional.

The excitation can be electrical (torque pulses, lateral magnetic force variation) or mechanical.  If either type of excitation corresponds to mechanical resonance frequency, there can be trouble.

With regard to torsional resonance, it is most often excited by impacting-type torque pulses from the load (such as reciprocating compressor). If torque pulse rate is an integer subharmonic of torsional resonant frequency, there can be problems.

Induction motors I think are less susceptible than sync motors because the low-resistance squirrel cage provides very heavy damping action for instantaneous deviation from steady state speed.

I think torsional analysis is not done by many users except for larger trains of equipment.   OEM's may do it for smaller pieces of equipment.

http://www.engdyn.com/papers/papers_torsional.htm
At this link you will find a nunmber of papers on torsional analysis and most are available free on-line pdf (others are available for phone call.  

For example, click on "Torsional Analysis of VFDs" and then look for the pdf icon near top right-hand corner of the page (2.3 Megabytes).

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RE: Electro-mechanical resonance frequency

jbartos

Is there any special relevance between torsional resonance of vfd and your paper: "Electromechanical model of a resonating nano-cantilever-based sensor for high-resolution and high-sensitivity mass detection"

I think it is safe to assume that anyone who can make it to this site knows how to use google. So spewing random google links with no relevance to the question does not help, in fact wastes people's time following unrelated links under the assumption that if someone posts them here they have some relevance.

If you are going to post links, may I suggest you limit it to links that you personally have determined have some relevance to the question.

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RE: Electro-mechanical resonance frequency

(OP)
Thanks for the input so far. I may not be using the correct lingo since I'm a mechanical guy. Let me describe it a little better.

At an instant in time, in the stator of a 4-pole motor there are 2 North poles and 2 South poles right? Simultaneously, on the rotor there are also 2 Norths and 2 Souths. We all know how they got there so we'll skip that part. The magnetic fields interact to pull the rotor around. This pull is the spring in my resonant system. The mass is of course the rotor.

So I'm looking at a torsional resonance in the motor itself. I expect this to be a high frequency, but what if its not. Or what if, I now use this motor with a VFD that may have many harmonics of line frequency? Does anyone check for this at design stage?




RE: Electro-mechanical resonance frequency

Comment on electricpete (Electrical) Mar 22, 2004 marked ///\\\
From my way of thinking, the resonance is mechancial. It can be lateral or torsional.
///Please, revisit my posted links for the idea of mathematical model of electromechanical system.
Specifically, Equation 5
V (x) = sqrt[0.533E W^3 x^3 (s-x)/[e l^4 (x-(s-x)ln|s/(s-x))|]] (V(m)) (5)
e is medium permittivity
Clearly, it can be seen that there is a mixture of electrical and mechanical variables.
This is consistent with my statement ""It just depends how the electromechanical equations, possibly differential equations are setup.""
Then, comes more difficult part, namely how to form the mathematical model to obtain the sought results about the torsional vibration/resonance.\\\

RE: Electro-mechanical resonance frequency

Suggestion to electricpete (Electrical) Mar 22, 2004 marked ///\\\
http://www.engdyn.com/papers/papers_torsional.htm
At this link you will find a nunmber of papers on torsional analysis and most are available free on-line pdf (others are available for phone call.   
///It is not quite explicit in the posted link which reference is covering electromechanical modeling that would include electromechanical resonance.
====
electricpete,

Is there any special relevance between electromechanical resonance of vfd and your papers dealing with torsional resonance?

I think it is safe to assume that anyone who can make it to this site knows how to use google. So spewing random google links with no relevance to the question does not help, in fact wastes people's time following unrelated links under the assumption that if someone posts them here they have some relevance.

If you are going to post links, may I suggest you limit it to links that you personally have determined have some relevance to the question. \\\

RE: Electro-mechanical resonance frequency

jb - your comment on possible electrical interaction in the resonance is accepted.  Regarding relevance of links, I would suggest rather than making a ridiculous argument that your link is relevant and mine is not, you just accept my comment as a constructive suggestion and refrain from repeatedly posting links direct from google without any consideration of relevance.

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RE: Electro-mechanical resonance frequency

Electro-mechanical resonance is links with low mechanical stiffness in the linkage or transmission connecting load to any type of motor.This low stiffness leads to low frequencies (even from 0.5Hz) and weak damping modes of load vibrations. Ones are occur upon action of motor torque and/or load (and other loads coupled with it) a forces.
The low stiffness often leads to serious problem with tuning of servo system especially depended by ratio of load-to-motor moments of inertia (mismatch ratio).
More details you may find from Tutorial and paper of George Ellis (Kollmorgen) and Richard H.Welch Jr.(Welch Enterprise).

RE: Electro-mechanical resonance frequency

Comment on electricpete (Electrical) Mar 23, 2004
jb - your comment on possible electrical interaction in the resonance is accepted.  Regarding relevance of links, I would suggest rather than making a ridiculous argument that your link is relevant and mine is not, you just accept my comment as a constructive suggestion and refrain from repeatedly posting links direct from google without any consideration of relevance.  
///Rather than claiming that your postings are relevant and others irrelevant, it would be better that you point out where the electro-mechanical resonance is actually appearing in your postings to satisfy the original posting request. I just feel sorry for criticizing others while delivering very little or nothing to the original posting.\\\

RE: Electro-mechanical resonance frequency

Quote (jartos):

I just feel sorry for criticizing others while delivering very little or nothing to the original posting

We have come to expect it from you. Apology accepted.

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RE: Electro-mechanical resonance frequency

Comment on the previous posting: Please, who are those "we"? I noticed that you operate as part of some kind of collective on this Forum. This is not the case in my participation in here. I am meeting the intent of this Forum by delivering eng-tips. Why should I apologize to some who cannot prove, evidence or reference properly their postings?

RE: Electro-mechanical resonance frequency

Inspector Gadget - I think you will find a good discussion at the link I provided.

There is a rambling long-winded discussion that I participated in at
http://www.vtab.se/PHP-NBoard/html/images/materiali/Forum2/HTML/001884.html

(note there are 2 pages of it... click on button near bottom of 1st page to get to 2nd page).

From my perspective, the induction motor field acts not like a spring, but like a damper.  Torque is proportional to slip.  I think if you build a math model on this including linearization about the steady state point, you will conclude the function of the torque produced by induction motor is equivalent to a damping element, not a spring. As such it does not introduce any new resonant frequency into the system.   I may be mistaken and I welcome someone to explain why an induction motor field should act like a spring.

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RE: Electro-mechanical resonance frequency

Sorry, the page I provided does not have any means to get to page 2. Here is page 2

http://www.reliability-magazine.com/ubb2000/ubb/Forum2/HTML/001884-2.html

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RE: Electro-mechanical resonance frequency

Inspector Gadget - Here I will try to provide a proof that the effect of the torque of an induction motor is to introduce damping (not spring action) into the system:

define w(t) = radian speed of rotor
define w0 = steady state speed
define w1(t) = deviation from steady state speed w1(t) = w(t) – w0.
theta(t) = position as function of t
theta0(t) = w0*t  = steady state position - revolves steadily as function of time
theta1(t) = deviation from steady state position = theta(t) –theta0

define Tmot = motor torque
define T0 = steady state motor torque
define T1(t) = deviation from steady state motor torque = Tmot-T0
define Tload = load torque
define Ttotal = total torque = Tmot+Tload

define wsync – syncrounous speed
k = proportionality constant between slip speed (wsync-w) and torque
Tmot = k*(wsync – w(t))
substitute in for w(t)

Tmot = k* (wsync – w0 – w1(t) )
Tmot = k*(wsync-w0) – k*w1(t)

recgognize k*(wsync-w0) = T0
Tmot = T0 – k*w1(t)

Ttotal = Tmot +Tload
Asssume Tload constant at steady state value Tload = –T0
Ttotal = Tmot – T0

substitute for Tmot
Ttotal =  T0 – k*w1(t) – T0 = -k*w1(t)

Ttotal = -k*w1(t) looks very much like damping equation Fdamp = -c * dx/dt = -c*v

F=ma type relationship is
Ttotal = J*d^2/dt^2 ( theta(t))
substitute in for theta(t)
Ttotal= J*[d^2/dt^2(theta1(t)+ theta0(t)]
But theta0(t) = w0*t, so d^2/dt^2(theta0(t)) = 0

Ttotal= J*d^2/dt^2(theta1(t)]
substitute in for Ttotal
-k*w1(t) = J*d^2/dt^2(theta1(t)]

substitute w1(t) = diff(theta1(t))

-k*diff(theta1(t)) = J*d^2/dt^2(theta1(t)]

This can be recognized as a damped system.  
The response to a perturbation in theta is theta(t) = theta0 * exp(-k/J).

=> induction motor torque coefficient k plays the role of damping.

* Note - if you have a syncrhonous motor then the field will introduce a spring which add a resonance to the system.

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RE: Electro-mechanical resonance frequency

Correction:
The response to a perturbation in theta is theta(t) = theta_initial * exp(-k*t/J).

(I don't want to re-use the symbol theta0)

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RE: Electro-mechanical resonance frequency

Onre more correction:
The response to a perturbation in theta is theta1(t) = theta_initial * exp(-k*t/J)

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RE: Electro-mechanical resonance frequency

(OP)
Epete,
Don't your equations assume there is only one spring to begin with? Where is the term for the force which accounts for nonlinear response in magnetic force due to varying the distance between poles in the rotor and stator? I do agree that the effects of resistance and inductance in the electrical circuit work to keep the vibration amplitude from going to infinity.

In the analagous mechanical system, the material which is selected for the spring not only determines the spring constant, it also determines a certain damping. As an extreme comparison, if I use a metal spring vs. a rubber one. So it is possible that the electromagnetic forces are not only dampening but storing energy.

RE: Electro-mechanical resonance frequency

My equations attempt to model the effect of the torque-producing field.  Yes there will be springs and imho they will all be mechanical (for instance coupling between motor and load).  The intent of the above excercize was to demonstrate that the torque-producing force between rotor and stator acts as a damper, not spring, therefore it will not introduce any new resonant frequency but may lower the amplitude of oscillation.

Consider that large syncronous machines have shorted-turn windings installed soley for the purpose of dampening low-frequency oscillations. These windings are roughly equivalent to squirrel cage windings.

If there were a force representing a spring created by the electrical field, it would show up somewhere as a term torque ~ k1* theta.  But induction motor is symmetric and one position of thete means no different than another.  The torque does not care about position of theta, it cares about relative motion w.  How can this represent a spring?

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RE: Electro-mechanical resonance frequency

In the previous discussion linked on the other board, you may have seen links to some word files which were very hard to read.  I have re-created the last word file in very different format as a pdf file which has much easier to read equation formatting (although still may not be straightforward depending on whether you have used a similar computer program to Maple).

The link is here:
http://www.brazosport.edu/~pschimpf/forums/engtips/TwoMassSpringInductionSimpleRev1.PDF

It solves a system of motor rotor inertia, compressor rotor inertia, coupling spring, coupling damping, and induction motor field which acts as dampener.  The exciting force is assumed to come from the load end.   The variable Xd (d for differential) is examined which presents differential position between motor rotor and compressor rotor i.e. torsional flexing of the coupling.

There is one root at zero frequency (I provide some discussion of interpretation with respect to response to step change in load at the end).  This zero frequency root I associate with the motor field.  There is one resonance at w=14 which is very close to that computed from compressor mass and coupling spring.    The frequency of this resonance may be altered some by the damping effect of the motor field.  imho, there is no new resonance created by the motor field because there is no spring action associated with the motor field.

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RE: Electro-mechanical resonance frequency

Comment on the previous posting: The posting link does not have addressed electrical variables or parameters. Therefore, the modeling is strictly mechanical. The original posting addresses "Electromechanical resonance." Clarifications are requested.

RE: Electro-mechanical resonance frequency

The effect of the transient motor torque (identified above as T1(t) above) is captured in the damping element C1. The justification for this approach is identified in my 2nd post today 3/26.

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RE: Electro-mechanical resonance frequency

Sorry, it is identified in my 3rd post today.

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RE: Electro-mechanical resonance frequency

I think 2 points deserved to be mentioned again.

1 - If we were discussing a sync motor, there would be a spring corresponding to the field and an associated resonance frequency. Not so for induction motor.

2 - In a vfd there may be harmonic torques which will serve as excitation.  The resonance excited by those torques (for induction motor) would be mechanical.

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RE: Electro-mechanical resonance frequency

Suggestion: Visit
http://www.ipst.org/TechPapers/2001/IPST01Paper240.pdf
For "Perceptions about new kinds of subsynchronous resonances":
The numerical calculation of different types of drives brought an important insight: also in systems with induction machines an electromechanical resonance can occur, especially during running up. Consequently the torque in the connection components between motor and main engine can reach values much bigger than the maximum stationary breakdown torque (see fig. 8). This highly depends on the mechanical-geometrical and the electromechanical attributes of the entire system. Also the inner mechanical damping has to be considered. As a result, no global predictions about the endangerment of a drive system can be made and must not be made.

RE: Electro-mechanical resonance frequency

The article linked above by jbarots discussing oscillating torque during startup of an induction motor.

 In the article I references Engineering Dynamics Paper “Torsional Analysis of VFD’s”, this oscillation is not discussed under system stiffness on pages 2 & 3.  It is discussed on page 7, more in context of a driving excitation.  Whether or not you choose to call this an electromechanical resonance is a matter of terminology. I can see support for both viewpoints, and I previously have accepted the comment that electromechanical resonances are present.

One logical question is why does the model I showed above not predict this behavior. The model I showed is based on torque proportional to slip.  We know this is true at steady state when speed is within a few percent of syncronous speed.  It is reasonable to expect it to be approximately true for small transients from steady state condition.   It is not reasonable to expect it to hold for faster transients or starting from zero speed.    Below breakdown torque, the torque vs slip curve no longer resembles a proportional relationship  and the torque no longer represents a damping effect.

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RE: Electro-mechanical resonance frequency

Comment: There is a record of generator shaft cracks due subsynchronous resonances caused by the series in-line capacitors in the transmission lines. This is what is normally considered electromechanical resonance in electrical power engineering. Of course, there are strictly mechanical resonances caused by mechanical dynamics linked to the load behavior, etc. I see that many above postings are strictly addressing mechanical dynamics and associated resonances. It is necessary to address the discussed problems in broader terms. It appears that this thread is slowly heading in that direction.

RE: Electro-mechanical resonance frequency

jb - I have never heard any reference to induction machine torsional failure associated with power system interaction as you describe.  What you describe is associated with syncronous machines.

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RE: Electro-mechanical resonance frequency

(OP)
Everyone, thanks for the input. This is really fascinating stuff.

Epete,
Please explain why you say this phenomenon only exists in synchonous machines. It may be my misunderstanding of how they work. I will go do some study. Don't VFD's have the potential to make torque pulses? Isn't the ouput wave actually made up of lots of square waves?  

RE: Electro-mechanical resonance frequency

(OP)
I'm wondering are there any motor/drive manufacturer engineers out there? Is this a concern for you?

RE: Electro-mechanical resonance frequency

IG - Yes vfd's can make torque pulses, which can excite mechanical resonances in induction machines.  I was referring to the discussion of subsyncronous resonance as a result of interaction with the power transmission system.  This applies to only to syncronous machines in my opinion.

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RE: Electro-mechanical resonance frequency

Comment on electricpete (Electrical) Mar 29, 2004 marked ///\\\
The article linked above by jbarots discussing oscillating torque during startup of an induction motor.  
///Yes.  Beside that, the paper also addresses:
1.
II. USUAL SSR PHENOMENA
The usual SSR phenomena caused by compensated transmission lines can be manifested in three forms: Induction generator effect (IGE), torsional interaction (TI) and torque amplification (TA). These phenomena may occur isolated or simultaneously, and when they occur they can cause damaging oscillations. Hazardous levels might be reached within 0.1 seconds.
2.
For calculation of the electrical resonance, the structure of the electrical system according to fig. 1 can be represented by a reduced model. The resonance frequencies depend on the short circuit capacity of the main system (fig. 4). For the analysis of SSR it is necessary to evaluate electrical frequencies close to:
for the steam turbine: fn - fm= 50 Hz - 18 Hz = 32 Hz
for the gas turbine: fn - fm = 50 Hz - 12 Hz = 38 Hz
where fn is the electrical frequency and fm is the mechanical resonance frequency.
3.
etc.
However, the generators are often considered for the subsynchronous (subharmonic) resonances, since the transmission lines are not directly connected to large induction motors. The impact of subharmonics would be somewhat similar to the detrimental impact on the generator rotors.\\\

RE: Electro-mechanical resonance frequency

Comment on electricpete (Electrical) Mar 29, 2004 marked ///\\\
jb - I have never heard any reference to induction machine torsional failure associated with power system interaction as you describe.  What you describe is associated with syncronous machines.  
///Yes, that is possible since, as I mentioned in my previous posting, the transmission lines are not directly connected to large induction motors. The impact of subharmonics would be somewhat similar to the detrimental impact on the generator rotors.\\\

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