Electro-mechanical resonance frequency 4

[InspectorGadget]

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?

 

[jbartos]

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

 

[electricpete]

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).

=====================================
Eng-tips forums: The best place on the web for engineering discussions.

 

[jbartos]

Comment: It just depends how the electromechanical equations, possibly differential equations are setup. Visit

http://www.mic.dtu.dk/research/biop... nano-can-based sensor for mass detection.pdf

for Equation 5

http://www.mtf.stuba.sk/veda/casopis/2004/cislo1/mudrik/mudrik.pdf

etc. There is a lot of it on Web

 

[electricpete]

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.

=====================================
Eng-tips forums: The best place on the web for engineering discussions.

 

[InspectorGadget]

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?

 

[jbartos]

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.\\

 

[jbartos]

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. \\\

 

[electricpete]

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.

=====================================
Eng-tips forums: The best place on the web for engineering discussions.

 

[blacksea]

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).

 

[jbartos]

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.\\

 

[electricpete]

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.

=====================================
Eng-tips forums: The best place on the web for engineering discussions.

 

[jbartos]

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?

 

[electricpete]

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.

=====================================
Eng-tips forums: The best place on the web for engineering discussions.

 

[electricpete]

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

=====================================
Eng-tips forums: The best place on the web for engineering discussions.

 

[electricpete]

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.

=====================================
Eng-tips forums: The best place on the web for engineering discussions.

 

[electricpete]

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)


=====================================
Eng-tips forums: The best place on the web for engineering discussions.

 

[electricpete]

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


=====================================
Eng-tips forums: The best place on the web for engineering discussions.

 

[InspectorGadget]

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.

 

[electricpete]

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?

=====================================
Eng-tips forums: The best place on the web for engineering discussions.