Posted 08 June 2006 01:37 PM
I read an article on modeling of magnetic pull in an induction motor that I found on google:
http://lib.tkk.fi/Diss/2003/isbn9512266830/article6.pdf

The following appears on page 2 under “Description of the Analysis”
============= DIRECT QUOTE ==================
“The calculation of the electromagnetic force acting in the induction motor is based on time-stepping, finite element analysis of the magnetic field. The details of the method have been presented in [12]. The magnetic field in the core region of the motor is assumed to be two-dimensional, and the twodimensional field equation is discretized by the finite element method. The effects of end region fields are taken into account approximately by constant end-winding impedances in the circuit equations of the windings. The field and the circuit equations are solved together as a system of equations. The time-dependence of the field is modeled by Crank-Nicholson method. The magnetic field, the currents and the potential differences of the windings are obtained in the solution of the coupled field and circuit equations. The forces are calculated by a method, based on the principle of the virtual work [13]. If the force is divided into a radial component in the direction of the shortest air gap and a tangential component perpendicular to the radial one, the components are almost independent of time (Fig. 1). The impulse method is utilized in the finite element analysis to calculate the force between the stator and the rotor. The details of the impulse method are presented in [14]. from its central position for a short period of time to one direction. This displacement excitation disturbs the flux density distribution, and by doing this, produces forces between the rotor and stator. Using spectral analysis techniques the frequency response function of the force is determined from the excitation and response signals. The length of the rectangular displacement pulse in the simulation was 0.005 s. The amplitude of the static pulse was 15 % of the air gap length. Total simulation time was 1.0 s with constant time-step of 0.05 ms. To increase the spectral resolution, the sample size was extended to be 2 s by adding zeros to the end of the sample. This leads to frequency resolution of 0.5 Hz. The discrete excitation and force signals were transformed into the frequency domain by the FFT without filtering or windowing. The number of sample points used in FFT was 8192. The frequency response function presents the electromagnetic forces per whirling radius as a function of whirling frequency. The assumption of the spatial linearity of the forces, which is shown to be valid for small values of rotor displacement in [10,11,15], is used in this study. The advantage of the impulse method is that from the results of one finite element analysis, the forces are obtained for a wide whirling frequency range. The motion of the rotor is obtained by changing the onelayer finite element mesh in the air gap. Second order isoparametric, triangular elements were used. Several simplifications have been made to keep the amount of computation to a reasonable level. The magnetic field is assumed to be two-dimensional. The laminated iron core is treated as a nonconducting magnetically non-linear medium, and the nonlinearity is modeled by a singe-valued magnetization curve. The homopolar flux, which may be associated with rotor eccentricity, is neglected."
============= END-OF-DIRECT QUOTE ==================

I would paraphrase what I think they are doing (the “impulse method”), it is as follows;
1 - Build a finite element model of a motor.
2 - Create a sort of impulse movement of the rotor. i.e. move rotor 15% of airgap distance off-center for a very short duration (0.005 sec) and then move it back. Record the resulting force. Call the displacement d(t) and the resulting force f(t).
2A – They say the force is very nearly constant in time... I assume they are ignoring pole pass modulation and looking at some kind of average radial outward force.
3 – Under the assumption of “linearity”, build a transfer function FRF(w) = F(w) / D(w) where D(w) is FFT of d(t) and F(w) is the FFT of f(t) and w is frequency. This gives Force/displacement transfer function FTF(w), which could roughly be viewed as a frequency-dependent negative spring constant associated with the by em force.
4 – Use the computed transfer function FRF(w) to make predictions about magnetic pull for varying whirling frequencies w.

I have an objection to their approach. They talk about linearity (“the assumption of the spatial linearity of the forces” for small rotor displacements) , but actually in order to apply superposition and a transfer function approach, we need not just linearity but a Linear Time Invariant (LTI) system. This means that even though the inputs and outputs (and state variables) vary with time, the system itself does not change with time. (In a mechanical system a spring whose stiffness changed with time would violate the time-invariant requirement). The system in their model does not seem to come anywhere close to being time-invarientt. Considering the input to be the the position of the rotor and the output to be the magnetic force, the motor supply voltages are contained within the system rather than being an input to the system. The motor terminal voltages clearly change with time and introduce a time-varying external influence on the currents and fluxes and forces which is not related to the input. It seems like the system does not meet time-invariance, which would invalidate the transfer function approach.

Looking at it in the time domain illustrates the error in a different (more intuitive) way. At a given location in the rotor the field is varying at 50hz (period of 20 milliseconds). They only ran one simulation. They had to make some assumption about the timing of their 5 millisecond pulse compared to the 20 millisecond electrical variation. Clearly if you inject the rotor-position-pulse at a time/place where the mmf is near a peak you will get a different answer then if you injected the rotor-position-pulse at a time and place where the mmf is near a zero. The model doesn’t use multiple injections.... only one. This would be satisfactory for a time-invariant system where we don’t care about timing of input compared to timing within the system (the system has no timing). It is not satisfactory for a time-variant system.

What do you guys think? Does their approach sound right? Am I missing something?

This message has been edited. Last edited by: electricpete,

Pete
The way you explain it sounds like they are off the mark.But let me also say I really am not in the same league as yourself and these people who performed this modeling.I just needed a good laugh and when I read their part it broke me up to think that a person like myself could read this many paragraphs and come up at the end feeling like I was smacked in the head and lost all my brain cells.It is good to know there is still so much in life to learn if one desires.I wll let you handle the motor talk and I will stick to what I know and soak up from the experts what I can.

I am by no means in the league with any experts, although maybe I do a good job at pretending that I am.

I realize this kind of post and discussion is pretty far into the theoretical area and not much of what we need to do our jobs. But I know there are a few on the board that enjoy the math stuff like I do and also quite a few who are interested in motor electromagnetic forces. This is one of the few articles I have been able to find available for free on the internet on the subject of motor e-m forces. (The Siemens article is another one... a lot more practical). If anyone has any other links I would be interested to see them.

This message has been edited. Last edited by: electricpete,

Pete
Don't get me wrong I did read with interest and I think that I grasp the concepts of your post.Please do post more when they are availible.Everybody needs to learn something new every day or I beleive that you are not truly living if you do not challenge yourself to do this on a regular basis.This is why I took to the predictive programs with a eye on the learnig curve and how long it would challenge me.So far It's batting a hundred.Motors for me is still a gray area as far as understanding the forces which apply to vibration monitoring.Your post was very interesting and I hope this tread does take off for a while to allow us all to learn a little more about all the effects on a motors magentics and electrical subtlties Thanx Lee

Can the authors reasonably argue that the rate of change in the dynamics of the system are 'slow' with respect to the perturbation?

Bill

Are you using the pulse as the perturbation?
Thanx Lee

Yes, I understood Bill to use “perturbation” to refer to the pulse.

The pulse duration is 5 msec and the system varies at 50hz (20 msec). I don’t think the system can be considered stable for the duration of the pulse.

But even if the pulse was very short << 1 msec (which would requires a much finer step size on finite-element simulation), the issue would still be that the snapshot of the system that we get by injecting the pulse will differ dependeing on what point in time you inject the pulse compared to the voltage cycle.

A general comment about the choice of the pulse (not directed toward anyone but just general information).

The fact that they used something similar to a short pulse makes this somewhat similar to a bump test (with force and displacement reversed).

Using FRF = Output (w) / Input (w) for an LTI system, we can choose any Input(w) function we can generate as long as it covers the range of frequencies of interest for the system response.

In this case the range of frequencies of interest would presumably include the plotted range of FRF 0 -100 hz. In particular of interest would be frequencies near running speed (25hz for this 4-pole 50hz motor) which would correspond to the dynamic eccentricity case and near 0hz which would correspond to the static eccentricity case.


If we set aside concerns about the method, the important results of the study are in general (for almost all frequencies), the parallel winding configuration generally gives lowest unbalanced magnetic forces and the series configuration gives the highest unbalanced magnetic force, and for series/parallel combination, we can reduce the unbalanced magnetic force by adding equalizing jumpers between points of like electric potential (make it act more like a parallel line).

This is in agreement with some other articles I have read recently. It can be explained roughly as follows:

* The point of smallest airgap has the highest magnetic permeance, lowest reluctance, and therefore presents the highest magnetizing impedance to the associated coils.

* If coils are connected completely in parallel, then constant voltage is applied to all coils, and the coils next to the smaller airgap will draw less magnetizing current (due to higher magnetizing impedance, thus tending to limit the increase in flux at the small gap that would otherwise occur. This limits the unbalanced magnetic pull which is caused by the flux unbalance on opposite sides of the machine.

* If coils are connected completely in series, then constant phase-to-phase voltage is applied accross a whole winding. Every coil in the winding has a partner coil in series which is 180 degrees mechanically opposite. So changing gap has no effect on total magnetizing impedance of the winding. The flux-limiting effect described above cannot occur.

* If you have series/parallel winding such as two-wye, then connecting points of like-potential will allow a certain amount of current redistribution and the winding will act more like the parallel case with some reduction in unbalanced magnetic pull.

This also plays some role in discussing the large slow-speed vertical motor I discussed in another post with unusual powerdown behavior even after repaired (rapid drop in vib upon powerdown indicating magnetic effects still present). In addition to other factors (flexible rotor, small airgap relative to machine size, skewed rotor bars), that is a pure series winding motor (single wye).

This message has been edited. Last edited by: electricpete,

My name is Timo Holopainen and I am one of the authors in the paper discussed above. One of my friends informed me about this page and I was very happy to read your argumentation related to the ”impulse method” and the behavior of parallel/serial paths of an electric machine.

The background of the impulse method is the numerical analyses, where the rotor was forced to a cylindrical whirling motion with various whirling frequencies (Arkkio et al. 2000). The total force exerted on the rotor and rotating at the same angular frequency as the whirling motion can be divided into the radial and tangential components. The results can be presented as frequency response function between the force and the whirling frequency. As Electricpete writes the static eccentricity corresponds to the whirling frequency 0 Hz and the dynamic eccentricity the rotation frequency. These results were validated with a experimental set up using a standard electric machine (15kW) on the magnetic bearings (Arkkio et al. 2000).

The calculation time using the above-mentioned forced whirling method was very long. The linearity between the eccentricity force and whirling radius was observed. In addition, the frequency response function, without parallel paths in the stator windings, was relatively simple. It occurred that the same information (FRF) could be generated by the above-mentioned ”impulse method”. It was some kind of a surprise, because the system is strongly non-linear (saturation of the magnetic material) and changing in time (rotating rotor, rotating magnetic fields, whirling motion).

So far, the impulse method seems to work for the synchronous force component induced by the whirling motion. The system between the total force and the whirling motion seems to be linear, homogeneous, time-invariant, and axially symmetric. The LTI requirements are close to these requirements. I admit openly that a solid theoretical background is still open. However, the numerical and experimental results support the approach. Some problems were observed with impulse method with a two-pole motor (Holopainen et al. 2005).

Here are some comments.

Electricpete 8.6.06: “They say the force is very nearly constant in time... I assume they are ignoring pole pass modulation and looking at some kind of average radial outward force.” => When the rotor is in a whirling motion the component of the total force vector rotating with the same frequency as the whirling motion is nearly constant. I suppose that the effect of pole pass modulation on the total force is minor, because the total force is integrated over the cylindrical air-gap.

Electripete 8.6.06: “…we need not just linearity but a Linear Time Invariant (LTI) system.” => There are numerical and experimental evidence that the system between the total force and the rotor motion fulfills the LTI requirements. However, the solid theoretical proof is currently missing. Locally, the system is clearly non-linear, but probably the symmetric properties of the system cancel out these effects in global sense.

Electripete 8.6.06: ”Clearly if you inject the rotor-position-pulse at a time/place where the mmf is near a peak you will get a different answer … The model doesn’t use multiple injections only one.” => This kind of problems appeared when the impulse method was applied for a two-pole motor (Holopainen et al. 2005, J. of Sound and Vibration). The remedy was to use several inputs (4) and average the results.

Electripete 8.6.06: ”The Siemens article is another one … a lot more practical” =>Pete, could you give the reference data of this article.

William_C._Foiles 9.6.06: ”Can the authors reasonably argue that the rate of change in the dynamics of the system are ’slow’ with respect to the perturbation?” => The main application area of ”impulse method” is to study the electromechanical interaction in rotordynamics and the unbalanced magnetic pull (UMP) induced by static/dynamic eccentricity. The relevant whirling frequencies are on the range -100Hz - +100Hz. I think that the rate of change in the main system dynamics are slow enough with respect to the perturbation. The main system dynamics includes the fundamental flux fields, the eccentricity flux fields, the stator winding currents, and the rotor winding currents.

Electripete 13.6.06: The pulse duration is 5 msec and the system varies at 50Hz (20 msec). I don’t think the system can be considered stable for the duration of the pulse.” => Not locally, but probably globally. This is really interesting phenomena and needs more work to settle it.

Additional information:

Additional public information can be read in my thesis: http://lib.tkk.fi/Diss/2004/isbn9513864057/

If you like to know the latest research activities in Europe, the literature search on the achievements of the following persons give a good picture: Antero Arkkio at Helsinki University of Technology (Finland), Seamus Garvey at Nottingham University (GB), Jan-Olof Aidanpää at Luleå University (Sweden), Lucia Frosini at University of Pavia and Paolo Pennacchi (Italy).

Thanks a lot for this discussion. It is really nice to get some feedback after many years of isolated research work.

Regards
Timo

Timo

Welcome to the forum and thanks for your detailed comments.

The Siemens article I mentioned is here:
http://www.sea.siemens.com/motorsbu/product/White%20Pap...ation%20Problems.pdf

I look forward to reading your comments and your linked articles (thesis, article1, article2) in the next few days. It looks like some great information.

I hope you will stick around the forum for awhile. We have a great group of people with diverse experiences and your contributions are very much appreciated.