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# twice line frequency radial forces in induction motor4

## twice line frequency radial forces in induction motor

(OP)
1 - Can anyone suggest a formula or reference for computing the total radial forces induction motor rotor in the presence of static eccentricity… as a function of air gap geometry, flux density and number of poles?  I believe there is a 2xLF and a constant (zero-hz) component.

Or

2 - can you explain the following statement from EASA Principles of Large AC Motors: “The magnitude of the twice line frequency forces in inversly proportional to the 4th power of the number of electrical poles. Thus, a four-pole motor would have only one-sixteenth the exciting force of a 2-pole motor”.  [it is not clear whether this assumes eccentricity or is merely discussing the distoring force applied at equal/opposite points on the stator which creates no net rotor force unless there is eccentricity].

I am somewhat at a loss to understand why the 2-pole motor forces are often presented as being larger than higher-pole motors. I understand the difference in stiffness of stator to the 2-pole mode shape, but that should affect the vibration response, not the exciting force.  Or is it perhaps the distortion of the airgap that increases the local flux that in turn increases the original magnetic distorting force?…. still in that case it is not obvious where the F~(1/p)^4 would come from.

Any thoughts?

### RE: twice line frequency radial forces in induction motor

I have no idea, but here is a person who might:

Professor Thomas Lipo, Univ. of Wisconsin-Madison,
email: lipo@engr.wisc.edu

Why not send him an email and see what he has to say.  He has written several books on motor design and motor control.  I have consulted him with past questions and he has been fairly responsive.

### RE: twice line frequency radial forces in induction motor

I'm sorry to double post; but at the end of the document I linked, there are several references cited at the end.  Most of it is probably interesting reading.

### RE: twice line frequency radial forces in induction motor

I found a half dozen formulas for Unbalanced Magnetic Pull (UMP) force in induction motors but they don't go beyond 1989 and most are 1960's and 1970's. Also , they are substantially different and I don't know which are the most complete in considering number of pole, circuits, saturation effects, etc. Heller, B. & Hamata,V.(1977) "Harmonic Field Effects in Induction Machines" Elsevier Scientific Publishing Co. seem to know all the ingredients but their book doesn't address motor design, per se, so they only offer no-load equations for 2 pole and 4 pole machines ;
f_eta=pi*R*l_e*(B_1*u/2*mu_0*[1-(eta*v/2*u)^2]*(eta*v/2*u)*omega_sub1. u&v are conductance parameters plotted against eta (eccentricity?) in their Fig.37. Omega is line frequency, B is flux density. mu is permeability, l_e is length of iron and R is gap or rotor radius. That equation is for 2 pole and a similar equation with B_p meaning peak flux density applies to >1 pole pair.
A more design oriented equation comes I believe from Ralph Rhudy of GE Motor Dept.
F_r=(171/n)*z*(B_g/100)^2* Gap section* K (in pounds)where
K=1-(g/g_0) and  g=g_0-(e_1+e_2)
e_1=Manufacturing eccentricity
e_2=Displacement eccentricity
g_0= concentric gap width
g= eccentic gap width
B_g=Average flux density
Gap section must be something like p1*D*l but is not told.
n=number of circuits
z=number of poles
This equation was used on several 1960's era water-cooled motor designs. Don't ask me how any of these equations become dimensionally sane unless permeability involves force. Other equations come from Covo (1954 ASME paper), Robinson (1943 ASME  paper), Cochran (1989 book) and a number of German engineers including Freise and Jordan (1962 ETZ-A paper) and Schuisky (1971 Elektrotech Maschinenbau paper). M.Bradford did some UMP testing in England  on a 6-pole motor partly reported in a 1966 Electrical Review paper. This is a rather complicated subject for this forum. If you want copies of some of the better stuff send a business address by FAX to J.Vanstone (518) 243-5333

### RE: twice line frequency radial forces in induction motor

(OP)
Thanks very much Mr Vanstone.  That looks like exactly what I have been looking for. I will contact you to discuss it futher.

etd.pdf

### RE: twice line frequency radial forces in induction motor

(OP)
Thanks jbartos. That looks like some good info.

### RE: twice line frequency radial forces in induction motor

Suggestion: Some of the above postings could also appear under mechanical engineering since there is very little or no electrical background needed. However, they are enlightening to electrical machinery enthusiasts.

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