## twice line frequency radial forces in induction motor

## 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.

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

Any thoughts?

**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

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

http://www.reliability-magazine.com/ubb2000/ubb/Forum2/HTML/001692.html

for another Forum where the author of this posting is busy,

http://www.framatech.com/ultracheck/pdf/empath-techpaper.pdf

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

http://www.sea.siemens.com/motorsbu/product/White%20Papers/VIBRATION%20PROBLEMS.pdf

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

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

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

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

http://scholar.lib.vt.edu/theses/available/etd-2421171249711311/

for more recent literature

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

etd.pdf

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

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

http://ee.tamu.edu/~empelab/publications.html

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

http://www.sea.siemens.com/motorsbu/product/White%20Papers/VIBRATION%20PROBLEMS.pdf

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