From several papers on UMP, it appears that parallel circuits in either stator circuits or rotor circuits (squirrel cages)reduce UMP loading and have additive effects. Papers by Tenhunen of Helsinki UTech at
and the same except /article4 discuss UMP with eccentric rotors and provide further insights into current equalizing effects. These were found in an aol/google search of "Unbalanced magnetic pull".
I've seen discussions indicating that startup suppression of current equalizing effects is related to reluctance effects.
Pertinent to UMP induced rotor-stator impacts at startup,Bradford's ERA report has an appendix II on "Calculation of Transient Vibration of the Rotor" which is not mentioned in his IEE paper. He determines UMP force (negative) spring constant, Kf, from measurements of transient UMP at known eccentricities and shaft elastic restoring stiffnesses, Ke, (with and without stator
deflection softening effects) and determines a stability constant Ks=Ke/Kf. The condition to prevent rotor touching the stator is (Ks+1/Ks-1)*sigma < g where sigma is initial rotor displacement from the center of the stator and g is the mean length of the airgap. For his 10 kW wound rotor test motor with 15.7 in. stator OD, 9.0 in. rotor OD, 4.5 in. shaft OD, 6.0 in. core length and 0.030 in. air gap length, he finds the maximum permissible startup rotor eccentricity to be 62% with stator deflection softening (about 28% with an infinitely stiff stator) and the vibration frequencies to be 123 Hz and 138 Hz with and without stator deflection softening. Since the measured transient UMP for the cage rotor motor was (at 10% eccentricity) 269 lbs. vs 284 lbs. for the wound rotor
motor, the cage rotor machine would not vary much in permissible eccentricity. Frequency differences may depend on rotor core stiffenening effects on shaft deflection which Bradford does not discuss. All of Bradford's numbers are in British Imperial units, not US units.