A three degrees of freedom model of the support structure of a non- ideal motor

Resumo

n rotating-unbalance-machine/structure systems, stable regime is when angular velocity is constant, all
energy supplied by the motor consumed by internal friction and energy dissipated by damping of structure. Energy
beyond this accelerates the system. Each energy level provided by the motor corresponds to stable constant angular
speed. H is the torque consumed by the motor internal friction. Summed to the R torque to overcome damping
forces of the support structure gives the S torque. L is the active motor torque provided. In an ideal system, the

motor provides power to go over the resonance peaks of the structure and achieve the rated motor speed. In a non-
ideal system, with limited power supply, an available motor torque level L can intercept the torque curve S

consumed by friction and the structure at a constant rotation point before or after the resonance peak. If before, is
a stable point of capture at resonance. Angular velocity no longer increases, stagnating before the peak, not
reaching higher rotation speed. Jumps happens when more energy is supplied to overcome this stagnation. There
comes a point the torque curve goes over the peak and intercepts the consumed torque curve further ahead in steady

higher angular velocity, no intermediate stable steady states. There is really no difference between ideal and non-
ideal systems. Only the available power level. A model considering mutual interaction support-structure/machine,

should always be used. In that sense, all systems are non-ideal. In practice, if the motor has enough power this
effect is negligible and we only consider interaction between the motor and the structure but not the reverse
interaction, simplifying the model. Literature is available on 1-DOF support structure models, with 2 coupled
autonomous equations of motion, 1 for the structure, 1 for the motor. In this paper we present a better representation
of a machine foundation moving in horizontal and vertical directions, with mass, stiffness and damping for each
one. Thus, we study 2 possible occurrences of the Sommerfeld Effect in the same model