Sommerfeld effect at forward and backward critical speeds in a rigid rotor shaft system with anisotropic supports

Abstract A rotor dynamic system requires high power/torque to accelerate through its resonance conditions or critical speeds to operate at a super-critical speed. Most practical drive sources are non-ideal in nature, i.e. they can only provide a limited amount of power to the rotor system. Thus, if there is insufficient power to overcome a resonance then the rotor speed may get arrested at that resonance or take a long time to escape from the resonance; and thereby damage the system. For the present analysis, a Direct Current (DC) motor is considered as the non-ideal prime mover for a rigid rotor shaft with unbalanced disk which is supported by flexible anisotropic supports/bearings. Due to the anisotropy in the supports, both forward and backward whirl motions of the rotor get excited. This causes a multi-Sommerfeld effect where two non-linear jump phenomena are manifested at the first forward and backward critical speeds during rotor coast up and coast down. When the two critical speeds are close to each other, a complex speed capture and jump phenomena occurs. Accordingly, the transitions through both resonance conditions are examined. At first, the analytical solutions are obtained under steady state assumption and then transient simulations are performed with the help of a bond graph (BG) model.