Simulation of Dry Friction Whirl and Whip with Rolling Effect between Rotor and Stator

The article is devoted to the calculation of the acting forces and amplitude-frequency characteristics for the rotor-stator system in a state of frictional contact. Unlike the known approaches, the normal pressure force between the rotor and stator is determined not only by the elasticity and damping of their materials at the point of contact and/or stator supports, but also by the bending complex stiffness of the entire rotor, which has conditionally received an additional bearing with a clearance. Such a quasi-static reaction of the rotor to contact with the stator, initially with Coulomb friction between them, is expanded to a dynamic contact with rolling friction of the rotor on the stator, dependent on the normal pressure force between them. In the proposed mathematical model and in the considered practical example, the motion equations are composed and solved in matrix form relative to the precession velocity and rotor displacements, based on the system (interrelated with the stator) elastic-inertial characteristics, as well as the coefficients of slipping and rolling friction, internal and external losses. The calculations established the final ranges of possible angular velocities for the continuous rolling of the rotor around the stator and showed the possibility of eliminating it by correcting only two system parameters, they are the rotor damping coefficient and the elastic modulus of the stator contact surface.

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