Simulating the Rolling of a Rotor Over a Stator with Dry Friction Whip and Whirl

The article is dedicated to the calculation of the acting forces and amplitude–frequency characteristics of the “rotor–stator” system in a state of frictional contact. Unlike known approaches, the normal pressure force between the rotor and stator is defined not only by the elasticity and damping of their materials at the contact point and/or the stator supports but also by the bending complex stiffness of the entire rotor, which can be conceptually treated as having an additional bearing with a clearance. This quasi-static reaction of the rotor to contact with the stator, initially characterized by Coulomb friction during slipping, is extended to dynamic contact with rolling friction of the rotor over the stator, which depends on the normal pressure force between them. In the proposed mathematical model and the practical example considered, the rolling equations are formulated and solved in matrix form concerning the precession speed and rotor displacements, based on system (interconnected with the stator) elastic-inertial characteristics, as well as coefficients of slipping and rolling friction, and internal and external losses. The calculations established finite ranges of possible angular velocities for uninterrupted rolling of the rotor over the stator and demonstrated the possibility of eliminating it by adjusting just two parameters of the system: the damping coefficient of the rotor and the modulus of elasticity of the stator’s contact surface.