Oscillation Frequency During Rolling with Slip of the Rotor with Many Degrees of Freedom Along the Stator

Abstract

A mathematical model of a flexible rotor with n degrees of freedom rolling around a flexible stator with slippage between them is proposed, as well as an approach to the exclusion of contact forces for dynamic analysis of the system. The angular velocity and amplitude of the reverse rotor precession are determined by matrix methods. It is shown that the break-in speed is not always equal to the product of the rotation speed by the ratio of the radius of the rotor to the radial clearance at the point of contact. In the case of slippage, it depends on one or another natural frequency of the rotor, which is supported by the stator, as well as on the coefficients of structural and contact friction. It was also shown that in fact, friction only sets the break-in speed, and the amplitude of the reverse precession (deflection of the rotor outside the contact point) is determined by the size of the gap at the contact point.