Studying the load jam modes within the framework of a flat model of the rotor with an auto­balancer

摘要

This paper reports the analytically investigated load jam modes (balls, rollers, pendulums) within a flat model of the balanced rotor on isotropic elastic-viscous supports carrying the auto-balancer with many identical loads.A physical-mathematical model of the rotor-auto-balancer system is described. The differential equations have been recorded for the system motion with respect to the coordinate system that rotates at constant speed. We have found all the steady modes of motion under which loads get stuck at a constant speed of rotation. In the coordinate system that rotates synchronously with loads, these movements are stationary.Our theoretical study has demonstrated that the load jam modes in the rotor-auto-balancer system are the single-parametric families of steady movements.Each jam mode is characterized by a certain load configuration and the appropriate frequency of jams.In the coordinate system that synchronously rotates with loads:– the rotor displacement is constant;– the parameter is the angle defining the direction of the rotor displacement vector;– loads take certain fixed positions relative to the rotor displacement vector; these positions depend on the rotor rotation speed.The auto-balancer with nb identical loads of different configurations has nb+1 loads. The total number of different types of load jam modes:– 2(nb+1), if nb is odd;– 2nb+1, if nb is even.The total number of different jam frequencies:– 3(nb+1)/2, if nb is odd;– 3nb/2+1, if nb is even.The total number of different characteristic speeds is nb+2. The characteristic speeds are the points of movement bifurcations because their transitions give rise to the emergence or disappearance of single-parametric families of movements that correspond to a certain jam mode. At these points, jam modes can acquire or lose stability.