Analytical study of auto-balancing within the framework of the flat model of a rotor and an auto-balancer with a single cargo

This paper reports the analytically established conditions for onset of auto-balancing case a flat rotor model on isotropic elastic-viscous supports and an auto-balancer with single load. The is statically unbalanced, rotation axis vertical. has cargo – pendulum, ball, or roller. balancing capacity equal to imbalance. physical-mathematical system described. differential equations motion are recorded in dimensionless form relative coordinate that rotates synchronously rotor. so-called main movement been found; it, balances it. linearized neighborhood movement. A characteristic equation constructed. It helped investigate stability (an mode) cases absence presence resistance forces system. was system: three rotational speeds, first always coincides resonance frequency; occurs when at speeds between second ones, above third speed; value significantly influenced by ratio weight mass system; monotonously increase Resistance affect both values their existence. Small do not change quality behavior With high forces, number decreases one. results applicable many cargoes it imbalance equals