Balancing of rotor in visco-elastic fixed casing with fixed point using auto-balancer

Abstract

The authors have studied the process of balancing statically unbalanced rotor placed in visco-elastic fixed casing with fixed point by autobalancer. The proposed research methodology may be standard in solving similar problems and includes the following stages: - derivation of simplified differential equations of motion of rotor's system linearized by the entered small parameter and by the system deviations from steady motion; - obtaining of closed system of differential equations for generalized coordinates defining rotor motion and its unbalance; - transformation of the equations to the dimensionless form, their complex folding and reduction to stationary form; - obtaining of characteristic equation and studying its roots. The results of the research are: it's possible to balance rotor only if a conditional composite rotor (formed by rotor and casing) is long; in this case rotor has only one critical speed and autobalancing occurs on its exceeding; at auto-balancing at first the fast motions of corrective weights stop relative to the rotor and then they move slowly relative to the rotor to auto-balancing positions.

Keywords

• rotor
• unbalance
• auto-balancer
• main motion
• stability of motion