Analytical and Experimental Analysis of a Self-Compensating Dynamic Balancer in a Rotating Mechanism

Abstract

A theoretical and experimental approach was used to investigate the motion and effectiveness of a Self-Compensating Dynamic Balancer (SCDB). This is a device intended to minimize the effects of rotor imbalance and vibratory forces on a rotating system during normal operation. The basic concept of an automatic dynamic balancer has been described in many U.S. patents. The SCDB is composed of a circular disk with a groove containing massive balls and a low viscosity damping fluid. The objective of this research is to determine the motion of the balls and how this ball motion is related to the vibration of the rotating system using both theoretical and experimental methods. The equations of motion the balls were derived by the Lagrangian method. Static and dynamic solutions were derived from the analytic model. To consider dynamic stability of the motion, perturbation equations were investigated by two different methods: Floquet theory and direct computer simulation. On the basis of the results of the stability investigation, ball positions which result in a balance system are stable above the critical speed and unstable at critical speed and below critical speed. To determine the actual critical speed of the rotating system used in the experimental work, a modal analysis was conducted. Experimental results confirm the predicted ball positions. Based on the theoretical and experimental results, when the system operates below and near the first critical speed, the balls do not balance the system. However, when the system operates above the first critical speed the balls can balance the system.

Analysis of the transient response of an automatic dynamic balancer for eccentric rotors

“…Theoretical studies, where the ADB is modelled using equations similar to (1) and (2), can be found in Refs. [1][2][3]14,15,17]. Similarly, experimental results can be found in Refs.…”

“…Similarly, experimental results can be found in Refs. [14,18]. For this study we focus on the case with only two balancing masses, that is, n = 2.…”

Two-plane automatic balancing: A symmetry breaking analysis

“…However, if the mass distribution of the rotor changes then the balancing procedure may need to be repeated. This limitation motivates the study of automatic balancers that use freely moving masses to dynamically compensate for the imbalance [1].…”

Automatic two-plane balancing for rigid rotors

“…The first study of an ABB was carried out by Thearle in 1932 [1], and the existence of a stable steady state at rotation speeds above the first critical frequency was demonstrated. More recently, the equations of motion for a planar Jeffcott rotor with an ABB have been derived using Lagrange's method [2,3,4]. In particular Green et al [4] use rotating coordinates to forge an autonomous system of governing equations.…”