The study has revealed an influence of the parameters of corrective weights (balls and cylindrical rollers) in auto-balancers on the balancing capacity and the duration of the transition processes of auto-balancing in fast-rotating rotors. A compact analytical function has been obtained to determine the balancing capacity of an auto-balancer (for any quantity of corrective weights – balls or rollers), with a subsequent analysis thereof. It is shown that the process of approach of the auto-balancing can be accelerated if the auto-balancer contains at least three corrective weights. It has been proved that at a fixed radius of the corrective weights the highest balancing capacity of an auto-balancer is achieved when the corrective weights occupy nearly half of the racetrack. The study has revealed that it is technically incorrect to formulate a problem of finding a radius of the corrective weights that would maximize the balancing capacity of the auto-balancer. The statement implies that if it is a ball auto-balancer, the racetrack is a sphere, but if it is a roller-type balancer, the racetrack is a cylinder. This leads to a practically useless result, suggesting that the highest balancing capacity is achieved by auto-balancers with one corrective weight. Besides, with n≥5 for balls and n≥8 for rollers, there happens a false optimization, which consists in several corrective weights being “excess”. Their removal increases the balancing capacity of the auto-balancer. It is correct (from the engineering point of view) that the mathematical task is to optimize the balancing capacity of an auto-balancer. Herewith, it is taken into account that the racetrack of the auto-balancer is torus-shaped, which restricts the radius of the corrective weights from the top. It is shown that the balancing capacity of an automatic balancer can be maximized if in a fixed volume the corrective weights have the largest possible radius and occupy almost a half of the racetrack. The research on the duration of the transition processes for the smallest value has produced the following conclusions: – to accelerate the achieving auto-balancing, the corrective weights should occupy nearly half of the racetrack; – the shortest time of the auto-balancing is achieved with three balls or five cylindrical rollers.

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An increase of the balancing capacity of ball or roller-type auto-balancers with reduction of time of achieving auto-balancing

The automatic balancing and undesirable nonsynchronous behavior of coupled oscillating configured flexible foundation and planar eccentric rotor equipped with a passive autobalancer (AB) system has been thoroughly investigated here. Specifically, it is described that the unified AB/rotor unit is attached to a foundation via a symmetric support and the foundation is also mounted on the spring-damper isolator which allows oscillating only vertically. Therefore, the AB/rotor unit dynamically interacts with the flexible foundation, which is quite analogous to well-known vertically coupled two-spring and two-mass oscillator. Although the single unit AB/rotor system is widely explored in the related AB studies, such coupled arrangement with AB discussed here has not been previously investigated and thus needs to be explored for further application of AB into various vibration isolation problems of other complicated machines/settings. Therefore, solutions for the synchronous stable balanced and the nonsynchronous unstable limit cycle response of AB/rotor/foundation system are obtained via a fixed equilibrium condition and a harmonic like balancing approach. Furthermore, the stability of each response is assessed via a perturbation and Floquet analysis and, for the system parameters and operating speeds, the undesirable coexistence of the wanted stable balanced synchronous response and undesirable nonsynchronous limit cycle has been thoroughly studied. Due to coupled oscillating feature, it is newly found that the multiple limit cycles are encountered in the range of supercritical speeds and more complicated coexistence is attracted into the system, as well as the damping parameters of coupled components (i.e., flexible foundation) influences of the undesirable limit cycle of AB on the particular supercritical speeds. The findings in this paper yield important insights for researchers wishing to utilize automatic balancing devices in more practical rotor systems coupled with additional vibrating mechanical subsystem such as a washing machine or a reciprocating air conditioning compressor with a flexible foundation.

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Supercritical Coexistence Behavior of Coupled Oscillating Planar Eccentric Rotor/Autobalancer System

A general model for passive balancing of supercritical shafts with experimental validation of friction and collision effects

Parametric studies on modified configurations of ball-type passive balancers for improved transient and steadystate responses

Recently, a new type of automatic ball balancer (ABB), called the ball-spring autobalancer (AB), has been proposed, which substantially eliminates the drawbacks of the traditional ABBs. In previous...

Ahmad M. Haidar

Papers

A general model for passive balancing of supercritical shafts with experimental validation of friction and collision effects

Parametric studies on modified configurations of ball-type passive balancers for improved transient and steadystate responses

Modified ball-type automatic balancer for rotating shafts: Analysis and experiment

Comprehensive Model and Experimental Validation of Passive Vibration Suppression for Supercritical Rotary Machines

Effect of Number of Tracks and Balancing Masses on Passive Balancing Performance