Simulation of two-plane automatic balancing of a rigid rotor

We present an analysis of a two-plane automatic balancing device for rigid rotors. Ball bearings, which are free to travel around a race, are used to eliminate imbalance due to shaft eccentricity or misalignment. The rotating frame is used to derive autonomous equations of motion and the symmetry breaking bifurcations of this system are investigated. Stability diagrams in various parameter planes show the coexistence of a stable balanced state with other less desirable dynamics.

/pdf/automatic-two-plane-balancing-for-rigid-rotors-287y8tvocf.pdf

Automatic two-plane balancing for rigid rotors

This paper concerns an analytical and experimental investigation into the dynamics of an automatic dynamic balancer (ADB) designed to quench vibration in eccentric rotors. This fundamentally nonlinear device incorporates several balancing masses that are free to rotate in a circumferentially mounted ball race. An earlier study into the steady state and transient response of the device with two balls is extended to the case of an arbitrary number of balls. Using bifurcation analysis allied to numerical simulation of a fully nonlinear model, the question is addressed of whether increasing the number of balls is advantageous. It is found that it is never possible to perfectly balance the device at rotation speeds comparable with or below the first natural, bending frequency of the rotor. When considering practical implementation of the device, a modification is suggested where individual balls are contained in separate arcs of the ball race, with rigid partitions separating each arc. Simulation results for a partitioned ADB are compared with those from an experimental rig. Close qualitative and quantitative match is found between the theory and the experiment, confirming that for sub-resonant rotation speeds, the ADB at best makes no difference to the imbalance, and can make things substantially worse. Further related configurations worthy of experimental and numerical investigation are proposed.

/pdf/investigation-of-a-multi-ball-automatic-dynamic-balancing-1kqi45bche.pdf

Investigation of a multi-ball, automatic dynamic balancing mechanism for eccentric rotors.

https://research-information.bris.ac.uk/files/3018174/abbexp_paper.pdf

Experimental investigation of a single-plane automatic balancing mechanism for a rigid rotor

The problem is motivated by observations of a rotor-pendula system, which derived from a new shale shaker To grasp the dynamic characteristics of the shale shaker, the key research is exploring the synchronous mechanism for the system, since synchronous state between rotors is closely related to the dynamic characteristics of the system In this paper, the dynamic equation of the rotor-pendula system is firstly derived by applying Lagrange’s equations Through Laplace’s transformation method, the approximate responses of the system in synchronous state are obtained, which is determined coupling coefficients and synchronous state of the system Then, the synchronous balance equation and the stability criterion of the system are obtained with Poincare method on which stable phase difference and synchronous behavior can be ascertained To verify the correctness of the theoretical analysis, numerical simulations are implemented by Runge–Kutta method, and it is shown that the synchronous behavior is determine

Synchronization characteristics of a rotor-pendula system in multiple coupling resonant systems

Automatic balancing devices comprising several balls or other moving elements in circular tracks can efficiently compensate rigid rotor unbalance in certain ranges of rotational speed. However, near critical speeds the vibration level can be comparatively high as a result of non-synchronous ball motions. The paper considers such non-synchronous motions of balancing elements. The characteristics of ball motions and the main factors influencing the investigated phenomenon are analyzed. The paper includes an analytical study of nonsynchronous motions, results of computer simulations and comparison with experimental data. Recommendations are given for the optimal choice of auto-balancing device parameters and other measures for decreasing vibrations near critical speeds.

Non-Synchronous Motions Near Critical Speeds in a Single-Plane Auto-Balancing Device

This paper presents an analytical study of single-plane automatic balancing of statically and dynamically unbalanced rigid rotors, considering also the effect of partial unbalance compensation and vibration reduction. We consider a rotor equipped with a self- balancing device consisting of a circular track with moving balls to compensate for rotor unbalance. The investigations include an analysis of the equations of motion and determination of conditions for existence and stability of synchronous motions. Different solutions for the existence conditions correspond to different types of synchronous motions, including compensatory motions, with the elements’ positions providing complete or partial compensation of unbalanced forces as well as reduction of vibrations. A stability analysis serves to determine the actual angular position of elements at any rotational speed and to find the speed range with stable unbalance compensation. Numerical simulations confirm the analytical results except for those in the immediate vicinity of critical speeds.

https://www.ovgu.de/ifme/zeitschrift_tm/2004_Heft1/sperling.pdf

Single-Plane Auto-Balancing of Rigid Rotors

Synchronous elimination as one of the possible methods of cancelling any harmful vibration resulting from the unbalance of rotary machines is considered. This method, introduced by Fesca and Thearle, involves the placement of unbalanced elements (e.g. ring, pendulum, ball balancers) on the rotor axis, which can occupy any angular position in relation to the rotor. Under defined conditions in the postcritical frequency range, there is a spontaneous placement of the corection elements such that they balance the rotor unbalance. Hedaya and Sharp generalized this method by combining two force balancers to compensate the unbalanced moment as well as the unbalanced force of a rigid rotor.

/pdf/self-synchronization-and-automatic-balancingin-rotor-3w3eug629j.pdf

Self-synchronization and Automatic Balancingin Rotor Dynamics

This article presents an analysis of several aspects of one- and two-plane automatic balancing devices of rigid rotors. The effect of partial compensation of unbalance and the decreasing of vibrations in the region beyond the first critical speed is studied analytically and confirmed by the results of computer simulations. The possibility of partial unbalance compensation is very important considering application of autobalancing devices to rotors with a large polar moment of inertia.

/pdf/partial-compensation-of-unbalance-by-oneand-two-plane-1vp60ed137.pdf

L. Sperling

Papers

Simulation of two-plane automatic balancing of a rigid rotor

Non-Synchronous Motions Near Critical Speeds in a Single-Plane Auto-Balancing Device

Single-Plane Auto-Balancing of Rigid Rotors

Self-synchronization and Automatic Balancingin Rotor Dynamics

Partial Compensation of Unbalance by Oneand Two-Plane Automatic Balancing Devices