Whirl Suppression in Hand-Held Power Tool Rotors Using Guided Rolling Balancers

Rajalingham, C.; Rakheja, Subhash

doi:10.1006/jsvi.1998.1780

Cited by 39 publications

(26 citation statements)

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“…This should first be carried out for an isotropic single-plane ABB, before then proceeding onto more complicated mechanical systems. However, even for the simplest case, it is likely that the inclusion of important damping effects could make the problem intractable [2]. Therefore, we prefer to proceed with a numerical bifurcation analysis in which further asymmetries of a two-plane ABB are considered.…”

Section: Symmetry Breaking Between the Racesmentioning

confidence: 99%

“…We consider the model given by (2)(3)(4), which is written with respect to inertial space frame coordinates, and includes the effect of support anisotropy. We again assume a constant rotation speedθ 0 = Ω, and so equation (3) will be neglected.…”

Section: Support Asymmetrymentioning

confidence: 99%

“…Because the imbalance does not need to be known beforehand, automatic balancers are ideally suited to applications where the imbalance changes with the operating conditions. For example, ABBs are currently used in machine tools, washing machines and optical disk drives [2,3,4].…”

Section: Introductionmentioning

confidence: 99%

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Two-plane automatic balancing: A symmetry breaking analysis

Rodrigues

Champneys

Friswell

et al. 2011

International Journal of Non-Linear Mechanics

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We present an analysis of a two-plane automatic balancing device for rotating machinery. The mechanism consists of a pair of races that contain balancing balls which move to eliminate imbalance due to rotor eccentricity or principal axis misalignment. A model is developed that includes the effect of support anisotropy and rotor acceleration. The symmetry of the imbalance is considered, and techniques from equivariant bifurcation theory are used to derive a necessary condition for the stability of balanced operation. The unfolding of the solution structure is explored and we investigate mechanical systems in which either the supports or the automatic ball balancer is asymmetric. Here it is shown that, provided the imbalance is small, the balanced state is robust to the considered asymmetries.

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Section: Symmetry Breaking Between the Racesmentioning

confidence: 99%

Section: Support Asymmetrymentioning

confidence: 99%

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Two-plane automatic balancing: A symmetry breaking analysis

Rodrigues

Champneys

Friswell

et al. 2011

International Journal of Non-Linear Mechanics

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“…This device consists of a finite number of balls which are free to move in a race at a fixed distance from the centre of rotation of the rotor, eventually balancing any eccentricity in the rotor. Possible applications of an ADB include the balancing of optical disc drives [10,11], washing machines [1], and machine tools [16]. However, principally due to unexpected instabilities, this device has never been successfully used in a commercial application.…”

Section: Introductionmentioning

confidence: 99%

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

Green

Champneys

Friswell

2006

International Journal of Mechanical Sciences

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This paper investigates the transient response of a dynamical system modelling an automatic dynamic balancing mechanism for eccentric rotors. By using recently developed computational techniques, pseudospectra of the linearisation of the system about an equilibrium are computed. This approach allows one to quantify which eigenvalues are most sensitive to perturbation. It is shown how the sensitivity of the eigenvalues directly influences the transient response. Furthermore, the effect which a variation of the damping coefficients has on the pseudospectra structure is considered. A transient growth due to the non-normality of the linearised system is shown to lead to an exponential decay or to a collapse back to the stable equilibrium; these effects are identified with the changes in the sensitivities of the eigenvalues under variation of the damping parameters. This provides a new insight into the full nonlinear system, in which qualitatively similar transient responses are shown to occur.

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“…In self balancing systems, the basic research was initiated by Thearle [2], [3], Alexander [4] and Cade [5]. Analysis for various self balancing systems can be encountered in references [6][7][8][9]. Equations obtained are for nonautonomous systems, these equations have limitations on complete stability analysis.…”

Section: Introductionmentioning

confidence: 99%

Self Balancing System for Rotating Mechanisms

Meraz

Yánez

Jimenez

et al. 2005

Rev. Fac. Ing. - Univ. Tarapacá

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A self balancing system analysis is presented which utilizes freely moving balancing bodies (balls) rotating in unison with a rotor to be balanced. Using Lagrange´s Equation, we derive the non-linear equations of motion for an autonomous system with respect to the polar coordinate system. From the equations of motion for the autonomous system, the equilibrium positions and the linear variational equations are obtained by the perturbation method. Because of resistance to motion, eccentricity of race over which the balancing bodies are moving and the influence of external vibrations, it is impossible to attain a complete balance. Based on the variational equations, the dynamic stability of the system in the neighborhood of the equilibrium positions is investigated. The results of the stability analysis provide the design requirements for the self balancing system. Keywords: Self balancing system, variational, Rayleigh disipation function. RESUMENSe presenta el análisis de un sistema de autobalance el cual utiliza bolas libres de movimiento rotando con el rotor que será balanceado. Se usa la ecuación de Lagrange para derivar un sistema de ecuaciones no lineales para un sistema autónomo con respecto a un sistema de coordenadas polares. De las ecuaciones de movimiento, se obtienen ecuaciones linealizadas variacionalmente y posiciones de equilibrio por el método de perturbación. A causa de la resistencia al movimiento, la excentricidad y el movimiento de los cuerpos libres que son provocados por la influencia de vibraciones externas, hace imposible obtener un balanceo completo. Basado en el método variacional, se investiga el comportamiento dinámico del sistema en la frontera de la posición de equilibrio. Los resultados del análisis de estabilidad proveen los requerimientos de diseño para el sistema de autobalance. In that case they adopted Stodola-Green rotor instead of the Jeffcott model. In this study, authors got a similar analysis for a flexible shaft and two self balancing systems on the ends. Describing the rotor centre with polar coordinates, the non-linear equations of motion for an autonomous system are derived from Lagrange´s equation. After a balanced equilibrium position and linearized equations in the neighborhood of the equilibrium position are obtained by the perturbation method and theoretically it shows that after critical speed rotor can be balanced. The system has a small lubrication on its balls and they are collocated themselves by inertial motion upper first natural frequency. The rotor with double self balancing system is shown in Fig. 1, where the shaft is supporting two self balancing systems on the ends. It is assumed that the shaft mass is negligible compared to the rotor mass. The XYZ coordinate system is a space-fixed inertia reference frame end the points C and G of both rotors are centroid and mass centre respectively. EQUATIONS OF MOTIONPoint O may be regarded as projection of the centroid C onto the axis O´Z. The ball balancer consists of a circular rotor with a groove contain...

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Whirl Suppression in Hand-Held Power Tool Rotors Using Guided Rolling Balancers

Cited by 39 publications

References 0 publications

Two-plane automatic balancing: A symmetry breaking analysis

Two-plane automatic balancing: A symmetry breaking analysis

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

Self Balancing System for Rotating Mechanisms

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