Two-plane automatic balancing: A symmetry breaking analysis

Abstract

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.

Application of the empirical criterion for the occurrence of auto-balancing for axisymmetric rotor on two isotropic elastic supports

“…Analytically the problems of determining the conditions for the occurrence of auto-balancing are solved for the concrete type auto-balancers [1,[3][4][5][6][7][8][9][10]. Therefore, the received results have special case character.…”

Parameter optimization of the centrifugal juicer with the ball auto-balancer under the impulse change of an unbalance by 3D modeling

“…-for classical and non-classical auto-balancers in the framework of rotor models, in which auto-balancers move in a plane-parallel manner [3]; -during balancing of the rigid rotor on two isotropic elastic supports statically by one two-ball auto-balancer [9] and dynamically by two two-ball auto-balancers [10]; -during dynamic balancing of the rigid rotor on two anisotropic elastic supports by two two-ball auto-balancers [11]; -during the static balancing of the rigid rotor, placed in a heavy elastic-viscous-fixed case with a small [12] and a large mass of an auto-balancer [13] by a single multi-ball auto-balancer.…”

“…-the principal possibility of balancing of a specific rotor by passive auto-balancers of any [3][4][5][6][7] or certain [3,[8][9][10][11][12][13][14][15][16][17][18] type; -the possibility of improvement of the accuracy of balancing and reduction of residual vibrations [2,[19][20][21][22]25];…”

“…Analytically, these processes have been studied in the few works [3,13,14,17,18]. This is due to the complexity of the differential equations, describing the motion of rotor systems with auto-balancers [3,[8][9][10][11][12][13][14][15][16][17][18]. Alternative methods of research are the numerical experiment and 3D modeling [9-11, 14-16, 25-27].…”

Empirical criterion for the occurrence of auto-balancing and its application for axisymmetric rotor with a fixed point and isotropic elastic support

“…This result makes it possible to determine conditions for the occurrence of autobalancing by the results of studying the stability of the main motions alone. This simplified approach is widely used when studying the process of auto-balancing and is applied, in particular, in papers [8][9][10][11][12][13][14][15][16][17][18][19][20][21].…”