Abstract
The authors of the study work out the differential equations of motion of a vertical rotor model on an elastic-dissipative suspension, balanced by a ball-type automatic balancing device. Often, the cross-section of the cavity of the body of the automatic balancing device is rectangular and during rolling the balls have two points of contact, in one of which the balls slide along the surface of the cavity. To prevent the balls from sliding, the inner surface of the cavity of the automatic balancing device is made in the shape of a torus, which provides one point of contact. The forces of gravity and the forces of resistance to the movement of the correcting weights are taken into account, and the model is drawn up for both viscous and dry friction forces inside the body of the automatic balancing device. The obtained mathematical model of the rotor makes it possible to study the transient and steady-state modes of motion of the rotor system.
Highlights
One of the design stages of a rotor system with a ball-type automatic balancing device (ABD) is the development and substantiation of the design model of the rotor and its mathematical model
The authors obtained a system of differential equations for a rotor system with a ball-type ABD, in which the inner space of the body is made in the shape of a torus, which provides a minimum resistance force to the motion of the ball and the best conditions for the location of balls in the auto-balancing mode
The proposed system of differential equations makes it possible to proceed to the study of simpler rotor systems with a vertical axis of rotation, equipped with an ABD, in which the balls move in both longitudinal and transverse directions
Summary
One of the design stages of a rotor system with a ball-type automatic balancing device (ABD) is the development and substantiation of the design model of the rotor and its mathematical model. The elaboration of new and improvement of existing rotor systems requires the solution of such complex mathematical models. In real conditions, during the acceleration of the rotor, the ball, for various reasons, inside the ABD body begins to move both along the treadmill and in the transverse direction, which can lead to the emergence of side steady modes that do not allow the ball to accelerate to the operating speed of the rotor This is confirmed by mathematical modelling of the conditions for acceleration of the weight, considered in [6]. The aim of this work is to obtain a mathematical model of a cantilever rotor system with a ball-type ABD in transient and steady-state modes taking into account the longitudinal and transverse movements of the balls inside the ABD body
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