Model of a vertical rotor with a ball-type automatic balancer

Work is aimed at the study of a rotor with a vertical axis and a fixed ball-type automatic balancer, whose body is placed concentrically in relation to the rotation axis. The rotor has disbalance that creates vibrations of the system. An automatic balancer with a torus-shaped body contains one ball-type corrective mass that freely rolls within the body of the automatic balancer both circle-wise and in cross-section. This reduces forces of resistance in the motion regime of a ball to the minimum, but simultaneously decreases the chance of putting the automatic balancer in motion. Experimental researches with the automatic balancer have proved that together with the working regime, when a ball stops in relation to the rotating body towards disbalance, there is a regime when a ball continuously moves in relation to the body of the balancer. A mathematical model containing four differential equations has been made for a rotor with an automatic balancer. The results of the calculations have shown that a ball of a balancer with a torus-shaped body has at least two motion regimes, one of which is a working regime, while another one is superfluous one

On the issue of acceleration of the compensating mass in an automatic balancing device with a horizontal axis of rotation

Among the ways to reduce vibrations of rotary machines with a vertical or horizontal axis of rotation is the use of ball-type automatic balancing devices. At the same time, the acceleration of compensating masses in the automatic balancing device with an annular cross-section of the housing showed that to accelerate the compensating masses to the operating speed of the rotor, it is necessary to provide the initial velocity due to the influence of gravity at the initial stage of acceleration. The value of the initial velocity of compensating masses depends on the parameters of the elastic suspension of the rotor, the size of the compensating mass, the coefficient of rolling friction between the compensating mass and the inner surface of the housing of the automatic balancing device and other parameters. In this work, the influence of the rolling friction coefficient and other parameters of the rotor system on the acceleration of compensating masses is studied, recommendations on the selection of parameters are given

Impact of dimensions of the compensating mass of the automatic balancer on its acceleration

The constructions of ball-type automatic balancing devices with a ball-shaped cross-section in the body are widely known. The specificity of such automatic balancers is the presence of several stable regimes of movement of compensating masses, though the choice of the dimensions of compensating masses and how it influences the operation of an automatic balancer have not been completely clarified issues yet. The given article is devoted to the clarification of the influence of dimensions of compensating masses on working conditions of the automatic balancer

On the issue of impact of anisotropy of the rotor elastic suspension on the performance of the automatic balancer

Experimental researches of a vertical rotor with a ball-type automatic balancer with a circular cross-section of the body have proved its efficiency in the reduction of vibrations of an out-of-balance rotor, however for acceleration of compensating masses till the rotor working velocity it is necessary to set initial velocity. A value of the initial velocity of compensating masses depends on the stiffness of the elastic rotor suspension. At the same time, real elastic suspensions of rotors possess nonhomogeneous elastic dissipative characteristics in directions. The research is aimed at determining the influence of anisotropy of the elastic rotor suspension on the acceleration of compensating masses. The authors give recommendations on the selection of parameters of a rotor suspension

Motion modes of the nonlinear mechanical system of the rotor autobalancer

The paper analyzes the possible motion modes of an unbalanced rotor with an auto-balancing device. It is shown that for given parameters of the system, there are several qualitatively different stable motion modes. Previously unknown types of motion modes are detected. It is found that for a given supercritical working rotor speed, the system can have at least three possible stable motion modes depending on the initial conditions of its motion. A qualitative analysis of the stability ranges of all possible motion modes of the system was performed

Acoustic Emission Leak Detection on a Technological Pipeline

Leak detection is one of the main tasks of pipeline inspection, as the extension of pipelines usually requires a pipeline repair capability. Reliable and fast detection of fluid leaks in pipelines is extremely important for seaports, where their branched system is located. The most frequent locations of pipeline leakages are seam weldings and flanged joints, which are most exposed to plastic deformation. The aim of this study was to detect leaks in a technological pipeline connecting two vertical bitumen storage tanks. Based on the spectral analysis of acoustic emission signals (AE), a characteristic picture of the pipeline micro-damage process course (leakage, delamination, cracking, rupture, etc.) was obtained

Model of a vertical rotor with an automatic balancer with two compensating masses

The use of automatic balancing devices in unbalanced rotor systems has proven their ability to reduce rotor vibrations in the super resonance zone of velocities. At the same time, the creation of efficient automatic balancing devices with a torus-shaped body and a circular cross-section is associated with the multimodal motion of the compensating masses, which makes the device unsuitable for operation. To ensure the acceleration of the compensating masses from the rest state to the working speed of the rotor, they need to be provided with some initial velocity. The magnitude of this velocity is influenced by the parameters of the elastic suspension of the rotor, the geometric parameters of the automatic balancing device, the rolling friction coefficient between the body and the compensating mass, etc. The work is devoted to the description of the vertical rotor model with an automatic balancer with two compensating masses. It also considers the effect of the rolling friction coefficient on the value of their initial velocity

Study of the area of attraction of the auto-balancing mode in a ball-type automatic balancing device with a horizontal axis of rotation

It is known that automatic balancing devices are capable of reducing vibrations in rotary systems in a superresonance velocity zone. However, the effectiveness of automatic balancing devices is related to the necessity of accelerating compensating masses. To ensure the acceleration of compensating masses from standstill to the operating speed of the rotor, they need to be provided some initial velocity. The value of this velocity is influenced by the parameters of the elastic suspension of the rotor, the geometrical parameters of the automatic balancer, the coefficient of rolling friction between the housing and the compensating mass, etc. The work is devoted to the study of a horizontal rotor model with an automatic balancer with one compensating mass, in particular the issue on the influence of the coefficient of viscous friction on the value of the area of attraction of the auto-balancing mode

On the issue of impact of anisotropy of the rotor elastic suspension on the performance of the automatic balancer

Experimental researches of a vertical rotor with a ball-type automatic balancer with a circular cross-section of the body have proved its efficiency in the reduction of vibrations of an out-of-balance rotor, however for acceleration of compensating masses till the rotor working velocity it is necessary to set initial velocity. A value of the initial velocity of compensating masses depends on the stiffness of the elastic rotor suspension. At the same time, real elastic suspensions of rotors possess nonhomogeneous elastic dissipative characteristics in directions. The research is aimed at determining the influence of anisotropy of the elastic rotor suspension on the acceleration of compensating masses. The authors give recommendations on the selection of parameters of a rotor suspension

On the issue of the motion of balls in a double pendulum

The paper considers a model of a vertical double pendulum with one suspension centre moving in a vertical plane. For the proposed system of pendulums, differential equations of motion and conditions for the collision of balls are obtained. When modelling the movement of pendulums, the central impact of the balls was considered for various variants of the movement of the suspension point: the suspension point oscillates in the vertical direction; the suspension point makes rotational movements in the vertical plane. In this case, various conditions of the central impact between the balls were considered: absolutely inelastic impact; absolutely elastic impact; impact with the transformation of impact energy (elastic impact). Comparison of the results of the numerical simulation and the results of experiments with the Kapitza pendulum in published sources confirmed the possibility of modelling an elastic impact between balls in a double pendulum and between balls in an autobalancer with a horizontal axis of rotation of the rotor