Auto-balancing Device Research Articles

Nonlinear dynamics of rotor of an auto-balancing ball device, considering eccentricity and changes in horizontal axes of rotation

This study is devoted to the dynamics of an auto-balancing device (ABD) when the rotor rotates at critical angular speeds. In this article, a model of an auto-balancing device (ABD) is proposed. The rotor is not only eccentric about the symmetry axis but also has a horizontal axis of rotation. A mathematical model is proposed based on the Lagrange equations; it describes the nonlinear motion of a balancing system (BS) with two running lines with a different number of balls, considering eccentricity, angular error, and changes in the horizontal axis of rotation. The nonlinear dynamics of the rotor motion with two running lines and two balls at a constant rotation speed and in the accelerating mode of the rotor motion is studied by a numerical method, taking into account the change in the horizontal axis of rotation.

On the Issue of Collision of Balls in an Auto-Balancing Device

Abstract The paper considers a model of a vertical double pendulum, which includes two balls suspended on rigid non-deformable threads to one centre of the suspension. For the proposed system of pendulums, differential equations of motion and conditions for collision of balls have been recorded. When simulating the motion of the pendulums, the central collision of the balls has been considered for various options of the motion of the suspension point: the suspension point is motionless; the suspension point oscillates in the vertical direction; the suspension point makes rotational motions in the vertical plane. Meanwhile, various conditions for the central collision between the balls have been considered: a perfectly inelastic collision; a perfectly elastic collision; a collision with transformation of collision energy (partially elastic collision). The results of numerical simulation are consistent with the behaviour of pendulums in real physical models, which makes it possible to simulate an elastic collision between balls when studying their acceleration in auto-balancing devices.

INFLUENCE OF CURRENT IMBALANCES AND CENTER POSITION HARDNESS ON VIBROACTIVITY OF HORIZONTAL DRUM MACHINES

The issues of reducing the vibration caused by rotating rotors at the frequency of the first rotor harmonic (so-called rotor vibration) are among the most important in the design, manufacture and operation of almost all types of modern rotary machines. The washing machine as an object of study of the dynamics and reduction of vibration and noise is of particular interest due to the constant presence of randomly located and wandering imbalance of laundry in the drum and low requirements for accuracy of its manufacture and assembly of parts and assemblies. A mathematical model of oscillations of a multiconnected tank-drum system on elastic suspensions for the main types of machines and spin centrifuges with a horizontal axis of rotation is created. The model is developed in a linear formulation based on the Lagrange equation of the II kind for a washing machine. The accuracy and adequacy of the mathematical model was tested directly on the field object by measuring noise, vibration, forces in the supports and stress distribution in the individual elements and components of the machine in the entire range of drum speeds. Studies of the nature of system oscillations depending on the change in position and attachment points of elastic and damping elements were performed using simulation in the Simulink environment. As a result of research, the basic requirements for the layout of horizontal rotary machines of the drum type were experimentally confirmed: the center of mass of the tank must lie on the axis of rotation of the drum; the axis of rotation of the drum should be the main central axis of inertia of the tank; the center of mass of the tank must coincide with the center of mass of the loaded drum; the center of rigidity of the system of elastic supports must coincide with the center of gravity of the tank, and the main axes of rigidity – with the main central axes of inertia of the tank; the main axes of the constant viscous friction must coincide with the main central axes of inertia of the tank. The results of the theoretical study were applied to the problem of evaluating the efficiency of a liquid auto-balancing device for a proper squeezing machine depending on its dynamics.

ВПЛИВ МОМЕНТНОЇ НЕЗРІВНОВАЖЕНОСТІ ТА ПОЛОЖЕННЯ ЦЕНТРУ ЖОРСТКОСТІ НА ВІБРОАКТИВНІСТЬ ГОРИЗОНТАЛЬНЫХ БАРАБАННИХ МАШИН

The issues of reducing the vibration caused by rotating rotors at the frequency of the first rotor harmonic (so-called rotor vibration) are among the most important in the design, manufacture and operation of almost all types of modern rotary machines. The washing machine as an object of study of the dynamics and reduction of vibration and noise is of particular interest due to the constant presence of randomly located and wandering imbalance of laundry in the drum and low requirements for accuracy of its manufacture and assembly of parts and assemblies. A mathematical model of oscillations of a multiconnected tank-drum system on elastic suspensions for the main types of machines and spin centrifuges with a horizontal axis of rotation is created. The model is developed in a linear formulation based on the Lagrange equation of the II kind for a washing machine. The accuracy and adequacy of the mathematical model was tested directly on the field object by measuring noise, vibration, forces in the supports and stress distribution in the individual elements and components of the machine in the entire range of drum speeds. Studies of the nature of system oscillations depending on the change in position and attachment points of elastic and damping elements were performed using simulation in the Simulink environment. As a result of research, the basic requirements for the layout of horizontal rotary machines of the drum type were experimentally confirmed: the center of mass of the tank must lie on the axis of rotation of the drum; the axis of rotation of the drum should be the main central axis of inertia of the tank; the center of mass of the tank must coincide with the center of mass of the loaded drum; the center of rigidity of the system of elastic supports must coincide with the center of gravity of the tank, and the main axes of rigidity – with the main central axes of inertia of the tank; the main axes of the constant viscous friction must coincide with the main central axes of inertia of the tank. The results of the theoretical study were applied to the problem of evaluating the efficiency of a liquid auto-balancing device for a proper squeezing machine depending on its dynamics.

Passive Balancing of the Rotor with an Auto-Balancing Device with a Viscous Incompressible Liquid

The use of liquid auto-balancers to compensate the operational changes in the imbalance of rotary systems without stopping them is of interest because of the relative structural simplicity of these devices, which are passive direct-acting regulators that do not require power supply and control systems to move correction masses. The experience of the study of passive auto-balancing devices (SBD) indicates that the existing theory (statements) of passive automatic balancing of the fluid is idealized and inaccurately describes the processes that occur with the working bodies during their operation. In particular, the lack of studies on the effect of liquid viscosity on the efficiency of self-balancing and the reasonableness of the selection of liquid during the development of fluid SBD demanded to analyse the operation of liquid SBD in the real system, taking into account the influence of liquid properties on the efficiency of the vertical rotor balancing process. It is shown that the efficiency of balancing increases with the approach of the angular velocity to the critical one and with the increase of the external resistance. The massive forces of the working fluid have less effect on the balancing efficiency than the viscosity for liquid SBDs.

Анализ поведения эксцентриситета уравновешивающей жидкости автобалансирующего устройства стиральных машин

Анализ поведения эксцентриситета уравновешивающей жидкости автобалансирующего устройства стиральных машин

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.

Investigation of Small Motions of Liquid in Cylindrical Chamber of Auto-Balancing Device

The article deals with the process of wave forming on the surface of a liquid in a chamber of auto-balancing device partially filled with a liquid for rotors with a vertical axis of rotation under non-stationary modes of the system's motion. In non-stationary processes, the possible wave formation causes a dynamic instability in the operation of the machine and the increase of vibrations under certain operating modes. In this article the case when the rotor is installed in elastic supports is solved, the joint movements of the rotor - liquid system are considered and their stability is investigated. DOI: http://dx.doi.org/10.5755/j01.mech.24.2.20402

Passage through resonance of a statically unbalanced rotor with an imperfect autobalancing device

Nonstationary modes of direct and inverse passage through resonance of unbalanced rotor equipped with an imperfectly mounted autobalancing device (ABB) are investigated. Two mathematical models are considered. The first one is the passage of the critical region with constant angular acceleration, and the second one is the rotor motion under the influence of a constant external torque. The study of the first model revealed that the presence of ABB significant negatively influences on the process of direct passage through resonance, and the maximum amplitude of whirling in this case can exceed the maximum amplitude in the steady state case. At the same time, during inverse passage through resonance, the influence of ABB is positive, and the maximum amplitude of whirling is much less than in the case of the direct passage through resonance. The investigation of the influence of viscous damping in the ABB revealed that too small damping influences negatively on the transient process dynamics, delaying the time of the rotor resonant vibrations until the moment of their stop. The study of the processes of acceleration and rundown of the rotor according to the second model confirms the main conclusions obtained from the first model.

Passage through the resonance of a statically unbalanced rotor with “imperfect” autobalancing device

Passage through the resonance of a statically unbalanced rotor with “imperfect” autobalancing device

INVESTIGATION OF BALANCES IN LIQUID AUTOBALANCING DEVICE AT MAXIMUM UNBALANCED FORCE

One of the most effective vibration isolation systems that are used in rotary machines including drum type washing machines are auto-balancing device (ABD). However, widespread use in washing machines ABD did not get what is due, primarily, to the complexity of designs ABD and the relatively low efficiency of some modes of rotation of the washing drum, as well as a lack of research parameters ABD. Striving for improved ABD has led to the need to develop advanced techniques to form the corrective masses, primarily, balancing fluids. In order to determine the rational parameters of liquid ABD carried out theoretical studies of the formation of the counterbalancing masses correction fluid, the results of which were presented in a number of scientific articles. An important factor is the formation of the balancing force, which must have an adequate response to the maximum input force effect. This article presents the results of a theoretical investigation of balances in liquid auto-balancing passive type device under the chosen conditions balancing corresponding to maximum unbalanced force. The dependences of the quantitative and qualitative indicators of efficiency of the process of balancing for different input design and operational factors. The criteria of efficiency of the process of balancing.

Dynamics of a rotor with an eccentric ball auto-balancing device

This paper is concerned with a statically unbalanced rotor equipped an automatic ball balancing device, whose axis of symmetry is different from that of the rotor. A simple model of a Jeffcott rotor is used to derive the motion equations of the system in fixed and rotating coordinate systems, as well as the equations that describe the steady-state modes of motion. The impossibility in principle is shown for a rotor with variable imbalance to have a balanced steady-state mode. For an auto-balancing device consisting of two balls, two types of unbalanced steady-states modes are shown to be feasible. It is proposed to call the steady-state mode with a constant residual vibration, whose amplitude is independent of the angular velocity and is equal to eccentricity of the balancer, half-balanced. A solution corresponding to a half-balanced mode is explicitly constructed and conditions for the existence and stability thereof are proposed. Numerical methods are used to construct two-parameter stability diagrams of a half-balanced steady-state mode and to examine unsteady states of rotor motion in the case where it rotates with steady angular velocity.

Evaluation of Gravitational Force Effect on Balancing Processes in Liquid-Type Autobalancing Devices

The article examines the effect of gravitational force on the operation of a liquid-type autobalancing device. Results of the mathematical analysis and experiments are presented. When performing a hydrodynamic calculation of the rotation speed the effects of gravitational and centrifugal forces as well as the effect of the liquid’s force friction against the housing are considered. The analysis results show that the speed at which the gravitational force in an autobalancing device may be negligible is greatly dependent upon the radius and coefficient of gravitation. Moreover, the less the gravitational coefficient and the greater the radius, the greater the angular velocity of an autobalancer. As a result of the conducted investigation, the speeds evaluating the possibility of using liquids as balancers at low rotation speeds are provided in this paper.

Efficiency of Balancing by Liquid-Type Automatic Balancing Devices

The article focuses on modelling the behaviour of a liquid-type automatic balancing device. To perform mathematical research the rotor model is used that contains a ring functioning as a vessel coupled to the rigid shaft being rotatable on bearings. Data on the influence of various factors on balancing accuracy are presented. The obtained modeling results indicate that the vibration amplitude at supercritical frequencies will decrease proportionally to the increase in the parameters of a liquid autobalancer. The performed calculation also reveals that the more the parameters of a liquid autobalancing device, the higher the efficiency of balancing. Provided the condition of the liquid sufficiency in the ring is satisfied, the independence of the rotor vibration amplitude from the mass of the liquid in the vessel is achieved. Critical rotor speed does not depend on the volume of the liquid in the ring if the condition of its sufficiency is met.

Auto-balancing of a rotor with an orthotropic elastic shaft

The self-balancing of a statically unbalanced orthotropic elastic rotor equipped with a ball auto-balancing device is investigated. Equations of motion in fixed and rotating systems of coordinates, as well as equations describing steady motions of the regular precession type, are derived using a simple model of a Jeffcott rotor. Formulae for calculating the amplitude-frequency and phase-frequency characteristics of the precessional motion of the rotor are obtained. It is established that the conditions for a steady balanced mode of motion for an orthotropic rotor to exist have the same form as for an isotropic rotor, but the stability region of such a mode for an orthotropic rotor is narrower than the stability region for an isotropic rotor. The unsteady modes of motion of the rotor in the case of rotation with constant angular velocity and in the case of passage through critical velocities with constant angular acceleration is investigated numerically. It is established that the mode of slow passage through the critical region for an orthotropic rotor is far more dangerous than the similar mode for an isotropic rotor.