Phase control of the transient resonance of the automatic ball balancer

Michalczyk, J.; Pakuła, Sebastian

doi:10.1016/j.ymssp.2015.11.001

Cited by 8 publications

(6 citation statements)

References 4 publications

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“…The mathematical model from [21] has been supplemented with the action of two rolling bearings-one on each side of the ABB's wall. Due to the arbitrary position of the balls in the ABB's chamber, the values of the rolling bearing reaction (P 1 ,P 2 ) will be different.…”

Section: Machine Bodymentioning

confidence: 99%

“…whereω t i j is the versor of rolling of the ith ball on the jth ball. The vector ω t ij determines the rolling direction and is calculated based on the vector of contact point velocity s relative to the ith ball center v τ i (21) and the relative velocity component of the ball's center (17) projected on the plane tangent to the ball at the contact point v τ ij (contact plane) according to the following equation:…”

Section: Contact Forces Between Ballsmentioning

confidence: 99%

“…It was assumed in the simulations that the stiffness and damping coefficients in the horizontal direction are half of those in the vertical direction according to [21]:…”

Section: Verificationmentioning

confidence: 99%

“…The balls inside such a chamber can freely move and rotate in either direction and this allows them to distribute in many possible ways in many layers. The mathematical model of the system of the machine with the ER and ABB-DC is partially based on the model from paper [21] that concerns the machine with ER and ABB-SC. The equations of motion have been supplemented with equations of motions in the rotor axis direction and with equations of rotational motion relative to two axes perpendicular to the rotor axis.…”

Section: Introductionmentioning

confidence: 99%

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Numerical effectiveness investigation of the automatic ball balancer with a deep chamber

Pakuła

2021

Acta Mech

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The article describes the simulation results of an unbalanced rotary machine with an automatic ball balancer with a deep chamber (ABB-DC) based on a mathematical model of such a system. The ABB chamber has a cylindrical shape and is filled with balls that can move freely in general motion. The model takes into account mutual collisions between the balls, as well as between the balls and the chamber. The model also includes friction forces and rolling resistance. The comparison of simulation results performed with two different construction types of the chamber, classic single-layer drum (ABB-SC) and ABB-DC, confirmed the better efficiency of the ABB-DC in the optimal range of the number of balls. The machine body movement was limited to planar motion. The correctness of such a limitation has been verified by analyzing waveforms of reaction forces of constraints and their moments. Waveforms were divided into transient and steady states. The results of the analysis indicate the additional constraints do not significantly affect machine body movements. However, this might affect the ball arranging process in the ABB chamber. The paper also presents details of performing numerical simulations based on the developed mathematical model and numerical tests to determine the optimal integration time-step.

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Section: Machine Bodymentioning

confidence: 99%

Section: Contact Forces Between Ballsmentioning

confidence: 99%

“…It was assumed in the simulations that the stiffness and damping coefficients in the horizontal direction are half of those in the vertical direction according to [21]:…”

Section: Verificationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Numerical effectiveness investigation of the automatic ball balancer with a deep chamber

Pakuła

2021

Acta Mech

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“…Extensive studies concerning synchronization of dynamic systems we can find in papers by Blechman (1971,2000), specific applications in papers, e.g. Michalczyk (2012), Michalczyk and Cieplok (2014) and more (Hou et al, 2017;Michalczyk and Pakuła, 2016;Zhao et al, 2011;Fang et al, 2015;Karmazyn et al, 2018;Francke et al, 2010). The principles of building vibrating machines with a vibratory drive are known (Goncharewich and Frolov, 1990;Michalczyk, 1995;Cieplok, 2009Cieplok, , 2018, in particular conditions of synchronous motion with distinction between working in the desirable and undesirable state.…”

Section: Introductionmentioning

confidence: 99%

Conditions for self-synchronization of inertial vibrators of vibratory conveyors in general motion

Cieplok¹,

Wójcik²

2020

Journal of Theoretical and Applied Mechanics

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The paper concerns the analysis of a self-synchronization process of inertial vibrators in general motion. These types of systems are found e.g. in the case of vibratory conveyors, in which the synchronization plane of vibrators is perpendicular to the plane of vibration of the conveyor trough. The analysis is focused on two basic issues related to movement of the vibrator. The first issue concerns conditions for obtaining stable motion in a configuration ensuring generation of useful vibrations. The second one is determination of the value of the synchronizing moment. In order to obtain analytical dependencies as simply as possible, we considered a typical build conveyor and the suspension, whose mathematical description we can bring to a diagonal form.In the paper, we paid attention to the consequences of using suspensions with highly directional properties, e.g. metal-elastomer vibration isolators.

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Off-axis vibration-elimination system of eccentric rotors with use of multiple automatic ball balancers

Pakuła

2022

Arch Appl Mech

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An automatic ball balancer (ABB) is a device that is used to automatically balance eccentric rotors. The main principle of working such a device is based on the self-synchronization phenomenon. It is typically used in rotary machines with unknown or variable imbalances. The automatic balancing process requires an ABB unit be installed on an eccentric rotor axis; thus, its application is very limited and usually comes with a redesign of the rotary machine. This paper presents a new method to eliminate the vibration of rotary machines by the use of multiple ABBs mounted away from rotor axis. The ABB, unlike the commonly used vibrator with the fixed eccentricity, has ability to adjust eccentricity during the operation. That ability allows to achieve dynamic equilibrium by the use of only two ABBs. The article introduces theoretical bases of dynamic equilibrium in the steady state of a rotary machine system with multi ABBs and proves the existence of a dynamic equilibrium with the use of only two ABBs. It also contains the optimization results of a system with the use of up to five ABBs. The objective function was defined as to minimize the size of ABBs. The smaller size of such ABBs allows us to significantly extend the range of their application.

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Phase control of the transient resonance of the automatic ball balancer

Cited by 8 publications

References 4 publications

Numerical effectiveness investigation of the automatic ball balancer with a deep chamber

Numerical effectiveness investigation of the automatic ball balancer with a deep chamber

Conditions for self-synchronization of inertial vibrators of vibratory conveyors in general motion

Off-axis vibration-elimination system of eccentric rotors with use of multiple automatic ball balancers

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