Passing through resonance of the unbalanced rotor with self-balancing device

Drozdetskaya, Olga; Fidlin, Alexander

doi:10.1007/s11071-021-06973-4

Cited by 5 publications

(8 citation statements)

References 11 publications

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“…- [11] -using the method of energy balance; - [12] -using the method of direct separation of motions; - [13] -using the averaging method for partially severely fading systems.…”

Section: Literature Review and Problem Statementmentioning

confidence: 99%

“…The methods used in [11][12][13] are somewhat cumbersome and time-consuming to use. They did not make it possible to investigate the form of all possible steady state motions of the vibratory machine, their stability, the possibility of ensuring over time the implementation of a certain (necessary) mode of motion by a vibratory machine.…”

Section: Literature Review and Problem Statementmentioning

confidence: 99%

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Selection and research of stability of the steady state motions of a single-mass resonance vibromating machine working on the Somerfeld effect

Filimonikhin

Yatsun

Matsui

et al. 2022

EEJET

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This paper has defined and investigated for stability the steady state modes of motion of a single-mass resonant vibratory machine. The vibratory machine has a platform that is supported by viscoelastic supports. The platform moves rectilinearly translationally. A vibration exciter is installed on the platform. The vibration exciter consists of N identical loads – balls, rollers, or pendulums. The center of mass of each load can move in a circle of a certain radius with a center on the longitudinal axis of the rotor. Each load, when moving relative to the body of the vibration exciter, is exposed to a viscous resistance force. It was established theoretically that with small forces of viscous resistance and any number of loads, the vibratory machine has jamming modes under which the loads that are collected form a conditional combined load and lag behind the rotor. In this case, there are two bifurcation speeds of the rotor. At speeds less than the first bifurcation speed, the vibratory machine has one single (first) jamming mode. When the first bifurcation speed is exceeded, the second and third jamming modes appear. When the second bifurcation speed is exceeded, the first and second jamming modes disappear. The first jamming mode is resonant. In the cases of two or more loads, the vibratory machine also has an auto balancing mode (no vibrations), under which the loads rotate synchronously with the body of the vibration exciter and mutually balance each other. With small forces of viscous resistance, the computational experiment found that odd jamming modes are stable if they are numbered in ascending order of the frequency of load jamming. An auto-balancing mode is stable at the rotor speeds above the resonance. For the onset of a resonant mode of motion of the vibratory machine, it is enough to slowly accelerate the rotor to a speed lower than the second bifurcation speed. The results reported here are applicable in the design of resonant single-mass vibratory machines with inertial vibration exciters of the ball, roller, or pendulum type.

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“…- [11] -using the method of energy balance; - [12] -using the method of direct separation of motions; - [13] -using the averaging method for partially severely fading systems.…”

Section: Literature Review and Problem Statementmentioning

confidence: 99%

Section: Literature Review and Problem Statementmentioning

confidence: 99%

Selection and research of stability of the steady state motions of a single-mass resonance vibromating machine working on the Somerfeld effect

Filimonikhin

Yatsun

Matsui

et al. 2022

EEJET

View full text Add to dashboard Cite

show abstract

“…Bharti et al [3] addressed the appearance of the Sommerfeld effect in the torsional vibrations of a double-Cardan joint driveline. Drozdetskaya and Fidlin used a particular type of averaging method, namely the averaging technique for partially strongly damped systems, to study the dynamics of an unbalanced motor with a passive self-balancing system [11].…”

Section: Actual Evolution Expected Evolution Natural Frequency Of The...mentioning

confidence: 99%

“…A direct inspection of system (11) reveals that it contains two nonangular real variables {a, } that are slow-they evolve with rate O(ε)-and two angular variables {β, φ} that are, in principle, fast-they evolve with rate O(1) unless ≈ 0 or ≈ 1. Hence, this is a suitable scenario for averaging over the fast angles (see Chapter 7 in [38] for a thorough treatment of this kind of techniques).…”

Section: Perturbation Approachmentioning

confidence: 99%

Stability of a nonideally excited Duffing oscillator

2022

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This paper investigates the dynamics of a Duffing oscillator excited by an unbalanced motor. The interaction between motor and vibrating system is considered as nonideal, which means that the excitation provided by the motor can be influenced by the vibrating response, as is the case in general for real systems. This constitutes an important difference with respect to the classical (ideally excited) Duffing oscillator, where the amplitude and frequency of the external forcing are assumed to be known a priori. Starting from pre-resonant initial conditions, we investigate the phenomena of passage through resonance (the system evolves towards a post-resonant state after some transient near-resonant oscillations) and resonant capture (the system gets locked into a near-resonant stationary oscillation). The stability of stationary solutions is analytically studied in detail through averaging procedures, and the obtained results are confirmed by numerical simulations.

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“…In autobalancing rotary systems, the Sommerfeld effect prevents the onset of autobalancing and is therefore undesirable [9][10][11][12][13][14]. Manifestations of the Sommerfeld effect in autobalancing systems were investigated in:…”

Section: Literature Review and Problem Statementmentioning

confidence: 99%

Determining experimentally the patterns of the manifestation of the Sommerfeld effect in a ball auto-balancer

Filimonikhin

Yatsun

Matsui

et al. 2022

EEJET

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This paper proposes an experimental method for studying the Sommerfeld effect in auto-balancers or exciters of resonant vibrations of pendulum, ball, or roller type. The method is based on the processing of signals acquired from analog sensors of rotations and vibration acceleration using regression analysis. The method is tested on a specially designed rotor bench on isotropic viscoelastic supports, which executes spatial motion, and an auto-balancer with one ball. Checking the accuracy of the method using stroboscopic lighting demonstrates the accuracy of determining the speed of rotation of the rotor, ball, oscillation frequency of the rotor, etc. with an error of several hundredths of a percent. When fixing the ball relative to the rotor, a classic inertial vibration exciter is obtained. The rotor has two resonant velocities. The Sommerfeld effect is almost not manifested. With a gradual increase in the frequency of the current, the rotor speed increases monotonously. There is no significant slip or jump in the rotor speed. There are two distinct peaks on the amplitude-frequency characteristic. Therefore, such a vibration exciter is not suitable for the excitation of resonant vibrations. With the free placement of the ball in the oil, the behavior of the system changes significantly in the vicinity of the first resonant velocity. The first narrow resonant peak disappears in the roto. Instead, there is a long, gentle resonant rise. It lasts at a current frequency of 9.4 Hz to 19.3 Hz. The amplitude at the reference point on the resonant rise increases from 0.7 mm to 2.84 mm. Therefore, by changing the frequency of the current, it is possible to smoothly change the amplitude of the rotor oscillations by almost 4 times. The maximum amplitude of rotor oscillations is the same as at the first resonance with a fixed ball. Due to the gentleness of the resonant rise, a freely installed ball itself is a reliable exciter of resonant vibrations

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Passing through resonance of the unbalanced rotor with self-balancing device

Cited by 5 publications

References 11 publications

Selection and research of stability of the steady state motions of a single-mass resonance vibromating machine working on the Somerfeld effect

Selection and research of stability of the steady state motions of a single-mass resonance vibromating machine working on the Somerfeld effect

Stability of a nonideally excited Duffing oscillator

Determining experimentally the patterns of the manifestation of the Sommerfeld effect in a ball auto-balancer

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