Sommerfeld effect in a two-disk rotor dynamic system at various unbalance conditions

Bisoi, Alfa; Samantaray, Arun Kumar; Bhattacharyya, Ranjan

doi:10.1007/s11012-017-0757-3

Cited by 20 publications

(4 citation statements)

References 29 publications

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“…Note that one finds the same behavior in rotor dynamics, where the Sommerfeld rotor leads to the same driving characteristic [2] when in Equation ( 12) the road factor z 0 Ω is replaced by the mass ratio of the unbalanced rotor, the translation velocity by the rotation speed ratio, and the driving force by the moment. More details on Sommerfeld effects in rotor dynamics are given in [16][17][18][19][20].…”

Section: Speed Driving Force Characteristic Of Traveling Vehiclesmentioning

confidence: 99%

Speed Oscillations of a Vehicle Rolling on a Wavy Road

Wedig

2021

Applied Sciences

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Every driver knows that his car is slowing down or accelerating when driving up or down, respectively. The same happens on uneven roads with plastic wave deformations, e.g., in front of traffic lights or on nonpaved desert roads. This paper investigates the resulting travel speed oscillations of a quarter car model rolling in contact on a sinusoidal and stochastic road surface. The nonlinear equations of motion of the vehicle road system leads to ill-conditioned differential-algebraic equations. They are solved introducing polar coordinates into the sinusoidal road model. Numerical simulations show the Sommerfeld effect, in which the vehicle becomes stuck before the resonance speed, exhibiting limit cycles of oscillating acceleration and speed, which bifurcate from one-periodic limit cycle to one that is double periodic. Analytical approximations are derived by means of nonlinear Fourier expansions. Extensions to more realistic road models by means of noise perturbation show limit flows as bundles of nonperiodic trajectories with periodic side limits. Vehicles with higher degrees of freedom become stuck before the first speed resonance, as well as in between further resonance speeds with strong vertical vibrations and longitudinal speed oscillations. They need more power supply in order to overcome the resonance peak. For small damping, the speeds after resonance are unstable. They migrate to lower or supercritical speeds of operation. Stability in mean is investigated.

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Section: Speed Driving Force Characteristic Of Traveling Vehiclesmentioning

confidence: 99%

Speed Oscillations of a Vehicle Rolling on a Wavy Road

Wedig

2021

Applied Sciences

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“…The calculation of the harvested power of the autoparametric absorber is given by Eqs. (17) and (18) that describe the dimension and dimensionless harvested power, respectively…”

Section: Engineering Problem and Mathematical Model Designmentioning

confidence: 99%

“…Therefore, near resonance, it appears that the additional power supplied to the motor only increases the amplitude of the response of the supporting structure while there is a little effect on the RPM of the motor. Eventually, enough power is supplied to the motor to initiate the jump, the operating frequency increases and the amplitude decreases, resulting in lower power consumption by the motor [10][11][12][13][14][15][16][17][18][19].…”

Section: Introductionmentioning

confidence: 99%

On vibration mitigation and energy harvesting of a non-ideal system with autoparametric vibration absorber system

et al. 2018

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This paper demonstrates that vibration mitigation and energy harvesting can be achieved simultaneously by using of an electricity-generating from autoparametric vibration absorber system (AVAS) and non-ideal system (NIS). The NIS consists of a simple portal frame excited by a small dc motor with eccentric mass, with limited power supply and located on the top. The AVAS consists of a cantilever beam with tip mass parallel coupled to NIS. A piezoelectric material is considered for energy harvesting installed in the base of the AVAS and an electric circuit is connected to the piezoelectric material in order to produce voltage output. Several numerical simulations were carried out focusing on the passage through the resonance of NIS, when the motor rotational frequency is near the portal frame natural frequency and when the non-ideal subsystem frequency is approximately twice the absorber beam frequency (two-to-one internal resonance). The results showed the existence of Sommerfeld effect in NIS and saturation phenomenon in the NIS-AVAS.

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“…In complex multi-degree of freedom or continuous systems, stronger Sommerfeld effects occur in higher modes, where the modal damping is generally low. 33 In those systems, suppression of Sommerfeld effect requires good deal of additional structural damping, which, in turn, can reduce the overall efficiency of the system by many folds. Therefore, targeted active or passive control energy transfer mechanisms in the neighbourhood of critical speeds are more viable solutions.…”

Section: Introductionmentioning

confidence: 99%

Efficiency considerations for Sommerfeld effect attenuation

Samantaray

2021

Proceedings of the Institution of Mechanical Engineers, Part C:

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In rotating machinery with a flexible foundation used for vibration isolation, the drive (motor) is designed to provide maximum power at the critical speed so that the rotor can be coasted up to a supercritical operating speed. Over the time, rotors develop some degree of unbalance and it may be impossible to balance the rotors in-situ, such as in a wind turbine. Therefore, oversized motors are used in anticipation of some unbalance. To promote passage through resonance, without altering the motor, various kinds of additional hardware and/or control mechanisms have been proposed in the past. On the other hand, simply increasing the foundation (or structural) damping reduces the amplitude of unbalance induced vibrations and the motor power requirement at the critical speed. This appears to be the simplest possible solution and has been proposed in relevant mathematical research. However, it is shown in this article that increasing foundation damping significantly reduces the overall system efficiency at the supercritical operating speed and it should not be at all considered as a meaningful engineering solution. In fact, the loss of efficiency due to the increased foundation damping is so large that it may not be compensated by a redesigned motor.

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Sommerfeld effect in a two-disk rotor dynamic system at various unbalance conditions

Cited by 20 publications

References 29 publications

Speed Oscillations of a Vehicle Rolling on a Wavy Road

Speed Oscillations of a Vehicle Rolling on a Wavy Road

On vibration mitigation and energy harvesting of a non-ideal system with autoparametric vibration absorber system

Efficiency considerations for Sommerfeld effect attenuation

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