Sommerfeld effect in a single-DOF system with base excitation from motor driven mechanism

Sinha, Anubhab; Bharti, Saurabh Kumar; Samantaray, Arun Kumar; Bhattacharyya, Ranjan

doi:10.1016/j.mechmachtheory.2020.103808

Cited by 17 publications

(6 citation statements)

References 33 publications

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“…As an alternative to averaging, many researchers have exploited the method of Direct Separation of Motions [4] for the analysis of nonideally excited oscillators [9,21,24,39,41,42,49,50]. Of course, together with the analytical and numerical research, experimental studies are critical to understand nonideally excited oscillations.…”

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

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

confidence: 99%

Stability of a nonideally excited Duffing oscillator

2022

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“…with the use of a DC-DC buck converter or high-frequency pulse width modulation (PWM) with shunt capacitor. Hundreds of articles and review papers [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28]31,36 and many text books [1][2][3][4][5]7,9 describe the preceding analysis and results, in similar or a little different manner. Apparently, the suppression of Sommerfeld effect by increasing the foundation damping is beneficial from the point of system operation and control, as proven by existence of all the operating speeds and also the ability to reach any operating speed directly.…”

Section: A Simple Mathematical Modelmentioning

confidence: 99%

“…[11][12][13] Speed entrainment can also occur at flutter instability boundary due to rotor shaft material/internal damping 14,15 or parametric resonance boundaries due to asymmetry in the rotor shaft and/or supports. 9,16 This typical phenomenon of resonance capture is common in industrial rotor dynamic systems, reciprocating compressors, 17 cam driven mechanisms, 18 vehicles, 19,20 etc., and its consequences can be very damaging. Experimental results for a real offshore wind turbine operation presented in Hu et al 21 and Yan et al 22 and for a real natural gas compression plant with a reciprocating compressor presented in 23 have shown resonance capture phenomena.…”

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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“…The jumping phenomenon started at critical operating speed (N = 212 rpm) in which the cam lost the contact with the follower. The critical operating speed of the cam was calculated by equating the summation of the weight and the spring force with the inertia force of the follower, [15]. The impact between the cam and the follower was considered based on impulse and momentum theory because the impact velocity was illustrated in the following equation:…”

Section: Experiments Testmentioning

confidence: 99%

Detachment Detection in Cam Follower System Due to Nonlinear Dynamics Phenomenon

Yousuf

2021

Machines

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The detachment between the cam and the follower was investigated for different cam speeds (N) and different internal distance of the follower guide from inside (I.D.). The detachment between the cam and the follower were detected using largest Lyapunov exponent parameter, power density function of Fast Fourier Transform (FFT), and Poincare’ maps due to the nonlinear dynamics phenomenon of the follower. The follower displacement and the contact force between the cam and the follower were used in the detection of the detachment heights. Multi-degrees of freedom (spring-damper-mass) systems at the very end of the follower were used to improve the dynamic performance and to reduce the detachment between the cam and the follower. Nonlinear response of the follower displacement was calculated at different cam speeds, different coefficient of restitution, different contact conditions, and different internal distance of the follower guide from inside. SolidWorks program was used in the numerical solution while high speed camera at the foreground of the OPTOTRAK 30/20 equipment was used to catch the follower position. The friction and impact were considered between the cam and the follower and between the follower and its guide. The peak of nonlinear response of the follower displacement was reduced to (15%, 32%, 45%, and 62%) after using multiple degrees of freedom systems.

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Sommerfeld effect in a single-DOF system with base excitation from motor driven mechanism

Cited by 17 publications

References 33 publications

Stability of a nonideally excited Duffing oscillator

Stability of a nonideally excited Duffing oscillator

Efficiency considerations for Sommerfeld effect attenuation

Detachment Detection in Cam Follower System Due to Nonlinear Dynamics Phenomenon

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