Self-oscillation Research Articles

The application of dither to mitigate curve squeal

Curve squeal is a highly disturbing tonal sound generated by rail vehicles like trains, metros or trams, when negotiating a sharp curve. The probability that squeal occurs increases with reduced curve radius of the track. Curve squeal noise is attributed to self-excited vibrations caused by stick/slip behaviour due to lateral creepage of the wheel tyre on the top of the rail. With respect to the large number of rolling stock units and the long lifetime of vehicles, there is an urgent need for a cheap and simple retrofitting measure to reduce curve squeal. Therefore, main objective of this paper is to investigate the potential to reduce curve squeal by means of active control in the form of dither in an efficient and robust way. Dither control has been applied in the field of mechanical engineering for systems including non-linear components. There it has been shown to suppress self-excited oscillations very efficiently. The control is an open-loop control. It consists in adding a forced vibration to the vibrational system. A time-domain model has been applied to investigate the mechanisms behind self-excited vibrations leading to curve squeal at the squealing noise rig at Chalmers University of Technology. The analysis showed, that in the presence of constant friction, the coupling between lateral and vertical direction is the driving mechanism for building up self-excited vibrations. Based on this insight, the potential of dither has been investigated. For the case considered here dither has the potential to reduce the overall kinetic energy on the wheel by more than 10 dB and on the rail by more than 20 dB. Further optimisation of dither forces with respect to the radiated sound power might increase this potential.

Mutual synchronization of self-excited acoustic oscillations in coupled thermoacoustic oscillators

Synchronization refers to the adjustment of rhythms of two nonidentical oscillators due to interaction. In this study, we report for the first time on the ability of computational fluid dynamics (CFD) to simulate the synchronization of self-sustained acoustic oscillations in two coupled thermoacoustic (TA) oscillators that interfere with each other through acoustic radiation. A bifurcation diagram containing both asynchronous and synchronous states is first mapped out by changing the end-to-end distance and the resonator length difference. It is found that the two TA oscillators are analogous to mutually coupled van der Pol oscillators with reactive coupling. Then, the dynamic characteristics of beating and periodic oscillations in asynchronous and synchronous states are analysed separately to facilitate the comprehension of the synchronization process. This research demonstrates that the CFD methodology provides a valuable numerical tool for studying the synchronization of thermally induced acoustic oscillations in TA systems.

Transition to chaos in a two-sided collapsible channel flow

The nonlinear dynamics of a two-sided collapsible channel flow is investigated by using an immersed boundary-lattice Boltzmann method. The stability of the hydrodynamic flow and collapsible channel walls is examined over a wide range of Reynolds numbers $Re$ , structure-to-fluid mass ratios $M$ and external pressures $P_e$ . Based on extensive simulations, we first characterise the chaotic behaviours of the collapsible channel flow and explore possible routes to chaos. We then explore the physical mechanisms responsible for the onset of self-excited oscillations. Nonlinear and rich dynamic behaviours of the collapsible system are discovered. Specifically, the system experiences a supercritical Hopf bifurcation leading to a period-1 limit cycle oscillation. The existence of chaotic behaviours of the collapsible channel walls is confirmed by a positive dominant Lyapunov exponent and a chaotic attractor in the velocity-displacement phase portrait of the mid-point of the collapsible channel wall. Chaos in the system can be reached via period-doubling and quasi-periodic bifurcations. It is also found that symmetry breaking is not a prerequisite for the onset of self-excited oscillations. However, symmetry breaking induced by mass ratio and external pressure may lead to a chaotic state. Unbalanced transmural pressure, wall inertia and shear layer instabilities in the vorticity waves contribute to the onset of self-excited oscillations of the collapsible system. The period-doubling, quasi-periodic and chaotic oscillations are closely associated with vortex pairing and merging of adjacent vortices, and interactions between the vortices on the upper and lower walls downstream of the throat.

Cantilever self-excited with a higher mode by a piezoelectric actuator

The sensitivity of vibration-type sensors can be improved using a higher resonating frequency of a cantilever resonator. Resonance in such systems can be achieved using a self-excited oscillation, which overcomes the difficulty of using an external excitation in viscous environments. To enhance the sensitivity of cantilever resonators, several groups have proposed ways to increase the natural frequency of the first mode by changing the cantilever geometry. However, the sensitivity can be further improved by using a self-excited oscillation with a higher mode in addition to the geometry-changing technique. In this study, we present a method to realize this goal. We perform a nonlinear analysis of the governing equation of a cantilever excited by a piezoelectric actuator. For each mode, we also clarify the dependence of the critical feedback gain on the location of a displacement sensor, the output of which is used for feedback control. With the aid of filters, we then devise a way to generate a self-excited oscillation with a higher mode associated with a desired higher natural frequency. Finally, we carry out experiments using a macro-cantilever and report the observation of a self-excited oscillation with the second natural frequency, which is higher than the first natural frequency.

Investigation of the Jet Characteristics and Pulse Mechanism of Self-Excited Oscillating Pulsed Jet Nozzle

Self-excited oscillation pulse jet technology is widely used to clean sediment from oil storage tanks. Its successful application is dependent on jet performance. As the cleaning requirements of the oil industry increase, it is necessary to optimise the structure of self-excited oscillation pulsed jet nozzles (SOPJNs) to optimise cleaning and energy efficiencies. In this study, the jet performance of a SOPJN is modelled and analysed based on computational fluid dynamics with consideration of a large eddy simulation and homogeneous cavitation. The modelling results are highly consistent with experimental results. The effects of the SOPJN’s inlet diameter, cavity diameter, cavity length, wall reflection angle, and inlet pressure on the jet’s peak velocity, oscillation frequency, and cavitation number were analysed. The results show that the oscillation frequency decreases with the increase of the inlet diameter d1, cavity diameter D, cavity length L and reflection angle of wall α. Optimisation of the SOPJN inlet diameter, cavity length, and wall reflection angle produced a jet with a high peak velocity and strong cavitation. The optimal nozzle cavity diameter strengthens cavitation, while the peak velocity fluctuates as the cavity diameter increases. The peak velocity increases with the inlet pressure, while the increasing rate of the peak velocity decreases. The results of this study can be used in the design and optimisation of similar nozzle structures for improved pulse jet cleaning.

Study on a Heuristic Wheelset Structure without Rail Corrugation on Sharply Curved Tracks

Rail corrugation on low rails of sharp railway curves is still a difficult problem to solve worldwide. Nearly all low rails of the sharp railway curves incur rail corrugation. In the present study, an active method to remedy rail corrugation was studied. From the viewpoint of the frictional self-excited oscillation of a wheelset-track system causing rail corrugation, the effect of wheelset structures on rail corrugation was studied. Three frictional self-excited oscillation models of wheelset-track systems with different wheelset structures were established, which include a heuristic wheelset structure and two being used in the railway industry. The incidence trends of the self-excited oscillations of these three wheelset-track systems were studied. It was found that the wheelset structure has an important effect on rail corrugation, and that the heuristic wheelset structure can restrain or get rid of rail corrugation. With the parameter sensitivity analysis, it was found that when the friction coefficient between the wheel and rail, rail gauge, rail cant, and sleeper span changes to some extent, the heuristic wheelset structure is robust enough to prevent rail corrugation. The proposed heuristic wheelset structure can be used as a potential solution to rail corrugation on sharply curved tracks.

Control of the oscillations of shock train using boundary layer suction

The isolator plays a major role in the scramjet engine by providing suitable pressure for the combustion process. It is situated between the inlet and the combustion chamber. The deceleration of supersonic flow into subsonic flow is achieved by a series of bifurcated normal shock waves referred to as “shock train”. The flow field is more complex with shock–shock interaction and shock boundary layer interaction. The presence of such flow inside the isolator can degrade the performance of the scramjet engine. The present study focuses on the self-excited shock train flow in an isolator and its control by partial removal of the boundary layer. The results examine the variation of the inlet to outlet pressure ratio with and without suction flow control. Numerical results indicate that the boundary layer suction will cause downstream movement of the shock train and the length of the shock train is reduced. The transformation of the shock train into a single curved normal shock is observed when the shock train present closer or upstream of the suction slot region. The obtained result shows the self-excited oscillation frequency in the range of 14-15 Hz. The suction control provides an advantage by 50% reduction in the amplitude of the shock train movement.

Numerical investigation on the control of cryogenic fluid oscillations by applying an external sound source

Self-excited oscillations that occur in the cryogenic helium tube system are seen as thermoacoustic instabilities. To increase the operation stability of the system and suppress the conversion of thermal energy into acoustic waves, one solution where an external sound source driven by a piston is applied to control oscillations in a helium tube system. In this work, a numerical study of minimizing self-excited oscillations is conducted. Oscillation frequency and amplitude of the coupling system of the helium tube system and the external sound source are acquired as functions of the piston speed and frequency. It is found that the suppression of pressure oscillations can be achieved when the driving frequency is far from the self-excited oscillation frequency of the cryogenic helium tube. Increasing the driving speed of the piston gives rise to the coupling oscillation amplitude, and the control strategy leads to 99.2% oscillation amplitude reduction. Moreover, the nonlinear dynamics behavior caused by the coupling of self-excited oscillations and the external sound source is revealed. Synchronization of frequency occurs when the system is coupled to the external sound source oscillating with different frequencies. Our findings could provide a guideline in minimizing self-excited oscillations in the cryogenic helium system.

Linear and nonlinear modeling of self-excited acoustic oscillations in a T-shaped thermoacoustic engine

Branch tubes are often used in thermoacoustic engines (TAEs) for acoustic power extraction or acoustic field adjustment. Their roles, although critical for the performance of the thermoacoustic system, are not fully understood yet. To address this issue, this study investigates the self-excited acoustic oscillations inside a T-shaped TAE where a branch tube is connected to a classical standing-wave TAE. First, system-level theoretical models based on the linear acoustic and thermoacoustic theories in the frequency domain were established to study the acoustic modes and their stability. System-wide computational fluid dynamics (CFD) simulations were carried out to simulate the evolution of the unstable acoustic modes from the initial start-up to the steady state in the time domain. Second, parametric studies on the coupling position of the branch tube and its length were conducted. The effects of the coupling position and branch length on the natural frequencies and mode shapes of the T-shaped TAE were determined by theoretical derivations and substantiated by CFD simulations. The growth/attenuation rate of each acoustic mode was also examined. The CFD results show that bifurcation in steady-state dynamics occurs when the coupling position is altered or the branch length is increased. The steady-state behavior of the T-shaped TAE can transit from limit-cycle oscillations to quasi-periodic oscillations, or vice versa. The theoretical and CFD methodologies in this work are valuable in comprehending the acoustic/dynamic characteristics of the T-shaped standing-wave TAE, providing useful guidelines for studying the coupling of external loads in traveling-wave thermoacoustic systems that usually have more complex structures but are inherently more efficient.

A combined oscillation cycle involving self-excited thermo-acoustic and hydrodynamic instability mechanisms

The paper examines the combined effects of several interacting thermo-acoustic and hydrodynamic instability mechanisms that are known to influence self-excited combustion instabilities often encountered in the late design stages of modern low-emission gas turbine combustors. A compressible large eddy simulation approach is presented, comprising the flame burning regime independent, modeled probability density function evolution equation/stochastic fields solution method. The approach is subsequently applied to the PRECCINSTA (PREDiction and Control of Combustion INSTAbilities) model combustor and successfully captures a fully self-excited limit-cycle oscillation without external forcing. The predicted frequency and amplitude of the dominant thermo-acoustic mode and its first harmonic are shown to be in excellent agreement with available experimental data. Analysis of the phase-resolved and phase-averaged fields leads to a detailed description of the superimposed mass flow rate and equivalence ratio fluctuations underlying the governing feedback loop. The prevailing thermo-acoustic cycle features regular flame liftoff and flashback events in combination with a flame angle oscillation, as well as multiple hydrodynamic phenomena, i.e., toroidal vortex shedding and a precessing vortex core. The periodic excitation and suppression of these hydrodynamic phenomena is confirmed via spectral proper orthogonal decomposition and found to be controlled by an oscillation of the instantaneous swirl number. Their local impact on the heat release rate, which is predominantly modulated by flame-vortex roll-up and enhanced mixing of fuel and oxidizer, is further described and investigated. Finally, the temporal relationship between the flame “surface area,” flame-averaged mixture fraction, and global heat release rate is shown to be directly correlated.

A numerical-analytical iterative method for solving an electrical oscillator equation

Self-excited oscillation problem occurring from a triode electrical circuit has been modelled by van der Pol. Until now, the exact solution to the van der Pol equation is not available. This paper focuses on finding a new method for solving the van der Pol equation simply and accurately. There exists several approximate iterative methods available in the literature for solving the van der Pol equation, such as, the successive approximation method. The successive approximation method is simple, but inaccurate for large time values. In this paper, we propose a new variant of numerical-analytical method, which is simple but accurate, for solving the van der Pol equation. Our new variant of numerical-analytical method solves the van der Pol equation from its equivalent system of first order ordinary differential equations. Our strategy leads to a simple implementation of the numerical-analytical method in the multistage way. Furthermore, computational experiments show that our proposed method is accurate for large sizes of time domain in solving the van der Pol equation.

PFC-Based Control of Friction-Induced Instabilities in Drive Systems

This paper is concerned with control-based damping of friction-induced self-excited oscillations that appear in electromechanical systems with an elastic shaft. This approach does not demand additional oscillations measurements or an observer design. The control system provides the angular velocity and damping control via the combination of a parallel feed-forward compensator (PFC) and adaptive λ-tracking feedback control. The PFC is designed to stabilize the zero dynamics of an augmented system and renders it almost strict positive real (ASPR). The proposed control approach is tested in simulations.

Multiple Steady and Oscillatory Solutions in a Collapsible Channel Flow

In this paper we study flow driven through a finite-length planar rigid channel by a fixed upstream flux, where a segment of one wall is replaced by a pre-stressed elastic beam subject to uniform external pressure. The steady and unsteady systems are solved using a finite element method. Previous studies have shown that the system can exhibit three steady states for some parameters (termed the upper, intermediate and lower steady branches, respectively). Of these, the upper and lower are stable to non-oscillatory perturbations, while the intermediate branch is always unstable. These upper and lower steady branches can (independently) become unstable to self-excited oscillations. We show that for some parameter combinations the system is unstable to both upper and lower branch oscillations simultaneously. However, we show that these two instabilities eventually merge together for large enough Reynolds numbers, exhibiting a nonlinear limit cycle which retains characteristics of both the upper and lower branches of oscillations. Furthermore, we show that increasing the beam pre-tension suppresses the region of multiple steady states but preserves the onset of oscillations. Conversely, increasing the beam thickness (a proxy for increasing bending stiffness) suppresses both multiple steady states and the onset of oscillations.

Subcritical Andronov-Hopf scenario for systems with a line of equilibria.

Using numerical simulation methods and analytical approaches, we demonstrate hard self-oscillation excitation in systems with infinitely many equilibrium points forming a line of equilibria in the phase space. The studied bifurcation phenomena are equivalent to the excitation scenario via the subcritical Andronov-Hopf bifurcation observed in classical self-oscillators with isolated equilibrium points. The hysteresis and bistability accompanying the discussed processes are shown and explained. The research is carried out on an example of a nonlinear memristor-based self-oscillator model. First, a simpler model including Chua's memristor with a piecewise-smooth characteristic is explored. Then, the memristor characteristic is changed to a function being smooth everywhere. Finally, the action of the memristor forgetting effect is taken into consideration.

Light-powered self-excited oscillation of a liquid crystal elastomer pendulum

Light-powered self-oscillation of liquid crystal elastomers(LCEs) has been extensively utilized in designing the promising and superb opto-mechanical systems and architectures with marvelous forms and functions, due to its diverse advantages, e.g. direct energy harvesting from the environment for motion actuation of active machines, generating periodic motion without additional human control, reducing system complexity and fulfilling portability. In this paper, the nonlinear dynamic model for light-powered motion of an LCE pendulum is originally proposed and self-excited oscillation can be triggered under constant illumination with the longitudinal contraction and relaxation of LCE fiber periodically. The self-sustained motion can be explained by the mechanism of positive linear damping and negative nonlinear damping which corresponds to a positive net work done by the LCE fiber. Various limit cycles and critical conditions for provoking self-excited oscillation are quantitatively presented for distinct physical parameters. The results show that self-excited oscillation can be regulated and controlled through the illumination angle, the initial angular velocity, the nondimensionalized damping coefficient, the nondimensionalized acceleration, the contraction coefficient and the light intensity. Furthermore, the period and the amplitude of self-excited oscillation generally depend on the intrinsic properties of the system, which possesses the great robustness. The nonlinear opto-mechanical vibration system of LCE pendulum proposed in this study can be applied to sensing environment, energy harvesting and motion actuation of active machines, etc.

Study on Passive Control of the Self-excited Thermoacoustic Oscillations Occurring in Combustion Systems

ABSTRACT Self-excited thermoacoustic oscillations seriously threaten the operation of combustion equipment. Various active and passive control methods for self-excited thermoacoustic oscillations have been proposed, while most existing methods are complex and difficult to implement. A new passive control method was expected to be proposed in the present study. The thermoacoustic oscillations occurring in asymmetrical two-dimensional combustion systems were investigated numerically. The control effects of the asymmetrical fuel-air feed conditions on thermoacoustic oscillations were examined. In addition, experimental tests were performed to further examine the control effects. The results showed that the oscillations would be encouraged in an asymmetrical combustion system if an appropriate standing wave was formed. The asymmetrical fuel-air feed conditions could affect the waveform and consequently influence the occurrence of thermoacoustic oscillations. The oscillations could be eliminated by adjusting the length or the inlet boundary condition for half of the fuel-air feed channels, and the combustion chamber did not need to be retrofitted. The passive control method was simple and easy to implement for eliminating thermoacoustic oscillations.

Nonlinear feedback self-excitation of modal oscillations in a class of under-actuated two degrees-of-freedom mechanical systems

Recently, scientists have utilized self-excited oscillations in many mechanical and micromechanical applications and accordingly, several experimental and theoretical research activities have been undertaken with the objective of artificially inducing self-excited oscillation in mechanical systems. This paper considers some theoretical aspects of generation of self-excited oscillation in a two degrees-of-freedom under-actuated spring–mass–damper system by centralized nonlinear feedback. The control force depends on the response of both masses. The proposed control law is slightly general in nature as it entails both collocated and non-collocated control as special cases. The response of the nonlinear feedback control is studied with the help of the method of averaging. The present study shows that by appropriately selecting the control gains it is possible to excite the desired mode(s) of oscillation irrespective of initial conditions. Even it is possible to excite dual mode oscillation having the characteristics of quasiperiodic oscillations. The theoretical analysis of the dynamics of the system with the control is validated by simulation results, performed in MATLAB Simulink.

Suppression of ground resonance in rotorcraft using active landing gear

This article examines the fundamental aspects of controlling ground resonance in rotorcraft equipped with actively controlled landing gear. Ground resonance is a mechanical instability affecting rotorcraft on the ground. It occurs at certain rotor speeds, where the lead–lag motion of the rotor couples with the motion of fuselage creating a self-excited oscillation. Typically, passive or semi-active lag dampers are used to avoid instability; however, these are undesirable from a design and maintenance perspective. Innovations in active landing gear for rotorcraft, such as articulated robotic legs, have provided an alternate approach to avoid the instability, eliminating the need for lag dampers with respect to ground resonance. This article extends classic ground resonance to include movable landing gear and identifies key physical parameters affecting dynamic behavior. Applying LQ optimal control to this model, it is shown that ground resonance instability can be eliminated using active landing gear as the control mechanism, even when there is no lag damping present in the rotor. In addition, while superior performance is achieved when landing gear movement can occur both longitudinally and laterally, it is still possible to stabilize ground resonance with inputs in a single direction, albeit with reduced performance.

Numerical simulation of the unsteady cavitating flow in a Francis turbine draft tube at Upper-Part-Load (UPL) conditions

At part-load conditions, Francis turbines experience the development of a precessing vortex rope in their draft tube (DT), rotating with a frequency between 0.2 and 0.5 times the runner frequency. It induces pressure pulsations at the precession frequency in the whole hydraulic system, undesirable vibrations and noise putting at risk the stability of the system and the lifetime of the machine components. In specific machines, a dramatic amplification of the noise and vibrations can be observed between 70% and 85% of the design conditions. In these cases, synchronous pressure pulsations with a high frequency, typically between 2 and 4 times the runner frequency, are observed, referred to as the so-called Upper-Part-Load (UPL) pulsations. These pulsations are induced by a self-excitation of the entire hydraulic system including the cavitation vortex rope at one of its high order eigenmodes. Besides, the cavitation vortex rope features an elliptical cross-section rotating around the vortex axis at a high frequency. In this manuscript, unsteady two-phase flow simulations using a Scaled-Adaptive-Simulation (SAS) turbulence model and ZGB cavitation model of a Francis turbine draft tube at 80% of the design condition are performed to clarify the mechanisms responsible for the formation of the elliptical shape of the vortex and the UPL pulsations. However, the numerical simulation with a constant inlet boundary condition cannot reproduce the UPL pulsation phenomenon since it is a self-excited oscillation at one eigenmode of the complete system, which is not considered. Therefore, the UPL pulsations component is extracted from the measured pressure fluctuations data by applying a band-pass filter and is then set as the inlet boundary condition in the numerical simulation. The flow field is therefore artificially excited which aims to confirm whether the same phenomenon can be observed and to compare with the flow field obtained with constant inlet boundary condition. The numerical simulations are validated by experimental results, and the wave propagation in the DT is clarified.

Self-excited Vibration of Ink Rollers

A vibration having a character of self-excited chatter oscillation known from machine tools is observed during intermittent motion of ink rollers of offset printing machines. This vibration occurs under specific operating conditions and is often accompanied by an increased noise level. To explain this unusual vibration behavior, a simple analytical model of two rollers interaction is derived. The calculated oscillation is compared with the measurement of ductor roller displacement. The model results confirm the possibility of self-excited vibration development in the presence of viscous forces, negative damping effects and continuous supply of external energy from roller rotation.