Frequency Lock Research Articles

Zero-Offset Frequency Locking of Lasers at Low Optical Powers With an Optical Phase Locked Loop

Zero-Offset Frequency Locking of Lasers at Low Optical Powers With an Optical Phase Locked Loop

Real-Time Frequency-Tracking Method Based on Interpolated Kalman Filter Using Vibration and Surface Noise

The variation of frequency is a significant indicator of the operation status of rotating machinery. Generally, the frequency is extracted and tracked in real-time based on the vibration signal produced by the rotating machinery. However, various interferences generated from contact sampling and transmitting result in difficulty in obtaining the frequency correctly in real-time from the vibration. To solve this problem, this paper presents an interpolated Kalman filter (IKF) based on the vibration and surface noise signals for real-time frequency tracking. First, the cross-correlation operation is performed on the vibration and surface noise signals sampled synchronously to enhance the energy concentration. After that, a frequency search procedure is carried out to calculate the input of the tracking task. Finally, an IKF-based frequency lock procedure is applied to eliminate the interferences and track the frequency in real time. Besides, a correction procedure is added to prevent the measurement process from tracking the frequency incorrectly. The performance of the proposed method is verified by the experiments based on an ARM-based test bench using standard signals and actual test signals.

Investigations on bifurcation behavior of wind turbine airfoil response at a high angle of attack

Design load and vibration for parked conditions are gaining in importance for large-scale modern wind turbines with increasing flexibility, especially edgewise vibration when the blade is at a high angle of attack. In this work, flow-induced vibration of the wind turbine airfoil at 90 degrees of attack angle is studied with the fluid-structure interaction (FSI) simulation. The unsteady aerodynamic force due to flow separation and vortex shedding at the high angle of attack causes the chordwise vibration of the airfoil. When the vortex shedding frequency fv gets close to the chordwise natural frequency fn of the airfoil, vortex-induced vibration (VIV) of high amplitude occurs accompanied with the frequency lock-in phenomenon. In the post lock-in regime, it is found that period-3 and torus bifurcation occur successively and the vibration response becomes aperiodic. Dynamic mode decomposition(DMD) technique is used to investigate the mechanism of bifurcation from the perspective of energy balance, through analyzing the vorticity field in the wake and pressure distribution on the airfoil surface. For the certain incoming velocity in the post lock-in regime, since the frequency of the DMD mode f=2fv/3 is close to the natural frequencyfn, both the vibration of frequency 2fv/3 and fv get excited, leading to the onset of bifurcation. The Lissajou curves are obtained through reconstructing the transient pressure of each DMD mode, which indicates that energy transfer mainly exists in modes f=fv. In addition, the reconstructed Lissajou curves based on the leading DMD modes agree well with the original time-domain Lissajou curves.

Improved VIV energy harvesting with a virtual damper–spring system

In recent years, energy harvesting systems driven by vortex induced vibrations (VIV) emerged as potential alternative to conventional rotor-based installations, in particular for low flow speeds in water. Best energy outputs are obtained when the flow-dependent VIV frequency locks in the natural frequency of the energy harvesting structure. However, placed in tidal currents or rivers with variable flow rates, the VIV frequency changes, leading to frequency mismatch with efficiency losses. In this paper, we present a new mechatronic experimental set-up to study the harvesting efficiency of a VIV driven cylinder under various flow rates. In particular, we explore options to improve harvesting efficiency by adding computer controlled virtual damping and stiffness to the mechanical system. The setup comprises an elastically mounted, single-degree-of-freedom cylinder within a low-speed water tunnel. Virtual damping and stiffness are applied by controlling the force exerted through a mechanically coupled DC motor. The experiments reveal that optimal values for damping and stiffness are consistent with previous results from the literature. The maximum energy conversion efficiency of around 18% is achieved when oscillation and vortex shedding frequencies are synchronized. The explored parameter space highlights in particular that mismatches between oscillation and vortex shedding frequency strongly decrease the achievable efficiency. By contrast, the peak efficiency is less sensitive to an increase of damping due to energy harvesting. All these observations suggest that VIV driven energy harvesting systems need a real-time structural stiffness control to maintain an economically acceptable efficiency under various flow conditions. In the near future, we plan to automate the structural stiffness control under various flow rates by testing Machine Learning algorithms with our mechatronic set-up.

Adaptive control of transonic buffet and buffeting flow with deep reinforcement learning

The optimal control of flow and fluid–structure interaction (FSI) systems often requires an accurate model of the controlled system. However, for strongly nonlinear systems, acquiring an accurate dynamic model is a significant challenge. In this study, we employ the deep reinforcement learning (DRL) method, which does not rely on an accurate model of the controlled system, to address the control of transonic buffet (unstable flow) and transonic buffeting (structural vibration). DRL uses a deep neural network to describe the control law and optimizes it based on data obtained from interaction between control law and flow or FSI system. This study analyzes the mechanism of transonic buffet and transonic buffeting to guide the design of control system. Aiming at the control of transonic buffet, which is an unstable flow system, the control law optimized by DRL can quickly suppress fluctuating load of buffet by taking the lift coefficient as feedback signal. For the frequency lock-in phenomenon in transonic buffeting flow, which is an unstable FSI system, we add the moment coefficient and pitching displacement to feedback signal to observe pitching vibration mode. The control law optimized by DRL can also effectively eliminate or reduce pitching vibration displacement of airfoil and buffet load. The simulation results in this study show that DRL can adapt to the control of two different dynamic modes: typical forced response and FSI instability under transonic buffet, so it has a wide application prospect in the design of control laws for complex flow or FSI systems.

Fluid and Structure Coupling Analysis on Frequency Locking of an Elastic Hydrofoil

Vortex-induced vibration (VIV) has always been a significant research topic in relation to marine structures, with structural resonance and locking vibrations liable to occur at particular Reynolds numbers. To investigate this problem, fluid–structure coupling simulations of an elastic hydrofoil within a viscous flow are conducted. The correlation between the structural response and vortex shedding was explored. By analyzing the frequency eigenvalues, the structural response and vortex shedding at different frequencies can be decoupled. The findings suggest that the self-sustainability of natural vibration plays a significant role in frequency lock-in once structural resonance has been triggered. The phase difference between the lift pulsation and vortex shedding is determined, and is confirmed to be a significant factor influencing the resonant vibration of elastic foils. This phase difference can be used to determine whether the lock-in phenomenon has occurred. It is also found that veering phase, the resonance appears as forced vibration, while at locking phase, the resonance appears as self-sustained vibration at a natural frequency.

Nonlinear shock-induced flutter of a compliant panel using a fully coupled fluid-thermal-structure interaction model

A comprehensive study has been conducted on the fully coupled aero-thermo-elastic interaction between a shock wave and a laminar boundary layer over a flexible surface with different thermal conditions. In this investigation, the flow is characterized by an oblique impinging shock on a laminar boundary layer over a compliant panel with a cavity pressure and temperature. To model the fluid–structure interaction (FSI), we have combined a finite element model of the structure with a high-order sharp interface immersed boundary method implemented in a finite-difference flow solver. We have analyzed the behavior of the FSI coupling over a wide range of parameters and various boundary conditions while the panel undergoes relaxation to its unexcited state or exhibits limit cycle oscillations. Notably, the panel oscillation and the fluctuations in the shear layer exhibit strong coupling and demonstrate a lock-in resonance frequency response. The colder wall conditions result in a reduced separation bubble and a raised aerodynamic pressure difference between the maximum and minimum instantaneous dynamic pressures, consequently amplifying the amplitude of panel oscillation. For the cases with thermal coupling, the behavior of panel oscillation is notably influenced by specific heat and thermal expansion coefficients. In these scenarios, the thermal state of the solid material emerges as the pivotal factor governing the sustained oscillation of the panel. The non-linear impact of the thermal dependency of the structural properties plays a crucial role in determining the stability of the coupled FSI system. The study revealed that the stable decaying sinusoidal oscillation undergoes a transformation into a limit-cycle oscillation when panel stiffness is affected by reduced temperature. During the sustained oscillation, a mode switch is observed between the first and second modes of deformation of the panel.

Dynamics of nonlinear beam-propeller system with different numbers of blades

The dynamics of elastic systems coupled with rotating bladed-rotors is rich and complex, and the blade number may have an influence on the in-vacuo system dynamics. This paper aims to model its nonlinear dynamics in-vacuo and study the effects of blade number on its dynamics. To this end, a nonlinear model consisting of a nonlinear inextensible beam, a motor assembly and a rotating propeller is developed. This model is linearized, and modal analyses are performed with different blade numbers. It is validated numerically and experimentally that a two-bladed propeller introduces time-varying characteristics, while the system is time-invariant with more than two blades. For the two-bladed case, frequencies in the non-rotating condition split into two frequency loci with increasing rotational speed; while with more than two blades, one frequency in the non-rotating condition increases and the other in the same pair decreases with increasing speed. A structural instability due to frequency lock-in is identified in two-bladed configuration, while not identified with more than two blades. The static deformation using the nonlinear model is calculated and validated against the experiment. In the stable speed range, the frequency response functions calculated using the nonlinear and linearized models do not show notable differences. In the unstable speed range with two-bladed propeller, the nonlinear model is consistent with the experiment in terms of unstable frequencies and bounded steady-state oscillations. The system vibration in the unstable speed range features forward whirling pattern, in which the beam vibration is close to the first bending pattern.

2-DOF vortex-induced vibration of two rigidly-connected cylinders in parallel and tandem arrangements by a Cartesian grid method

A Cartesian grid fluid structure interaction (FSI) method with GPU acceleration is presented to simulate the vortex induced vibration (VIV) of two rigidly-connected cylinders in parallel and tandem arrangements. A highly efficient ghost cell method is adopted to treat arbitrary moving boundaries, and the motion equations of 2-DOF (Two-Degree-Of-Freedom) are solved by a RK4 (fourth-order Runge-Kutta) scheme. We investigated the variation pattern of the reduced velocity with the motion and dynamic responses, the phase switching, and the wake mode under three gap distances, two arrangements, and two mass ratios. It is found that the frequency lock-in occurs in a significantly larger reduced velocity for two cylinders compared with the single cylinder. The maximum response amplitudes of the displacement and force coefficients on two cylinders can be larger or smaller than those on the single cylinder depending on the tested conditions. Also, the soft lock-in phenomenon is observed for a small gap distance. Phase switching occurs several times for a large gap distance due to the wake effects. Furthermore, diverse wake modes are observed including merging, splitting, and impinging of the vortices. Especially, a new wake mode is found at a medium gap distance in the parallel arrangement.

The Gardner Problem on the Lock-In Range of Second-Order Type 2 Phase-Locked Loops

Phase-locked loops (PLLs) are nonlinear automatic control circuits widely used in telecommunications, computer architecture, gyroscopes, and other applications. One of the key problems of nonlinear analysis of PLL systems has been stated by Floyd M. Gardner as being “to define exactly any unique lock-in frequency.” The lock-in range concept describes the ability of PLLs to reacquire a locked state without cycle slipping and its calculation requires nonlinear analysis. The present work analyzes a second-order type 2 phase-locked loop with a sinusoidal phase detector characteristic. Using the qualitative theory of dynamical systems and classical methods of control theory, we provide stability analysis and suggest analytical lower and upper estimates of the lock-in range based on the exact lock-in range formula for a second-order type 2 PLL with a triangular phase detector characteristic, obtained earlier. Applying phase plane analysis, an asymptotic formula for the lock-in range which refines the existing formula is obtained. The analytical formulas are compared with computer simulation and engineering estimates of the lock-in range. The comparison shows that engineering estimates can lead to cycle slipping in the corresponding PLL model and cannot provide a reliable solution for the Gardner problem, whereas the lower estimate presented in this article guarantees frequency reacquisition without cycle slipping for all parameters, which provides a solution to the Gardner problem.

Numerical study on weakening vortex-induced vibration of semi-ring diversion type component

Conventional spoiler components are commonly employed to mitigate vortex-induced vibration (VIV), but their effectiveness varies significantly. Therefore, detailed comparative studies should be made between different components and a more comprehensive suppression method will be proposed. In this paper, numerical simulations are conducted to explore the weakening effect of hydrodynamic shapes on VIV of structures. Different spoiler components, including rectangular spoiler, fairing, and fin plate are investigated, and for further optimization, a novel concept of semi-ring diversion type component is proposed. The attenuation effects of different components on vibration are compared. In addition, sensitivity analyses of the diversion component, including slit width (XW), front angle (α), and nozzle size (BL), are conducted at various reduced velocities to determine the optimal sizes. Results indicate that traditional spoiler components have inherent shortcomings in terms of weakening efficiency, which can only reduce the maximum resonance value (Ay(max)) to 50%–77%, extend the dimensionless critical velocity (Ucr) by −0.5–1.5, and shorten the length of frequency lock-in interval to 2.5–3, compared to the bare cylinder. The diversion component effectively reduces the frequency of vortex shedding around the cylinder. The optimal vibration damping effect is achieved when XW = 0.03, α = 60°, and BL = 0.11. Compared to the bare cylinder, the structure shows a substantial reduction in resonant frequency by 69%, a threefold decrease in the length of the frequency lock-in interval, a 68.2% reduction in Ay(max) and a delay in Ucr of 2.65, demonstrating a potential mitigation device for VIV.

An improved van der Pol wake oscillator model for a 1DOF circular cylinder undergoing vortex induced vibrations

An optimization procedure is presented for prescribing the empirical coupling parameters of a modified coupled van der Pol (VDP) wake oscillator and mass–spring–damper system for a one degree of freedom (1DOF) circular cylinder system undergoing vortex induced vibrations (VIV). This approach allows for the generalization of the traditional VDP model to cover a large VIV parameter range. The procedure is developed using experimental data covering the parameter space: 3<U∗<11, 8<m∗<20, 0.003<ζ<0.063, ReD=4000. The VDP model contains empirical coupling coefficients that describe the regime specific dynamic damping, ϵ, and wake coupling, β. Two calibration procedures are considered and the improvements over the traditional VDP model in predicting the VIV response are discussed. Subsequently, a regression fit is used to prescribe the two empirical coupling coefficients as functions of m∗, ζ and U∗. The generalized model results in a better prediction of the VIV response in terms of identification of lock-in regimes, lock-in frequency and amplitude response over several regimes when compared to the classical models. The use of a functional representation replaces the need for using tables and reduces user input for determining regime-specific coupling coefficients.

Adaptation of the Facchinetti, de Langre and Biolley model for the hydroelastic vortex-induced vibrations of a cantilevered flat plate

This paper examines the ability of coupled system models, derived from the Facchinetti, de Langre and Biolley model, to fit the vortex-induced vibrations observed on a cantilevered rectangular flat plate, with zero angle of attack, in a hydrodynamic tunnel. Two VIV areas have been scrutinized. The first one for 0.6×105≤Re≤105 and the second one for 4.5×105≤Re≤7×105 where two distinct hydrodynamic excitation mechanisms, characterized by two Strouhal numbers, successively lock the first bending and first torsional mode of the plate respectively. For the bending VIV, exhibiting weak fluid–structure coupling, good results were obtained using a hybrid model for which a structure oscillator forced at ωv1=2πSt1U/D is coupled with a wake oscillator associated to the second Strouhal number. Regarding the torsional VIV, amplitude response and successive frequency lock-in have been satisfactorily reproduced using a structure oscillator (in rotation) coupled with two distinct wake oscillators.

Nonlinear vortex-induced vibration of wind turbine towers: Theory and experimental validation

Vortex-induced vibration (VIV) of wind turbine tower is a common occurrence in practical engineering, significantly impacting the safety and reliability of structure. An effective method is developed to investigate the VIV characteristics of a wind turbine tower with an elastic foundation and a lumped mass. To simulate the fluid–structure interaction, the van der Pol equation is utilized. The equations of motion of wind turbine tower, accounting for aerodynamic force, are established using Hamilton’s principle and the assumed mode method, and they are solved by the method of multiple scales. Modal functions of the wind turbine tower are obtained through the finite element method (FEM). The analysis further explores the influences of various parameters on the VIV characteristics of wind turbine tower. The results show that the VIV occurs within the frequency lock-in and multi-value ranges, and the critical wind speeds are mainly determined by the diameters of the segments near the tower top. Moreover, as the lumped mass increases or the foundation stiffness decreases, the occurrence of VIV shifts to lower wind speeds. A wind tunnel experiment of a scaled wind turbine tower model validates the frequency lock-in range of the VIV analysis results.

On the Added Modal Coefficients of a Rotating Submerged Cylinder Induced by a Whirling Motion—Part 1: Experimental Investigation

The operation of submerged rotating machines, such as marine current or tidal turbines, can present deleterious fluid phenomena that may provoke extreme structural vibrations. To predict their dynamic responses, it is necessary to know the added modal coefficients of their runners under a whirling motion. For that purpose, a bespoke test rig was designed to investigate the added modal coefficients of a submerged cylinder, which could rotate at different speeds both in air and completely submerged in water inside a cylindrical tank. First, the modes of vibration were experimentally measured by exciting the cylinder with a push-release method during steady tests or with ramps in rotating speed during transient tests. The calculated natural frequencies and damping ratios were then used in a mathematical model of the dynamic system to calculate the added modal coefficients. During steady tests, the natural frequencies and damping ratios of the whirling modes changed significantly as a function of the rotating speed. Additionally, a whirling mode was observed to change its direction at a given rotating speed. During transient tests, rotating speed ramps with high accelerations were found to present lower lock-in amplitude and frequencies. Moreover, fast downward ramps presented lock-in amplitudes four times higher than fast upward ramps. Consequently, the added modal coefficients changed accordingly as a function of the rotating speed, ramp acceleration, and ramp direction. For these reasons, it was confirmed that the modal responses of submerged rotating bodies must be calculated for each operational rotating speed, even at low velocities, and for each transient event in order to precisely predict their vibration behaviors.

Experimental investigation of transonic buffeting, frequency lock-in and their dependence on structural characteristics

Transonic buffet is a phenomenon that appears in compressible flow around an airfoil and plays a substantial role in the limitation of the flight envelope of commercial aircraft. If the structural natural frequencies of the wing are similar to the buffet frequency, the oscillation of the compression shock, fluid, and structure may interact (transonic buffeting) and lead to strong loads and potential structural failure. Numerical research has shown that structural parameters can have a significant effect on the onset point of shock oscillations as well as on the typology of the fluid–structure interaction, which presented classical structural excitation, modal veering, or frequency lock-in.The aim of this research is a systematic experimental investigation to examine the structural effects and the lock-in phenomenon. It provides a partial validation of the numerical results available in the literature. A lightweight, elastically-suspended wing model (OAT15A profile) was tested in the Trisonic Wind Tunnel Munich. Optical measurement techniques were deployed to non-intrusively observe the flow-induced density gradient field (background-oriented Schlieren) and the structural deformation and displacement of the wing (digital image correlation). Mass ratios varied from 282 to 322 and the half-chord-based, reduced natural pitch frequency ranged from 0.169 to 0.280. The experimental results confirm the existence of frequency lock-in, an interaction dominated by the structural mode that presents high but limited pitch amplitudes for natural pitch frequencies above the natural buffet frequency. The effects of mass ratio and natural pitch frequency on the interaction are discussed. A substantial effect of the mass ratio on the onset of buffeting and the resulting pitch amplitude for frequency lock-in was discovered.

Investigations on lock-in vortex-induced vibration of an airfoil at a high angle of attack based on detached eddy simulation

Large-scale modern wind turbines at standstill are prone to vortex-induced vibration (VIV). In this study, coupled fluid–solid dynamics of the wind turbine airfoil at a 90° attack angle are performed using the detached eddy simulation. The fully developed vibration responses with different structural dampings are explored in detail. The frequency lock-in regime is determined, and the corresponding phase differences between the lift and displacement are presented with the Lissajous curve. The dominant surface pressure mode and wake flow exhibit significant three-dimensional flow characteristics in unlock-in conditions, while a strong spanwise correlation in lock-in conditions is detected. The pressure fluctuation on the suction side in the lock-in state is observed to be more significant than in the unlock-in state. The effect of the distributed airfoil surface pressure on VIV is evaluated by considering the contribution value and the cyclic aerodynamic work density. With the decrease in structural damping, the aerodynamic work near the leading edge gets enhanced and the negative work region is reduced, leading to a higher amplitude of VIV. The beat vibration and hysteresis behavior at the critical reduced velocity are also analyzed in both the time domain and frequency domain.

Nonlinear energy sink-based study on vortex-induced vibration and control of foil-cylinder coupled structure

The interference of blade wake flow can pose a threat to the safety of flexible tower structures. In order to investigate the influence of airfoil position parameters on the VIV characteristics and the vibration reduction effect of nonlinear energy sinks (NES) on the cylinder, a flexible tower under the influence of blade wake flow is used as a reference, and a dynamic simulation model of an airfoil-twin degree-of-freedom cylindrical coupled structure is established based on computational fluid dynamics (CFD), structural dynamics, and nested grid techniques. The accuracy of the numerical model established in this paper is verified by comparing it with experimental data from foreign literature. The calculation results indicate that airfoils in different positions cause changes in the amplitude and frequency ratios of the cylinder and can either delay or enlarge the frequency lock-in interval of the cylinder. Under the influence of airfoil wake, the column experiences more severe vibrations. The NES can absorb the vibrational energy of the cylinder, and setting appropriate NES parameters can reduce the resonance response between the cylinder and the shedding vortices in the wake of the airfoil. This helps to change the shedding mode of the vortex and effectively suppress the VIV of the cylinder.

Spectrally-Sliced Coherent Receiver Utilizing a Gain-Switched Optical Frequency Comb

The spectrally-sliced coherent receiver is an attractive solution for future optical access network applications where cost is a sensitive factor, as it enables reduced bandwidth of the analog front-end components and analog-to-digital convertors when compared to a conventional intradyne coherent receiver. In a proof-of-concept experiment, we demonstrate a single-polarization 50 Gb/s QPSK C-band transmission experiment over 40 km of standard (G.652) fiber using receiver bandwidths as low as 6.25 GHz and also utilize an array of local oscillator lines derived from an injection locked gain-switched optical frequency comb, which can be realized as a compact photonic integrated circuit. This paper also analyses the influence of optical frequency comb properties on the quality of the reconstructed signal. The critical parameters considered in this study include comb power and flatness, mutual comb line coherence, and the comb line suppression ratio after demultiplexing the comb lines. We have shown that with practically achievable comb parameter values, the receiver can operate with less than a 1 dB sensitivity penalty compared to a conventional intradyne receiver. The scheme has the potential to provide a low-cost coherent receiver solution for next-generation access networks.

A Portable Chip-Based NMR Relaxometry System With Arbitrary Phase Control for Point-of-Care Blood Analysis.

In this article, we present a portable NMR relaxometry system optimized for the point-of-care analysis of body liquids such as blood. The presented system is centered on an NMR-on-a-chip transceiver ASIC, a reference frequency generator with arbitrary phase control, and a custom-designed miniaturized NMR magnet with a field strength of 0.29 T and a total weight of 330 g. The NMR-ASIC co-integrates a low-IF receiver, a power amplifier, and a PLL-based frequency synthesizer on a total chip area of 1100 × 900 μm 2. The arbitrary reference frequency generator enables the use of conventional CPMG and inversion sequences, as well as modified water-suppression sequences. Moreover, it is used to implement an automatic frequency lock to correct temperature-induced magnetic field drifts. Proof-of-concept measurements on NMR phantoms and human blood samples show an excellent concentration sensitivity of v[Formula: see text] = 2.2 mM/[Formula: see text]. This very good performance renders the presented system an ideal candidate for the future NMR-based point-of-care detection of biomarkers such as the blood glucose concentration.