Order Harmonics Research Articles

Observation of dynamics of harmonic order self-adaptation in optoacoustically mode-locked fiber laser

Observation of dynamics of harmonic order self-adaptation in optoacoustically mode-locked fiber laser

A coupled dynamics model for studying the outer ring fault characteristics and mechanisms of axle-box bearings in urban rail vehicles

With the rapid and large-scale development of urban rail transit in China, the operational safety of urban rail vehicles is highly concerned. The axle-box bearing, as the core component of vehicle bogies, directly determines the operational safety and quality of vehicles. To ensure the service performance of axle-box bearings, their fault characteristics should be monitored and diagnosed in time. A more realistic and in-depth understanding of fault characteristics is a prerequisite for fault diagnosis. Thus, a double-rows tapered roller bearing (DTRB)-vehicle-track coupled dynamic model was built via the co-simulation in this paper, which comprehensively considers a DTRB model with the localised outer ring raceway fault, as well as the flexibilities of the wheelset, axle-box, and bogie frame. Its correctness and rationality were verified by the theoretical comparison and the field test. The results indicate that the distribution of contact load is consistent with the theoretical value, the fault features of the outer ring raceway can be found in the periodic impulse of the roller-raceway contact load. The slip rates of rolling elements are less than 4.3 %. Compared with the field test, the fault order harmonics in the order spectrum of the simulation are closer to the theoretical fault characteristic order under variable and constant speed conditions, and the maximum error is only 0.37 %. Therefore, the proposed coupled dynamic is correct and can be employed to investigate the fault characteristics of axle-box bearings in urban rail vehicles.

XUV yield optimization of two-color high-order harmonic generation in gases

Abstract We perform an experimental two-color high-order harmonic generation study in argon with the fundamental of an ytterbium ultrashort pulse laser and its second harmonic. The intensity of the second harmonic and its phase relative to the fundamental are varied while keeping the total intensity constant. We extract the optimum values for the relative phase and ratio of the two colors which lead to a maximum yield enhancement for each harmonic order in the extreme ultraviolet spectrum. Within the three-step model, the yield maximum can be associated with a flat electron return time versus return energy distribution. An analysis of different distributions allows to predict the required relative two-color phase and ratio for a given harmonic order, total laser intensity, fundamental wavelength, and ionization potential.

Azimuthal asymmetries in lepton and heavy-quark pair production in UPCs

Azimuthal modulations in lepton and heavy-quark pair production in ultraperipheral collisions (UPCs) of highly charged ions are investigated. The modulations in the azimuthal angles of the sum and difference of the transverse momenta of the pair of particles in the final state, as well as of the transverse impact parameter, arise from the collisions of unpolarized and polarized photons. A full description of the cross section in terms of Generalized Transverse Momentum Dependent parton distributions (GTMDs) for photons is given including a careful consideration of the Fourier transform to impact parameter space. In particular, this leads to a feed-in mechanism among harmonics of different orders, which in principle generates harmonics of all (even) orders. Wherever comparable, our analytical results for the azimuthal modulations agree with those presented in other papers on this topic. Compared to these other works, we separate effects that arise from the anisotropies of the GTMDs from those that do not and retain terms proportional to the mass of the produced particles, as they are relevant for muon, charm and bottom quark production. We show that the normalized differential cross section changes considerably with the produced particle mass, which should be discernible in UPCs at RHIC and LHC. For the numerical results we adopt several models for the photon GTMD correlator, and find that all of them are in fairly good agreement with each other and with UPC data from STAR. We also present results for various azimuthal modulations for RHIC kinematics, where we compare e+e− production with the production of heavier particles, and for LHC kinematics, focusing on μ+μ− production. These results exhibit interesting mass-dependent features in the asymmetries that may help study the anisotropies arising from the underlying photon GTMD description.

Analysis of No‐Load Normal Vibration in Single‐Sided Permanent Magnet Synchronous Linear Motors With Different End Structures

ABSTRACTThis paper investigates the no‐load normal vibrations of single‐sided permanent magnet synchronous linear motors (S‐PMSLMs) with different end structures, addressing a significant gap in the current literature. By employing the Maxwell stress tensor method, analyzes the harmonic orders and frequencies of the no‐load normal force density are analyzed. Comparative research between the comb‐type auxiliary tooth (CTAT) and conventional auxiliary tooth (C‐AT) structures indicates that while the CTAT marginally increases the amplitude of the no‐load normal force density, it significantly reduces harmonic amplitudes and vibration levels. The theoretical and simulation analyses are validated through no‐load vibration experiments, providing valuable insights for the design optimization of S‐PMSLMs, particularly beneficial for high‐speed transportation systems that require high precision and reliability.

Modulating and Carrier-Based Dodecagonal Space Vector Pulse Width Modulation Technique With Fifth and Seventh Order Harmonic Elimination for Split-Phase OEIM

Modulating and Carrier-Based Dodecagonal Space Vector Pulse Width Modulation Technique With Fifth and Seventh Order Harmonic Elimination for Split-Phase OEIM

Modeling and Suppression Method of Low Order Harmonics for Three-Level Inverter With Small Capacitance Value

Modeling and Suppression Method of Low Order Harmonics for Three-Level Inverter With Small Capacitance Value

Experimental Study of the Influence of Even Harmonics on Flame Extinguishing by Low-Frequency Acoustic Waves with the Use of High-Power Extinguisher

The acoustic technique appears to be a novel and innovative way to extinguish flames, in which properly generated waves emitted by a high-power sound source are used for extinguishing purposes. The highest extinguishing efficiency is demonstrated by low-frequency waves. In practice, changing the parameters of the acoustic signal results in the possibility of universal and reusable use of the extinguisher, which is limited only by access to the power supply, unlike the currently known traditional methods of fighting fire (such as gases, foams, and extinguishing powders). The purpose of this paper is to analyze whether flame extinguishing by low-frequency acoustic waves is possible using signals containing higher harmonics with the use of large and very large powers delivered to the sound source, which is a scientific novelty. Analyzing the extinguishing capabilities of low-frequency acoustic waves allows one to fill the gap in the literature. This paper presents the results of research in the range of the influence of even sinusoidal harmonics on the extinguishing of flames originating from organic substances. For this purpose, in the experimental part, a high-power acoustic extinguisher and a point source of flames, i.e., a candle containing paraffin wax, were applied. The capabilities of the acoustic method in flame extinguishing have been experimentally demonstrated. The results address both the power that had to be delivered to the sound source of a high-power acoustic extinguisher to extinguish flames and the sound pressure level at which this phenomenon was observed. The added value is also to analyze how the order of even harmonics affects the process of acoustic extinguishment of flames (the order of harmonics for each fundamental frequency was varied from two to ten). Furthermore, the potential benefits and limitations of this method are explained, and future research directions are presented.

The Unsteady Shock-Boundary Layer Interaction in a Compressor Cascade – Part 1: Measurements With Time-Resolved PIV

Abstract Time-resolved PIV is performed in the transonic cascade to elucidate the shock-boundary layer interaction. Measurements are conducted in the center blade passage of the cascade at a sampling frequency of 20 kHz or 0.18 convective time units (CTU) for the acquisition of multiple time sequences with duration of approx. 2000 CTU. The sampling rate is sufficient to capture fluctuations of the separating region and accompanying movements of the shock system. To align both instantaneous density variations in the shock system and velocity data obtained in spatially separated regions, shadowgraphs are acquired synchronously with TR-PIV recordings at the same sampling rate. An analysis of power spectral densities along near-wall rows in PIV data reveals the chord-wise spatial distribution of specific peaks and bands. The upstream propagation of disturbances beyond the excursion range of the main shock was demonstrated for the dominant buffet frequency as well as for the high-frequency tone and its first harmonic using cross-correlation maps. A spectral proper orthogonal decomposition (SPOD) indicates that upstream of the main shock oblique shock waves occur at higher order harmonics of the fundamental buffet frequency as well for specific high-frequency tones. To locate possible sources of distinct tones at the entrance of the center passage, a SPOD of high-speed schlieren recordings is performed, capturing the shock systems in three neighboring blade passages. Results indicate that with these high-frequency tones opposing vibrations of bow and lip shocks occur for neighboring blades.

Analysis of the Influence of Time Harmonics on the Leakage Coefficient of Canned Permanent Magnet Synchronous Motors

At present, the influence of time-harmonic currents on the leakage flux coefficient of canned permanent magnet synchronous motors (CPMSMs) remains unclear. Therefore, this paper investigates and summarizes the effects of inverter time-harmonic currents on the leakage flux coefficient of the CPMSM. A 1.5 kW, 9000 RPM (Revolutions Per Minute) CPMSM is used as the research subject. Based on a finite element model, the leakage flux coefficients under sinusoidal and non-sinusoidal supply conditions are calculated using the magnetic flux density integration method. Additionally, the study examines changes in the leakage flux coefficient under different harmonic orders and amplitudes. The results indicate that the introduction of fifth and seventh time-harmonic currents by the inverter reduces the leakage flux coefficient, which helps to improve the utilization of the permanent magnets. This research significantly contributes to enriching the theory of inverter-fed permanent magnet motors.

Data-driven model for marine engine fault diagnosis using in-cylinder pressure signals

Effective diagnosis of marine engines that is crucial for safe and reliable ship operations requires fidel tools for the identification of critical faults. However, the unavailability of extensive measured data-sets corresponding to engine faulty conditions renders the development of such tools challenging. This study aims to develop a data-driven fault estimation model considering information extraction methods and regression techniques of low computational effort, namely multiple linear and polynomial regression. The required data-sets for healthy and faulty conditions for four critical faults and their combinations are generated by employing a calibrated zero-dimensional thermodynamic model representing a marine four stroke medium speed diesel engine, which is validated against engine shop trial measurements. Fourier analysis of the derived in-cylinder pressure profiles is employed to calculate the coefficients of the harmonic orders. Several harmonics coefficients sets are used as input to the regression models to estimate the severity of the four considered faults. The results demonstrate that initial 20 harmonics are sufficient to effectively estimate the severity for each fault, whereas polynomial regression is highly effective, exhibiting R 2 values greater than 98 % . This study provides insights on the data-driven simultaneous faults severity estimation, and as such it impacts the advancement of cost-effective diagnostic methods for marine engines.

Saddle point analysis on selective enhancement of high-order harmonic generation

We theoretically demonstrate control of selective enhancement of the near-cutoff odd order harmonic generation by dual-color chirped laser field. The sharp enhancements of a single harmonic order ranging from H37 to H59 (λ h =21.6nm-13.5nm) are achieved by adjusting the intensity of the fundamental frequency field. The saddle point method is applied to the analysis of high-order harmonic generation using the distorted-waveform laser field. A series of orbits of principal contribution to enhancement are extracted using the saddle point method, and the enhancement of the key orbits’ interference is reconstructed by quantum orbital theory. Through the analysis of the interference mechanism of enhancement, we give a full explanation of the dependence of enhanced harmonic order on laser intensity.

Electron series resonance excited in the 27.12 MHz magnetron sputtering discharge

Abstract Electron series resonance (ESR) excited in a 27.12 MHz magnetron sputtering discharge was investigated. By analyzing the discharge impedances, the imaginary part of the impedance was found to undergo a transition from capacitive to inductive at varying radio-frequency (RF) power, and the conditions for ESR excitation were satisfied at 27.12 MHz magnetron sputtering. By analyzing the discharge current and its higher-order harmonics, the near-sinusoidal current waveform and weak second-order harmonic were obtained, showing a weak nonlinear effect of the RF current. However, for the magnetron sputtering discharge, the nonuniform magnetic field has a significant effect on the sheath width and transverse current, making the sheath thinner and the transverse current smaller. As a result, a small capacitive reactance was obtained, and the inductive reactance was easily canceled. Therefore, the ESR excited in the 27.12 MHz magnetron sputtering was caused by the strong effect of the nonuniform magnetic field and the weak second-order current harmonic (H2). By estimating the ESR frequency ω res,B , the second-order current harmonic (54.24 Hz) was found to be responsible for ESR excitation.

Spatial variations in numerical wave tanks with active wave generating–absorbing system

Wave–structure interaction can be investigated in detail by numerical experiments, such as Navier–Stokes solvers with Volume Of Fluid models to capture the free surface. The quality of the wave field in such Numerical Wave Tanks largely depends on the boundary conditions to generate or/and absorb the waves. In case of regular waves, instead of obtaining a uniform wave field throughout the wave tank, spatial variations in crest height and trough depth are found with beat lengths smaller than the wave length. In this paper, three different wave absorbing boundary conditions are investigated for their effects on the wave field uniformity: the Original Sommerfeld Boundary Condition, a Generalized Sommerfeld Boundary Condition, and a method including Relaxation Zones. An extensive analysis, involving the decomposition of the waves into incident and reflected waves at first order and higher order harmonics is required to explain the phenomenon of spatial variations. It is concluded that Relaxation Zones provide the most spatially uniform wave fields, at the cost of larger computational domains. The spatial variations in the Original and Generalized Sommerfeld Boundary Conditions are found to also be contributed from the superposition of the second order incident bound waves and the second order reflected free waves. This effect is found to be more significant for steeper waves. A graded mesh method at the absorbing side of the tanks is proposed to minimize the spatial variations.

Influence of Winding Configurations and Stator/Rotor Pole Combinations on Field Back-EMF Ripple in Switched Flux Hybrid Excited Machines

Similar to armature back electromotive force (armature back-EMF), the back-EMF also exists in the field winding of hybrid excited machines. However, the existence of field back electromotive force (field back-EMF) is harmful to the safe and stable operation of machine systems, e.g., higher losses, lower efficiency, higher torque ripple, and reduced control performance. This paper systematically investigates the influence of armature/field winding configurations together with stator/rotor pole combinations on the field back-EMF ripple in hybrid excited machines with switched-flux stators. The two-dimensional (2D) time-stepping finite element modeling and prototyping experiments are used for the research. The investigated field and armature coil pitches equal to 1, i.e., non-overlapped windings. The influential factors that are investigated in this paper mainly include the number of layers of field/armature windings, the number of field/armature coils, and the stator/rotor pole combinations. The results show that the field back-EMF’s harmonic order and peak-to-peak value are closely associated with field/armature winding configurations and stator/rotor pole combinations under various conditions. Finally, for validation of the results predicted by the finite element method, a prototype machine is built and tested. Overall, non-overlapped double-layer armature and field windings are recommended for the hybrid excited switched flux machines with various stator/rotor pole combinations to realize relatively lower field back-EMF under different conditions.

Harmonics suppression in frequency domain for fringe projection profilometry with arbitrary phase shifts

In phase-shifting fringe projection profilometry, nonlinearities of the used devices affect measurement accuracy by induing harmonics in fringe signals. The resulting errors are manifested as ripple artifacts in the measured phase maps. Especially when phase shifts are not uniform, the error artifacts have unpredictable profiles and complicated frequency components thus being not easy to eliminate. To solve this problem, this paper suggests a method for suppressing effects of fringe harmonics when using arbitrary phase shifts. For doing it, this paper derives the frequency transfer function that explicitly represents the response of the phase-shifting algorithm to each order of fringe harmonics, and then uses this function to deduce a method that allows one to estimate the coefficients of harmonics from spectrum of the calculated complex fringe pattern. By iteratively subtracting off the estimated harmonics from the calculated complex fringe pattern, fringe phases are calculated accurately. Simulation and experimental results demonstrate that this method significantly suppresses the influence of fringe harmonics on measurement results and, simultaneously, it preserves edges and details of the measured object from being blurred.

(Invited) Fourier Transformed AC Voltammetry and Relationship to Electrochemical Impedance Spectroscopy

Fourier Transformed AC Voltammetry (FTACV) commonly employs a single frequency sinusoidal waveform superimposed onto a DC ramped potential. If the amplitude is large enough, non-linearity in the faradaic electron transfer response leads to detection of the aperiodic DC, fundamental harmonic, second harmonic and a series of higher order harmonics. The features of the faradaic response are governed by the thermodynamics in combination with the kinetics of the electron transfer process and coupled chemistry, with the higher order AC components being particularly sensitive to the electrode kinetics. Importantly, the second harmonic ideally, but third and higher in practice, are devoid of background current arising from double layer capacitance charging or other processes. Many variations of FTACV are also available. For example, a single sinewave with no DC ramp or instead of a single sine wave, two, three or multiple sinewaves can be superimposed onto the DC ramp, or a square wave can be employed. Electrochemical Impedance Spectroscopy (EIS) represents one limit of applying multiple sine waves, traditionally at a fixed DC potential but now more commonly also onto a ramped DC potential. Thus, it can now be recognised there is large family of AC methods are available that are all governed by closely related instrumental and theoretical principles. In the first part of this lecture, data analysis by FTACV for the well-known Fc0/+ process(Fc = Ferrocene) will be extended to the rarely studied Fc+/2+ reaction which is an Fe(III) to Fe(IV) reaction accessible at very positive potentials in ionic liquids at glassy carbon and boron doped diamond electrodes. Novel features relevant to the Fc0/+/2+ reaction sequence, anomalous background current, ionic liquid voltammetry, and carbon electrodes at very positive potentials emerge from analysis of single sine wave FTACV based on comparisons of simulated responses and experimental data, use of multiparameter fitting by data optimisation and Bayesian inference. The lecture will then conclude by considering the implications of using an analogous approach to analyse data obtained by application of multiple sine waves rather than a single sine wave and the relationship to data analysis as in EIS where equivalent circuit analysis has been employed instead of models based on thermodynamics combined with electrode and chemical kinetics.

Control Strategy for Disc Coreless Permanent Magnet Synchronous Motor with LC Filter

The disc coreless permanent magnet synchronous motor has the advantages of a short axial size, high power density, and small volume. Due to the coreless structure, its inductance is very small, which results in a serious current ripple and an unacceptable torque ripple if driven from a conventional inverter. This can be solved by installing an LC filter between the inverter and the motor. However, an undesirable resonance phenomenon is induced by the LC filter. In this paper, a new capacitive current feedback active damping (CCFAD) strategy is proposed. Instead of current sensors in the capacitor branch, a state observer is introduced to estimate the capacitance current. The observer is designed with double sliding mode surfaces, which reduces the order of the system. Compared to conventional capacitive current feedback, no additional current sensors are required, reducing the system cost. Besides the resonant harmonics, the phase current contains obvious fifth and seventh harmonics due to the special plane structure of the rotor. The proportional-integral-resonance (PIR) controller, instead of the traditional PI controller, is designed to suppress lower order harmonics. The experiment results show that current ripples due to resonance and rotor structure are suppressed significantly.

Breaking Abbe's diffraction limit with harmonic deactivation microscopy.

Nonlinear optical microscopy provides elegant means for label-free imaging of biological samples and condensed matter systems. The widespread areas of application could even be increased if resolution was improved, which the famous Abbe diffraction limit now restrains. Super-resolution techniques can break the diffraction limit but most rely on fluorescent labeling. This makes them incompatible with (sub)femtosecond temporal resolution and applications that demand the absence of labeling. Here, we introduce harmonic deactivation microscopy (HADES) for breaking the diffraction limit in nonfluorescent samples. By controlling the harmonic generation process on the quantum level with a second donut-shaped pulse, we confine the third-harmonic generation to three times below the original focus size of a scanning microscope. We demonstrate that resolution improvement by deactivation is more efficient for higher harmonic orders and only limited by the maximum applicable deactivation-pulse fluence. This provides a route toward sub-100-nanometer resolution in a regular nonlinear microscope.

Nested active regions anchor the heliospheric current sheet and stall the reversal of the coronal magnetic field

During the solar cycle, the Sun's magnetic field polarity reverses due to the emergence, cancellation, and advection of magnetic flux towards the rotational poles. Flux emergence events occasionally cluster together, although it is unclear if this is due to the underlying solar dynamo or simply by chance. Regardless of the cause, we aim to characterise how the reversal of the Sun's magnetic field and the structure of the solar corona are influenced by nested flux emergence. From the spherical harmonic decomposition of the Sun's photospheric magnetic field, we identified times when the reversal of the dipole component stalls for several solar rotations. Using observations from sunspot cycle 23 to present, we located the nested active regions responsible for each stalling and explored their impact on the coronal magnetic field using potential field source surface extrapolations. Nested flux emergence has a more significant impact on the topology of the coronal magnetic field than isolated emergences as it produces a coherent (low spherical harmonic order) contribution to the photospheric magnetic field. The heliospheric current sheet, which separates oppositely directed coronal magnetic fields, can become anchored above nested active regions due to the formation of strong opposing magnetic fluxes. Further flux emergence, cancellation, differential rotation, and diffusion, then effectively advects the heliospheric current sheet and shifts the dipole axis. Nested flux emergence can restrict the evolution of the heliospheric current sheet and impede the reversal of the coronal magnetic field. The sources of the solar wind can be more consistently identified around nested active regions because the magnetic field topology remains self-similar for multiple solar rotations. This highlights the importance of identifying and tracking nested active regions to guide the remote-sensing observations of modern heliophysics missions.