Resonant Frequency Band Research Articles

A novel performance prediction method for harmonic reducers based on the trend-enhanced Fisher’s discriminant ratio-Wiener process

Abstract Harmonic reducers, as core components of industrial robots, play a critical role in maintaining robot health. Performance degradation assessment and remaining useful life (RUL) prediction are essential for ensuring the operational reliability of such robots. To address the multistage characteristics and stochastic uncertainties in the performance degradation of harmonic reducers, a performance prediction method based on Fisher’s discriminant ratio and Wiener process is proposed. Firstly, the health indicator construction is defined as an optimization problem based on Fisher’s discriminant ratio and trend monotonicity constraints. By leveraging the sum of the multiplication of frequency amplitudes and optimized weights, precise segmentation of the multistage degradation process over the entire lifecycle is achieved. Notably, the optimized weights can automatically identify the resonance frequency bands caused by damage. Subsequently, a nonlinear Wiener process model with a drift coefficient in the form of a power function is established. The probability density function expression for RUL is derived based on the concept of first hit time. Additionally, a logarithmic likelihood function for the unknown parameters in the degradation model is constructed. The experimental results indicate that the proposed method surpasses the other two Wiener process models in terms of root mean square error, mean absolute percentage error, and cumulative relative accuracy. This provides robust support for preventive maintenance decision-making for harmonic reducers.

Design implementation analysis of multi-band antenna for terrestrial applications

A multi-band antenna is proposed for terrestrial applications above 5 GHz. The design includes one director element, three split ring resonators (SRR), and a printed patch antenna on a FR4 substrate to make the miniature structure. The novelty is the addition of “C” split rings and one identical stub linked to the partial ground into the radiating element, which improves impedance matching and radiation characteristics across the target bands. The prototype is designed with five distinct resonance frequencies and radiation patterns compared to those produced by the patch, the director and resonators are added. Return loss simulation results and measured radiation pattern findings are validated and analyzed. The antenna produces a gain of 7.84 dB, overall efficiency of 84.76 %, and a VSWR of 1.8 at 7 GHz frequency, which is achieved due to the peculiar features of the FR4 and it is highly suitable for traditional communication. VSWR, gain, and radiation efficiency are all higher on this antenna than they are on a typical multiband antenna. At 20 GHz, the designed antenna band is efficient to operate with five dissimilar resonant frequency bands, pinpointed at 7.224 GHz, 10.723 GHz, 13.808 GHz, 17.014 GHz and 19.549 GHz through different impedance bandwidths.

Adaptive cyclic content ratiogram: a new signal decomposition method for bearing concurrent fault diagnosis

Fast kurtogram (FK) has been proven to be an effective tool for resonance frequency band detection, which is widely used in bearing fault diagnosis. However, FK is not robust to impulsive noise, and its frequency band segmentation rule is fixed, which leads to over-decomposition or under-decomposition of the fault resonance frequency band in its signal decomposition results. Therefore, an adaptive cyclic content ratiogram is proposed in this paper. Firstly, based on the energy distribution of vibration signals on different frequency components, the frequency spectral segmentation is performed adaptively, and multiple sub-signals containing different frequency components are obtained. Secondly, the ratio of cyclic content (RCC), which cannot only more accurately characterize the cyclostationarity of bearing fault impacts but also be insensitive to impulsive noise, is applied to evaluate the fault feature information contained in each sub-signal separately. In the meanwhile, considering that fault characteristic frequency information is required in the process of RCC evaluation, the proposed method performs adaptive fault characteristic frequency detection for each sub-signal based on the envelope spectrum. The RCC maximization is used to locate the fault resonance frequency band. Also, combined with the estimated fault characteristic frequencies, the proposed method can achieve the extraction of concurrent fault features. Simulation and experimental data verify the effectiveness of the proposed method.

Broadband Aircraft Noise Attenuation Across Low and High Frequencies Using Structured Materials

Controlling broadband noise throughout the spectrum, from low to high frequencies, is a significant challenge for the aerospace, transportation, and construction industries. Although recent research has focused on low-frequency noise control solutions using acoustic metamaterial designs, the narrow-band resonances of these materials remain a limitation. This paper presents a structured material system which addresses this limitation by proposing a parallel assembly of structured materials, enabling broadening of the resonance frequency band from low to high frequencies. The study involves an arrangement of structured metamaterials and Helmholtz Resonators embedded in a layer of glass wool. By meticulously grouping individual resonant frequencies, the proposed assembly effectively attenuates noise over the frequency range of interest. The present research contributes to the development of lasting solutions for aircraft noise across a broad frequency spectrum, showing promising potential for significant noise reduction within practical constraints.

Quad-Band 1 × 4 Linear MIMO Antenna for Millimeter-Wave, Wearable and Biomedical Telemetry Applications.

In this paper, we present the design of a millimeter-wave 1 × 4 linear MIMO array antenna that operates across multiple resonance frequency bands: 26.28-27.36 GHz, 27.94-28.62 GHz, 32.33-33.08 GHz, and 37.59-39.47 GHz, for mm-wave wearable biomedical telemetry application. The antenna is printed on a flexible substrate with dimensions of 11.0 × 44.0 mm2. Each MIMO antenna element features a modified slot-loaded triangular patch, incorporating 'cross'-shaped slots in the ground plane to improve impedance matching. The MIMO antenna demonstrates peak gains of 6.12, 8.06, 5.58, and 8.58 dBi at the four resonance frequencies, along with a total radiation efficiency exceeding 75%. The proposed antenna demonstrates excellent diversity metrics, with an ECC < 0.02, DG > 9.97 dB, and CCL below 0.31 bits/sec/Hz, indicating high performance for mm-wave applications. To verify its properties under flexible conditions, a bending analysis was conducted, showing stable S-parameter results with deformation radii of 40 mm (Rx) and 25 mm (Ry). SAR values for the MIMO antenna are calculated at 28.0/38.0 GHz. The average SAR values for 1 gm/10 gm of tissues at 28.0 GHz are found to be 0.0125/0.0079 W/Kg, whereas, at 38.0 GHz, average SAR values are 0.0189/0.0094 W/Kg, respectively. Additionally, to demonstrate the telemetry range of biomedical applications, a link budget analysis at both 28.0 GHz and 38.0 GHz frequencies indicated strong signal strength of 33.69 dB up to 70 m. The fabricated linear MIMO antenna effectively covers the mm-wave 5G spectrum and is suitable for wearable and biomedical applications due to its flexible characteristics.

Performance Evaluation and Comparative Analyses of Tuned Inerter Damper for Stochastic Base Excited Structures Based on Hybrid H2/H∞ Optimization

Compared with tuned mass damper, tuned inerter damper (TID) has higher damping efficiency and lightweight characteristic if appropriate optimal methods are selected. Generally, [Formula: see text] or [Formula: see text] optimal methods are adopted to determine the optimal parameters of TID individually. But the vibration mitigation performance of the TID under near resonance frequency band based on [Formula: see text] optimization is less than [Formula: see text] optimization, but the peak frequency response based on [Formula: see text] optimization will be greater than [Formula: see text] optimization at the same time. Dual-characteristic-based vibration control may not be achievable based on [Formula: see text] or [Formula: see text] criteria, respectively. For this reason, hybrid [Formula: see text] optimization can be adopted. In this work, closed-form expressions are derived for the control of structural displacement responses based on hybrid [Formula: see text] optimal method. The vibration mitigation performance of the different optimized TIDs is evaluated considering the single-degree-of-freedom and multi-degrees-of-freedom systems are subjected to typical ground motions excitation. Results illustrate that because of the use of the optimal stiffness ratio of [Formula: see text] optimization and very close value of [Formula: see text] optimizations’ nominal damping ratio in [Formula: see text] optimization, [Formula: see text] optimization shows ‘dual characteristics’ in different excitation situations. Specifically, the peak response and structural fundamental frequencies’ response in displacement frequency response function using hybrid [Formula: see text] optimal methods are between [Formula: see text] and [Formula: see text] optimization, which indicates an excellent and balanced control performance combining the advantages of [Formula: see text] and [Formula: see text] optimal solutions. Hence, this hybrid method is more suitable for more complex ground motions excitation to control critical structural responses instead of single characteristic excitation. And the comprehensive vibration control in dynamic time histories analyses can be achieved by this dual characteristic-based optimal strategy. When designing the specific TID, hybrid [Formula: see text] optimization can be considered as the best choice for its compatibility and high adaptability for complex practical engineering scenarios with random and diverse excitations.

Resonance frequency band structure in heterojunction of one-dimension string-ball chain system

Using the concept of heterostructures in semiconductor physics and the similarity between the Schrödinger equation and the vibration equation of the one-dimension string-ball chain system, we create a heterojunction in our string-ball chain system by assembling a string-ball chain with two kinds of mass in a lattice-matched and an unmatched system and study the two systems through first-principle calculation, theoretical analysis, and experiment perspectives. A discontinuity in the frequency dependence is observed in the matched system, while a phase transition is discovered in the unmatched system. A proper theoretical analysis based on the wave function is also given to explain these phenomena.

Energy harvesting for a vibration isolation system with negative stiffness under harmonic excitation

ABSTRACT In this paper, an energy harvesting system with a negative stiffness structure is established, whose main purpose is to achieve good vibration isolation, and at the same time, the system can also achieve the purpose of energy harvesting. In order to analyse the system model, the amplitude–frequency response equations for the displacement, induced voltage and electric power of the system when the system is in the main resonance state are obtained by using the multiscale method, and their amplitude–frequency response curves are plotted. In addition, we obtained the existence conditions for the system to satisfy Smale's horseshoe chaos using the Melnikov function. And the phase diagram and Poincaré mapping of the system were obtained using the fourth-order Runge–Kutta method. Numerical results show that the system has some energy harvesting performance along with vibration isolation. Variations in the parameters of the system affect the resonance frequency band and co-oscillation amplitude of the system as well as the nonlinear characteristics of the system itself.

Cyclostationary harmonic product spectrum with its application for rolling bearing fault resonance frequency band adaptive location

Harmonic product spectrum (HPS) is an important tool in bearing fault diagnosis because it can quickly locate the fault resonance frequency band. However, its frequency band division strategy easily leads to over- or under-decomposition. This might cause the decomposed signal to contain too little fault information or too much interference. Although an adaptive HPS based on scale space representation for frequency band division is proposed, its frequency band division is driven by the data characteristics of the signal itself, rather than the fault characteristics in signal. It is difficult to completely separate faults from signals by frequency band division without considering fault characteristics. Therefore, an adaptive frequency band segmentation strategy aiming at fault characteristic, i.e., cyclostationarity, maximization is designed and introduced to improve HPS, thus proposing a new optimal fault resonance band location technique. It can achieve fault resonance band location accurately and resist the influence of various noise interferences.

Adaptive resonance demodulation semantic-induced zero-shot compound fault diagnosis for railway bearings

For the challenges of diverse compound faults and low identification accuracy of railway bearings, a new zero-shot diagnosis model based on adaptive resonance demodulation semantic is proposed for the compound fault diagnosis of railway bearings. The model adopts adaptive resonance demodulation to identify the optimal resonance frequency band rich in fault information in bearing signals, and constructs the single and compound fault semantics of samples without separating the compound fault signals, thus improving the interpretability of semantic features. Moreover, spatial Euclidean distance is used to measure the similarity of features and semantics in the mapping space, which enables the identification of unknown compound faults by single faults. Verification through railway bearing data shows that this model effectively improves the compound fault identification accuracy under zero samples and is better than the comparison models. The research results can provide theoretical reference for the research and application of railway bearing fault diagnosis.

Down-film as a new non-frame porous material for sound absorption

Down-polyethylene film material has been introduced for the first time as an excellent non-frame sound absorber, showing a distinctively outstanding performance. It contains down fiber adjacent to each other without firm connection in between, forming a structure of elastic fiber network. The unique structure has broadband response to sound wave, showing non-synchronous vibration in low and middle frequency and synchronous vibration in middle and high frequency. The broadband resonance in middle and high frequency allows the structure to achieve complete sound absorption in resonance frequency band. Moreover, down-polyethylene film material possesses forced vibration, corresponding sound absorption coefficient has been obtained based on vibration theory. The down-film sound absorption material has the characteristics of light weight, soft, environment-friendly, and has excellent broadband sound absorption performance.

Adaptive semiactive control of structure with magnetorheological dampers using wavelet packet transform

Conventional active controllers generally adopt initial dynamic properties of intact structures to calculate optimal control force for magnetorheological damper, which eventually leads to ideal damping force of the device. Also, they cannot assure trade-off between damping force and response reduction under non-stationary excitations. To this end, an adaptive semiactive control algorithm for magnetorheological damper is proposed. Using wavelet packet transform, an improved control law determines optimal control forces in terms of resonant and non-resonant frequency bands in time interval. Both frequency bands are established based on natural frequency(ies) of structures, making damping force rely on actual structural properties and achieving trade-off under non-stationary disturbances. A refined clipped-optimal control algorithm is then deployed to convert optimal control force to the device’s voltage. A numerical study of a six-degree-of-freedom structure under four near- and far-fault ground accelerations reveals that the scheme outperforms existing controllers while attaining cost-effectiveness of damping force versus response alleviations.

An adaptive Morlet wavelet-based iterative filtering method for locating informative frequency band

Locating the informative frequency band of rolling bearing fault signals is of great significance for feature extraction and fault diagnosis. Benefiting from the adjustable center frequency and bandwidth as well as the similarity to impulse-like characteristics induced by bearing failures, Morlet wavelets are commonly used in resonance demodulation. However, fault impulses are highly susceptible to contamination by strong noise, which impedes the efficacy of existing wavelet parameter selection strategies and frequency band optimization methods. In this paper, an adaptive Morlet wavelet-based iterative filtering (AMIF) method is proposed for frequency band optimization under strong noise. The resonance frequency band is pinpointed based on adaptive Morlet wavelet filter banks, with off-band noise being canceled and fault features being refined during the level-by-level filtering process. Additional iterative operations are leveraged to enhance fault features of in-band signals to facilitate the optimization of the filtering parameters. Effectiveness of the proposed AMIF method and its superiority over the wavelet packet transform-based kurtogram and minimum entropy deconvolution are verified through simulation and experimental analysis. The results demonstrate that AMIF can accurately localize the informative frequency band, thereby extracting high-quality fault features, making it suitable for bearing fault diagnosis under strong noise condition with different fault types.

Investigation of Gear Meshing Vibration and Meshing Impact Resonance Intensity Assessment

Abstract Gear drive is one of the most widely used transmission forms. Its vibration analysis plays an important role in design and operation. Considering the gear meshing resonance phenomenon (MRP), the paper analyzes the influences of rotating speed and load on meshing resonance intensity (MRI). Based on the gear meshing impact mechanism, meshing force variation during the engagement process were obtained. It was considered as meshing impacts exerted on the gear system. By comparing the maximum meshing force under different circumstances, it was found that rotating speeds and loads were positively related to meshing forces. The vibration signals with different load torques and rotating speeds obtained from the gear pair were analyzed. The experiment results showed that the intensity of meshing impact increased with the increases of both rotating speed and load. It was also observed that due to the MRP, the gear meshing frequency was modulated to the resonance frequency band as meshing impacts. Consequently, the resonance frequency band contained most of the energy of the meshing impact. An indicator called resonance energy ratio (RER) was defined to represent the proportion of resonance energy due to meshing impact. The simulation and experiment result show that the proposed RER indicator can well assess the intensity of the vibration. By comparing the RER values of 20 sets of gear vibration data, the influences of rotating speed and load on MRI were discussed. The result shows that the proposed method is helpful to the vibration assessment and condition monitoring in different operational states.

SEACKgram: a targeted method of optimal demodulation-band selection for compound faults diagnosis of rolling bearing

Rolling bearing plays an important role in carrying and transmitting power in rotating machinery, and the bearing fault is easy to lead to mechanical accidents, resulting in huge losses and casualties. Therefore, the condition monitoring and diagnosis of rolling bearings are very important to improve the safety of equipment. Compound fault is a common fault evolved from the initial defect, which is characterized by randomness, coupling, concealment, and secondary. The existence of these characteristics brings great challenges to the accurate diagnosis of compound faults. In the diagnosis of compound faults, the traditional methods that select the single optimal demodulation frequency band for analysis and identification sometimes cannot completely extract multiple fault components, which are prone to miss diagnosis and misdiagnosis. In order to solve this problem, the SEACKgram method is proposed by constructing a Square Envelope Unbiased Autocorrelation Correlation Kurtosis (SEACK) index. The frequency band of the original signal is divided by the Maximal Overlap Discrete Wavelet Packet Transform, and the SEACK index is used to quantitatively describe the fault signals of different frequency bands. According to the different fault periods, the resonant frequency bands of the maximum SEACK value are selected, then the resonance band signal is analyzed by square envelope spectrum, and the fault type is identified according to the fault characteristic frequency. The simulated and experimental vibration signals of rolling bearings with compound faults are used to verify the feasibility of the proposed method. The results show that the proposed SEACKgram can improve the accuracy of compound faults identification and would be applied in engineering practice to a certain extent.

A Novel Method for Identifying Resonance Frequency Band in Weak Bearing Fault Diagnosis of Electric Driving System

Because of the uncertainty of the structure and environment of the electric driving system (EDS), the fault signature of the rotating mechanism is complicated. A novel method based on Hilbert transform with modified fast kurtogram (HTMFK), which is used for identifying the bearing faults in the EDS, is proposed. The modified principle and algorithm flow of the proposed method are derived. A high pass filter based on the frequency band identified by HTMFK is constructed and applied to fault diagnosis. Simulation signals demonstrate the ability of demodulating signals and identifying the fault resonance band. The bearing fault bench experiment of EDS is carried out in a semianechoic chamber. The corresponding fault tests are conducted according to different operating conditions. The applicability of HTMFK is verified by comparing the square envelope spectrums. Compared with other methods, the proposed method identifies the fault resonance frequency band more effectively and expands the application range of bearing fault diagnosis in EDS.

Mitigating low-frequency broadband aircraft noise through a structured assembly of acoustic material and devices

Addressing the challenge of attenuating low-frequency broadband noise emerges as a critical concern within the fields of aeronautics, ground transportation, and construction industries, requires innovative solutions for enhanced acoustic control. Over the last few decades, the literature has seen an increase in low-frequency noise control solutions centered around acoustic metamaterial designs. These proposed technologies exhibit promising acoustic performance, especially proving superior to conventional sound insulation materials in constrained spaces, such as in aerospace applications. Despite the efficacy of typical metamaterials in attenuating tonal noise through narrow resonant frequency maxima, practical applications reveal some challenges, as even slight variations in tonal noise frequencies can compromise the overall effectiveness of such solutions. In response to this, the present paper introduces a novel thin acoustic metamaterial design aimed at improving broadband noise attenuation at low frequencies. This design uses carefully arranged structured metamaterials within a fiberglass layer to create optimal resonance frequency bands for maximum low-frequency noise attenuation. Performance assessment in the low-frequency domain employed COMSOL Multiphysics finite element methods, predicting sound absorption coefficient and transmission loss. Results confirm the effectiveness of the proposed metamaterial design, showcasing broad noise attenuation at low frequencies.

Research on Nonlinear Vibration of Dual Mass Flywheel Considering Piecewise Linear Stiffness and Damping

Nonlinear torsional vibration differential equation of the nested arc-shaped short spring dual mass flywheel (DMF) is established, considering the piecewise linear stiffness and damping of the spring. The first-order approximate analytical solution under sinusoidal excitation and the amplitude–frequency characteristic function are obtained by means of the average method which verified by the Runge–Kutta (R–K) method. The effects of the parameters of input excitation, inertia, and piecewise linear stiffness and damping of DMF on the resonant amplitude, resonant frequency band, and equivalent linear natural frequency of the system are analyzed. The results show that the amplitude–frequency characteristic curve bending and jumping with the changes of excitation frequency and the peak of resonant amplitude can be obviously reduced by increasing the inertia of the primary flywheel and decreasing the inertia of the secondary flywheel. The complex nonlinear dynamic phenomena such as Period 1, quasi-periodic, and chaos are obtained by analyzing the forced vibration response under the different excitation frequencies.

Response of photosynthesis and electrical reactions of wheat plants upon the action of magnetic fields in the Schumann resonance frequency band

ABSTRACT Alternating magnetic fields (MF) with Schumann resonance frequencies accompanied the development of living organisms throughout evolution, but today it remains unclear whether they can have a special biological effect in comparison with surrounding non-resonant frequencies. This work shows some stimulating effect of extremely low-frequency MFs on morphometric parameters and the activity of physiological processes in wheat (Triticum aestivum L.). It is shown that the MF effect is more pronounced for transient processes – photosynthesis reactions and changes in electrical potential caused by turning on light. For light-induced electrical reactions, the dependence of the severity of the effect on the frequency of the applied MF was demonstrated. It is shown that the most pronounced effect occurs in the 14.3 Hz field, which corresponds to the second harmonic of the Schumann resonance. The predominant sensitivity of signal-regulatory systems gives reason to assume the influence of MFs with Schumann resonance frequencies on the interaction of plants with environmental factors under conditions of a changed electromagnetic environment. Such conditions can occur, for example, with an increase in lightning activity caused by climate change, which serves as the basis for the generation of Schumann resonances, and with the development of artificial ecosystems outside the Earth’s atmosphere.

Broadband low frequency noise attenuation using thin acoustic metamaterials for aircraft cabin noise mitigation

Broadband noise attenuation at low frequencies is a challenge for the aeronautical, ground transportation and construction industries. In the past few decades, various low frequency noise control solutions, based on acoustic metamaterials designs, have been presented in the literature. The proposed technologies showed promising acoustic performance and are considered as better solutions when compared to conventional sound insulation materials in application fields such as aerospace, where the available space for their integration is extremely limited. The noise attenuation of typical metamaterials is characterized by very narrow resonant frequency maxima which represent a good solution for tonal noise. However, in practical applications, the slight variations of the tonal noise frequencies may render a metamaterial ineffective. This paper presents a thin acoustic metamaterial design for improved broadband noise attenuation at low frequencies. The geometry is an assembly of structured materials arranged in parallel and embedded in a layer of fiberglass. The two structured materials are designed such that their resonant frequencies are optimally regrouped to create a resonant frequency band of maximum attenuation at low frequencies. A thermo-viscous acoustics approach was solved numerically with COMSOL Multiphysics in the frequency domain to predict the sound absorption coefficient and the normal incidence sound transmission loss of the proposed metamaterial design. The results obtained show a wide frequency band noise attenuation for this metamaterial at low frequencies.