Frequency Spectrum Of Vibrations Research Articles

A Physics-Based Model-Data-Driven Method for Spindle Health Diagnosis, Part I: Modeling of Geometric Faults

Abstract The spindle determines the performance of machine tools; hence, monitoring its health is essential to maintain machining productivity and avoid costly downtimes. The magnitudes and locations of wear and cracks in the bearing balls and races gradually develop which are difficult to detect. This article presents a physics-based digital model of the spindle with bearing faults, worn contact interface between the shaft and tool holder, and spindle imbalance. The wear of races and balls is considered in the bearing model. The worn taper contact interface and the spindle imbalance are included in the digital model. The spindle's dynamic model is used to simulate the vibrations at any location in the spindle assembly where sensors can be mounted for online monitoring. The wear type and bearing location are correlated with the frequency spectrum of vibrations at operating speeds. The proposed fault models are used to analyze the critical signal features and experimentally validated by the frequency extracted from a damaged spindle in Part II. The physics-based digital model is used to train data analytic models to detect spindle faults in Part III.

Gas Turbine Anomaly Detection under Time-Varying Operation Conditions Based on Spectra Alignment and Self-Adaptive Normalization

Gas turbine vibration data may exhibit considerable differences under time-varying conditions, which poses challenges for neural network anomaly detection. We first propose a framework for a gas turbine vibration frequency spectra process under time-varying operation conditions, assisting neural networks’ ability to capture weak information. The framework involves scaling spectra for aligning all frequency components related to rotational speed and normalizing frequency amplitude in a self-adaptive way. Degressive beta variational autoencoder is employed for learning spectra characteristics and anomaly detection, while a multi-category anomaly index is proposed to accommodate various operating conditions. Finally, a dataset of blade Foreign Object Damage (FOD) fault occurring under time-varying operating conditions was used to validate the framework and anomaly detection. The results demonstrate that the proposed method can effectively reduce the spectra differences under time-varying conditions, and also detect FOD fault during operation, which are challenging to identify using conventional methods.

Dynamic response analysis of piled embankment and train derailment evaluation subjected to seismic and high-speed train loads

Based on a train-rail-piled embankment three-dimensional finite element model, the vibration displacement, acceleration and frequency spectrum of the rail and subgrade caused by combined seismic and high-speed train loads was investigated. On this basis, performance of piled embankment under combined seismic and high-speed train loads was analyzed. Numerical examples indicate that the seismic load dominates the ground displacement and the moving train load has negligible effects on the ground displacement. However, the moving train load has a significant effect on the rail vibration displacement during earthquakes. The rail and subgrade vibration displacement of piled embankment under combined seismic and moving train loads is obviously lower than that of ordinary subgrade, and its dominant frequency tends to transfer from high to middle and low frequency compared with ordinary subgrade, indicating that pile embankment has a good vibration reduction effect. Moreover, the derailment coefficient and lateral displacement of piled embankment is obviously decreased, which provides important guidance that pile embankment has significant vibration reduction effect and thus it can effectively prevent derailment or overturning during earthquakes.

Influence of the Manipulator Configuration on Vibration Effects

Abstract Vibration analysis of industrial robots is one of the key issues in the context of robotisation of machining processes. Low-frequency vibrations result from flexibility in manipulator joints. Within the scope of the article, a model of a two-link robot manipulator was built. Dynamic equations of motion were formulated to study the influence of the robot arm configuration on vibration effects. Based on numerical simulations, the frequency spectrum of vibrations of the robot’s links was determined, and tests were carried out in a number of configurations, obtaining a map of resonant frequencies depending on the configuration of the manipulator. Experimental studies were then carried out, which confirmed the conclusions from the simulation studies. The results obtained confirm that the positioning of the manipulator’s links has a significant effect on vibration effects. Tests conducted using a vision system with a motion amplification application made it easier to interpret the results. The formulated mathematical model of the manipulator generates results that coincide with the results of experimental studies.

Reduction of a fan vibration activity in a life support system of oil and gas stations

Relevance. Electromechanical fans are widely used in life support systems of oil and gas stations, operate in conditions of vibration, high rotational speeds and loads. Design, technological and operational reasons influence vibration activity of an electromechanical device. The greatest "contribution" to the existing vibrations, according to the frequency spectrum, is made by the imperfection of the design elements of the ball bearing. They are: separator movement, variable stiffness under the action of radial load, interaction of micro-dimensions of working surfaces, facet and waviness of working surfaces of rings and balls. In addition, the resulting vibrations negatively affect both the reliability and durability of the fan. Since it is technically impossible to completely eliminate the vibration activity of an electromechanical device, it is advisable to reduce it with the help of a technical solution by introducing a damping element into a kinematic circuit of the vibration source. In this regard, the development of a damping device is an integral technical task that helps to reduce the vibration activity of technical life support systems of oil and gas stations, as well as to improve the quality of environmental conditions of human life. To reduce vibration activity, a damper design is proposed that takes into account various types of energy dissipation. However, given the dense spectrum of vibration frequencies from ball bearings, a viscous friction element is introduced into the damper design. To determine the effectiveness of reducing vibration activity, a model of the damper in question was made based on the developed 3D model. For tests in determining the effectiveness of applying a viscous friction element, two variants of the damper design were used. In the first version of the damper design, there was no viscous friction element, and in the second version there was one. According to the test results of the damper layouts, it can be seen that the developed technical solution to reduce the vibration activity of the electromechanical device has practical confirmation. The studies underlying the developed design of the damper with a viscous friction element allows for reduction in the vibration amplitude. Object. Electromechanical device in operating mode. Aim. To describe the vibration activity in the operating mode of an electromechanical device in the entire spectrum of disturbing effects acting along the axes, taking into account the imperfect geometry of ball bearing parts; to develop a damper for reducing the vibration activity level in the electromechanical device. Methods. Vibration diagnostics, computational mathematics, measuring instruments, software "Vibration recorder-F", "Vibration Recorder-M2", "Logger"-recorder and "Bearing". Results. The paper demonstrated the effectiveness of the proposed technical solution to reduce the vibration amplitude in the operating frequency range of the electromechanical device rotor up to 4 times compared with the corresponding maximum amplitude value without its use.

Bridge Frequency Identification Using Cross-Power Spectra of Vehicle Vibrations from Multiple Moving Speeds

In recent years, a rapid bridge health monitoring technology has been developed using an instrumental moving vehicle. Using recorded vehicle vibration data, bridge frequencies are identified for bridge health monitoring or finite element model updating. Target bridge frequencies with significant amplitudes in the vehicle’s vibration frequency spectra are expected to be found. However, in the coupled vehicle–bridge interaction (VBI) system, bridge vibration-relevant vehicle dynamics might not be noticeable. The bridge frequency would be difficult to identify because of the potential influence of road roughness. To resolve this difficulty, a novel bridge frequency identification method is proposed to mitigate the negative effects of road roughness. First, theoretical derivations are done to ascertain the VBI system dynamic characteristics considering road surface roughness. Our findings showed that the road roughness-relevant vehicle dynamics are closely related with the traveling speed, whereas the bridge frequency remains approximately constant. Theoretical investigations indicated that cross-power spectra between vehicle dynamics at multiple moving speeds are effective to mitigate the negative effects of road roughness. Presumably, it is feasible to identify the target bridge frequency from the cross-power spectra. Both the dynamic characteristics of the VBI system and the effectiveness of the proposed method for bridge frequency identification were examined using finite element simulations and laboratory experiments. Compared to existing methods, the proposed method is widely applicable to real-world situations and difficulties.

Experimental Detection of Lubrication Characteristics in a Solid–Liquid Two-Phase Flow Supported Bearing-Rotor System Using Vibration Monitoring Techniques

This work aims to investigate the friction and vibration behaviors of a liquid–solid two-phase flow supported bearing-rotor system for the early monitoring and assessing of oil contamination resulting from externally ingested particles. Based on a Jeffcott rotor test rig, the lubricating oil in journal bearing was mixed with micron-scale silica particles of different sizes and concentrations. The vibration monitoring techniques utilizing eddy current, photoelectric, and piezoelectric sensors were conducted to detect the rotor displacement amplitude and bearing acceleration online. According to the quantitative evaluation, the vibration frequency spectrum, shaft trajectory, and the bearing surface characteristics were analyzed and classified at different conditions of particle parameters. Furthermore, the lubricating mechanism at bearing interface which possesses a strong interactive coupling effect with rotor vibration was deduced and illustrated. The results showed that although the sizes of ingested micron particles were less than the minimum oil-film thickness, they usually exhibited detrimental effects on the flow stability and fluid support. As the particle size or concentration increased, the interaction between particles and bearing surfaces led to the burrs in time-domain waveform, reverse displacements in rotor orbit, higher frequency harmonics in vibration spectrum, and the scratches on the bearing surface. The occurrence of continuous three-body friction could induce misalignment, blockage, oil starvation, and rub-impact fault. Furthermore, the detectability of particle contamination and damage microstructure of bearing surface was described for reference.

ГЕОДИНАМІКА

The main purpose of the study is to identify the relationship between changes in water level and soil deformation, where the cyclic change in loads on the reservoir bed is the stress deviator, i.e., the PSPP reservoir acts as an oscillator of transverse vibrations, and the soil extensometer performs the function of reading and recording these vibrations. Methodology. Solution of the problem requires recording the time series of water level fluctuations and extensometer sensor fluctuations on all depth horizons. It is also necessary to perform a fast Fourier transform for water level fluctuations separately and similarly to each extensometer sensor fluctuation. We need to separately calculate the signal power spectrum of all sensors in the soil, and compare the amplitude-frequency, phase-frequency components of the power spectra of water level oscillations and vertical oscillations of the extensometer sensors. Results. During the studies, it was found that the PSPP reservoir is a source of low-frequency vibrations in a wide spectral range. These vibrations have a very long wavelength, measured in tens of thousands of kilometers, which can propagate over long distances, both along the front of geological layers and in depth. Scientific innovation. The research in this article allows us to more accurately assess the frequency spectrum of vibrations and identify possible resonance phenomena that may occur in soils during the operation of a power facility. In addition, this study was conducted in a specific region, which makes it possible to obtain more accurate data on the impact of low-frequency vibrations on the geosystem in this region. Thus, this paper may be of interest to specialists in the field of geotechnics, geology, and energy. It can also be used in the planning and operation of other power facilities in similar conditions. Practical significance. Low-frequency waves can be detected by seismic instruments such as seismometers. The results of this study will help to correct the analysis and interpretation of seismograms, which is important for understanding the processes occurring in the hydroelectric power plant operation area.

Research on vibration mechanism of the low-to-medium-speed maglev train-track-at-ground-structure system

The at-ground-structure supports the maglev track on the subgrade segment and receives the subgrade’s equally distributed elastic support to ensure the holding track running of the maglev train. A complicated maglev train-track-at-ground-structure coupled system is produced, negatively affecting the stable operation of the train. To explore the vibration mechanism, an elaborate maglev train-track-at-ground-structure coupled system was established considering active levitation control, and field tests confirmed the reliability of the numerical method. Firstly, the natural frequencies of track-at-ground-structure were investigated. Then, characteristics of this coupled system were examined in terms of its dynamic interaction mechanism, dynamic response characteristics and vibration frequency spectrum distribution. Finally, the vehicle-induced resonance mechanism and anti-vibration methods of the at-ground-structure were analyzed. The results show that the high-frequency vibrations exist in both the F-rail and at-ground-structure obviously, and create varied wavelengths affecting the maglev train’s running stability. The high frequency resonance phenomena easily produce when loading frequency of neighboring levitation forces is near to fundamental frequency of at-ground-structure, and disappears while the two frequencies are avoided.

Нестационарные колебания в системе из двух связанных осцилляторов в условиях кубической нелинейности и кубической связи. Часть 1. Мультирежимный характер колебаний

The task about the excitation of magnetoelastic vibrations in geometry of magnetostriction transducer which contains normal magnetized ferrite plate excited by alternating magnetic field is investigated. It is proposed the model presentation of transducer in the view of two connected oscillators first of its corresponds to magnetic part of structure and the second correspond to elastic its part. The first oscillator is linear and the second is nonlinear. The nonlinearity and connection have cubic character. In dependence from the excitation level it is found five basal regimes of vibrations: №1 – synchronize, №2 – three-multiplication of frequency, №3 – chaos, №4 – gigantic oscillations, №5 – delayed stabilization. In these regimes the time-evolvent of vibrations and its parametric portraits in coordinates displacement – derivative from displacement and also frequency spectra of forced vibrations are investigated. The regimes №1б №2 are stable. The vibrations in this regimes are harmonic and complete determined. The regimes №3-№5 are non-stable. The vibrations in this regimes has chaotic or near to chaotic character. On the level of excitation the stable regimes are separated from non-stable by sharp threshold. By the overcoming of which the vibration amplitude increases by sharp jump over two-three orders. By the excitation on non-stable regimes it is established the application on the main vibrations the attendant vibrations. The frequency of attendant vibrations is higher than excitation frequency on two-three orders. The amplitude of attendant vibrations is smaller than the main vibrations amplitude more then two orders. It is proposed the model of attendant vibrations excitations. On the basis of this model the quantity appreciation of vibrations character in non-stable regimes. The recommendations for future development of investigations are proposed.

Analytical estimation of the natural frequency of vibrations of a flat lattice

A formula is derived for calculating the first natural frequency of vibrations of a statically determined regular lattice with an arbitrary number of panels and masses uniformly distributed over the nodes. Comparison with the minimum frequency from the numerical solution of the problem of the vibration frequency spectrum of the structure shows the high accuracy of the derived assessment. It is shown that for some number of panels, the design allows for kinematic variability. The influence of the lattice attachment method on the natural frequency is studied. Keywords: truss, lattice, vibration frequency, induction, Maple, Dunkerley estimate, attachment method.c216@ya.ru

Investigation of nonlinear oscillations of high rise flue gas stacks under various kinematic effects

A detailed analysis of the current state of the problem is presented in the article. A mathematical model is given to assess the dynamic behavior of high-rise structures, considering geometric nonlinearity (nonlinear dependence of strains on displacements) under periodic kinematic effects and the own weight of the structure. The unsteady forced oscillations of the high-rise flue gas stack of the Novo-Angrenskaya HPP were studied considering the geometric dimensions of the stack and the physical and mechanical characteristics of the material of the structure. The influence of dissipation in the material, leading to rapid or gradual damping of vibrations depending on the frequency spectrum of natural vibrations in one direction or another, as well as geometric nonlinearity, leading to an increase in the amplitude of vibrations at a low energy dissipation in the structure, and resonant impact, causing significant displacements of the structure. The predominant effect of energy dissipation in the material on the pattern of the dynamic behavior of a high-rise structure is observed compared to geometric nonlinearity.

ARMORED HULLS OF DOMESTIC ARMORED PERSONNEL CARRIERS: COMPUTER AND MOCK-UP MODELING OF DYNAMIC PROPERTIES

At the stage of design research of armored bodies of lightly armored vehicles it is extremely important to determine the range of their natural frequencies and natural forms of oscillation. For this purpose, the finite element method is usually used. It is necessary to substantiate the parameters of the finite element model, which provide an acceptable level of accuracy of numerical modeling of dynamic properties of this type of structures. For this purpose, data from parallel numerical and experimental studies of the mock-up of the armored hull of the armored personnel carrier are used. The mock-up of the upper projection of the armored hull is made in the appropriate scale. The material is sheet steel. This mock-up is subjected to dynamic excitation on a vibrating table. Resonant excitation frequencies are recorded, as well as the natural vibration forms. Shock-pulse excitation of the armored hull’s mock-up was also performed. The response to this excitation is recorded using accelerometers. Then, the spectrum of natural vibration frequencies is determined from these oscillograms. In parallel, numerical modeling of natural frequencies and natural vibration forms of the armored hull’s mock-up is carried out. After that, the results of numerical and experimental studies are compared. By varying the parameters of the finite element model, a satisfactory correspondence between the results of numerical calculations and experimental measurements is achieved. In particular, the following are determined: the acceptable type of used finite elements; the number of finite elements required to satisfy the accuracy of numerical modeling of the dynamic properties of similar structures; zones of the recommended thickening-rarefaction of a grid of finite elements, etc. According to the research results, the parameters of finite-element models have been established, which can be used to study the dynamic processes and properties of full-scale armored hulls of lightly armored vehicles.
 Keywords: lightly armored vehicle, mock-up, natural frequency, spectrum of natural vibration frequencies

BeO nanotube as a promising material for anticancer drugs delivery system

In this research, the application of BeO nanotube (BeONT) as a nanocarrier for Fluorouracil (5-FU) anticancer drug has been studied by density functional theory (DFT) approach. The method ωB97XD with 6-31 G** basis set were employed. A precise surface study, shows that there are two directions for 5-FU adsorption that did not deliver any of the imaginary frequency vibrational spectra, identifying that all relaxation structures are at the lowest energy level. Based on our calculations, the energy of adsorption for 5FU@BeONT structures are range −120 to −168 kJ/mol, in the gas phase and −395 to 4-00 kJ/mol in the aqueous phase. The highest and the lowest values of adsorption energy are both in strong physical adsorption. Due to receiving an electronic charge from 5-FU, BeONT exhibited a p-type semiconducting feature for all positions. In addition, based on natural bond orbital (NBO) analysis, the direction of charge transfer was from fluorine’s σ orbitals of the drug to n* orbitals (O and Be atoms) of BeONT with a considerable amount of transferred energy. BeONT can be employed as a potential strong carrier for 5-FU drugs for practical purposes based on our findings.

Developing Novel Gas Discharge Emitters of Acoustic Waves in Air for Nondestructive Testing of Materials.

This study was devoted to the development of novel devices and a methodology intended for generating ultrasonic waves in an air medium by using atmospheric pressure gas discharge. In the proposed electrode system, the discharge process was accompanied by the generation of acoustic waves on the emitter surface and, consequently, in the ambient air. The gas discharge emitter vibrations were analyzed by applying the technique of Scanning Laser Doppler Vibrometry (SLDV). It was shown that the magnitude of displacements matched the corresponding characteristics of classical piezoelectric and magnetostrictive transducers. The use of the Fast Fourier transform procedure supplied amplitude-frequency spectra of vibrations generated by the gas discharge emitter. The amplitude-frequency spectrum analysis showed that the proposed emitter was able to generate acoustic waves in the air with frequencies from 50 Hz to 100 kHz, and such a device can be used for the nondestructive testing (NDT) of materials. The results of the statistical analysis of vibration displacements in the repetitive pulsed mode were discussed. A non-stable characteristic of the vibration displacement of the emitter membrane was demonstrated. The parameters of such instability were associated with the features of gas discharge processes. In the experiments, the proposed gas discharge emitter was used in combination with SLDV for inspecting carbon-fiber-reinforced polymer composites. The experiments demonstrated the possibility of using an air-coupled gas discharge transmitter to generate acoustic waves in NDT applications.

Vibrations of launch vehicle fairings with conical shape

Vibrations of launch vehicle conical fairings are investigated. Fairings are simulated using thin conic shells. The modal analysis of a thin elastic shell is based on the use of the developed finite element model of an inhomogeneous shell. In general, the technique makes it possible to investigate the geometrically nonlinear deformation, stability, and post-buckling behavior of a wide class of thin elastic shells. The modal analysis of the structure is implemented at each step of the static thermomechanical load. The subspace iteration method is used to determine the spectrum of the lowest vibration frequencies of shells of an inhomogeneous structure. The shell behavior analysis method is based on the relations of the three-dimensional theory of thermoelasticity and uses the finite element moment scheme. A thin elastic shell is simulated by a universal solid isoparametric finite element. The parameters of natural vibrations of conical shells of revolution with different thicknesses are investigated. Comparison of the calculation results obtained by the finite element moment scheme with the data of other authors shows a fairly good agreement between the solutions.

Application of vibration diagnostics methods in the creating of elements of personal electric transport

The study of vibration loading of the main elements of personal electric vehicles and the search for ways to reduce vibration characteristics was conducted. The issues of measuring vibration arising on a bicycle, which is driven by human muscle power and an electric drive, are considered. Measurements of vibration acceleration and frequency spectra in a certain area of motion were carried out using the “Octave-101VM” spectrum analyzer in three stages. At the first stage, the electric bike was driven by a pedal drive, at the second – by an electric drive, at the third – the pedals and the electric drive worked in parallel. As a result of the tests carried out, it was found that the greatest vibration occurred in the “Motor” mode during the use of an electric bicycle, the least vibration occurred when driving with the electric motor turned off. It was found that the electric drive increases the vibration level (at the same time, the electric bike does not exceed the maximum permissible values of vibration levels on all axes). In order to reduce the vibration arising from the electric motor on a personal electric vehicle, a 3D computer model has been developed and an airless wheel mover has been manufactured using this model on a 3D printer (a wheel for an electric scooter with internal damping has been manufactured). Bench tests have shown that the developed wheel, in comparison with a pneumatic tire, has a smaller (up to 45 %) contact spot. The results obtained can be used in the development of competitive products, in particular personal electric vehicles.

Dehydrogenation versus deprotonation of disaccharide molecules in vacuum: a thorough theoretical investigation.

Dehydrogenation and deprotonation of sucrose and trehalose molecules in vacuum is theoretically studied by using ab initio calculations in the framework of the density functional theory. The differences in the structural, electronic, energetic and vibrational properties of dehydrogenated and deprotonated molecules are discussed, depending on the site from which the hydrogen atom or the proton has been removed. The dehydrogenated molecules are found to be stable, regardless of which hydrogen atom is removed. This contrasts with the instability of the deprotonated molecules, where break-ups or structural reorganizations of the molecule are observed in 20–30% of the cases, but only when the hydrogen atom whose proton is removed was bonded to a carbon atom. Considering the stability and possible rearrangements of the hydrogen network of the deprotonated/dehydrogenated molecule, the formation of additional hydrogen-bridge bonds compared with the nominal molecule appears to be more pronounced for the deprotonated molecules than for the dehydrogenated ones. Moreover, our calculations show that the hydrogen-transfer energy barriers are usually larger for the deprotonated molecules than for the dehydrogenated ones. Finally, compared with the nominal molecule, the vibrational frequency spectrum is shifted to lower frequencies for both the dehydrogenated and the deprotonated molecules.

Kinematic analysis and estimation of the frequency of natural oscillations of a planar lattice

Introduction. A statically determined regular symmetrical rectangular lattice is fixed on two supports. The mass of the lattice is distributed over its nodes. A kinematic analysis is presented that reveals the variability of the lattice for a certain number of panels. An algorithm for searching for the distribution of virtual velocities of lattice nodes in this case is described. A formula is derived for the dependence of the lower estimate of the first frequency of natural oscillations of the structure on the number of panels from the range of permissible values.
 
 Materials and methods. Calculation of forces in the bars of a statically determinate lattice is performed by the method of cutting out nodes using Maple computer mathematics system operators. To determine the rigidity of the structure, the Maxwel – Mohr formula is used on the assumption that the elastic moduli and cross-sectional areas of all lattice rods are the same.
 
 Results. It is shown that when the number of panels is a multiple of three, the determinant of the matrix of the system of equilibrium equations degenerates, and the system becomes an instantly variable mechanism. A corresponding picture of the distribution of knot velocities is given. Using the approximate Dunkerley estimate, a formula is derived for the dependence of the lower limit of the first oscillation frequency of the truss on the number of panels. The generalization of a series of particular solutions to an arbitrary number of panels is performed in the Maple system by induction.
 
 Conclusions. The proposed lattice model admits an analytical solution for the lower estimate of the first natural frequency. Comparison of the result with the numerical solution obtained for the lowest frequency of the entire frequency spectrum of natural lattice vibrations shows its high accuracy. It is shown that the error of the found analytical estimate decreases with an increase in the number of panels. The solution can be used in optimization problems and for a preliminary assessment of the designed structure.

Vibrational dynamics of the OD stretch in an atomistic simulation of HDO in H2O

An all-atom molecular dynamics (MD) simulation of dilute HDO in H2O was used to obtain vibrational frequency spectra from the classical MD trajectories and a wavelet-based method was developed to obtain the frequency-frequency correlation functions (FFCFs) of the OD stretch vibrations. Time constants were obtained on the order of 30 fs, 150–260 fs and 3.2–3.6 ps. An OD covalent bond length correlation function was calculated and a long-timescale decay constant of 1.73 ps was obtained, similar to experimental values that range from 1.45 ps to 1.8 ps. An O-O hydrogen bond length correlation function was calculated and found to exhibit an oscillation at 150 fs and a long-timescale decay time of 3.47 ps, both in good agreement with the FFCFs. Such results suggest that the spectral diffusion observed in FFCFs can be primarily attributed to fluctuations in O-O distances. An OD stretch energy correlation function was calculated, which consists of exponential decay with a time constant of 1.13 ps. The energy correlation function also exhibits two oscillations that are indicative of resonant energy transfer processes involving the OD stretch.