Vibration Displacement Research Articles

Design and compression-induced bandgap evolution of novel polygonal negative stiffness metamaterials

The paper proposes a novel polygonal negative stiffness (NS) metamaterial composed of folded beams and stiffening walls, which exhibits excellent performance in attenuating waves over a broad frequency range and shows compression-induced bandgap evolution characteristics. Dispersion relation and bandgaps for the propagation of elastic waves in NS metamaterials are calculated utilizing a semi-analytical periodic spectral method (PS-SAFE). The results demonstrate that broadband bandgaps can be achieved in the proposed polygonal NS metamaterials. Mode analysis and transmission spectrum are utilized to explain the underlying mechanisms of wave attenuation. Furthermore, appropriate deformation conditions are applied to the NS metamaterials to realize compression-induced bandgap evolution, which shows that compression-induced configuration variations significantly impact the frequency range and bandwidth of the bandgaps. As the deformation increases, folded beams enter the elastic instability stage, and the internal stress change strongly influence the vibration displacement modes, leading to various symmetric and antisymmetric displacement vibration modes within a similar frequency range, forming low-frequency broadband bandgaps. This work provides valuable insights into the design of advanced materials for low-frequency broadband wave attenuation.

Inter-shaft Bearing Fault Diagnosis Based on Aero-engine System: A Benchmarking Dataset Study

In this paper, the aero-engine test with inter-shaft bearing fault is carried out, and a dataset is proposed for the first time based on the vibration signal of rotors and casings. First, a test rig based on a real aero-engine is established, driven by motors and equipped with a lubricating system. Then, the aero-engine is disassembled and assembled following the specification process, and the inter-shaft bearing with artificial fault is replaced. Next, the aero-engine test is conducted at 28 groups of high and low pressure speeds. Six measuring points are arranged, including two displacement sensors to test the displacement vibration signals of the low pressure rotor and four acceleration sensors to test the acceleration vibration signals of the casing. The test results are integrated into an inter-shaft bearing fault dataset. Finally, based on the dataset in this paper, frequency spectrum, envelope spectrum, CNN, LSTM and TST are used for fault diagnosis, and the results are compared with those of CWRU and XJTU datasets. The results show that the characteristic fault frequency cannot be found directly in the spectrum and envelope spectrum corresponding to this paper's dataset but in CWRU and XJTU datasets. Using CNN, LSTM and TST for fault diagnosis of the dataset in this paper, the accuracy is 83.13%, 85.41% and 71.07%, respectively, much lower than the diagnosis results of CWRU and XJTU datasets. It can be seen that the dataset in this paper is closer to the actual fault diagnosis situation and is a more challenging dataset. This dataset provides a new benchmark for the validation of fault diagnosis methods. Mendeley data: https://github.com/HouLeiHIT/HIT-dataset.

A NARX Model-Based Condition Monitoring Method for Rotor Systems.

In this study, we developed a data-driven frequency domain analysis method for rotor systems using the NARX (Nonlinear Auto-Regressive with eXternal input) model established by system vibration signals. We propose a model-based index of fault features calculated in a multi-frequency range to facilitate condition monitoring of rotor systems. Four steps are included in the proposed method. Firstly, displacement vibration signals are collected at multiple monitored rotating speeds. Secondly, the collected signals are processed as output data and the corresponding input data is generated. Then, NARX models are developed with input and output data to characterize the rotor system. Finally, the NRSF (Nonlinear Response Spectrum Function)-based nonlinear fault index is calculated and compared to the healthy condition. An experimental application to the misaligned rotor system is also demonstrated to verify its effectiveness. Our results indicate that the value of the index directly reflects the severity of the misaligned fault.

Drilling-vibration response characteristics of rocks based on Hilbert–Huang transform

Currently, there are no in-situ methods to quantify drilling-vibration response characteristics of different lithologies. Here, we quantified the vibration responses of four lithologies (limestone, sandstone, coal, and mudstone) using a combination of theoretical deduction and numerical simulation. First, a drilling-vibration model of a particular rock was established, and the differential equations of motion and vibration responses to rock/drill bit interactions with the formation were derived. Next, finite-element simulation was adopted to simulate the rock/drill-bit interactions of the four lithologies. Finally, the Hilbert–Huang transform (HHT) was applied to extract characteristic waveforms, frequency bands, peak frequencies, and marginal spectra of vibration signals. Simulations revealed that the highest and lowest vibration responses were observed in limestone and mudstone, respectively. Vibration acceleration was proportional to the Young's modulus of rocks, whereas vibration displacement and velocity were inversely proportional to Young's modulus, compressive strength, and density. Based on the HHT results, among the four lithologies, vibration responses had the largest characteristic frequency segments and peak frequencies in limestone (28.1–34.6 kHz and 33.4 kHz, respectively), whereas those of mudstone were the smallest (15.6–21.3 kHz and 19.6 kHz, respectively). The results of this study provide a theoretical basis for establishing an identification method and expert knowledge database of lithology based on drilling-vibration responses.

Stability control of high-speed magnetic levitation turbomolecular pumps with shock-excited disturbance

The disturbance suppression of magnetic levitation turbomolecular pumps is a critical problem in industrial applications. This work addresses the stability control of high-speed magnetic levitation turbomolecular pumps with shock-excited disturbance. A disturbance suppression method based on improved linear extended state observer is proposed to attenuate the impact of external low-frequency disturbing force on a magnetic levitation turbomolecular pump. Firstly, a linear extended state observer of an active magnetic bearing is obtained by analyzing the rotor dynamics model. Then, the detailed descriptions of external disturbance suppression method using linear extended state observers and adaptive notch filters are discussed for the system. The boundary condition of the parameters of the improved linear extended state observer is determined. The root loci of the closed-loop system with improved linear extended state observers is also investigated. Finally, simulation and experimental results on a magnetic levitation turbomolecular pump show the applicability of the proposed method. The results show that the proposed method can attenuate the rotor vibration displacement caused by impact by 46.9%.

Fatigue condition assessment of subsea pipelines under vortex induced vibration and cyclical lateral displacement

ABSTRACT Subsea pipeline may suffer from vortex-induced vibration (VIV) and cyclical lateral displacement (CLD), which can result in fatigue failure of subsea pipeline. This paper presents a fatigue damage assessment of subsea pipelines under VIV and CLD. A finite element model of pipeline considering the pipe–soil coupling action is developed, and dynamic response of subsea pipeline under VIV and CLD is implemented to obtain time history of equivalent stress. The integrated fatigue damage of subsea pipeline under VIV and CLD is estimated using Palmgren–Miner linearly cumulative fatigue damage theory. The effect of pipe diameter, span length, pipe length and tidal period on fatigue damage of subsea pipelines under CLD is analyzed. A case study of a subsea pipeline in the strong tide area is performed. The results show the fatigue life of pipeline under VIV and CLD is 14.1 years, which is 2.3 years lower than the pipeline under VIV alone. The study can support more accurate estimation of fatigue life of subsea pipelines.

A tuning fork gyroscope with drive-sense orthogonal thin-walled holes for high sensitivity

A tuning fork gyroscope (TFG) with orthogonal thin-walled round holes in the driving and sensing directions is proposed to improve sensitivity. The thin walls formed by through holes produce stress concentration, transforming the small displacement of tuning fork vibration into a large concentrated strain. When piezoelectric excitation or detection is carried out here, the driving vibration displacement and detection output voltage can be increased, thereby improving sensitivity. Besides, quadrature coupling can be suppressed because the orthogonal holes make the optimal excitation and detection positions in different planes. The finite element method is used to verify the benefits of the holes, and the parameters are optimized for better performance. The experimental results show that the sensitivity of the prototype gyroscope with a driving frequency of 890.68 Hz is 100.32 mV/(°/s) under open-loop driving and detection, and the rotation rate can be resolved at least 0.016 (°/s)/Hz, which is about 6.7 times better than that of the conventional TFG. In addition, the quadrature error is reduced by 2.7 times. The gyroscope has a simple structure, high reliability, and effectively improves sensitivity, which is helpful to guide the optimization of piezoelectric gyroscopes and derived MEMS gyroscopes.

Modulated orthogonal cutting system realized by piezo stack actuation and linear guide coupling

Modulation-assisted machining (MAM) employs low-frequency feed-direction tool vibration to enhance conventionally continuous cutting processes such as turning, drilling, and boring operations. The development of a suitable tool vibration system is critical for the success of MAM. In this paper, a tool vibration system realized by using piezo stack actuation and linear guide coupling was designed and constructed. The performance of the system was evaluated by conducting orthogonal tube face turning tests on AISI 1045 steel using a range of cutting and modulation conditions. Cutting forces and tool vibration displacement were measured and analyzed. A mechanistic force model based on the variable uncut chip thickness was used to predict the variable primary cutting and feed forces in MAM which showed good agreement with the measured forces. Furthermore, It was found that the vibration amplitude with cutting was reduced when compared to the vibration amplitude without cutting. The reduction in vibration amplitude was predictable as it depends on the feed force and the stiffness of the system. The results indicate good control ability of the tool vibration system across a wide range of cutting and modulation conditions.

Depicting Defects in Metallic Glasses by Atomic Vibrational Entropy.

Due to the chaotic structure of amorphous materials, it is challenging to identify defects in metallic glasses. Here we tackle this problem from a thermodynamic point of view using atomic vibrational entropy, which represents the inhomogeneity of atomic contributions to vibrational modes. We find that the atomic vibrational entropy is correlated to the vibrational mean-square displacement and polyhedral volume of atoms, revealing the critical role of vibrational entropy in bridging dynamics, thermodynamics, and structure. On this method, the local vibrational entropy obtained by coarse-graining the atomic vibrational entropy in space can distinguish more effectively between liquid-like and solid-like atoms in metallic glasses and establish the correlation between the local vibrational entropy and the structure of metallic glasses, offering a route to predict the plastic events from local vibrational entropy. The local vibration entropy is a good indicator of thermally activated and stress-driven plastic events, and its predictive ability is better than that of the structural indicators.

Dynamic response of the hybrid honeycomb sandwich panel with zero Poisson’s ratio under low-speed impact

The dynamic response of the hybrid honeycomb sandwich panel under low-speed impact is studied. According to Hamilton’s principle and first-order shear deformation theory, the motion equation of the hybrid honeycomb sandwich panel is deduced. Then the Navier method and Duhamel’s integral are used to solve the vibration displacement of panels. Besides, the mass-spring (MS) model is used to calculate the contact force between the honeycomb sandwich panel and the impactor. The results of this model are compared with those of Abaqus and published studies, which verifies the feasibility of the theoretical model in this paper. Based on the developed theoretical model, the influences of the unit cell angle, cell wall length, cell wall thickness, core layer height and impact speed on the dynamic response of sandwich panels have been studied. The results show that under the same low-speed impact, the maximum lateral displacement of hybrid sandwich panels was 11.65% smaller than that of conventional sandwich panels when honeycomb parameter θ = 60°, and was 15.45% when honeycomb parameter The energy absorption character of the hybrid honeycomb sandwich panel are better than those of the traditional hexagonal honeycomb sandwich panel and the concave hexagonal honeycomb sandwich panel.

Multi-field coupling and free vibration of a sandwiched functionally-graded piezoelectric semiconductor plate

Sandwiched functionally-graded piezoelectric semiconductor (FGPS) plates possess high strength and excellent piezoelectric and semiconductor properties, and have significant potential applications in micro-electro-mechanical systems. The multi-field coupling and free vibration of a sandwiched FGPS plate are studied, and the governing equation and natural frequency are derived with the consideration of electron movement. The material properties in the functionally-graded layers are assumed to vary smoothly, and the first-order shear deformation theory is introduced to derive the multi-field coupling in the plate. The total strain energy of the plate is obtained, and the governing equations are presented by using Hamilton’s principle. By introducing the boundary conditions, the coupling physical fields are solved. In numerical examples, the natural frequencies of sandwiched FGPS plates under different geometrical and physical parameters are discussed. It is found that the initial electron density can be used to modulate the natural frequencies and vibrational displacement of sandwiched FGPS plates in the case of nano-size. The effects of the material properties of FGPS layers on the natural frequencies are also examined in detail.

Monocular vision based 3D vibration displacement measurement for civil engineering structures

Vibration displacement of civil structures are crucial information for structural health monitoring (SHM). However, the challenges and costs associated with traditional physical sensors make displacement measurement difficult. In recent years computer vision (CV) techniques have been employed for measuring vibration displacement in civil structures. There has been a growing interest in CV-based three-dimensional (3D) displacement measurement, as it provides comprehensive information for structural health assessment. Most existing methods use multi-view geometry, requiring multiple cameras for depth measurement. This paper proposes a new system for measuring the 3D vibration displacement utilising a single camera. Instead of using multi-view geometry, deep neural networks are utilised to learn the depth of scenes from monocular images. Compared with the multi-view methods, the proposed 3D measurement system with monocular vision is more cost-effective and much more convenient to set up and use in practice, avoiding the complicated calibration and object matching between multiple cameras. Experimental tests are conducted in the laboratory to investigate the feasibility of the proposed system. Physical displacement sensors are equipped with the testing structure to provide the ground truth data. The results demonstrate that the proposed monocular 3D displacement system is able to produce reasonable 3D full-field displacement measurement, which makes monocular image based CV system a promising approach to achieve 3D displacement measurement, with its obvious advantages in cost and convenience compared to the traditional sensor-based or multi view CV-based methods.

Research on Active Precontrol Strategy for Shape and Performance of Helicopter Spiral Bevel Gears

Gear vibration becomes unmanageable under extreme conditions, which shortens the time between overhauls of the helicopter reducer and affects the service efficiency of helicopters. For this purpose, an active precontrol strategy for shape and performance was developed for spiral bevel gear (SBG) systems, thus prolonging the reliable service period of helicopters. Firstly, the perfect pinion surface was built based on the preset contact path (CP) and transmission error (TE). Secondly, through a combination of tooth contact analysis (TCA) and loaded tooth contact analysis (LTCA), the loaded transmission error (LTE), meshing stiffness (MS), and meshing impact (MI) of the SBG transmission were obtained. Thirdly, an eight-degrees-of-freedom (8-DOF) dynamic model was built, and a simplified dynamic model was generated based on this. As regards the dynamic response, the root mean square of normal vibration acceleration (RMA) of the SBG transmission was obtained by solving the differential equation of motion. The RMA of the SBG transmission was also analysed based on the basic theory of vector structural mechanics. Finally, an optimization model aimed at reducing the RMA of the SBG transmission was established using ease-off, and a redesigned SBG transmission with good dynamic performance was obtained through optimization. Simulation analysis showed that the LTE and MS amplitudes of the optimized gear were smaller than those of the original gear. The impact force and impact velocity of the optimized gear were 27.02% and 25.81%, respectively, lower than those of the original gear. The RMA value of the optimized gear was much lower than that of the original gear. The normal vibration velocity and displacement of the optimized gear transmission were also cut down. Therefore, the design approach can effectively increase the performance of gear transmission.

Rotating box multi-objective visual tracking algorithm for vibration displacement measurement of large-span flexible bridges

Visual displacement measurement methods for flexible structural bodies like large-span bridges has gained wide popularity in recent years, but practical applications still have some limitations. For instance, when acquiring images of large-span flexible bridges at a distance, the slight angular tilt of the detection target due to irregular vibrations can cause extremely serious misfit errors in the displacement curves returned by the vision measurement algorithm. To improve the reliability of vibration displacement measurement of flexible structural bodies, this paper takes the bridge subjected to external excitation in the acquired image sequence as the object of vibration displacement measurement and uses a designed high-precision displacement measurement algorithm for a single-stage rotating target tracking anchor-free box to track the vibration displacement of the target in the flexible structural body. We first extract multi-scale feature information of bridge model image sequences using the improved YOLOv5-s backbone network and combine the Transformer self-attention mechanism with PANet to perform a top-down and bottom-up bi-directional fusion of target feature maps at three different scales to achieve semantic feature fusion of shallow and deep information. Second, the improved Efficient Decoupled Head performs the detection of rotating target centroid offset and bounding box size. Finally, the detected results are passed into the multi-objective tracking algorithm ByteTrack, which strengthens the spatio-temporal correlation between frames and obtains a better-fitting vibration displacement curve. The validation and comparison of traditional visual measurement methods and deep learning measurement methods on cable-stayed bridge models, small arch bridges, and large span bridges show that the vibration displacement trajectories regressed by the algorithm in this paper have the best fit with the actual vibration displacement trajectories, which also verifies that the algorithm in this paper has good potential for engineering applications and implementation space in the field of condition monitoring of flexible structural bodies.

Ply angle effects on cavitating flow induced structural response characteristics of the composite hydrofoils

The objective of this paper is to experimentally investigate the structural response characteristics of composite hydrofoils with different ply angles. A synchronous measurement system composed of the high-speed camera, the laser Doppler vibrometer, the flow rate regulation system and the pressure regulation system is established. The results show that the composite hydrofoil with +45° ply angle promotes the cavitation inception and has the most severe cavitation behavior at the same cavitation number. Relatively significant structural vibration can be observed in the sheet and cloud cavitation regimes. From the incipient cavitation to the supercavitation regimes, the probability density distribution of vibration velocity of the composite hydrofoils gradually deviates from the normal distribution. The structural displacement responses for different hydrofoils have quasi-periodic characteristics. The dominant vibration displacement frequency is consistent with the cavity shedding frequency and cavitating area pulsation frequency. The cavitation number range of frequency lock-in satisfies composite hydrofoil with +45° ply angle > composite hydrofoil with −45° ply angle > composite hydrofoil with 0° ply angle.

Extreme detectable vibration frequency limited by rolling shutter camera imaging of laser speckles.

The row scanning mechanism of a rolling shutter camera can be used to infer high-frequency information from a low-frame-rate video. Combining the high intensity of laser speckle and high row-sampling rate of a rolling shutter, extreme detectable vibration frequency limited by rolling shutter camera imaging is experimentally demonstrated. Using a commercially available industrial camera at a frame rate of 70 fps, a vibration signal with a frequency of 14.285 kHz is extracted that corresponds to an inter-row sampling period of 35 µs and a sampling frequency of 28.57 kHz. Connected component and centroid alignment algorithms are used to extract the inter-row vibration displacement. The parameters that limit the highest and lowest detectable frequencies are discussed.

Study on water hammer effect and tubing string vibration in high-pressure high-production gas wells

The transient internal flow in high-pressure high-production gas wells generates severe water hammer and tubing string vibration, which accelerates fatigue damage, joint wear, thread loosening, and other wellbore integrity problems. Based on the analysis of transient flow in gas wells, a mathematical model for fluid pressure surge and the induced tubing string vibration is developed and validated by similarity experiments. This method considers fluid-structure interaction, initial loads of tubing string, and compressibility of natural gas, and can fill the gap in quantification of water hammer pressure and tubing sting dynamic load in high-pressure high-production gas wells. On this basis, the effects of valve closure time, production rate, liquid content, and tubing string structure on transient flow and tubing string characteristics are analyzed systematically. The calculations show that wellhead pressure increases rapidly, and pressure wave propagates along tubing string to induce vibrations in the string after an instantaneous shut-in at the wellhead. During this transient process, fluid pressure and axial stress at wellhead reach their maximum valves. Owing to the fixed constraint effect of wellhead and downhole packer, the lack of restrictions on tubing distant from wellhead and packer enhances the severity of axial vibration. As valve closure time increases, the maximum wellhead pressure, tubing vibration displacement, and velocity gradually decrease. Therefore, the most direct way to control water hammer effect and tubing string vibration is to extend the shut-in time or prevent a rapid shut-in of gas well. The methods used in this study and the results obtained therein can serve as both a theoretical framework and practical foundation for the prediction and control of water hammer effect and tubing string vibration in high-pressure high-production gas wells.

Dynamometric cutting tool

The aim was to develop, manufacture and test a technically simple dynamometer for monitoring the cutting process during boring and turning. An S20R-SSSCR09 right-hand cutter was selected as a research object. To register the cutting force and vibration movements of the cutter tip in tangential and radial directions, the cutter was equipped with four KF5P1-10-400-A-12 strain gauges mounted according to a half-bridge scheme. The bending stiffness of the cutter in two directions was measured by a DOU-3-01 compression dynamometer and a DDP-10A dial indicator. The cutter natural frequency was determined by a vibrogram of damped bending vibrations. The dynamometric boring tool was tested on a DMG NEF 400 turning machine by turning a workpiece made of 20X steel, 79 mm in diameter with a 200 mm extension, at a spindle rotational frequency of 600 r/min, a cutting depth of 0.8 mm and a longitudinal feed of 0.103 mm/turn. According to the conducted review of modern turning dynamometers and their designs, strain gauging of cutting tools is the simplest technical solution when carrying out boring procedures. The bending stiffness of the cutter in tangential and radial directions comprised 0.6 and 1.058 N/μm, respectively. The conversion coefficients for displacements in these directions were 3.5 and 4.2 μm/V, respectively. The mutual influence of registration of radial on tangential and tangential on radial displacements was 7.7% and 2.8%, respectively. The obtained vibrograms showed that the turning process under the given machining conditions is accompanied by distinct auto-oscillations of the cutter with a frequency of 561 Hz. Therefore, strain gauging of cutting tools provides information in the form of vibrograms about the two most important parameters of the cutting process dynamics – force and vibration displacements. The main advantages of the presented dynamometric cutting tool include its design simplicity, possibility of manufacturing in laboratory conditions, low cost and insensitivity to temperature and axial feed force variations.

Adaptive backstepping dynamic sliding mode control for maglev turning motor spindle based on limited time preset performance

In the process of turning a maglev motorized spindle, there are problems such as system model time-varying, cross-coupling of control parameters, difficult measurement of system state variables, and nonlinear characteristics of active magnetic bearings, which lead to the inevitable cutting chatter phenomenon, difficult control algorithm design, and then the reduction of workpiece surface quality and accuracy, affecting machining efficiency and tool life. In this paper, the “multimodal-distributed parameter” model is extended to the “magnetic bearing-rotor-workpiece” variable mass turning process. An adaptive backstepping fast dynamic terminal sliding mode control is designed to address the model’s time-varying parameters and cross-coupling issues. In view of the difficulty in measuring the vibration displacement at the cutting point, the displacement field reconstruction method was introduced to reconstruct the vibration displacement field online and provide effective feedback for the previously designed control strategy. Finally, the proposed controller is applied to adjust and control the turning process of a maglev motorized spindle and compared with other advanced controllers. The simulation results show that the proposed control method has a better control effect than other control methods in the presence of unmodeled dynamics, uncertainties, and external disturbances.

Cable vibration measurement based on broad-band phase-based motion magnification and line tracking algorithm

Cables are important components of cable-supported bridges and the measurement of cable vibration is very useful for the condition assessment of bridges. The recently developed computer vision (CV) based vibration measurement method has many merits over the traditional contact method. However, most existing CV-based methods require installing the artificial targets on the structure and are only suitable for situations with large vibration amplitude. Therefore, this study proposes a method based on the broad-band phase-based video motion magnification (BPVMM) and the line tracking algorithms for the vibration measurement of cables with small-amplitude vibration. The BPVMM algorithm is used to magnify the small vibrations and the line tracking algorithm is used to extract the vibration displacement from the magnified video for the final identification of cable frequencies. The proposed method is then verified by the laboratory cable test and the field test of a cable-stayed bridge. The results indicate that using the BPVMM algorithm to magnify the small vibration can significantly improve the identification accuracy of displacements and frequencies. The proposed method performs motion magnification over a wide frequency band including all the frequencies of interest, without prior knowledge of the structure frequencies, which greatly improves the computational efficiency and facilitate the measurement of cable vibration under environmental excitation in practical applications.