Vibration Displacement Signals Research Articles

Investigation of a Method for Identifying Unbalanced States in Multi-Disk Rotor Systems: Analysis of Axis Motion Trajectory Features

The operational state of a rotor system directly affects its working efficiency, and the axis trajectory can accurately characterize this state. Therefore, a method for extracting axis motion trajectory characteristics based on distance sequence representation is established. First, the axis trajectory sample signal is constructed from the original vibration displacement signal. Singular value decomposition (SVD) is performed on the sample signal to obtain effective components, resulting in a purified and denoised axis motion trajectory signal. Next, the axis motion trajectory signal is centralized and normalized. Feature extraction is then performed on the axis motion trajectory signal. Based on the different curvatures of various regions in the axis motion trajectory graph, data points are adaptively selected. The distances between the selected data points and a unique fixed point are calculated in the two-dimensional plane, resulting in a feature signal that characterizes the axis motion trajectory graph. This completes the extraction of the axis motion trajectory characteristics. Different rotational speeds, additional weights, and changes in rotor arrangement types are applied to a multi-disk rotor test rig to obtain measured data for various unbalanced states, validating this method. The results show that this method effectively characterizes the axis motion trajectory with strong generality.

Multi-fault classification of rotor systems based on phase feature of axis trajectory in noisy environments

As it is difficult to distinguish multiple rotor faults with similar dynamic phenomena in noisy environments, a multi-fault classification method is proposed by combining the extracted trajectory phase feature, a parameter-optimized variational mode decomposition (VMD) method and a light gradient boosting machine (LightGBM) model. The trajectory phase feature is extracted from an axis trajectory by fusing the frequency, amplitude, and phase information related to rotor motion and can comprehensively describe the dynamic characteristics induced by different rotor faults. First, the vibration displacement signals in two orthogonal directions are collected to construct the axis trajectories with 12 rotor states including healthy, unbalance, misalignment, single crack, multiple cracks, and a mixture of them. Second, the trajectory phase feature is extracted from the vectorized axis trajectories, and the frequency spectra of trajectory phase angles under different rotor faults are analyzed through Fourier transform. Finally, a parameter-optimized VMD method combined with a LightGBM model is applied to classify multiple faults of rotor systems in different noisy environments based on the extracted trajectory phase feature. The 12 rotor states can be classified into nine categories based on the harmonic information of 1X–7X components (X is the rotating frequency of a rotor system) and other components with smaller amplitudes in the frequency spectra of trajectory phase angles. The average classification accuracy of the 12 rotor states exceeds 93.0%, and the recognition rate for each kind of fault is greater than 77.5% in noisy environments. The simulated and experimental results demonstrate the effectiveness and adaptability of the proposed multi-fault classification method. This work can provide a reference for the condition monitoring and fault diagnosis of rotor systems in engineering.

Using Semantic Segmentation Network to Measure Vibration Displacement of Rotating Body

Compared with traditional vibration measurement sensors, visual vibration displacement measurement technology has many advantages, such as long-distance, non-contact and non-interference. However, when it comes to complex working conditions or inconvenient pre-processing scene, visual measuring techniques usually can’t produce results with the high precision needed for vibration analysis. In this paper, we proposed a visual measurement algorithm for vibration displacement of rotating body using semantic segmentation network by taking a high-speed industrial camera as the image acquisition medium and rotor as the experimental object. To make the network better applicable to segmentation of rotating body targets in different illumination, blur and similarity contexts, the cross stage partial (CSP) connections, concat channel fusion module and shuffle attention (SA) are purposefully incorporated into proposed CMCS convolution module. During calculating the loss in the training network stage, we add the binary cross-entropy loss and Dice-loss to solve the problem of serious imbalance between positive and negative samples caused by remote photography. The vibration signal synchronously collected by eddy current sensor is exploited as standard signal to compare the different segmentation algorithms quantitatively and qualitatively. The experimental results show that the RMSE between vibration displacement signal regressed by our segmentation algorithm and standard signal is the smallest, and the time domain diagram, frequency domain diagram and shaft orbit diagram are also more fitted to the standard signal curve, which provides valuable guidance for the visual vibration displacement measurement of rotating body in complex industrial setting.

Application of Fault Diagnosis Method Combining Finite Element Method and Transfer Learning for Insufficient Turbine Rotor Fault Samples.

Deep learning has led to significant progress in the fault diagnosis of mechanical systems. These intelligent models often require large amounts of training data to ensure their generalization capabilities. However, the difficulty of obtaining turbine rotor fault data poses a new challenge for intelligent fault diagnosis. In this study, a turbine rotor fault diagnosis method based on the finite element method and transfer learning (FEMATL) is proposed, ensuring that the intelligent model can maintain high diagnostic accuracy in the case of insufficient samples. This method fully exploits the finite element method (FEM) and transfer learning (TL) for small-sample problems. First, FEM is used to generate data samples with fault information, and then the one-dimensional vibration displacement signal is transformed into a two-dimensional time-frequency diagram (TFD) by taking advantage of the deep learning model to recognize the image. Finally, a pre-trained ResNet18 network was used as the input to carry out transfer learning. The feature extraction layer of the network was trained on the ImageNet dataset and a fully connected layer was used to match the specific classification problems. The experimental results show that the method requires only a small amount of training data to achieve high diagnostic accuracy and significantly reduces the training time.

Force Identification Based on Response Signals Captured with High-Speed Three-Dimensional Digital Image Correlation

Structural Health Monitoring (SHM) systems allow three types of diagnostic tasks to be performed, namely damage identification, loads monitoring, and damage prognosis. Only if all three tasks are correctly fulfilled can the useful remaining life of a structure be estimated credibly. This paper deals with the second task and aimed to extend state-of-the-art in load identification, by demonstrating that it is feasible to achieve it through the analysis of response signals captured with high-speed three-dimensional Digital Image Correlation (HS 3D-DIC). The efficacy of the proposed procedure is demonstrated experimentally on a frame structure under broadband vibration excitation. Full-field vibration displacement signals are captured with the use of two high-speed cameras and processed with 3D-DIC. Loads are identified with two different algorithms based on inverting the Frequency Response Function (FRF) matrix and modal filtration (MF). The paper discusses both methods providing their theoretical background and experimental performance.

Автоколебания клетей стана тандема холодной прокатки 2000 Магнитогорского металлургического комбината

One of the problems of cold rolling of thin strips is self-excited chatter vibrations, which lead to the appearance of various defects. High-frequency self-oscillations can lead to defects related to surface quality, low-frequency ones with high amplitude levels can lead to gusts of thin bands or even severe accidents of the rolling mill itself. As a rule, self–oscillations occur suddenly at high rolling speeds, more than 20 m / s and thin strips, the thickness is usually around 300-700 microns. For the normal operation of the rolling mill, it is necessary to use special systems for monitoring the vibration state and preventing the occurrence of self-oscillations. The control system for exceeding the critical vibration level generates signals from the automated control system of the mill to eliminate self-oscillations. The critical vibration level is determined by the spectral composition using the fast Fourier transform (FFT). When self-oscillations occur, lowfrequency components from 5 to 20 Hz prevail, frequencies in the range of the third octave from 100 to 200 Hz and frequencies of the fifth octave from 400 to 800 Hz. The cold rolling mill 2000 of the Magnitogorsk Iron and Steel Works combines a tandem five-cell mill and a continuous etching unit. There is no regular vibration monitoring system at the mill, warning and elimination of self-oscillations occurs in manual mode. With the use of research vibration equipment, experimental studies have been conducted on the possibility of using technological parameters to control and prevent the occurrence of self-oscillations. The moment of occurrence of self-oscillations can be controlled by the vibrations of the hydraulic tensioning device (GNU) of the mill. Processing of the vibration displacement signal of the measuring channel of the GNU FFT

Research on diagnosis method of centrifugal pump rotor faults based on IPSO-VMD and RVM

Centrifugal pump is a key part of nuclear power plant systems, and its health status is critical to the safety and reliability of nuclear power plants. Therefore, fault diagnosis is required for centrifugal pump. Traditional fault diagnosis methods have difficulty extracting fault features from nonlinear and non-stationary signals, resulting in low diagnostic accuracy. In this paper, a new fault diagnosis method is proposed based on the improved particle swarm optimization (IPSO) algorithm-based variational modal decomposition (VMD) and relevance vector machine (RVM). Firstly, a simulation test bench for rotor faults is built, in which vibration displacement signals of the rotor are also collected by eddy current sensors. Then, the improved particle swarm algorithm is used to optimize the VMD to achieve adaptive decomposition of vibration displacement signals. Meanwhile, a screening criterion based on the minimum Kullback-Leibler (K-L) divergence value is established to extract the primary intrinsic modal function (IMF) component. Eventually, the factors are obtained from the primary IMF component to form a fault feature vector, and fault patterns are recognized using the RVM model. The results show that the extraction of the fault information and fault diagnosis classification have been improved, and the average accuracy could reach 97.87%.

Establishment and analysis of nonlinear frequency response model of planetary gear transmission system

Abstract. Based on the lumped parameter theory, a nonlinear bending torsion coupling dynamic model of planetary gear transmission system was established by considering the backlash, support clearance, time-varying meshing stiffness, meshing damping, transmission error and external periodic excitation. The model was solved by the Runge–Kutta method, the dynamic response was analyzed by a time domain diagram and phase diagram, and the nonlinear vibration characteristics were studied by the response curve of the speed vibration displacement. The vibration test of the planetary gearbox was carried out to verify the correctness of frequency domain response characteristics. The results show that the vibration response in the planetary gear system changes from a multiple periodic response to a single periodic response with the increase in input speed. Under the action of the backlash, time-varying meshing stiffness and meshing damping, the speed vibration displacement response curves of internal and external meshing pairs appear to form a nonlinear jump phenomenon and have a unilateral impact area, and the system presents nonlinear characteristics. The nonlinear vibration of the system can be effectively suppressed by decreasing the mesh stiffness or increasing the mesh resistance, while the vibration response displacement of the system increases by increasing the external exciting force, and the nonlinear characteristics of the system remain basically unchanged. The backlash is the main factor affecting the nonlinear frequency response of the system, but it can restrain the resonance of the system in a certain range. The spectrum characteristics of the vibration displacement signal of the planetary gearbox at different speeds are similar to the simulation results, which proves the validity of the simulation analysis model and the simulation results. It can provide a theoretical basis for the system vibration and noise reduction and a dynamic structural stability design optimization.

Bandwidth and noise analysis of high-Q MEMS gyroscope under force rebalance closed-loop control

The force-to-rebalance (FTR) closed-loop detection method is commonly used to expand the bandwidth (BW) for micro-electro-mechanical system (MEMS) gyroscopes with low-frequency split and high-quality factors. However, the relationship between the BW and output noise is often incompatible; thus, reducing the detection accuracy of the gyroscope. This paper presents an analysis of the BW and noise spectra under modulation-demodulation FTR gyroscopes. The expressions for the BW and the noise-equivalent rate (NER) spectrum are derived to explore the effects of the loop gain on the BW and NER. It is demonstrated that the gain of the amplifier circuit is maximally transferred to the vibration displacement signal conversion part, which can reduce the output noise without affecting the BW. The simulation and experimental results on the Cobweb-like disk resonator gyroscope show that the derived expressions of BW and NER are correct, and the noise optimization method is effective, which provides an idea for the realization of a high-precision MEMS gyroscope.

An Experimental Approach on Beating in Vibration Due to Rotational Unbalance

This paper proposes a study in theoretical and experimental terms focused on the vibration beating phenomenon produced in particular circumstances: the addition of vibrations generated by two rotating unbalanced shafts placed inside a lathe headstock, with a flat friction belt transmission between the shafts. The study was done on a simple computer-assisted experimental setup for absolute vibration velocity signal acquisition, signal processing and simulation. The input signal is generated by a horizontal geophone as the sensor, placed on a headstock. By numerical integration (using an original antiderivative calculus and signal correction method) a vibration velocity signal was converted into a vibration displacement signal. In this way, an absolute velocity vibration sensor was transformed into an absolute displacement vibration sensor. An important accomplishment in the evolution of the resultant vibration frequency (or combination frequency as well) of the beating vibration displacement signal was revealed by numerical simulation, which was fully confirmed by experiments. In opposition to some previously reported research results, it was discovered that the combination frequency is slightly variable (tens of millihertz variation over the full frequency range) and it has a periodic pattern. This pattern has negative or positive peaks (depending on the relationship of amplitudes and frequencies of vibrations involved in the beating) placed systematically in the nodes of the beating phenomena. Some other achievements on issues involved in the beating phenomenon description were also accomplished. A study on a simulated signal proves the high theoretical accuracy of the method used for combination frequency measurement, with less than 3 microhertz full frequency range error. Furthermore, a study on the experimental determination of the dynamic amplification factor of the combination vibration (5.824) due to the resonant behaviour of the headstock and lathe on its foundation was performed, based on computer-aided analysis (curve fitting) of the free damped response. These achievements ensure a better approach on vibration beating phenomenon and dynamic balancing conditions and requirements.

Application of Axis Orbit Image Optimization in Fault Diagnosis for Rotor System

The shape characteristic of the axis orbit plays an important role in the fault diagnosis of rotating machinery. However, the original signal is typically messy, and this affects the identification accuracy and identification speed. In order to improve the identification effect, an effective fault identification method for a rotor system based on the axis orbit is proposed. The method is a combination of ensemble empirical mode decomposition (EEMD), morphological image processing, Hu invariant moment feature vector, and back propagation (BP) neural network. Experiments of four fault forms are performed in single-span rotor and double-span rotor test rigs. Vibration displacement signals in the X and Y directions of the rotor are processed via EEMD filtering to eliminate the high-frequency noise. The mathematical morphology is used to optimize the axis orbit including the dilation and skeleton operation. After image processing, Hu invariant moments of the skeleton axis orbits are calculated as the feature vector. Finally, the BP neural network is trained to identify the faults of the rotor system. The experimental results indicate that the time of identification of the tested axis orbits via morphological processing corresponds to 13.05 s, and the identification accuracy rate ranges to 95%. Both exceed that without mathematical morphology. The proposed method is reliable and effective for the identification of the axis orbit and aids in online monitoring and automatic identification of rotor system faults.

Research on Shaking Table Test of Earthquake Simulation Based on Hybrid Integration Algorithm

Aiming at the problem of poor accuracy of acceleration waveform reproduction during the shaking table test of earthquake simulation, a hybrid integration algorithm based on seismic acceleration signal is proposed to control the trend term error. The low-frequency attenuation integral algorithm in the frequency domain is used to integrate the original seismic acceleration signal once to obtain the vibration velocity signal, then, the polynomial fitting integration algorithm is introduced to integrate of the vibration velocity signal once in the time domain to obtain the vibration displacement signal. Through these two integrals, the sensitivity of low frequency band during frequency domain integration and the accumulation of small errors in time domain are reduced. Finally, the hybrid integration algorithm is used to perform seismic wave reproduction experiments on the seismic simulation shaker and good results are obtained, which proves that the hybrid integration calculation has high practical value and practical significance in improving the accuracy of the vibration table waveform reproduction.

Research on roundness error extraction method for precision machine tool spindle based on least square method

Based on the application requirement of online measurement and evaluation for roundness error of precision machine tool spindle, a specific method is proposed to fit the spindle roundness error based on the least square method according to the characteristics of the roundness error. Firstly, aiming to the radial vibration displacement signal of spindle, which collected by the sensor, a multi-harmonic signal with speed frequency of spindle as the fundamental frequency is constructed, and then the least square method is used to fit the amplitudes and phases of each harmonic signals. Finally, according to the fitting results, the rotation error and the interference of higher-order noise signals are eliminated, and the contour signal with only roundness error of the spindle is reconstructed, and then the roundness error of the spindle is evaluated by appropriate evaluation method. The simulation system of rotation and roundness errors separation for spindle system is developed, and the feasibility and accuracy of least square method to fit the spindle roundness error are verified by simulation analysis.

A Revised Hilbert⁻Huang Transform and Its Application to Fault Diagnosis in a Rotor System.

As a classical method to deal with nonlinear and nonstationary signals, the Hilbert–Huang transform (HHT) is widely used in various fields. In order to overcome the drawbacks of the Hilbert–Huang transform (such as end effects and mode mixing) during the process of empirical mode decomposition (EMD), a revised Hilbert–Huang transform is proposed in this article. A method called local linear extrapolation is introduced to suppress end effects, and the combination of adding a high-frequency sinusoidal signal to, and embedding a decorrelation operator in, the process of EMD is introduced to eliminate mode mixing. In addition, the correlation coefficients between the analyzed signal and the intrinsic mode functions (IMFs) are introduced to eliminate the undesired IMFs. Simulation results show that the improved HHT can effectively suppress end effects and mode mixing. To verify the effectiveness of the new HHT method with respect to fault diagnosis, the revised HHT is applied to analyze the vibration displacement signals in a rotor system collected under normal, rubbing, and misalignment conditions. The simulation and experimental results indicate that the revised HHT method is more reliable than the original with respect to fault diagnosis in a rotor system.

Chatter mitigation for the milling of thin-walled workpiece

During the milling process of thin-walled workpiece, chatter is the major obstacle in achieving desired accuracy and productivity of the final part due to its low rigidity. In this paper, a novel method is proposed to mitigate the chatter of the thin-walled workpiece by submerging the milling system in viscous fluid. To evaluate the effectiveness of the presented method, the influence of the viscous fluid on the milling force coefficients is investigated, and the modal parameters of the thin-walled workpiece are identified under dry and viscous conditions respectively. It is found that compared with the dry milling, the milling force coefficients reduce significantly under viscous fluid condition due to the lubrication. Besides, the damping of the milling system increases substantially under viscous fluid condition, and the natural frequencies of the milling system decrease owing to the added mass of the viscous fluid. The milling stability lobe diagrams are predicted based on the numerical integration method by taking multiple modes of the thin-walled workpiece into consideration. A series of milling tests are conducted to verify the stability lobe diagrams and confirm the effectiveness of the proposed approach. The vibration displacement signals are measured and then analyzed in time-frequency domain to demonstrate the state of the milling process. Moreover, the surface finishes of the thin-walled workpieces are compared. The results show that the thin-walled workpiece chatter could be suppressed greatly with the proposed method and higher stability limit can be achieved.

Structural vibration monitoring and operational modal analysis of offshore wind turbine structure

In order to reduce the structural failure and accident occurrence of the offshore wind turbine, the researches on structural operational safety of offshore wind turbine based on the measured data during the operation periods should be carried out and considered as the key way to solve these problems. However, the current researches are only focused on numerical simulation, model experiment and theoretical analysis and ignore the structural vibration characteristics analyzed from condition monitoring and prototype observation data from the actual wind turbine structure. To compensate for this study defect, the structural vibration displacement signals of one Chinese offshore wind power prototype under different conditions were obtained based on a long-term prototype observation in order to achieve the comprehensive and systematic research on vibration response characteristics and operational modal analysis of measured structure. Considering the complicated operational environment of offshore wind turbines, the structural response regular pattern and vibration safety are also discussed emphatically under different conditions such as standstill, normal operational, startup, shutdown and extreme typhoon status. Simultaneously, the integral operational modal identification method of offshore wind turbine in the range of full power is proposed based on traditional and modified stochastic subspace identification technologies, and further the modal identification results and the relationship between structural modal parameters and environmental/operational factors are also illustrated in this paper. The researches on the structural vibration characteristics and operational modal analysis of offshore wind turbine not only provide powerful data and technology support for the operation safety evaluation, but also provide the necessary theoretical and practical bases for the design and maintenance of wind turbine structures.

Modal Testing Based on Single Point Laser Continuous Plane Scanning Vibration Measurement

Vibration Measurement Jigang Wu, Bin Qin, Xuejun Li, Zengzeng Yang Hunan University of Science and Technology/Hunan Provincial Key Laboratory of Health Maintenance for Mechanical Equipment, jgwuhust@gmail.com Hunan University of Science and Technology/Hunan Provincial Key Laboratory of Health Maintenance for Mechanical Equipment, qinbin505@sina.com Hunan University of Science and Technology/Engineering Research Center of Advanced Mine Equipment, Ministry of Education, hnkjdxlxj@163.com, yzz430104@yahoo.cn Abstract A high precision and fast testing method for pure modal of vibration body by continuous constant speed plane scanning vibration measurement using single point laser doppler vibrometer is proposed. According to pure modal theory, the relationship between the vibration displacement signal which obtained by continuous scanning the free vibration string which both ends are fixed with single point laser vibrometer and the modal shapes of the string is established theoretically based on the investigation of free vibration of a string which both ends are fixed. The processing method for the actual vibration signal is investigated, and the calculating method for the upper and lower alternate envelope of vibration displacement signal is proposed. The modal test platform based on single point laser continuous constant speed plane scanning vibration measurement is put up, and the validity of the modal testing method is verified by the modal testing of thin sheet beam.

Synthetic Amplitude Spectrum and Its Extensions for Analyzing the Two Perpendicular Directional Vibration Displacement Signals of a Rotating Rotor

Classical Amplitude Spectrum analysis and Full Amplitude Spectrum analysis exhibit deficiencies in analyzing the two perpendicular directional vibration displacement signals of a rotating rotor. The shape of Classical Amplitude Spectrum is influenced by the installing position of its sensor. Neither Classical Amplitude Spectrum nor Full Amplitude Spectrum can indicate the actual radial rotor vibration amplitude on every frequency. Therefore, the previous two methods are not convenient to be used in rotating machine diagnoses. To solve these problems, this paper proposes a new rotor vibration analyzing tool here called Synthetic Amplitude Spectrum (SAS). The paper discusses the principle of SAS analysis, provides the specific making process of SAS, and applies it to two other current important analyzing methods in rotating machine diagnoses, resulting in two SAS extensions. The two extensions include a short-time SAS array tool for rotor vibration time-frequency analysis and a SAS waterfall plot tool for analyzing rotor vibration during machine startup or shutdown. The experiments and theoretical analysis showed that SAS and its two extension methods are not influenced by the installation position of the two sensors, and each amplitude of the spectrums can represent the actual radial rotor vibration amplitude on the frequency.

Dynamic Test Experimental Studies on Printing Pressure Based on Two-Dimensional Holospectum

a proper printing pressure is a basic condition for realizing offset printing and is also quality guarantee of printed products. The printing pressure should be adjusted on time according to different thickness of paper and requirements. At present, the printing pressure is mainly tested statically and pre-commissioned by experiences, so it can not reflect size of the real printing pressure and no dynamic commissioning can be carried out. In this paper, the hoho-spectrum analysis method was adopted to analyze the vibration displacement signals of cylinders, so as to obtain central displacement of two cylinders and distance and to indirectly obtain pressure between the two cylinders. The test results showed that the method could test the printing pressure effectively and dynamically.