Vibration Components Research Articles

Investigation of microtremors observed at historic masonry townhouse buildings after Nepal earthquake

The Gorkha earthquake in 2015 was a recent large-scale earthquake that caused severe damage to many historic masonry buildings in the Kathmandu Valley, Nepal. The authors conducted a visual inspection survey of seismically damaged buildings after the earthquake in the historic town district of Bhaktapur in the Kathmandu Valley. The first part of this paper reports the distribution of the historic masonry buildings for each damage level in the surveyed area. A concentrating zone of severely-damaged buildings was explicitly found in the damage-level distribution map. Almost half of all the surveyed buildings were severely damaged during the earthquake, and most of these were historic masonry townhouse buildings. In the second part, the ambient vibration characteristics of the conventional historic masonry buildings in Bhaktapur are investigated. Typical dwelling houses in a historic town district in Nepal, which generally formed terraced houses built around a courtyard, were targeted for the measurement. Thus, the influence of adjacent buildings, which makes it difficult to identify the predominant natural frequencies from building vibration measurements, was also observed. Microtremor measurements using two accelerometers were conducted at 11 historic masonry buildings to investigate the discrimination degree for identifying the predominant natural frequency of conventional townhouse buildings. The estimated primary natural frequencies of these buildings were compared with the results of the screening model analysis. The advantages of using the proposed screening model analysis to improve the uncertainty of the first natural frequency identification by the microtremor measurement are discussed. Additional measurements of the microtremors at 4 of the 11 measured buildings were conducted using a different location combination of the two acceleration sensors. The sensors were placed between two different floors, and the transfer functions of each floor were investigated to observe the predominant vibration components on the floors in the entire building. Moreover, the coherence values observing the in-plane correlation of the floor responses were also analyzed for the dataset measured at two points separated on the same floor. Finally, an effective method for measuring the microtremors is discussed to improve the assessment of the vibration characteristics of conventional historic masonry buildings in Nepal.

Magnetic Actuator Capable of In-Plane Movement by Phase Control of Vibration Components

Aging of large steel structures, such as giant bridges, tanks, and power generation facilities, has become a major problem. In this study, a new magnetic actuator that can move freely on a planar magnetic material is proposed. Using the phase difference between the vibrations of five vibration components, the movement velocity and angle of the actuator can be controlled in the horizontal and vertical planes. The motion of the actuator was analyzed by applying the energy method, and the results were compared with measured values. The measured and calculated values were in relatively good agreement. By measuring the relationship between the input current to the electromagnet and the amplitude of the vibration components at several points, the design index for the magnetic actuator can be predicted by the calculations.

Supplemental Peak Filters for Advanced Disturbance Rejection on a High Precision Endeffector for Robot-Based Inline Metrology

This article presents a metrology platform (MP) as high precision endeffector of a robot with a tailored disturbance rejection scheme in order to enable high-resolution measurements directly in a production line. The MP is installed on a gantry robot for in-plane positioning and has an electromagnetic actuator for vertically positioning its mover. It can mount a compact measurement tool for high precision topography measurements, which are typically sensitive to external vibrations, introducing relative motion between the measurement tool and the sample. To compensate these vibrations, the MP mover vertically tracks the sample by feedback control, maintaining a constant distance between sample and measurement tool. In order to reject broad-band floor vibrations as well as narrow-band vibrations, revealed by the analysis and introduced by the robots servo control, the designed high-bandwidth proportional-integral differential based controller is supplemented by peak filters tailored to the narrow-band vibration components. A method for designing these peak filters depending on the location of the narrow-band disturbance relative to the crossover frequency is presented. The resulting controller enables a tracking error as small as 15 nm (rms), which is 50% smaller than the error without the peak filters, demonstrating the effectiveness of the MP in enabling high-resolution inline measurements.

A novel fault diagnosis method of rotating machinery via VMD, CWT and improved CNN

The rolling bearings play a vital role in mechanical production and transportation. However, when it appears abnormal, the fault characteristics are weak and different to be extracted in vibration signals which generally include pulse information reflecting fault type, independent vibration components caused by other normal mechanical components, noise in the surrounding environment, and so on.A hybrid method for rolling bearing fault diagnosis based on variational modal decomposition (VMD), continuous wavelet transform (CWT), convolutional neural network (CNN) and support vector machine (SVM) suitable for processing small samples is proposed. The pre-processed data are first subjected to VMD processing, and then the IMF reconstructed data are overlapped and sampled to obtain a two-dimensional time-frequency image using CWT. Then, a CNN model is constructed with selected hyperparameters, and image training samples are input into the CNN for model training. Finally, the pre-trained CNN model is selected to learn the test sample set layer by layer to realize the extraction of fault features and use SVM instead of Softmax function to identify and classify the faults.The effectiveness of the proposed method is verified with the Case Western Reserve University (CWRU) bearing vibration data and spindle device failure test bench dataset, where the classification accuracy of the former averaged 99.9% and that of the latter averaged 90.15%. The results validate the feasibility of the method and outperform traditional CNN models, feature extraction-based methods and other methods in terms of diagnostic accuracy.

Estimation of High-Frequency Vibration Parameters for Airborne Terahertz SAR Using Chirplet Decomposition and LS Sequential Estimators

Due to the short wavelength of the terahertz wave, airborne terahertz synthetic aperture radar (THz-SAR) suffers from echo phase errors caused by the high-frequency vibration of the platform. These errors will result in defocusing and the emergence of ghost targets, which will degrade the quality of the image. Therefore, it is necessary to compensate for phase errors in order to bring the image into focus. This paper proposes a multi-component high-frequency vibration parameter estimation method based on chirplet decomposition and least squares (LS) sequential estimators, which differs from other methods that can only be applied to simple harmonic vibrations. In particular, we first obtain the instantaneous chirp rate (ICR) of the signal by chirplet decomposition. Then, we employ the LS sequential estimators in conjunction with separable regression technique (SRT) to estimate vibration parameters. The estimated parameters are subsequently used to re-establish the ICR components for each vibration component and these parameters are further re-estimated to improve their accuracy. Based on the estimated parameters, phase compensation functions can be constructed to suppress the defocusing and ghost targets in airborne THz-SAR imaging. Simulated results on point targets and distributed imaging scenes demonstrate that the proposed method is accurate and reliable even at low signal-to-noise ratios (SNRs).

Scorecard Model-Based Motion Stability Evaluation of Manipulators for Robot Training

Motion stability is vital for the industrial application of robotic manipulators; therefore, its evaluation becomes an important task for robot training. This paper proposes an evaluation system based on the scorecard model to evaluate the stability performance of manipulators. Firstly, the wavelet modulus maximum filtering method is employed to divide the vibration signal into structural vibration components and motion-generated vibration components. Secondly, the evaluation index (EI) is designed based on the processed data to judge whether the vibration signal of the moving process is stable. Finally, the scorecard model is proposed to evaluate the stability of vibration samples, including the process of attribute extraction, binning, WOE coding, feature selection, logistic regression, and score transformation. Additionally, an endpoint localization method is employed to segment the vibration signal of a continuously moving manipulator into single-step motion segments, making it possible to score the motion subprocesses. Experiments are conducted on physical robotic arms to verify the effectiveness of the proposed scheme, and the results show that the model can reasonably score the motion stability of robotic arms for robot training.

Acute Effects of Static Stretching Combined with Vibration and Nonvibration Foam Rolling on the Cardiovascular Responses and Functional Fitness of Older Women with Prehypertension.

Simple SummaryThirty-seven percent of the US adult population have prehypertension, and a quarter to half of these over 65 years of age progress to hypertension in four years. Along with healthy diet, exercise or physical activity is one of the critical lifestyle factors for this population. General exercise recommendation or prescription to individuals who have cardiovascular risks is provided by organizations such as ACSM and AHA, but more detailed information and research are still needed. As the first component of any exercise program, finding the proper warm-up routine is important. We aimed to examine the acute immediate effects of three different warm-up protocols on cardiovascular responses and functional fitness testing in older women with prehypertension. Thirteen qualified subjects went through three protocols (static stretching with and without foam rolling, and stretching with vibration rolling) in three different sessions. Blood pressure was not altered only in the static stretching with foam rolling condition. Interestingly, adding the vibration component to the stretching increased the upper body flexibility and stretching. We therefore suggest the combination of static stretching with foam rolling as the safe and effective protocol for older women with prehypertension.We compared the effects of three warm-up protocols (static stretching (SS), static stretching with vibration foam rolling (SS + VFR), and static stretching with nonvibration foam rolling (SS + FR) on the blood pressure and functional fitness performance in older women with prehypertension. Thirteen older women went through different protocols in separate visits, and their systolic (SBP) and diastolic (DBP) blood pressure, heart rate, mean arterial pressure, brachial pulse pressure (BPP), functional fitness test (back scratch (BS), chair-sit-and-reach, 30 s arm curl (AC), 30 s chair stand, 2 min step, 8-foot up and go), and single-leg standing balance (SLB) were recorded. The SBP and BPP were significantly higher after SS and SS + VFR than after SS + FR. Both SS + FR and SS + VFR significantly improved the 2 min step, when compared with SS. Additionally, SS + VFR significantly improved the BS and AC performance. However, compared with SS and SS + FR, SS + VFR significantly reduced the SLB performance. Therefore, SS + FR may be a better warm-up protocol for older women in maintaining blood pressure. On the other hand, even though SS + VFR induced superior shoulder flexibility, aerobic endurance, and arm strength, it could impair balance.

Experimental Assessment of a Broadband Vibration and Acoustic Emission Sensor for Rotorcraft Transmission Monitoring

Modern rotorcrafts rely on Health and Usage Monitoring Systems (HUMS) to enhance their availability, reliability, and safety. In those systems, data related to the health of key mechanical components is acquired, in addition to typical flight condition history data such as speed and torque. Commercial HUM systems usually rely on vibration measurements to assess the condition of shafts, gears, and bearings; using techniques such as spectral analysis, harmonic analysis, vibration trend and others. Recent research has shown that acoustic emissions (AE) can be advantageous in the detection of mechanical faults, in particular detecting very early small defects on bearings and gears, providing extra time for maintenance planning. However, the addition of extra sensors adds complexity and weight to the HUMS system, which is undesirable. This research is an experimental study to assess the monitoring capabilities of a broadband sensor, able to cover both low frequency vibration components as well as ultrasonic events, hence combining the benefits of both in a single compact sensing unit. The experimental results obtained from an instrumented rig using healthy components as well as seeded faults show the ability of the sensor to detect high frequency events, and compares the performance of the sensor in the low frequency range with a commercial accelerometer.

Universalization of the elastic system of vibration feeders with vertical electromagnetic vibration drive

Vibrating feed bins with electromagnetic drive are widely used in the automation of production processes in mechanical engineering and instrument engineering. They are used for feeding miniature, small, or medium-sized parts to automated production equipment. This equipment is used in automatic lines, automated complexes, or any other flexible automated production facilities. These devices are most widely used for loading parts to assembly positions in automated assembly complexes. In this case, the parts fed to these positions must be located in a certain stable position. Various orientation tools are used for this purpose. They are located directly on the transport trays in the bins of these devices. Therefore, for reliable operation of orientation devices, the movement of parts on the trays should be smooth without sensitive tossing. The designs of vibrating hopper feeders with a hopper connected to a reactive plate by a directional elastic system in the form of a lattice torsion bar are considered. An electromagnetic vibration exciter is placed between the torsion flanges. The disadvantage of such vibration feeders is low productivity in operating modes, especially when there are increased requirements for the smooth movement of transported parts. An increase in the productivity of such feeders is carried out by increasing the amplitude of hopper vibrations in the direction of movement of parts, that is, the horizontal component of vibrations. However, this also leads to an increase in the vertical component, since vibrations are carried out at an angle to the feeder transport tray. When the vertical component of vibrations increases, the transportation of parts switches to the intensive tossing mode. A further increase in the oscillation amplitude leads to a violation of the normal mode of vibrational transport. Modern production involves the modernization of existing structures, as well as the creation of new models of machines with high technical and economic indicators Therefore, the universalization of existing equipment and the development of new machine schemes is an important task for developers and manufacturers of technological equipment, since even a minimal improvement in its technological or operational indicators can lead to a significant economic effect. The paper considers a complex of additional elements used that make it possible to universalize the design of vibrating hopper feeders with electromagnetic drives having a directional elastic system. These changes make it possible to adjust the horizontal component of the device hopper vibrations at a constant vertical one. Additional structural elements are proposed that increase the range of application of such feeders.

A novel adaptive bandwidth selection method for Vold–Kalman filtering and its application in wind turbine planetary gearbox diagnostics

The planetary gearbox transmission system in wind turbines has complex structures and generally operates under non-stationary conditions. Thus its measured responses are of high complexity and nonlinearity, which brings a great challenge in the development of reliable condition monitoring techniques for the planetary gearbox transmission system. As a prevalent and effective tool for analyzing the non-stationary vibration signal with strong nonlinearity, the Vold–Kalman filtration technique has excellent capabilities of tracking the targeted harmonic components of vibrations, which can significantly benefit planetary gearbox fault diagnostics. However, the tracking accuracy is heavily enslaved to the selection of the rational bandwidth for the Vold–Kalman filter. An inappropriate bandwidth could impair the characteristics of the targeted harmonic responses, and as a consequence, the monitoring process becomes no longer reliable. To address this issue, a novel bandwidth selection methodology for the Vold–Kalman filter is developed in this paper. Through comprehensively depicting the targeted harmonic response using features in multiple domains, the rational bandwidth can be selected for Vold–Kalman filtering, and then, a reliable monitoring process can be ensured. Additionally, a tacho-less speed estimation procedure is utilized in this paper to acquire the instantaneous rotational speed from the vibration signal directly. With the rational bandwidth and the estimated rotational speed, the desired harmonic components of vibrations can be adaptively extracted and tracked through the Vold–Kalman filter with high accuracy, and at the same time, the irrelevant or unwanted components are excluded completely. The effectiveness and superiority of the proposed adaptive Vold–Kalman filtration for wind turbine planetary gearbox diagnostics are demonstrated and validated experimentally.

The numerical investigation on the effects of support conditions and flanges during the water impact of a thin elastic plate

The water impact of plates can represent a broad of slamming problems in marine and offshore engineering, such as the wet-deck slamming of a multi-hull vessel, the slamming of the coastal structures like breakwaters, and slamming induced by the sloshing of the LNG ships. This paper has studied the water impact of an elastic plate with/without flanges. The main focus is on the influences of the support conditions and the flanges.For elastic structures, especially thin-walled structures, different support conditions lead to different structural responses. Therefore, it is necessary to investigate the effects of support conditions. The results showed that the stronger the constraint, the higher the vibration frequency of the structure, the greater the force. But the deformation is much smaller.On the other hand, we simulate the water impact of the flat plates with flanges, which is quite different from previous studies in which a rigid plate is considered only. The results of wavelet analysis show that the flanges can reduce the high-frequency components of structure vibration. The amplitudes of the high-frequency components decay over time sharply. Eventually, the responses with a frequency between 40 and 60 Hz remain and are less affected by the flanges.The FSI simulation is carried out with ANSYS commercial software. VOF model is used in the fluid solver, finite element method is used in structure solver, and the partitioned method is used to couple the solvers. Compared with other methods, there is no simplification in the partitioned approach. Therefore, it can reflect the whole slamming process more accurately.

Detection of rail local defects using in-service trains

As track components deteriorate, their interaction dynamic response will alter accelerations on the train. Measuring acceleration on train components is a method to conduct condition monitoring of track defects. The measured signal can be used for the detection of rail surface defects which implement impacts on measured accelerations. In this paper, the axle-box acceleration (ABA) is measured in a subway as a case study. Fourier transform (FFT), empirical mode decomposition (EMD) and ensemble EMD (EEMD) methods are used to study accelerations relative to the track. Wheel frequencies are calculated using finite element method (FEM) to determine frequency couplings. Velocity-dependent/independent components and source of excitation of the measured signal are distinguished. Results indicated that the FFT approach can be applied for both velocity-dependent and velocity-independent vibration components for frequencies up to 680 Hz. Also, the EEMD method can be used to distinguish the impact component of the measured signal.

Friction-Excited Oscillation of Air Conditioner Rotary Compressors: Measurements and Numerical Simulations

The oscillation of a rotary compressor was measured and analyzed in the frequency and time domains. The harmonic wavelet transform was used to dissolve the oscillation signal into a series of single-frequency components. A power spectrum analysis of the single-frequency components shows that there are many vibration components whose frequencies are one, double, triple, quadruple, and even tens of times the rotating frequency. An envelope spectrum analysis shows that some single-frequency components originate from the friction-excited oscillation of the compressor. A full-size mode-coupling model of the rotary compressor was established to forecast the friction-excited oscillation of the compressor using the transient dynamics method and the complex eigenvalue method. The measurement results are consistent with the predictive results. A sensitivity analysis of the main parameters shows that the coefficient of friction has a major impact on the development tendency of the friction-excited oscillation of rotary compressors.

Effects of whole-body vibration on driver drowsiness: A review

Introduction: Whole-body vibration has direct impacts on driver vigilance by increasing physical and cognitive stress on the driver, which leads to drowsiness, fatigue and road traffic accidents. Although sleep deprivation, sleep apnoea and alcohol consumption can also lead to driver drowsiness, exposure to steady vibration is the factor most readily controlled by changes to vehicle design, yet it has received comparatively less attention. Methods: This review investigated interrelationships between the various components of whole-body vibration and the physiological and cognitive parameters that lead to driver drowsiness, as well as the effects of vibration parameters (frequency, amplitude, waveform and duration). Vibrations transmitted to the driver body from the vehicle floor and/or seat have been considered for this review, whereas hand-arm vibration, shocks, acute or transient vibration were excluded from consideration. Results: Drowsiness is affected by interactions between the frequency, amplitude, waveform and duration of the vibration. Under optimal conditions, whole-body vibration can induce significant drowsiness within 30 min. Low frequency whole-body vibrations, particularly vibrations of 4–10 Hz, are most effective at inducing drowsiness. This review notes some limitations of current studies and suggests directions for future research. Conclusions: This review demonstrated a strong causal link exists between whole-body vibration and driver drowsiness. Since driver drowsiness has been established to be a significant contributor to motor vehicle accidents, research is needed to identify ways to minimise the components of whole-body vibration that contribute to drowsiness, as well as devising more effective ways to counteract drowsiness. Practical Applications: By raising awareness of the vibrational factors that contribute to drowsiness, manufacturers will be prompted to design vehicles that reduce the influence of these factors.

Vibration Detection and Localization Using Modified Digital Coherent Telecom Transponders

We demonstrate a vibration detection and localization scheme based on bidirectional transmission of telecom signals with digital coherent detection at the receivers. Optical phase is extracted from the digital signal processing blocks of the coherent receiver, from which the vibration component is extracted by bandpass filtering, and the position along the cable closest to the vibration's epicenter is recovered by correlation. We demonstrate our scheme first using offline experiment with 200-Gb/s DP-16QAM, and we report field trial results over installed fiber to detect real-world vibration events.

Whole-Body Vibration Experienced by Pilots, Passengers and Crew in Fixed-Wing Aircraft: A State-of-the-Science Review

Before the coronavirus pandemic, there were 4.5 billion passenger movements by aircraft annually; this is expected to recover after the pandemic. Despite the large numbers of flights per year, there are few reports of whole-body vibration in fixed-wing aircraft. This paper reports a review of literature intended to collate reported data related to exposure to whole-body vibration. Following a filtering process to select relevant articles, a literature search elicited 26 papers reporting measurements of vibration. These included measurements made in the cockpit and cabin, and for pilots, crew and passengers. Aircraft included military, commercial and passenger aircraft, turboprops, jets and piston prop aircraft. There was a lack of consistency on measurement method and analysis, and few met the full requirements of ISO 2631-1. However, measurements showed significant components of vibration at frequencies largely attenuated by the ISO frequency weighting filters, but have been shown to be important in terms of human vibration perception. Propeller aircraft showed strong tonal components in vibration frequency spectra. There was also a significant effect of the flight phase in the vibration exposure. It is recommended that the body of literature related to human response to whole-body vibration on aircraft is augmented with further studies in order to understand in-flight experiences and to optimize human health, wellbeing, comfort and performance.

Different Types of Continuous Track Irregularities as Sources of Train-Induced Ground Vibration and the Importance of the Random Variation of the Track Support

Irregularities of the track are a main cause of train-induced ground vibration, and track maintenance is of great importance. Although geometric irregularities at the wheel-rail contact are widely used, other types of irregularities, such as stiffness irregularities, irregularities from different track positions and irregularities in the wave propagation, were analysed in the present study. The track behaviour was investigated by a multi-beam-on-soil model. This track model is coupled with a vehicle model to calculate the vehicle–track interaction. The track model was also used for the track filtering, which transfers a track support error to the equivalent rail irregularity or, conversely, the sharp axle pulse on the rail to a smoother pulse on the soil. In the case in which this filtering varies randomly along the track, the pulses of the moving static load induce a certain ground vibration component (“the scatter of axle pulses”). This effect was calculated by the superposition of axle pulses in the frequency domain and by a stochastic simulation. Simultaneous vehicle, track and soil measurements at a certain site were used to evaluate the different excitation and ground vibration components. The agreement between calculations and axle-box and soil measurements is good. The ground vibrations calculated from rail irregularities and corresponding dynamic loads, however, clearly underestimate the measured ground vibration amplitudes. Only the static load that is moving over a varying track support stiffness can produce the important mid-frequency ground vibration component by the scatter of axle pulses.

Nonlinear analysis of cylindrical gear dynamics under varying tooth breakage

Linear and nonlinear analyses served to detect the degree of tooth damage in a cylindrical gear. The gear in question is widely used in industrial applications and is often subject to gear tooth damage. Multiple-sourced vibrations affecting the test stand may distort or conceal the vibration components responsible for tooth failure. Given its construction, the test stand offers low stiffness, and additional control and measurement equipment further contribute to overall vibrations. Therefore, the vibration signal is likely to contain various disturbances, which further hinder correct diagnosis. Basic vibroacoustic signal analysis methods, which were employed at a preliminary stage, failed to produce unambiguous and satisfactory results. Hence, nonlinear recurrence analysis of gear operation dynamics was applied. It is assumed that the occurrence of damage to the gear will impede the regularity of drive transmission. The adopted research method addresses the limitations of a two-state diagnosis of gear condition (no damage/damage) by allowing the extent of gear tooth damage to be specified.

Video-Based Vibration Measurement for Large Structure: A Spatiotemporal Disturbance-Adaptive Morphological Component Analysis

Recently, phase-based motion estimation method is able to extract the full-field vibration of large structure from video, which has attracted widely attention. However, it suffers from diverse disturbances in the realistic measurement, such as periodic texture pattern from the surface and shake caused by unstable tripod. To address this issue, a spatiotemporal disturbance-adaptive morphological component analysis (DAMCA) is proposed in this paper. This method focuses on separating texture component from structure component in each video frame, and separating shake component from vibration component in the global motion signal extracted from video. Firstly, it constructs a spatiotemporal model to remove the disturbances respectively from the space domain and time domain of the video. Subsequently, it incorporates morphological component analysis (MCA) into this model, aiming to obtain the optimal separation results in the space domain and time domain by finding the sparsest representations of different components. Finally, to adapt to various texture surfaces, MCA is developed in the space domain by exploiting the low rank structure of the texture’s sparse representation. Similarly, to adapt to various shake, MCA is also developed in the time domain. Simulated and actual test demonstrate the effectiveness and accuracy of the proposed method. Spatiotemporal DAMCA has valuable potential to acquire video-based vibration measurement for large structure with the disturbances involving texture surface and tripod shake.

USE OF DISCRETE WAVELET ANALYSIS OF VIBRO-ACOUSTIC SIGNALS TO DETECT BEARING DEFECTS OF ROTATING ELECTRIC MACHINES

The paper shows that one of the most effective methods for processing the time realization of a vibro-acoustic signal from electrical machines is a discrete wavelet transform. At the same time, due to the lack of built-in tools for separating periodic and aperiodic components in the latter, it significantly complicates the process of identifying periodic disturbing factors, which makes it necessary to develop new approaches to identifying periodic components of vibration based on discrete wavelet transform, which can be caused by a number of defects in rotating electrical machines. A new integral highly informative numerical criterion for the presence of bearing defects, obtained on the basis of a discrete wavelet transform of a vibro-acoustic signal of an electric machine, is proposed. It has been found that upon detection of the indicated defect, it is advisable to analyze the frequency bands, which include the rotor frequency and its first harmonic components. The expediency of using the parent wavelet function of higher orders upon detection of the indicated defect has been theoretically substantiated and experimentally proved. It is shown that, based on considerations of simplifying the mathematical apparatus of calculation and increasing the flexibility of the diagnostic system, it is advisable to use the Daubechies wavelet family, the calculation of the coefficients of which involves the use of a clear mathematical algorithm. The necessary duration of time realizations of vibration is theoretically substantiated and experimentally confirmed, which is advisable to use when determining the proposed highly informative numerical criterion. It is shown that the duration of such realizations should be significantly longer than the period of rotation of the rotor of the electric machine.