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EN
The Timoshenko beam theory caters for transverse shear deformations, which are more pronounced in short beams. Previous works were examined, and Hamilton’s principle was used in deriving the governing equation. This research considers two dimensions (2-D): heat and displacement response. A more comprehensive mathematical expression that incorporates this 2-D model on the vibration of a coupled Timoshenko thermoelastic beam and axial deformation effect is formulated. The significance of this model will be expressed through its finite element method (FEM) formulation. The results compared favourably with those of previous works. It was re-established that the amplitude of deflections, as well as cross-sectional rotations, increases considerably as the aspect ratio of the beam decreases. In this way, for larger aspect ratios, the response of the beam is like the quasi-static heating condition. This is expected since the increase in the aspect ratio of the beam reduces its structural stiffness and consequently its natural frequencies. So, the amplitude and temporal period of its vibrations become greater. The beam under the applied thermal loading experiences thermally-induced vibrations. Also, the dynamic solution is substantially influenced by the coupling between strain and temperature fields. The results also reveal that the aspect ratio of the beam could have a significant impact on the vibratory response of the beam. Specifically, it is proportional to the amplitude and temporal period of the thermally-induced vibrations of the beam.
EN
The idea of Industry 4.0 indicates Condition Based Maintenance (CBM) and Predictive Maintenance (PdM) as fundamental maintenance strategies in modern factories. CBM and PdM could be implemented with use of on-line continuous monitoring and diagnostic systems and also as a program of systematic examinations of asset condition done by maintenance personnel. Using data collected from hand held instruments and from on-line systems it is possible to build full image of current asset condition and predict probable faults in the future. This paper presents system of condition monitoring and diagnosing of main drive of industrial press line. The system uses diagnostic data coming from different sources like vibration, electrical and thermal measurements. Application of different types of data makes the system hybrid and allows improve diagnostic inference process. The article describes how the system is designed and implemented.
PL
Idea Przemysłu 4.0 wskazuje Condition Based Maintenance (CBM) oraz Predictive Maintenance (PdM) jako podstawowe strategie służb utrzymania ruchu w nowoczesnych fabrykach. CBM i PdM mogą zostać wdrożone z wykorzystaniem ciągłego monitoringu w trybie online oraz systemów diagnostycznych, a także systematycznej kontroli stanu urządzenia przeprowadzanej przez personel utrzymania ruchu. Używając danych zgromadzonych za pomocą przyrządów ręcznych, a także systemów pracujących w trybie online możliwym jest zbudowanie kompletnego obrazu aktualnego stanu urządzenia i przewidywanie potencjalnych awarii w przyszłości. Poniższa publikacja opisuje system diagnostyczny przemysłowej linii pras. System wykorzystuje dane pochodzące z różnych źródeł: drgania, natężenie prądu elektrycznego i pomiarów temperatury. Różnorodność danych sprawia, że system staje się hybrydowy, co pozwala usprawnić wnioskowanie diagnostyczne. Artykuł opisuje proces projektownia takiego systemu oraz jego implementację.
EN
The paper formulates and formalises a method for selecting parameters of the tuned mass damper (TMD) for primary systems with many degrees of freedom. The method presented uses the properties of positive rational functions, in particular their decomposition, into simple fractions and continued fractions, which is used in the mixed method of synthesis of vibrating mechanical systems. In order to formulate a method of tuning a TMD, the paper discusses the basic properties of positive rational functions. The main assumptions of the mixed synthesis method is presented, based on which the general method of determining TMD parameters in the case of systems with many degrees of freedom was formulated. It has been shown that a tuned mass damper suppresses the desired resonance zone regardless of where the excitation force is applied. The advantages of the formulated method include the fact of reducing several forms of the object’s free vibration by attaching an additional system with the number of degrees of freedom corresponding to the number of resonant frequencies reduced. In addition, the tuned mass damper determined in the case of excitation force applied at a single point can be attached to any element of the inertial primary system without affecting the reduction conditions in this way. It results directly from the methodology formalised in the paper. As part of the paper, numerical calculations were performed regarding the tuning of the TMD to the first form of free vibration of a system with 3 degrees of freedom. The parameters determined were subjected to analysis and verification of the correctness of the calculations carried out. For the considered case of a system with 3 degrees of freedom together with a TMD, time responses of displacement, from each floor, were generated to excitation induced by a harmonic force equal to the first form of vibration of the basic system. In addition, in the case of the parameters obtained, the response of the inertial element system to which the TMD was attached to random white noise excitation was determined.
EN
This paper is devoted to the development of an effective system for monitoring the technical condition of the axle boxes of rolling stock. To this end, the possibility of solving problems of fault diagnostics based on the theory of fuzzy sets is considered. This allows one note such difficult-to-formalise factors as experience and intuition of a highly qualified expert specialist. It showed that an expert system-based monitoring approach allows evaluation of the technical condition of the axle boxes, characterised by internal and external operating uncertainty. It also proposed the use of parameters such as vibration and noise for comprehensive monitoring of the technical condition of axle box units together with temperature. Furthermore, the combination of these diagnostic parameters and expert system’s possibility to receive all necessary information about the condition of the most critical components of the axle boxes in real-time and analyse the changes in their operational parameters was explored. The stages of modelling an expert system in the Fuzzy Logic Toolbox package of the MATLAB computing environment are presented.
5
Content available remote Measurements of vibration using a high-speed camera - comparative tests
EN
In the technical diagnostics and monitoring of high dynamic processes high-speed cameras are getting wider application. Recorded images sequence analysis of an object position makes possible to study also the oscillating movement. In this paper results of some exploratory research of test vibration signals are presented. The aim of the study was to examine the possibility of applying high-speed camera to vibration measurements in the frequency range up to 1000 Hz. The performed tests consisted in the simultaneous registration and analysis of vibration test signals using 4 alternative measuring systems. and then the determination of the frequency characteristics of vibration acceleration, total corrected (Wh characteristics) and uncorrected vibration acceleration values. The results of recorded image analyses of oscillating movement were compared with results of vibration acceleration measurements obtained using laser and piezoelectric transducers. Vibration acceleration spectra, the uncorrected and corrected (Wh characteristics) total vibration acceleration values were determined. Based on the achieved results, some limitations and conditions for the application of the high-speed camera used for vibration analyses have been identified. The test results confirmed the possibility of use of high-speed camera for research of low frequency vibration even at low displacements.
EN
Results of research about influence of mechanical and electromagnetic phenomena on electric motor vibration in different supply options has been shown in this paper. Three different supply options have been taken under consideration: typical star connection, single-phase connection with work capacitor and connection through an inverter. Vibration signals recorded on electric motor end shield and frame has been digitally processed using Multi-Synchronous Averaging (MSA). This technique allowed to decompose total vibration signal into signals associated with mechanical and electromagnetic phenomena occurring in electric motor. The comparison of rms values and spectra shapes of total and decomposed vibration signals has been made. Energy shares of previously mentioned phenomena in vibration signal for different supply options has been also estimated.
EN
Most of machine breakdowns relate to bearing failures thus it is very important to diagnose bearing conditions. The main purpose of the study was to classify the condition of bearings and identify defective ones based on visual inspection and the values of classic parameters of the acceleration signal vibration, such as Peak, RMS, Kurtosis. The results were compared to parameters provided by the SPM method. All vibration parameters were estimated for high pass filtered signals where filters had following cut-off frequencies 0.5; 1, 2, 5 and 8 kHz. Bearings were tested on the laboratory test bench being built at the Silesian University of Technology. Based on the signal analysis and visual inspections it can be stated that there is agreement in the assessment of the conditions between the parameters of the SPM method and the Peak and RMS parameters. It was observed that the sensitivity to the existence of low-intensity defects increases when the vibration parameters are determined for signals in the band above 2kHz.
EN
Two models of vibrations of the Euler–Bernoulli beam under a moving force, based on two different versions of the nonlocal gradient theory of elasticity, namely, the Eringen model, in which the strain is a function of stress gradient, and the nonlocal model, in which the stress is a function of strains gradient, were studied and compared. A dynamic response of a finite, simply supported beam under a moving force was evaluated. The force is moving along the beam with a constant velocity. Particular solutions in the form of an infinite series and some solutions in a closed form as well as the numerical results were presented.
PL
W artykule przedstawiono wybrane wyniki monitoringu wychyleń wieży Szybu II KWK „Borynia-Zofiówka” Ruch „Borynia”. Monitoring realizowany był z wykorzystaniem opracowanego w Głównym Instytucie Górnictwa systemu monitoringu drgań i wychyleń opartego na laserowym czujniku drgań i wychyleń. Zaprezentowano wychylenia zarejestrowane w lipcu 2020 r. za pomocą czujników umieszczonych na wysokości kół linowych oraz na wysokości zastrzału Szybu II. Wychylenie mierzono w kierunkach E-W i N-S. Dokonano analizy wyników monitoringu wychyleń oraz wpływu temperatury na ich wartość.
EN
The paper presents selected results of monitoring of inclination of Shaft II of Coal Mine “Borynia-Zofiówka” Plant “Borynia”. The monitoring was conducted by means of vibration and inclination monitoring system developed at Central Mining Institute which is based on the laser vibration and inclination sensor. The inclination results recorded in July 2020 by sensors placed at the height of the rope pulleys and on the strut were presented. The inclination was measured in E-W and N-S directions. The analyses of the inclination monitoring results and the influence of the temperature on its value were also performed.
10
Content available remote Damping of vibration in an electric drive system with a long elastic coupling
EN
In the paper the uncomplicated structure of the active limiter of current reference for a BLDC motor control system is proposed. The limiter allows for uninterruptible operation of a speed controller due to the automatically adjusted rate of change of angular velocity reference depending on actual moment of inertia. The results of investigations, which confirm the effectiveness of the proposed structure, are presented.
PL
W artykule zaproponowano nieskomplikowaną strukturę aktywnego ogranicznika prądu zadanego w układzie regulacji prędkości kątowej silnika BLDC, która umożliwia bezprzerwowe działanie regulatora prędkości dzięki automatycznemu dostosowaniu szybkości narastania prędkości zadanej do dowolnego momentu bezwładności. Zaprezentowano wyniki badań, które potwierdzają skuteczność działania proponowanej struktury.
PL
W artykule przedstawiono drganiową metodę diagnozowania silników trakcyjnych wzbudzanych magnesami trwałymi, które są wykorzystywane m.in. w pojazdach elektrycznych. Metoda wykorzystuje właściwości maszyn elektrycznych z magnesami trwałymi, a mianowicie zjawisko indukowania się napięcia w uzwojeniu twornika pod wpływem drgań mechanicznych wirnika względem stojana. Przedstawiono genezę metody, podobieństwo do elektrodynamicznego czujnika drgań, wyniki obliczeń oraz badań laboratoryjnych mających na celu detekcję częstotliwości, które odpowiadają wibracjom, wymuszonych niewywagą wirnika.
EN
This article presents a vibration diagnostic method designed for permanent magnets (PM) traction motors. Those machines are commonly used in traction drives of electrical vehicles. Specific structural properties of machines excited by permanent magnets are used in this method – electromotive force (EMF) generated due to vibrations. This work presents: the method genesis, the similarity of permanent magnet machine and vibration sensor, results of calculations and laboratory tests.
EN
An active method of vibration control of a smart sandwich plate (SSP) using discrete piezoelectric patches is investigated. In order to actively control the SSP vibration, the plate is equipped with three piezoelectric patches that act as actuators. Based on the classical plate theory, a finite element model with the contributions of piezoelectric sensor and actuator patches on the mass and stiffness of the sandwich plate was developed to derive the state space equation. LQR control algorithm is used in order to actively control the SSP vibration. The accuracy of the present model is tested in transient and harmonic loads. The applied piezoelectric actuator provides a damping effect on the SSP vibration. The amplitudes of vibrations and the damping timewere significantly reducedwhen the control is ON.
EN
A severe oscillation, accompanied with an abnormal “click” sound, of a fuel feeding pipe system during valve closing, when the feeding flowrate reaches a certain value, is observed experimentally. A fluctuation model in which stiffness and damping coefficients of the vibration system are time varying is proposed. Each coefficient is composed of two parts, one of which is constant and the other is time varying. Based on this model, simulation transients of the vibration displacement, velocity and pressure in the pipe are presented. Simulations of the pressure transients are compared with experimental data detected by pressure transducer, which shows that both have fluctuations in the transient process at a large flowrate.
EN
A floating ladder track is established in the present paper as a next-generation non-ballasted track system. The three-dimensional model consists of a track (mass-spring-damping system) and the underlying soil. Rectangular pulse loading with an amplitude of 60 kN is considered as the wheel loading system. A time domain coupled finite element with a semi-infinite absorbing boundary condition is employed using FEM software. Due to axial symmetry of the model instead of the track axle, only half of the model is simulated. It is observed that the performance of the floating ladder track is better in mitigating measured vibration than that of the traditional ballasted track. Numerical results of the floating ladder track reveal that the increase of damping and stiffness yields more vibration responses, which is a straight nonlinear relationship. Although increasing density of the protective layer decreases vibrations on the ground, it has no effect on structural components of the track except for the protective layer. Furthermore, this kind of track is more effective at a closer distance to the source of vibrations.
EN
The article deals with atwo-mass above resonant oscillatory system of an eccentric-pendulum type vibrating table. Based on the model of a vibrating oscillatory system with three masses, the system of differential equations of motion of oscillating masses with five degrees of freedom is compiled using generalized Lagrange equations of the second kind. For given values of mechanical parameters of the oscillatory system and initial conditions, the autonomous system of differential equations of motion of oscillating masses is solved by the numerical Rosenbrock method. The results of analytical modelling are verified by experimental studies. The two-mass vibration system with eccentric-pendulum drive in resonant oscillation mode is characterized by an instantaneous start and stop of the drive without prolonged transient modes. Parasitic oscillations of the working body, as a body with distributed mass, are minimal at the frequency of forced oscillations.
EN
The aim of the current paper is to investigate a small airplane model propeller of class F2D according to requirements of Fédération Aéronautique Internationale (FAI, or World Air Sports Federation). In some cases, practical tests show that F2D models with flexible propellers produce specific extra noise and increase flight speed in comparison with “rigid” propellers. Therefore, the following hypothesis could be proposed: flexible characteristics of the increased noise are related to the resonant eigenfrequencies of the propeller. The operating range of the F2D class propeller (28,000-35,000 rpm) is close to or equal to the eigenfrequency resonance. The current investigation addresses dynamic/flexible vibrations of elastic propeller during engine run and researches dynamic parameters of the propeller as well as the contribution of these parameters to the model flight characteristics. To resolve this type of a problem, a stand, which allows completing a physical investigation of flexible propeller vibration modes and dynamic characteristics was created.
PL
Celem artykułu jest przedstawienie wyników badań śmigła małego modelu samolotu zaliczanego do klasy F2D (według klasyfikacji Fédération Aéronautique Internationale, FAI). W niektórych przypadkach testy wykazały, że modele F2 z giętkimi śmigłami, w porównaniu do śmigieł sztywnych, wydają dodatkowy hałas i zwiększają prędkość samolotu. Dlatego wysunięto hipotezę, że elastyczne charakterystyki zwiększonego hałasu są powiązane z rezonansem częstotliwości własnych śmigła. Zakres pracy śmigła klasy F2D (28 000-35 000 obr/min) jest zbliżony do jego częstotliwości własnych. Badania dotyczą elastycznych wibracji dynamicznych śmigła giętkiego w czasie rozruchu silnika i są nakierowane na wyznaczanie parametrów dynamicznych i ich wpływu na charakterystyki lotu modelu. Wykonano i opisano stanowisko, na którym przeprowadzono testy modalne drgań giętkiego śmigła. Na tej podstawie uzyskano charakterystyki dynamiczne.
EN
A dynamic advancement of the design of combustion engines generates a necessity of introduction of strategies of operation based on the information related to their technical condition. The paper analyzes problems related to vibration based diagnostics of valve clearance of a piston combustion engine, significant in terms of its efficiency and durability. Methods of classification have been proposed for the assessment of the valve clearance. Experiments have been performed and described that aimed at providing information necessary to develop and validate the proposed methods. In the performed investigations, the vibration signals were obtained from a triaxial accelerometer located in the engine cylinder head. A parameterization of the obtained vibration signal has been carried out for the engine operating under different engine loads, rotation speeds and valve clearance settings. The parameterization pertained to the specific features of the vibration signals, the derivative of the vibration signal as a function of time as well as the envelope of this derivative. In the first approach, the authors developed a classifier in the form of a set of binary trees that additionally allowed distinguishing the features significant in terms of the identification of adopted classes. For comparison, the authors also developed classifiers in the form of a neural network as well as a k-nearest neighbors algorithm using the Euclidean metric. Based on the performed investigations and analyses a method of valve clearance assessment has been proposed.
PL
Dynamiczny rozwój konstrukcji silników spalinowych generuje potrzebę wprowadzenia strategii eksploatacji jednostek napędowych, opartej na znajomości ich stanu technicznego. W artykule poddano analizie zagadnienia, związane z drganiową diagnostyką luzu zaworów tłokowego silnika spalinowego, istotnego ze względu na efektywność pracy silnika i jego trwałość. Zaproponowano wykorzystanie metod klasyfikacji do oceny poprawności luzu zaworowego. Przeprowadzono i opisano eksperymenty, które miały na celu dostarczenie informacji koniecznych do zbudowania i zweryfikowania zaproponowanych metod. W przeprowadzonych badaniach pozyskano sygnały drganiowe z trójosiowego czujnika przyspieszeń drgań zlokalizowanego na głowicy silnika. Dokonano parametryzacji uzyskanych przebiegów czasowych sygnału drganiowego dla silnika pracującego pod różnym obciążeniem, z różnymi prędkościami obrotowymi oraz z różnymi luzami zaworowymi. Parametryzacja dotyczyła zarówno cech sygnału przyspieszeń drgań, pochodnej przyspieszeń drgań względem czasu jak i obwiedni tej pochodnej. W pierwszym podejściu zbudowano klasyfikator w postaci zbioru drzew binarnych, który przy okazji pozwolił na wyodrębnienie istotnych, ze względu na przyjęte klasy, cech. Dla porównania zbudowano także klasyfikatory w postaci sieci neuronowej jak i algorytmu k – najbliższych sąsiadów z metryką euklidesową. Na podstawie przeprowadzonych badań i analiz zaproponowano metodę oceny luzu zaworowego.
EN
This paper aims to analyse the results of the comparative study of the characteristic frequencies, in terms of Power Spectral Density (PSD), generated by an SKF6322 bearing in a rotational blower. Among all the analysed frequencies, we have focused on the ones generated by the shaft rotation speed, the one on the blades and the ones of the SKF6322 bearing, such as the tracks, the cage and the balls. For this study, we followed the ISO 10816 criteria, both in the sampling part and in the data analysis, using the speed values in terms of PSD, which improves the results in both high and low frequencies. This study can be used to predict the performance of bearings and their future failure, determining the most decisive frequency, the one with the highest incidence and the relative influence of each one on the different positions and monitoring coordinate axes. This procedure can be applied to improve the predictive maintenance protocol in order to improve the performance, efficiency and reliability of the equipment with bearings in their systems.
EN
Entropy measurements are an accessible tool to perform irregularity and uncertainty measurements present in time series. Particularly in the area of signal processing, Multiscale Permutation Entropy (MPE) is presented as a characterization methodology capable of measuring randomness and non-linear dynamics present in non-stationary signals, such as mechanical vibrations. In this article, we present a robust methodology based on MPE for detection of Internal Combustion Engine (ICE) states. The MPE is combined with Principal Component Analysis (PCA) as a technique for visualization and feature selection and KNearest Neighbors (KNN) as a supervised classifier. The proposed methodology is validated by comparing accuracy and computation time with others presented in the literature. The results allow to appreciate a high effectiveness in the detection of failures in bearings (experiment 1) and ICE states (experiment 2) with a low computational consumption.
EN
In this paper, the author presents a study of vibrations in a passenger vehicle and the possible influence on driver’s body in the process of natural operation. The author describes the dependence of engine size and additional equipment as the possible primary source of the vibration variations and their further propagation in the entire vehicle structure. The analysis was performed on the passenger cars with naturally aspirated and turbocharged gasoline engines. The aim of this study was to verify the level of vibrations in the vehicle structure with these particular engines, especially influence of downsized power unit, during various state of engine operation. The second goal was to examine the vibrations in the specified location related to driver’s body. The measuring method used piezoelectric accelerometers, which were attached to the designated locations in the vehicle and were able to detect variations of the acceleration. The signals were collected as characteristics in the time domain. In order to achieve frequency domain for spectral analyses, the author applied the Fast Fourier Transform (FFT).
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