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EN
This paper performs the fatigue life analysis of the radial Cylindrical Roller Bearings (CRBs) with consideration of various roller end-flange shapes such as toroidal-toroidal, spherical-toroidal, and spherical-conical. A novel formula for each flange contact deformation in cylindrical roller bearing with different roller end-flange geometry including toroidal geometry is developed. Inner ring misalignment angle and radial deflection results obtained from the present study are verified with numerical and experimental results from the literature. The results approach to that of literature when the flange is changed from toroidal geometry to conical geometry. Using formulas developed in the present study, the effect of various roller end-flange geometries on the bearing life is investigated for different external loadings. It is observed that the bearing life increases when the roller end and flange are changed to toroidal geometry.
EN
In this study, a multi-pad bump-type foil thrust bearing with a taper-land height profile is investigated. A detailed thermo-elastohydrodynamic (TEHD) finite element (FE) model is used comprising all bearing pads instead of only a single pad. Although the single-pad reduction approach is commonly applied, it can not accurately account for the different temperatures, loads, and power losses for individual pads in the case of misalignment. The model accounts for the deformations of the foils on each pad via a Reissner-Mindlin-type shell model. Deformations of the rotor are calculated via the Navier-Lamé equations with thermoelastic stresses and centrifugal effects. The temperature of the top foil and the rotor are calculated with the use of heat diffusion equations. The temperature of each lubricating air film is obtained through a 3D energy equation. Film pressures are calculated with the 2D compressible Reynolds equation. Moreover, the surrounding of the bearing and runner disk is part of the thermodynamic model. Results indicate that the thermal bending of the runner disk as well as top foil sagging are key factors in performance reduction. Due to the bump-type understructure, the top foil sagging effect is observed in simulation results. The study at hand showcases the influence of misalignment between the rotor and the bearing on the bearing performance.
EN
The linear feed axes are critical subsystems in many production machines and have important responsibilities such as transporting workpieces and tools in the process. Therefore, the component’s working condition is crucial for the production of high-quality products. Because these systems gradually deteriorate, it is necessary to detect these changes and occurring faults with condition monitoring systems. In this study, the motor current of feed axes is monitored for axis misalignment that occurs during or after assembly. We conduct diagnosis with Fast Fourier Transform (FFT) and statistical methods in order to differentiate different misalignment scenarios and operating constraints of the feed axis. Different states are achieved by simulating left and right axis misalignment and operating the table at different speeds and strokes.
PL
W artykule przedstawiono charakterystykę porównawczą akcelerometrów lotniczych. Omówiono przeznaczenie czujników przyspieszeń stosowanych w lotnictwie oraz dokonano przeglądu ich konstrukcji ze względu na rodzaj zastosowanego przetwornika rodzaju sygnału. Zdefiniowano błędy mające wpływ na niepewność pomiaru. Analizie poddano przyrządy kilku producentów, reprezentujące różne metody pomiarowe spośród akcelerometrów klasycznych, jak i wykonanych w technologii MEMS. Wskazano sensory cechujące się najmniejszymi błędami.
EN
The article presents the comparative characteristics of aviation accelerometers. There were discussed several issues like the purpose of acceleration sensors in aviation or their design with respect to the type of signal transducer used. Errors affecting the accuracy of measurement have been defined. Instruments from several manufacturers, representing various measurement methods used in classical accelerometers as well as those with MEMS technology applied have been analysed. The sensors with the smallest errors were indicated.
EN
The present article investigates the dynamic behavior of a fully assembled turbogenerator system influenced by misalignment. In the past, most of the researchers have neglected the foundation flexibility in the turbogenerator systems in their study, to overcome this modelling error a more realistic model of a turbogenerator system has been attempted by considering flexible shafts, flexiblecoupling, flexible bearings and flexible foundation. Equations of motion for fully assembled turbogenerator system including flexible foundations have been derived by using finite element method. The methodology developed based on least squares technique requires forced response information to quantify the bearing–coupling–foundation dynamic parameters of the system associated with different faults along with residual unbalances.The proposed methodology is tested for the various level of measurement noise and modelling error in the system parameters, i.e., 5% deviation in E (modulus of elasticity) and ρ (density), respectively, for robustness of the algorithm. In a practical sense, the condition analyzed in the present article relates to the identification of misalignment and other dynamic parameters viz. bearing and residual unbalance in a rotor integrated with flexible foundation.
EN
In rotating machineries, misalignment is considered as the second most major cause of failure after unbalance. In this article, model-based multiple fault identification technique is presented to estimate speed-dependent coupling misalignment and bearing dynamic parameters in addition with speed independent residual unbalances. For brevity in analysis, a simple coupled rotor bearing system is considered and analytical approach is used to develop the identification algorithm. Equations of motion ingeneralized co-ordinates are derived with the help of Lagrange’s equation and least squares fitting approach is used to estimate the speed-dependent fault parameters. Present identification algorithm requires independent sets of forced response data which are generated with the help of different sets of trial unbalances. To avoid/suppress the ill-conditioning of regression equation, independent sets of forced response data are obtained by rotating the rotor in clock-wise and counter clock-wise directions, alternatively. Robustness of algorithm is checked for different levels of measurement noise.
PL
W pracy skupiono się na problemie niewyosiowania układów napędowych z silnikiem indukcyjnym. Przedstawiono wybrane metody wykrywania niewspółosiowości oparte na analizie prądu stojana, drgań mechanicznych i modułu wektora przestrzennego prądu stojana. Zaprezentowano zdjęcia z kamery termowizyjnej pokazujące wpływ niewyosiowania na elementy konstrukcyjne układu napędowego. Badania laboratoryjne przeprowadzono na silniku indukcyjnym małej mocy. Zaprezentowane wyniki zostały podsumowane uwagami i wnioskami końcowymi.
EN
The study is focused on the problem of a misalignment of drive systems with induction motor. The paper presents selected methods of detecting misalignment based on the analysis of: stator current, mechanical vibrations and space vector module of the stator current. Pictures from a thermal imaging camera, showing the impact of the misalignment on components of the drive system, are presented. Laboratory tests were carried out on the low-power induction motor. Comments and the final conclusions summarize presented results.
EN
The numerical calculations of the hydrodynamic lubrication of slide bearings can be carried out by modelling the oil flow for a given value of height of bearing lubrication gap. On the basis of the assumed height of the lubrication gap, the values of hydrodynamic pressures, load carrying capacities, friction forces, temperatures, can be determined. The bearing lubrication gap height can be influenced by many effects, e.g. misalignment between the shaft axis and the axis of the sleeve, vibrations, varying load, change in the viscosity value of lubricating oil caused by changes in temperature, pressure, shear rate or by oil ageing, wear of journal and sleeve surfaces. This article presents the results of numerical simulations concerning the influence of the misalignment between the axis of shaft and the axis of sleeve of the sliding conical bearing on its hydrodynamic lubrication, by taking into account the position of the plane in which the misalignment occurs. In this study, there was defined an angle between the plane in which the misalignment occurs and the plane in which lies the line of centres of corresponding bearing without misalignment. In this research, to investigate the impact of the position of the plane in which the misalignment occurs, the CFD software, designed to solve general flow phenomena, was used. It was assumed, that the bearings operate in a steady state conditions, the flow in the bearing lubrication gap is laminar and non-isothermal. A lubricating oil has shear properties as the Ostwald-de Waele fluid.
EN
In this paper, taking a single span flexible rotor system with two discs as the research object, the finite element model of the rotor-bearing system is established. The stator is simplified as a group of equispaced points along the circumference and the rotor as a point based on the contact dynamic theory. The rotor-stator rubbing is simulated using multiple point-point contact elements, the separation and the contact of the rotor and stator are determined by the change of the cylindrical gap, and the rotor and stator model are coupled by nonlinear contact force. By adopting the augmented Lagrangian method to deal with contact constraint conditions, Coulomb friction model to simulate rotor-stator frictional characteristics, the responses of the rotor system with rubbing are analyzed. The effects of rotating speeds and rubbing stiffness on normal rubbing forces are discussed under asymmetrical rotor-stator clearance conditions. The results show that there may be different rubbing forms (local rubbing and full rubbing) and transient impact forces under four cases with rotating speeds. Rubbing stiffness has the greatest effects on the rubbing force, the amount of misalignment affects mainly the transient impact force and does not affect the normal rubbing force at the stable rubbing stage.
PL
Analizowano układ wirnika z dwoma dyskami. Symulowano tarcie między wirnikiem i stojanem a separacja była uwzględniana jako zmiana cylindrycznej szczeliny.
PL
W artykule przedstawiono problem doświadczalnego wyznaczania najważniejszych parametrów metrologicznych akcelerometrów MEMS. Szczegółowo omówiono zagadnienie justowania akcelerometrów względem stanowiska badawczego. Wskazano na niewyjustowanie akcelerometru jako najistotniejsze źródło błędów wskazań tych przyrządów. Podano wartości niektórych parametrów metrologicznych dla przykładowych akcelerometrów. Odniesiono się do podobnych prac prowadzonych przez różne ośrodki badawcze na świecie.
EN
paper addresses the issue of determining metrological parameters of MEMS accelerometers in an experimental way. Methodology of performing such studies as well as the related test rig are presented by the author in [1]. Short discussion on similar works carried out by others, reported e.g. in [2-4], [8-10], [14-15], is included. Much attention is paid to the problem of aligning the accelerometer in the test rig. The obtained results proved that misalignment is a factor affecting the sensor accuracy most significantly. That can be clearly observed by comparing the courses in Figs. 2 and 3, where the misalignment almost directly increased the error of sensor indications. Such errors as cross-axis (or transverse) sensitivity, perpendicularity of the sensitive axes and hysteresis are briefly addressed in Sections 4-6. Yet even though magnitudes of these errors are not significant in the case of dual-axis accelerometers that have been tested, it may turn out that it is not so in the case of triaxial accelerometers . It is shown that owing to compensation of systematic errors (such as the cross-axis sensitivity or misalignment) or even elimination of various kinds of errors (e.g. misalignment, errors resulting from the accepted way of calibration) an improvement in sensor performance may be achieved. At the end, some parameters as estimators of the accuracy of MEMS accelerometers are proposed.
EN
It is very difficult to unambiguously define the symptoms of misalignment of rotating elements of machine on the basis of vibration spectrum. With numerous states of inefficiency the picture of amplitude-frequency characteristic which is the basic tool of vibrodiagnostics is similar. Loose coupling or rubbing of the rotor's moving parts against fixed elements cause large vibration velocity amplitudes for the sequence of ultra-harmonics of the rotational frequency, similarly as in the case of drive system misalignment. The author analyzes the character of the rotor's longitudinal vibrations in which there is a large misalignment of shafts joined by coupling with spring elements in a form of a plastic insert with high hardness. It is also showed how the response of the system to the axial force changes in the case where spring element is damaged.
PL
Jednoznaczne określenie symptomów występowania niewspółosiowości wirujących elementów maszyny na podstawie widma drgań jest zagadnieniem bardzo trudnym. Przy licznych stanach niesprawności obraz charakterystyki amplitudowo-częstotliwościowej, będącej podstawowym narzędziem wibro-diagnostyki, jest podobny. Luz w łożysku lub ocieranie części ruchomych wirnika o elementy nieruchome są przyczyną dużych wartości amplitud prędkości drgań dla kolejnych ultraharmonicznych częstotliwości obrotowej, analogicznie jak w przypadku niewspółosiowości w układzie napędu. Autor analizuje charakter drgań wzdłużnych wirnika, w którym występuje duża niewspółosiowość wałów łączonych sprzęgłem z elementem sprężystym w postaci wkładki wykonanej z tworzywa sztucznego o dużej twardości. Pokazano również jak zmienia się odpowiedź układu na wymuszenie siłą osiową w przypadku, gdy element sprężysty ulega uszkodzeniu.
PL
Dotychczasowe obliczenia trwałości łożysk wału oparte są na założeniu, iż wszystkie łożyska wału są współosiowe. Oprócz tego łożyska traktuje się jak podpory doskonale sztywne o charakterze przegubowym. W rzeczywistości dokładne wykonanie osadzeń łożysk w niektórych przypadkach jest niemożliwe, a w łożyskach występują ugięcia sprężyste, które wpływają na przebieg linii wału oraz mają wpływ na trwałość łożysk. Celem tej pracy jest określenie wpływu niewspółosiowości łożysk w połączeniu z ugięciami w łożyskach na trwałość łożyskowania wału trzypodporowego.
EN
Up to now calculations of shaft bearing durability were based on the assumption that all of shaft bearings were collinear. Additionally bearings were treated usually as an ideally stiff articulated supports. In reality, hard-grade work of bearing mounting in some cases is impossible, elastic deflections occurred in bearings influence on shaft line's course and on bearings durability. The aim of the work was determination of impact of bali bearings misalignment in connection with bearings deflection on bearing stability of three-bearing shaft.
EN
The essence of the present work is an innovative methodology consisting in creation and presentation of complex diagnostic relations in the form of "defect maps", which allow mapping the machine technical state in certain domain of random events represented by defects. In the case of the bearing misalignment defect, which is the subject of the present article, the "domain of events" is the area of possible bearing dislocations and the "technical state" may be expressed e.g. by vibrations of the machine elements. The effect of this work is complete set of maps, which present distribution of bearing vibration as functions of individual bearing displacements. Within this work various types of bearing misalignment maps were constructed, intended for various applications in the turbogenerator diagnostic system. The defect maps methodology applied here for presentation of the bearing misalignment effects has been generalized and proposed as the idea of presentation of a machine response to certain class of defects.
PL
Istotą niniejszej pracy jest innowacyjna metodyka polegająca na tworzeniu i prezentacji złożonych relacji diagnostycznych w formie "map defektów", które pozwalają odwzorowywać stan techniczny maszyny w pewnym obszarze zdarzeń losowych reprezentowanych przez defekty. W przypadku defektu rozosiowania łożysk, który jest przedmiotem niniejszego artykułu "obszar zdarzeń" może być wyrażony np. przez drgania elementów maszyny. Efektem pracy jest kompletny zestaw map, które prezentują rozkład drgań łożysk jako funkcję indywidualnych przemieszczeń łożysk. W ramach tej pracy zostały utworzone różne rodzaje map skutków przemieszczeń łożysk, przeznaczone dla różnorodnych zastosowań w systemie diagnostycznym turbogeneratora. Metodyka map defektów, zastosowana tu do prezentacji efektów rozosiowania łożysk została uogólniona i zaproponowana jako sposób prezentacji odpowiedzi maszyny na pewną klasę defektów.
14
Content available remote Monitorowanie nieosiowości napędów elektrycznych z silnikami indukcyjnymi
PL
W artykule przedstawiono problemy wykrywania i oceny nieosiowości w napędach z silnikami indukcyjnymi. Omówiono możliwości monitorowania nieosiowości na podstawie harmonicznych o charakterystycznych częstotliwościach, otrzymywanych w wyniku analizy widmowej prądu stojana oraz drgań mechanicznych. Przedstawiono stanowisko laboratoryjne umożliwiające regulację niewyosiowania oraz przykłady widm częstotliwościowych prądu fazowego oraz drgań badanego silnika dla napędu prawidłowo wyosiowanego i rozosiowanego równolegle w poziomie i pionie. Przeprowadzone badania laboratoryjne wykazały w pełni możliwość monitorowania on-line w szerokim zakresie nieosiowości napędu poprzez wykrywanie i ocenę charakterystycznych częstotliwości w widmach prądu stojana i drgań.
EN
The issues related to the detection and analyses of the misalignment in induction motor drive are presented in this paper. The possibility of the application of the stator current and mechanical vibration spectrum analysis to motor condition monitoring is discussed. The laboratory setup is briefly described and the selected current and mechanical vibration spectra are demonstrated in case of aligned and misaligned drive systems. The experimental results confirm that the proposed analysis method of current and vibration spectra can be applied to on-line monitoring of the induction motor drive misalignment.
EN
The inherent problems of rotating machine dysfunction are often caused by shaft misalignment. This defect generates some important loads and vibrations, and can lead to a premature failure of the bearing, the shaft, or the clutch. In this study we propose a model of a clutch having eleven degree of freedom and three types of nonlinearity introduced by dry friction, double-stages stiffness and splines clearances. The Coulomb friction formulations and splines clearance functions are smoothened before they are applied to the nonlinear system. The calculation of the dynamic response of the clutch is done by the Runge Kutta method. The dynamic behaviour of both a faultless clutch system and clutch system containing a parallel and angular misalignment defect are compared in the time domains. Finally, the effects of a harmonically varying load on the dynamic response of the defected clutch system with nonlinear dry friction and under sinusoidal torque excitation are analysed.
EN
The paper aims at illustrating effects of computer simulated bearing misalignment defect in a power turbogenerator. The results are presented in the form of journal trajectories of all turbo-set bearings as the effect of displacing two most vulnerable machine bearings. The analysis is limited to misalignment of the bearings in horizontal and vertical directions by the maximum acceptable range calculated with regard to permissible bearing vibration. Shape and dimensions of bearing trajectories are interpreted basing on theory of hydrodynamic lubrication of bearings. It was shown that relative journal trajectories carry much important information about dynamic state of the machine, indicating also the way in which bearings are loaded. The article shows the potential of using trajectory patterns for diagnosing misalignment defects in rotating machines and suggests including sets of trajectory patterns to the knowledge base of the machine diagnostic system.
PL
W artykule przedstawiono rezultaty komputerowej symulacji defektu rozosiowania łożysk turbogeneratora wielkiej mocy. Wyniki zostały zaprezentowane w formie trajektorii czopów wszystkich łożysk turbozespołu jako skutku przemieszczenia dwu najbardziej newralgicznych łożysk tej maszyny. Analiza jest ograniczona do rozosiowania tych łożysk w kierunku poziomym i pionowym o maksymalną dopuszczalną wielkość obliczoną ze względu na drgania łożysk. Kształt i wymiary trajektorii łożysk są interpretowane na podstawie hydrodynamicznej teorii smarowania. Pokazano, że względne trajektorie czopów niosą wiele ważnych informacji o stanie dynamicznym maszyny, wskazując także na sposób obciążenia łożysk. Artykuł wskazuje na możliwości użycia obrazów trajektorii do celów diagnostyki defektu rozosiowania w maszynach wirnikowych i sugeruje włączenie obrazów trajektorii do bazy wiedzy systemu diagnostycznego maszyny.
EN
The article presents results of research oriented on creating a pattern of the dynamic state of a turboset in the presence of a defect consisting in the misalignment of its bearings. The work contains the exemplary set of three-dimensional graphs, which illustrate vibration levels of all bearings as a function of displacement of each turboset bearing in any direction in relation to its base position. Graphs showing division of the area of the expected bearing dislocations into the sub-areas of permissible and prohibited dislocations have been then created. The work was done by means of computer simulation of bearing misalignments in the numerical model of 13K215 turboset by means of MESWIR computer code package. Relations between bearing dislocations and the dynamic state of the machine compose a set of diagnostic relations, which can be included to the base of diagnostic knowledge on the machine and used in its diagnostic system.
PL
W artykule przedstawiono wyniki badań mających na celu utworzenie obrazu stanu dynamicznego turbozespołu w obecności defektu polegającego na rozosiowaniu jego łożysk. Praca zawiera przykładowe zbiory trójwymiarowych wykresów, które ilustrują poziom drgań wszystkich łożysk turbozespołu jako funkcje przemieszczenia jego wszystkich łożysk w dowolnym kierunku w stosunku do ich bazowego położenia. Stworzone zostały wykresy pokazujące podział obszaru możliwych przemieszczeń łożysk na podobszary dozwolonych i zabronionych przemieszczeń. Prace wykonano poprzez symulacje komputerowe przemieszczeń łożysk w numerycznym modelu turbozespołu 13K215 pakietem oprogramowania MESWIR. Związki między przemieszczeniem łożysk i stanem dynamicznym maszyny tworzą zbiór relacji diagnostycznych, który może być włączony do bazy wiedzy diagnostycznej maszyny i użyty w jej systemie diagnostycznym.
EN
The article presents results of the research oriented on determining a set of diagnostic relations referring to a special, but relatively common class of turboset defects, consisting in the misalignment of great turbine set bearings with respect to their designed base positions. The paper discusses a collection of types of the diagnostic relations obtained via simulation calculations of the dynamic state of the machine in steady-state operation and transient conditions. Numerical calculations were carried-out, with the aid of a package of MESWIR codes, on a model turbine set in which the bearings have been dislocated by the maximum permissible range. For this purpose the maximum permissible misalignments of all seven turbine set bearings were calculated. The research makes it possible to formulate a system of diagnostic relations connected with the bearing lateral dislocation defect, which can make the knowledge basis for a diagnostic system.
19
Content available remote On the thermal effects in hydrodynamic journal bearings
EN
This paper presents recent works on temperature effects in hydrodynamic journal bearings. This is an over-view of several specific thermal problems encountered particularly in fixed geometry and tilting-pad journal bearings. The temperature-viscosity variation, the heat transfer, the change in bearing clearance, the thermal and mechanical deformations, the flow regime, the transient regime, the risk of seizure, the dynamic loading as well as the misalignment are successively discussed.
20
Content available remote Some Dynamic Effects of Gear Couplings in Rotor Systems
EN
This is a brief survey on dynamic effects due to the presence of a strongly non-linear gear coupling in an otherwise linear rotor system. Numerical results show strong influences of the gear coupling on the system behavior, and a high sensitivity to parameter variations. Proper misalignment can stabilize the rotor (the model of the gear coupling characteristic is the topic of a paper under preparation).
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