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EN
In this study, a method of determining the heat flux, which reaches the surface of a charge, has been presented with the use of an inverse analysis. The research on the heating process of a square 15HM steel charge was conducted in a natural gas-fired laboratory furnace. The inverse solution was based on the search of the minimum standard error between the measured and the calculated temperatures. The temperature of the charge has been calculated by the finite element method, solving the heat conduction equation for a square charge heated on all the surfaces. As a result, the mean value of the heat flux on each of the heated surfaces of the charge was estimated.
EN
The article presents a model of heat transfer between two solid surfaces remaining in contact under the effect of the force applied. The presented results were obtained from the authors’ own studies conducted with the application of a new method of determining the heat flux transferred between these surfaces. The method consists of two stages: the experiment and numerical calculations. The experimental tests include temperature measurements in specific points in two samples remaining in contact with each other. The numerical part uses the inverse solution and the finite element method for the calculation of the heat flux on the contact surface. An analysis was performed on the effect of the steel grade used in the tests on the result of heat transfer determination in contact phenomena. The calculations were conducted with the application of proprietary software using the inverse method integrated with FEM.
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Content available remote Method for solving inverse problems encountered in monitoring of thermal stresses
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EN
A method for solving one- and multidimesional inverse problems of transient heat conduction is presented. The method is formulated in a matrix form, so problems with large numbers of unknown boundary parameters in bodies of complex geometry can be solved. Three examples illustrate the accuracy of presented method.
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EN
Determining the boundary conditions of heat transfer in steel manufacturing is a very important issue. The heat transfer effect during contact of two solid bodies occurs in the continuous casting steel process. The temperature fields of solids taking part in heat transfer are described by the Fourier equation. The boundary conditions of heat transfer must be determined to get an accurate solution to the heat conduction equation. The heat flux between the tool and the object processed depends mainly on temperature, pressure and time. It is very difficult and complicated to accomplish direct identification and determination of the boundary conditions in this process. The solution to this problem may be the construction of a process model, performing measurements at a test stand, and using numerical methods. The proposed model must be verified on the basis of parameters which can easily be measured in industrial processes. One of them is temperature, which may be used in inverse methods to determine the heat transfer coefficient. This work presents the methodology for determining the heat flux between two solid bodies staying in contact. It consists of two stages – the experiment and the numerical computation. The problem was solved by using the finite element method (FEM) and a numerical program developed at AGH University of Science and Technology in Krakow. The findings of the conducted research are relationships describing the value of the heat flux versus the contact time and surface temperature.
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EN
The basic formulas concerning the inversion are presented in the paper. Examples of the author's studies on the possibility of the localization of zones of increased vibroactivity by means of the inverse method are given. The inverse method is very sensitive to the position of substitute sources. This feature can be used for the determination of the position of actual sources. The accuracy of the method depends also on the distribution of the observation points. The dependence of the position of substitute sources on their acoustic power level is discussed in the paper as well. The distribution of the acoustic fields around the air compressor is given as an example. The~measurements were performed at the points distributed on a semi-sphere. Both the amplitude and phase of the acoustic pressure were determined at each measuring point. On the basis of the results obtained, the zones of increased acoustic emission were searched for.
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EN
In technological process of steel industry heat transfer is a very important factor. Heat transfer plays an essential role especially in rolling and forging processes. Heat flux between a tool and work piece is a function of temperature, pressure and time. A methodology for the determination of the heat transfer at solid to solid interface has been developed. It involves physical experiment and numerical methods. The first one requires measurements of the temperature variations at specified points in the two samples brought into contact. Samples made of C45 and NC6 steels have been employed in physical experiment. One of the samples was heated to an initial temperature of: 800°C, 1000°C and 1100°C. The second sample has been kept at room temperature. The numerical part makes use of the inverse method for calculating the heat flux and at the interface. The method involves the temperature field simulation in the axially symmetrical samples. The objective function is bulled up as a dimensionless error norm between measured and computed temperatures. The variable metric method is employed in the objective function minimization. The heat transfer coefficient variation in time at the boundary surface is approximated by cubic spline functions. The influence of pressure and temperature on the heat flux has been analysed. The problem has been solved by applying the inverse procedure and finite element method for the temperature field simulations. The self-developed software has been used. The simulation results, along with their analysis, have been presented.
EN
The results of the calculations of the local heat transfer coefficient HTC and a heat flux HF on the face of a cylindrical sample made of 1.0503 steel are presented. The sample was cooled from a temperature of approx. 930°C in a mineral oil having a temperature equal to 50°C. The experiments were performed for three speeds of the oil stream (0.2, 0.4 and 0.6 m/s). The oil stream was directed perpendicularly to the cooled surface. The temperature of each sample was measured with 4 thermocouples and recorded with a frequency of 10 Hz. The maximum values of HTC always occurred in the axis of the sample and were in the range of 8000 to 10,000 W/(m2 K). The results are presented in the form of useful graphs showing the dependence of HTC and HF on the surface temperature for various velocities of cooling oil. The calculations were made with self-developed software using the inverse solution of the boundary heat conduction problem.
EN
The inverse method was applied to determine the heat flux reaching the charge surface. The inverse solution was based upon finding the minimum of the error norm between the measured and calculated temperatures. The charge temperature field was calculated with the finite element method by solving the heat transfer equation for a square charge made of 15HM steel heated on all its surfaces. On the basis of the mean value of heat flux, the value of the heat transfer coefficient at each surface was determined depending on the surface temperature of the material heated.
EN
In the presented paper magnesium alloy wire drawing process for medicine application is investigated. The magnesium alloy has a low plasticity at room temperature and cold drawing process is difficult. That why predicting of wire fracture is very important from theoretical and technological point of view. Analyzing of tensile test of magnesium alloys in micro and macro scale using results from 10000N Tensile/Compression Stage for the SEM, allow to understand a numerical model of fracture phenomena. The propose of this aim is to developed a mathematical model of flow stress for magnesium alloy and work out a parameters of fracture criterion using inverse method.
PL
W niniejszym artykule rozpatrzono proces ciągnienia stopów magnezu dla zastosowań w chirurgii. Stopy magnezu mają niską plastyczność w temperaturze pokojowej dlatego proces ciągnienia na zimno jest trudny, a nawet praktycznie niemożliwy. Dlatego przewidywanie procesu pękania jest istotne z technologicznego i praktycznego punktu widzenia. Analiza próby rozciągania w mikrokomorze "10000N Tensile/Compression Stage for the SEM" w skali makro oraz skali mikro, pozwoliła na zrozumienie procesu pękania tych stopów. Celem niniejszej pracy jest opracowanie krzywych płynięcia oraz modelu matematycznego procesu pękania rozpatrywanych stopów magnezu oraz implementacja tych modeli do kodu metody elementów skończonych.
EN
The paper concerns the engineering design of guide vane and runner blades of hydraulic turbines using the inverse problem on the basis of the definition of a velocity hodograph, which is based on Wu’s theory [1, 2]. The design concerns the low-head double-regulated axial Kaplan turbine model characterized by a very high specific speed. The three-dimensional surfaces of turbine blades are based on meridional geometry that is determined in advance and, additionally, the distribution of streamlines must also be defined. The principles of the method applied for the hydraulic turbine and related to its conservation equations are also presented. The conservation equations are written in a curvilinear coordinate system, which adjusts to streamlines by means of the Christoffel symbols. This leads to significant simplification of the computations and generates fast results of three-dimensional blade surfaces. Then, the solution can be found using the method of characteristics. To assess usefulness of the design and robustness of the method, numerical and experimental investigations in a wide range of operations were carried out. Afterwards, the so-called shell characteristics were determined by means of experiments, which allowed to evaluate the method for application to the low-head (1.5 m) Kaplan hydraulic turbine model with the kinematic specific speed (»260). The numerical and experimental results show the successful usage of the method and it can be concluded that it will be useful in designing other types of Kaplan and Francis turbine blades with different specific speeds.
EN
This study presents an inverse heat transfer method to estimate the time history of a local heat flow into the work-piece during milling of AISIH13 with considering a 3D thermal model. Temperatures are measured using thermocouples within the work-piece providing input data for the inverse solver. The conjugate gradient method is used as an inverse solver to predict the local time dependent heat flow distribution on the cutting surfaces as well as the temperature distribution in the work-piece. A moving point heat source and a moving plane heat source with different heat source velocity is considered to investigate their influence on the estimated heat flow. Results indicate a good agreement between the experimental and estimated data with an average root mean square error less than 0.2 ◦C. It can be observed that the heat flow distribution is a function of heat source geometry, cutting speed and feed rate, but the temperature distribution is a weak function of geometry of the moving heat source. Changes of temperature with depth are studied. This study suggests that the developed inverse model can be successfully applied for estimating the heat flow and thermal field in the work-piece during milling.
EN
Ceramic Sr(Ce0.95Y0.05)O3-delta was equilibrated at an ambient air (either wet or dry) and Ar-H2 atmospheres. After the step change of gas atmosphere, the equilibration kinetics was monitored by measuring weight change. Fick’s second law was applied to the experimental kinetic data (the in verse method) to obtain the chemical diffusion coefficient, Dchem. The determined Dchem indicates the complex processes in volving creation and transport of both oxygen vacancies and protonic defects in the studied material.
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Content available remote Identification of transient thermal boundary conditions in complex-shape bodies
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EN
The following paper presents a method for solving one- and multidimensional inverse boundary heat conduction problems. The method is used to estimate an unknown thermal boundary condition on an inner surface of complex-shape elements. Next, the Finite Element Method can be used to calculate thermal stresses caused by other loads such as, for instance, internal pressure. The developed method is tested using the measured temperatures generated from a direct solution. Transient temperature distribution obtained from method presented below is compared with the values obtained from the direct solution. Next, method is used to estimate an unknown thermal boundary condition on an inner surface of a thick-walled Y-branch. Solution is based on measured temperature transients at two points inside the elementary wall thickness.
PL
W artykule zostały porównane wyniki obliczeń pola temperatury wsadu uzyskane z wykorzystaniem modeli zaczerpniętych z literatury oraz własnym modelem wymiany ciepła. Wartość współczynnika wymiany ciepła została uzyskana z badań własnych z zastosowaniem nowej metodyki określania strumienia ciepła przepływającego między powierzchniami wymieniającymi ciepło. Składa się ona z dwóch etapów: eksperymentu i obliczeń numerycznych. Badania eksperymentalne zawierają pomiary zmian temperatury w określonych punktach w dwóch próbkach pozostających w kontakcie. Część numeryczna wykorzystuje rozwiązanie odwrotne i metodę elementów skończonych do obliczania strumienia ciepła na powierzchni styku.
EN
The results of calculations of the temperature field of the deformed material conducted using heat transfer coefficient form literature are compared with that obtained for developed heat transfer boundary condition model. The developed heat transfer boundary condition model has been obtained using a new methodology for determining heat flux transferred between two solid surfaces. The methodology consists of two parts: experimental and numerical one. The experimental part involves measurements of temperature at specific points in the two samples brought into contact. The numerical part uses an inverse method and the finite element method to calculate the heat flux at the interface.
PL
Przedstawiono zastosowanie zmodyfikowanej metody inverse do wyznaczania funkcji opisującej krzywe płynięcia stali St4S. Rozważania prowadzono dla wyników próby ściskania próbek walcowych na plastometrze krzywkowym przy temperaturach 950, 1050, 1150 °C oraz przy prędkościach odkształcenia 6, 30 i 63 s do -1 . Zaproponowana modyfikacja polegała na poszukiwaniu współczynników funkcji w oparciu o wartości parametrów odkształcenia (odkształcenia, prędkości odkształcenia, temperatury) obliczone przy użyciu metody elementów skończonych. Dzięki takiemu algorytmowi obliczeń pominięto stosowanie czasochłonnych metod optymalizacyjnych. Zastosowana metoda pozwoliła uzyskać szybką zbieżność pomiędzy teoretycznymi i doświadczalnymi wartościami sił.
EN
Application of a modified inverse method for the determination of flow curves for the St4S steel has been presented. The flow curves for this steel were determined from compression test performed with cylindrical samples at the temperatures of 950, 1050 and 1150 °C at the strain rates of 6, 30 and 63 s to -1 . The proposed modification of the inverse method is based on a search for flow stress function coefficients using the values of deformation parameters (strain, strain rate, temperature) obtained from the finite element method simulation. This calculation algorithm does not require time-consuming optimization methods and enables rapid obtaining of an agreement between the theoretical and experimental force values.
EN
Inverse methods allow for an acoustic assessment of machines on the bases of analysis of acoustic field parameters. Modeling of the vibroacoustic energy radiation from the sound source to the receiver and the knowledge of the true value of an acoustic pressure at the measuring points allows to reverse the propagation path and thus to determine the parameters of the source itself. Inverse methods can be applicable in the identification of vibroacoustic energy sources and in the sound radiation assessment. Reciprocity methods are often used together with inverse methods. The inverse method is very sensitive to the position of the substitute sources. This feature can be also utilized for the determination of the position of the actual sources. In the article are presented the examples from research carried by the author of machines in view of estimating the possibility to locate the zones of increased vibroactivation by the method of inversion. The computable procedure let estimate both the location and partial acoustic powers of noise sources on the base of the acoustic field's parameters
PL
Metody inwersyjne pozwalają na ocenę akustyczną maszyn na podstawie analizy parametrów pola akustycznego. Metody inwersji w wibroakustyce mogą znaleźć zastosowane w problemach identyfikacji źródeł energii wibroakustycznej i ocenie promieniowania dźwięku. Bardzo często z metodami inwersji łączone są metody wzajemnościowe. Metoda inwersji jest bardzo wrażliwa na lokalizację źródeł zastępczych. Własność" ta może być również wykorzystana do wyznaczania położenia źródeł rzeczywistych. Wrażliwość metody zależy także od rozmieszczenia punktów obserwacji. W artykule przedstawiono przykłady z przeprowadzonych przez autora badań pod kątem oszacowania możliwości lokalizacji obszarów o zwiększonej wibroaktywności metodą inwersji. Procedury obliczeniowe pozwoliły na podstawie parametrów pola akustycznego oszacować zarówno położenie, jak i cząstkowe moce akustyczne złożonych źródeł dźwięku.
PL
Współczynnik wymiany ciepła na powierzchni płyty osłoniętej ekranem cieplnym i bez osłony wyznaczano z zastosowaniem rozwiązania odwrotnego. Badania chłodzenia płyty przeprowadzono na zaprojektowanym i wykonanym stanowisku badawczym. Pomiar temperatury płyty ze stali EN 1.4724 realizowano za pomocą 9 termoelementów typu K umieszczonych 2 mm pod powierzchnią chłodzoną. Proces chłodzenia w powietrzu realizowano w 2 wariantach: w obecności ekranu aluminiowego oraz bez ekranu. Podczas chłodzenia mierzono temperaturę płyty od 800oC do około 40oC. Rozwiązanie równania przewodzenia ciepła w chłodzonej płycie oparto na metodzie elementów skończonych. Zastosowano nieliniowe funkcje kształtu opisane wielomianami Hermite’a. Przeprowadzono testy dokładności rozwiązania odwrotnego, które wykazały jego poprawność. Rozkład współczynnika wymiany ciepła w czasie aproksymowano za pomocą parabolicznych funkcji kształtu.
EN
An inverse method has been applied in to determine the heat transfer coefficient on the surface of a plate protected by a thermal shield and without protection. For purposes of the analysis a dedicated test stand has been designed. Temperature measurement of EN 1.4724 steel was executed with nine K type thermocouples placed 2 mm under the cooled surface. The cooling process in air was executed in two modes: with and without the aluminum shield. The temperature has been measured during plate cooling from 800oC to about 40oC. The solution of the heat conduction equation in the cooled plate was based on the finite element method. Nonlinear shape functions described by Hermite polynomials have been applied. The accuracy of the inverse solution has been tested and justified. The distribution of heat transfer coefficient in time was approximated with the use of quadratic shape functions.
20
Content available remote Tomografia sejsmiczna w górnictwie
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PL
Prędkościowa tomografia sejsmiczna jest techniką bezinwazyjnego obrazowania budowy wewnętrznej próbek skalnych, masywu skalnego, struktur geologicznych itp. w skalach począwszy od ułamka metra do tysięcy kilometrów. Otrzymywane tą techniką przestrzenne rozkłady prędkości fal P i S są zwykle interpretowane w kontekście strukturalnej budowy badanego górotworu. Jednakże, z punktu widzenia zastosowań w górnictwie jednym z najważniejszych elementów badania tomograficznego jest próba interpretacji otrzymanego obrazu tomograficznego pod kątem stanu naprężeń w górotworze. Osiągnąć to można albo przez próbę korelacji aktywności sejsmicznej z anomaliami rozkładu prędkości albo przez interpretacje anomalii prędkości pod kątem zmiennego w przestrzeni pola naprężeń. Niezależnie od wybranego podejścia dla poprawnej interpretacji tomogramów bardzo ważna jest ocena wiarygodności otrzymanych pól prędkości. Celem niniejszej pracy jest przybliżenie zasad tomografii sejsmicznej oraz wspomnianego powyżej dwoistego podejścia do praktycznej interpretacji wyników badań tomograficznych.
EN
The seismic velocity tomography is a non-destructive technique of imaging of the structure of rock samples, rock mass, geological structures etc. at scales ranging from centimetres up to thousands of metres. The obtained by use of this technique spatial distributions of P and S waves are usually interpreted in the context of the internal structure of the imaged rock mass. However, from the point of view of applications in mining one of the most important elements of tomographic inversion is the attempt of interpretation of the obtained tomographic image in the context of the state of stresses in the rock mass. This can be achieved either by an attempt of correlation of seismic activity with anomalies of the velocity distribution or by the interpretation of velocity anomalies in terms of lithological parameters. Independently of the chosen approach, for correct interpretation of tomograms very important is the assessment of reliability of obtained velocity fields. The aim of the present work is the approximation of seismic tomography rules and mentioned above dual approach to the practical interpretation of tomographic investigation results.
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