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1

Rotor blade vibration simulator of steam turbine with aliasing frequencies up to 25 Hz

Piechowski L., Rządkowski R., Troka P., Piechowski P., Szczepanik R.

Transactions of the Institute of Fluid-Flow Machinery

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2016

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nr 134

121--129

EN

The tip-timing measurement of rotor blade vibration of a real turbine is very expensive. An electronic simulator of unshrouded steam turbine rotor blade vibrations for aliasing frequencies up to 25 Hz is presented in this paper. The results of the simulated blade vibrations were compared with ones carried out on a real steam turbine. The simulator can be also used to: calibrate the measurement channels, help in the designing and manufacturing new tip-timing systems, and check the reliability of other tip-timing systems.

2

Studies on unsteady operation of a turbojet engine and an intake channel of a supersonic aircraft

Kowalski M., Szczepanik R.

Journal of KONES

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2014

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Vol. 21, No. 2

143--151

EN

The paper explains how to analyse possible disturbances in the intake air stream and their impact on engine operation. The introduction outlines possible reasons that induce disorders in the intake air stream. Then the substantial differences in operational characteristics between a centrifugal and an axial compressor are enlightened. The phenomenon of an unsteady compressor, referred to as the compressor stall, is explained through presentation of the process phases when air stream detaches from the surfaces of the compressor blades. Then the paper presents how disturbances in the air stream propagate down subsequent stages of the engine compressor with the emphasis on the fact that the air stream is not able to affect the full height of blades but usually only a portion of them. In addition, the mechanism of the unsteady operation of the engine (compressor) is presented on the graph that shows fuel consumption Q as a function of the engine rpm n. Attention is drawn to the fact that the phenomenon of the engine unsteady operation is associated with the so called rotating areas of air detachments that revolute in the same direction as the engine rotor itself but their rotation speed is lower than the rotor rpm. Consequently, flame downstream the area of detachment may go out for a moment and then quickly reappear, since air is kept supplied at quite high rates. If the foregoing process fails to go in phase with the rotating areas of air detachment, it may even lead to a total flameout of the engine. Then the unsteady operation of the intake channel is discussed in details, as it is frequently mismatched with the compressor stall. The mechanism of the phenomenon origination and the consequences it entails is presented with adequate details by means of appropriated graphs. In addition, the paper explains the phenomenon of beats in the intake channel, which is a result of detachment of the wall-adjacent layer of air flow just downstream the perpendicular shock wave in the intake channel. The effect of beats frequency often leads to the engine stall. The paper ends up with conclusions, in which it is emphasized that studies on the phenomenon and familiarity with the process are extremely important for the safety of flights.

3

The rate of decohesion of a gas turbine blade as assessed with the X-ray computed tomography (CT)

Chalimoniuk M., Szczepanik R, Błachnio J.

Journal of KONES

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2013

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Vol. 20, No. 3

89--96

EN

The overheating of the material is among major reasons for failures/damages to gas turbine blades throughout the entire process of operating aircraft turbine engines. The essential method of diagnosing condition of the blades is metallographic examination being however a destructive technique. The paper has been intended to discuss one of non-destructive testing (NDT) methods, i.e. the X-ray computed tomography (CT), and capabilities of applying it to diagnose changes in condition of gas turbine blades. ‘Tomography’ is a comprehensive term to define a set of diagnostic techniques to produce three-dimensional images that present cross-sections through detail items under scrutiny. The CT is a transmission diagnostic technique that allows layered models (images) of details to be acquired. Most commonly, it is used in research laboratories and throughout the process of the product quality inspection. The paper delivers findings of the preliminary investigation into the assessment of health/maintenance status of gas turbine blades by means of the X-ray computed tomography. The results gained have been successfully verified using the metallographic examination techniques. It has been found that the radiographic imaging method enables recognition of types, sizes, and locations of internal faults in the blades while generating three-dimensional images thereof. Presented are capabilities of the high-resolution X-ray inspection machine with computed tomography (CT), V/tome/x, furnished with a 300 kV tube, and the CT data processing capabilities of the VG Studio Max software solution, high-performance CT reconstruction included (using an optional module). At the same time work is under way with the X-ray tube for nanotomography with the 0.5 􀁐m resolution to examine, in particular, modern composite materials.

4

Investigation of the dynamic properties of engine fan titanium rotor blades in a high manoeuvrability aircraft in FOD aspect

Szczepanik R.

Journal of KONES

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2013

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Vol. 20, No. 2

371--376

EN

A current problem concerning the use of military and civilian aircraft is the damage caused to turbine compressor blades by ‘foreign objects’. Here the term ‘foreign objects’ means small stones, pieces of metal, cement pitch, asphalt, etc., left on runways and taxiways. Foreign objects also include ice and iced lumps of snow as well as birds sucked into aircraft engine air ducts. All such objects pose a serious threat to proper engine operation. They are very harmful in two respects. One is the direct danger during flight when a bird or some other object is sucked into the engine. The other danger is in what might occur in later flights if the engine, especially the compressor and turbine blades, are not inspected for durability reassessment. This paper presents an analysis of how the size and distribution of defects on blade edges affect, the frequencies and fatigue strength of titanium blades in the first four stages of a high manoeuvrability jet engine fan (low pressure compressor). In particular, damaged high manoeuvrability aircraft fan stage rotor blades and measured natural vibration frequencies and logarithmic decrement of damping of high manoeuvrability aircraft fan titanium blades are presented in the paper.

5

Examination of the dynamic properties of 1st stage rotor blades in one - pass engine compressors under operating conditions

Szczepanik R

Journal of KONES

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2013

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Vol. 20, No. 3

395--404

EN

This article includes studies of vibration and stress amplitudes in the Is' stage rotor blades of jet trainer one-pass engine compressors before and after refurbishment in operating conditions. The presented results were obtained using SAD-2 blade vibration amplitude registering and measuring apparatus. The same tests were carried on the same one-pass engine after modernisation. Example oscillograms from the vibration tests of the 16 blades are shown in this article, where show the vibrations of three randomly selected one-pass engines after refurbishment (marked 1, 2 and 3) out of a total of 50 engines. The engine vibration spectra cover the full rotation speed range. The difference between the vibration amplitudes of 1st stage rotor blades, in one-pass engine compressors before and after the refurbishment, is results from the difference in how the blades were attached to the disc. Before modernisation the hammer-type root was used, whereas after refurbishment dovetail-type fittings were applied. Furthermore, it was confirmed that there is nocoupling via the blade disc occurred when the blades were arranged on the disc according to the sinusoidal order of their free vibration frequencies. In such cases recorded vibration amplitudes remain within the average range (from 100 to 120 MPa in terms of stress).

6

Early detection of fatigue cracks in turbine aero - engine rotor blades during flight

Szczepanik R.

Journal of KONES

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2013

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Vol. 20, No. 1

337--342

EN

The author shows results of research done in the Air Force Institute of Technology concerning design, development and implementation of modern diagnostic systems for aero-engines. The papers gives brief description of a project of a new advanced monitoring system basing on non-contact blade-vibration measurement. Recent monitoring systems for engines offer a great potential to reduce the high maintenance costs of aircraft while increasing reliability and safety. These systems check for abnormal engine responses to detect failures, saving lives and reducing secondary damage to the aircraft. A phenomenon of dynamic change of an aero-engine compressor blades natural frequency in course of fatigue cracks propagation in their roots on the example of a Polish turbojet engine is described. On the ground of this phenomenon main working principles of a device, which measures vibrations of turbine engine rotor blades with application of the noninterfering discrete method (MDPh), used for early detection of first stage compressor blade cracks are discussed. Typical representation of the first stage compressor blades vibration during engine acceleration, representation of the first stage blades vibration during engine acceleration and deceleration with steady-state stator distortions, crack initiation and propagation symptoms in blades, comparison of blade vibration spectra of the same blades for different conditions are presented in the paper.

7

Analysis of 1st stage compressor rotor blade stress and vibration amplitudes in one-pass jet engine

Szczepanik R.

Journal of KONES

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2013

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Vol. 20, No. 4

441--450

EN

This paper considers 1st stage compressor blade dynamics in the one-pass jet engines of trainer aircraft. Research was carried out on an engine test bench using the SAD system and its results were compared with those obtained using the tensometric approach. In this paper presented basic dynamic properties of rotor blades, bench test of rotor blade dynamics, Bench tests of the dynamic behaviour of blades subjected to external impacts and then Comparison of strain gauge and SAD tip-timing results. Then discusses the results of tests assessing the accuracy of the 1987 ITWL device by comparing strain gauge signals with those recorded by SAD apparatus in a running engine. It also presented simultaneous vibration readings of all the rotor blades at selected rotation speeds. Also shows that increased stress in these blades may be due to repeated engine surges, normal and hot engine surges, entry into the engine of a foreign object. Among others selection and layout of rotor blades in the 1st stage of a one-pass engine compressor, stress amplitudes for rotor blade, stress in rotor blade, stress amplitudes, free inlet flow and smooth engine acceleration, vibration amplitudes, asynchronous vibrations are presented in the paper.

8

Dynamic reliability of rotor hot section turbine blade

Szczepanik R., Rokicki E., Rzadkowski R.

Scientific Problems of Machines Operation and Maintenance

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2012

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Vol. 47, nr 1

75--88

EN

Non-contact vibration measurements for turbine blades in an aircraft engines are hindered by the very low level of vibration amplitudes and high temperatures. Thus high-temperature inductive sensors and data processing algorithms were developed by the Air Force Institute of Technology (ITWL) for the diagnosis of gas turbines. These sensors are suitable for a long-term operation at temperatures typical for gas turbines and can withstand vibrations that occur during the operation of jet engines. Measurement results have shown that turbine blade vibrations in a jet engine achieve an average amplitude of approximately 0.1 mm in nominal conditions and usually no higher than 0.4 mm in resonance conditions. ITWL conditioning methods using technologically advanced circuits for triggering and data acquisition make it possible to measure blade tip deflection with an accuracy of over 0.01 %. The obtained resolution is sufficient to estimate blade vibration frequency and identify the vibration mode shape.

PL

Bezdotykowe pomiary drgań łopatek wirnikowych turbin silników lotniczych charakteryzują małe amplitudy drgań łopatek i praca w wysokich temperaturach czynnika roboczego. Wysokotemperaturowe czujniki indukcyjne i algorytmy przetwarzania danych opracowane przez autorów w Instytucie Technicznym Wojsk Lotniczych pozwalają na diagnostykę łopatek turbin gazowych. Czujniki mogą pracować długotrwale w temperaturach typowych dla turbin gazowych. Mierzą również drgania rezonansowe występujące podczas pracy silników odrzutowych. Opracowane układy kondycjonujące wspierane przez zaawansowane technologicznie układy wyzwalania i rejestracji pozwoliły na uzyskanie w metodzie tip-timingu dokładności pomiaru lepszej od 0,01%. Uzyskana dokładność pozwala na rozpoznanie form drgań łopatek i ułopatkowanego wieńca łopatek.

9

Reliability of middle bearing in SO-3 jet engine

Szczepanik R., Rokicki E., Spychała J., Rzadkowski R.

Scientific Problems of Machines Operation and Maintenance

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2011

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Vol. 46, nr 4

59--70

EN

In the last years damages of the middle bearing of SO-3 engines were the reasons of serious air incidents. In this paper the peak detector analysis of tip-timing data has been applied as an alternative method of studying the results of experimental research. Measurements of seventh stage compressor rotor blade vibrations were made using the tip-timing method at the AFIT. The experimental analyses concerned both an SO-3 engine with a middle bearing in a good technical condition and an engine with a damaged middle bearing. A numerical analysis of the free vibration of the seventh stage blade was conducted to verify the experimental ones. The seventh compressor rotor blade of an SO-3 engine (close to the middle bearing) was modelled using an FE model and its natural frequencies were calculated. The method presented in this paper enables prediction of middle bearing failure in an SO-3 engine 33 minutes before it happens.

PL

W ostatnich latach uszkodzenia środkowego łożyska silnika typu SO-3 były przyczynami poważnych zdarzeń lotniczych. W niniejszym artykule, jako alternatywna metoda do analizy danych uzyskanych metodą „tip-timing” podczas badań eksperymentalnych, został zastosowany detektor szczytowy. Pomiary drgań łopatek siódmego stopnia sprężarki zostały przeprowadzone z wykorzystaniem metody „tip-timing” w ITWL. Badania eksperymentalne dotyczyły zarówno silnika z łożyskiem środkowym o dobrym stanie technicznym, jak i łożyska uszkodzonego. W celu weryfikacji badań eksperymentalnych wykonano analizy numeryczne drgań własnych łopatek siódmego stopnia wirnika sprężarki. Łopatki tego stopnia, znajdującego się w strefie łożyska środkowego, zamodelowano, używając metody elementów skończonych, a następnie wyliczono ich częstotliwości drgań własnych. Metoda przedstawiona w artykule umożliwiła zidentyfikowanie symptomów uszkodzenia łożyska środkowego silnika SO-3 na 33 minuty przed awarią.

10

Dynamic analysis of first stage compressor bladed disk of an aircraft engine

Rzadkowski R., Drewczyński M., Soliński M., Maurin A., Maciejewska A., Szczepanik R.

Problemy Eksploatacji

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2011

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nr 1

157-165

EN

There have been a number of SO-3 first stage compressor blade failures. An experiment was carried out on a first stage rotor blade in the compressor of an SO-3 engine at the Air Force Institute of Technology in Warsaw. The natural frequencies of rotor blades were measured. Next, the tip-timing measurement of rotor blade was done in an engine working at various speeds. Various operation conditions were assumed, such as the presence of a foreign object in the engine inlet. Structure and flow calculations were carried out to compare the experimental results. An FEM was used to calculate the natural frequencies of a mistuned bladed disk. The FLUENT code was used to calculate the unsteady forces acting on rotor blades. The mistuned bladed disk was forced to vibrate when rotating at 15000 rpm.

PL

Odnotowano wiele uszkodzeń łopatek wirnikowych pierwszego stopnia sprężarki silnika SO-3. W Instytucie Technicznym Wojsk Lotniczych w Warszawie przeprowadzono cykl eksperymentów na łopatkach wirnikowych pierwszego stopnia sprężarki silnika SO-3. Zmierzono częstotliwości drgań własnych łopatek wirnikowych. Wykonano pomiary przemieszczeń łopatek wirnikowych metodą tip-timing dla różnych prędkości obrotowych wirnika. W trakcie badań uwzględniono także obecność obcego ciała we wlocie silnika. Przeprowadzono obliczenia numeryczne przepływu w pierwszym stopniu sprężarki i drgającej ułopatkowanej tarczy, w celu porównania z wynikami otrzymanymi z badań eksperymentalnych. Metoda elementów skończonych zastosowana została do analizy drgań wymuszonych ułopatkowanej tarczy z łopatkami różniącymi się wymiarami geometrycznymi, dla nominalnej prędkości obrotowej n=15 000 obr./min. Program FLUENT zastosowany został do obliczenia niestacjonarnych sił działających na łopatki wirnikowe.

11

Zastosowanie sztucznych sieci neuronowych w modelowaniu przebiegu procesów tribologicznych w układach: paliwowym oraz łożyskowania silnika lotniczego

Dzięgielewski W., Sarnecki J., Szczepanik R.

Logistyka

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2009

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nr 3

CD-CD

PL

W referacie przedstawiono problematykę zastosowania sztucznych sieci neuronowych w modelowaniu procesów tribologicznych zachodzących w układach: paliwowym oraz łożyskowania silnika lotniczego. Zaprezentowano przykłady zastosowań sieci neuronowych w projektach badawczych realizowanych w Instytucie Technicznym Wojsk Lotniczych, przy wykorzystaniu rzeczywistych danych pomiarowych. Badania były realizowane w ramach pracy naukowej finansowanej ze środków na naukę w latach 2005-2008 jako oddzielne projekty badawcze.

EN

The paper deals with problems of tribological processes characterization and modelling with use of artificial neural networks (ANNs). Examples of ANNs application in research projects carried out in the Air Force Institute of Technology (AFIT) are given. Research were carried out due to financing from budget assets for years 2005-2008 as two different research projects.

12

Stator clocking in SO3 compressor first stage rotor blades

Rządkowski R, Gnesin V, Kolodyazhnaya L, Szczepanik R

Zeszyty Naukowe. Cieplne Maszyny Przepływowe - Turbomachinery / Politechnika Łódzka

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2008

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nr 133

299--308

EN

Numerical calculations of the 3D transonic flow of an ideal gas through three-row compressor stage including the clocking effects are presented. The approach is based on the solution of the coupled aerodynamic-structure problem for the 3D flow through the turbine stage in which fluid and dynamic equations are integrated simultaneously in time. There has been performed the calculation for the stage of the compressor with rotor blades of 0.163 m. The aeroelastic characteristics are obtained for different position of the stator rows. The clocking effect influence the stability region of the rotor blades.

13

Zarys metody wyznaczenia ryzyka uszkodzenia i trwałości zmęczeniowej wybranych elementów konstrukcji lotniczych w warunkach eksploatacji z zastosowaniem wzoru Parisa dla m różnego od 2.

Szczepanik R., Tomaszek H., Jasztal M.

Zagadnienia Eksploatacji Maszyn

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2007

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Vol. 42, nr 3

99-110

PL

W artykule przedstawiony jest zarys metody określenia ryzyka uszkodzenia katastroficznego elementu konstrukcji w aspekcie zmęczenia pracującego pod obciążeniem zmiennym, jakie powstaje w czasie lotu statku powietrznego. Otrzymane zależności zostały następnie wykorzystane do oszacowania trwałości zmęczeniowej dla przyjętego poziomu ryzyka powstania uszkodzenia. Zasadniczą sprawą w przedstawionym artykule jest określenie funkcji rozkładu przyrostu pęknięcia w funkcji nalotu statku powietrznego. Do modelowania wzrostu pęknięcia w funkcji nalotu zastosowano równanie różnicowe, z którego po przekształceniu otrzymano równanie Fokkera-Plancka. Rozwiązaniem tego równania jest poszukiwana funkcja gęstości długości pęknięcia.

EN

Method of damage risk and fatigue life determination selected aircraft's elements in using condition has been presented in this paper. Authors took into consideration stress intensity factor and Paris formula for m nequ 2 as a starting point for mathematical model creation. Fatigue crack growth model was created on the basis of partial differential equation type Fokker-Planck.

14

Zarys metody określania rozkładu czasu narastania pęknięcia elementu do wartości granicznej w warunkach zmęczenia w procesie eksploatacji statku powietrznego.

Szczepanik R., Tomaszek H., Jasztal M.

Zagadnienia Eksploatacji Maszyn

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2006

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Vol. 41, nr 3

81-89

PL

W artykule została podana probabilistyczna metoda określania rozkładu czasu wzrostu pęknięcia zmęczeniowego od wartości granicznej dla wybranych elementów statku powietrznego w procesie eksploatacji. W metodzie tej bazowano od strony fizycznej na współczynniku intensywności naprężeń i wzorze Parisa. Dynamikę narastania pęknięcia zmęczeniowego scharakteryzowano przy pomocy równania Fokkera-Plancka. W wyniku rozwiązania tego równania otrzymano funkcję gęstości długości pęknięcia zmęczeniowego. Funkcja ta posłużyła do wyznaczenia funkcji gęstości czasu przekraczania wartości dopuszczalnej przez bieżącą wartość długości pęknięcia.

EN

The study includes two main ventures: - determination of distribution of time fatigue crack growth depending on aircraft's flying time for chosen structure's element - carried out results (in first point) were basis for determination of distribution of time fatigue growth to limiting value (acceptable). Authors took into consideration stress intensity factor and Paris formula as a starting point for mathematical model creation. Fatigue crack growth model was created on the basis of partial differential equation type Fokker-Planck.

15

Niektóre charakterystyki rozkładu czasu przekraczania stanu granicznego (dopuszczalnego).

Szczepanik R., Tomaszek H.

Zagadnienia Eksploatacji Maszyn

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2006

|

Vol. 41, nr 1

99-105

PL

Ocena niezawodności urządzeń w procesie eksploatacji z wykorzystaniem zmian wartości parametrów diagnostycznych i ich stanów granicznych prowadzi do potrzeby poszukiwania rozkładów czasu przekraczania przez bieżącą wartość parametru wartości dopuszczalnej. W pracy [1] podjęto próbę analitycznego wyznaczenia takiego rozkładu w pewnych ustalonych warunkach eksploatacji urządzenia. Niniejsza praca jest uzupełnieniem pracy [1] i zawiera wyznaczenie niektórych charakterystyk rozkładu czasu przekraczania wartości granicznej.

EN

Evaluation of device's reliability in exploitation process with use of change of value diagnostic parameters and their limiting state require distribution of time of exceed a limiting state. In the [1] paper authors made an effort to determine in analytical way the distribution in established exploitation condition. Present paper is completion [1] paper and include determine selected characteristic distribution of time exceed a limiting state. Present paper include proof that function f(t)Zd is a density function with specific parameters of distribution. In order to practical use of distribution of time of exceed a limiting state we would prepare graph of different constant and limiting value of diagnostic parameters.

16

Free vibrations analysis of shrouded bladed discs with one loose blade

Rządkowski R., Kwapisz L., Drewczyński M., Szczepanik R., Rao J.S.

TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk

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2006

|

Vol. 10, No 1

83-95

EN

As a failure of rotor blades in a gas turbine was reported, the rotating-mode shapes of flexible shrouded bladed disc assemblies were calculated using a finite element approach. Rotational effects, such as centrifugal stiffening were accounted for, and all couplings between the flexible parts were allowed. The spin softening effects were neglected. A dynamic analysis of the shrouded bladed disc demonstrated that it was designed with a sufficient safety region of resonance. In case of one blade getting loose, it is vibrating in resonance.

17

Complex approach to aircraft systems and structure safety and realibility

Szczepanik R.

Journal of KONES

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2006

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Vol. 13, No. 4

445-451

EN

This paper presents new technologies employed in aircraft system engineering that are necessary to ensure a sufficient level of aviation equipment operation safety. New technical condition identification and examination technologies involving non destructive testing methods are presented, as well as methods of hourly and calendar TBOs' extension. A computer system for reliability assessment SAN is presented and the system's extension into a comprehensive system of flight security assessment and appraisal that enables assurance of a sufficient level of aviation equipment operation security. Reliability assessment system SAN, methods of aircraft technical condition assessment, digital flight performance recorders, in-flight load recording system KAM-500, rotating machine diagnostic system, with real-time diagnostics, comprehensive system of flight safety analysis and assessment are among other presented in the paper. Rapid development of research equipment, software tools, and more and more complex tested items (aircrafts and their modules) enforce development and refinement of applied research methodologies selected research methodologies applied by the Air Force Institute of Technology in aircraft systems examination.

18

Problems of assessment the operational safety of a combat aircraft using safety systems

Szczepanik R., Tomaszek H., Żurek J.

Journal of KONBiN

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2006

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No. 2

47--56

EN

In this study we present an outline of a method of assessment of the aircraft pilot safety when an ejection seat is used. Two methods are presented. The first method concerns a case when a seat must be used due to failures during flight, which do not occur too often. The second one applies to cases when a pilot must be ejected as a result of his opponent’s/ enemy’s action (armed conflict) with combat means and the structure of an aircraft is destroyed.

19

Metoda określania rozkładu czasu do przekroczenia stanu granicznego.

Szczepanik R., Tomaszek H.

Zagadnienia Eksploatacji Maszyn

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2005

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Vol. 40, nr 4

35-44

PL

W niniejszej pracy podjęto próbę określenia niezawodności i trwałości urządzenia wykorzystując funkcję gęstości czasu przekroczenia stanu granicznego. Celem głównym opracowania było wyznaczenie analitycznej postaci rozkładu czasu przekroczenia stanu granicznego. Mając wyznaczoną postać funkcji gęstości czasu przekroczenia stanu granicznego określono wzory na niezawodność i trwałość urządzenia dla ustalonych warunków.

EN

In this paper authors presented evaluation of distribution of time of exceed a limiting state (acceptable). Presented method was based at selected dominant diagnostic parameter which describe technical state of device. Dynamics of change the parameter during exploitation process authors describe through given below equation. As a solution of the equation authors received density function of change value diagnostic parameter. Furthermore authors describe probability of exceed limiting value by current value of diagnostic parameter Q(t;zd). Density function of distribution of first time of exceed over acceptable value zd was described. On the basis of this density function authors received reliability and durability equations for specific conditions of device's work.

20

Zarys metody oceny niezawodności i trwałości urządzeń lotniczych z uwzględnieniem stanów granicznych

Szczepanik R., Tomaszek H.

Problemy Eksploatacji

|

2005

|

nr 3

247--256

PL

W niniejszej pracy podjęto próbę określenia niezawodności i trwałości urządzenia, wykorzystując funkcję gęstości czasu przekroczenia stanu granicznego. Celem głównym opracowania było wyznaczenie analitycznej postaci rozkładu czasu przekroczenia stanu granicznego. Mając wyznaczoną postać funkcji gęstości czasu przekroczenia stanu granicznego, określono wzory na niezawodność i trwałość urządzenia dla ustalonych warunków.

EN

In this paper authors presented evaluation of device reliability and durability with use of density function of limiting state overflow time. The main aim of this research was determination of analytical form of limiting state overflow time distribution. Paper include: - selection of diagnostic parameter for determination of technical state and their limiting state, - description in probabilistic way change of diagnostic parameter value (under the influence of destruction process), - estimate of chance limiting state overflow, - with use of probability of limiting state overflow authors determined analytical for of density function limiting state overflow time. On the basis of density function limiting state overflow time authors describe reliability and durability of deviation for fixed condition.