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1

The new approach to identification of parametric and momentary damages on the basis of Lindeberg – Levy’s model

Lindstedt P., Sudakowski T., Kułaszka A.

Journal of KONBiN

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2017

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No. 43

5--22

EN

The new approach for the assessment of reliability condition of the exploited system, based on the appropriate analysis of changes in the current parameters of technical condition aRb and the regulation condition aRc, determined from the compressed condition equation (1 and 2). While analyzing the course of momentary parameters for technical condition aRb and the regulation condition aRc, it was observed that the parametric and momentary damages can be identified on the basis of quantitative relations between momentary threshold value dpr and corresponding momentary permissible value dpr dop, which are calculated from equation (7, 8, 9) resulting from Lindeberg– Levy’s theorem. It is assumed that the damages are prevailing, when for the moment θii:dpri dopi. With the number of damages (damage map), reliability parameters for each moment of exploitation of technical object (before the catastrophic damages will occur) can be determined. Parametric damages (expected lifetime E(T) and standard deviation of expected lifetime σE(T) provides the reasonable information for the appropriate planning of the servicing of exploitative objects.

PL

Przedstawione w artykule nowe podejście do metody oceny stanu niezawodności eksploatowanego układu polega na odpowiedniej analizie zmian bieżących parametrów stanu technicznego aRb i stanu regulacji aRc, wyznaczonych ze sprzężonych równań stanu (1 i 2). Analizując przebiegi chwilowych wartości parametrów stanu technicznego aRb i stanu regulacji aRc dostrzeżono, że uszkodzenia parametryczne i chwilowe mogą być identyfikowane na podstawie ilościowych relacji między chwilową wartością progową dpr a odpowiadającą jej chwilową wartością dopuszczalną dpr dop, które oblicza się ze wzorów (7, 8, 9) wynikających z twierdzenia Lindeberg’a – Levy’ego. Zakłada się, że uszkodzenie istnieje wtedy, gdy dla chwili θii:dpri dopi. Dysponując liczbami uszkodzeń (mapą uszkodzeń) można wyznaczyć parametry niezawodnościowe dla każdej chwili eksploatacji obiektu technicznego (przed pojawieniem się uszkodzeń katastroficznych). Parametry uszkodzeń (oczekiwany czas życia E(T) i odchylenie standardowe oczekiwanego czasu życia σE(T) są przystępną informacją do odpowiedniego planowania obsług eksploatacyjnych obiektów.

2

Prediction of estimates of technical object’s reliability on the basis of damage determined from lindberg levy’s claim and multiplicity of the set specified from ergodicity stream damage

Lindstedt P., Sudakowski T., Grądzki R.

Journal of KONES

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2013

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Vol. 20, No. 1

179--184

EN

During the exploitation one problem still unsolved is that of determining reliability characteristics for single (individual or small set) technical object. This particularly concerns identification of damage set (parametrical and momentary) as well as determination of substitute cardinality of objects set, where in fact this equals 1, 2, 3 at the most. The article presents a method of determining parametrical and momentary damages from iteration equations: D K= aRb DK + bRbU , (1) UW = aRc U + bRc DK , (2) where: DK – complex diagnostic signal, UW – net environment signal (manner of use), aRb – technical condition parameter, aRc – exploitation condition parameter (exploitation potential), bRb – parameter of environment (manner of use) influence intensity on technical condition, bRc – intensity parameter of technical condition (physical wear) influence on technical object operation quality. Assumption is made that if current value of aRb technical condition parameter is higher than aRb dop (permissible) stemming from central limit theorem, parametrical damage occurs and analogically if value of exploitation condition parameter aRc is higher that aRc dop, momentary damage occurs. Additional assumption is made that substitute cardinality of objects set might be deputized by properly long observation of single object, as resulting from assumption of damage flux ergodicity. Therefore, having damages number (parametrical and momentary) and large enough substitute cardinality for a single object, unreliability estimators might be calculated and thus reliability characteristics of technical object. Presented method of determining reliability characteristics is based on virtually not dangerous parametrical and momentary damages that occur before extremely dangerous catastrophic damage. Method has been verified in practices on bearing systems of two pump complexes of second grade pump station in Jurowce Water Purification Plant of Białystok Water Department.

3

The assessment of object usability on the basis of instantaneous values of technical condition and regulation state parameters

Lindstedt P., Sudakowski T.

Journal of KONES

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2012

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Vol. 19, No. 2

305-312

EN

In the process of using a complex technical object, it is deregulated, worn and its reliability is decreased. Therefore, it is required that its status, technical state and reliability should be observed during its normal use and handling. The results of such observations allow a synthetic (complex) assessment of suitability of the object, determining its ability to properly carry out its tasks in accordance with its intended purpose. A continuous observation of changes of technical condition on the basis of relationship between the diagnostic signals (output) and the input signals (environment) allow evaluation of the regulation state of the object [4, 5]. An innovative method of assessment of the operated system usability presented in the article concerns an adequate analysis of the changes to aRb technical condition and aRc, regulation state current parameters formed from coupled equations of state (1 and 2) [1, 2, 3, 7]. While analysing the waveforms of instantaneous values of aRb technical condition and aRc regulation state parameters, it has been observed that parameter and instantaneous damage can be identified on the basis of quantitative relationships between the instantaneous threshold value of dpr and the corresponding instantaneous value of dpr dop, which are calculated from the following formulas (7, 8, 9). It is assumed that damage exists if for the instant theta i . dpri greather than d prdop i . Having the quantity of damage, reliability characteristics can be determined for every time of technical object exploitation (prior to the occurrence of catastrophic damage) [6].

4

Premises of operational method of calculation of reliability of machines on the base of parametric and momentary symptoms of damage

Sudakowski T.

Acta Mechanica et Automatica

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2009

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Vol. 3, no. 4

73-79

EN

In the article presented was the practical method of calculation of standard reliability characteristics of technical objects of unchanging and changeable structure during their work, based only on parametric and momentary symptoms of damage, the method of determination of symptoms of parametric damage on the base of diagnostic and momentary information and on the base of information about the state of adjustment of the object.

5

Method of prediction of reliability characteristics of a pumping station on the base of diagnostic information

Lindstedt P., Sudakowski T.

Journal of KONBiN

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2008

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No. 2 (5)

207-237

EN

It the assessment of technical state in process of opinion of state ability technical object was required (diagnostics) and the reliability state (theory of reliability). It the investigation of relationships in article was conducted between diagnostic state and reliability of technical object. It the innovatory method of use the diagnostic information was introduced in figure "the numbers of diagnostic threshold" to mark of reliability profiles of object. It was passed method the use so the appointed reliability profiles in process of optimization of service given technical object.

PL

W procesie oceny stanu zdatności obiektu technicznego wymaga się oceny stanu technicznego (diagnostyka) i stanu niezawodnościowego (teoria niezawodności). W artykule przeprowadzono badania związków między stanem diagnostycznym, a niezawodnosciowym obiektu technicznego. Przedstawiono nowatorską metodę wykorzystania informacji diagnostycznej w postaci "liczb przekroczneń progów diagnostycznych" do wyznaczenia charakterystyk niezawodnościowych obiektu. Podano sposób wykorzystania tak wyznaczonych charakterystyk niezawodnościowych w procesie optymalizacji obsługi danego obiektu technicznego.

6

Prediction the bearing reliability on basis diagnostic information

Lindstedt P., Sudakowski T.

Journal of KONBiN

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2007

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No. 1 (3)

27-49

EN

The new complex method of diagnostics of helicopter's turbine engine Allison 250 in work was. This method be bases on complex diagnostic signals of resulting with simultaneous use three autonomic methods of diagnosing (functional diagnosing, wibroacustic diagnosing and tribologic diagnosing) and of surroundings described with number of crossings of diagnostic sill timbers of these signals. This way of description permits to establish between diagnostic signals quantitative reports and the surroundings and the state of technical object. It the diagnostics was conducted of arrangement bearings two engines Allison 250 built-up on helicopter PZL - KANIA. It was showed , that captured in this way diagnostic signals can be used to prediction of reliability profiles of arrangement bearings.

PL

W pracy przedstawiono nową kompleksową metodę diagnostyki turbinowego silnika śmigłowcowego Allison 250. Metoda ta bazuje na kompleksowych sygnałach diagnostycznych wynikających z jednoczesnego zastosowania sygnałów trzech autonomicznych metod diagnozowania (funkcjonalnej, wibroakustycznej i tribologicznej) i sygnałów otoczenia opisanych liczbą przekroczeń progów diagnostycznych tych sygnałów. Ten sposób opisu pozwala ustalić ilościowe relacje między sygnałami diagnostycznymi i otoczenia i stanu technicznego obiektu. Przeprowadzono diagnostykę układu łożyskowania dwóch silników Allison 250 zabudowanych na śmigłowcu PZL - KANIA. Wykazano, że ujęte w ten sposób sygnały diagnostyczne mogą być wykorzystane do predykcji charakterystyk niezawodnościowych układu łożyskowania.