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Methodology for assessing the probabilistic condition of an asset based in concepts of structural reliability “PCBM - Probabilistic Condition Based Maintenance”
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XV Portuguese Conference on Fracture, PCF 2016, 10-12 February 2016, Paço de Arcos, Portugal XV Portuguese Conference on Fracture, PCF 2016, 10-12 February 2016, Paço de Arcos, Portugal
Methodology for assessing the probabilistic condition of an asset Methodology for assessing the probabilistic condition of an asset based inonconcepts of2016, structural reliability XV Portuguese Conference Fracture, PCF 10-12 February 2016, Paço de Arcos, Portugal based in concepts of structural reliability Thermo-mechanical modeling of a highBased pressure turbine blade of an “PCBM - Probabilistic Condition Maintenance” “PCBM - Probabilistic Condition Based Maintenance” airplane gas turbine engine Fernando Teixeiraa, Jánes Landre Juniorb* a Fernando Teixeira , Jánes Landre Juniorcb* a b PUC MINAS, Pontifícia de Minas, Gerais, Av. Dom José Gaspar,Deus 500, Belo P.Católica Brandão V. Infante , A.M. * Horizonte, Brasil
a
ab
PUC MINAS, Pontifícia Católica de Minas Gerais, Av. Dom José Gaspar, 500, Belo Horizonte, Brasil DepartmentbPUC of Mechanical Engineering, Instituto Superior Técnico, Universidade de Lisboa, Av.Horizonte, Rovisco Pais, 1, 1049-001 Lisboa, MINAS, Pontifícia Católica de Minas Gerais, Av. Dom José Gaspar, 500, Belo Brasil Portugal b IDMEC, Department of Mechanical Engineering, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1, 1049-001 Lisboa, Portugal Abstract c CeFEMA, Department of Mechanical Engineering, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1, 1049-001 Lisboa, Abstract Portugal a
The purpose of this paper is to propose a methodology for assessing the probabilistic condition of an asset with the introduction Thethe purpose this paper(Probabilistic is to propose Condition a methodology assessing theasprobabilistic of an asset withCBM the introduction of conceptofof PCBM Basedfor Maintenance) an extensioncondition of the existing concept (Condition of the concept of PCBM Conditionreliability Based Maintenance) as anwill extension existingthe concept CBM (Condition Based Maintenance). The(Probabilistic concepts of structural and its methods be usedoftothe evaluate structural integrity of a Abstract Based Maintenance). The concepts of structural reliability and its methods will be used to evaluate the structural integrity mechanical system. The evaluation will be held through the probability of failure of this system and its reliability index. of Thea mechanical system. The will be held through theresults, probability of failure ofbethis systemdemanding its reliability index. The During operation, modernloads. aircraft engine components aresimulations subjected to increasingly operating conditions, system willtheir be subject to evaluation dynamic From experimental will performed and the correlations between system will be toand dynamic loads. From experimental results, simulations will betopossibility performed andusing the types correlations between especially thesubject high pressure (HPT) blades. conditions causetothese parts undergo different of time-dependent the probabilistic model theturbine deterministic will beSuch conducted in order verify the of this methodology to the probabilistic model and the deterministic bethe conducted in order to verify thewas possibility of using thistomethodology to degradation, one of which is creep. A modelwill using finite element method (FEM) developed, in order be able to predict support the decision-making process. the creep behaviour of HPT blades. Flight data records (FDR) for a specific aircraft, provided by a commercial aviation support the decision-making process. company, were used to obtain © 2016 The Authors. Published bythermal Elsevierand B.V.mechanical data for three different flight cycles. In order to create the 3D model © 2016, PROSTR (Procedia Structural Integrity) Hosting by Elsevier All rights needed the FEM analysis, aElsevier HPT blade was Ltd. scanned, andreserved. its chemical composition and material properties were © 2016 Theforunder Authors. Published by B.V. scrap Peer-review responsibility of the Scientific Committee of PCF 2016. Peer-review under responsibility of the Scientific Committee of PCF 2016. obtained. under The data that was gathered was fed into the FEM and different simulations were run, first with a simplified 3D Peer-review responsibility of the Scientific Committee ofmodel PCF 2016. rectangular block shape, in order to better establish the model, and then with the real 3D mesh obtained from the blade scrap. The Keywords: Structural reliability, Fatigue, maintenance overall expected behaviourFatigue, in terms of displacement was observed, in particular at the trailing edge of the blade. Therefore such a Keywords: Structural reliability, maintenance model can be useful in the goal of predicting turbine blade life, given a set of FDR data.
1. © Introduction 2016 The Authors. Published by Elsevier B.V. 1. Introduction Peer-review under responsibility of the Scientific Committee of PCF 2016. The structural reliability is a relatively new issue in terms of science, it has been developing rapidly in recent TheThe structural reliability isformulation a relatively issue Method; in terms of science, it has been developing rapidlyStreletskii in recent years. first innew structural safety problems can be attributed to Mayer (1926), Keywords: High mathematical Pressure Turbine Blade; Creep; Finite Element 3D Model; Simulation. years. The first mathematical formulation in structural safety problems can be attributed to Mayer (1926), Streletskii (1947) and Wierzbicki (1936). They found that the strength and load parameters are random variables, therefore, for (1947) and Wierzbicki (1936). They found that the strength and load parameters are random variables, therefore, for each frame, there is a failure probability associated. each frame, there is a failure probability associated. * Corresponding author. Tel.: +55-31-3319-4910; fax: +55-31-3319-4910. address:author. [email protected] *E-mail Corresponding Tel.: +55-31-3319-4910; fax: +55-31-3319-4910. E-mail address: [email protected] 2452-3216 © 2016 The Authors. Published by Elsevier B.V. 2452-3216 © 2016 Authors. Published Elsevier B.V. Peer-review underThe responsibility of theby Scientific Committee of PCF 2016. Peer-review underauthor. responsibility the Scientific Committee of PCF 2016. * Corresponding Tel.: +351of218419991. E-mail address: [email protected] 2452-3216 © 2016 The Authors. Published by Elsevier B.V.
Peer-review under responsibility of the Scientific Committee of PCF 2016. 2452-3216 © 2016, PROSTR (Procedia Structural Integrity) Hosting by Elsevier Ltd. All rights reserved. Peer review under responsibility of the Scientific Committee of PCF 2016. 10.1016/j.prostr.2016.02.025
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Author name / Structural Integrity Procedia 00 (2016) 000–000 Fernando Teixeira et al. / Procedia Structural Integrity 1 (2016) 181–188
These concepts were developed by Freudenthal in the 50s The formulations and functions involved were difficult to solve, so reliability analysis of the practical applications were only possible with the pioneering work of Cornell and Lind in the late '60s and early '70s. From the 70s different projects were developed by various researchers with respect to structural reliability applied in the design phase as well as evaluation of existing structures and the development of methods for optimizing these analyzes. In terms related to evaluating the structural reliability of existing structures, Diamantidis (1987) examines, in a general way on the implementation of probabilistic methods in the assessment of the structural reliability of existing structures with the application of the FORM method ("First Order Reliability Method" ) in offshore structures. Vanhazebrouck (2008) proposed a method based on the concepts of structural reliability and application of the FORM method ("First Order Reliability Method"), to evaluate the residual strength of pipeline defects caused by corrosion. Amaral (2011) also carried a review of corroded metal ducts, observing the evolution over time of the security index for various operating conditions. Câmara (2011) used the concepts of structural reliability to support the process of defining inspections on ships structures subject to fatigue and corrosion. Carvajalino (2013) evaluated the probability of failure of natural gas pipelines and oil for different events that occur in the life of a structure. Soares (2013) determined the reliability of a rectangular steel plate subjected to compressive stress with nonuniform corrosive wear on its surface and its evolution over the time. In terms of structural reliability as a support tool to the decision-making process, Gomes (2013) proposes an optimization of risks in random processes of corrosion and fatigue through strategies for inspection and maintenance. In several works, there are initiatives for the assessment of existing structures by means of structural reliability concepts. These concepts are used to support the decision making process regarding inspections and maintenance policies. However, an objective and systematic approach to the use of the parameters generated by the analysis of structural reliability for application in operations for the maintenance engineering still requires further development. Thus, the intention of this work is to contribute to the decision making process, for possible interventions in an asset or structure, through a methodology for assessing the safety level and probability of failure through structural reliability. A concept to this methodology will be developed. This concept will be given the name of PCBM (Probabilistic Condition Based Maintenance) as an extension of the existing concept of CBM (Condition Based Maintenance) where the own safety index and the probability of failure becomes the monitoring variable. By monitoring the evolution of safety parameters and probability of failure over time, the ideal time for a intervention can be established, as well as changes in the operational aspects to the asset back to an acceptable level of safety. Nomenclature
Pf
G(U )
N
R
max min f (U )
CPM COV
Probability of failure Failure function Reliability index Number of cycles Ultimate stress Maximum stress Minimum stress Probability density function Cycles per minute Coefficient of variation
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2. Structural reliability According to Melchers (1999), the study of structural reliability is related to the calculation and prediction of the probability of limit state violation for a structural engineering system at any time during their life. In other words it can be said that the structural reliability principles is to determine the probability of failure of a structure and thus the characterization of its safety index. The probability of failure and its safety index can be evaluated either in the design phase and operational phase. According to Nowak and Collins (2012), the concepts of structural reliability can be applied both in designs of new structures for the evaluation of existing structures. For use of the concepts of structural reliability and its methods, some definitions are essential. 2.1. Failure According to NBR 5462, failure is the end of the ability of an item to perform its required function. The failure of a system or asset is the loss of ability this item to perform the function for which it was designed. This definition may well be used for a structure or an asset in specific, regarding compliance or non-compliance with its function. 2.2. Limit state Ditlevsen and Madsen (1996), the limit state concept is related to a specific requirement of the structure, in which the structure is in a point of not meeting this requirement. This definition is not as clear as that of Nowak and Collins (2012), "the state boundary is the borderline between the desired performance and the undesired of a structure." In the other words the boundary between the fault state and the no failure state. 2.3. Limit state function The structural reliability analysis is based on the existence of a limit state function or failure function G(U) Sagrilo (1994). U = (U1,U2,…,Un), The set of random variables involved in the analysis. The limit state function G(U) is defined as the limit G(U)=0 between failure domain and no failure, G(U) < 0 e G(U) > 0 respectively. See figure 1.
Figure 1 – Limit state example
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2.4. Failure probability and safety index An important parameter for evaluating a structure is its probability of failure. The probability of failure is related to the values of the failure function are located in fault region.
Pf PG(U ) 0
(1)
Since f(U) the probability density function of all variables involved in the phenomenon, the probability of failure can be written as:
Pf fu (U )du
(2)
F
Figure 2 illustrates the two-dimensional case.
Figure 2 – Two – dimensional case – Melchers (1999)
Set the probability of failure, the safety index or reliability index can be defined as:
1 ( Pf )
(3)
3. Maintenance engineering In general the maintenance function can be defined as a set of technical and managerial actions taken throughout the life of the asset to maintain or restore its required function Shin and Jun (2015). According to the expectations of the maintenance function, various techniques have been developed to improve the maintenance of assertiveness. In this context, Moubray (2000), divided the evolution of maintenance generations in a timeline, described in figure 3. This development is directly related to the expectations of each season.
Fernando Teixeira et al. / Procedia Structural Integrity 1 (2016) 181–188 Author name / Structural Integrity Procedia 00 (2016) 000–000
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Figure 3 – Changing maintenance techniques – Moubray (2000)
Regarding the types of maintenance will be given focus on condition based maintenance. 3.1. Condition Based Maintenance (CBM) The condition-based maintenance, or predictive maintenance, is nothing more than the name suggests, a preventive maintenance on an asset based on the operating condition of this asset. An important feature of this type of maintenance is the monitoring of equipment by measurements carried out when it is fully operational, enabling higher availability. Predictive maintenance stands out for its characteristic anticipation of the diagnosis of possible faults in assets. It is held close to the fault or the most appropriate time considering other operational requirements (BRANCO FILHO, 2006). These activities based on the results of quantitative periodic inspections, which are performed by measuring parameters to monitor the degradation and to detect fault signals. It is usually known as predictive maintenance. (XENOS, 2004). Predictive maintenance can still be defined as the follow-up activity of certain parameters of the equipment to indicate their performance in a systematic way, in order to identify the exact moment of the intervention (Kardec and Carvalho, 2002). 4. Methodology The methodology for implementation of the concept and development follows the following steps: 4.1. Experimental model definition It was built an experimental model consisting of an electric motor 0.25cv, which drives three shafts with diameters of 12.7 mm, 19.0mm and 25.4mm. In each of these axes, one steel disc lies coupled. This disc aims to promote a dynamic effort to the shaft. It was installed on each axis a steel sheet to promote wear. The collection and
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measurement system was installed in the wear plates for measuring stresses and strains. See figure 4. The results presented in this article are related to the axis of 12.7mm.
Figure 4 – Experimental model
4.2. Failure mode and limit function The failure mode chosen for the study was the fatigue failure mode. Based on the fracture mechanic equations, it was obtained the following limit function:
( max min ). R G (U ) 5,14. R .N 0, 2476 2. R max min
(4)
4.3. Deformation data collection and stress definition Deformation data were collected by extensometry. They were performed in two situations, with speed of 970 CPM and 1512 CPM. The data collected were modeled by FEM to determine the stress on the shaft. Figure 5 shows the model built in FEM
Figure 5 – Model in FEM
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4.4. Probability distributions for the maximum and minimum stresses With the maximum and minimum stresses acting on the shaft, it was determined the probability distribution model that best fit the data to the rotations of 970 CPM and 1512 CPM respectively. Tables 1 and 2 show a summary of these distributions for the rotations of 970 CPM and 1512 CPM.
Table 1. Summary 970 CPM. Variable
Mean
Maximum stress (MPa)
37.2940
Minimum stress (MPa) Ultimate stress (MPa)
Standard deviation
COV
Distribution
4.1570
0.1115
lognormal
36.6870
4.5130
0.1230
lognormal
380.00
22.8670
0.0602
lognormal
Table 2. Summary 1512 CPM. Variable
Mean
Standard deviation
COV
Distribution
Maximum stress (MPa)
46.5967
3.3152
0.0712
lognormal
Minimum stress (MPa)
43.8729
3.8730
0.0883
lognormal
Ultimate stress (MPa)
380.00
22.8670
0.0602
lognormal
4.5. Structural reliability method, probability of failure and reliability index The method FORM (First Order Reliability Method) was chosen. Table 3 shows the summary of the probability of failure and reliability index values for 970 CPM and 1512 CPM. Table 3. Summary of reliability analysis Rotation (CPM)
Structural reliability method
Probability of failure (%)
Reliability index
970
FORM
5.4076e-062
16.5736
1512
FORM
8.2679e-020
9.0341
5. Conclusions Despite the probabilities of failure are very small, this experiment shows that the results of probability of failure were higher for the 1512 CPM compared with the 970CPM, as well as the stresses on the shaft. Common sense, for a simplified situation like this would indicate a 'risk' greater for a system with higher stresses. The probability of failure and the reliability index shown in Table 3 confirm this situation. The results still are in a preliminary and need more tests, but opens a perspective for the use of the failure probability or safety index as a monitoring variable. Thus it will expand the concept of condition-based maintenance to probabilistic condition based maintenance. Experiments in real systems and the development of limits for possible failure modes are required for full implementation and development of this concept.
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References ABNT (1994), Associação Brasileira de Normas Técnicas, NBR 5462: Confiabilidade e Mantenabilidade, Rio de Janeiro. Amaral,R.S., Análise de Segurança de Dutos Com Defeitos de Corrosão. UFOP, Ouro Preto, Brasil 2011. Branco, F.G., Dicionário de Termos de Manutenção, Confiabilidade e Qualidade. Rio de Janeiro: Editora Ciência Moderna Ltda., 2000. Branco, F.G., Indicadores e Índices de Manutenção. Rio de Janeiro: Editora Ciência Moderna Ltda., 2006 Camara C.M., Aplicações de Confiabilidade Estrutural em Projetos e em Planejamento de Manutenção de Návios Submetidos à Fadiga e Corrosão. COPPE/UFRJ, Rio de Janeiro, Brasil, 2011. Carvajalino, J.J.L., Acoplamento de Estados Limites na Avaliação da Confiabilidade Estrutural de Dutos e Estruturas. PUC-RJ, Rio de Janeiro, Brasil, 2010. Cornell,C.A., A Probabilistic-Based Structural Code, ACI Journal, Ttle No 66-85, December 1969, pp. 974-985. Diamantidis, D. Reliability assessment of existing structures, A.S. Veritas Research. Howik, Norway, 1987. Ditlevsen, O., Madsen, H.O., Structural Reliability Methods, Baffins Lane, Chichester: John Wiley & Sons Inc., 1996. Freudenthal, A.,M., Safety and the Probability of Structural Failure, ASCE Transactions, Vol. 121, 1956, pp 1337-1397. Gomes, W.J.S., Otimização de riscos sob processos aletatórios de corrosão e fadiga. USP/Escola de Enhenharia de São Carlos, 2013. Lind, N.C. and A.G. Davenport, Towards Practical Application of Structural Reliability Theory, ACI SP-31, 1972, pp. 63-110. Mayer, M., T., Die Sicherhit der Bauuverke und ihreBerechnungnachGrenzkraften, Springer-Verlag, Berlin, 1926. Melchers, R.E., Structural Reliability Analysis And Prediction, John Wiley & Sons, Chichester, 1999 Moubray, J. (2000), Reliability-centred Maintenance (RCMII) Aladon, Grã Bretanha. Nowak, A.S., Reliability of Structures, CRC Press 2012 Pinto, A. K. e Xavi, J. Nr. (1999), Manutenção: função estratégica, Qualitymark, Rio de Janeiro. Pinto, A. K. e Xavier, J. N. (2007), Manutenção: função estratégica, Qualitymark, Rio de Janeiro Sangrilo,L.V.S., Análise de Confiabilidade Estrutural Utilizando os Métodos Analíticos FORM e SORM. COPPE/UFRJ, Rio de Janeiro, Brasil,1994. Shin, Jong-Ho e Jung, Hang-Bae, 2015, “On condition based maintenance policy”, Journal of computacional design and engineering, 2 (2015), pág 119-127. Soares, G.C.,Garbatov, C., Silva J.E., Reliability Assessment of a Steel Plate Subjectes to Distributed and Localized Corrosion Wastage. CENTEC, Lisbon, Portugal, 2013. Streletskii,N.,S., Foundations of Statistical Account of Factor of Safety of Structural Strengh, State Publishing House for Buildings, Moscow, 1947. Vanhazebrouck, M.V., Análise de Dutos Corroídos por Meio de Confiabilidade Estrutural. PUC-PR, Curitiba, Brasil, 2008. Viana, H. R. G. (2002), PCM, Planejamento e controle da manutenção, Qualitymark, Rio de Janeiro. Wierzbicki, W., Safety of structures as a Probabilistic Problem, Przeglad, Technivzny, Polish, 1936. Xenos, H. G. Gerenciando a Manutenção Produtiva. Nova Lima: INDG Tecnologia e Serviços Ltda, 2004
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XV Portuguese Conference on Fracture, PCF 2016, 10-12 February 2016, Paço de Arcos, Portugal XV Portuguese Conference on Fracture, PCF 2016, 10-12 February 2016, Paço de Arcos, Portugal
Methodology for assessing the probabilistic condition of an asset Methodology for assessing the probabilistic condition of an asset based inonconcepts of2016, structural reliability XV Portuguese Conference Fracture, PCF 10-12 February 2016, Paço de Arcos, Portugal based in concepts of structural reliability Thermo-mechanical modeling of a highBased pressure turbine blade of an “PCBM - Probabilistic Condition Maintenance” “PCBM - Probabilistic Condition Based Maintenance” airplane gas turbine engine Fernando Teixeiraa, Jánes Landre Juniorb* a Fernando Teixeira , Jánes Landre Juniorcb* a b PUC MINAS, Pontifícia de Minas, Gerais, Av. Dom José Gaspar,Deus 500, Belo P.Católica Brandão V. Infante , A.M. * Horizonte, Brasil
a
ab
PUC MINAS, Pontifícia Católica de Minas Gerais, Av. Dom José Gaspar, 500, Belo Horizonte, Brasil DepartmentbPUC of Mechanical Engineering, Instituto Superior Técnico, Universidade de Lisboa, Av.Horizonte, Rovisco Pais, 1, 1049-001 Lisboa, MINAS, Pontifícia Católica de Minas Gerais, Av. Dom José Gaspar, 500, Belo Brasil Portugal b IDMEC, Department of Mechanical Engineering, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1, 1049-001 Lisboa, Portugal Abstract c CeFEMA, Department of Mechanical Engineering, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1, 1049-001 Lisboa, Abstract Portugal a
The purpose of this paper is to propose a methodology for assessing the probabilistic condition of an asset with the introduction Thethe purpose this paper(Probabilistic is to propose Condition a methodology assessing theasprobabilistic of an asset withCBM the introduction of conceptofof PCBM Basedfor Maintenance) an extensioncondition of the existing concept (Condition of the concept of PCBM Conditionreliability Based Maintenance) as anwill extension existingthe concept CBM (Condition Based Maintenance). The(Probabilistic concepts of structural and its methods be usedoftothe evaluate structural integrity of a Abstract Based Maintenance). The concepts of structural reliability and its methods will be used to evaluate the structural integrity mechanical system. The evaluation will be held through the probability of failure of this system and its reliability index. of Thea mechanical system. The will be held through theresults, probability of failure ofbethis systemdemanding its reliability index. The During operation, modernloads. aircraft engine components aresimulations subjected to increasingly operating conditions, system willtheir be subject to evaluation dynamic From experimental will performed and the correlations between system will be toand dynamic loads. From experimental results, simulations will betopossibility performed andusing the types correlations between especially thesubject high pressure (HPT) blades. conditions causetothese parts undergo different of time-dependent the probabilistic model theturbine deterministic will beSuch conducted in order verify the of this methodology to the probabilistic model and the deterministic bethe conducted in order to verify thewas possibility of using thistomethodology to degradation, one of which is creep. A modelwill using finite element method (FEM) developed, in order be able to predict support the decision-making process. the creep behaviour of HPT blades. Flight data records (FDR) for a specific aircraft, provided by a commercial aviation support the decision-making process. company, were used to obtain © 2016 The Authors. Published bythermal Elsevierand B.V.mechanical data for three different flight cycles. In order to create the 3D model © 2016, PROSTR (Procedia Structural Integrity) Hosting by Elsevier All rights needed the FEM analysis, aElsevier HPT blade was Ltd. scanned, andreserved. its chemical composition and material properties were © 2016 Theforunder Authors. Published by B.V. scrap Peer-review responsibility of the Scientific Committee of PCF 2016. Peer-review under responsibility of the Scientific Committee of PCF 2016. obtained. under The data that was gathered was fed into the FEM and different simulations were run, first with a simplified 3D Peer-review responsibility of the Scientific Committee ofmodel PCF 2016. rectangular block shape, in order to better establish the model, and then with the real 3D mesh obtained from the blade scrap. The Keywords: Structural reliability, Fatigue, maintenance overall expected behaviourFatigue, in terms of displacement was observed, in particular at the trailing edge of the blade. Therefore such a Keywords: Structural reliability, maintenance model can be useful in the goal of predicting turbine blade life, given a set of FDR data.
1. © Introduction 2016 The Authors. Published by Elsevier B.V. 1. Introduction Peer-review under responsibility of the Scientific Committee of PCF 2016. The structural reliability is a relatively new issue in terms of science, it has been developing rapidly in recent TheThe structural reliability isformulation a relatively issue Method; in terms of science, it has been developing rapidlyStreletskii in recent years. first innew structural safety problems can be attributed to Mayer (1926), Keywords: High mathematical Pressure Turbine Blade; Creep; Finite Element 3D Model; Simulation. years. The first mathematical formulation in structural safety problems can be attributed to Mayer (1926), Streletskii (1947) and Wierzbicki (1936). They found that the strength and load parameters are random variables, therefore, for (1947) and Wierzbicki (1936). They found that the strength and load parameters are random variables, therefore, for each frame, there is a failure probability associated. each frame, there is a failure probability associated. * Corresponding author. Tel.: +55-31-3319-4910; fax: +55-31-3319-4910. address:author. [email protected] *E-mail Corresponding Tel.: +55-31-3319-4910; fax: +55-31-3319-4910. E-mail address: [email protected] 2452-3216 © 2016 The Authors. Published by Elsevier B.V. 2452-3216 © 2016 Authors. Published Elsevier B.V. Peer-review underThe responsibility of theby Scientific Committee of PCF 2016. Peer-review underauthor. responsibility the Scientific Committee of PCF 2016. * Corresponding Tel.: +351of218419991. E-mail address: [email protected] 2452-3216 © 2016 The Authors. Published by Elsevier B.V.
Peer-review under responsibility of the Scientific Committee of PCF 2016. 2452-3216 © 2016, PROSTR (Procedia Structural Integrity) Hosting by Elsevier Ltd. All rights reserved. Peer review under responsibility of the Scientific Committee of PCF 2016. 10.1016/j.prostr.2016.02.025
2 182
Author name / Structural Integrity Procedia 00 (2016) 000–000 Fernando Teixeira et al. / Procedia Structural Integrity 1 (2016) 181–188
These concepts were developed by Freudenthal in the 50s The formulations and functions involved were difficult to solve, so reliability analysis of the practical applications were only possible with the pioneering work of Cornell and Lind in the late '60s and early '70s. From the 70s different projects were developed by various researchers with respect to structural reliability applied in the design phase as well as evaluation of existing structures and the development of methods for optimizing these analyzes. In terms related to evaluating the structural reliability of existing structures, Diamantidis (1987) examines, in a general way on the implementation of probabilistic methods in the assessment of the structural reliability of existing structures with the application of the FORM method ("First Order Reliability Method" ) in offshore structures. Vanhazebrouck (2008) proposed a method based on the concepts of structural reliability and application of the FORM method ("First Order Reliability Method"), to evaluate the residual strength of pipeline defects caused by corrosion. Amaral (2011) also carried a review of corroded metal ducts, observing the evolution over time of the security index for various operating conditions. Câmara (2011) used the concepts of structural reliability to support the process of defining inspections on ships structures subject to fatigue and corrosion. Carvajalino (2013) evaluated the probability of failure of natural gas pipelines and oil for different events that occur in the life of a structure. Soares (2013) determined the reliability of a rectangular steel plate subjected to compressive stress with nonuniform corrosive wear on its surface and its evolution over the time. In terms of structural reliability as a support tool to the decision-making process, Gomes (2013) proposes an optimization of risks in random processes of corrosion and fatigue through strategies for inspection and maintenance. In several works, there are initiatives for the assessment of existing structures by means of structural reliability concepts. These concepts are used to support the decision making process regarding inspections and maintenance policies. However, an objective and systematic approach to the use of the parameters generated by the analysis of structural reliability for application in operations for the maintenance engineering still requires further development. Thus, the intention of this work is to contribute to the decision making process, for possible interventions in an asset or structure, through a methodology for assessing the safety level and probability of failure through structural reliability. A concept to this methodology will be developed. This concept will be given the name of PCBM (Probabilistic Condition Based Maintenance) as an extension of the existing concept of CBM (Condition Based Maintenance) where the own safety index and the probability of failure becomes the monitoring variable. By monitoring the evolution of safety parameters and probability of failure over time, the ideal time for a intervention can be established, as well as changes in the operational aspects to the asset back to an acceptable level of safety. Nomenclature
Pf
G(U )
N
R
max min f (U )
CPM COV
Probability of failure Failure function Reliability index Number of cycles Ultimate stress Maximum stress Minimum stress Probability density function Cycles per minute Coefficient of variation
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2. Structural reliability According to Melchers (1999), the study of structural reliability is related to the calculation and prediction of the probability of limit state violation for a structural engineering system at any time during their life. In other words it can be said that the structural reliability principles is to determine the probability of failure of a structure and thus the characterization of its safety index. The probability of failure and its safety index can be evaluated either in the design phase and operational phase. According to Nowak and Collins (2012), the concepts of structural reliability can be applied both in designs of new structures for the evaluation of existing structures. For use of the concepts of structural reliability and its methods, some definitions are essential. 2.1. Failure According to NBR 5462, failure is the end of the ability of an item to perform its required function. The failure of a system or asset is the loss of ability this item to perform the function for which it was designed. This definition may well be used for a structure or an asset in specific, regarding compliance or non-compliance with its function. 2.2. Limit state Ditlevsen and Madsen (1996), the limit state concept is related to a specific requirement of the structure, in which the structure is in a point of not meeting this requirement. This definition is not as clear as that of Nowak and Collins (2012), "the state boundary is the borderline between the desired performance and the undesired of a structure." In the other words the boundary between the fault state and the no failure state. 2.3. Limit state function The structural reliability analysis is based on the existence of a limit state function or failure function G(U) Sagrilo (1994). U = (U1,U2,…,Un), The set of random variables involved in the analysis. The limit state function G(U) is defined as the limit G(U)=0 between failure domain and no failure, G(U) < 0 e G(U) > 0 respectively. See figure 1.
Figure 1 – Limit state example
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2.4. Failure probability and safety index An important parameter for evaluating a structure is its probability of failure. The probability of failure is related to the values of the failure function are located in fault region.
Pf PG(U ) 0
(1)
Since f(U) the probability density function of all variables involved in the phenomenon, the probability of failure can be written as:
Pf fu (U )du
(2)
F
Figure 2 illustrates the two-dimensional case.
Figure 2 – Two – dimensional case – Melchers (1999)
Set the probability of failure, the safety index or reliability index can be defined as:
1 ( Pf )
(3)
3. Maintenance engineering In general the maintenance function can be defined as a set of technical and managerial actions taken throughout the life of the asset to maintain or restore its required function Shin and Jun (2015). According to the expectations of the maintenance function, various techniques have been developed to improve the maintenance of assertiveness. In this context, Moubray (2000), divided the evolution of maintenance generations in a timeline, described in figure 3. This development is directly related to the expectations of each season.
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Figure 3 – Changing maintenance techniques – Moubray (2000)
Regarding the types of maintenance will be given focus on condition based maintenance. 3.1. Condition Based Maintenance (CBM) The condition-based maintenance, or predictive maintenance, is nothing more than the name suggests, a preventive maintenance on an asset based on the operating condition of this asset. An important feature of this type of maintenance is the monitoring of equipment by measurements carried out when it is fully operational, enabling higher availability. Predictive maintenance stands out for its characteristic anticipation of the diagnosis of possible faults in assets. It is held close to the fault or the most appropriate time considering other operational requirements (BRANCO FILHO, 2006). These activities based on the results of quantitative periodic inspections, which are performed by measuring parameters to monitor the degradation and to detect fault signals. It is usually known as predictive maintenance. (XENOS, 2004). Predictive maintenance can still be defined as the follow-up activity of certain parameters of the equipment to indicate their performance in a systematic way, in order to identify the exact moment of the intervention (Kardec and Carvalho, 2002). 4. Methodology The methodology for implementation of the concept and development follows the following steps: 4.1. Experimental model definition It was built an experimental model consisting of an electric motor 0.25cv, which drives three shafts with diameters of 12.7 mm, 19.0mm and 25.4mm. In each of these axes, one steel disc lies coupled. This disc aims to promote a dynamic effort to the shaft. It was installed on each axis a steel sheet to promote wear. The collection and
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measurement system was installed in the wear plates for measuring stresses and strains. See figure 4. The results presented in this article are related to the axis of 12.7mm.
Figure 4 – Experimental model
4.2. Failure mode and limit function The failure mode chosen for the study was the fatigue failure mode. Based on the fracture mechanic equations, it was obtained the following limit function:
( max min ). R G (U ) 5,14. R .N 0, 2476 2. R max min
(4)
4.3. Deformation data collection and stress definition Deformation data were collected by extensometry. They were performed in two situations, with speed of 970 CPM and 1512 CPM. The data collected were modeled by FEM to determine the stress on the shaft. Figure 5 shows the model built in FEM
Figure 5 – Model in FEM
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4.4. Probability distributions for the maximum and minimum stresses With the maximum and minimum stresses acting on the shaft, it was determined the probability distribution model that best fit the data to the rotations of 970 CPM and 1512 CPM respectively. Tables 1 and 2 show a summary of these distributions for the rotations of 970 CPM and 1512 CPM.
Table 1. Summary 970 CPM. Variable
Mean
Maximum stress (MPa)
37.2940
Minimum stress (MPa) Ultimate stress (MPa)
Standard deviation
COV
Distribution
4.1570
0.1115
lognormal
36.6870
4.5130
0.1230
lognormal
380.00
22.8670
0.0602
lognormal
Table 2. Summary 1512 CPM. Variable
Mean
Standard deviation
COV
Distribution
Maximum stress (MPa)
46.5967
3.3152
0.0712
lognormal
Minimum stress (MPa)
43.8729
3.8730
0.0883
lognormal
Ultimate stress (MPa)
380.00
22.8670
0.0602
lognormal
4.5. Structural reliability method, probability of failure and reliability index The method FORM (First Order Reliability Method) was chosen. Table 3 shows the summary of the probability of failure and reliability index values for 970 CPM and 1512 CPM. Table 3. Summary of reliability analysis Rotation (CPM)
Structural reliability method
Probability of failure (%)
Reliability index
970
FORM
5.4076e-062
16.5736
1512
FORM
8.2679e-020
9.0341
5. Conclusions Despite the probabilities of failure are very small, this experiment shows that the results of probability of failure were higher for the 1512 CPM compared with the 970CPM, as well as the stresses on the shaft. Common sense, for a simplified situation like this would indicate a 'risk' greater for a system with higher stresses. The probability of failure and the reliability index shown in Table 3 confirm this situation. The results still are in a preliminary and need more tests, but opens a perspective for the use of the failure probability or safety index as a monitoring variable. Thus it will expand the concept of condition-based maintenance to probabilistic condition based maintenance. Experiments in real systems and the development of limits for possible failure modes are required for full implementation and development of this concept.
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