Assessment of Fatigue Damage Features in a Piping System Using Signal Processing Approach

Transcription

1 PROCESSING (SIP8), Istanbul, Turkey, May 27-3, 28 Assessment o Fatigue Damage Features in a Piping System Using Signal Processing Approach 1 S. ABDULLAH, 2 M. LOMAN, 3 N. JAMALUDDIN, 4 A. ARIFIN, 5 Z. MOHD NOPIAH AND 6 M.Z. NUAWI Department o Mechanical & Materials Engineering Universiti Kebangsaan Malaysia 436 Bangi, Selangor MALAYSIA Abstract: - This study ocuses on the assessment o atigue damage in a piping system. Strain loading data was acquired using the atigue data acquisition devices on a lab scale piping system. Speciically, the data was measured on the rough and smooth piping suraces simultaneously where the strain gauges were mounted on both o the piping suraces. In this study, three dierent water low rates were operated in the experiments which were normal, maximum and variable. The normal water low rate was then assumed as the reerence low rate or the subsequent atigue analysis. The recorded strain signal was then analysed using the requency and time-requency method, and the short-time Fourier transorm was applied to explain the damage situation. The atigue data rom the experiment was employed to calculate the atigue damage o this piping system. Key-Words: - Fatigue damage, Strain loading, Piping system, Flow rates, Time-requency analysis. 1 Introduction To assure sae and reliable service lie but also or an optimised maintenance strategy, it is necessary to have a precise estimation o lietime consumption o critical components. A lie monitoring system is usually understood as a computerised system which takes data rom transducers itted to a piece o plant and calculates on-line the theoretical creep and atigue damage experienced by the plant due to operation and hence the remanent lie o the plant. These systems have historically been itted mainly to large boiler plant but are applicable to other high temperature plant as well [1]. It is important to evaluate structural integrity o highly pressurized piping or power plants. The wall thickness o a pressurized pipe is designed to satisy a corrosion margin [2]. A study o atigue damage is necessarily done since single pipe damage could not be detected unless the whole piping system must be replaced with the new one. The signal processing method was used in this study in order to create an estimation system o atigue ailure detection. 2 Literature Background 2.1 Fatigue damage Fatigue is a localised damage process o a component produced by cyclic loading. It is the cumulative process consisting o crack initiation, propagation and inal racture o component. During cyclic loading, localised plastic deormation may occur at the highest stress site. This plastic deormation induces permanent damage to the component and a crack develops. As the component experiences an increasing number o loading cycles, the length o the crack (damage) also increases. Ater a certain number o cycles, the crack will cause the component to ail [3]. The atigue damage starts when the component goes into service and is subjected to some orm o cyclic stress. As the material is subjected to repeated cyclic loads, additional atigue damage occurs. This atigue damage is cumulative (non-reversible) in nature and progresses until a atigue crack orms. I the crack is not detected by inspection and the aected equipment is placed back into service, the crack grows until the component ails by leak (typically seen as washouts on drill pipe tubes), brittle racture, or gross plastic deormation due to overload o the remaining cross sectional area [4]. Current industrial practice or atigue lie prediction is to use the Palmgren-Miner (PM) linear damage rule [5]. For strain-based atigue lie prediction, this rule is normally applied with strainlie atigue damage models. The irst strain-lie model is the Coin-Manson relationship, i.e. σ b ε ( ) ( ) c a = 2N + ε 2N (1) E ISBN: ISSN:

2 PROCESSING (SIP8), Istanbul, Turkey, May 27-3, 28 where E is the material modulus o elasticity, ε a is a true strain amplitude, 2N is the number o reversals to ailure, is a atigue strength σ coeicient, b is a atigue strength exponent, ε is a atigue ductility coeicient and c is a atigue ductility exponent. 2.2 Signal analysis Power spectral density (PSD) A PSD is a normalised density plot describing the mean square amplitude o each sinusoidal wave with respect to its requency [6]. The PSD presents the vibrational energy distribution o the signal across the requency domain. Each requency step value o the PSD is characterised by amplitude, A k, deined as A = 2 Δ S (2) ( ) k k iωt ( ω) = ω( t τ ) e x STFT = X τ, (3) where the Fourier transorm o the windowed signal is x(t)e -iωt, ω is the requency and τ is the time position o the window [11]. The result o this transormation is a number o spectra, each localised in a windowed segment. The time-requency resolution depends on the selection o the window length. The time window length is deined as Δt and the requency bandwidth is Δω. The area o the segment is given by the product Δω and Δt. Considering the relationship between time and requency, i.e. Δω = 1/Δt or ΔωΔt=1 (3) It can be seen that a good time localisation (when Δt is small) or requency localisation (when Δω is small) can be obtained, but not both simultaneously. Thereore the time window length Δt and the requency bandwidth Δω are interrelated. where S( k ) is the underlying PSD o the signal and k is the harmonic requency. The PSD can be as an input or generating a time-varying signal by perorming the IDFT or IFFT. However, the time series which was generated rom IFFT is not as accurate as the original signal, the PSD does not contain the original signal phase inormation. The assumptions o the signal phase content can be made in order to regenerate a statistically equivalent time history. For example, i the time history is taken rom an ergodic stationary or Gaussian and random process, the phase is purely random between -π and +π radians [7,8] Short-time Fourier transorm (STFT) STFT is a method o time-requency analysis which aims to produce requency inormation which has a localisation in time. It provides inormation about when and at what requencies a signal event occurs [9]. The STFT approach assumes that i a timevarying signal is divided into several segments, each can be assumed stationary or analysis purposes. The Fourier transorm is applied to 24 each o the segments using a window unction, which is typically nonzero in the analysed segment and is set to zero outside [1]. The most important parameter in the analysis is the window length, which is chosen so as to isolate the signal in time without any distortions. The STFT was developed rom the Fourier transorm, and it is mathematically deined as 3 Methodologies In this study, the strain signal was measured on a lab scale piping system called Hydraulic Bench. The luid tested was water. Control valves at each pipe were used to open, close and control the low rate in the piping. In this case, both o the valves were set up to the similar conditions in order to gain the signals or both o pipe suraces. The sections measured were the two horizontal pipes with dierent surace eatures which were rough and smooth suraces at three dierent low rates. The atigue data acquisition system, called SOMAT edaq, was used or data acquisition. The input signals were variable amplitude (VA) loading sampled at 5 Hz. The original strain signals or piping were as illustrated in Fig. 1. The GlyphWorks was then used to calculate the atigue damage o the pipes ISBN: ISSN:

3 PROCESSING (SIP8), Istanbul, Turkey, May 27-3, 28 Fig. 1 The original atigue signal or smooth (let side) and rough (right side) pipe at normal, maximum and variable low rate 4 Results and Discussions 4.1 Frequency analysis The Power Spectral Density method was used to convert the time domain signal into the requency domain. It indicated each o requency existed in the signal. The distribution o vibrational signal energy across the requency domain can be observed using this method. The plot o PSD or rough pipe surace can be seen in Fig The time domain signal was converted into timerequency domain using the STFT method. This method allows us to determine the requencies at a particular time. The high amplitude events in time domain signal was represented by the narrow and wide band power spectrum in the time-requency representation. It can be seen clearly in the Fig. 3 that the narrow band high amplitude signals in the original time history occurred as a number o events with narrow bandwidths in the time-requency mapping added with requency inormation. The same thing happened to the wide band signals in both igures as circled. High amplitude events Amplitude [microstrain] Time[seconds] Fig. 3 Representation o smooth pipe signal at maximum low in time history and STFT (d) Fig. 2 Signals or rough suraced pipe in time history and PSD at normal, maximum and (d) variable low rate Fig. 4 shows the example o time-requency representation o the rough surace pipe at normal, maximum and variable low rates. The characteristics o atigue damage events varied or the three types o low rate. It was because, though every low rate had a number o atigue damage events, but the time and requency localisations o the events were dierent as can be seen in the igures. Obviously, the highest energy amplitude occurred at normal low rate compared to the variable and maximum low rate as can be seen in Table Time-requency analysis ISBN: ISSN:

4 PROCESSING (SIP8), Istanbul, Turkey, May 27-3, 28 represents the highest point o atigue damage. Each colour o the plot presents dierent levels o energy which were dark blue or the lowest, ollowed by blue, green, yellow, orange and red. Fig. 4 STFT localisation or rough pipe at normal, maximum and variable low rate Table 1 Total o Energy or Rough Pipe Flow rate Total o energy Normal 1.6 x 1 7 Maximum.212 x 1 7 Variable.323 x 1 7 Fig. 5 The atigue damage histograms or smooth pipe at normal, maximum and variable low rate 4.3 Fatigue damage analysis The strain-lie module in GlyphWorks was utilised to calculate the atigue damage or smooth and rough pipe suraces. The atigue damage calculation was based on the Coin-Manson relationship in Equation (1). Thus, the atigue damage (D) can then be calculated as in Equation (5): 1 D = (5) N The atigue damage histogram or smooth pipe surace was shown in Fig. 5, while Fig. 6 showed the atigue damage histogram or rough surace pipe at three dierent low rates. The red colour plot ISBN: ISSN:

5 PROCESSING (SIP8), Istanbul, Turkey, May 27-3, 28 Fig. 6 Fatigue damage histograms or rough pipe at normal, maximum and variable low Rate The atigue damage ratios or both signals are tabulated in Table 2 and 3. The ratio was calculated with reerence to the normal water low rate. For the smooth pipe surace, the atigue damage ratio o maximum and variable low rates with respect to normal low rate was 75% and 189%. It means that the atigue damage or the maximum low rate was lower than o the normal low rate. In other way, the atigue damage or variable low rate is larger than o the normal low rate. Table 2 Fatigue damage ratio or smooth pipe Flow rate Damage Ratio Normal x1-7 - Maximum 18.79x1-7 75% Variable x % The same thing happened or rough surace pipe where the atigue damage ratio o maximum and variable low rates is 68% o the normal low rate and 114%, respectively o the normal low rate Table 3 Fatigue damage ratio or rough pipe Flow rate Damage Ratio Normal 156.x1-7 - Maximum x1-7 68% Variable x % 5 Conclusion In this study, the atigue damage value obtained or both types o pipe surace indicated that the maximum low rate contributed the lowest atigue damage in the piping system. The atigue damage ratios at variable low rates are higher or the smooth and rough pipe suraces. The signal processing approach used in this study was able to veriy the atigue events in piping system. This paper has demonstrated the combination approach o signal analysis and atigue lie assessment o piping system. By applying the shorttime Fourier transorm (STFT), the atigue damage events in piping was able to be clariied rom the eatures obtained. This combination could be a very useul tool or the reliable and quick analysis o the structural integrity o piping system. Reerences: [1]K. Majle, H. Purper, B. Wilson, K. Rohler, H. Lehmann, J. Garcia, J. Fernandez, A New monitoring System or Piping Systems in Fossil Fired Power Plants, International Journal o Pressure Vessel & Piping, Vol.66, 1996, pp [2]K. Miyazaki, A. Nebu, M. Ishiwata, K. Hasegawa, Fracture Strength and Behavior o Carbon Steel Pipes With Local Wall Thinning Subjected to Cyclic Bending Load, Nuclear Engineering and Design, Vol.214, 22, pp [3] YL. Lee, J. Pan, RB. Hathaway, ME. Barkey, Fatigue Testing and Analysis (Theory and Practice), Elsevier Butterworth-Heinemann, 25. [4] SR. Gokhale, R. Zoanni, N. Zheng, and DW. Everage, TH. Hill, Advances in Drillpipe Fatigue Management, Society o Petroleum Engineers (SPE) Annual Technical Conerence and Exhibition,Caliornia, USA, 27. [5] S. Abdullah, JC. Choi, JA. Giacomin, JR. Yates, Bump Extraction Algorithm or Variable Amplitude Fatigue Loading, International Journal o Fatigue, Vol.28, 26, pp [6] S. Abdullah, Wavelet Bump Extraction (WBE) or Editing Variable Amplitude Fatigue Loadings, PhD Thesis, University o Sheield, 25.A. [7] A. Halpenny, A requency domain approach or atigue lie estimation rom inite element analysis, paper presented at International Conerence on Damage Assessment o Structures (DAMAS 99), Dublin, Ireland, [8]Q. Li, L.Minnetyan, and CC. Chamis, Computational simulation under PSD atigue loading, Proceedings o Structures Structural Dynamics and Materials Conerence, Seattle, USA, 16-19th April, 21, pp [9]Matlab User s Guide, Matlab 5.2, The Math Works, [1]S. Patsias, Extraction o Dynamic Characteristics rom Vibrating Structures Using Image Sequences, Ph.D. Thesis, The University o Sheield, United Kingdom, 2. [11]CK. Chui, Introduction to Wavelets, Academic Press, New York, ISBN: ISSN: