Fatigue Lie Assessment Using Signal Processing Techniques S. ABDULLAH 1, M. Z. NUAWI, C. K. E. NIZWAN, A. ZAHARIM, Z. M. NOPIAH Engineering Faculty, Universiti Kebangsaan Malaysia 43600 UKM Bangi, Selangor, MALAYSIA Abstract: - This paper presents the atigue lie assessment using signal processing approaches which study on the characteristics o the atigue signal in requency and time-requency domain. The signals used in this research were variable amplitude atigue signal which consisted o a synthetic data and experimentally measured data. As requency domain method is one o the techniques to analyse random signal, it can be applied to observe strain characteristic o the signal in requency domain. Thus, Power Spectral Density (PSD) algorithm was used to gain the power distribution o the input signals. The short-time Fourier transorm (STFT) method was then used to transorm the input signal into the time-requency domain. The transormation o time domain signal into time-requency domain provides the power distribution display with respect to the particular time and requency inormation. From the power distribution gained, the atigue damage eatures can be identiied. Finally, the lie estimation o the components was calculated in order to study its durability. Key-Words: - Automotive, Fatigue, Fatigue road loadings, Signal processing, Simulation, Variable amplitude. 1 Introduction For many automotive components, the primary mode o ailure can be attributed to atigue damage resulting rom the application o variable amplitude loading. Predicting the lie o part stressed above the endurance limit is at best a rough procedure especially or components like automobile engine, steering and suspension parts [1]. For these cases, the strain-based approach is commonly used to predict atigue lie [2]. The strain-lie atigue model relates the plastic deormation that occurs at a localized region where atigue cracks begin to the durability o the structure. This model is oten used or ductile materials at relatively short atigue lives. This approach can also be used where there is little plasticity at long atigue lives. Thereore, this is a comprehensive approach that can be used in place o the stress-based approach. In signal processing approach, the atigue signal can be analysed in requency domain and time requency domain. Frequency analysis data is typically presented in graphical orm as Power Spectral Density (PSD). Essentially a PSD display the amplitude o each sinusoidal wave o a particular requency. Frequency is given on the x-axis. The mean squared amplitude o a sinusoidal wave at any requency can be determined by inding the area under the PSD over that requency range [3]. The short-time Fourier transorms (STFT) or windowed Fourier transorm is one o the methods or transorming the time domain signal into the timerequency domain. In addition, the STFT adapted the Fourier transorm to analyse only a small section o the signal at one speciic time [4]. Finally, the STFT provides inormation on when and at what requencies a signal occurs. In this paper, two atigue signals were analysed using signal processing approach in order to observe the signal characteristics in requency and timerequency domain. The atigue lie or each signal was then predicted using strain lie based to study the durability o the structures under variable amplitude loading. 2 Methodology The methodology o this activity involves the atigue data measurement and also atigue data analysis. The purpose o this type o analysis is to veriy the durability o a component ater being aected by a spectrum atigue loading, which lead to the improvement o the structural integrity o any related system. Two data sets have been used or this study, named as T1 (a synthetic data) and T2 (experimentally measured data). The logic o creating T1, as shown in Fig. 1a, was to observe the data processing ability to deal with any signal containing large transients in a small amplitude background, so that the high amplitude events which lead to the atigue damage can be properly identiied [5,6]. This data was deined with 16,000 data points and sampled at 400 Hz. It consists o a combination o sinusoidal and random signals o ISSN: 1790-5117 221
various amplitudes and requencies, and it was intentionally deined to be a mixture o both high amplitude events and low amplitude harmonic background. The second, named as T2 (see Fig. 1b), is a atigue strain signal that was measured on a component o a speciic structural system. It was sampled at 200 Hz or a total o 30,000 data points that produced a total record length o 150 seconds. This signal exhibits a slight change in mean o the whole signal with a little low requency content. This data set was chosen because it contained many transient events in the signal background. The data was measured using atigue data acquisition system, called SOMAT edaq, and urther analysis or both T1 and T2 was perormed using the sotware developed by ncode International, i.e. GlyphWorks. Fig. 2 shows the schematic arrangement or data collection and analysis. Data collection (a) (b) Fig. 1: Data collected or the analysis GlyphWorks Data analysis Fig. 2: The concept o data collection and analysis 3 Results and Discussions: Signal Analysis The analysis o the collected data or both T1 and T2 was statistically carried out in order to determine the meaningul statistical properties or the atigue damage analysis. This global signal statistical analysis is also being perormed or determining determination o the signal behaviour. The signal root-mean-square (r.m.s.) value, which is the 2nd statistical moment, is used to quantiy the overall energy content o the oscillatory signal. The kurtosis, which is the signal 4th statistical moment value, is also being used to quantiy the nongaussianity o the data since it is highly sensitive to outlying data among the instantaneous values. For both data sets, these statistical parameters are tabulated in Table 1. Table 1: The statistical values or T1 and T2 Signal Mean Root- Kurtosis length [seconds] [με] mean- square [με] T1 80-0.0192 1.4835 7.5696 T2 150 2.6044 11.4873 3.6738 The power spectral density (PSD) analysis is later being perormed or observing the distribution o vibrational signal energy across the requency domain. A PSD is used to convert a signal rom the time domain to the requency domain using the ast Fourier transorm (FFT) method. In the relation o the PSD with the FFT, the PSD is a normalised density plot describing the mean square amplitude o each sinusoidal wave with respect to its requency. The plot o PSD or both T1 and T2 can be seen in Fig. 3, showing that both signals contain the atigue damage eatures in the low requency distribution. It shows the same argument with the theoretical indings, i.e. the low amplitude events o the atigue cycles can be ound in the higher requency distribution o a requency spectrum. With the application o low pass ilter, these high requency cycles with low strain amplitude can be removed. Short-time Fourier transorm (STFT) is a method o time-requency analysis which aims to produce requency inormation which has a localisation in time [7]. It provides inormation about when and at what requencies a signal event occurs. The STFT approach assumes that i a time-varying signal is divided into several segments, each can be assumed stationary or analysis purposes. The Fourier transorm is applied to each o the segments using a window unction and 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. ISSN: 1790-5117 222
components, it is also easible to predict crack initiation so as to avoid atigue ailure by monitoring and preventing the part rom ailure at the appropriate time. A atigue lie estimate is usually made in such cases by means o a strain-based approach [2,8,9]. (a) Fig. 3: The plots o PSD showing the vibrational energy distributed at lower requency range or: (a) T1, (b) T2 Fig. 4 shows the distribution o time-requency localisation o a random signal, or also known as the power spectrum mapping o the STFT. In Fig. 4a, ive localisation areas (other than blue colour mapping) can be seen which indicate the presence o the ive segments o high amplitude events in the synthetic signal o Fig. 1a. This result shows that the capability o the STFT localisation method to be used as the eatures extraction or the determination o atigue damage events. The same argument can also be made or the experimental signal o Fig. 1b, or which its STFT localisation plot is presented in Fig. 4b. In this igure, some o higher (other than blue colour mapping) can be ound across the signal length, showing the occurrence o atigue damage events at those areas. 4 Results and Discussions: Fatigue Lie Assessment The service loads o mechanical structures or systems are typically analysed or atigue lie using crack growth approaches. This approach is suitable or high capital value items such as large aircrat, the space shuttle, pressure vessels and oil rigs [2]. The ability to inspect or cracks and monitor their growth until a maximum allowable deect size is reached, normally enables the useul lie to be extended beyond the original design sae lie. For these (b) Fig. 4 The STFT plots showing the localisation mapping or: (a) T1, (b) T2 The strain-lie atigue models relate the plastic deormation that occurs at a localised region where atigue cracks begin to the durability o the structure. This model is oten used or ductile materials at relatively short atigue lives. This approach is also used where a little plasticity is acceptable at long atigue lives. Thereore, strain-based approaches are comprehensive and can be used in place o stressbased approaches. Current industrial practice or atigue lie prediction is to use the Palmgren-Miner (PM) linear damage rule. For strain-based atigue lie prediction, this rule is normally applied with strain-lie atigue damage models, such as the Coin-Manson relationship, i.e. σ ' b ' ε ( ) ( ) c a = 2N + ε 2N (1) E where E is the material modulus o elasticity, εa is a true strain amplitude, 2N is the number o reversals to ailure, σ is a atigue strength coeicient, b is a ISSN: 1790-5117 223
atigue strength exponent, ε is a atigue ductility coeicient and c is a atigue ductility exponent. According to the analysis presented in this paper using both signals, the atigue lie assessment was perormed using the GlyphWorks sotware package. The basic procedure o perorming this kind o durability analysis is the application o service load (atigue data) onto a component which was abricated rom the designated material. Thereore, the SAE1018 carbon steel was selected or the purpose o simulation, and also this kind o material are also being used in the piping industry. The strain-lie curve that indicates the atigue lie at speciic strain amplitudes was presented in Fig. 5. Fig. 6 shows the histogram plots o the atigue damage potential, showing highest point o atigue damage in the red colour. This damage value was calculated using the Coin-Manson relationship, based on the N value when reerring to Equation (1). Thus, the atigue damage (D) can then be calculated as in Equation (2): 1 D = (2) N Using both Equation (1) and (2), the atigue lives or both signals were calculated and are presented in Table 2. Signal length [seconds] Fatigue lie Blocks to ailure] Total time to ailure [hours] T1 80 1.491 x 10 9 3.31 x 10 7 T2 150 1.760 x 10 3 73.3 Fig. 6: The histogram plots exhibiting the atigue damage distribution or the analysed signals: (a) T1, (b) T2 Fig. 5: The strain-live curve or SAE1018 carbon steel Table 2: The atigue lie values or T1 and T2 5 Conclusions This works has been presented in order to expose a better overview o structural integrity assesment o structural or system components using the combinantion approach o signal analysis and atigue lie assessment. It can be said as a new approach introduced to the structural integrity reseach since the last decade. In this paper, two atigue strain loadings, or later called signals, which exhibiting the variable amplitude pattern has been analysed using the MatLab (or signal analysis) and the GlyphWorks (or atigue lie assessment) ISSN: 1790-5117 224
sotware packages. With the application o the shorttime Fourier transorm (STFT), the atigue damage eatures can be identiied. Later part o this paper, the atigue lives or both signals were calculated, indicating how long a component can be lasted without ailure under the given strain loading. Finally, it is suggested that the approach presented in this paper can be then be applied or determining the lie span o any metallic structures. Reerences: [1] A. Conle, R. Landgra, A atigue analysis program or ground vehicle components, Proceedings o the International Conerence on Digital Techniques in Fatigue, London, 1983, pp. 1 28. [2] NE. Dowling. Mechanical Behaviour o Materials: Engineering Methods or Deormation Fracture and Fatigue, 2 nd ed., Prentice Hall, New Jersey, 1999. [3] nsot User Manual, 2001, ncode International Ltd., Sheield. [4] Matlab User s Guide, Matlab 5.2, The Math Works, 1998. [5] S. Abdullah and A. Zaharim. Using the orthogonal wavelet transorm to identiy atigue eatures in variable amplitude atigue loadings, WSEAS Transactions on Signal Processing, Vol. 2, Issue 10 (October 2006), 2006, pp. 1416 1420. [6] S. Abdullah, J.C Choi, J.A Giacomin, and J.R Yates. Bump extraction algorithm or variable amplitude atigue loadings, International Journal o Fatigue, Vol. 28, No. 7, 2006, pp. 675-691. [7] W.J Staszewski, Wavelet based compression and eature selection or vibrational analysis, Journal o Sound and Vibration, Vol. 211, No. 5, 1998, pp 735-760. [8] J.A Collins. Failure o Materials in Mechanical Design, Wiley, New York.1981. [9] J.H Yan, X.L Zheng and K. Zhao, Experimental investigation on the small-loadomitting criterion, Int. J. Fatigue, Vol. 23, 2001, pp 403-415. ISSN: 1790-5117 225