The need to generate realistic strain signals at an automotive coil spring for durability simulation leading to fatigue life assessment

Mechanical Systems and Signal Processing 94 (2017) 432–447

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The need to generate realistic strain signals at an automotive coil spring for durability simulation leading to fatigue life assessment T.E. Putra a,⇑, S. Abdullah b, D. Schramm c, M.Z. Nuawi b, T. Bruckmann c a

Department of Mechanical Engineering, Universitas Syiah Kuala, 23111 Banda Aceh, Indonesia Department of Mechanical and Materials Engineering, Universiti Kebangsaan Malaysia, 43600 UKM-Bangi, Malaysia c Departmental Chair of Mechatronics, Universität Duisburg-Essen, 47057 Duisburg, Germany b

a r t i c l e

i n f o

Article history: Received 10 September 2016 Received in revised form 8 February 2017 Accepted 12 March 2017

Keywords: Acceleration Automotive Durability Fatigue life Wavelet transform

a b s t r a c t This study aims to accelerate fatigue tests using simulated strain signals. Strain signals were acquired from a coil spring involving car movements. Using a mathematical expression, the measured strain signals yielded acceleration signals, and were considered as disturbances on generating strain signals. The simulated strain signals gave the testing time deviation by only 1.5%. The wavelet-based data editing was applied to shorten the strain signals time up to 36.7% and reduced the testing time up to 33.9%. In conclusion, the simulated strain signals were able to maintain the majority of fatigue damage and decreased the testing time. Ó 2017 Elsevier Ltd. All rights reserved.

1. Introduction A better way to access durability on a component, such as coil springs, is through service loads [1,2]. Durability analysis requires knowledge of service loads since these loads are used for the laboratory testing of a component in engineering practices. Thus, early in the product development process, engineers need to predict stress and strain histories for the purpose of modelling and designing for mechanical fatigue [3]. Strain signal acquisition processes, however, are very expensive, intrusive, time consuming, not error-free and require high levels of skill and training [2,4]. Automotive product development has risks such as high costs and low success rates [5]. Measuring errors arise from variations that are uncontrolled and generally unavoidable [6]. They change both the amplitude and mean stress, and thus, greatly influences fatigue damage. The errors, caused by interference of physical processes and imperfection in measuring apparatuses, not only occupy a large amount of amplitude cycles and make durability tests difficult, but also hinder an accurate fatigue life prediction due to additional amplitude cycles. In the strain signal published by Oh [7], for example, various levels of noise were imposed on the pure signal damage. Thus, fatigue monitoring of a structure has been limited by the available practical technique of current strain sensors [8]. An accurate measurement of strains, from which the stresses can be determined, is one of the most significant predictors of fatigue life [9].

⇑ Corresponding author. E-mail addresses: [email protected] (T.E. Putra), [email protected] (S. Abdullah), [email protected] (D. Schramm), [email protected] (M.Z. Nuawi), [email protected] (T. Bruckmann). http://dx.doi.org/10.1016/j.ymssp.2017.03.014 0888-3270/Ó 2017 Elsevier Ltd. All rights reserved.

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From an economic perspective, automotive companies are looking for a solution to reduce costs in order to remain competitive [10,11]. Because the strain signal at a coil spring cannot be measured directly with a high degree of accuracy, especially during normal driving, it was desirable to develop a simulation for generating strain signals. Thus, the main objective of the current study is to propose techniques to develop fatigue-based strain signals by utilising computer-based simulation with consideration of road surface profiles that may lead to fatigue failure. To the best of the author’s knowledge, no such simulation was previously proposed. Therefore, the simulation is expected to bring greater meaning in automotive industries involving strain signal acquisitions. There are requirements that should be considered when generating a new fatigue random load history, such as [12]: (1) load cycles should correspond to the rainflow counting method as a standard procedure for determining damage events, (2) sequence of load cycles should be maintained, (3) damage resulting from the new load history should be the same as the original load history, and (4) the new load history should be shorter in length than the original load history to decrease the testing time, by deleting small load cycles and merging smaller ones. The rest of this paper is organised as follows: Section 2 describes the materials and methods used, the detailed experimental results and discussion are set out in Section 3, and then, Section 4 is the conclusion followed by a comprehensive list of references. 2. Materials and methods 2.1. Strain signal acquisition The frontal coil spring of an automobile with 1300 cc capacity was used as a case study. It uses a passive McPherson strut suspension system with the spring stiffness and the damping coefficient of 18,639 N/m and 15,564 N s/m, respectively. The selected material for the simulation was the SAE5160 carbon steel since it is commonly employed in automotive industries for fabricating a coil spring [13]. Its material properties are tabulated in Table 1. A strain signal acquisition was performed, by placing a strain gauge at the critical area of the component. Thus, a dynamic analysis was performed for determining the stress distributions at the coil spring. A force of 3600 N was applied on the bottom of the component model and the upper was fixed, considering the car weight of 10,600 N as well as the passengers and the load carried of 3800 N. The total force was divided by four because the car weight and the passengers were assumed to uniformly distribute to four springs [14]. The analysis was performed with load amplitude varying from 0 to 3600 N. The boundary condition of the component is shown in Fig. 1. The stress distributions were measured to find the critical area of the coil spring. Thus, a strain gauge could be installed in the correct position. The position of the strain gauge installation was selected based on the possibility of higher stress area based on the finite element analysis. The strain gauge was connected to the data logging instrument through a connector. A fatigue data logger was used to record the strain signals measured by the strain gauge. Measuring parameters were set up to align the strain gauge reader, set the type of collected strain signals, set the strain signal storage area and upload the strain signals from the fatigue data logger into the computer. According to Ilic [16], the sampling frequency for a strain signal acquisition should be greater than 400 Hz, so that the essential components of the signal are not lost. Using a collection rate higher than 500 Hz can increase the upper limit of the frequency range as small amplitude and high frequency load cycles will be captured. Collecting load histories at a frequency of 500 Hz is sufficient to detect and capture all damaging load cycles [17], and the selection of 500 Hz was seemingly suitable for the on-site strain signal collection. After installing the equipments, the car was then driven on urban and rural road surfaces at velocities of 30 km/h to 40 km/h and 20 km/h to 40 km/h, respectively. The velocities above were matched with an average car speed when driven on specified road conditions [16,18,19]. Furthermore, the measured strain signals were the input into a mathematical expression for generating acceleration signals. 2.2. Acceleration signal generation A method that has been used to classify a vibration is based on its degree of freedom. A mass-spring-damper system with single degree of freedom can be characterised by Fig. 2. A single degree of freedom system was considered in the study Table 1 Mechanical properties of the SAE5160 carbon steel Source: nCode [15] Properties

Values

Ultimate tensile strength, Su (MPa) Material modulus of elasticity, E (GPa) Yield strength (MPa) Fatigue strength coefficient, r0 f (MPa) Fatigue strength exponent, b Fatigue ductility exponent, c Fatigue ductility coefficient, e0 f Cyclic strain-hardening exponent Cyclic strength coefficient (MPa) Poisson ratio

1584 207 1487 2063 0.08 1.05 9.56 0.05 1940 0.27

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Fig. 1. The boundary condition of the coil spring.

Ps

Sprung mass x k

ẋ

Pi

Pd

ẍ

d

Unsprung mass

P

Fig. 2. A mass-spring-damper system and its free body diagram.

assuming the vibrations act in each suspension without affecting other suspensions. According to the Newton second law of motion, all forces have both magnitude and direction. As the mass-spring-damper system moves in response to an applied force P, forces induced are a function of both the applied force and the motion in the individual components. The governing equation of this system can be derived from the law as:

Pi þ Pd þ Ps ¼ P

ð1Þ

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where Pi is the inertial force, Pd is the damping force and Ps is the spring force. The equation of motion may then be expressed as:

m€x þ dx_ þ kx ¼ P

ð2Þ

where m is the mass of object, d is the damping coefficient, k is the spring stiffness, € x is the acceleration, x_ is the velocity and x is the displacement. The equation of motion for a damped forced vibration represented by Eq. (2) is separated into internal and external forces. Internal forces are found on the left side of the equation, and external forces are specified on the right side. External forces induced from engine operations, tyres and the like have an influence on the simulation results, however, they were not considered due to limitations observed in the equipment and the software package. Thus, the equation of motion became a damped free vibration, generated as follows:

m€x þ dx_ þ kx ¼ 0

ð3Þ

Then, the acceleration € x is derived as:

€x ¼ 

dx_  kx m

ð4Þ

Since the displacement x was known, the velocity x_ might be determined through differentiation of the time-dependent displacement. Expanding Eq. (4), it is obtained:

€x ¼ 


 d @x  kx @t m

ð5Þ

where t is the time. Shearing forces cause shearing deformation. An element subjected to shear does not change in length but undergoes a change in shape. The change in angle at some point of an element is called the shear strain c, where this kind of strain is associated to torsion in a spring. It is expressed as:

c¼

x D0

ð6Þ

where D0 is the original unloaded diameter. Substituting Eq. (6) into (5), the acceleration € x results:

€x ¼ 

  d @ðc@tD0 Þ  kcD0

ð7Þ

m

Based on Eq. (7), a model was developed. The model was constructed from graphical blocks with input and output ports that were connected by drawing lines. The measured strain signals were used to obtain velocities, and the velocities were utilised to obtain acceleration signals. In the schematic diagram in Fig. 3, block A was used to input the strains. The strains were presented in block B as a graph, and were provided as values in block C. The strains were then transformed into the displacements using block D, containing the coil spring original unloaded diameter. Block E functioned to transform the displacements into the velocities and the velocities were then transformed into the accelerations using block F. The values of the damping coefficient and the spring stiffness were inputs in block G. The spring stiffness was also the input in block H together with the mass. Finally, the accelerations were viewed in block I and were provided as values in block J. The fatigue-based acceleration signals were the input for the multi-body dynamic (MBD) simulation for simulated strain signal generation.

Fig. 3. Schematic diagram for generating acceleration signals.

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2.3. Simulated strain signal generation The simplest force elements are springs and dampers, as shown in vibration model in Fig. 2, which are passive elements. An active force element was admitted in which the force was determined by a given control law from observed position and velocity variables [20]. In the current study, the force was resulted from Eq. (7) and the schematic diagram in Fig. 3. A modelling methodology based on object orientation and equations for dynamic systems had been used for generating a strain signal having behaviour similar to the actual strain signal. A commercial software package was used to model the threedimensional mechanical multi-body system of the coil spring. The software, developed by Elmqvist [21], was an early effort to support physical modelling. The shear strain c is generated by inverting Eq. (3) and submitting Eq. (6) into it. re-arranging Eq. (3), it is obtained:

kcD0 ¼ m€x  dx_

ð8Þ

_ Finally, the equation solves for the shear strain c, by integrating the acceleration € x to obtain the velocity x:

c¼

R m€x  d x€ kD0

ð9Þ

In the schematic diagram developed based on Eq. (9) as shown in Fig. 4, the coil spring responses in terms of strain were observed in order to reach the main objective of the study. In the simulation, block A was designed to input a variable data set. This block was then connected to the translational mechanics in block B determining the movement of the coil spring system. Block C defined the coordinate system, including the gravity of 9.81g, and block D defined the degree of freedom. Block E was the coil spring system to input the damping coefficient and the spring stiffness, while the mass was the input for block F. Block G was the sensor transforming the variable data set into accelerations. In block I, the strains were determined based on the input in block H, which was the original unloaded diameter of the coil spring. Finally, the simulated strain signals caused by the accelerations were provided in block J. Furthermore, for the segment by segment validation, the simulated strain signals were extracted to obtain damaging segments. 2.4. Fatigue feature extraction In real applications, fatigue random time histories are mostly long and often contain a mixture of lower and higher amplitude cycles. In relation to this issue, the fatigue damage associated with the lower amplitude cycles may be minimal. Consequently, engineers want to eliminate the non-damaging cycles from the original histories collected at a component and accelerate fatigue tests for the reasons of time and cost [12,22]. In automotive applications, a modified signal should have less than 10% deviation compared to the original signal [23,24]. A difference of 10% is used considering that at least 10% of an original signal contains lower amplitude cycles which lead to minimal fatigue damage. Removing these lower amplitude cycles, a final modified signal with potential for damage corresponding to the original signal is obtained. This range is important to ensure that the resulted modified signal is as close as possible to the original signal; so as to keep the majority of fatigue damage, the vibration energy and the amplitude range.

Fig. 4. Schematic diagram for generating strain signals.

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Thus, the durability testing can often be accelerated by the use of the lower amplitude cycle removal technique, known as fatigue data editing (FDE) [25], to produce a new shortened fatigue signal as required which contains high amplitude cycles. The idea behind this technique is that lower amplitude events do not cause much fatigue damage. The FDE is defined as a method to identify and extract higher amplitude segments that lead to fatigue damage in a signal. On the other hand, lower amplitude segments are removed because they theoretically contribute to a minimum amount of fatigue damage. The shortest modified fatigue signal without compromising the original features is the main criterion in the FDE. The approach achieves the accelerated fatigue test considering less than the complete set of an original fatigue signal since only a subset of the signal is required to produce the same amount of damage. Therefore, the FDE is widely utilised; especially in automotive fields. For the development of the FDE algorithm, the required input was the distribution of the wavelet-based energy for the achievement of fatigue resistance characteristics. The wavelet transform is a significant tool for representing local features of a signal. It cuts a time domain signal into various frequency components by applying multi-resolution analysis, namely through the usage of a variety of window sizes determining the resolution. Applying a windowed technique, it changes the window along the signal and calculates the spectrum for each position. Different window sizes are used because lower frequency signals can be analysed using a wider window size since the oscillations are slower compared to a high frequency signal requiring smaller sized windows. This process is repeated several times with the window slightly shorter or longer for each new cycle. In the end, the result is a set of time-frequency representations of the signal with different resolutions. The wavelet transform presents information in both time and frequency domains simultaneously. It provides information on when and at what frequency the signal changes occur. The main profit of the wavelet transform is the ability to analyse the local area also known by the local analysis [26]. The continuous wavelet transform (CWT) is defined as the sum over all time of a signal multiplied by the scale [27]. It is conducted on each reasonable scale, producing abundant data, and is used to determine the values of a continuous decomposition so as to accurately reconstruct the signal [26]. The wavelet transform begins with a basic function, called the mother wavelet, scaled to display the signal being analysed. Using the mother wavelet, the signal is moved from a space to a scale domain in order to provide the localised features of the signal. A mother wavelet must be carefully chosen so that the content of the son wavelet is largely similar to that of the analysed signal to ensure good results. Although many new and complicated basic functions have been proposed to improve the effectiveness of wavelet-based methods, to date, no general guideline has been proposed for the correct selection of a mother wavelet. At the same time, little attention has been paid to the inherent deficiencies of the wavelet transform [28]. Thus, the chosen mother wavelet was Morlet since it results in an internal energy plot that is similar to the fatigue damage distribution, because it is more sensitive to amplitude changes in a strain signal. The wavelet transform, particularly Morlet, possess its own priority than other transformations in the time-frequency domain. The Morlet wavelet has a great potential for predicting fatigue failure [29,30]. The Morlet wavelet is one of the advanced mother wavelets that involve the CWT [31]. Morlet et al. [32,33] modified the Gabor works [34] to keep the same wavelet shape over equal octave intervals. The Morlet wavelet can be described by the following equation:

wðtÞ ¼

1

p1=4

ei2pf 0 t et

2 =2

ð10Þ

where f0 is the frequency at the central of the mother wavelet W. Wavelet decomposition calculates the resemblance index, also called as the coefficient [35]. The coefficient is the result of a signal regression generated at different scales in a wavelet, establishing the correlation between the wavelet and a section of the signal being analysed. Higher coefficient indicates strong resemblance, whereas a lower coefficient indicates weak resemblance [26]. The wavelet coefficient WC of the CWT is expressed with the following integral [36]:

1 WC ðp;qÞ ¼ pffiffiffi p

Z

þ1 1

  tq dt F ðtÞ w p

ð11Þ

where F is the signal amplitude, q is the time shifting and p is the scale index. The scaling factor allows controlling the shape of the basic wavelet and balances the time and frequency resolutions. Decreasing the scale index increases the frequency resolution but decreases the time resolution. When the scale index tends to zero, the wavelet becomes a cosine function which has the finest frequency resolution, and when it tends to infinity, the wavelet has the finest time resolution. So, there always exists an optimum scale index that has the best time-frequency resolution for a certain signal localised in the time-frequency plane. The Morlet wavelet coefficient and the energy are presented in Fig. 5. Through the two-dimensional display in the time-frequency domain, the level of coefficient is estimated based on the contours of different colours, whereby, white indicates the highest magnitude level, followed by yellow, brown and black, respectively. The colour intensity at each x-y point is proportional to the absolute value of the wavelet coefficient as a function of the dilation and translation parameters [37]. One of the earliest practical applications of the Morlet wavelet came from the analysis of earthquake voice record by Goupillaud et al. [38]. Since then, it has been extensively used in many engineering applications. The Morlet wavelet was not only used in engineering fields, but was also successfully applied in the field of health for detecting heart sound [39] and for measuring blood flow velocity [40] as well as in the field of science for identifying dominant orientations in a porous medium [41]. According to the reading and the knowledge of the author, however, the Morlet wavelet is still rarely used in

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Strain (µe)

438

600 400 200 0 -200 0

20

40

60

Scale

Time (s) (a) 120 100 80 60 40 20 0 0

200 150 100 50 20

40

60

40

60

Energy (µe2/Hz)

Time (s)

4

x 10

(b)

5

2 0 0

20 Time (s)

(c) Fig. 5. Analysis of the wavelet transform: (a) time series signal, (b) wavelet coefficient and (c) wavelet-based energy.

the scope of fatigue studies. A fatigue study associated with the Morlet wavelet by Kim and Melhem [29] suggested that the wavelet-based approach offered great promise for damage detection and health monitoring of concrete beams. Another fatigue study related to the Morlet wavelet was by Lin and Zuo [30]; it developed an adaptive wavelet filter to detect periodic impulses automatically for recognition of gear tooth fatigue cracks. Although the wavelet transform has not been able to reliably give fatigue life yet, it can give better results than other methods. It gives a new dimension in the field of fatigue research, although its use is still in the preliminary stages. In this study, the wavelet-based FDE applied a method removing lower amplitude energy. Fig. 6 shows the FDE computational algorithm flowchart. The wavelet transform was employed to convert a time domain signal into the time-frequency domain displaying the wavelet coefficient in time and frequency axes simultaneously in two dimensions, as observed in the time-frequency surface. The wavelet coefficient provided a display of the energy distribution of a particular time and frequency by squaring the coefficient at each time interval. The wavelet-based signal internal energy  e can be expressed as follows [42]:

eðp;qÞ ¼

Z

þ1

1

jWC ðtÞ j2 dt

ð12Þ

Based on Eq. (12), the distribution of energy was decomposed into the time domain spectrum by taking the magnitude cumulative value for an interval of time. The energy was then utilised to detect the amplitude changing in the strain signals. A lower scale in the wavelet coefficient shows a higher frequency and has a smaller strain amplitude, which means this cycle has a lower energy, indicating a minimum or no potential for fatigue damage. A larger scale in the wavelet coefficient shows a lower frequency and higher strain amplitude, indicating this cycle has a higher energy causing fatigue damage [37]. Clearly, lower frequency shows a higher magnitude and lower magnitude distribution is shown in higher frequency events. Identification of the peak-valley could be used to cut the strain signals so that each segment contains a number of certain peaks and valleys, according to the need of the study. This is especially useful for fatigue signals, because characteristics of the peak-valley are dominant in the rainflow method used for the calculation of the number of cycles [12]. Thus, an algorithm was developed to produce a new magnitude taking the points of peak and valley only by comparing the magnitude values. Furthermore, highly fatigue damaging segments in the strain signals were extracted, based on high energy distribution, in order to result in segments contributing to fatigue damage. Energy gate value (EGV), which is the energy spectrum variable, was then applied as a parameter to determine the minimum magnitude level to be retained in the wavelet domain. Let the maximum wavelet-based energy be emax, then, the EGV is represented as:

EGV ¼ ehmax

ð13Þ

where h is the multiplicative factor that can be any positive number. Energies that were higher than the EGV should be maintained based on their positions on the time axis in order to produce segments contributing to cumulative fatigue damage for further analysis. Instead, all energies that were less than the EGV were removed. Because segments consisting of a low mag-

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439

START

A strain signal with higher amplitudes

Energy obtained from the strain signal

Energy distribution in peak-valley series Starting point End point EGV

Damaging segment indentification

Segments with higher energy

Non-damaging (red) and damaging (blue) segments

Damaging segments are reattached to produce a mission strain signal

Is the error < 10 %?

No

Yes Signal analysis

STOP Fig. 6. Flowchart of the developed FDE algorithm.

nitude represent segments with low fatigue damage, the fatigue characteristic extraction was expected to be able to maintain the majority of fatigue damage in the strain signals. The selection of a retained segment was based on energy loss, which occurs when the selected segment was at the beginning of the swing so that it ends. The starting point of the segment was the valley point if the previous peak was higher than the peak after the valley point. Meanwhile, the endpoint of the segment was the valley point if the peak after the point was higher than the peak before the point. Thus, the identification of the extracted segment was performed by finding the inverse of two points (on each peak). Once all the extracted segments were identified, the energy time history was then scrapped to remove lower energy (less than the EGV) contained in the range of the original time history. The positions of the extracted segments were then transferred to the original strain signal in the time domain for the removal of segments that were not

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required. The segments to be removed were then cut from the original strain signal based on the position of the segments. The extraction concept above refers to the concept of the cut-off level used in the extraction in the time domain by Stephens et al. [23]. To obtain the optimum EGV, the maintained segments were then merged with each other to form a shorter modified strain signal, in comparison to the original strain signal, but had equivalent behaviour to the original strain signal. A different EGV resulted in a differently modified strain signal. After increasing the EGV, a shorter modified strain signal was produced because more magnitude cycles were under the higher EGV. Therefore, resulting strain signal was shorter when more segments were removed. However, the edited strain signal at a higher EGV provided real decline in maintaining the original characteristics of the strain signal. If the obtained modified strain signal did not meet the criteria, the EGV was reduced to obtain the required modified strain signal. After decreasing the EGV, the characteristics of the modified strain signal increased and were even equal to the original characteristics. The question then arose how accurate the simulation was in generating strain signals. Thus, it was decided to validate the strain signals by performing fatigue tests. 2.5. Fatigue tests The strain-life approach is accurate enough for fatigue life assessments, since it considers plastic forming events that exist in a local area. The approach is usually applied to ductile materials since the low cycle fatigue of small components [43–45], which is only within 103 cycles [2,46,47], do not require high operating costs and do not require extensive crack observation in which the failure occurs. The strain-life approach is actually based on the linear relation between a stress amplitude and a number of cycles, which was introduced by O. H. Basquin in 1910. The elastic and the plastic strains were combined to obtain a correlation between the fatigue life and the strain, known as the Coffin-Manson model [48], which is the basis of the strainlife approach. It is defined as follows:

e¼

r0f E

ð2Nfi Þb þ e0f ð2Nfi Þc

ð14Þ

where e is the strain amplitude, r0 f is the fatigue strength coefficient, E is the material modulus of elasticity, Nfi is the number of cycles to failure for a particular stress range and mean, b is the fatigue strength exponent, e0 f is the fatigue ductility coefficient and c is the fatigue ductility exponent. Fatigue damage was determined using the Palmgren-Miner linear cumulative fatigue damage rule based on a number of repeated simple or complex loads. The number of cycles was determined using the rainflow cycle counting method. The fatigue damage for each loading cycle Di can be calculated as follows:

Di ¼

1 Nfi

ð15Þ

The Palmgren-Miner rule is then used to calculate the cumulative fatigue damage D of a loading block, and it is defined as follows:

D¼

X  ni  Nfi

ð16Þ

where ni is the number of applied cycles at a particular stress level for each block loading. Fatigue damage has a range of zero to one, where zero indicates no damage (infinite cycles to failure) and one is assumed as failure (one cycle to failure) [49]. Aside from fatigue life assessment using the strain-life approach, cyclic tests were conducted as well. The main reasons to perform variable amplitude loading (VAL) fatigue tests in the study were to validate the fatigue life of the simulated and edited strain signals and to show the time reduced from using the edited strain signals. The major reason for carrying out a VAL fatigue test [1,50] was the fact that a prediction of fatigue life under this complex loading is impossible by any hypothesis [51,52]. A VAL fatigue test is principally carried out like a constant amplitude loading (CAL) fatigue test on different loading levels, with a given load being continuously repeated until a failure is obtained. The only difference is that in cases of CAL, the amplitude (or range) remains unchanged. Thus, VAL fatigue tests are more complicated and often more time consumption and expensive than CAL fatigue tests [53]. The fatigue testing specimens were designed according to ASTM E606-92 [54], as shown in Fig. 7. The geometry and the dimensions of the specimens were specified along with appropriate grips for the fatigue testing machine used. The specimens were fabricated using computer numerical controls and grinding machines and were mechanically polished [55] in order to ensure complete removal of machining marks in the testing section. A sand paper with a grit size of 240 was used to give the rounded shape and the finer 1500 grades gave a suitable surface finish. Since fatigue cracks begin to occur at irregular surfaces, the condition of a specimen surface is important in fatigue tests. It reduced stress concentration to prevent crack initiation at those sites. The tests were performed at the room temperature, which was 20 °C [56]. Strain signals were converted into the stresses using the Ramberg-Osgood equation [57], described as:

 1=n0

r r e¼ þ 0 E

K

ð17Þ

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Fig. 7. A specimen for the fatigue test: (a) specimen geometry and dimensions in millimeter and (b) photograph of the specimen.

Collect the strain signal Generate the acceleration signal Determine the simulated strain signal Extract the actual and simulated strain signals Develop the edited strain signal Perform the fatigue test Determine the fatigue life Fig. 8. Process flow of the developed simulation.

where r is the stress, K0 is the cyclic strength coefficient and n0 is the cyclic strain hardening exponent. The material modulus of elasticity, the cyclic strain hardening exponent and the cyclic strength coefficient are provided in Table 1. The stresses could then be converted into the loads as the input for the fatigue testing machine using the following expression:

r¼

P A0

ð18Þ

where A0 is the original unloaded cross-sectional area. The cross-sectional area for the equation was 18 mm coming from the area of gauge length of the specimens. Reversed VAL fatigue tests were performed, where frequency at 100 Hz [47,58] was selected. There is no effect of higher frequency on crack initiation [58,59]. The influence of frequency on a fatigue testing result is often considered minimal for frequencies reaching 1000 Hz [47]. Fig. 8 shows the general process of the current study. 3. Results and discussion 3.1. Simulated strain signals The stress concentration experienced by the coil spring is provided in colour contours in Fig. 9. Areas with the highest stress concentration are represented by red, followed by orange, yellow, green and blue, respectively. Red areas had a maximum von Mises stress of 1.199 MPa occurred at node 3463. Referring to Table 1, the maximum stress was very low compared to the yield strength, which was 1.487 GPa, indicating the force did not cause a failure to the component. Through the stress distributions, the parts receiving high loading were known. Thus, a strain sensor could be installed in the correct position. The strain signal acquisition had been carried out to find time series strain loadings at the coil spring affected by road surfaces. The strain signals produced by the strain gauge were a VAL because the component actually experienced various

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The critical area

Fig. 9. Stress distributions of the coil spring.

Strain (µe)

amplitudes. The total recorded length was each 60 s for 30,000 data points, as shown in Fig. 10, which were sufficient for observing fatigue-based strain signal behaviour and evaluating fatigue life. The urban strain signal, called S1, provided lower amplitude range. Higher amplitude range could be seen in the rural strain signal, called S2. The rural road gave higher amplitudes than the urban road because its surface was uneven. Furthermore, the actual strain signals were the input for observing vibration responses using the strain model developed in Section 2.2 in order to yield acceleration signals. Referring to Eq. (7), the main inputs for the model were the strains, the damping coefficient, the spring stiffness, the mass, as well as the original diameter, and the acceleration responses could be observed. Since all the parameters were known, the model yielded the corresponding acceleration. Trends of the acceleration for the urban and rural strain signals are shown in Fig. 11. It is an interesting fact that a lot of random vibrations that occur should have a Gaussian distribution. Accelerations occur around a fixed point and have a zero-mean over time [60]. Referring to Eq. (7), the acceleration is parallel to the strain. The strain with higher amplitudes produced the acceleration with higher amplitudes as well. These were in line with the strain signals provided in Fig. 10. The rural acceleration signal gave higher amplitudes because it was produced from the strain signal measured on an uneven surface. This indicated that the road surface gave higher vibration energy since it also had higher strain amplitude. Furthermore, the acceleration signals were the input into the MBD simulation in order to yield subsequent strain signals. The fatigue-based strain signals were generated by utilising the acceleration model developed in Section 2.3 based on Eq. (9).

800 400 0 -400 -800 -1200 -1600

0

20

40

60

40

60

Time (s)

Strain (µe)

(a)

800 400 0 -400 -800 -1200 -1600

0

20 Time (s) (b)

Fig. 10. Time histories of the actual strain signals: (a) S1-urban and (b) S2-rural.

443

Acceleration (g)

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4

x 10

-3

0 -4 0

20

40

60

40

60

Acceleration (g)

Time (s) 4

x 10

(a)

-3

0 -4 0

20 Time (s)

(b) Fig. 11. Time histories of the acceleration signals: (a) urban and (b) rural.

To run the MBD simulation, the accelerations that resulted from the previous strain model, the damping coefficient, the spring stiffness and the original diameter as well as the mass were the inputs. The time series of the simulated strain signals are shown in Fig. 12. It reflected the high uniformity, indicating that the probability of similarity between the actual and simulated strain signals was big. The simulated strain signals, however, changed the actual amplitude ranges. This was because the equation of motion used to develop the simulated model being simplified, without considering external forces. The frequency spectra for the strain signals are shown in Fig. 13. The differences in the frequency were because the equation of motion used to develop the simulated model was being simplified, without considering external forces. The variations of the fixed frequency appeared as distinctive peaks, that occurred between 0 Hz and 60 Hz. These peaks were caused by higher energy that occurred at lower frequency. At this lower frequency, the energy was transferred by non-linear processes, and then exponentially decreased towards a higher frequency and was eventually lost as heat. Other than these peaks, the strain signals generally showed broad peaks (or what one might call a hill) at higher frequency range. This illustrated that high fatigue loadings occurred at lower frequency oscillations due to the peaks; while the existing high frequency loading was in the form of vibrations, having lower amplitudes. For the next validation procedure, both the actual and simulated strain signals were extracted using the wavelet transform to generate damaging segments and then form edited strain signals. 3.2. Strain signal segmentation

Strain (µe)

For the segment by segment validation, the actual strain signals were extracted using the wavelet-based FDE technique developed in Section 2.4. Time series energy magnitudes need to be converted into the form of peak-valley series. Eq. (13) was then utilised to detect the locations of a higher amplitude in the strain signals based on the magnitude spectrum. Thus, highly fatigue damaging events in the strain signals were identified and extracted to produce damaging segments. A cutting level parameter, called EGV, was used for the extraction of fatigue features.

800 400 0 -400 -800 -1200 -1600 0

20

40

60

40

60

Time (s)

Strain (µe)

(a) 800 400 0 -400 -800 -1200 -1600 0

20 Time (s) (b)

Fig. 12. Time histories of the simulated strain signals; (a) S3-urban and (b) S4-rural.

Energy (µe2/Hz)

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x 10 8 6 4 2 0 0

Energy (µe2/Hz)

444

x 10 8 6 4 2 0 0

5

Actual

20

40 60 Frequency (Hz)

Simulation

80

100

(a)

5

Actual

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40 60 Frequency (Hz)

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80

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(b) Fig. 13. Frequency spectra comparisons in the range of 0–100 Hz: (a) urban and (b) rural.

Strain (µe)

S1 was extracted at 4500 le2/Hz, meanwhile 4600 le2/Hz was applied to S2. The EGVs were chosen because most of the energies were below the EGVs. The energies with a magnitude exceeding the EGVs were maintained, whereas the energies with a magnitude less than the EGVs were removed from the strain signals. Lower energy segments were assumed to be nondamaging segments, hence if these lower energy sections were removed, it should not affect the damage relevance and the original properties of the strain signals. After all the strain signals were extracted, retained higher energies were obtained. Furthermore, based on the time positions of the retained higher energies and referring to the actual strain signals in Fig. 10, maintained segments were obtained. The maintained segments were damaging segments since they had slightly more energies than the EGV. Meanwhile, the removed segments were non-damaging segments because the energy of the segments was lower than the EGV. The extraction produced segments that were not uniform in lengths because the FDE technique extracted the time series based on the energy contents. Maintenance of the original characteristics was important in the FDE to ensure that the resulted modified strain signals were similar to the actual strain signals. Thus, the effects of the removal at a single EGV should be considered so that the retained segments meet the criteria required in the FDE, i.e. maintaining 90% of fatigue damage. Therefore, the retained segments were reattached into a single strain signal to validate if the extraction performed satisfied the requirement, as shown in Fig. 14. The strain signals were extracted with a deviation of fatigue damage by 10% [23,24]. From the changes in fatigue damage, an optimum EGV for each strain signal was determined based on its ability (in reference to the modified strain signal) to produce the shortest strain signal with a minimum fatigue damage deviation. Controlling the difference in fatigue damage, these edited strain signals had characteristics that were close to the original features. The decreasing number of cycles caused the fatigue damage in the modified strain signals to also decrease, since fatigue damage is derived from the number of cycles. The edited S1 strain signal, called S5, gave the 48.6-s mission strain signal. This short strain signal gave 18.9% reduction in length, as the result of the lower energy amplitude removal. The fatigue damage was 9.7% rate of reduction compared to the

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40

60

40

60

Time (s)

Strain (µe)

(a) 800 400 0 -400 -800 -1200 -1600 0

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(b) Fig. 14. Time histories of the edited actual strain signals; (a) S5-urban and (b) S6-rural.

445

Strain (µe)

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800 400 0 -400 -800 -1200 -1600 0

20

40

60

40

60

Time (s)

Strain (µe)

(a) 800 400 0 -400 -800 -1200 -1600 0

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(b) Fig. 15. Time histories of the edited simulated strain signals; (a) S7-urban and (b) S8-rural.

original fatigue damage. Furthermore, the edited S2 strain signal, called S6, gave the 38-s mission strain signal, containing at least 91.1% of the original fatigue damage. With respect to time retention, only 63.3% of the original signal time length was retained. The reduction of fatigue damage indicated that these EGVs did not change the strain signal behaviour, since the reductions were in the required range, at ±10% of the difference. In the next task of the study, S3 and S4 were edited as well. The extraction of S3 and S4 was based on higher amplitude locations in S1 and S2, respectively. Due to the actual and simulated strain signals being extracted at the same positions, the total of segments resulted from the extraction of S3 and S4 was equivalent to the segments resulted from the extraction of S1 and S2, respectively. The damaging segments were then assembled together to produce edited strain signals as well. The edited strain signals of S3 and S4, called S7 and S8, respectively, are shown in Fig. 15. S7 and S8 had similar lengths as S5 and S6, respectively, which were 48.6 s and 38 s since they were extracted at the same positions. In order to validate the strain data, the simulation-based strain signals were compared to the actual strain signals by performing fatigue tests. 3.3. Fatigue life The original actual strain signal of the urban road (S1) required at least 412 reversals of blocks until failure and the time required was more than 34.3 h. The increase of the time by 0.7% or 34.6 h was obtained using the original simulated urban strain signal (S3) providing 415 reversals of blocks. When the length of S1 could be reduced up to 18.9% in the edited actual strain signal (S5) with 456 reversals of blocks without affecting the fatigue damage content, the time required to perform the fatigue test could be reduced up to 10.3%, or about 30.8 h. In S5, the lower strain amplitudes contained in S1 were removed, and thus, accelerated the fatigue test. The time could be reduced once more using the edited simulated strain signal (S7) since the lower amplitudes contained in the strain signal were removed as well. The strain signal gave 400 reversals of blocks and just needed 27 h until failure in the fatigue test. In total, the time could be reduced more than 21.2%. A similar condition could be seen in the rural strain signal. The time needed to perform the fatigue test for the original actual strain signal of the rural road (S2) was 11.4 h, involving 137 reversals of blocks. The time was increased by 1.5% using the original simulated strain signal (S4) with 139 reversals of blocks. Only 8.1 h and 7.5 h were needed to perform the test using the edited actual (S6) and simulated (S8) strain signals, involving 153 and 143 reversals of blocks, respectively, or 29.3% and 33.9% faster than the time needed for S2, because of the lower strain amplitude removal in the FDE technique. Considering the requirements stated in Section 1, the simulated strain signals were able to maintain the original cycle sequences, the actual and simulated strain signals had equivalent fatigue damage, and the simulated strain signals decreased the fatigue testing time. The laboratory experiments involving the acceleration of the durability testing showed that the fatigue tests with the simulated strain signals needed a much shorter time than tests with the original strain signals, but had similar potential fatigue damage. 4. Conclusion The study proposed a computer-based simulation for generating strain signals with consideration of road surface profiles that may lead to a fatigue failure. Furthermore, the wavelet-based fatigue data editing was applied to shorten the strain signals time up to 36.7%, containing at least 91.1% of the original fatigue damage. For validation purposes, fatigue tests were performed using the actual and simulated strain signals. The fatigue testing time required until failure for the original actual strain signal was up to 34.3 h. Using the simulated strain signals, however, it saved testing time by more than 33.9%. The results from this research bode well for increasing the connection between the virtual and real worlds of durability testing. Thus, the economic effects may be reduced by applying current fatigue technologies. This work helps engineers in automo-

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