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Engineering Failure Analysis

journal homepage: www.elsevier.com/locate/engfailanal

Predicting the fatigue life of an automotive coil spring consideringroad surface roughness

T.E. Putra⁎, Husaini, M.N. MachmudDepartment of Mechanical Engineering, Universitas Syiah Kuala, 23111 Banda Aceh, Indonesia

A R T I C L E I N F O

Keywords:Coil springFatigue lifeRoad surfaceStrain

A B S T R A C T

The current work aims to determine the life of an automotive coil spring due to road surfaceroughness. Strain gages were installed at the critical and the non-critical areas of the coil springand driven the vehicle on road surfaces at different speeds. Driving the vehicle on the rural roadresulted in 88.4% and 83.9% decreases in the useful life in comparison to the highway and theurban roads, respectively. It concluded that, a road surface with bumps, holes and uneven tarpatch as well as driving behavior like turns, speed changes, accelerations and brakes affects thecar component life significantly.

1. Introduction

The collision and the friction arising between the car tires and the road surface generate vibrations which cause problems in thevehicle components and the quality of the drive. After a vehicle is subjected to a sudden shock impulse, the tires tend to move fromtheir initial positions, and the whole vehicle experiences its effect. Hence, constituents of the vehicles' suspension like the system ofsprings and shock absorbers need to be replaced every five years or if the car has been driven over a distance of 73,500 km [1]. About13.18% of 24.2 million constituents of automotive suspensions have been reported to cause huge liability [2].

Stiffness and low fatigue life are problems occurring to a coil spring [3–4]. The presence of residual stresses on a component couldaffect the component durability. If these resulted stresses are retained for a long time, they could increase the likelihood of anoccurrence of the fatigue failure of that component. Currently, the strain-life procedure is extensively used, and it is related to thePalmgren-Miner linear cumulative fatigue damage rule used in ascertaining the fatigue life of structural design [5]. However, theapproach gives different results in fatigue life assessments [6].

Since the strain-life approach is not for an accurate fatigue life assessment, experimental fatigue tests are the best option [7–8].Most of the fatigue tests, however, only involve a constant amplitude loading (CAL) since variable amplitude loading (VAL) fatiguetests are complex and sometimes could be time-consuming. They are even costlier than CAL fatigue tests [9–11]. Considering the factthat most fatigue signals in actual applications are VALs and any hypothesis cannot predict the fatigue lives of these complexloadings, the current study aims to investigate the fatigue life of an automotive coil spring subjected the strains acquired on roadsurfaces. Utilizing a VAL for a fatigue test, the results obtained are expected more reliable.

https://doi.org/10.1016/j.engfailanal.2020.104722Received 16 April 2019; Received in revised form 15 June 2020; Accepted 2 July 2020

⁎ Corresponding author.E-mail address: edi@unsyiah.ac.id (T.E. Putra).

Engineering Failure Analysis 116 (2020) 104722

Available online 07 July 20201350-6307/ © 2020 Elsevier Ltd. All rights reserved.

T

2. Experimental setup

2.1. Strain signal measurement

A dynamic analysis was carried out for estimating the stress distribution on the coil spring. The stress was determined using thevalue of the impact and the direction towards which the force was exerted, the perimeter, modulus of elasticity and the Poisson ratio.A force of 3,600 N was subjected to the component bottom while keeping the upper region fixed. The car weight was considered as10,600 N, while the weight of the other load and passengers was considered to be 3,800 N. Furthermore, the estimated overall forcewas then divided by four, as it was assumed that the weight of the car and the passengers would be uniformly distributed on the fourcoil springs. The magnitude of the load used to carry out the cyclic analyses was from 0 to 3,600 N. Fig. 1 presents the boundarycondition of the component. The SAE5160 carbon steel was chosen as the material for the simulation. It is commonly used in severalautomotive companies for the fabrication of the coil springs. It physical properties is illustrated in Table 1.

In case of issues where the stresses are concentrated in a few areas, some small elements are recommended for these regions.Hence, a high-quality mesh must be used, which indicates a preference for the element meshes having acceptable shape properties.However, with an increase in the number of elements, the computational time also increases. Therefore, it is important to limit theactual number of elements. A mesh type that has eight sides (tetrahedral) is mainly believed to be acceptable and is presumed to be a

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

Table 1Mechanical properties of the SAE5160 carbon steel [13]

Properties Values

Ultimate tensile strength (MPa) 1,584Material modulus of elasticity (GPa) 207Yield strength (MPa) 1,487Fatigue strength coefficient (MPa) 2,063Fatigue strength exponent −0.08Fatigue ductility exponent −1.05Fatigue ductility coefficient 9.56Cyclic strain hardening exponent 0.05Cyclic strength coefficient (MPa) 1,940Poisson ratio 0.27

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high-quality mesh that can be used for boundary representation of the solid model. It also used to generate a detailed result. Meshingwas done by using a set of nodes to separate the geometry of the model components thereby producing smaller pieces called elements[12]. The von Mises yield criterion was then applied to all the minor portions.

Meshing of the coil spring is shown in Fig. 2. A thousand properly-shaped 4-node tetrahedrons showed effective results. Thesimulation must also considers the number of nodes since it can be conducted more efficiently and rapidly, compared to a very highnode number, to acquire similar and accurate results. Thus, based on global seeds, the analysis acquired 3,710 elements with the helpof 10,999 nodes.

Fig. 3 presents the colour contour of the stress concentration in the coil spring. In the figure, the areas having the highest amountof stress concentration is shown in red, which is followed by regions in orange, yellow, green and blue, respectively. The areas in redshowed a maximal von Mises stress value of 1.199 MPa. It could be deduced in Table 1 that the maximum stress was extremely lowwhen compared to the 1.48 GPa yield strength and this depicts that the force did not cause any deficiency to the coil spring.According to Zhu et al. [14], compressed springs usually break at the turning point which is between the bearing coil and the firstactive coil. This is as a result of the turning force because there is little or no space between the bearing coil and the primary activecoil.

Once the critical area had been identified, a strain gage was placed in that area. One more strain gage was also placed in the non-critical area, as shown in Fig. 4. The strain signals were collacted at 500 Hz [15]. After that, the vehicle must be driven on thehighway, the urban and the rural roads with speed limits of 70–80 km/h, 30–40 km/h and 20–40 km/h, respectively.

2.2. Fatigue behavior

A strain signal is commonly characterized by statistics representing its characteristics. Hence, statistical parameters are used forthe pattern monitoring and the random signal classification [16]. The statistical parameters have been applied in engineering pro-blems and are seen to be valuable indicators describing fatigue failure. They help in evaluating the randomness of a fatigue signal.Some of the commonly used statistical parameters which help in observing the strain signal behavior include standard deviation (SD),root-mean square (r.m.s.) and kurtosis.

For a signal Fj with various data n, the mean value x̄is calculated:

Fig. 2. Meshing of the coil spring.

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∑==

xn

F¯ 1

j

n

1j

(1)

The SD is a measure of how spread out the data values is around the mean. The SD for sampling data Fj that are more than 30 aredisplayed below:

∑= −=

SDn

F x1 ( ¯)j

n

1j

2

(2)

The SD for sampling data Fj that are less than 30 are also illustrated below:

∑=−

−=

SDn

F x11

( ¯)j

n

1j

2

(3)

The SD was utilized to observe the strain signal distributions. If the SD is lesser, it implies that all the marks on the dataset are

Fig. 3. Stress distributions of the coil spring.

Fig. 4. The locations of strain gage installation.

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close to the values of the mean. But if the SD is more, it implies that the target is further away from the values of the mean.r.m.s. is described as:

∑==

r m sn

F. . . 1

j

n

1j2

(4)

The r.m.s is defined as the internal oscillation energy noted for the distinctive data. When the r.m.s value is small, it indicates thatthe signal shows lower internal energy. On the other hand, a higher r.m.s indicates that the signal displays a significantly higherinternal energy.

Kurtosis is another exponential parameter that was investigated. This factor is seen to be sensitive to the pierce in data, whichimply the maximal progression in a time-series. The mathematical statement below is used to calculate the kurtosis K for the distinctdata set Fj:

∑= −=

Kn SD

F x1( )

( ¯)j

n

41

j4

(5)

The kurtosis value for the Gaussian distribution is nearer to 3.0 [17]. A kurtosis lower than 3.0 denotes a stationary data, and avalue above 3.0 represents a non-stationary data [18]. Researches were conducted on fatigue using statistical parameters, such as forestimating the cross-wind fatigue of wind-stimulated structures [17], while standard deviation was used to detect the resistance of thefracture when stressed and the toughness of polymer materials [19].

2.3. Fatigue life assessment

The precise evaluation of fatigue duration can be performed using the strain-life procedure. This procedure is used for flexiblematerials [5–6,20]. It is also dependent on the linear relationship between the stress amplitudes σ and the number of cycles Nf. [21].Hence, stress σ is depicted as:

= ′σ σ NΔ2

(2 )f fb

(6)

In the equation, Δσ is the stress range, σ'f is the fatigue strength coefficient and b is the fatigue strength exponent. The elastic strainεe is obtained by dividing Eq. (6) by the material modulus of elasticity E:

=′

εσE

N(2 )ef

fb

(7)

As the stress-life approach is applicable in the high cycle regimes, the following equation is used for representing the lineardamage rule for the low cycle regimes with regards to the plastic strain range εp:

= ′ε ε N(2 )p f fc (8)

where ε'f is the fatigue ductile coefficient and c is the fatigue ductile exponent. Thus, the total strain ε is produced as follows:

= +ε ε εe p (9)

The elastic and the plastic strains were combined to generate a relationship between the strain and the fatigue life, called theCoffin-Manson model [22–23], that can be defined as:

=′

+ ′εσE

N ε N(2 ) (2 )ff

bf f

c(10)

The fatigue nature of engineering substances is oversensitive to the mean stress [5], and it has been observed to alter the low andhigh cycle fatigue regimes [24–25]. The procedure is dependent on the mean stress impact which is examined using the Morrowmodel [26]. The Morrow model is a kind of strain-life model, and it is stated as follows:

=′ −

+ ′εσ σ

EN ε N(2 ) (2 )f

fb

f fcmean

(11)

where σmean is the mean stress. Additionally, Smith, Watson, and Topper recommended another mean stress adjustment model. TheSWT parameter [27] is expressed exponentially as:

=′

+ ′ ′ +σ εσE

N σ ε N(2 ) (2 )ff

bf f f

b cmax

22

(12)

where σmax is the maximum stress amplitude.Cumulative fatigue damage is obtained by adding the regular and sheer energy for every peak-valley in all loading. Hence, this is

affected by variable amplitude and frequency cycles. The fatigue damage for all the loading cycles Di is stated below:

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=DN1

if (13)

Afterward, the Palmgren-Miner linear cumulative fatigue damage rule [28–29] was used to calculate the cumulative fatiguedamage D of the loading, and this is stated as follows:

∑ ⎜ ⎟= ⎛⎝

⎞⎠

D nN

i

f (14)

where ni is the number of applied cycles. The fatigue damage is from 0 to 1. 0 depicts no damage or endless cycles towards failurewhile 1 depicts a failure or one sequence towards failure.

Furthermore, VAL fatigue tests were conducted to determine the life of the coil spring based on the strain signals acquired at thecritical and non-critical areas. The VAL fatigue test is performed the same way the CAL fatigue test is conducted but at differentloading levels with a particular load repeated continuously until failure occurs. The only dissimilarity is that in the CAL test, theamplitude is always unaltered. Factors like the material used, sample geometry, loading range, frequency and features of a fatiguetesting machine must be taken into consideration when conducting a VAL fatigue test [10,30–31].

Fig. 5 depicts all the fatigue testing samples that were produced per ASTM E606-92 [32]. When the fatigue cracks expand onuneven surfaces, the state of the model plays an essential part during fatigue testing. It can reduce the concentration of the stressthereby prohibiting the inception of cracks at specific points.

The strain signals were changed into stress with the aid of the Ramberg-Osgood equation [33], outlined below:

= + ′⎛⎝

⎞⎠

′

ε σE

K σE

n

(15)

where K' is the cyclic strength coefficient and n' is the cyclic strain hardening exponent. Consequently, the stress was transformed intoloads that were used as an input value in the fatigue testing device with the aid of the expression described below:

=σ PA0 (16)

where P is the applied force and A0 is the initial unloaded cross-sectional area.The reversed VAL fatigue tests were conducted using a 100 Hz frequency value. The scientists did not observe any increase in

frequency on the crack initiation. The outcome of the rates obtained from the fatigue test results was mostly low for frequencies thatwere close to 1,000 Hz [31,34–37]. The whole tests were performed at a room temperature of 20 °C [32].

3. Results and discussion

The strain signals received by the strain gauge was examined to be a VAL due to the various amplitudes that were tested by thecomponent. The signals for the 15,000 data sets lasted for 30 s and was reported and illustrated in Figs. 6–8 for the highway, urbanand rural roads, respectively. The highway road gave the lowest amplitude range. For the critical area, the strains were distributedbetween−49.9 µε and 66.3 µε; meanwhile for the non-critical area, they were distributed between−96 µε and 55.6 µε. Higher rangewas in the urban road, distributed between 40.3 µε and 214.3 µε for the critical area and between−83.7 µε and 118.2 µε for the non-critical area. The rural road, however, had the highest amplitude range. The strains for the road surface were distributed between−141.9 με and 179 με for the critical area and between −121.9 με and 203.8 με for the non-critical area. The rural road had greateramplitudes than the other roads as a result of its uneven surface.

Table 2 shows the statistical values for each signal. Except for the non-critical highway strain signal having a negative mean value

Fig. 5. A fatigue testing sample: (a) sample geometry and dimensions, (b) photograph of the sample.

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of−7.6 με, which indicated that the strain signal was compressive, the other strain signals were tensile with a mean value of 13.4 με,122.6 με, 20.1 με, 39.2 με and 41.4 με for the critical highway, the critical urban, the non-critical urban, the critical rural and the non-critical rural, respectively. Since the rural road providing a higher amplitude, it had the most substantial SD, which was 37.2 με and25.6 με for the critical and the non-critical areas, respectively, indicating that the strains were distributed far from the mean value.Meanwhile, SD for the highway road was 21.1 με and 14.7 με, and for the urban road was 18.8 με and 15.2 με.

The urban road had the largest r.m.s. The critical regions had 124.1 με while the non-critical region had 25.2 με and this impliesthat the strain signal on this road had greater vibration energy than the other roads. The r.m.s of the highway road had an r.m.s of 25με and 16.6 με, while the rural road had an r.m.s of 54.1 με and 48.7με. Furthermore, the strain signals measured at the non-criticalarea provided higher kurtosis values, which were 3.0, 5.8 and 6.8 for the highway, the urban and the rural roads, respectively;meanwhile the critical area gave a kurtosis value of 1.8, 2.3 and 3.3. Hence, the critical highway and urban roads had kurtosis below3.0 and were presumed to have stationary behavior while the rest were classified as having non-stationary behavior because theirkurtosis were more than 3.0 [17].

Table 3 summarized the fatigue results. If a material has some loads at the stress or strain level, the fatigue damage can becalculated according to the number of cycles near the failure. According to the results, the number of cycles for the critical highway,

Fig. 6. Time histories of the highway strain signal: (a) critical, (b) non-critical.

Fig. 7. Time histories of the urban strain signal: (a) critical, (b) non-critical.

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the non-critical highway, the critical urban, the non-critical urban, the critical rural and the non-critical rural strain signals was3,023, 3,013, 3,021, 2990, 3,013 and 2,907, respectively. The rural strain signal had the greatest strain amplitude that causedmaximum stress in the spring, hence the strain signals were observed to have the greatest fatigue damage, as shown in Fig. 9. Thecritical rural strain signal gave the fatigue damage of 5.19 × 10−4, 6.35 × 10−4 and 7.14 × 10−4 damage per block for the Coffin-Manson, Morrow and SWT models, respectively; meanwhile the non-critical rural strain signal gave the fatigue damage of 4.31x10−4,4.83x10−4 and 5.22x10−4 damage per block.

The critical highway strain signal provided the fatigue damage of 3.10 × 10−5, 6.03 × 10−5 and 8.25 × 10−5 damage per block;meanwhile the non-critical highway strain signal gave the fatigue damage of 2.86 × 10−5, 2.86 × 10−5 and 2.87 × 10−5 damageper block. Finally, the critical urban strain signal provided a fatigue damage of 4.16 × 10−5, 8.26 × x10−5 and 1.15 × 10−4 damageper block; meanwhile the non-critical urban strain signal gave a fatigue damage of 7.09 × 10−5, 7.87 × 10−5 and 8.45 × 10−5

damage per block. Generally, the critical areas gave higher fatigue damage, indicating that the finite element analysis performed wasaccurate.

Based the fatigue testing results, the critical highway strain signal required not less than 1,211 reversals of blocks for failure to

Fig. 8. Time histories of the rural strain signal: (a) critical, (b) non-critical.

Table 2Comparison of statistical values among the signals.

Statistical parameters Highway Urban Rural

Critical Non-critical Critical Non-critical Critical Non-critical

Mean (με) 13.4 −7.6 122.6 20.1 39.2 41.4SD (με) 21.1 14.7 18.8 15.2 37.2 25.6r.m.s. (με) 25 16.6 124.1 25.2 54.1 48.7Kurtosis 1.8 3.0 2.3 5.8 3.3 6.8

Table 3Comparison of fatigue values among the signals.

Properties Highway Urban Rural

Critical Non-critical Critical Non-critical Critical Non-critical

Number of cycles 3,023 3,013 3,021 2,990 3,013 2,907Fatigue damage (damage per block)

Coffin-Manson 3.10 × 10−5 2.86 × 10−5 4.16 × 10−5 7.09 × 10−5 5.19 × 10−4 4.31 × 10−4

Morrow 6.03 × 10−5 2.86 × 10−5 8.26 × 10−5 7.87 × 10−5 6.35 × 10−4 4.83 × 10−4

SWT 8.25 × 10−5 2.87 × 10−5 1.15 × 10−4 8.45 × 10−5 7.14 × 10−4 5.22 × 10−4

Fatigu life (reversals of blocks until failure)1,211 3,489 868 1,183 140 192

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occur within or after some time of 3,027 min. For the non-critical area, the time needed was more than 8,722 min with 3,489reversals of blocks. It indicated that the strain signal acquired at the non-critical area gave longer useful life, which was more than188%. The urban and rural roads showed similar conditions. The urban and rural roads exhibited identical features. The time used toconduct the fatigue test for the critical non-rural strain signal was about 2,169 min, with 868 reversals of blocks. The time wasincreased by 36.3% utilizing the non-critical urban strain signal, which was more than 2,957 min with 1,183 reversals of blocks.While the critical rural showed the least testing time because it had the greatest strain amplitudes. The fatigue test was performedwithin 350 min using 140 reversals of blocks. The time was increased by 36.8% or less than 480 min utilizing the non-critical ruralstrain signal, involving 192 reversals of blocks.

4. Conclusion

The current work studies the effect of the roughness of road surfaces to the life of a coil spring. Strain gages were placed in thecritical and the non-critical areas of the component and then driven the car on road surfaces at different speeds. The strain signalscollected at the critical areas provided much shorter fatigue life in comparison to the strain signals collected at the non-critical areas,which was more than 36%. There was an 88.4% increase in the durability of the spring coil in the highway road and 83.9% increasein the sustainability of the spring coil in urban road in comparison to the rural road, meanwhile the urban road gave 28.3% decreasein comparison to the highway road.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared toinfluence the work reported in this paper.

Acknowledgements

The authors would like to express their gratitude to Universitas Syiah Kuala for financial support for this research through thegrant No. 55/UN11.2/PP/SP3/2019.

Appendix A. Supplementary material

Supplementary data to this article can be found online at https://doi.org/10.1016/j.engfailanal.2020.104722.

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