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Influence of tire sizes over automobile body spectrum loads and fatigue damage accumulation
Materials and Design 67 (2015) 385–389
Contents lists available at ScienceDirect
Materials and Design journal homepage: www.elsevier.com/locate/matdes
Technical Report
Influence of tire sizes over automobile body spectrum loads and fatigue damage accumulation Clayton Mamedes Angelo a,b, Fernando Antônio Costa Machado a, Cláudio Geraldo Schön b,⇑ a b
Volkswagen do Brasil, Via Anchieta km 23.5, 09823-901 São Bernardo do Campo, SP, Brazil Department of Metallurgical and Materials Engineering, Escola Politécnica da Universidade de São Paulo, Av. Prof. Mello Moraes, 2463, 05508-900 São Paulo, SP, Brazil
a r t i c l e
i n f o
Article history: Received 18 September 2014 Accepted 29 November 2014 Available online 8 December 2014
a b s t r a c t Design specifications in automobile project and construction lead, in recent models, to the preference of using increasingly larger and slender tires. The tire and wheel set, however, is instrumental in determining the loads which act in the entire structure, in particular, in the vehicle body. The influence of different tire sizes and profiles over the load spectra obtained in a rough road test track was investigated by instrumenting fourteen points in the body of a typical passenger’s car. It is shown that increased tire sizes lead to more severe loads, which are reflected in higher damage, as estimated by the use of the linear rule. Ó 2014 Elsevier Ltd. All rights reserved.
1. Introduction Design and structure performance, in an ideal world, should work together, hand-in-hand. In the real world, however, sometimes they lead to diverging specifications to the project. This is particularly true in applications where the customers aesthetic preferences must be considered, as in the case of an automobile project. An example of this situation is found in the recent tendency to use larger tire diameter and wheels, which require a smaller tire profile due to geometric restrictions [1]. The tire/wheel set, however, is one of the most important components of the vehicle’s suspension. The tire is responsible for the contact between vehicle and ground, which may vary from a perfectly plane high speed lane, to a mud-covered rough road in a rural area of a tropical country. The tire is responsible for the transfer of load between the structure and the ground, load which is responsible for the vehicle movement (its ultimate goal). Following Gillespie [2] the main design objectives concerning the tire are: Support vertical load, while cushioning against road shocks. Develop longitudinal forces for acceleration and breaking. Develop longitudinal forces for cornering. The tire plays, therefore, a capital role in defining the structural loads (particularly the cyclic ones) which are observed in service. Changes in the tire profile will probably affect these loads, which ⇑ Corresponding author. Tel.: +55 11 3091 5726; fax: +55 11 3091 5243. E-mail addresses: [email protected] (C.M. Angelo), fernando. [email protected] (F.A. Costa Machado), [email protected] (C.G. Schön). http://dx.doi.org/10.1016/j.matdes.2014.11.060 0261-3069/Ó 2014 Elsevier Ltd. All rights reserved.
are directly responsible for the fatigue durability of the structure. To the knowledge of the authors, no systematic investigation of the dependence of automobile load spectrum on tire size and profile has been reported to date. Existing standardized automobile spectra are limited to suspension parts [3]. The aim of the present work is to perform this study and, using linear damage accumulation [4,5], discuss their prospective effect on fatigue durability in different points of a vehicle body. 2. Material and methods Fourteen points in a light passenger’s vehicle body were instrumented using unidirectional LY1 certified extensometers (Hottinger Baldwin Messtechnik GmbH, Darmstadt). The use of unidirectional extensometers is justified, since in all positions the maximum principal stress direction is known. The positions were grouped into three areas, two critical and one non-critical (for control), which were grouped by position (left or right) in the vehicle body frame. The selected critical positions were the rear door area and the rear side members (rear axle attachment points). As a noncritical position, the rear fuel tank bracket was selected. Table 1 lists the measurement points and their respective position. Details of the precise positioning of the extensometers can be found in Ref. [6]. The vehicle was loaded with 80% of its nominal capacity, corresponding to 720 kg in the front axle, 582 kg in the rear axle (total load: 1302 kg) and was mounted with four different wheel/tire configurations, which are listed in Table 2. The tire size is indicated following international standards (in Brazil, ABNT NBR NM 250 [7]. For example, tire P 185/75 R14 identifies a tire used in personal vehicles (P) with 185 mm outer diameter, 75% aspect ratio (the
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Damage, D was measured using the Pålmgren–Miner’s rule [8] which states that:
Table 1 Measuring point positioning in the car body frame. Point
Position
Side
1–3 4–7 8–10 11–12 13–14
Rear door area Fuel tank bracket Rear door area Rear side members Rear side members
Left – Right Left Right
Table 2 Tire sizes and pressure settings used for the experiments. Values in parenthesis are given in PSI. Configuration
Tire pressure [kPa] Front
175/75 195/55 195/50 205/45
R14 R15 R16 R16
227.5 213.7 213.7 213.7
Rear (33) (31) (31) (31)
241.3 248.2 248.2 241.3
(35) (36) (36) (35)
ratio between width and height in the visco-elastic torus), with radial construction, mounted in a 14 inches wheel rim [6]. After instrumentation, the vehicle, mounted with each tire configuration, was conducted over a controlled proving track with a rough road. All subsequent measurements were performed with the same vehicle and in the same track, with controlled speed for each road section. The same steel is used in all measured points. For the purpose of damage quantification, it is assumed that its S-N curve is defined by a Basquin equation with exponent m = 3 and a definite fatigue limit (N f = 2 106) of rf = 70 MPa.
3. Results and discussion Fig. 1 shows examples of the acquired spectra, corresponding to point 12 from Table 1, as a function of tire size. The spectra of the remaining points show similar qualitative features. The spectra are composed by blocks of intense cyclic stresses, intermixed with relatively calm regions. These spectra are also qualitatively similar to the ones measured in other automotive parts, as reported by Zakaria et al. [9] in the case of the engine mount bracket of a passenger’s vehicle and by Kadhim et al. [10] in the case of as lower suspension arm. Petracconi et al. [11] also instrumented a tow hook assembly of a passenger’s vehicle, obtaining a spectrum with qualitative similarities to the ones obtained in the present work. The standardized CARLOS spectra, on the other hand, show similar behavior as the ones obtained in the present work, but without the calm regions [12,13]. By visible inspection, one observes that the spectra are affected by the tire size, in the sense that larger tire diameters lead to more severe cyclic stresses (more numerous peak stress events). The presented spectra correspond to the raw acquired data, for meaningful usage in testing these data need to be edited [14–17].
150
175/75R14
100
100
50
50
0
ð1Þ
Ni
where summation in i runs over the classes of an histogram compiled using the rainflow technique, based on the measured spectra, ni corresponds to the number of cycles observed for the given class, and Ni corresponds to the prediction of the number of cycles for fracture using the adopted Basquin equation.
195/55R15
0
-50
-50
-100
-100
-150
-150 0
250
500
750 1000 1250 1500 1750
0
250
500
750
1000 1250 1500
time [s]
time [s]
(a)
(b)
150
150
195/50R16
100
100
50
50
σ [MPa]
σ [MPa]
X ni i
σ [MPa]
σ [MPa]
150
D¼
0
0
-50
-50
-100
-100
-150
205/45R16
-150 0
250
500
750
1000 1250 1500
0
250
500
750
1000 1250 1500
time [s]
time [s]
(c)
(d)
Fig. 1. Examples of vehicle body spectra acquired in Point 12 (rear side members, left, see Table 1) as a function of the different tire sizes: (a) 175/75R14, (b) 195/55R15, (c) 195/50R16 and (d) 205/45R16.
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stress amplitude [MPa]
50
175/75R14 195/50R16 195/55R15 205/45R16
40 30 20 10 0 0
10
20
30
40
50
60
frequency [Hz] Fig. 2. Spectral analysis of the signals shown in Figs. 1(a– d), measuring point 12 (rear side members, left).
The spectral analysis of the signal (Fig. 2) shows that the different tire sizes do not affect significantly the vibrations modes of the structure. The spectra are dominated by a single broad vibration mode around 19 Hz, which corresponds to most of the large intensity load cycles, a second, weaker, mode can be observed around 35 Hz, which presents slightly more intense cycles for the tires with 195 mm diameter. Fig. 3 shows the load cycle histograms obtained using the rainflow counting technique for sample measuring points in the vehicle body structure. In general the histograms show similar
300
14
200 150 100
1000
10000 100000 1e+06
8 6
Point 4
1e+07
fuel tank bracket
0 100
1e+08
(a)
(b) 300
175/70R14 195/55R15 195/50R16 205/45R16
Δσ [MPa]
100
1e+08
200 150 100 50
Point 8
1e+07
175/70R14 195/55R15 195/50R16 205/45R16
250
150
rear door area, right
1000
10000 100000 1e+06
# cycles
200
0 100
1000
# cycles
250
Δσ [MPa]
10
2
300
50
12
4 Point 1
rear door area, left
0 100
175/70R14 195/55R15 195/50R16 205/45R16
16
Δσ [MPa]
Δσ [MPa]
18
175/70R14 195/55R15 195/50R16 205/45R16
250
50
qualitative features, in with number of cycles and stress amplitude are related approximately by an inverse exponential rule (less severe amplitudes are exponentially more frequent). In all cases, the stress amplitudes corresponding to tire 175/75R14 are less severe than the ones obtained with the other tire sizes. The differences are more subtle when comparing tires 195/55R15 and 195/ 50R16 with tire 205/45R16, with the later presenting more severe, but infrequent, stress peaks. Regarding the different positions, one observes that the critical positions (points 1, 8 and 12) show larger stress amplitudes. The fuel tank bracket (point 4), as an example of a non-critical region, show considerably weaker stress cycles. A certain degree of asymmetry is observed in the loading of the structure, as represented by the comparison between measuring points 1 and 8. This effect is expected due to the asymmetry of the own structure (for example, the position of the fuel tank) and of the track. Fig. 4 shows the compilations of relative damage data for the points which belong to the rear door area (left, points 1–3 and right, points 8–10). In this figure, and in the following, the damage is represented with reference to the case of tire 195/50R15. A clear trend is observed in all points, with the largest relative damage observed for the 205/45R16 tire and the smallest relative damage for the tire 175/75R14. Tire 195/55R16 shows slightly higher relative damage, compared with tire 195/50R15, which is, however, intermediate to both extreme cases. Point 2 is a special case, and results in larger relative damage for the 195/55R16 tire. The asymmetry in the structure loading is remarkable, especially for the case of the 205/45R16 tire.
Point 12
rear side member, left
10000 100000 1e+06
1e+07
1e+08
0 100
1000
10000 100000 1e+06
# cycles
# cycles
(c)
(d)
1e+07
1e+08
Fig. 3. Sample stress amplitude histograms calculated using the rainflow technique in positions: (a) point 1 – rear door area, left, (b) point 4 – fuel tank bracket, (c) point 8 – rear door area, right and (d) point 12 – rear side members, left. Notice the different stress scale in (b).
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250
205/45R16 195/55R16 195/50R15 175/75R14
relative damage
200 150
left
right
100 50 0 Point 1 Point 2 Point 3 Point 8 Point 9 Point 10
Measuring point Fig. 4. Compilation of relative damage data for the points corresponding to the rear door area (left side, points 1–3 and right side, points 8–10).
relative damage
250 200
205/45R16 195/55R16 195/50R15 175/75R14
150
left
right
100 50
Finally, Fig. 6 shows the compilation of relative damage data for the fuel tank bracket region. In this case the trend is not confirmed for the 205/45R16 and 175/75R14 tires at all points and the situation is more complex for the comparison between tires 195/55R16 and 195/50R15, in which the severity relation is inverted (for points 4, 5, and 6). One has to remind that the overall stress levels in this region are much smaller than in the other regions of the vehicle body (corresponding to the fact that the fuel tank bracket is not a critical region for structural integrity). In spite of the limitations of the linear rule [8], the present results suggest that tire size and geometry has an impact in the development of the cyclic loads in the vehicle body structure and that, in particular, the present design tendency of using larger and more slender tires result in more severe loads in the structure. It is not possible to state that the structural reliability of these vehicle bodies is jeopardized by this substitution, variable amplitude fatigue experiments using the present spectra would be needed to test this hypothesis, but the use of 205/45R16 tires result, certainly, in more severe damage compared with the 175/75R14 case. For instance, Zakaria et al. [18] recently investigated load sequence effects in the fatigue durability of an engine mount bracket of a passenger’s vehicle, concluding that fatigue life of the investigated part is significantly affected by the use of different load sequences. It would also be worthwhile to crosscheck the present results with analytical or numerical models, to investigate the influence of tire stiffness and mass upon the developed structural vibration modes. Spinelli et al. [19] recently discussed the interplay between finite element modeling and physical tests for vehicle project validation. Also, a classification of the load events as the one recently introduced by Yunoh et al. [20] could be attempted.
0 Point 11
Point 12
Point 13
Point 14
Measuring point Fig. 5. Compilation of relative damage data for the points corresponding to the rear side members (left, points 11 and 12 and right, points 13 and 14).
250
relative damage
200
205/45R16 195/55R16 195/50R15 175/75R14
150 100 50 0 Point 4
Point 5
Point 6
Point 7
Measuring point Fig. 6. Compilation of relative damage data for the points corresponding to the fuel tank bracket (points 4–7).
Fig. 5 shows the compilation of relative damage data for the points which belong to the rear side members (left, points 11 and 12 and right, points 13 and 14). The same trend observed in the case of the rear door area is observed here, with the most severe relative damage occurring for the case of the 205/45R16 tire and the least severe relative damage occurring for the 175/75R14 tire. In this case, however, tire 195/55R16 shows relative damage levels similar to the 205/45R16 tire, differing from the relative damage observed for the 195/50R15 tire.
4. Conclusions The cyclic load spectra of a passenger’s vehicle body running a rough testing track have been measured for the case of four different wheel and tires sets, in fourteen points in the structure (ten in critical positions and four in non-critical positions). The results show that all spectra present similar qualitative features, mixing periods of relative calm and periods of extreme cyclic perturbations. The spectral analysis shows a single broad peak around 19 Hz, which contains most of the more intense cyclic loads and a secondary peak around 35 Hz, which shows a varying importance in function of the selected tire sizes. The measured spectra, after compilation using the rainflow counting technique, result in qualitative similar stress amplitude histograms, which show an approximate inverse exponential dependence of the cyclic stress levels and the number of cycles. In all cases, however, it is observed that the 175/75R14 tire leads to less severe cycles. The remaining tire sizes show similar cyclic load distributions, and the differences are concentrated in the less frequent large amplitude cycles, which are more severe for the case of the 205/45R16 tire compared with the 195/50R16 and 195/ 55R15 tires. A damage estimation using the linear rule confirms that the cyclic load severity is larger in the case of tire 205/45R16, followed by the 195/50R16 tire, then by the 195/55R15 tire and, finally, by the 175/75R14 tire in the critical positions. The situation in the non-critical positions is less obvious, but still, it is consistent with a picture in which fatigue damage in the vehicle body increases when larger tires are used. Acknowledgments This work has been financially supported by the Brazilian National Research Council (CNPq, Brasília-DF, Brazil), and by the
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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES, Brasília-DF, Brasil). The support by Volkswagen do Brasil SA, in the form of measurements, is gratefully acknowledged. References [1] de Paula M. Design disaster: three ways cars are getting worse. Forbes Mag 2011 [date accessed 25.11.14] [date accessed 25.11.14]. [8] Schijve J. Fatigue of structures and materials in the 20th century and the state of the art. Int J Fatigue 2003;25:679–702. [9] Zakaria KA, Abdullah S, Ghazali MJ. Comparative study of fatigue life behavior of AA6061 and AA7075 alloys under spectrum loadings. Mater Des 2013;49:48–57.
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[10] Kadhim NA, Abdullah S, Ariffin AK. Effect of fatigue data editing technique associated with finite element analysis on the component fatigue design period. Mater Des 2011;32:1020–30. [11] Petracconi CL, Ferreira SE, Palma ES. Fatigue life simulation of a rear tow hook assembly of a passenger car. Eng Fail Anal 2010;17:455–63. [12] Sander M, Richard HA. Fatigue crack growth under variable amplitude loading. Part I: Experimental investigation. Fatigue Fract Eng Mater Struct 2006;29:291–301. [13] Heuler P, Frost M, Rochlitz H. Ansätze zur Lastannahme für die PKWBetriebsfestigkeitauslegung. Mater Werkst 2011;42(4):279–88. [14] Stephens RI, Dindinger PM, Gunger JE. Fatigue damage editing for accelerated durability testing using strain range and SWT parameter criteria. Int J Fatigue 1997;19:599–606. [15] Oh CS. Application of wavelet transform in fatigue history editing. Int J Fatigue 2001;23:241–50. [16] Abdullah S, Choi JC, Giacomin JA, Yates JR. Bump extraction algorithm for variable amplitude fatigue loading. Int J Fatigue 2006;28:675–91. [17] Shafiullah AKM, Wu CQ. Generation and validation of loading profiles for highly accelerated durability tests of ground vehicle components. Eng Fail Anal 2013;33:1–16. [18] Zakaria KA, Abdullah S, Ghazali MJ, Azhari CH. Influence of spectrum loading sequences of fatigue life in a high-temperature environment. Eng Fail Anal 2013;30:111–23. [19] Spinelli DM, Scozzafave CC, Spinelli D, Bose Filho WW. From numerical simulations to materials testing homologation: a biaxial fatigue reliability prediction for structural components. Mater Charact 2013;16(6):1237–45. [20] Yunoh MFM, Abdullah S, Nopiah ZM, Nuawi MZ, Ismail N. Fatigue feature classification for automotive strain data. IOP Conf Ser Mater Sci Eng 2012;36:012031.
Contents lists available at ScienceDirect
Materials and Design journal homepage: www.elsevier.com/locate/matdes
Technical Report
Influence of tire sizes over automobile body spectrum loads and fatigue damage accumulation Clayton Mamedes Angelo a,b, Fernando Antônio Costa Machado a, Cláudio Geraldo Schön b,⇑ a b
Volkswagen do Brasil, Via Anchieta km 23.5, 09823-901 São Bernardo do Campo, SP, Brazil Department of Metallurgical and Materials Engineering, Escola Politécnica da Universidade de São Paulo, Av. Prof. Mello Moraes, 2463, 05508-900 São Paulo, SP, Brazil
a r t i c l e
i n f o
Article history: Received 18 September 2014 Accepted 29 November 2014 Available online 8 December 2014
a b s t r a c t Design specifications in automobile project and construction lead, in recent models, to the preference of using increasingly larger and slender tires. The tire and wheel set, however, is instrumental in determining the loads which act in the entire structure, in particular, in the vehicle body. The influence of different tire sizes and profiles over the load spectra obtained in a rough road test track was investigated by instrumenting fourteen points in the body of a typical passenger’s car. It is shown that increased tire sizes lead to more severe loads, which are reflected in higher damage, as estimated by the use of the linear rule. Ó 2014 Elsevier Ltd. All rights reserved.
1. Introduction Design and structure performance, in an ideal world, should work together, hand-in-hand. In the real world, however, sometimes they lead to diverging specifications to the project. This is particularly true in applications where the customers aesthetic preferences must be considered, as in the case of an automobile project. An example of this situation is found in the recent tendency to use larger tire diameter and wheels, which require a smaller tire profile due to geometric restrictions [1]. The tire/wheel set, however, is one of the most important components of the vehicle’s suspension. The tire is responsible for the contact between vehicle and ground, which may vary from a perfectly plane high speed lane, to a mud-covered rough road in a rural area of a tropical country. The tire is responsible for the transfer of load between the structure and the ground, load which is responsible for the vehicle movement (its ultimate goal). Following Gillespie [2] the main design objectives concerning the tire are: Support vertical load, while cushioning against road shocks. Develop longitudinal forces for acceleration and breaking. Develop longitudinal forces for cornering. The tire plays, therefore, a capital role in defining the structural loads (particularly the cyclic ones) which are observed in service. Changes in the tire profile will probably affect these loads, which ⇑ Corresponding author. Tel.: +55 11 3091 5726; fax: +55 11 3091 5243. E-mail addresses: [email protected] (C.M. Angelo), fernando. [email protected] (F.A. Costa Machado), [email protected] (C.G. Schön). http://dx.doi.org/10.1016/j.matdes.2014.11.060 0261-3069/Ó 2014 Elsevier Ltd. All rights reserved.
are directly responsible for the fatigue durability of the structure. To the knowledge of the authors, no systematic investigation of the dependence of automobile load spectrum on tire size and profile has been reported to date. Existing standardized automobile spectra are limited to suspension parts [3]. The aim of the present work is to perform this study and, using linear damage accumulation [4,5], discuss their prospective effect on fatigue durability in different points of a vehicle body. 2. Material and methods Fourteen points in a light passenger’s vehicle body were instrumented using unidirectional LY1 certified extensometers (Hottinger Baldwin Messtechnik GmbH, Darmstadt). The use of unidirectional extensometers is justified, since in all positions the maximum principal stress direction is known. The positions were grouped into three areas, two critical and one non-critical (for control), which were grouped by position (left or right) in the vehicle body frame. The selected critical positions were the rear door area and the rear side members (rear axle attachment points). As a noncritical position, the rear fuel tank bracket was selected. Table 1 lists the measurement points and their respective position. Details of the precise positioning of the extensometers can be found in Ref. [6]. The vehicle was loaded with 80% of its nominal capacity, corresponding to 720 kg in the front axle, 582 kg in the rear axle (total load: 1302 kg) and was mounted with four different wheel/tire configurations, which are listed in Table 2. The tire size is indicated following international standards (in Brazil, ABNT NBR NM 250 [7]. For example, tire P 185/75 R14 identifies a tire used in personal vehicles (P) with 185 mm outer diameter, 75% aspect ratio (the
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Damage, D was measured using the Pålmgren–Miner’s rule [8] which states that:
Table 1 Measuring point positioning in the car body frame. Point
Position
Side
1–3 4–7 8–10 11–12 13–14
Rear door area Fuel tank bracket Rear door area Rear side members Rear side members
Left – Right Left Right
Table 2 Tire sizes and pressure settings used for the experiments. Values in parenthesis are given in PSI. Configuration
Tire pressure [kPa] Front
175/75 195/55 195/50 205/45
R14 R15 R16 R16
227.5 213.7 213.7 213.7
Rear (33) (31) (31) (31)
241.3 248.2 248.2 241.3
(35) (36) (36) (35)
ratio between width and height in the visco-elastic torus), with radial construction, mounted in a 14 inches wheel rim [6]. After instrumentation, the vehicle, mounted with each tire configuration, was conducted over a controlled proving track with a rough road. All subsequent measurements were performed with the same vehicle and in the same track, with controlled speed for each road section. The same steel is used in all measured points. For the purpose of damage quantification, it is assumed that its S-N curve is defined by a Basquin equation with exponent m = 3 and a definite fatigue limit (N f = 2 106) of rf = 70 MPa.
3. Results and discussion Fig. 1 shows examples of the acquired spectra, corresponding to point 12 from Table 1, as a function of tire size. The spectra of the remaining points show similar qualitative features. The spectra are composed by blocks of intense cyclic stresses, intermixed with relatively calm regions. These spectra are also qualitatively similar to the ones measured in other automotive parts, as reported by Zakaria et al. [9] in the case of the engine mount bracket of a passenger’s vehicle and by Kadhim et al. [10] in the case of as lower suspension arm. Petracconi et al. [11] also instrumented a tow hook assembly of a passenger’s vehicle, obtaining a spectrum with qualitative similarities to the ones obtained in the present work. The standardized CARLOS spectra, on the other hand, show similar behavior as the ones obtained in the present work, but without the calm regions [12,13]. By visible inspection, one observes that the spectra are affected by the tire size, in the sense that larger tire diameters lead to more severe cyclic stresses (more numerous peak stress events). The presented spectra correspond to the raw acquired data, for meaningful usage in testing these data need to be edited [14–17].
150
175/75R14
100
100
50
50
0
ð1Þ
Ni
where summation in i runs over the classes of an histogram compiled using the rainflow technique, based on the measured spectra, ni corresponds to the number of cycles observed for the given class, and Ni corresponds to the prediction of the number of cycles for fracture using the adopted Basquin equation.
195/55R15
0
-50
-50
-100
-100
-150
-150 0
250
500
750 1000 1250 1500 1750
0
250
500
750
1000 1250 1500
time [s]
time [s]
(a)
(b)
150
150
195/50R16
100
100
50
50
σ [MPa]
σ [MPa]
X ni i
σ [MPa]
σ [MPa]
150
D¼
0
0
-50
-50
-100
-100
-150
205/45R16
-150 0
250
500
750
1000 1250 1500
0
250
500
750
1000 1250 1500
time [s]
time [s]
(c)
(d)
Fig. 1. Examples of vehicle body spectra acquired in Point 12 (rear side members, left, see Table 1) as a function of the different tire sizes: (a) 175/75R14, (b) 195/55R15, (c) 195/50R16 and (d) 205/45R16.
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stress amplitude [MPa]
50
175/75R14 195/50R16 195/55R15 205/45R16
40 30 20 10 0 0
10
20
30
40
50
60
frequency [Hz] Fig. 2. Spectral analysis of the signals shown in Figs. 1(a– d), measuring point 12 (rear side members, left).
The spectral analysis of the signal (Fig. 2) shows that the different tire sizes do not affect significantly the vibrations modes of the structure. The spectra are dominated by a single broad vibration mode around 19 Hz, which corresponds to most of the large intensity load cycles, a second, weaker, mode can be observed around 35 Hz, which presents slightly more intense cycles for the tires with 195 mm diameter. Fig. 3 shows the load cycle histograms obtained using the rainflow counting technique for sample measuring points in the vehicle body structure. In general the histograms show similar
300
14
200 150 100
1000
10000 100000 1e+06
8 6
Point 4
1e+07
fuel tank bracket
0 100
1e+08
(a)
(b) 300
175/70R14 195/55R15 195/50R16 205/45R16
Δσ [MPa]
100
1e+08
200 150 100 50
Point 8
1e+07
175/70R14 195/55R15 195/50R16 205/45R16
250
150
rear door area, right
1000
10000 100000 1e+06
# cycles
200
0 100
1000
# cycles
250
Δσ [MPa]
10
2
300
50
12
4 Point 1
rear door area, left
0 100
175/70R14 195/55R15 195/50R16 205/45R16
16
Δσ [MPa]
Δσ [MPa]
18
175/70R14 195/55R15 195/50R16 205/45R16
250
50
qualitative features, in with number of cycles and stress amplitude are related approximately by an inverse exponential rule (less severe amplitudes are exponentially more frequent). In all cases, the stress amplitudes corresponding to tire 175/75R14 are less severe than the ones obtained with the other tire sizes. The differences are more subtle when comparing tires 195/55R15 and 195/ 50R16 with tire 205/45R16, with the later presenting more severe, but infrequent, stress peaks. Regarding the different positions, one observes that the critical positions (points 1, 8 and 12) show larger stress amplitudes. The fuel tank bracket (point 4), as an example of a non-critical region, show considerably weaker stress cycles. A certain degree of asymmetry is observed in the loading of the structure, as represented by the comparison between measuring points 1 and 8. This effect is expected due to the asymmetry of the own structure (for example, the position of the fuel tank) and of the track. Fig. 4 shows the compilations of relative damage data for the points which belong to the rear door area (left, points 1–3 and right, points 8–10). In this figure, and in the following, the damage is represented with reference to the case of tire 195/50R15. A clear trend is observed in all points, with the largest relative damage observed for the 205/45R16 tire and the smallest relative damage for the tire 175/75R14. Tire 195/55R16 shows slightly higher relative damage, compared with tire 195/50R15, which is, however, intermediate to both extreme cases. Point 2 is a special case, and results in larger relative damage for the 195/55R16 tire. The asymmetry in the structure loading is remarkable, especially for the case of the 205/45R16 tire.
Point 12
rear side member, left
10000 100000 1e+06
1e+07
1e+08
0 100
1000
10000 100000 1e+06
# cycles
# cycles
(c)
(d)
1e+07
1e+08
Fig. 3. Sample stress amplitude histograms calculated using the rainflow technique in positions: (a) point 1 – rear door area, left, (b) point 4 – fuel tank bracket, (c) point 8 – rear door area, right and (d) point 12 – rear side members, left. Notice the different stress scale in (b).
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250
205/45R16 195/55R16 195/50R15 175/75R14
relative damage
200 150
left
right
100 50 0 Point 1 Point 2 Point 3 Point 8 Point 9 Point 10
Measuring point Fig. 4. Compilation of relative damage data for the points corresponding to the rear door area (left side, points 1–3 and right side, points 8–10).
relative damage
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205/45R16 195/55R16 195/50R15 175/75R14
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Finally, Fig. 6 shows the compilation of relative damage data for the fuel tank bracket region. In this case the trend is not confirmed for the 205/45R16 and 175/75R14 tires at all points and the situation is more complex for the comparison between tires 195/55R16 and 195/50R15, in which the severity relation is inverted (for points 4, 5, and 6). One has to remind that the overall stress levels in this region are much smaller than in the other regions of the vehicle body (corresponding to the fact that the fuel tank bracket is not a critical region for structural integrity). In spite of the limitations of the linear rule [8], the present results suggest that tire size and geometry has an impact in the development of the cyclic loads in the vehicle body structure and that, in particular, the present design tendency of using larger and more slender tires result in more severe loads in the structure. It is not possible to state that the structural reliability of these vehicle bodies is jeopardized by this substitution, variable amplitude fatigue experiments using the present spectra would be needed to test this hypothesis, but the use of 205/45R16 tires result, certainly, in more severe damage compared with the 175/75R14 case. For instance, Zakaria et al. [18] recently investigated load sequence effects in the fatigue durability of an engine mount bracket of a passenger’s vehicle, concluding that fatigue life of the investigated part is significantly affected by the use of different load sequences. It would also be worthwhile to crosscheck the present results with analytical or numerical models, to investigate the influence of tire stiffness and mass upon the developed structural vibration modes. Spinelli et al. [19] recently discussed the interplay between finite element modeling and physical tests for vehicle project validation. Also, a classification of the load events as the one recently introduced by Yunoh et al. [20] could be attempted.
0 Point 11
Point 12
Point 13
Point 14
Measuring point Fig. 5. Compilation of relative damage data for the points corresponding to the rear side members (left, points 11 and 12 and right, points 13 and 14).
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205/45R16 195/55R16 195/50R15 175/75R14
150 100 50 0 Point 4
Point 5
Point 6
Point 7
Measuring point Fig. 6. Compilation of relative damage data for the points corresponding to the fuel tank bracket (points 4–7).
Fig. 5 shows the compilation of relative damage data for the points which belong to the rear side members (left, points 11 and 12 and right, points 13 and 14). The same trend observed in the case of the rear door area is observed here, with the most severe relative damage occurring for the case of the 205/45R16 tire and the least severe relative damage occurring for the 175/75R14 tire. In this case, however, tire 195/55R16 shows relative damage levels similar to the 205/45R16 tire, differing from the relative damage observed for the 195/50R15 tire.
4. Conclusions The cyclic load spectra of a passenger’s vehicle body running a rough testing track have been measured for the case of four different wheel and tires sets, in fourteen points in the structure (ten in critical positions and four in non-critical positions). The results show that all spectra present similar qualitative features, mixing periods of relative calm and periods of extreme cyclic perturbations. The spectral analysis shows a single broad peak around 19 Hz, which contains most of the more intense cyclic loads and a secondary peak around 35 Hz, which shows a varying importance in function of the selected tire sizes. The measured spectra, after compilation using the rainflow counting technique, result in qualitative similar stress amplitude histograms, which show an approximate inverse exponential dependence of the cyclic stress levels and the number of cycles. In all cases, however, it is observed that the 175/75R14 tire leads to less severe cycles. The remaining tire sizes show similar cyclic load distributions, and the differences are concentrated in the less frequent large amplitude cycles, which are more severe for the case of the 205/45R16 tire compared with the 195/50R16 and 195/ 55R15 tires. A damage estimation using the linear rule confirms that the cyclic load severity is larger in the case of tire 205/45R16, followed by the 195/50R16 tire, then by the 195/55R15 tire and, finally, by the 175/75R14 tire in the critical positions. The situation in the non-critical positions is less obvious, but still, it is consistent with a picture in which fatigue damage in the vehicle body increases when larger tires are used. Acknowledgments This work has been financially supported by the Brazilian National Research Council (CNPq, Brasília-DF, Brazil), and by the
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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES, Brasília-DF, Brasil). The support by Volkswagen do Brasil SA, in the form of measurements, is gratefully acknowledged. References [1] de Paula M. Design disaster: three ways cars are getting worse. Forbes Mag 2011 [date accessed 25.11.14]
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[10] Kadhim NA, Abdullah S, Ariffin AK. Effect of fatigue data editing technique associated with finite element analysis on the component fatigue design period. Mater Des 2011;32:1020–30. [11] Petracconi CL, Ferreira SE, Palma ES. Fatigue life simulation of a rear tow hook assembly of a passenger car. Eng Fail Anal 2010;17:455–63. [12] Sander M, Richard HA. Fatigue crack growth under variable amplitude loading. Part I: Experimental investigation. Fatigue Fract Eng Mater Struct 2006;29:291–301. [13] Heuler P, Frost M, Rochlitz H. Ansätze zur Lastannahme für die PKWBetriebsfestigkeitauslegung. Mater Werkst 2011;42(4):279–88. [14] Stephens RI, Dindinger PM, Gunger JE. Fatigue damage editing for accelerated durability testing using strain range and SWT parameter criteria. Int J Fatigue 1997;19:599–606. [15] Oh CS. Application of wavelet transform in fatigue history editing. Int J Fatigue 2001;23:241–50. [16] Abdullah S, Choi JC, Giacomin JA, Yates JR. Bump extraction algorithm for variable amplitude fatigue loading. Int J Fatigue 2006;28:675–91. [17] Shafiullah AKM, Wu CQ. Generation and validation of loading profiles for highly accelerated durability tests of ground vehicle components. Eng Fail Anal 2013;33:1–16. [18] Zakaria KA, Abdullah S, Ghazali MJ, Azhari CH. Influence of spectrum loading sequences of fatigue life in a high-temperature environment. Eng Fail Anal 2013;30:111–23. [19] Spinelli DM, Scozzafave CC, Spinelli D, Bose Filho WW. From numerical simulations to materials testing homologation: a biaxial fatigue reliability prediction for structural components. Mater Charact 2013;16(6):1237–45. [20] Yunoh MFM, Abdullah S, Nopiah ZM, Nuawi MZ, Ismail N. Fatigue feature classification for automotive strain data. IOP Conf Ser Mater Sci Eng 2012;36:012031.