- Email: [email protected]
The prediction methodology for tire’s high speed durability regulation test using a finite element method
Accepted Manuscript The prediction methodology for tire’s high speed durability regulation test using a finite element method Seongrae Kim, Hanseok Park, Byungwoo Moon, Kideug Sung, Jae-Mean Koo, Chang-Sung Seok PII: DOI: Reference:
S0142-1123(18)30460-2 https://doi.org/10.1016/j.ijfatigue.2018.08.036 JIJF 4832
To appear in:
International Journal of Fatigue
Received Date: Revised Date: Accepted Date:
17 June 2018 16 August 2018 29 August 2018
Please cite this article as: Kim, S., Park, H., Moon, B., Sung, K., Koo, J-M., Seok, C-S., The prediction methodology for tire’s high speed durability regulation test using a finite element method, International Journal of Fatigue (2018), doi: https://doi.org/10.1016/j.ijfatigue.2018.08.036
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
The prediction methodology for tire’s high speed durability regulation test using a finite element method Seongrae Kim1, Hanseok Park1, Byungwoo Moon2, Kideug Sung1, Jae-Mean Koo2, ChangSung Seok2* 1
2
R&D Center, Nexen Tire Corporation, Yangsan, Gyeongnam 626-230, Korea School of Mechanical Engineering, Sungkyunkwan University, Suwon, Gyeonggi 440-746, Korea
ABSTRACT In the tire industry, indoor accelerated life tests as regulations have been performed to ensure tire durability performances instead of outdoor field test. The finite element method has been widely used to minimize real test time and cost, but prediction method for accelerated life test had hardly been made in the past. This study presents a rational methodology to predict the tire’s failure life at the steel belt edge region due to high speed regulation test. Based on the finite element analysis and fatigue characteristic of rubber material, a method to determine exact failure time is proposed. The steady-state rolling analysis by FEM to get strain energy density range(∆SED) at the steel belt edge region and fatigue test of rubber compound to obtain ∆SED- number of cycle(Nf) curve were used. The reliability of proposed prediction method was verified by real indoor test.
1. INTRODUCTION After the invention of a tire, the initial purpose of the development has focused on safety and long mileage, but in order to improve the vehicle's performance due to various performance requirements for use, the tire has been developed with a very complicated structure. The durability of the tire performance is one of the most important performances metric in terms of the vehicle's protection and passenger’s safety, so it should be a top priority during tire development. Fig. 1 shows the typical structure of the radial tire. Recently, as energy and environment problems are emerging as global issues, studies on vehicle’s energy source and fuel efficiency have been performed actively. In the view point of the vehicle, the development of hybrid and electric vehicle has been expanded, and in the viewpoint of the tire, the design to minimize rolling resistance related to vehicle’s fuel efficiency has been required. However, electric and hybrid vehicles have relatively high weight due to battery and an additional source of power comparing to the general passenger car, while tires decrease weight to minimize rolling resistance. Because of these trends on the durability of a tire work as conflicting conditions, in recent years, tire durability issues has been magnified in the tire industry. The durability test in normal driving condition is very difficult and time-consuming task. Generally, tires have longer lifetime by failure than that of tread wear, and field test cannot ensure driver’s safety, so failure test under normal vehicle driving condition is almost impossible. Thus, to simulate tire's failure mode by the indoor test, each group and country such as Economic Commission for Europe(ECE) in the European countries and the Federal Motor Vehicle Safety Standards(FMVSS) in North America have regulations for accelerated life test, and it has been used as a essential test in order to export tires.1-2 This indoor accelerated life test has been used as a substitute for durability test in the field. Among regulation accelerated life tests, high speed durability test is performed to simulate fatigue failure at the steel belt edge region as shown in Fig. 2 by increasing driving speed under constant load until tire's failure. The prediction of tire's performances using a finite element analysis has been widely used to *Corresponding author. Email : [email protected]
minimize the test time and cost and to increase developer’s degrees of freedom. The previous research on prediction methods for the tire’s durability using a finite element analysis has simply used stress, strain, and energy under static or dynamic state, 3-4 or predicted real life under normal driving condition by combining fracture mechanics.5-7 However, generally, tire developers have referred regulation test results than tire's absolute lifetime in the field, so the necessity of prediction method to simulate accelerated life test has been emerged recently. Therefore, this study presents a new prediction methodology to judge acceptance or refusal for the high speed durability regulation test using a finite element method, fatigue life equation of rubber compound, and regulation test procedure.
Fig. 1 The structure of radial tire
Fig. 2 Steel belt edge crack example
2. THE REGULATION TEST METHOD OF HIGH SPEED DURABILITY LIFE 2.1 ECE R30 Test Method The high speed durability regulation test is a representative indoor accelerated life test to simulate fatigue failure at the steel belt edge region, and there are various test methods as required for each country such as ECE R30 and FMVSS109. 1-2 However, the basic test method that increases driving speed in accordance with the test step under a constant load is the same for all test regulations, but according to test methods, inflation pressure, load, and cycle of increasing speed are different due to tire's speed symbol. Fig. 3 shows a high speed driving test machine used for regulation tests. In this study, among the regulation test methods of high speed durability, the ECE R30 test method that is most commonly used with FMVSS109 was used to predict the tire's regulation life.
Fig. 3 AKRON high speed test machine
*Corresponding author. Email : [email protected]
2.2 Failure Mechanism of High Speed Durability The roles of steel belt have largely classified two kinds. The first role is to protect the body ply from external impact, and the second role is to enhance the stability by making the contact area wide between the road and tread surfaces. However, in terms of structural safety, a steel belt is able to protect the inside of the tire from external impact, but has a very weak structure at the steel belt edge region due to several reasons such as delamination between composite materials, local stress concentration in the stiffness discontinuity point and the inter-laminar shear strains to develop in the circumferential direction between cross-laminated steel belt layers with opposite cords angles as shown in Fig. 4.8 Under normal driving conditions, after an effective crack initiates, the crack propagation life until failure accounts for most of the tire's durability because it is assumed fatigue problem under constant load or deformation.6 However, under the high speed endurance test that increases the driving speed, since driving times in the each speed step are not much longer than those in the normal state, once an effective initial crack initiates, it does not take a long time until failure. This is because of the fatigue problem at high speed environment, in other words, high stress, strain, and energy acting on the steel belt edge mainly contributes to tire’s failure. For this reason, since tire's lifetime problem during high speed durability test can be mostly explained by crack initiation life, the tire's life prediction problem under high speed driving should be approached by crack initiation rather than crack propagation.
Fig. 4 Illustrations of test results by ECE R30 HSP test
3. FATIGUE LIFE CURVE OF RUBBER COMPOUND 3.1 Specimen and Fixture The specimen's dimension and shape designed in accordance with ASTM D4482-07(Rubber property - extension cycling fatigue test)9 to evaluate the tensile and the fatigue characteristics of rubber compounds. The thickness of the specimen was 1.4 mm, and initial crack was not given. The dimension and shape of the specimen are shown in Fig. 5. ASTM D4482-07 recommends using the mean value of 10 specimens per single test condition, so the fixture was produced to fix 10 specimens at once. In addition, the rectangular cover plate was designed to give surface pressure in order to minimize the slip between the test fixture and the specimens. Fig. 6 shows the final fixture shape.
*Corresponding author. Email : [email protected]
Fig. 5 Specimen dimension
Fig. 6 Fixture for rubber fatigue test
3.2 Fatigue Test Equipment The fatigue test equipment was configured, and temperature chamber for the 80℃ environment test was installed as shown in Fig. 7 and Fig. 8. During the high speed durability regulation test, a lot of heat builds up, and is accumulated at the steel belt edge region, and cracks propagate between the layers. So the fatigue test under high temperature(80℃) should be conducted to consider a high temperature environment.11-12 The number of cycles of the specimen until failure was taken using a proximity sensor and counter. When the crank rotates, a high-frequency oscillation-type proximity sensor is engaged by the change of electrostatic capacity between the detected object and the ground by electromagnetic induction. At this time, the number of the cycle was counted by the number of times that the sensor is activated. To cope with sudden failure, a PC camera was used to confirm the test progress.
Fig. 7 Fatigue test machine for rubber compounds
*Corresponding author. Email : [email protected]
Fig. 8 Fatigue test machine equipped temperature chamber 3.3 Fatigue Test Method Specimens were installed at a movable bar and crosshead, and the fatigue tests were carried out under displacement-control using a crank. In the high temperature(80℃) environmental test, to synchronize the specimen's temperature with chamber temperature, fatigue tests were started after maintaining temperature in the chamber at 80℃ for 15 minutes. Tests were conducted at a maximum strain of 1.74, 1.36, 0.96, 0.75 and 0.54, and strain ratio(R) = 0. Displacements were controlled by the position of crank holes. In the first 1,000 and 10,000 cycles, the test machine was stopped and compensated by as much as the extended length of the slip, and tests were conducted with compensating of the extension length every 24 hours. ASTM D4482-07 suggested the test conditions of 1.7 ± 0.17 Hz with sinusoidal waveform life as in Fig. 9, but in the research performed by Mars, et al.10, the frequency and waveform had less effect on the fatigue test, so the test’s frequency was set to 1.93 Hz, and a haversinusoidal waveform was used in this study. Also, the minimum strain was constantly maintained at zero, and displacement control was utilized to apply loads.
Fig. 9 Waveform type
*Corresponding author. Email : [email protected]
3.4 Fatigue Test Result The most failure mode of high speed durability regulation test is failure due to rapid crack growth between steel belt plies. The fatigue test for the steel belt compound under high temperature(80℃) was conducted because the effective initial crack occurring rapid failure is generated in the steel belt compound. And we converted strain-Nf curve to ∆SED-Nf curve using tensile test result as shown in Fig. 10. Eq. (1) shows life estimation equation derived ∆SED-Nf curve.
Fig. 10 ∆SED-Nf test result (1)
Where, N f : Crack Initiation Life SED : Strain Energy Density Range 4. PREDICTION METHODOLOGY
4.1 The Prediction Procedure In this study, to predict the high speed regulation durability test, steady-state rolling analysis using a finite element method and fatigue characteristic test of the rubber compound were used. The specific prediction procedure is as follows: (1) Using the standard test, tensile and fatigue characteristic test are performed, and fatigue life equation from the ∆SED-Nf curve is derived. (2) Using a finite element analysis, ∆SED values are obtained at the steel belt edge region according to the driving speed. (3) Crack initiation life(Nf) is calculated according to the driving speed by substituting obtained ∆SED value to fatigue life equation of the rubber compound. (4) Driving distance is calculated according to driving speed using a dynamic rolling radius and crack initiation life(Nf) *Corresponding author. Email : [email protected]
(5) In the regulation test procedure, driving time and speed are multiplied, and cumulative driving distance is calculated through test step. (6) By comparing life distance via analysis and via regulation test procedure, reversed point of the life distance is looked for, and the point as an initial failure of life is defined. (7) Errors are compensated from total failure life through an analysis procedure until failure life calculating each speed, and this compensated life is defined as the final regulation life. 4.2 The Calculation of High Speed Durability Life Fig. 11 shows the prediction procedure of the tire's failure life in accordance with the driving speed using ∆SED-speed curve by a steady-state rolling analysis and with fatigue life equation of the rubber compound. As shown in the figure, we can get the number of cycle until failure by inputting the ∆SED values into the fatigue estimation equation for the rubber compound, and then calculate driving distance until failure by multiplying repetition life and circumferential length at each driving speed which can be calculated as in Eq. (2). Where, D f is the estimated driving distance until failure, N f is the number of cycle of specimens, and DRR is the dynamic rolling radius of the tire. (2)
Fig. 11 Life calculation procedure 4.3 Judgment Procedure of Failure Point The exact failure criteria of the regulation life cannot be suggested only by calculating failure life in accordance with driving speed through analysis, so the decision criteria is required to see whether the *Corresponding author. Email : [email protected]
design can be passed over the regulation lifetime or not. Table 1 shows the judgment method of initial failure life using the high speed durability regulation test procedure. In this figure, test distance through a regulation test is increasing cumulatively as speed increases, but failure driving distance by simulation is decreasing along the driving speed. In this table, we can find the reversed point of the lifetime between test calculation and the simulation, and define this point as an initial failure life. This can be identified in the failure judgment curve as shown in Fig. 12. In this figure, the prediction life indicates the distance until failure at each speed step when assuming that driving is constant, and the test life indicates cumulative driving distance considering the driving time at each speed step. For example, in the Table 1, when the tire is driving constantly by the prediction method at the speed of 220 km/h, the crack at the steel belt edge region is initiated after driving at 344.11km, but the cumulative driving distance at a speed of 220 km/h due to the regulation test procedure is still 138.33 km, so it is under failure life, and it is assumed that it has not yet failed. However, the difference between the prediction distance and the test distance decreases as the driving speed increases, and the distances are reversed about the point of 240 km/h - 9 min. In other words, if we assume constant driving through analysis under 240 km/h, failure is estimated after driving at 250.5km. At this point, the cumulative driving distance by the test method is calculated at 251 km in the test step, 240 km/h 9 min., and exceeding 250.5 km as the essential driving distance to fail. So this point is defined to be the initial failure life. Table 1 Initial failure judgment table Speed (km/h)
Time (min)
Cumulative distance by test step(DC)
Driving distance by FEA(DD)
200
20
66.67
<
472.55
210
10
101.67
<
402.94
220
10
138.33
<
344.11
230
20
215
<
294.41
240
9/10
251/255
>
250.5
250
10
296.67
>
216.94
260
10
340
>
186.90
270
10
385
>
161.44
280
10
431.67
>
139.81
290
10
480
>
121.40
Remark
Failure point
Real indoor regulation test is of cumulative distance by driving time for each speed step, but prediction result is the driving distance up to the failure at the each driving speed, so the error compensation procedure should be needed as much as the driving history before the initial failure life. Fig. 13 shows the error compensation map, and the area of the map presents a driving distance. Fig. *Corresponding author. Email : [email protected]
13(a) is the driving distance by prediction method, and Fig.13(b) is the driving distance by indoor test procedure. We can see that the driving distance up to the failure by simulation is much higher than that of the test method. For this reason, the error compensation should be needed as much as the error distance in Fig. 13(b) after defining the initial failure point. The equation to compensate errors can be defined like Eq. (3), where, is the final driving distance until failure, is the initial driving distance until failure, is the previous step speed of initial failure speed, is driving speed at speed step, is the driving time at speed step, and is driving time at initial failure step on test method. ,
Fig. 12 Failure judgment curve
(a) Simulation distance (b) Indoor test distance Fig. 13 Error compensation map
5. FINITE ELEMENT ANALYSIS 5.1 Steady-State Rolling Finite Element Analysis
*Corresponding author. Email : [email protected]
(3)
The steady-state rolling analysis using a commercial finite element analysis program ABAQUS V6.11 was used to simulate the rolling state of the tires. The steady-state rolling analysis has a demerit that nodes should be located on the same streamline to be able to analyze steady rolling state, but because it has a merit to be able to realize dynamic behavior of the rotating system using implicit code, it has been widely used for analysis of axisymmetric rotating system.13 The steady-state rolling analysis procedure of tire is shown in Fig. 14. Tires are a representative nonlinear and large deformation analysis problem, so in this study, we used Mooney-Rivlin coefficients for each rubber compound and elastic modulus and Poisson's ratio for the reinforced materials. In addition, the rebar layer method provided by ABAQUS was used for the reinforced cord, and cord-rubber composite materials were defined by embedding a rebar layer in the rubber compound element. Material properties of rubber compounds and reinforcement cords used in this study are shown in Table 2 and 3. The failure due to the high speed durability test is mostly occurred at the steel belt edge region, so the ∆SED value was obtained at the inter-layer of the steel belt edge region as shown in Fig. 15. ∆SED value is defined by the difference between maximum SED and Minimum SED in the circumferential direction of the steel belt edge region.
Fig. 14 Steady-state rolling analysis procedure
Fig. 15 ∆SED extraction position
*Corresponding author. Email : [email protected]
Table 2 Material properties of rubber compounds Compounds
C1
C2
Tread
0.5361
0.0382
Cap ply
0.7377
0.1432
Steel belt
0.7858
0.0589
Body ply
0.6504
0.03434
Inner liner
0.1697
0.1717
Sidewall
0.2197
0.2482
Rim strip
0.3031
0.5415
Bead filler
0.9300
0.1991
Table 3 Material properties of embedded cords Cords
E(MPa)
Steel belt(Steel)
205,000
0.29
Body ply(Polyester)
3,900
0.40
Cap ply(Nylon)
2,600
0.40
5.2 Strain Energy Density Simulation According to Driving Speed ∆SED values at the steel belt edge region in accordance with the driving speed step should be obtained using a finite element method to calculate the prediction life for each driving speed by the regulation test method. However, the steady-state rolling analysis has a convergence problem in the high speed range, moreover, it is inefficient to perform F.E. analysis in the every speed step because of the excessive analysis time. Therefore, as shown in Fig. 16, to get energy value in the high speed range with a stable convergence and minimum analysis time, at first, finite element analyses in every speed step were carried out up to 140km/h step, and then the second order regression equation was derived based on the analysis results to get energy values over 150km/h. Fig. 17 shows the ∆SED curves for three different tires in accordance with the driving speed. The *Corresponding author. Email : [email protected]
ranking of the ∆SED values at the steel belt edge region does not translate in parallel but is changed as moving from low speed to high speed. It has been verified that tire's failure life has different tendency in accordance with driving speed. We can deduce this is because tires have sensitive or insensitive designs along their contour or structure, so to observe transition tendency of energy in accordance with driving speed is more rational than stress-strain analysis under static state to predict high speed failure life.
Fig. 16 ∆SED-Speed curve
Fig. 17 Energy curve along rolling speed
*Corresponding author. Email : [email protected]
6. VERIFICATION OF PREDICTION METHODOLOGY To verify the confidence of the proposed method in this study, a high speed durability regulation test was performed via the ECE R30 test method with 8 tire samples like Table 4. Each sample was tested twice, and the mean value was taken to ensure repeatability of the verification test. In the result of the test, the crack propagated from the steel belt edge to the interply between the steel belt layers as shown in Fig. 18. Using the same tire models with the test samples, high speed durability lifetime was predicted by the proposed method in this study, and in Table 5, the comparison between the test and the prediction results is presented. At first, the mean accuracy for the test samples was calculated, and then the correlation coefficient between the prediction and the test result were analyzed as shown in Fig. 19. The average accuracy of 8 sample tires was about 92%, and the correlation coefficient was about 95% as shown in Table 5 and Fig. 19. From the result, the lifetime prediction methodology suggested in this study must be reliable, considering complex construction of the tire with hyperelasticity and cord-rubber composite materials. Especially, since the prediction results caused by the errors have a tendency of lower value than those of the test, this prediction methodology is able to guarantee a conservative design, considering the durability to ensure the safety of the drivers and the passengers.
Fig. 18. − Failure Mode
Fig. 19 Correlation between test and prediction *Corresponding author. Email : [email protected]
Table 4 Verification test samples Tire
Size
Load index
Speed symbol
A
195/65 R15
91
T
B
195/65 R15
89
S
C
195/65 R15
89
T
D
205/65 R16
95
H
E
205/65 R16
94
H
F
205/65 R16
94
H
G
205/65 R15
99
T
H
195/65 R15
91
H
Table 5 Verification test results Indoor test result Tire
Prediction result
Accuracy (%)
Driving distance(km)
Life (km/h-min.)
Driving distance(km)
Life (km/h-min.)
A
442.0
260-05
425.0
260-01
96.2
B
398.2
240-10
336.5
230-04
84.5
C
382.2
240-10
344.8
240-01
90.2
D
435.8
270-03
434.7
270-03
99.7
E
447.0
270-06
448.7
270-06
99.6
F
449.3
270-06
420.0
260-10
93.5
G
319.0
230-05
244.0
210-04
76.5
H
415.8
260-09
398.5
260-05
95.8
Average
92.0
*Corresponding author. Email : [email protected]
7. CONCLUSION In this study, a new prediction methodology has been suggested for the tire's high speed durability regulation test. The suggested prediction method used a steady-state rolling analysis by a FEM and fatigue life equation for the rubber compound, and it was verified by comparing it to the indoor regulation tests. The summaries of this study are as follows: 1. The systematic methodology to predict failure driving distance along the speed has been suggested with a strain energy density using steady-state rolling analysis by a FEM and fatigue life equation for rubber compound at the steel belt edge region. 2. The rational judgment method has been suggested to calculate the absolute regulation life. The initial failure lifetime could be calculated by comparing the cumulative driving distance by the regulation test procedure, and the prediction result of the tire's failure life along driving speed, and final failure lifetime could be obtained by compensating the error of the driving distance as much as driving history would be before initial failure life. 3. In the tire's high speed durability case, life trends were different between low and high speeds. This is because tires have sensitive or insensitive design along their contour or structure, so this study claims that strain energy density analysis in accordance with driving speed is necessary to predict high speed durability using a FEM. 4. In the result of the verification tests with a total of 8 tire samples, the accuracy was 92%, and the correlation coefficient was 95%, so it must be a very reliable result considering hyperelastic and nonlinear characteristics of the tire, and this method can be useful to improve high speed regulation life.
Acknowledgement
This work was supported by the Nexen Tire Corporation. This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (No. 2015R1A2A1A10055230). REFERENCES 1. UNECE Regulation No.30 Revision 3, 2007. 2. US. DOT. Laboratory test procedure for FMVSS No.109. NHTSA, 2005. 3. Ogawa H, Furuya S, Koseki H, Iida H, Sato K, Yamagishi K. A study on the contour of the truck and bus radial tire. Tire Science and Technology 1990; 18(4): 236-261. 4. Yan X, Wang Y, Feng X. Study for the endurance of radial truck tires with finite element modeling. Mathematics and Computers in Simulation 2002; 59(6): 471-488. 5. Kabe K, Rachi K, Takahashi N, Kaga Y. Tire design methodology based on safety factor to satisfy tire life (Simulation approach to truck and bus tire design. Tire Science and Technology 2005; 33(4): 195-209. 6. Han YH, Becker EB, Fahrenthold EP, Kim DM. Fatigue life prediction for cord-rubber composite tires using global-local finite element method. Tire Science and Technology 2004; 32(1): 23-40. 7. Lee DW, Kim SR, Sung KD, Park JS, Lee TW, Huh SC. A study on the fatigue life prediction of tire belt-layers using probabilistic method. JMST 2013; 27(3): 673-678. 8. Gent AN, Walter JD. The Pneumatic Tire. NHTSA, 2005. 9. ASTM D4482-07. Standard test method for rubber property-extension cycling fatigue. ASTM *Corresponding author. Email : [email protected]
Standard 2007: 691-699. 10. Mars WV, Fatemi A. Factors that Affect the Fatigue Life of Rubber: A Literature Survey. Rubber Chemistry and Technology 2004; 77(3): 391-412. 11. Park CG, Oh BS, Moon H Y. Analysis of the temperature variation in a running tire. KSAE 1998; 7(2): 202-209. 12. Park HC, Youn SK, Song TS, Kim NJ. Analysis of distribution in a rolling tire due to strain energy dissipation. KSME 1997, 21(5): 746-755. 13. Kim SR, Lee KM, Song BC, Sung KD. The development of rolling resistance estimation method of tires using steady-state rolling analysis method. KSAE, Autumn Conference 2010: 1645-1649.
*Corresponding author. Email : [email protected]
Highlights -
New rational methodology to predict the accelerated life test
-
Acceptance or refusal for the regulation lifetime
-
Accelerated life test to shorten developing time
- Procedure to predict accelerated life test (material fatigue test, finite element analysis, method to predict life, and verification test)
*Corresponding author. Email : [email protected]
S0142-1123(18)30460-2 https://doi.org/10.1016/j.ijfatigue.2018.08.036 JIJF 4832
To appear in:
International Journal of Fatigue
Received Date: Revised Date: Accepted Date:
17 June 2018 16 August 2018 29 August 2018
Please cite this article as: Kim, S., Park, H., Moon, B., Sung, K., Koo, J-M., Seok, C-S., The prediction methodology for tire’s high speed durability regulation test using a finite element method, International Journal of Fatigue (2018), doi: https://doi.org/10.1016/j.ijfatigue.2018.08.036
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
The prediction methodology for tire’s high speed durability regulation test using a finite element method Seongrae Kim1, Hanseok Park1, Byungwoo Moon2, Kideug Sung1, Jae-Mean Koo2, ChangSung Seok2* 1
2
R&D Center, Nexen Tire Corporation, Yangsan, Gyeongnam 626-230, Korea School of Mechanical Engineering, Sungkyunkwan University, Suwon, Gyeonggi 440-746, Korea
ABSTRACT In the tire industry, indoor accelerated life tests as regulations have been performed to ensure tire durability performances instead of outdoor field test. The finite element method has been widely used to minimize real test time and cost, but prediction method for accelerated life test had hardly been made in the past. This study presents a rational methodology to predict the tire’s failure life at the steel belt edge region due to high speed regulation test. Based on the finite element analysis and fatigue characteristic of rubber material, a method to determine exact failure time is proposed. The steady-state rolling analysis by FEM to get strain energy density range(∆SED) at the steel belt edge region and fatigue test of rubber compound to obtain ∆SED- number of cycle(Nf) curve were used. The reliability of proposed prediction method was verified by real indoor test.
1. INTRODUCTION After the invention of a tire, the initial purpose of the development has focused on safety and long mileage, but in order to improve the vehicle's performance due to various performance requirements for use, the tire has been developed with a very complicated structure. The durability of the tire performance is one of the most important performances metric in terms of the vehicle's protection and passenger’s safety, so it should be a top priority during tire development. Fig. 1 shows the typical structure of the radial tire. Recently, as energy and environment problems are emerging as global issues, studies on vehicle’s energy source and fuel efficiency have been performed actively. In the view point of the vehicle, the development of hybrid and electric vehicle has been expanded, and in the viewpoint of the tire, the design to minimize rolling resistance related to vehicle’s fuel efficiency has been required. However, electric and hybrid vehicles have relatively high weight due to battery and an additional source of power comparing to the general passenger car, while tires decrease weight to minimize rolling resistance. Because of these trends on the durability of a tire work as conflicting conditions, in recent years, tire durability issues has been magnified in the tire industry. The durability test in normal driving condition is very difficult and time-consuming task. Generally, tires have longer lifetime by failure than that of tread wear, and field test cannot ensure driver’s safety, so failure test under normal vehicle driving condition is almost impossible. Thus, to simulate tire's failure mode by the indoor test, each group and country such as Economic Commission for Europe(ECE) in the European countries and the Federal Motor Vehicle Safety Standards(FMVSS) in North America have regulations for accelerated life test, and it has been used as a essential test in order to export tires.1-2 This indoor accelerated life test has been used as a substitute for durability test in the field. Among regulation accelerated life tests, high speed durability test is performed to simulate fatigue failure at the steel belt edge region as shown in Fig. 2 by increasing driving speed under constant load until tire's failure. The prediction of tire's performances using a finite element analysis has been widely used to *Corresponding author. Email : [email protected]
minimize the test time and cost and to increase developer’s degrees of freedom. The previous research on prediction methods for the tire’s durability using a finite element analysis has simply used stress, strain, and energy under static or dynamic state, 3-4 or predicted real life under normal driving condition by combining fracture mechanics.5-7 However, generally, tire developers have referred regulation test results than tire's absolute lifetime in the field, so the necessity of prediction method to simulate accelerated life test has been emerged recently. Therefore, this study presents a new prediction methodology to judge acceptance or refusal for the high speed durability regulation test using a finite element method, fatigue life equation of rubber compound, and regulation test procedure.
Fig. 1 The structure of radial tire
Fig. 2 Steel belt edge crack example
2. THE REGULATION TEST METHOD OF HIGH SPEED DURABILITY LIFE 2.1 ECE R30 Test Method The high speed durability regulation test is a representative indoor accelerated life test to simulate fatigue failure at the steel belt edge region, and there are various test methods as required for each country such as ECE R30 and FMVSS109. 1-2 However, the basic test method that increases driving speed in accordance with the test step under a constant load is the same for all test regulations, but according to test methods, inflation pressure, load, and cycle of increasing speed are different due to tire's speed symbol. Fig. 3 shows a high speed driving test machine used for regulation tests. In this study, among the regulation test methods of high speed durability, the ECE R30 test method that is most commonly used with FMVSS109 was used to predict the tire's regulation life.
Fig. 3 AKRON high speed test machine
*Corresponding author. Email : [email protected]
2.2 Failure Mechanism of High Speed Durability The roles of steel belt have largely classified two kinds. The first role is to protect the body ply from external impact, and the second role is to enhance the stability by making the contact area wide between the road and tread surfaces. However, in terms of structural safety, a steel belt is able to protect the inside of the tire from external impact, but has a very weak structure at the steel belt edge region due to several reasons such as delamination between composite materials, local stress concentration in the stiffness discontinuity point and the inter-laminar shear strains to develop in the circumferential direction between cross-laminated steel belt layers with opposite cords angles as shown in Fig. 4.8 Under normal driving conditions, after an effective crack initiates, the crack propagation life until failure accounts for most of the tire's durability because it is assumed fatigue problem under constant load or deformation.6 However, under the high speed endurance test that increases the driving speed, since driving times in the each speed step are not much longer than those in the normal state, once an effective initial crack initiates, it does not take a long time until failure. This is because of the fatigue problem at high speed environment, in other words, high stress, strain, and energy acting on the steel belt edge mainly contributes to tire’s failure. For this reason, since tire's lifetime problem during high speed durability test can be mostly explained by crack initiation life, the tire's life prediction problem under high speed driving should be approached by crack initiation rather than crack propagation.
Fig. 4 Illustrations of test results by ECE R30 HSP test
3. FATIGUE LIFE CURVE OF RUBBER COMPOUND 3.1 Specimen and Fixture The specimen's dimension and shape designed in accordance with ASTM D4482-07(Rubber property - extension cycling fatigue test)9 to evaluate the tensile and the fatigue characteristics of rubber compounds. The thickness of the specimen was 1.4 mm, and initial crack was not given. The dimension and shape of the specimen are shown in Fig. 5. ASTM D4482-07 recommends using the mean value of 10 specimens per single test condition, so the fixture was produced to fix 10 specimens at once. In addition, the rectangular cover plate was designed to give surface pressure in order to minimize the slip between the test fixture and the specimens. Fig. 6 shows the final fixture shape.
*Corresponding author. Email : [email protected]
Fig. 5 Specimen dimension
Fig. 6 Fixture for rubber fatigue test
3.2 Fatigue Test Equipment The fatigue test equipment was configured, and temperature chamber for the 80℃ environment test was installed as shown in Fig. 7 and Fig. 8. During the high speed durability regulation test, a lot of heat builds up, and is accumulated at the steel belt edge region, and cracks propagate between the layers. So the fatigue test under high temperature(80℃) should be conducted to consider a high temperature environment.11-12 The number of cycles of the specimen until failure was taken using a proximity sensor and counter. When the crank rotates, a high-frequency oscillation-type proximity sensor is engaged by the change of electrostatic capacity between the detected object and the ground by electromagnetic induction. At this time, the number of the cycle was counted by the number of times that the sensor is activated. To cope with sudden failure, a PC camera was used to confirm the test progress.
Fig. 7 Fatigue test machine for rubber compounds
*Corresponding author. Email : [email protected]
Fig. 8 Fatigue test machine equipped temperature chamber 3.3 Fatigue Test Method Specimens were installed at a movable bar and crosshead, and the fatigue tests were carried out under displacement-control using a crank. In the high temperature(80℃) environmental test, to synchronize the specimen's temperature with chamber temperature, fatigue tests were started after maintaining temperature in the chamber at 80℃ for 15 minutes. Tests were conducted at a maximum strain of 1.74, 1.36, 0.96, 0.75 and 0.54, and strain ratio(R) = 0. Displacements were controlled by the position of crank holes. In the first 1,000 and 10,000 cycles, the test machine was stopped and compensated by as much as the extended length of the slip, and tests were conducted with compensating of the extension length every 24 hours. ASTM D4482-07 suggested the test conditions of 1.7 ± 0.17 Hz with sinusoidal waveform life as in Fig. 9, but in the research performed by Mars, et al.10, the frequency and waveform had less effect on the fatigue test, so the test’s frequency was set to 1.93 Hz, and a haversinusoidal waveform was used in this study. Also, the minimum strain was constantly maintained at zero, and displacement control was utilized to apply loads.
Fig. 9 Waveform type
*Corresponding author. Email : [email protected]
3.4 Fatigue Test Result The most failure mode of high speed durability regulation test is failure due to rapid crack growth between steel belt plies. The fatigue test for the steel belt compound under high temperature(80℃) was conducted because the effective initial crack occurring rapid failure is generated in the steel belt compound. And we converted strain-Nf curve to ∆SED-Nf curve using tensile test result as shown in Fig. 10. Eq. (1) shows life estimation equation derived ∆SED-Nf curve.
Fig. 10 ∆SED-Nf test result (1)
Where, N f : Crack Initiation Life SED : Strain Energy Density Range 4. PREDICTION METHODOLOGY
4.1 The Prediction Procedure In this study, to predict the high speed regulation durability test, steady-state rolling analysis using a finite element method and fatigue characteristic test of the rubber compound were used. The specific prediction procedure is as follows: (1) Using the standard test, tensile and fatigue characteristic test are performed, and fatigue life equation from the ∆SED-Nf curve is derived. (2) Using a finite element analysis, ∆SED values are obtained at the steel belt edge region according to the driving speed. (3) Crack initiation life(Nf) is calculated according to the driving speed by substituting obtained ∆SED value to fatigue life equation of the rubber compound. (4) Driving distance is calculated according to driving speed using a dynamic rolling radius and crack initiation life(Nf) *Corresponding author. Email : [email protected]
(5) In the regulation test procedure, driving time and speed are multiplied, and cumulative driving distance is calculated through test step. (6) By comparing life distance via analysis and via regulation test procedure, reversed point of the life distance is looked for, and the point as an initial failure of life is defined. (7) Errors are compensated from total failure life through an analysis procedure until failure life calculating each speed, and this compensated life is defined as the final regulation life. 4.2 The Calculation of High Speed Durability Life Fig. 11 shows the prediction procedure of the tire's failure life in accordance with the driving speed using ∆SED-speed curve by a steady-state rolling analysis and with fatigue life equation of the rubber compound. As shown in the figure, we can get the number of cycle until failure by inputting the ∆SED values into the fatigue estimation equation for the rubber compound, and then calculate driving distance until failure by multiplying repetition life and circumferential length at each driving speed which can be calculated as in Eq. (2). Where, D f is the estimated driving distance until failure, N f is the number of cycle of specimens, and DRR is the dynamic rolling radius of the tire. (2)
Fig. 11 Life calculation procedure 4.3 Judgment Procedure of Failure Point The exact failure criteria of the regulation life cannot be suggested only by calculating failure life in accordance with driving speed through analysis, so the decision criteria is required to see whether the *Corresponding author. Email : [email protected]
design can be passed over the regulation lifetime or not. Table 1 shows the judgment method of initial failure life using the high speed durability regulation test procedure. In this figure, test distance through a regulation test is increasing cumulatively as speed increases, but failure driving distance by simulation is decreasing along the driving speed. In this table, we can find the reversed point of the lifetime between test calculation and the simulation, and define this point as an initial failure life. This can be identified in the failure judgment curve as shown in Fig. 12. In this figure, the prediction life indicates the distance until failure at each speed step when assuming that driving is constant, and the test life indicates cumulative driving distance considering the driving time at each speed step. For example, in the Table 1, when the tire is driving constantly by the prediction method at the speed of 220 km/h, the crack at the steel belt edge region is initiated after driving at 344.11km, but the cumulative driving distance at a speed of 220 km/h due to the regulation test procedure is still 138.33 km, so it is under failure life, and it is assumed that it has not yet failed. However, the difference between the prediction distance and the test distance decreases as the driving speed increases, and the distances are reversed about the point of 240 km/h - 9 min. In other words, if we assume constant driving through analysis under 240 km/h, failure is estimated after driving at 250.5km. At this point, the cumulative driving distance by the test method is calculated at 251 km in the test step, 240 km/h 9 min., and exceeding 250.5 km as the essential driving distance to fail. So this point is defined to be the initial failure life. Table 1 Initial failure judgment table Speed (km/h)
Time (min)
Cumulative distance by test step(DC)
Driving distance by FEA(DD)
200
20
66.67
<
472.55
210
10
101.67
<
402.94
220
10
138.33
<
344.11
230
20
215
<
294.41
240
9/10
251/255
>
250.5
250
10
296.67
>
216.94
260
10
340
>
186.90
270
10
385
>
161.44
280
10
431.67
>
139.81
290
10
480
>
121.40
Remark
Failure point
Real indoor regulation test is of cumulative distance by driving time for each speed step, but prediction result is the driving distance up to the failure at the each driving speed, so the error compensation procedure should be needed as much as the driving history before the initial failure life. Fig. 13 shows the error compensation map, and the area of the map presents a driving distance. Fig. *Corresponding author. Email : [email protected]
13(a) is the driving distance by prediction method, and Fig.13(b) is the driving distance by indoor test procedure. We can see that the driving distance up to the failure by simulation is much higher than that of the test method. For this reason, the error compensation should be needed as much as the error distance in Fig. 13(b) after defining the initial failure point. The equation to compensate errors can be defined like Eq. (3), where, is the final driving distance until failure, is the initial driving distance until failure, is the previous step speed of initial failure speed, is driving speed at speed step, is the driving time at speed step, and is driving time at initial failure step on test method. ,
Fig. 12 Failure judgment curve
(a) Simulation distance (b) Indoor test distance Fig. 13 Error compensation map
5. FINITE ELEMENT ANALYSIS 5.1 Steady-State Rolling Finite Element Analysis
*Corresponding author. Email : [email protected]
(3)
The steady-state rolling analysis using a commercial finite element analysis program ABAQUS V6.11 was used to simulate the rolling state of the tires. The steady-state rolling analysis has a demerit that nodes should be located on the same streamline to be able to analyze steady rolling state, but because it has a merit to be able to realize dynamic behavior of the rotating system using implicit code, it has been widely used for analysis of axisymmetric rotating system.13 The steady-state rolling analysis procedure of tire is shown in Fig. 14. Tires are a representative nonlinear and large deformation analysis problem, so in this study, we used Mooney-Rivlin coefficients for each rubber compound and elastic modulus and Poisson's ratio for the reinforced materials. In addition, the rebar layer method provided by ABAQUS was used for the reinforced cord, and cord-rubber composite materials were defined by embedding a rebar layer in the rubber compound element. Material properties of rubber compounds and reinforcement cords used in this study are shown in Table 2 and 3. The failure due to the high speed durability test is mostly occurred at the steel belt edge region, so the ∆SED value was obtained at the inter-layer of the steel belt edge region as shown in Fig. 15. ∆SED value is defined by the difference between maximum SED and Minimum SED in the circumferential direction of the steel belt edge region.
Fig. 14 Steady-state rolling analysis procedure
Fig. 15 ∆SED extraction position
*Corresponding author. Email : [email protected]
Table 2 Material properties of rubber compounds Compounds
C1
C2
Tread
0.5361
0.0382
Cap ply
0.7377
0.1432
Steel belt
0.7858
0.0589
Body ply
0.6504
0.03434
Inner liner
0.1697
0.1717
Sidewall
0.2197
0.2482
Rim strip
0.3031
0.5415
Bead filler
0.9300
0.1991
Table 3 Material properties of embedded cords Cords
E(MPa)
Steel belt(Steel)
205,000
0.29
Body ply(Polyester)
3,900
0.40
Cap ply(Nylon)
2,600
0.40
5.2 Strain Energy Density Simulation According to Driving Speed ∆SED values at the steel belt edge region in accordance with the driving speed step should be obtained using a finite element method to calculate the prediction life for each driving speed by the regulation test method. However, the steady-state rolling analysis has a convergence problem in the high speed range, moreover, it is inefficient to perform F.E. analysis in the every speed step because of the excessive analysis time. Therefore, as shown in Fig. 16, to get energy value in the high speed range with a stable convergence and minimum analysis time, at first, finite element analyses in every speed step were carried out up to 140km/h step, and then the second order regression equation was derived based on the analysis results to get energy values over 150km/h. Fig. 17 shows the ∆SED curves for three different tires in accordance with the driving speed. The *Corresponding author. Email : [email protected]
ranking of the ∆SED values at the steel belt edge region does not translate in parallel but is changed as moving from low speed to high speed. It has been verified that tire's failure life has different tendency in accordance with driving speed. We can deduce this is because tires have sensitive or insensitive designs along their contour or structure, so to observe transition tendency of energy in accordance with driving speed is more rational than stress-strain analysis under static state to predict high speed failure life.
Fig. 16 ∆SED-Speed curve
Fig. 17 Energy curve along rolling speed
*Corresponding author. Email : [email protected]
6. VERIFICATION OF PREDICTION METHODOLOGY To verify the confidence of the proposed method in this study, a high speed durability regulation test was performed via the ECE R30 test method with 8 tire samples like Table 4. Each sample was tested twice, and the mean value was taken to ensure repeatability of the verification test. In the result of the test, the crack propagated from the steel belt edge to the interply between the steel belt layers as shown in Fig. 18. Using the same tire models with the test samples, high speed durability lifetime was predicted by the proposed method in this study, and in Table 5, the comparison between the test and the prediction results is presented. At first, the mean accuracy for the test samples was calculated, and then the correlation coefficient between the prediction and the test result were analyzed as shown in Fig. 19. The average accuracy of 8 sample tires was about 92%, and the correlation coefficient was about 95% as shown in Table 5 and Fig. 19. From the result, the lifetime prediction methodology suggested in this study must be reliable, considering complex construction of the tire with hyperelasticity and cord-rubber composite materials. Especially, since the prediction results caused by the errors have a tendency of lower value than those of the test, this prediction methodology is able to guarantee a conservative design, considering the durability to ensure the safety of the drivers and the passengers.
Fig. 18. − Failure Mode
Fig. 19 Correlation between test and prediction *Corresponding author. Email : [email protected]
Table 4 Verification test samples Tire
Size
Load index
Speed symbol
A
195/65 R15
91
T
B
195/65 R15
89
S
C
195/65 R15
89
T
D
205/65 R16
95
H
E
205/65 R16
94
H
F
205/65 R16
94
H
G
205/65 R15
99
T
H
195/65 R15
91
H
Table 5 Verification test results Indoor test result Tire
Prediction result
Accuracy (%)
Driving distance(km)
Life (km/h-min.)
Driving distance(km)
Life (km/h-min.)
A
442.0
260-05
425.0
260-01
96.2
B
398.2
240-10
336.5
230-04
84.5
C
382.2
240-10
344.8
240-01
90.2
D
435.8
270-03
434.7
270-03
99.7
E
447.0
270-06
448.7
270-06
99.6
F
449.3
270-06
420.0
260-10
93.5
G
319.0
230-05
244.0
210-04
76.5
H
415.8
260-09
398.5
260-05
95.8
Average
92.0
*Corresponding author. Email : [email protected]
7. CONCLUSION In this study, a new prediction methodology has been suggested for the tire's high speed durability regulation test. The suggested prediction method used a steady-state rolling analysis by a FEM and fatigue life equation for the rubber compound, and it was verified by comparing it to the indoor regulation tests. The summaries of this study are as follows: 1. The systematic methodology to predict failure driving distance along the speed has been suggested with a strain energy density using steady-state rolling analysis by a FEM and fatigue life equation for rubber compound at the steel belt edge region. 2. The rational judgment method has been suggested to calculate the absolute regulation life. The initial failure lifetime could be calculated by comparing the cumulative driving distance by the regulation test procedure, and the prediction result of the tire's failure life along driving speed, and final failure lifetime could be obtained by compensating the error of the driving distance as much as driving history would be before initial failure life. 3. In the tire's high speed durability case, life trends were different between low and high speeds. This is because tires have sensitive or insensitive design along their contour or structure, so this study claims that strain energy density analysis in accordance with driving speed is necessary to predict high speed durability using a FEM. 4. In the result of the verification tests with a total of 8 tire samples, the accuracy was 92%, and the correlation coefficient was 95%, so it must be a very reliable result considering hyperelastic and nonlinear characteristics of the tire, and this method can be useful to improve high speed regulation life.
Acknowledgement
This work was supported by the Nexen Tire Corporation. This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (No. 2015R1A2A1A10055230). REFERENCES 1. UNECE Regulation No.30 Revision 3, 2007. 2. US. DOT. Laboratory test procedure for FMVSS No.109. NHTSA, 2005. 3. Ogawa H, Furuya S, Koseki H, Iida H, Sato K, Yamagishi K. A study on the contour of the truck and bus radial tire. Tire Science and Technology 1990; 18(4): 236-261. 4. Yan X, Wang Y, Feng X. Study for the endurance of radial truck tires with finite element modeling. Mathematics and Computers in Simulation 2002; 59(6): 471-488. 5. Kabe K, Rachi K, Takahashi N, Kaga Y. Tire design methodology based on safety factor to satisfy tire life (Simulation approach to truck and bus tire design. Tire Science and Technology 2005; 33(4): 195-209. 6. Han YH, Becker EB, Fahrenthold EP, Kim DM. Fatigue life prediction for cord-rubber composite tires using global-local finite element method. Tire Science and Technology 2004; 32(1): 23-40. 7. Lee DW, Kim SR, Sung KD, Park JS, Lee TW, Huh SC. A study on the fatigue life prediction of tire belt-layers using probabilistic method. JMST 2013; 27(3): 673-678. 8. Gent AN, Walter JD. The Pneumatic Tire. NHTSA, 2005. 9. ASTM D4482-07. Standard test method for rubber property-extension cycling fatigue. ASTM *Corresponding author. Email : [email protected]
Standard 2007: 691-699. 10. Mars WV, Fatemi A. Factors that Affect the Fatigue Life of Rubber: A Literature Survey. Rubber Chemistry and Technology 2004; 77(3): 391-412. 11. Park CG, Oh BS, Moon H Y. Analysis of the temperature variation in a running tire. KSAE 1998; 7(2): 202-209. 12. Park HC, Youn SK, Song TS, Kim NJ. Analysis of distribution in a rolling tire due to strain energy dissipation. KSME 1997, 21(5): 746-755. 13. Kim SR, Lee KM, Song BC, Sung KD. The development of rolling resistance estimation method of tires using steady-state rolling analysis method. KSAE, Autumn Conference 2010: 1645-1649.
*Corresponding author. Email : [email protected]
Highlights -
New rational methodology to predict the accelerated life test
-
Acceptance or refusal for the regulation lifetime
-
Accelerated life test to shorten developing time
- Procedure to predict accelerated life test (material fatigue test, finite element analysis, method to predict life, and verification test)
*Corresponding author. Email : [email protected]