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Rolling deformation of truck tires: Measurement and analysis using a tire sensing approach
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ScienceDirect
Journal of Terramechanics
Journal of Terramechanics 61 (2015) 33–42 www.elsevier.com/locate/jterra
Rolling deformation of truck tires: Measurement and analysis using a tire sensing approach Yi Xiong ⇑, Ari Tuononen Vehicle Engineering Group, Department of Engineering Design and Production, Aalto University, P.O. Box 14300, 02015 Espoo, Finland Received 8 April 2015; received in revised form 13 July 2015; accepted 20 July 2015
Abstract Measurements on rolling tire deformation provide deep insights into the mechanism of generating tire forces and moments. For free rolling tires, substantial attention has been given to the rolling resistance because of its significant impact on the fuel consumption and CO2 emissions. This paper attempts to investigate the rolling resistance force through measurements of the rolling deformation of truck tires using a tire sensing approach. An optical tire sensor system is used to measure rolling tire deformation, which includes the deformed inner profile, sidewall deformation, and tread deformation. Measurements were conducted on a test truck for both new and used tires. In addition, the influences from operational factors such as wheel load and inflation pressure on tread deformation were examined and analyzed. Ó 2015 ISTVS. Published by Elsevier Ltd. All rights reserved.
Keywords: Tire deformation; Tire sensor; Rolling resistance; Tread deformation; Tire wear
1. Introduction The tire-road interface produces all the forces and moments used to alter the vehicle state through cruising, accelerating, braking, and cornering. These forces and moments are generated through deformations of rolling tires under vertical loads. Understanding of the mechanism of generating those forces and moments is the basis for vehicle system dynamics and control. Regarding tire forces and moments which affect tire handling and ride comfort, empirical tire models such as the Magic Formula (Pacejka, 2005), semi-physical tire models such as F-Tire (Gipser, 2007), and physical tire models using finite element models (Ghoreishy, 2008) have been proposed and widely used. However, for the free rolling tire force, specifically the rolling resistance, there are few precise physical tire
⇑ Corresponding author. Tel.: +358 504 335713.
E-mail address: yi.xiong@aalto.fi (Y. Xiong). http://dx.doi.org/10.1016/j.jterra.2015.07.004 0022-4898/Ó 2015 ISTVS. Published by Elsevier Ltd. All rights reserved.
models (Shida et al., 1999; Cho et al., 2013; Behnke and Kaliske, 2015) in existence, due to limited knowledge of the fundamental mechanisms of rolling resistance. The rolling resistance is defined as the energy dissipation per unit distance travelled for a free rolling tire moving in a straight direction. The viscoelastic rubber compounds in the tires, which are cyclically deformed by the road, result in an asymmetric normal stress distribution which has a shifted equivalent force located at the leading half of the contact patch. Such an equivalent force and torque are called rolling resistance force and torque. In fact, rolling resistance is an energy dissipation process to overcome the resistive force and thus drive the tire forward. The necessity and importance of lowering the rolling resistance to improve energy efficiency and reduce carbon emission in transport is therefore well recognized. For modern radial tires, it has been established that the tire rolling resistance accounts for as much as 17–21% of the total fuel consumption of ground vehicles, while the
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contribution is even higher for heavy duty vehicles (Gent and Walter, 2005). In the tire industry, great efforts have been devoted to the development of new compounds, tire contours and tread pattern design, which have greatly improved the rolling resistance performance. However, the rolling deformation of tire parts, especially the tread area, which makes the primary contribution to rolling resistance, still has not been measured. The main challenges in this measurement are the lack of proper measurement instruments, in addition to the harsh environment at the tire-road interface. Tire sensing is an emerging approach to measure tire states such as deformations and to provide information about the tire-road interface including friction level (Singh et al., 2013; Matsuzaki et al., 2015), footprint dimension (Niskanen and Tuononen, 2014), and maximum sinkage (Naranjo et al., 2014), etc., for vehicle control and tire development applications. Several studies (Hong et al., 2013; Zhang et al., 2013; Tuononen, 2009) have demonstrated the ability of tire sensing to reveal the mechanism of generating tire force and to estimate corresponding forces. In a previous study (Xiong and Tuononen, 2014), an optical measurement system using a one-dimensional laser sensor was developed to investigate the rolling resistance mechanism through tread deformation measurements on a passenger car tire. The measurement gave promising results but was only able to measure the deformation of one tread element during rolling. However, the tread deformation is not uniform along the tire cross-section. A two-dimensional (2D) laser measurement system was therefore developed to examine tire deformation over a wider area. This paper reports a recent application of this 2D sensor system on rolling deformation measurements for truck tires. The main contribution of this work lies in the investigation of the possibility for studying the rolling resistance mechanism using a tire sensing system which measures rolling deformations of a truck tire. Rolling deformations such as the deformation of the inner profile, the loaded radius, sidewall deformation, and tread deformation of
truck tires were measured. In addition, the deformations of both new and worn tires under different operational factors were compared and analyzed. 2. Material and methods 2.1. Tire sensors To measure tire deformations, especially tread deformations, an optical tire sensor system has recently been developed (Xiong and Tuononen, 2014). This non-contact sensing method is able to work in a harsh environment without affecting the local deformation. As shown in Fig. 1(a), the rolling deformation of a tire is measured by two laser triangulation sensors, Laser Sensor 1 (Keyence LJ-V7300) and Laser Sensor 2 (Keyence LK-H150), and the rolling deformation is determined by accurately measuring the rotation angle of the wheel. The Laser Sensor 1 is a two-dimensional laser profilometer with an ultra-high-speed sampling rate and large measurement range. To measure a larger region of interest, a sensor support with designated tilt angles was utilized to orient the laser towards a specific angle (Fig. 1(b)). Then, the sensor module was embedded into the sensor housing and mounted on a steel rim by means of tread attachments. To measure the angular position of the 2D laser profilometer, an optical encoder (2048 counts/revolution) within a slip ring unit (Michigan Scientific SR 20AW/T1024) was used. In addition, the Laser Sensor 2 was used to measure the dynamic loaded radius (the distance from the wheel rotation axis to the road). The proposed system is based on the measurements as follows: the sidewall height L1; the loaded radius L2, and; the sensor circumferential position h. According to the geometric relationship, the tread thickness could be calculated as: Z tread ¼ L2 ðL1 þ Loffset ÞCosh
Fig. 1. (a) Methodology for the tire sensor system; and (b) prototype for the tire sensor system.
ð1Þ
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Compared with the original tread thickness, the tread deflection can be obtained. For measurements conducted on the drum, the curvature of the drum should be considered and Eq. (1) should be modified, as demonstrated in Xiong and Tuononen (2014). 2.2. Measurement tires During the measurement, a commercially available truck tire (385/55 R22.5) was used as the test tire type. The test tire, which is regroovable, has two circumferential grooves and laterally distributed sipes. Comparison measurements were made between a brand new and a used tire that has experienced in-service wear. The tire profile and a mechanical offset Loffset were precisely measured by coordinate measuring machines. As shown in Fig. 2, the groove depth was measured to be 11.5 mm and 6.5 mm for the new tire and used tire, respectively. In addition, it is shown that the laterally distributed sipe has been worn out on the used tire. The Cartesian coordinate system defined in this work is depicted in Fig. 3. The tread deformation coordinate along the centerline of the tire cross-section pointed downwards, the lateral coordinate is aligned with the horizontal line in the interface plane, and the contact patch coordinate points towards the direction the tire is travelling. In addition, a 9 mm wide rubber stripe was glued to the tire inner liner. This rubber stripe serves two purposes. The first is to convert measurements obtained in the laser sensor coordinates to the aforementioned coordinate system. Moreover, it allows for the possible lateral movement of the carcass to be examined.
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set to zero and the slip ratio was assumed to be zero. Considering the minor influence of speed on the rolling resistance at velocities less than 100 km/h (Kim and Savkoor, 1997) and the lack of a long enough proving ground, all experiments were conducted only with one velocity at 5 km/h. However, measurements with different velocities should also be conducted in further studies. The wheel load applied on the measured tire was adjusted by alternating the pressure of the air spring. The cold inflation pressure was adjusted and checked before each measurement. Measurements were conducted for five different wheel loads and three different inflation pressures for both new and worn tires. For each operational condition, a test run of at least 20 cycles was performed. 2.4. Data processing The Laser Sensor 1 provides a direct measurement of the inner profile of the tire during rolling. Due to the high
2.3. Data collection As shown in Fig. 4, the measured tire was assembled on a truck (SISU Polar). Experiments were performed in a parking area at Aalto University, Finland, where the cross-section of the road has a crown shape that slopes at 2.6 percent from either side of the road centerline. Operational factors are controlled as follows. The truck was driven in a straight line at a constant speed of 5 km/h. Also, neither a brake nor a drive torque was applied to the wheel. In other words, the slip angle was
Fig. 3. Coordinate system and location of the rubber strip on the measurement tire.
Fig. 2. Worn tire (left) and new tire (right) used in the measurement.
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Fig. 4. Assembly of the instrumented tire on a truck.
sampling frequency and limited reflectivity of the rubber surface, outliers, which have unreasonably high and low values compared to the surrounding data, were observed in the raw data. To eliminate those outliers, a filter based on the cumulative probability neighbor median (Ismail et al., 2010) was used to process data. The filtered signal shows clear peaks when the tire was being deformed by the road (Fig. 5). Because of the large measurement range of the laser profilometer, the system can examine the tire rolling deformation over a large cross sectional area, which covers parts of the sidewall, shoulder, and crown. Such measurements can also be used to characterize the tire enveloping behavior over cleats. However, one limitation of this system is the deformed tire inner profile of a full rotation is updated only once per revolution. Measurement signals from the Laser Sensor 2 include both periodic errors and random noise. The principle cause of the periodic errors was mainly the eccentric alignment between the rotating axes of the tire and slip ring. To reduce such error, a pattern recognition procedure was defined to compensate for such error. On the other hand, the random
noise from road roughness (texture less than 1 mm) can be smoothed by a Butterworth low-pass fitter. Fig. 6 illustrates the signal processing procedure and corresponding results for the external laser measurement. The error bars represent the standard deviations of the measured loaded radius under each specific operational condition. Compared with other errors in the system, this is the dominant error which limits the measurement system performance. 3. Results and discussion In this section, measurement results on the sidewall and tread deformations, as well as the footprint characteristics are presented for both worn and new tires. In addition, measured rolling tire deformations are analyzed in the context of rolling resistance and tire wear. 3.1. Sidewall deformation While the tread deformation accounts for a major part of tire rolling resistance losses, the sidewall deformation
Fig. 5. Deformed inner profiles measured by Laser Sensor 1.
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Fig. 6. Data processing procedure for loaded radius measurements.
is typically responsible for an additional 15% loss (Gent and Walter, 2005). Because the Laser Sensor 1 is embedded into the rim, the sidewall height, which is defined as the distance from the rim to the tire inner liner, can be directly measured. Sidewall height measurements for a full tire rotation under different wheel loads are compared in Fig. 7. The deformation peaks occur during the contact between the tire and road, and the largest deformation is obtained at the highest load. On the other hand, the radius of the non-contact parts shows an opposite trend with wheel load, i.e., the radius of the non-contact parts becomes larger with increasing loads. This is due to the high extensional stiffness of the tire belt for a radial tire, which is almost in-extensible (Gong, 1993). Moreover, the volume of pressurized air does not change with increasing loads which also results in the non-contact parts were pushed outwards. In addition, a previous study (Tuononen, 2011) indicates a dependence between the magnitude of the sidewall deformation and the wheel load. Considering that observation, the wheel loads applied in this study might not actually be constant due to the dynamics of the truck suspension. To represent three
Fig. 7. The tire sidewall deformation under various load conditions (inflation pressure = 7.0 bar).
distinguished load level, measurements under three different loads (5 kN, 15 kN, and 25 kN) are presented in the following sections. 3.2. Tread deformation 3.2.1. Non-uniform deformation The information on tread deformation is of great interest to tire designers to develop low rolling resistance tires, as the non-uniform deformation is a direct result of viscoelastic rubber compounds under a cyclic deformation. In a previous study (Xiong and Tuononen, 2014), an asymmetric tread deformation along the longitudinal direction was observed and correlated the rolling resistance for a passenger car tire. For truck tire measurements, this has also been observed in most cases. Fig. 8 illustrate an example of a tread deformation measurement at a 5.5 bar and 25 kN condition. The void area in the measured deformation is due to the measurement dead zone caused by the rubber strip described in Section 2.2. To better visualize the asymmetric deformation, the centroid of each profile, which represents the asymmetry of deformation, are also plotted in both the top and side views. It can be seen that most centroids are located in the leading half of the contact patch. This again confirms that the asymmetric tread deformation along the longitudinal direction is directly linked to the rolling resistance. On the other hand, a few centroids at the edges of the footprints are observed to be located slightly in the trailing half of the contact patch. The reasons might be the following: (1) the tread deformation is small on the edge of the footprint and of comparable magnitude to the system errors; (2) for a new tire, the shoulder is deformed by the road later than other components, and therefore the major contact in the trailing half. In addition, it is interesting to note that the tread has a smaller deformation than the sidewall component.
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Fig. 8. The non-uniform tread deformation (wheel load = 25 kN, inflation pressure = 5.5 bar).
However, according to thermal finite element simulations reported in Behnke and Kaliske (2015), Cho et al. (2013), the sidewall component, despite having larger deformations, dissipates less energy than the tread. This is mainly due to the difference in the material properties between the compounds in these two components. Namely, to obtain better grip and abrasion, highly viscoelastic compounds are used for the tread, while the sidewalls use low viscoelastic compounds to reduce heat buildup and optimize cracking resistance (Gent and Walter, 2005). It can
be seen that the performance of the rolling resistance not only depends on the magnitude of deformation but also on the rubber volume and material properties. 3.2.2. Operational factor effect As shown in both Figs. 9 and 10, the influence of wheel load on tread deformation was investigated under three load conditions (5 kN, 15 kN, and 25 kN) for both new and worn tires. For the new tire, the wheel load has an opposite effect on the deformation level in the shoulder
Fig. 9. Measured tread deformations of a new tire under various loads and inflation pressures.
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Fig. 10. Measured tread deformations of a worn tire under various loads and inflation pressures.
part compared to the crown part. The deformation level of the shoulder parts increases with increasing load, whereas the crown parts show an opposite trend. This is due to the load shift effect in the lateral direction of the tire as discussed in the previous section. The same observations are reported in a previous tread deformation measurement on a passenger car tire (Xiong and Tuononen, 2014) and in normal contact stress measurements (Pottinger, 1992; De Beer et al., 2012). For the worn tire, no significant effect on the change in wheel load was observed. To examine the effects of tire inflation pressure on tire tread deformation, measurements were conducted at three inflation pressures (5.5 bar, 7.0 bar, and 8.5 bar) for both new and worn tires. For the new tire, the tire inflation pressure has an apparent influence on the tread deformation pattern. A Hertz contact-like deformation is observed at the 8.5 bar and 5 kN condition. This is a result of the reduced tire crown radius caused by the high inflation pressure and low wheel load, which causes the tire crown to be deformed by the road first. However, for the worn tire, the comparison indicates that, similar to the effect of the load, the inflation pressure has no significant influence on tread deformation pattern and the largest tread
deformation was always found on the shoulder part for worn tires. Because the tread along the cross-section has an evenly distributed volume and has homogenous material properties, the magnitude of the tread deformation in this sense represents the energy dissipation, which results in the rolling resistance. It can be seen that for a new tire, the deformation in shoulder area contributes more to the rolling resistance at a high load and low inflation pressure condition; whereas, the deformation in crown area contributes more at a low load and high inflation pressure condition. However, for a worn tire, the deformation in shoulder area always contributes more to the rolling resistance. In general, the tread deformation is greatly influenced by operational factors, such as the tire inflation pressure and wheel load. Moreover, the sensitivity of the deformation to changes in operational factors is also dependent on tire structures and mechanical properties (Clark and Schuring, 1988). 3.2.3. Wear effect In-service wear is an evitable process that continuously alters the behavior of a tire over its whole lifetime. In fact,
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wear not only reduces the volume of the tread compound and flattens the shape of the tire outer tread surface but also stiffens the tire tread. As shown in Fig. 6, such effects, due to both tire structure and material properties, will increase the tire vertical stiffness and therefore reduce the loaded radius. Moreover, changes to the tire handling characteristics caused by tire wear is also observed in Xiong et al. (2014). For the tread parts, comparison between Figs. 9 and 10 shows that the worn tire exhibits a smaller deformation than the new tire under the same operational condition. In addition, the worn tire does not clearly show the lateral shift of largest deformation with load increase which was observed in the new tire. This can be mainly explained by stiffening of the tread due to wear. Moreover, the outer contour of the worn tire also became flattened. It can be seen at the wear effect also has a great influence on the non-uniform deformation of the tread parts, thus changing the tire crown contour. This in turn accelerates the uneven tread wear (Cho et al., 2005). According to measurements in Luchini et al. (2001), used tires have a generally decreasing trend in rolling resistance with tire usage. This can be related to the measured tread deformation because a worn tire has a smaller tread deformation. Together with a decreasing volume of tread compound, the observation of a lower rolling resistance with worn tires is expected. Current international standards and labelling regulations only evaluate the rolling resistance performance for new tires. However, the above discussion implies that the whole life-time rolling resistance performance of tire should also be considered. 3.3. Footprints analysis The footprint of the tire-road contacts reflects the states of the tire and road, as it is relatively sensitive to changes in the tire structure, operational factors, and road conditions. This paper only studies the partial footprint obtained from
the measurements, which was limited by the measurement range of the laser profilometer. To analyze the footprint evolution against operational factors, as shown in Fig. 11, the following indexes are measured to characterize the footprint. The contact width W, contact length L, and contact area A are used to compare the dimension of the footprint. Moreover, the footprint-shape coefficient (Liang et al., 2013) is used to describe the footprint shape and is defined as follows: k ¼ ðb1 þ b2 Þ=180
ð2Þ
where b1 and b2 are internal angles between the footprint’s longitudinal boundaries and central line. The value of the footprint shape coefficient has the following physical meanings: if the value is larger than 1, the footprint has a concave shape; if the value is equal to 1, the footprint has a rectangular shape; and if the value is smaller than 1, the footprint has a convex shape. An image processing tool was developed to batch extract the footprint feature based on the tire deformation measurements in Figs. 9 and 10. The footprint characteristics under different operating conditions are summarized in Table 1. It is observed that the contact area decreases with decreasing wheel load and increasing inflation pressure. In addition, the worn tire has a smaller contact area than the new tire in most cases. An exception is found for measurements conducted at a 5.5 bar and 5 kN condition. Moreover, although both the contact length and width decrease with decreasing wheel load and increasing inflation pressure, the new and worn tires show different trends. The new and the worn tires have a longer contact in the contact length and width, respectively, which are both related to the corresponding footprint shapes. According to the shape coefficient, it seems that at higher load conditions, the footprint becomes more rectangular for the new tire and more concave for the worn tire. This observation implies the uneven wear on the shoulder components will be accelerated when the worn tire is subjected to a higher load, even if the load has not exceeded the nominal load.
Fig. 11. Footprint characteristics on an example footprint.
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Table 1 Footprint characteristics under different wheel load and inflation pressure conditions. New tire
Worn tire
5.5 bar
7.0 bar
8.5 bar
5.5 bar
7.0 bar
8.5 bar
Contact area (cm2)
5 kN 15 kN 25 kN
52.4 55.2 68.2
46.9 53.2 65.2
37.5 47.5 56.2
57.6 51.4 63.1
45.9 49.1 57.4
51.7 45.1 41.5
Contact length (cm)
5 kN 15 kN 25 kN
10.2 10.2 11.7
9.4 10.0 10.9
7.7 9.1 10.1
8.7 7.9 9.4
7.6 8.3 9.4
7.6 8.2 8.6
Contact width (cm)
5 kN 15 kN 25 kN
5.8 7.4 8.4
5.8 7.4 8.2
5.8 5.8 5.8
8.6 8.6 8.8
8.2 8.3 8.2
7.6 7.6 7.6
Shape coefficient ()
5 kN 15 kN 25 kN
0.85 0.91 0.90
0.84 0.89 0.93
0.85 0.84 0.98
1.03 1.04 1.11
1.06 1.06 1.13
1.11 1.12 1.10
4. Conclusions
References
The rolling tire deformations of a truck tire, including both the sidewall and tread deformations, were measured with a 2D optical tire sensor system to provide insight into the mechanism of rolling resistance generation. For tread deformation, non-uniform deformations were observed along both the longitudinal and lateral directions. On one hand, such asymmetric deformation in the longitudinal direction is a direct indication of tire rolling resistance; on the other hand, such non-uniform deformation in the lateral direction implies that contributions from separate components to rolling resistance are different under various operational conditions. Measurements on the new tire imply that for a high load and low inflation pressure, the deformation in the shoulder area will contribute more to rolling resistance. In an opposite manner, for a low load and high inflation pressure, the deformation in the crown area will contribute more. Meanwhile, the deformation in the shoulder area always contributes more to the rolling resistance for the worn tire. This will in turn accelerate the wear process on the shoulder area. This work provides a fundamental understanding on the mechanism of generating rolling resistance. This work offers the tire designer quantitative tread deformation measurements to verify finite element simulation results and to optimize tire construction and materials for better rolling resistance and wear performances. In addition, the measured deformation cycles can be used as a more realistic input in the testing of rubber compounds.
Behnke, R., Kaliske, M., 2015. Thermo-mechanically coupled investigation of steady state rolling tires by numerical simulation and experiment. Int. J. Non. Linear. Mech. 68 (1), 101–131. Cho, J.R., Shin, S.W., Yoo, W.S., 2005. Crown shape optimization for enhancing tire wear performance by ANN. Comput. Struct. 83 (12– 13), 920–933. May. Cho, J.R., Lee, H.W., Jeong, W.B., Jeong, K.M., Kim, K.W., 2013. Numerical estimation of rolling resistance and temperature distribution of 3-D periodic patterned tire. Int. J. Solids Struct. 50 (1), 86–96. Cho, J.R., Lee, H.W., Jeong, W.B., Jeong, K.M., Kim, K.W., 2013. Finite element estimation of hysteretic loss and rolling resistance of 3-D patterned tire. Int. J. Mech. Mater. Des. 9 (4), 355–366. September. Clark, J.D., Schuring, D.J., 1988. Load, speed and inflation pressure effects on rolling loss distribution in automobile tires. Tire Sci. Technol. 16 (2), 78–95. April. De Beer, M., Maina, J.W., van Rensburg, Y., Greben, J.M., 2012. Toward using tire-road contact stresses in pavement design and analysis. Tire Sci. Technol., 246–271 Gent, A.N., Walter, J.D., The Pneumatic Tire. The National Highway Traffic Safety Administration, 2005. Ghoreishy, M., 2008. A state of the art review of the finite element modelling of rolling tyres. Iran. Polym. J. 17 (8), 571–597. Gipser, M., 2007. FTire – the tire simulation model for all applications related to vehicle dynamics. Veh. Syst. Dyn. 45 (sup1), 139–151. January. Gong, S. A study of in-plane dynamics of tires, Delft University, 1993. Hong, S., Erdogan, G., Hedrick, J.K., Borrelli, F., 2013. Tyre–road friction coefficient estimation based on tyre sensors and lateral tyre deflection: modelling, simulations and experiments. Veh. Syst. Dyn. 51 (5), 627–647. Ismail, M.F., Yanagi, K., Fujii, A., 2010. An outlier correction procedure and its application to areal surface data measured by optical instruments. Meas. Sci. Technol. 21 (10), 105105. October. Kim, S., Savkoor, A.R., 1997. The contact problem of in-plane rolling of tires on a flat road. Veh. Syst. Dyn. 27 (S1), 189–206. Liang, C., Wang, G., An, D., Ma, Y., 2013. Tread wear and footprint geometrical characters of truck bus radial tires. Chinese J. Mech. Eng. 26 (3), 506–511. May. Luchini, J.R., Motil, M.M., Mars, W.V., 2001. Tread depth effects on tire rolling resistance. Tire Sci. Technol. 29 (3), 134–154. July. Matsuzaki, R., Kamai, K., Seki, R., 2015. Intelligent tires for identifying coefficient of friction of tire/road contact surfaces using three-axis accelerometer. Smart Mater. Struct. 24 (2), 025010.
Acknowledgements The research leading to these results was performed within the LORRY project (www.lorryproject.eu) and received funding from the European Community’s Seventh Framework Programme (FP7/2007-2013) under Grant agreement No. 314463.
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Naranjo, S.D., Sandu, C., Taheri, S., Taheri, Sh., 2014. Experimental testing of an off-road instrumented tire on soft soil. J. Terramechanics 56 (12), 119–137. Niskanen, A.J., Tuononen, A.J., 2014. Three 3-axis accelerometers fixed inside the tyre for studying contact patch deformations in wet conditions. Veh. Syst. Dyn. 52 (Suppl.1), 287–298. March. Pacejka, H. Tyre and Vehicle Dynamics. In: second ed. Elsevier, 2005. Pottinger, M.G., 1992. The three-dimensional contact patch stress field of solid and pneumatic tires. Tire Sci. Technol. 20 (1), 3–32. Shida, Z., Koishi, M., Kogure, T., Kabe, K., 1999. A rolling resistance simulation of tires using static finite element analysis. Tire Sci. Technol. 27 (2), 84–105. April. Singh, K.B., Ali Arat, M., Taheri, S., 2013. An intelligent tire based tireroad friction estimation technique and adaptive wheel slip controller
for antilock brake system. J. Dyn. Syst. Meas. Control 135 (3), 031002. February. Tuononen, A.J., 2009. On-board estimation of dynamic tyre forces from optically measured tyre carcass deflections. Int. J. Heavy Veh. Syst. 16. Tuononen, A.J., 2011. Laser triangulation to measure the carcass deflections of a rolling tire. Meas. Sci. Technol. 22 (12). Xiong, Y., Tuononen, A.J., 2014. A laser-based sensor system for tire tread deformation measurement. Meas. Sci. Technol. 25 (11), 115103. Xiong, Y., Zhuang, Y., Tuononen, A.J. Assessment of brush model based friction estimator using lateral vehicle dynamics. In: The12th International Symposium on Advanced Vehicle Control (AVEC), 2014, pp. 300–305. Zhang, Y., Yi, J., Liu, T., 2013. Embedded flexible force sensor for in-situ tire–road interaction measurements. IEEE Sens. J. 13 (5), 1756–1765.
ScienceDirect
Journal of Terramechanics
Journal of Terramechanics 61 (2015) 33–42 www.elsevier.com/locate/jterra
Rolling deformation of truck tires: Measurement and analysis using a tire sensing approach Yi Xiong ⇑, Ari Tuononen Vehicle Engineering Group, Department of Engineering Design and Production, Aalto University, P.O. Box 14300, 02015 Espoo, Finland Received 8 April 2015; received in revised form 13 July 2015; accepted 20 July 2015
Abstract Measurements on rolling tire deformation provide deep insights into the mechanism of generating tire forces and moments. For free rolling tires, substantial attention has been given to the rolling resistance because of its significant impact on the fuel consumption and CO2 emissions. This paper attempts to investigate the rolling resistance force through measurements of the rolling deformation of truck tires using a tire sensing approach. An optical tire sensor system is used to measure rolling tire deformation, which includes the deformed inner profile, sidewall deformation, and tread deformation. Measurements were conducted on a test truck for both new and used tires. In addition, the influences from operational factors such as wheel load and inflation pressure on tread deformation were examined and analyzed. Ó 2015 ISTVS. Published by Elsevier Ltd. All rights reserved.
Keywords: Tire deformation; Tire sensor; Rolling resistance; Tread deformation; Tire wear
1. Introduction The tire-road interface produces all the forces and moments used to alter the vehicle state through cruising, accelerating, braking, and cornering. These forces and moments are generated through deformations of rolling tires under vertical loads. Understanding of the mechanism of generating those forces and moments is the basis for vehicle system dynamics and control. Regarding tire forces and moments which affect tire handling and ride comfort, empirical tire models such as the Magic Formula (Pacejka, 2005), semi-physical tire models such as F-Tire (Gipser, 2007), and physical tire models using finite element models (Ghoreishy, 2008) have been proposed and widely used. However, for the free rolling tire force, specifically the rolling resistance, there are few precise physical tire
⇑ Corresponding author. Tel.: +358 504 335713.
E-mail address: yi.xiong@aalto.fi (Y. Xiong). http://dx.doi.org/10.1016/j.jterra.2015.07.004 0022-4898/Ó 2015 ISTVS. Published by Elsevier Ltd. All rights reserved.
models (Shida et al., 1999; Cho et al., 2013; Behnke and Kaliske, 2015) in existence, due to limited knowledge of the fundamental mechanisms of rolling resistance. The rolling resistance is defined as the energy dissipation per unit distance travelled for a free rolling tire moving in a straight direction. The viscoelastic rubber compounds in the tires, which are cyclically deformed by the road, result in an asymmetric normal stress distribution which has a shifted equivalent force located at the leading half of the contact patch. Such an equivalent force and torque are called rolling resistance force and torque. In fact, rolling resistance is an energy dissipation process to overcome the resistive force and thus drive the tire forward. The necessity and importance of lowering the rolling resistance to improve energy efficiency and reduce carbon emission in transport is therefore well recognized. For modern radial tires, it has been established that the tire rolling resistance accounts for as much as 17–21% of the total fuel consumption of ground vehicles, while the
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contribution is even higher for heavy duty vehicles (Gent and Walter, 2005). In the tire industry, great efforts have been devoted to the development of new compounds, tire contours and tread pattern design, which have greatly improved the rolling resistance performance. However, the rolling deformation of tire parts, especially the tread area, which makes the primary contribution to rolling resistance, still has not been measured. The main challenges in this measurement are the lack of proper measurement instruments, in addition to the harsh environment at the tire-road interface. Tire sensing is an emerging approach to measure tire states such as deformations and to provide information about the tire-road interface including friction level (Singh et al., 2013; Matsuzaki et al., 2015), footprint dimension (Niskanen and Tuononen, 2014), and maximum sinkage (Naranjo et al., 2014), etc., for vehicle control and tire development applications. Several studies (Hong et al., 2013; Zhang et al., 2013; Tuononen, 2009) have demonstrated the ability of tire sensing to reveal the mechanism of generating tire force and to estimate corresponding forces. In a previous study (Xiong and Tuononen, 2014), an optical measurement system using a one-dimensional laser sensor was developed to investigate the rolling resistance mechanism through tread deformation measurements on a passenger car tire. The measurement gave promising results but was only able to measure the deformation of one tread element during rolling. However, the tread deformation is not uniform along the tire cross-section. A two-dimensional (2D) laser measurement system was therefore developed to examine tire deformation over a wider area. This paper reports a recent application of this 2D sensor system on rolling deformation measurements for truck tires. The main contribution of this work lies in the investigation of the possibility for studying the rolling resistance mechanism using a tire sensing system which measures rolling deformations of a truck tire. Rolling deformations such as the deformation of the inner profile, the loaded radius, sidewall deformation, and tread deformation of
truck tires were measured. In addition, the deformations of both new and worn tires under different operational factors were compared and analyzed. 2. Material and methods 2.1. Tire sensors To measure tire deformations, especially tread deformations, an optical tire sensor system has recently been developed (Xiong and Tuononen, 2014). This non-contact sensing method is able to work in a harsh environment without affecting the local deformation. As shown in Fig. 1(a), the rolling deformation of a tire is measured by two laser triangulation sensors, Laser Sensor 1 (Keyence LJ-V7300) and Laser Sensor 2 (Keyence LK-H150), and the rolling deformation is determined by accurately measuring the rotation angle of the wheel. The Laser Sensor 1 is a two-dimensional laser profilometer with an ultra-high-speed sampling rate and large measurement range. To measure a larger region of interest, a sensor support with designated tilt angles was utilized to orient the laser towards a specific angle (Fig. 1(b)). Then, the sensor module was embedded into the sensor housing and mounted on a steel rim by means of tread attachments. To measure the angular position of the 2D laser profilometer, an optical encoder (2048 counts/revolution) within a slip ring unit (Michigan Scientific SR 20AW/T1024) was used. In addition, the Laser Sensor 2 was used to measure the dynamic loaded radius (the distance from the wheel rotation axis to the road). The proposed system is based on the measurements as follows: the sidewall height L1; the loaded radius L2, and; the sensor circumferential position h. According to the geometric relationship, the tread thickness could be calculated as: Z tread ¼ L2 ðL1 þ Loffset ÞCosh
Fig. 1. (a) Methodology for the tire sensor system; and (b) prototype for the tire sensor system.
ð1Þ
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Compared with the original tread thickness, the tread deflection can be obtained. For measurements conducted on the drum, the curvature of the drum should be considered and Eq. (1) should be modified, as demonstrated in Xiong and Tuononen (2014). 2.2. Measurement tires During the measurement, a commercially available truck tire (385/55 R22.5) was used as the test tire type. The test tire, which is regroovable, has two circumferential grooves and laterally distributed sipes. Comparison measurements were made between a brand new and a used tire that has experienced in-service wear. The tire profile and a mechanical offset Loffset were precisely measured by coordinate measuring machines. As shown in Fig. 2, the groove depth was measured to be 11.5 mm and 6.5 mm for the new tire and used tire, respectively. In addition, it is shown that the laterally distributed sipe has been worn out on the used tire. The Cartesian coordinate system defined in this work is depicted in Fig. 3. The tread deformation coordinate along the centerline of the tire cross-section pointed downwards, the lateral coordinate is aligned with the horizontal line in the interface plane, and the contact patch coordinate points towards the direction the tire is travelling. In addition, a 9 mm wide rubber stripe was glued to the tire inner liner. This rubber stripe serves two purposes. The first is to convert measurements obtained in the laser sensor coordinates to the aforementioned coordinate system. Moreover, it allows for the possible lateral movement of the carcass to be examined.
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set to zero and the slip ratio was assumed to be zero. Considering the minor influence of speed on the rolling resistance at velocities less than 100 km/h (Kim and Savkoor, 1997) and the lack of a long enough proving ground, all experiments were conducted only with one velocity at 5 km/h. However, measurements with different velocities should also be conducted in further studies. The wheel load applied on the measured tire was adjusted by alternating the pressure of the air spring. The cold inflation pressure was adjusted and checked before each measurement. Measurements were conducted for five different wheel loads and three different inflation pressures for both new and worn tires. For each operational condition, a test run of at least 20 cycles was performed. 2.4. Data processing The Laser Sensor 1 provides a direct measurement of the inner profile of the tire during rolling. Due to the high
2.3. Data collection As shown in Fig. 4, the measured tire was assembled on a truck (SISU Polar). Experiments were performed in a parking area at Aalto University, Finland, where the cross-section of the road has a crown shape that slopes at 2.6 percent from either side of the road centerline. Operational factors are controlled as follows. The truck was driven in a straight line at a constant speed of 5 km/h. Also, neither a brake nor a drive torque was applied to the wheel. In other words, the slip angle was
Fig. 3. Coordinate system and location of the rubber strip on the measurement tire.
Fig. 2. Worn tire (left) and new tire (right) used in the measurement.
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Fig. 4. Assembly of the instrumented tire on a truck.
sampling frequency and limited reflectivity of the rubber surface, outliers, which have unreasonably high and low values compared to the surrounding data, were observed in the raw data. To eliminate those outliers, a filter based on the cumulative probability neighbor median (Ismail et al., 2010) was used to process data. The filtered signal shows clear peaks when the tire was being deformed by the road (Fig. 5). Because of the large measurement range of the laser profilometer, the system can examine the tire rolling deformation over a large cross sectional area, which covers parts of the sidewall, shoulder, and crown. Such measurements can also be used to characterize the tire enveloping behavior over cleats. However, one limitation of this system is the deformed tire inner profile of a full rotation is updated only once per revolution. Measurement signals from the Laser Sensor 2 include both periodic errors and random noise. The principle cause of the periodic errors was mainly the eccentric alignment between the rotating axes of the tire and slip ring. To reduce such error, a pattern recognition procedure was defined to compensate for such error. On the other hand, the random
noise from road roughness (texture less than 1 mm) can be smoothed by a Butterworth low-pass fitter. Fig. 6 illustrates the signal processing procedure and corresponding results for the external laser measurement. The error bars represent the standard deviations of the measured loaded radius under each specific operational condition. Compared with other errors in the system, this is the dominant error which limits the measurement system performance. 3. Results and discussion In this section, measurement results on the sidewall and tread deformations, as well as the footprint characteristics are presented for both worn and new tires. In addition, measured rolling tire deformations are analyzed in the context of rolling resistance and tire wear. 3.1. Sidewall deformation While the tread deformation accounts for a major part of tire rolling resistance losses, the sidewall deformation
Fig. 5. Deformed inner profiles measured by Laser Sensor 1.
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Fig. 6. Data processing procedure for loaded radius measurements.
is typically responsible for an additional 15% loss (Gent and Walter, 2005). Because the Laser Sensor 1 is embedded into the rim, the sidewall height, which is defined as the distance from the rim to the tire inner liner, can be directly measured. Sidewall height measurements for a full tire rotation under different wheel loads are compared in Fig. 7. The deformation peaks occur during the contact between the tire and road, and the largest deformation is obtained at the highest load. On the other hand, the radius of the non-contact parts shows an opposite trend with wheel load, i.e., the radius of the non-contact parts becomes larger with increasing loads. This is due to the high extensional stiffness of the tire belt for a radial tire, which is almost in-extensible (Gong, 1993). Moreover, the volume of pressurized air does not change with increasing loads which also results in the non-contact parts were pushed outwards. In addition, a previous study (Tuononen, 2011) indicates a dependence between the magnitude of the sidewall deformation and the wheel load. Considering that observation, the wheel loads applied in this study might not actually be constant due to the dynamics of the truck suspension. To represent three
Fig. 7. The tire sidewall deformation under various load conditions (inflation pressure = 7.0 bar).
distinguished load level, measurements under three different loads (5 kN, 15 kN, and 25 kN) are presented in the following sections. 3.2. Tread deformation 3.2.1. Non-uniform deformation The information on tread deformation is of great interest to tire designers to develop low rolling resistance tires, as the non-uniform deformation is a direct result of viscoelastic rubber compounds under a cyclic deformation. In a previous study (Xiong and Tuononen, 2014), an asymmetric tread deformation along the longitudinal direction was observed and correlated the rolling resistance for a passenger car tire. For truck tire measurements, this has also been observed in most cases. Fig. 8 illustrate an example of a tread deformation measurement at a 5.5 bar and 25 kN condition. The void area in the measured deformation is due to the measurement dead zone caused by the rubber strip described in Section 2.2. To better visualize the asymmetric deformation, the centroid of each profile, which represents the asymmetry of deformation, are also plotted in both the top and side views. It can be seen that most centroids are located in the leading half of the contact patch. This again confirms that the asymmetric tread deformation along the longitudinal direction is directly linked to the rolling resistance. On the other hand, a few centroids at the edges of the footprints are observed to be located slightly in the trailing half of the contact patch. The reasons might be the following: (1) the tread deformation is small on the edge of the footprint and of comparable magnitude to the system errors; (2) for a new tire, the shoulder is deformed by the road later than other components, and therefore the major contact in the trailing half. In addition, it is interesting to note that the tread has a smaller deformation than the sidewall component.
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Fig. 8. The non-uniform tread deformation (wheel load = 25 kN, inflation pressure = 5.5 bar).
However, according to thermal finite element simulations reported in Behnke and Kaliske (2015), Cho et al. (2013), the sidewall component, despite having larger deformations, dissipates less energy than the tread. This is mainly due to the difference in the material properties between the compounds in these two components. Namely, to obtain better grip and abrasion, highly viscoelastic compounds are used for the tread, while the sidewalls use low viscoelastic compounds to reduce heat buildup and optimize cracking resistance (Gent and Walter, 2005). It can
be seen that the performance of the rolling resistance not only depends on the magnitude of deformation but also on the rubber volume and material properties. 3.2.2. Operational factor effect As shown in both Figs. 9 and 10, the influence of wheel load on tread deformation was investigated under three load conditions (5 kN, 15 kN, and 25 kN) for both new and worn tires. For the new tire, the wheel load has an opposite effect on the deformation level in the shoulder
Fig. 9. Measured tread deformations of a new tire under various loads and inflation pressures.
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Fig. 10. Measured tread deformations of a worn tire under various loads and inflation pressures.
part compared to the crown part. The deformation level of the shoulder parts increases with increasing load, whereas the crown parts show an opposite trend. This is due to the load shift effect in the lateral direction of the tire as discussed in the previous section. The same observations are reported in a previous tread deformation measurement on a passenger car tire (Xiong and Tuononen, 2014) and in normal contact stress measurements (Pottinger, 1992; De Beer et al., 2012). For the worn tire, no significant effect on the change in wheel load was observed. To examine the effects of tire inflation pressure on tire tread deformation, measurements were conducted at three inflation pressures (5.5 bar, 7.0 bar, and 8.5 bar) for both new and worn tires. For the new tire, the tire inflation pressure has an apparent influence on the tread deformation pattern. A Hertz contact-like deformation is observed at the 8.5 bar and 5 kN condition. This is a result of the reduced tire crown radius caused by the high inflation pressure and low wheel load, which causes the tire crown to be deformed by the road first. However, for the worn tire, the comparison indicates that, similar to the effect of the load, the inflation pressure has no significant influence on tread deformation pattern and the largest tread
deformation was always found on the shoulder part for worn tires. Because the tread along the cross-section has an evenly distributed volume and has homogenous material properties, the magnitude of the tread deformation in this sense represents the energy dissipation, which results in the rolling resistance. It can be seen that for a new tire, the deformation in shoulder area contributes more to the rolling resistance at a high load and low inflation pressure condition; whereas, the deformation in crown area contributes more at a low load and high inflation pressure condition. However, for a worn tire, the deformation in shoulder area always contributes more to the rolling resistance. In general, the tread deformation is greatly influenced by operational factors, such as the tire inflation pressure and wheel load. Moreover, the sensitivity of the deformation to changes in operational factors is also dependent on tire structures and mechanical properties (Clark and Schuring, 1988). 3.2.3. Wear effect In-service wear is an evitable process that continuously alters the behavior of a tire over its whole lifetime. In fact,
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wear not only reduces the volume of the tread compound and flattens the shape of the tire outer tread surface but also stiffens the tire tread. As shown in Fig. 6, such effects, due to both tire structure and material properties, will increase the tire vertical stiffness and therefore reduce the loaded radius. Moreover, changes to the tire handling characteristics caused by tire wear is also observed in Xiong et al. (2014). For the tread parts, comparison between Figs. 9 and 10 shows that the worn tire exhibits a smaller deformation than the new tire under the same operational condition. In addition, the worn tire does not clearly show the lateral shift of largest deformation with load increase which was observed in the new tire. This can be mainly explained by stiffening of the tread due to wear. Moreover, the outer contour of the worn tire also became flattened. It can be seen at the wear effect also has a great influence on the non-uniform deformation of the tread parts, thus changing the tire crown contour. This in turn accelerates the uneven tread wear (Cho et al., 2005). According to measurements in Luchini et al. (2001), used tires have a generally decreasing trend in rolling resistance with tire usage. This can be related to the measured tread deformation because a worn tire has a smaller tread deformation. Together with a decreasing volume of tread compound, the observation of a lower rolling resistance with worn tires is expected. Current international standards and labelling regulations only evaluate the rolling resistance performance for new tires. However, the above discussion implies that the whole life-time rolling resistance performance of tire should also be considered. 3.3. Footprints analysis The footprint of the tire-road contacts reflects the states of the tire and road, as it is relatively sensitive to changes in the tire structure, operational factors, and road conditions. This paper only studies the partial footprint obtained from
the measurements, which was limited by the measurement range of the laser profilometer. To analyze the footprint evolution against operational factors, as shown in Fig. 11, the following indexes are measured to characterize the footprint. The contact width W, contact length L, and contact area A are used to compare the dimension of the footprint. Moreover, the footprint-shape coefficient (Liang et al., 2013) is used to describe the footprint shape and is defined as follows: k ¼ ðb1 þ b2 Þ=180
ð2Þ
where b1 and b2 are internal angles between the footprint’s longitudinal boundaries and central line. The value of the footprint shape coefficient has the following physical meanings: if the value is larger than 1, the footprint has a concave shape; if the value is equal to 1, the footprint has a rectangular shape; and if the value is smaller than 1, the footprint has a convex shape. An image processing tool was developed to batch extract the footprint feature based on the tire deformation measurements in Figs. 9 and 10. The footprint characteristics under different operating conditions are summarized in Table 1. It is observed that the contact area decreases with decreasing wheel load and increasing inflation pressure. In addition, the worn tire has a smaller contact area than the new tire in most cases. An exception is found for measurements conducted at a 5.5 bar and 5 kN condition. Moreover, although both the contact length and width decrease with decreasing wheel load and increasing inflation pressure, the new and worn tires show different trends. The new and the worn tires have a longer contact in the contact length and width, respectively, which are both related to the corresponding footprint shapes. According to the shape coefficient, it seems that at higher load conditions, the footprint becomes more rectangular for the new tire and more concave for the worn tire. This observation implies the uneven wear on the shoulder components will be accelerated when the worn tire is subjected to a higher load, even if the load has not exceeded the nominal load.
Fig. 11. Footprint characteristics on an example footprint.
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Table 1 Footprint characteristics under different wheel load and inflation pressure conditions. New tire
Worn tire
5.5 bar
7.0 bar
8.5 bar
5.5 bar
7.0 bar
8.5 bar
Contact area (cm2)
5 kN 15 kN 25 kN
52.4 55.2 68.2
46.9 53.2 65.2
37.5 47.5 56.2
57.6 51.4 63.1
45.9 49.1 57.4
51.7 45.1 41.5
Contact length (cm)
5 kN 15 kN 25 kN
10.2 10.2 11.7
9.4 10.0 10.9
7.7 9.1 10.1
8.7 7.9 9.4
7.6 8.3 9.4
7.6 8.2 8.6
Contact width (cm)
5 kN 15 kN 25 kN
5.8 7.4 8.4
5.8 7.4 8.2
5.8 5.8 5.8
8.6 8.6 8.8
8.2 8.3 8.2
7.6 7.6 7.6
Shape coefficient ()
5 kN 15 kN 25 kN
0.85 0.91 0.90
0.84 0.89 0.93
0.85 0.84 0.98
1.03 1.04 1.11
1.06 1.06 1.13
1.11 1.12 1.10
4. Conclusions
References
The rolling tire deformations of a truck tire, including both the sidewall and tread deformations, were measured with a 2D optical tire sensor system to provide insight into the mechanism of rolling resistance generation. For tread deformation, non-uniform deformations were observed along both the longitudinal and lateral directions. On one hand, such asymmetric deformation in the longitudinal direction is a direct indication of tire rolling resistance; on the other hand, such non-uniform deformation in the lateral direction implies that contributions from separate components to rolling resistance are different under various operational conditions. Measurements on the new tire imply that for a high load and low inflation pressure, the deformation in the shoulder area will contribute more to rolling resistance. In an opposite manner, for a low load and high inflation pressure, the deformation in the crown area will contribute more. Meanwhile, the deformation in the shoulder area always contributes more to the rolling resistance for the worn tire. This will in turn accelerate the wear process on the shoulder area. This work provides a fundamental understanding on the mechanism of generating rolling resistance. This work offers the tire designer quantitative tread deformation measurements to verify finite element simulation results and to optimize tire construction and materials for better rolling resistance and wear performances. In addition, the measured deformation cycles can be used as a more realistic input in the testing of rubber compounds.
Behnke, R., Kaliske, M., 2015. Thermo-mechanically coupled investigation of steady state rolling tires by numerical simulation and experiment. Int. J. Non. Linear. Mech. 68 (1), 101–131. Cho, J.R., Shin, S.W., Yoo, W.S., 2005. Crown shape optimization for enhancing tire wear performance by ANN. Comput. Struct. 83 (12– 13), 920–933. May. Cho, J.R., Lee, H.W., Jeong, W.B., Jeong, K.M., Kim, K.W., 2013. Numerical estimation of rolling resistance and temperature distribution of 3-D periodic patterned tire. Int. J. Solids Struct. 50 (1), 86–96. Cho, J.R., Lee, H.W., Jeong, W.B., Jeong, K.M., Kim, K.W., 2013. Finite element estimation of hysteretic loss and rolling resistance of 3-D patterned tire. Int. J. Mech. Mater. Des. 9 (4), 355–366. September. Clark, J.D., Schuring, D.J., 1988. Load, speed and inflation pressure effects on rolling loss distribution in automobile tires. Tire Sci. Technol. 16 (2), 78–95. April. De Beer, M., Maina, J.W., van Rensburg, Y., Greben, J.M., 2012. Toward using tire-road contact stresses in pavement design and analysis. Tire Sci. Technol., 246–271 Gent, A.N., Walter, J.D., The Pneumatic Tire. The National Highway Traffic Safety Administration, 2005. Ghoreishy, M., 2008. A state of the art review of the finite element modelling of rolling tyres. Iran. Polym. J. 17 (8), 571–597. Gipser, M., 2007. FTire – the tire simulation model for all applications related to vehicle dynamics. Veh. Syst. Dyn. 45 (sup1), 139–151. January. Gong, S. A study of in-plane dynamics of tires, Delft University, 1993. Hong, S., Erdogan, G., Hedrick, J.K., Borrelli, F., 2013. Tyre–road friction coefficient estimation based on tyre sensors and lateral tyre deflection: modelling, simulations and experiments. Veh. Syst. Dyn. 51 (5), 627–647. Ismail, M.F., Yanagi, K., Fujii, A., 2010. An outlier correction procedure and its application to areal surface data measured by optical instruments. Meas. Sci. Technol. 21 (10), 105105. October. Kim, S., Savkoor, A.R., 1997. The contact problem of in-plane rolling of tires on a flat road. Veh. Syst. Dyn. 27 (S1), 189–206. Liang, C., Wang, G., An, D., Ma, Y., 2013. Tread wear and footprint geometrical characters of truck bus radial tires. Chinese J. Mech. Eng. 26 (3), 506–511. May. Luchini, J.R., Motil, M.M., Mars, W.V., 2001. Tread depth effects on tire rolling resistance. Tire Sci. Technol. 29 (3), 134–154. July. Matsuzaki, R., Kamai, K., Seki, R., 2015. Intelligent tires for identifying coefficient of friction of tire/road contact surfaces using three-axis accelerometer. Smart Mater. Struct. 24 (2), 025010.
Acknowledgements The research leading to these results was performed within the LORRY project (www.lorryproject.eu) and received funding from the European Community’s Seventh Framework Programme (FP7/2007-2013) under Grant agreement No. 314463.
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Naranjo, S.D., Sandu, C., Taheri, S., Taheri, Sh., 2014. Experimental testing of an off-road instrumented tire on soft soil. J. Terramechanics 56 (12), 119–137. Niskanen, A.J., Tuononen, A.J., 2014. Three 3-axis accelerometers fixed inside the tyre for studying contact patch deformations in wet conditions. Veh. Syst. Dyn. 52 (Suppl.1), 287–298. March. Pacejka, H. Tyre and Vehicle Dynamics. In: second ed. Elsevier, 2005. Pottinger, M.G., 1992. The three-dimensional contact patch stress field of solid and pneumatic tires. Tire Sci. Technol. 20 (1), 3–32. Shida, Z., Koishi, M., Kogure, T., Kabe, K., 1999. A rolling resistance simulation of tires using static finite element analysis. Tire Sci. Technol. 27 (2), 84–105. April. Singh, K.B., Ali Arat, M., Taheri, S., 2013. An intelligent tire based tireroad friction estimation technique and adaptive wheel slip controller
for antilock brake system. J. Dyn. Syst. Meas. Control 135 (3), 031002. February. Tuononen, A.J., 2009. On-board estimation of dynamic tyre forces from optically measured tyre carcass deflections. Int. J. Heavy Veh. Syst. 16. Tuononen, A.J., 2011. Laser triangulation to measure the carcass deflections of a rolling tire. Meas. Sci. Technol. 22 (12). Xiong, Y., Tuononen, A.J., 2014. A laser-based sensor system for tire tread deformation measurement. Meas. Sci. Technol. 25 (11), 115103. Xiong, Y., Zhuang, Y., Tuononen, A.J. Assessment of brush model based friction estimator using lateral vehicle dynamics. In: The12th International Symposium on Advanced Vehicle Control (AVEC), 2014, pp. 300–305. Zhang, Y., Yi, J., Liu, T., 2013. Embedded flexible force sensor for in-situ tire–road interaction measurements. IEEE Sens. J. 13 (5), 1756–1765.