EXPERIMENTAL ANALYSIS OF A CONTACT PATCH FORM OF A ROLLING TIRE: INFLUENCE OF SPEED, WHEEL LOAD, CAMBER AND SLIP ANGLE

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1 EXPERIMENTAL ANALYSIS OF A CONTACT PATCH FORM OF A ROLLING TIRE: INFLUENCE OF SPEED, WHEEL LOAD, CAMBER AND SLIP ANGLE Pavel Sarkisov *, Günther Prokop, Steffen Drossel Technische Universität Dresden, Chair of Automotive Engineering Germany Sergey Popov Bauman Moscow State Technical University, Chair of Wheeled Vehicles Russian Federation ABSTRACT The first steps on the way to autonomous driving are already made: Advanced Driver Assistance Systems (ADAS) control vehicle motion based on a number of real-time measurements. Control algorithms of such systems like Electronic Stability Program (ESP), Emergency Steering Assist (ESA) and Active Rollover Prevention (ARP) consider a tire as a black box. If the tire instead of a black box becomes a sensor, for example, for friction potential, operational efficiency of these systems can be improved. Towards this necessity comes so called Intelligent Tire Technology : According to it a module of tire pressure monitoring system is mounted not on the rim, but on the tire. Consequently an integrated acceleration sensor can gain relevant information for driver assistance systems. Finnish scientists Arto Niskanen and Ari Tuononen have proposed a promising algorithm to estimate the friction potential of a rolling tire: A high-bandwidth acceleration sensor on a tire inner liner shows perceptibly different signals of radial acceleration within the grip and slip region of a contact patch of a braking tire. A goal of this research is to understand physical background of a contact patch formation and to investigate applicability the described method for friction potential estimation in different rolling conditions. First, a change of a contact patch shape depending upon tire rolling speed, camber and slip angle was investigated experimentally. Then these observations were introduced in a physical tire model. Based on this model there was investigated an influence of rolling conditions like brake slip, camber and slip angle on quality of friction potential estimation with proposed method. There were generated insights regarding applicability of the method not only for longitudinal slip (braking tire), but also for lateral slip (cornering tire) and combined slip. Sarkisov 1

2 MOTIVATION The first steps on the way to the automated driving are already made: the Advanced Driver Assistance Systems (ADAS) control the vehicle motion based on a number of real-time measurements. The control algorithms of such systems like Electronic Stability Program (ESP), Emergency Steering Assist (ESA) and Active Rollover Prevention (ARP) consider a tire as a black box. If the tire instead of the black box becomes a sensor for friction coefficient and lateral force, the operational efficiency of these systems can be improved. Towards this necessity comes so called Intelligent Tire Technology : according to it a module of tire pressure monitoring system is mounted not on the rim, but on the tire. Consequently the information from an integrated acceleration sensor can be used by assistance systems [1]. This concept represents a number of benefits, both for ego-vehicle and for following vehicles: the most promising ones are depicted on the figure 1. STATE OF THE ART One approach to friction potential estimation Finnish scientists Arto Niskanen and Ari Tuononen have proposed a promising algorithm to estimate the friction potential of a rolling tire. They have put three acceleration sensors on the inner surface of the tire carcass. Analyzing the change of radial acceleration in the contact patch they have succeeded to detect aquaplaning effects [2]. Next they have measured a braking wheel [3]. The higher is braking torque, the smaller is grip region in the contact patch and the bigger is slip region in it. The signal of the radial acceleration shows clearly these two regions: it has practically constant value in the grip region (because the sensor literally stands still) and perceptibly oscillated values in the slip region (because the sensor slides along a rough road surface and oscillates in vertical direction, Fig. 2). Figure 2. Measurement results of braking wheel by A. Niskanen and A. Tuononen [3]. Figure 1. Tasks for tire as a sensor (Background picture: AUDI AG, Presskit 08/15) But in order to clarify, how to get the relevant information from in-tire sensor in a most efficient way, it is necessary to understand several phenomena of tire behavior. The main insight is following: with help of acceleration sensor it is possible to get lengths of a grip and slip regions in a contact patch. An origin of the slip is not important for the sensor. Here arises the first question: Can this approach be used not only by braking, but also by accelerating and cornering? Additionally to it, several important features of this approach have to be considered. Sarkisov 2

3 Firstly it does not directly provide absolute value of the slip limit. On the one hand, this estimation cannot be directly used for other vehicles or for surface characterization. But on the other hand, it shows real proportion between sliding and gripping in the contact patch for the ego-tire. Secondly, one sensor provides data only once per revolution. Hence, these data can be used for egotire only if friction conditions do not change much on a scale of one revolution, or for a rear tire and other vehicles via Car2X-communication. Thirdly, one sensor provides the lengths of the regions only for one longitudinal cross-section of the tire. At that point further questions arise. Contact patch shape, and consequently strain figure in it, may depend upon wheel load, camber angle, slip angle and angular velocity. Can the relation between grip and slip regions, measured on the one longitudinal cross-section of the contact patch, be reliably extrapolated to the whole contact patch area? What is the necessary number of sensors and what are their optimal positions? In order to answer these questions it is necessary to understand the physical background of processes in the rolling tire. Tire contact patch analysis The shape of a contact patch of a rolling tire under kinematic excitation has been estimated with help of finite elements methods [4, 5] or directly on a motionless tire [6]. Mentioned papers have shown a significant influence of slip angle on the contact patch shape and its strain figure. It is remarkable that the mentioned application of acceleration sensors [3] delivers reproducible data regarding the length and position of a contact patch. For the investigation of tire aquaplaning there were used three sensors [7-9], but in order to understand the shape of a contact patch more sensors are required. MISSION STATEMENT A goal of this research is to understand the physical background of a contact patch formation and to investigate applicability the described method for friction potential estimation [3]. On the way to this goal it is necessary: - to investigate experimentally the change of a contact patch shape depending upon tire rolling speed, camber and slip angle; - to develop a simulation model for strain analysis in the contact patch; - to analyse applicability of the method for lateral and combined slip (cornering tire); - to determine required amount and optimal position of the acceleration sensors; For the purpose of direct experimental observation of the contact patch shape there was selected an approach to measure acceleration, but with higher resolution than before. RESEARCH METHODOLOGY As it was shown in [7-9], three acceleration sensors located on the half of tire width provide an acceptable estimation of contact patch shape, but only if it is symmetric about the longitudinal axis. As far as the contact patch of a cornering tire is not symmetric, the number of sensors has to be at least doubled. Considering the reference sensor in the middle plane of the tire, seven sensors are required (Fig. 3). Figure 3. Seven acceleration sensors inside the tire were used to obtain seven values of contact patch length and to reconstruct its shape. Sarkisov 3

4 For this application there was selected a widebandwidth acceleration sensor (range: ±500 g; nonlinearity: 2 %; bandwidth: 20 khz). In order to separate influence of the tread blocks and grooves between them on the acceleration measurement, two different samples were used: a complete tire and a tire carcass without tread layer. During each revolution of a tire the signal of radial acceleration depicts specific reproducible elements: On the figure 4 there is depicted exemplary measurement result for complete tire and the carcass, both were rolling with 100 km/h and were loaded with 7 kn. Because of the form of the signal, which has two steps, there was selected a median filter with the window size of 11. In the free part of the tire the radial acceleration is nearly constant (AB, Fig. 4). Approaching the contact patch, tire curvature increases, hence the acceleration value grow too (BC0). Then (C0E) the value drops rapidly to the value of centrifugal acceleration of the point on a drum (EF). Next happen same effects backwards (FH0, H0K, KA'). A typical problem of the in-tire sensor is the fact that a sensor has nonzero length [10, 11]. Because of the length of the sensor the drop C0E and growth FH0 are smoothed instead of being stepwise. Resulting from this problem the absolute value of the contact patch length can be hardly determined, but it is enough to perform comparison study. For this purpose there were defined terms conditional start, end and length of the contact patch : The middle points of radial acceleration drop CD and rise GH are assumed to be conditional start and end of the contact patch respectively, the distance between them conditional length. As distinct from points C, D, G and H, the positions of conditional start and end are assumed, not measured. Figure 5 exemplifies this description. The seven acceleration sensors are called with capital letters: sensors A G. For comparison there is shown the footprint of the non-rolling tire on the same drum with the same wheel load. The difference between static footprint and the measured with acceleration sensors contact patch length is not considered intentionally, because the values of conditional contact patch length are reliable enough to describe qualitative change of the contact patch shape, they are not reliable enough to detect the absolute value of the contact patch length. EXPERIMENTAL OBSERVATIONS Next subchapters summarize the observations regarding the change of the contact patch shape in relation to different influencing factors. During all following tests the vertical position of wheel was continuously adjusted in order to keep the wheel load on the same given level. As far as a tire is a flexible body, its rotation causes radial deformation because of centrifugal forces. This effect may change not only the contact patch, but also the vertical reaction force. With the increasing speed the wheel had to be Figure 4. Measurement of radial acceleration in tire and carcass, one revolution. Sarkisov 4

5 Figure 5. A comparison of the footprint measurement of non-rolling tire and a measurement of the contact patch length with acceleration sensors. lifted to keep the same wheel load: Carcass rate is 1 mm per 100 km/h; tire rate is 1.5 mm per 100 km/h. This result illustrates well the influence of the tread mass. Contact patch geometry depending upon rolling speed Even though vertical position of the wheel was adjusted and the wheel load was kept the same, both tire and carcass show light continuous growth of the contact patch length with the speed, the rate is ca % per 100 km/h. As a reference serve results of [12]: in this paper there was used an in-tire strain sensor. The strain curve within one revolution describes similar tire curvature. Variation of rolling speed has also shown no significant influence on contact patch length. Correlation of these results stands for reliability of the applied method. This rate was observed for wheel all load values (3, 5, 7 kn), with both camber values of 0 and -4. The same effect was found by cornering (tire was rolling with 3 slip angle, carcass with 1 ). Contact patch geometry depending upon camber angle Camber angle variation in the range causes linear change of the contact patch length, both for tire and carcass and for all three values of wheel load. The rate of the length change achieves 12 % per degree of camber in the sensors A and G, and is zero in the middle sensor D. As far as tire form is symmetric about longitudinal middle plane, two shapes of the contact patch, measured with positive and negative slip angle values, are also symmetric about longitudinal plane of the tire. Hence, on the figures 6-8 there are shown measurements of the sensors, which are located on one half of the tire: from middle (sensor D) to right-hand sidewall (sensor G). The change of the contact patch happens in a linear manner, contact patch stays symmetrical around the lateral axis (fig. 6). Sarkisov 5

6 tire combines carcass lateral deformation and tread shear. For the purpose of separation of these effects the first measurement series was performed with the tire carcass sample, which has no tread layer. Figure 7 gives an overview of contact patch length in four cross sections (D G) for three wheel load values. The same test of the complete tire with the tread layer shows qualitatively same results, but the difference of contact patch length is lower, because the tire deformation is smaller (Fig. 8). Figure 6. Positions of conditional contact patch start and end points by camber variation of the tire for three wheel load values. Contact patch geometry depending upon slip angle The focus of this analysis is a contact patch change in the linear range of slip angle: With help of FE-methods it was shown in a number of papers [4, 5] that the contact patch shape change is connected with lateral and longitudinal deformation of tire. Taking into account tire structure, it is reasonable to conclude that the tire contact patch shape is mainly determined by carcass deformation. But cornering Figure 7. Positions of conditional contact patch start and end points by slip angle variation of the carcass for three wheel load values. Sarkisov 6

7 2. Contact patch shape changes with slip angle in asymmetric manner: leading and trailing edges differ significantly (unlike the case of camber variation, Fig. 9-10); 3. Contact patch shape changes with slip angle in a non-linear manner in regard to slip angle (again unlike the case of camber variation). The carcass measurement visualizes the saturation of carcass lateral deformation (and consequently lateral force) very well: linear range for carcass is just from 0 to 1, and the length values starting from 2.5 receive practically no change anymore. Numerically considered, the change rate of contact patch length achieves 15 % per 1 of slip angle for tire and 25 % per 1 of slip angle for carcass. Figure 8. Positions of conditional contact patch start and end points by slip angle variation of the tire for three wheel load values. Summary of the experimental analysis In order to evaluate contact patch shape, through the seven positions there was interpolated a polynomial curve (order 3 to 5). This approach helps to visualize shapes and summarize the conclusions, which are reproducible and valid for different wheel load values: 1. The change of the contact patch shape depending upon the rolling speed can be neglected; Figure 9. Interpolated leading (top) and trailing (bottom) edges of the contact patch by 7 kn wheel load. Sarkisov 7

8 Figure 10. Interpolated leading (top) and trailing (bottom) edges of the contact patch by 7 kn wheel load, camber angle is In all conducted measurements the contact patch length in the tire middle plane (sensor D) is insensitive to speed, camber or slip angle variation. Next these observations have to be considered in a physical model in order to investigate the adaptability of the friction potential estimation method in case of cornering tire. SIMULATION TOOL For the purpose of research the model has to be able to consider two dimensional contact patch and flexible carcass of the tire. As the basis there was selected structure, which describes carcass with model flexible belt (beam) on elastic foundation and tread with two-dimensional array of brush elements, constructed on the belt [13] (Fig. 11). The observed changes of the contact patch shape were introduced in this model, considering their physical background: this change is linearly connected with the lateral deflection of the tire carcass, not with the slip angle. It explains observed non-linearity in the contact patch shape change in respect to slip angle. The model was validated with measured transient response of lateral force and aligning torque to slip angle step. This tool makes it possible to analyze stain figure in the contact patch: to calculate utilized friction potential, to separate longitudinal and lateral components of it and to analyze sliding speed. Relevant modeling conditions Firstly, the model discretizes the contact patch into a number of elementary areas. Shear of each area is described with one brush element. For current analysis the element dimensions were set to 4.2 mm x 4.2 mm. Consequently, simulated strain figure shows the slip region borderline with resolution of 4.2 mm. Secondly, the used structure of the model considers lateral deflection of the carcass precisely, but neglects carcass longitudinal flexibility, because it is usually much lower (stiffer) as lateral one. Due to this, the model utilizes same friction potential with lower longitudinal slip values, as real tire does. Still this structure is valid enough to meet the set goal of this research. Thirdly, in order to get bigger contact patch, the analysis is conducted for the wheel load according to tire load index (7 kn). Figure 11. Structure of the physical model, which considers tire carcass and tread separately. Sarkisov 8

9 Fourthly, as long as sensor delivers required data once per revolution, processes are considered in a steady state. Next there will be considered single cases of rolling with the focus on strain figure in the contact patch. up to the slip limit. Simulation results show practically same behavior for driving slip. Simulation results Figures 12, 14, 16 and 17 depict strain figures in the contact patch in different conditions as a top view on the tire carcass and contact patch. Figures 13, 15 and 18 show tire excitation (slip angle, camber, brake slip) on upper diagrams and utilized friction potential. The model makes it possible to consider utilization rate of this potential in longitudinal kk ssss and lateral kk ssss directions separately as well as whole utilization rate kk ss : kk ssss = FF xx μμff zz (Equation 1) kk ssss = FF yy μμff zz (Equation 2) kk ss = kk ssss 2 + kk ssss 2 = FF xx 2 +FF yy 2 μμff zz (Equation 3) where FF xx, FF yy and FF zz are longitudinal, lateral force and wheel load respectively, μμ is friction coefficient. The model also shows the lengths of grip and slip regions in a given longitudinal crosssection of a tire, which represent the data measured by acceleration sensor in order to estimate friction potential. In the most steady-state rolling conditions tread shear develops close to linearly from zero (leading edge) to slip limit. It is fair to say that described approach cannot reasonably notice utilization of friction potential in range from 0 to 0.5, because in these cases grip region is negligibly small, but shear forces are non-zero. Hence, the measured lengths of grip region ll gg and slip region ll ss can be recalculated to the estimated rate of utilized friction potential kk eeeeee in a following way: Figure 12. Strain figure of the tire rolling straight ahead with brake slip of -7.5 %. The estimation error of utilized potential rate is below 5 %, as long as rate exceeds 0.5. Figure 13 depicts a specific delay between real potential utilization and measured value. kk eeeeee = 1 ll gg 2 ll ss +ll gg (Equation 4) Rolling straight ahead with brake slip features symmetric contact patch, strain figure depicts linear growth of longitudinal shear deformation Figure 13. Real and estimated rate of utilized friction potential rate of the tire rolling straight ahead with brake slip excitation. Sarkisov 9

10 It is caused primarily by discretization of the contact patch and low speed of rolling (3 km/h). For the steady-state rolling with the operational speed this delay decreases significantly. At 0.12 s the sensor shows small increase of utilized potential, which does not corresponds to reality. This error is caused by disadvantage of the estimation principle: last row of brush elements carry less vertical force than others, thus elements in the last row start to slide even with small excitation and sensor notices it. Rolling with camber angle (-4 ) causes practically no sliding, but features different contact patch shape. It becomes relevant once tire is rolling with both camber and brake slip (Fig. 14). Still the estimation error stays below 5 % (Fig. 15). Figure 15. Real and estimated rate of utilized friction potential rate of the cambered tire (-4 ) with brake slip excitation. Figure 14. Strain figure of the tire rolling with camber angle of -4 and brake slip of -7.5 %. Rolling with the slip angle (3 ) emphasizes asymmetric shape of the contact patch, hence, asymmetric strain figure (Fig. 16). An application of the brake slip by cornering tire (Fig. 17) moves borderline between grip and slip regions forward, but this line has still same form as leading edge. Because of this effect, the rate between grip and slip regions in different longitudinal cross-sections of the tire is different. The sensor in the middle still provides estimation with error below 5 %. (Fig. 18). Figure 16. Strain figure of the tire cornering with slip angle of 3. For all described cases it is fair to conclude that the form of borderline between grip and slip regions is primarily defined by leading edge of the contact patch, because in the described cases steady-state shear deformation grows linearly starting from zero on the leading edge. Sarkisov 10

11 Even though the contact patch shape varies significantly with camber or slip angle, estimation of utilized friction potential rate with one sensor located in the middle plane does provide for considered conditions high accuracy (above 95 %). An additional aspect, which is relevant for the method, is a sliding speed in a sliding region. These values are compared for the four described cases on the figure 19. The skyrocketing of the curves on the last row of the contact patch is caused by decrease of the vertical load on them, so the shear forces pull the blocks back in initial condition. Apart from last rows, the values of the sliding speed for four cases have same order of magnitude. Figure 17. Strain figure of the tire cornering with slip angle of 3 with brake slip of -7.5 %. Figure 19. A comparison of sliding speed values in the sliding region of a contact patch depending upon the rolling conditions. It was determined that the sliding speed in the sliding region of the contact patch of a tire, cornering with slip angle of 3, corresponds to the sliding speed of the straight ahead rolling tire with brake slip of -5 %. As far as both values belong to a linear range of longitudinal or lateral force generation, it is fair to confirm the reasonability of application of the described estimation method not only for braking, but also for cornering tire. Figure 18. Real and estimated rate of utilized friction potential rate of the cornering tire after slip angle step (3 ) and additional brake slip excitation. SUMMARY AND OUTLOOK Important insights of this research can be summarized in a following way: Sarkisov 11

12 1. Contact patch shape: - does not change significantly with rolling speed variation; - changes with camber variation linearly (up to 12 % per 1 ), shape stays symmetric; - changes with slip angle variation slightly nonlineraly (up to 15 % per 1 ), shape becomes asymmetric; - experience practically no change in the middle longitudinal plane of the tire. 2. According to the simulation results based on developed physical model: - even though the strain figures feature asymmetry, one sensor located in the middle plane of a tire provides estimation of utilized friction potential in range from 0.5 to 1 with error below 5 % for longitudinal slip (braking tire), lateral slip (cornering tire) and combined slip. - The sliding speed in the sliding region of the contact patch of the cornering tire with slip angle of 3 corresponds to the sliding speed of the straight ahead rolling tire with brake slip of -5 %. This observation confirms the reasonability of application of the described estimation method not only for braking, but also for cornering tire. According to the trends of automotive industry, the next task is to expand this method in order to be able to know the background of the measured ratio between lengths of grip and slip region: how high is longitudinal and lateral component of it? Can a driver assistance system apply more brake torque or increase steering angle? This challenge may serve as a promising objective for further research. The results of current investigation improve an understanding of contact patch physics and contribute to development of one promising method of tire friction potential estimation, which is strongly necessary at the present day for enhancement of driver assistance system, development of autonomous driving and improvement of the road traffic safety. REFERENCES [1] Tiberio, E. & Morinaga, H Bridgestone s CAIS Technologie für eine detaillierte Fahrbahnzustandsklassifizierung. 11. ÖAMTC Symposium Reifen und Fahrwerk, Wien, Austria. [2] Tuononen, A. et al Tyre contact length on dry and wet road surfaces measured by three-axial accelerometer. Mechanical Systems and Signal Processing, (52-53): [3] Niskanen, A., Tuononen, A., Tireroad contact condition measurements by an intelligent tire. Tire Technology Expo [4] Jo, H.Y. et al Development of Intelligent Tire System, SAE Technical Paper ( ). [5] Kuwayama, I. et al Development of Large and Narrow Tire Technology as Ologic, Proceedings of 23rd Aachen Colloquium Automobile and Engine Technology 2014, [6] Gim, G & Choi, Y Role of tire modeling on the design process of a tire and vehicle system. Korea ADAMS User Conference. 11, 8-9. [7] Matilainen, M. & Tuononen, A., Tyre contact length on dry and wet road surfaces measured by three-axial accelerometer. Mechanical Systems and Signal Processing, Issue 52-53, pp [8] Niskanen, A. & Tuononen, A. J., Three 3-Axial Accelerometers Fixed Inside the Tyre for Studying Contact Patch Deformations in Wet Conditions. Vehicle System Dynamics, 52(5), pp [9] Niskanen, A. & Tuononen, A. J., Three Three-Axis IEPE Accelerometers on the Inner Liner of a Tire for Finding the Tire-Road Friction Potential Indicators. Sensors, 15(8), pp [10] Kubba, A., Tire strain measurement system using piezoelectric elements. Tire Technology Expo [11] Lee, H., Kim, M.T. & Taheri, S Direct Estimation of Tire contact features using strain-based intelligent tire. Tire Technology Expo [12] Kim, S., Kim, K.-S. & Yoon, Y.-S., Development of a tire model based on an analysis of tire strain obtained by an intelligent tire system. International Journal of Automotive Technology, 16(5), pp [13] Sarkisov, P., Prokop, G., Popov, S The non-steady-state tire model as a set of physical submodels for driver assistance systems analysis. P. Pfeffer (Ed.). Proceedings of 6th International Munich Chassis Symposium, pp Sarkisov 12