Measurement of Tire-Pavement Contact Tri-Axial Stress Distribution Based on Sensor Array

Abstract

A tire’s three-dimensional stress for pavement is an important cause of asphalt pavement disease. In order to study the contact stress distribution between the tire and the pavement under real conditions, a sensor that can measure the tri-axial stress synchronously is designed, and a complete measurement system is established. The variation trend and stress value of tri-axial stress under steady rolling of the tire were obtained, and the stress distribution characteristics were analyzed. The results show that the stress in the three directions near the tire shoulder is greater than that in the crown area, and the stress peak moves gradually from front to back with the rolling of the tire. Compared with the simplified simulation model, these results provides valuable suggestions for exploring the real tire-pavement interaction.

1. Introduction

Fatigue cracking of asphalt pavement is one of the main problems of asphalt pavement damage [1]. Pavement damage not only reduces driving comfort and pavement service life, but also directly threatens vehicle driving safety [2]. The top-down cracking (TDC) may be initiated on the surface of the pavement, and it is the main form of pavement distress [3]. As shown in Figure 1, initially, the cracks develop vertically, and then mesh-shaped cracks gradually appear horizontally and vertically staggered and eventually extend from the pavement surface to the subgrade. Once the crack runs through the surface layer, it will cause rainwater and other impurities to penetrate between the structure layer of the pavement, resulting in loose asphalt loose and the peeling of the surface layer, which increases the stress concentration effect at the crack edge, and greatly reduces the service life of the pavement in a short time [4]. It is widely believed that TDC development is not ascribable to a single cause, but rather to the combination of multiple factors. Traffic loadings are the main factor in TDC development. TDC develops in a localized way as a result of the tire-pavement contact stresses, which can determine the onset of tensile and/or shear stresses at or near the wheel path. Because of the localized nature of the phenomenon, the tire characteristics are of great importance, as they strongly affect the contact stresses. For thick pavements, the main TDC mechanism is related to the localized tire-pavement contact stresses, which strongly depend on the tire characteristics and determine the onset of critical tensile and/or shear stresses on the pavement surface. For thin pavements, a global bending-induced mechanism (linked to the pavement structural response to traffic loadings) prevails [5]. By measuring the tire contact stress distribution under the real-time load and analyzing the mechanical response between the tire and the pavement surface, we can not only explore the structural damage and distress mechanism of the asphalt pavement, but also optimize the asphalt pavement design model so that the performance of the pavement can reach the standard over the whole service period and the maintenance cost is the lowest.

In order to study the changing characteristics of the contact stress between tire and pavement surface, the contact shape of tire and pavement surface should be clarified first. In the design specifications of Chinese asphalt pavement [6], the elastic layer continuum theory under double circular uniform load is adopted for calculation. The contact surface of the default tire and the pavement is round, and only the load is evenly distributed. Obviously, this method is more simplified than the actual situation. The contact area of the tread in the static state can be effectively obtained by the thermal paper method footprint, paint method footprint, stress plate, and other methods [7]. With the increase of the mass of the load, the area of contact with the tire pavement also increases, but increased tire stress will lead to the opposite result [8]. However, these methods cannot measure the contact area of the rolling tire, and many scholars use simulation software for tire-pavement contact modeling analysis [9,10,11,12]. The change in vehicle working condition is the key factor affecting the change in contact stress, the peak value of contact stress under braking conditions is greater than that at rest, and shear stress has a considerable effect on the development of ruts and vertical cracks. In the process of simulation, in order to reduce the amount of calculation and shorten the calculation time, it is usually simplified to the tire pattern and pavement texture. Different model simplification methods will cause different stress distribution results [13], so some damage phenomenon on the pavement surface cannot be correctly explained. It is difficult to accurately obtain a tri-axial stress distribution under real conditions by simulation methods. Studies have shown that the distribution of tire-pavement contact stress is complicated, usually consisting of longitudinal, lateral, vertical stress [14,15,16]. In the actual environment, the tire type [17], inflatable pressure [18], pavement texture [19], and vehicle load [20] have a great impact on the distribution of contact stress. In view of this, many scholars have further developed a direct measurement method based on sensors, which can better analyze the mechanical characteristics of tires and pavement. Howell [21] designed the sensor to measure the static contact stress of aircraft tires. Chell.F [22] used a polyvinylidene fluoride (PVDF) sensor to study the dynamic measurement of the contact stress between the tire and pavement surface. Douglas [23,24], used an electric motor to drive a wheel on a large ring road. Because it is limited by the rotating arms, the rolling tire is different from the real conditions. De Beer [25,26] measured the contact stress of heavy trucks; however, the speed was only 0.3 m/s. The L -shaped sensor developed by Gabriel Angelache [27] did not consider the pavement texture and tire pattern. Yi Xie [28] buried the pressure sensor into the rectangular asphalt concrete and measured the vertical stress distribution of reduced-diameter tires. Intelligent methods such as ultrasonic [29] and image processing technology [30] are also gradually applied to this measurement, and the accuracy of which depends solely on the algorithm. In practical applications, environmental noise, vibration impact and other factors cause limited use of precision instruments. In the early stage, we designed a sensor to measure the tri-axial stress in the tire-pavement contact area and obtained some preliminary data of sensor performance [31]. In this paper, we improved the structure of the sensor, changed the type of strain gauge, and established a complete real-vehicle test platform, including master systems and subsystems. This paper presents only the results of stress distributions on three orthogonal directions measured in the contact patch of a 215/50R17 car tire with 2.4 bar inflation pressure, at 16 km/h speed, and in free rolling conditions.

2. Sensor Design

The center of mass of the tire is taken as the origin to establish a three-dimensional spatial coordinate system, as shown in Figure 1, in which Fx is the driving direction, which is defined as longitudinal, Fy is the vertical driving direction, referred to as lateral, and Fz is the vertical. The dynamic load applied by the tire mainly includes moving load, impact load and random load superposition.

2.1. Sensor Structure

The upper layer material of the high-grade highway is usually SMA-13 or AC-13 asphalt concrete with a particle size of 13 mm. In a real pavement surface, the tire pavement contact path is usually supported by a textured surface, sensors, and surrounding pins that mimic road aggregates in asphalt. The assembly layout and single structure of the improved sensor array are shown in Figure 2. The middle sensitive area of the strain sensor is a hollow, four-sided, thin-walled structure with a thickness of 0.8 mm and a width of 10 mm. In order to ensure that the strength of the thin-walled structure can meet the requirements of the high-speed rolling of heavy truck tires, and considering the actual machining capacity of the machine tool, the width of the top of the single sensor is designed to be 15 mm, and the width of the base is 16.5 mm. The hollow in the middle of the thin wall is used to add the measuring bridge circuit, and the wire is connected to the data acquisition system through the circular hole in the center of the sensor. The diameter of the base of the sensor is 13 mm, and the 3 mm slot is designed to ensure that the sensor will not rotate when fixed on the base.

2.2. FEA and Strain Gauge Arrangement

The finite element software ANSYS (19.0) was used to conduct finite element analysis on the elastic body, and the stress and strain changes under the stress state were simulated to obtain the best position for attaching strain gauge. In fact, the sensor and the bottom plate are fixed tightly and are seamless. In order to simplify the analysis, fixed constraints are used to analyze the bottom of a single sensor. Under static conditions, considering the tire contact area, maximum load, strength of sensor material, and impact strength, the value of calibration force in three directions is determined by calculation as 700 N, which is conservative in distance from the maximum limit measured by the sensor. The sensor is made of 17-4PH martensitic stainless steel. This grade of the material has the characteristics of high strength, high hardness, and corrosion resistance. After heat treatment, the mechanical performance of the sensor is better. There are 33,648 nodes and 18,852 units in finite element mesh division. Due to the symmetrical structure of the sensor, an equivalent analysis can be carried out in the directions of Fx and Fy. When a horizontal force Fx (Fy) 700 N is applied to the top of the sensor, both sides of the sensor through the hole are compressed, and the orange part should be equivalent to 0.0012135, and a positive strain is generated at symmetrical sites. In this way, the stress in the Fx or Fy direction can be measured by sticking a strain gauge to measure the strain in the sensitive area. When a vertical downward force of Fz 700 N is applied to the top, the strain at the four top angles in the middle part of the sensor is the most sensitive, and the strain value is about 0.00011321. Since XY strain gauges have been attached to the lower part and Z strain gauges to the upper part, it is more appropriate.

The strain gauge is a very sensitive device. When pasted onto the surface of the elastic body, it generates the same strain as the component. When the strain gauge is stretched or compressed, the resistance value changes, and the resistance value is converted into voltage or current. Based on the stress-strain analysis of the elastic element, the sensitivity of the sensor can be improved, and the coupling effect can be reduced by appropriately arranging the strain gauge to form the measuring bridge.

According to the FEA analysis in this chapter, in order to ensure sufficient sensitivity of the sensor, the structure of the strain gauge is arranged on the elastic body, as shown in Figure 3.

The X and Y directions are symmetrical, and two pieces of feather strain gauge are pasted, respectively, totaling four pieces. A single feather strain gauge contains two independent resistance wires, so two pieces can form a set of full bridge circuits. Where R1 and R4 are stretched as a positive strain, R2 and R3 are compressed as a negative strain, thus forming a Wheatstone bridge for measuring the X direction. Similarly, bridge formation in Y direction and X direction is the same. R5 and R8 are stretched as a positive strain, and R6 and R7 are compressed as a negative strain, but the direction is orthogonal to the X direction. In the Z direction, two groups of strain gauges are connected in a series to form a group of bridge arms. R9 and R12 are pasted vertically and compressed after being stressed, R10 and R11 are pasted horizontally and stretched after being stressed, and four rectangular strain gauges are pasted in the Z direction to form the full bridge circuit. The advantage of the sample arrangement is that the vertical stress measurement is more uniform. R_Ni and R_S are temperature compensation resistance and zero adjustment resistance, respectively. After the completion of the strain gauge pastes and electric bridge connection, the outer end of the sensor is sealed with silicone to protect the measuring circuit.

2.3. Calibration

When the sensor is produced, the range, sensitivity, repeatability, and other parameters are determined, which can be obtained by calibration. The relationship between the deformation of the elastomer and the measuring circuit is almost linear. Some interference can be eliminated by the decoupling matrix method. The laboratory gravity acceleration is 9.794 m/s², and the standard weight calibration platform is used for the static calibration of the strain sensor. The sensor calibration process is shown in Figure 4. Firstly, the sensor is fixed horizontally on the special bracket, and the X direction is vertically downward, and the side of the sensor is attached directly below the loading boom. The weight is increased step-by-step by 100 N, and the relationship between the load and A/D conversion voltage is obtained through the data acquisition system. Then, the sensor was rotated 90° horizontally to obtain the calibration data in the Y-direction in the same way. After the XY direction measurement is complete, place the sensor vertically with the top surface close to the boom and calibrate the Z direction.

Calibration results are shown in Figure 5. Because the XY direction is symmetrical, the curve shape is almost consistent with the data. When the maximum load is 700 N, the output voltage of the XY direction sensor is about 2.521 V, and the output voltage of the Z direction is about 1.213 V. The linearity of the three directions was excellent.

In order to ensure full contact between the tire and the sensor, a total of 27 sensors were made to form the sensor array. The average sensitivity of all sensors is shown in

Table 1. Sensors’ average sensitivity.

	X Direction	Y Direction	Z Direction
Sensitivity(mV/V)	0.54379	0.51827	0.23914

. We have calibrated all sensors separately. In the acquisition system, the calibrated data of each data channel and sensor is one-to-one corresponding, which makes the measurement results more accurate.

3. Measurement System Architecture

3.1. Master System

The master system architecture of the measurement is shown in Figure 6. The master system consists of sensor array and acquisition system. Each sensor can measure three directions and contains three channels. A total of 81 measurement channels are required for 27 sensors. There are 27 sensors arranged in a straight line, as shown in the purple square in Figure 6. The other parts are support pins simulating asphalt pavement. The sensors are made of metal, and the friction coefficient of their surface is quite different from that of the asphalt pavement. The sensor array is fixed by the frame and is horizontal with the surface of the pavement. A shielded cable is used to connect the sensor and the acquisition system. Because of the large number of sensor channels, data acquisition is carried out by grouping method. A single chassis consists of eight acquisition cards, and one acquisition card can collect eight signals, and each card uses a high-speed Gigabit Ethernet protocol. The acquisition card has a flash memory, and when the data is blocked, it still saves the data and uploads it after the network is restored.

3.2. Subsystem

The main system and the subsystem are synchronized to ensure the consistency of the experimental data recording of all instruments. The actual speed of the vehicle, the contact angle between the tire and the sensor, and the data acquisition time are all important for the experiment. The main components of the subsystem are as follows:

• Laser speedometer: Because there is a certain error between the vehicle speedometer and the actual speed, the laser speedometer can accurately measure the relationship between the longitudinal displacement and time of the vehicle.
• Auxiliary camera: The ground marking is perpendicular to the sensor and parallel to the driving direction. The camera is attached to the underside of the car’s bumper, and it can record in real time, making sure that the tire runs over the sensor vertically.
• Infrared trigger device: The front and rear sensors are respectively equipped with a set of infrared trigger switches. When the tire blocks the first switch, the trigger acquisition system is activated. When the tire is detected to leave, the data recording stops.

4. Real Vehicle Experiment

The whole vehicle mass (including the driver) of the test car was 1502 kg. The test tire was a Michelin PRIMACY 4215/50R17 radial tire, and the tire inflation pressure was 2.4 bar. On the test pavement, the car accelerated gradually from the test starting point to 16 km/h and maintained that speed in a straight line through the sensor. During the test, the contact state between the tire and the sensor is shown in Figure 7. On the left is the front view and side view of the contact between the tire and the pavement surface. With the assistance of the camera, the car straightened the body and the tire rolled over the sensor vertically, reducing the error caused by the incident angle. The sensors and the surrounding pins’ assembly heights are the same. The purpose of this assembly is not only to avoid tire bounce, but also to ensure that the sensor and the tire completely make contact. The data acquisition and processing system is shown on the right of Figure 7. The software can realize filtering and amplification of sensor voltage signals. The three signals are grouped together, and the test data is stored in parallel at a rate of 2 kHz.

5. Results and Discussion

Since the tire surface has a pattern and there is a gap between each sensor and the tire rubber is viscoelastic, the tire pattern will be partially embedded in the sensor; some sensors may only partially contact the tire, with the rest in the tire groove. However, the surface of the sensor is a whole, and the part without contact will also have stress, so the stress measured here is the average stress. Because the experiment used car tires, and tire patterns are closely spaced, there will not be a sensor completely in the gap between the situations.

It can be observed from Figure 8 that the sensor data is consistent, and the tire is in good contact with the sensor. The 3D image reflects that the longitudinal stress changes in a sinusoidal trend, and the driving direction is specified as positive. By combining Figure 9, Figures 11 and 13, it can also be seen that the contact shape of the tire path in the free rolling state is approximately a rounded rectangle with a slight bulge in the middle. The stress on both sides is more concentrated than the middle position of the contact surface. The contact stress between the tire and pavement surface is divided into longitudinal stress, lateral stress, and vertical stress. The left front wheel is selected as the experimental wheel. The minimum is about −97 kPa, as can be seen in Figure 9. The positive FX area of the whole contact surface is greater than the negative Fx area, and the maximum positive value is much greater than the negative direction. Thus, under the condition of uniform tire rolling, the forward stress of the pavement surface is greater than the backward stress, and the asphalt is squeezed, leading to the push between the surface layer and the base layer. If the local asphalt is unstable, it is easy to form irregular uplift deformation.

Figure 10 shows the transformation of lateral stress; the maximum value is about 110 kPa, the minimum value −110 kPa, the tire surface is made of rubber material, and the surface will swell when the pressure is applied. Let the right be the positive direction. Take the rightmost contact imprint as an example. The rightmost sensor will be stressed to the right, but the sensor near the left gully will be subject to the opposite direction. There is almost no pattern in the middle part of the experimental tire, so the change of the transverse stress is relatively gentle. The irregular pattern of the tire is the key factor affecting the transverse stress. It can be seen from Figure 11 that the five tire ribs correspond to the results of 10 projection results in order, and the direction and shape of the lateral stress distribution are largely affected by the relative position of the sensor component relative to the sensor element.

The most important source of vertical stress is tire load. It can be seen from Figure 12 that the maximum vertical stress is about 394 kPa with a half-sinusoidal distribution. It can be seen from Figure 13 that, in the rolling state, the vertical stress concentrates on the position behind the contact surface, which is caused by the viscoelasticity of tire rubber and the flow of compressed air in the tire. In addition, the stress on the outer edge of the tire is greater than that in the center of the tire. The long-term effect has led to the plastic deformation of the asphalt pavement. The middle of the wheel is sunken, and the two sides are bulged to form ruts.

6. Conclusions

In order to further study the contact stress distribution between the tire and the pavement, the sensor structure and strain gauge layout were improved, and the sensor calibration and correction were carried out. The sensor array considered the real pavement texture. A high-speed data acquisition system and testing platform were established to measure the tri-axial stress distribution of car tire under 2.4 bar inflation pressure. The following conclusions can be drawn:

• In the constant speed of the tire, the tri-axial stress distribution is uniform and greater than the static state. The longitudinal and vertical stress values near the tire shoulder are greater than those near the tire crown, and the lateral stress is greatly affected by the asymmetric pattern of the tire.
• Due to the elasticity of rubber and the fluidity of compressed gas in the tire, the peak stress will gradually move from front to back with the rolling of the tire, and the maximum stress has a certain lag.
• The characteristics of the three-way stress distribution can be used to further explain the causes of pavement damage and provide a comparison basis for a simulation experiment.

While the influence of a single directional stress is straightforward, the influence of a multi-dimensional stress is more complicated. The accurate measurement results of the triaxial stress of the tire-pavement contact patch can provide a reference for pavement design, tire rolling resistance, and friction analysis.