CN118190788B - A method and device for measuring tire-road friction coefficient - Google Patents

Abstract

The invention belongs to the technical field of tire testing, and discloses a tire-road friction coefficient measurement method and device, comprising: S1, independently changing friction loads _FX , _FY and vertical load W, and measuring sidewall strain; S2, using contact surfaces with different friction coefficients to independently change loads _FX , _FY and W, the contact surface being a rubber plate, an aluminum plate, a patterned acrylic force plate or a polytetrafluoroethylene plate; S3, assuming that the strain generated on the sidewall is proportional to each load acting on the tire, and is the linear sum of the strains caused by each load; S4, using the measured value of the intermediate strain _εm to determine each load acting on the tire; S5, obtaining the values of _FX , FY and _W by solving their equations, and then calculating the friction coefficient μ by dividing the square root of the sum of the squares of _FX and _FY by W.

Description

A method and device for measuring tire-road friction coefficient

Technical Field

The invention belongs to the technical field of vehicle tire-road adhesion coefficient testing, and in particular relates to a tire-road friction coefficient measuring method and device.

Background Art

In recent years, technologies for measuring road conditions, especially the friction coefficient of roads, have been developed to improve the safety of automobiles. If the friction coefficient between tires and roads can be measured in real time, the performance of advanced driver assistance systems (ADAS) such as anti-lock braking systems (ABS) and automatic braking systems can be improved. In addition, if the ability to alert drivers to icy roads based on the measurement of road friction coefficient is developed, and the measured road surface information is shared between vehicles, these systems will be able to better contribute to the prevention of traffic accidents. In addition, autonomous driving systems that mainly control vehicle behavior are expected to be used in the near future. The measurement of friction coefficient is essential for autonomous driving systems to be able to stably control the steering and braking of vehicles in road environments under various weather conditions.

In this context, research work on measuring the road friction coefficient while the vehicle is moving is currently underway. For example, based on measurements such as vehicle speed, acceleration, and shaft torque, several studies have been conducted to identify road conditions and measure the road friction coefficient by simulation using tire and vehicle models, dynamic analysis, and data processing using extended Kalman filters. However, these studies require accurate vehicle and tire models, and obtaining accurate estimates is difficult. In addition, a method has been proposed to install a six-component force sensor on the wheel hub to measure the loads acting on the tire in multiple directions to obtain the road friction coefficient. However, the sensor is difficult to install, and its weight and price are high, making it difficult for consumers to use. The authors of this study also considered a method for measuring the friction coefficient using wheel strain in three-axis direction loads acting on the tire and road. However, the generated strain on the wheel is small, the determination of the measurement point is difficult, and in some cases, the signal-to-noise ratio and resolution of the measurement results are not sufficient for actual measurement. In addition, a method for estimating road conditions from images captured on the road surface has been proposed. However, estimating the road friction coefficient is difficult because it is easily affected by weather.

Therefore, many studies have focused on the tire, which is the only component in contact with the road surface, as shown in Figure 1(a). In particular, these studies measure the friction coefficient using sensors embedded in the inner surface of the tire tread, where, unfortunately, large deformations tend to occur, as shown in Figure 1(b).

Yimazoglu et al. proposed a method to measure the friction coefficient between the tire and the road surface by detecting tire deformation using magnets and magnetic field sensors embedded inside the tire tread. Sergio et al. and Matsuzaki and Todoroki proposed a method to measure tire deformation using changes in the electrical properties of the tire, namely the impedance and capacitance caused by changes in the state of the steel wire inside the tire. Hiraoka et al., b and Matsuzaki et al. tried to use digital image correlation technology combined with a camera mounted on the wheel to measure the deformation of the inner surface of the tire tread. Khaleghian et al. used a triaxial accelerometer mounted on the inner surface of the tire tread, a uniaxial accelerometer mounted on the chassis, and a wheel speed sensor to estimate the type of road surface. Lee et al. also proposed a method to estimate the matching road surface condition through machine learning, which uses the acceleration waveforms of the tire circumferential and radial directions and attaches the accelerometer to the inner surface of the tire tread.

Several researchers have also attempted to determine the friction coefficient of the road surface by measuring the strain on the inner surface of the tire tread. Matsuzaki et al. used photolithography to create a rubber sensor suitable for measuring the strain on the inner surface of the tire tread. Garcia-Pozuelo et al. measured tire deformation and expected that the results could identify tire contact state parameters. Yunta et al. proposed a method for measuring the friction coefficient in the tire width direction. The algorithm uses fuzzy theory and multiple strain sensor outputs processed in the tread. They believe that the strain on the inner surface of the tire tread is affected by the lateral load and bending angle when the vehicle turns. Mendoza-Petit et al. developed an algorithm that uses fuzzy theory to estimate the load acting on the tire contact patch based on the strain on the inner surface of the tire tread and the slip angle, and compared the experimental results with those obtained using automotive simulation software (CarSim).

The reference proposes a sensor consisting of a rigid rod mounted on a flat plate, which can measure the load applied to the tip of the sensor through the deformation generated on the flat plate. The sensor is mounted on the inner surface of the tire tread and is used to measure the friction coefficient of the road surface. So far, its usability has been confirmed.

However, when the tire touches the ground, the inner surface of the tire tread will deform significantly, as shown in Figure 1(b), and the protrusions on the road surface often cause large local deformations. Therefore, the sensor installed on the inner surface of the tire tread is prone to fall off or break. Therefore, it is difficult to install sensors on the inner surface of the tire tread, so it remains a challenge to perform stable measurements. In addition, the load distribution acting on the bottom of the tire during the grounding process is easily affected by the grounding area, and it is difficult to determine the load acting on the tire as a whole based on the local deformation caused by the bottom of the tire.

In contrast, the deformation of the sidewall is expected to be less affected by local deformation than by the entire contact patch of the tire compared to the inner surface of the tire tread. Hariri et al. demonstrated that the deformation of the sidewall of the tire has a good correlation with the vertical road surface excitation and developed a tire strain sensor that can be adhered to the tire. Their results showed that there is a good correlation between the sensor output and a relatively large load. Although Yunta et al. believed that measuring the strain of the sidewall is difficult, they did not fully study the location of application and its relationship with the load acting on the tire contact patch. The authors of the present invention studied the measurement of the road friction coefficient based on the sidewall strain and believed that the longitudinal friction load and the vertical load acting on the tire ground can be measured, thereby deriving the road friction coefficient under limited conditions where the lateral friction load does not work. Previous studies have shown that the strain on the tire sidewall is linearly related to the load and is of sufficient size to be accurately measured with foil strain gauges. However, in actual vehicle driving, lateral friction loads act on the tire, and detecting the road friction coefficient during skidding is very important for preventing accidents.

Through the above analysis, the problems and defects of the prior art are as follows:

1. Technical route 1: Based on measurements such as vehicle speed, acceleration, and shaft torque, and using extended Kalman filters for data processing, to identify road conditions and measure road friction coefficient. This technical route requires precise vehicle and tire models, and obtaining accurate estimates is difficult.

2. Technical route 2: Install a six-component force sensor to measure the loads in multiple directions acting on the tire to measure the friction coefficient. This is relatively accurate, but it is difficult to install and the cost is difficult to control.

3. Technical Route 3: Visual Image Method for Estimating Road Conditions It is difficult to estimate the road friction coefficient because it is easily affected by the weather.

4. Technical route 4: The method of installing sensors on the inner surface of the tire tread for measurement is firstly difficult to install, and secondly it is affected by the ground contact area, and it is difficult to perform stable measurements based on the local deformation caused by the bottom of the tire.

Summary of the invention

In view of the problems existing in the prior art, the present invention provides a tire-pavement friction coefficient measurement method and device.

The present invention is achieved by a tire-road friction coefficient measurement method, comprising:

S1, the friction loads F _X , F _Y and the vertical load W are varied independently and the sidewall strain is measured.

S2, using different friction coefficients of the contact surface to change the load F _X , F _Y and w independently, the contact surface is a rubber plate, aluminum plate, patterned acrylic force plate or polytetrafluoroethylene plate;

S3, assuming that the strain induced in the sidewall is proportional to each load acting on the tire and is the linear sum of the strains caused by each load;

S4, using the measured value of the intermediate strain ε _m to determine the various loads acting on the tire;

S5, by solving the equations for F _X , F _Y and W to obtain their values, and then dividing the square root of the sum of the squares of F _X and F _Y by W to calculate the friction coefficient μ.

Furthermore, the relationship between the side wall strain and each load in S4 is defined as follows:

ε _m (α)＝k(α)·F _X +l(α)·F _Y +m(α)·W+n(α) (1)

Where k(α), l(α), m(α), and n(α) are experimental constants for a rotation angle of α; K(α), l(α), and m(α) are proportional constants; and n(α) is the intercept. Although the intercept n(α) is essentially zero, it has a very small value due to the slight tilt of the strain gauge.

Furthermore, in S5, since F _X , F _Y , and W are unknown, the three-dimensional first-order simultaneous equations are derived from Eq (1) at three different rotation angles αi (i=1-3), and the following values are obtained:

By solving the equations for F _X , F _Y , and W , we can find their values and then calculate the friction coefficient μ by dividing the square root of the sum of the squares of F _X and F _Y by W, as follows:

However, the selected rotation angle combination α _i (i=1,2,3) results in extremely poor conditions for the simultaneous equations. In this case, no accurate solution can be obtained; the values of the experimental constants k(α), l(α), m(α) and n(α) are obtained in the calibration experiment, and at the same time, the appropriate rotation angle combination α _i (i=1,2,3) is determined based on the condition number C of the two modules of the first coefficient matrix on the right side of formula (2).

Another object of the present invention is to provide a tire-pavement friction coefficient measuring device for realizing the tire-pavement friction coefficient measuring method, which is composed of a two-degree-of-freedom translation mechanism that applies a vertical load and a friction load on the tire, a drive unit that rotates the tire, a contact surface, and a force plate that can measure three axial loads between the tire and the contact surface. The translation mechanism can move the contact surface vertically in the z-axis direction and horizontally in the x-axis direction relative to the coordinate system O-XYZ. When the tire rotates, the tangential velocity relative to the contact surface is in the y-axis direction. The rotation angle of the tire is represented by α, and the direction of the friction load acting on the tire contact surface is represented by θ.

Furthermore, the tire-road friction coefficient measuring device applies a vertical load W on the tire, pushing the force plate upward to the bottom surface along the z-axis direction; in this case, when the tire rotates, the longitudinal friction load F _X acts on the tire ground contact surface; when the force plate moves horizontally along the Y-axis direction, the lateral friction load F _Y acts on the tire surface; by changing the rotation speed of the tire and the horizontal movement speed of the translation mechanism loading device, the ratio of the F _X value to the F _Y value can be changed; the direction of the friction load F, calculated as the square root of the sum of the squares of F _X and F _Y , can be adjusted; the friction coefficient of the tire ground contact surface can also be adjusted by changing the material of the top plate on the force plate.

Another object of the present invention is to provide a computer device, the computer device includes a memory and a processor, the memory stores a computer program, when the computer program is executed by the processor, the processor executes the steps of the tire-pavement friction coefficient measurement method.

Another object of the present invention is to provide a computer-readable storage medium storing a computer program, which, when executed by a processor, enables the processor to execute the steps of the tire-pavement friction coefficient measurement method.

In combination with the above technical solutions and the technical problems solved, the advantages and positive effects of the technical solutions to be protected by the present invention are as follows:

First, the present invention uses an experimental device that simulates the complete slip state of the tire to study the strains generated in the radial, circumferential and median directions of the tire sidewall under triaxial loads, and confirms that the median strain can better reveal the influence of the load acting on the tire.

The median strain of the tire sidewall varies linearly with respect to the longitudinal and lateral friction loads and the vertical load of the tire. Therefore, an experimental equation for the relationship between the tire sidewall strain and the triaxial load is derived.

Based on this experimental equation, a three-dimensional first-order simultaneous equation was derived, and the three strains generated by the tire at different rotation angles during one rotation were used to measure the triaxial load, thereby obtaining the road friction coefficient. The constants involved in the experimental equation were obtained through calibration experiments.

In order to select the appropriate rotation angle combination, the present invention introduces the condition number of the two norms of the matrix for the numerical analysis of the three-dimensional simultaneous equations. When the set condition number of the rotation angles satisfied is less than 20, the mean square error of the friction coefficient is less than 0.2, which is sufficient to detect the difference in road conditions.

To validate the proposed method, experiments were conducted under triaxial loading conditions on four different friction coefficients of the contact patch. The proposed method was verified to be able to measure the triaxial loads acting on the tire and the friction coefficient of the tire contact patch under low speed and full slip conditions using a tire rotation device. The measurement accuracy was optimal for a set of rotation angles with a condition number of 12.5, with a mean square error of the friction coefficient of approximately 0.07.

Second, in the invention, strain gauges attached to the tire sidewall are used to measure the triaxial load and road friction coefficient using strain values at three different rotation angles during one rotation of the tire. In addition, attaching strain gauges at three locations will enable real-time measurement. Therefore, it is necessary to optimize the attachment angles and spacing angles of the three strain gauges so that the number of states of the tire in one rotation is good, which will be the subject of future work. In addition, optimizing the attachment positions of the three strain gauges by finite element analysis can not only achieve higher-precision measurements, but also help to apply the proposed measurement method to other tires. In addition, previous studies have considered a method for measuring the road friction coefficient using the strain generated on the wheel. Therefore, the present invention will study which measurement method based on the strain on the tire sidewall or wheel is superior through actual vehicle running tests, including practicality such as measurement accuracy, manufacturing cost, and maintenance management. If an intelligent tire capable of measuring the road friction coefficient is constructed based on the proposed method, it will contribute to the development of automobile measurement control and road surface detection.

Third, the expected benefits and commercial value of the technical solution of the present invention after transformation are:

1. From the perspective of driving safety, the technical solution of the present invention measures the road friction coefficient in real time, which can improve the performance of advanced driver assistance systems (ADASs) such as anti-lock braking systems (ABS) and automatic braking systems. Traditional and intelligent driving vehicles equipped with this technology can improve safety performance indicators and reduce the probability of driving safety accidents.

2. From the perspective of vehicle performance, this technical solution can accurately and quickly measure the road adhesion coefficient, which can help improve the control effect of vehicle braking performance, such as braking distance, handling stability and driving smoothness, and improve the competitiveness of vehicle products.

Based on the above two points, the implementation of this technical solution in vehicles can increase market share and industry competitiveness, and the expected benefits and commercial value are well evaluated.

Fourth, the technical solution of the present invention fills the technical gap in the industry at home and abroad:

Many studies have been conducted to measure the road friction coefficient using the strain on the inner surface of the tire tread, which is the only part in contact with the road surface. However, the sensor installed on the inner surface of the tire tread is easy to fall off or be damaged because the protrusions on the road surface will deform significantly locally. Therefore, the present invention proposes a method for measuring the road friction coefficient using the strain on the tire sidewall. The proposed method has been proven to be able to measure the load acting on the tire and the friction coefficient of the tire contact surface under low speed and full slip conditions, filling the technical gap.

Fifth, the present invention uses the sidewall of the tire instead, which can obtain stable measurement results because the sidewall of the tire is more difficult to deform locally compared to the inner surface of the tire tread. First, using an experimental device that simulates a fully slipping state of the tire, the present invention measures the relationship between the triaxial load acting on the tire ground and the strain generated on the tire sidewall. Subsequently, the present invention establishes an experimental formula to express this relationship and designs a method for measuring the road friction coefficient. The results confirm that even under the action of triaxial loads, the friction coefficient of multiple friction surfaces can be accurately measured using the method proposed in this article. The measurement of the tire adhesion coefficient under low speed and full slip conditions is achieved with high accuracy. From this perspective, the technical difficulty of measuring the tire-road adhesion coefficient has been solved.

Fifth, the technical solution of the present invention overcomes traditional technical prejudices:

The general technical route for the tire-road adhesion coefficient is mainly based on estimation, such as visual estimation, Kalman filter estimation, fusion estimation, etc.; there is no low-cost, convenient direct or indirect measurement method. The present technical solution has improved the sensor measurement solution, and changed the sensor measurement method installed inside the tire to the tire sidewall through a lower-cost strain gauge method. Combined with the independently invented tire test bench (Figure 3) and the derived formula, it can realize the rapid measurement of the corresponding strain value changes under different adhesion coefficient roads and different rotation angles, improve the measurement accuracy of the tire-road adhesion coefficient, and reduce the measurement cost. From this dimension, the technical solution of the present invention overcomes the traditional technical prejudice and provides more reference value for subsequent research.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG1 is a schematic diagram showing the details of the tire structure and the characteristic position of the sensor installation provided by an embodiment of the present invention;

FIG2 is a schematic diagram of a method for measuring tire sidewall strain provided by an embodiment of the present invention;

3 is a schematic diagram of an experimental device composed of a tire rotating device, a force plate, and a translation mechanism and a matching vehicle testing method provided by an embodiment of the present invention;

4 is a schematic diagram of strains in three axial directions corresponding to a rotation angle α=150° when the friction load _FX is about -1150N, the friction load _FX is 762N, and the vertical load W is 2540N, provided by an embodiment of the present invention;

FIG5 is a schematic diagram of the relationship between the median strain ε _m and F _X , F _Y , and W at α=150° provided in an embodiment of the present invention;

FIG6 is a schematic diagram of experimental constants obtained from the calibration experiment of the embodiment of the present invention;

7 is a schematic diagram of the relationship between a set of three selected rotation angles and a condition number (when the rotation angle is fixed at 190°) provided in an embodiment of the present invention;

FIG8 is a schematic diagram of the relationship between the measured value and the true value based on the mid-axis strain provided by an embodiment of the present invention;

9 is a flow chart of a tire-road friction coefficient measurement method provided by an embodiment of the present invention;

FIG. 10 is a flow chart of the calculation process of the tire-pavement friction coefficient measurement method provided in an embodiment of the present invention.

DETAILED DESCRIPTION

In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

In view of the problems existing in the prior art, the present invention provides a tire-pavement friction coefficient measurement method and device, which will be described in detail below in conjunction with the accompanying drawings.

1. Measurement of side wall strain

The present invention uses a snow tire, as shown in FIG2, because this type of tire is often used in situations where the road surface tends to have a low friction coefficient. When the tire contact surface is subjected to a load from the road surface, the tire will deform in three dimensions. In accordance with the deformation of the tire caused by the load acting on the contact surface, in-plane strain is generated on the tire sidewall surface.

A triaxial strain gauge is installed on the tire sidewall, and its location is 15 mm from the boundary between the tire and the wheel.

The measurement position on the sidewall is selected at a radial distance of 15 mm from the boundary between the tire and the wheel, as shown in Figure 2. In order to study the characteristics of the sidewall strain when the tire rotates once, a triaxial strain gauge (parameters: resistance 120Ω, gauge length 2.0 mm) is attached to the position so that the measurement direction is circumferential, radial to the tire, and between circumferential and radial. Here, by selecting the direction where the strain changes significantly and the absolute value is large during one rotation of the tire, the triaxial load is measured from the strain at three different rotation angles.

2. Experimental Equipment

The device shown in FIG3 is used to apply loads when the tire rotates. The device consists of a two-degree-of-freedom translation mechanism that applies vertical loads and friction loads to the tire, a drive unit that rotates the tire, a contact surface, and a force plate that can measure three axial loads between the tire and the contact surface. The translation mechanism can move the contact surface vertically in the z-axis direction and horizontally in the x-axis direction relative to the coordinate system O-XYZ, as shown in FIG3. When the tire rotates, the tangential velocity relative to the contact surface is in the y-axis direction. As shown in FIG3, the rotation angle of the tire is represented by α, and the direction of the friction load acting on the tire contact surface is represented by θ.

In the test, a vertical load W is applied to the tire, pushing the force plate upward to the bottom surface in the z-axis direction. In this case, the longitudinal friction load F _X acts on the tire contact surface when the tire rotates. When the force plate moves horizontally in the y-axis direction, the lateral friction load F _Y acts on the tire surface. By changing the rotational speed of the tire and the horizontal movement speed of the translation mechanism loading device, the ratio of the F _X value to the F _Y value can be changed. Therefore, the direction of the friction load F, calculated as the square root of the sum of the squares of F _X and F _Y , can be adjusted. The translation mechanism loading device and the tire drive unit are assumed to simulate the situation of a small car with a mass of about 1 ton supported by 4 tires. The specifications of the device are listed in Table 1. The maximum load W and F reach about 2500N. The force plate is designed to measure triaxial loads up to 2500N in each direction and contains 12 spring elements with attached strain gauges. The measurement resolution of 20N was determined by calibration of the force plate. The output signals of the strain gauges attached to the tire sidewall and the force plate were recorded using a data recorder system with a sampling frequency of 50Hz. Furthermore, it was confirmed that the strain signal contained no temperature drift. The tire rotation angle was determined with a resolution of 0.3°, synchronizing the logging data with the operating commands of the tire rotation device.

Table 1 Experimental equipment parameters

In addition, the friction coefficient of the tire contact patch can be adjusted by changing the material of the top plate on the force plate. The slip between the tire and the contact patch that can be achieved using this device is a complete slip state in which the tire rotates relative to the contact patch without translational motion. The experiments described in the following chapters were all carried out at room temperature and the tire friction speed was low; this confirmed that friction heat and vibration have little effect on the strain output.

3. Measurement of the relationship between side wall strain and load

3.1. Example of sidewall strain measurement

Figure 4 shows an example of the measurement of strains ε _i (i=c, r, m) along the three axes relative to the tire rotation angle. The subscripts c, r, and m represent the circumferential, radial, and intermediate strains, respectively. The figure shows that when the contact surface is a smooth acrylic plate, the vertical load W is 2540N, the tire longitudinal friction load F _X is -1150N, and the lateral friction load F _Y is 762N. The direction of the friction load θ in Figure 3 is approximately 33.5°

As shown in FIG4 , the strain ε _m in the middle direction changes significantly and has a large value. It can be seen that ε _m can reflect the significant effect of the load on the tire. The present invention uses the measured value of the middle strain ε _m to explore the determination of the vertical load (W) and the friction load (F _X and F _Y ) acting on the tire contact surface.

3.2. Measurement results of the relationship between tire load and sidewall strain

In order to study the basic relationship between tire load and sidewall strain, the friction load F _X , F _Y and vertical load W were changed independently, and the sidewall strain was measured. Table 2 lists the main measurement conditions. In the experiment, the loads F _X , F _Y and w were changed independently using contact surfaces with different friction coefficients. The contact surfaces were rubber plates, aluminum plates, patterned acrylic force plates or polytetrafluoroethylene plates, as shown in Table 2, fixed on the measured force plates.

In the experiment of changing friction load F _X , the target value of vertical load W is set to 2500N, and F _X changes in three steps in the negative direction as the tire rotates. In the experiment of changing friction load F _Y , the target value of vertical load W is 1370N. When the tire rotates at rest, the force plate moves horizontally along the positive and negative directions of the Y axis, and F _Y changes in 6 steps. In the experiment, the vertical load W changes in three steps, and the target value of friction load F _X is set to -1162N.

In the above experiments, the friction speed is set to 30 mm/s, that is, the relative speed between the tire and the contact surface in the direction of the friction load θ, as shown in Figure 2. Other experimental conditions of the above three experiments are shown in Table 2.

Figure 5 shows the relationship between the intermediate strain _εm and these measured loads. These relationships apply to the case where the tire is rotated at an angle α of 150°, as shown in Figure 3, and Figures 5(a), (b), and (c) are the results for the friction loads F _X , F _Y and the vertical load W, respectively. These figures show the relationship between the measured strains and the values measured by the force plate when the strain gauge is located at α = 150° under the experimental conditions listed in Table 2. As shown in Figure 5, the relationship between the strain and F _X , F _Y , and W is a strong linear relationship when α = 150°. It should be noted that the intercept is not zero in any of the graphs. These intercept values are the strains generated by the vertical load W that generates the friction load shown in Figures 5(a) and (b), and the strain generated by F _X that simulates the actual operating conditions shown in Figure 5(c). Based on the results of multiple experiments under the conditions shown in Table 2, the approximate line was obtained in the same way as Figure 5. The average values and standard deviations of the slopes and intercepts are summarized in Table 3, which shows that the results shown in Figure 5 are highly repeatable. Although the details are omitted, the same trends in the linearity and reproducibility of the strain are observed at other rotation angles α.

Table 2 Experimental conditions of vertical load W of about 2500N, friction load F _Y of 0N, vertical load W of about 1370N, friction load F _X of 0N, F _Y varying friction load F _X of 0N, and experiment of varying vertical load W when friction load F _X is about ±1162N and friction load F _Y is 0N.

4. Method for measuring friction coefficient using sidewall strain

It is assumed that the strain induced on the sidewall is proportional to each load acting on the tire and is the linear sum of the strains caused by each load. The present invention uses the measured value of the intermediate strain ε _m shown in Figure 2 to determine each load acting on the tire. Therefore, the relationship between the sidewall strain and each load is defined as follows:

ε _m (α)＝k(α)·F _X +l(α)·F _Y +m(α)·W+n(α) (1)

Where k(α), l(α), m(α), and n(α) are experimental constants at a rotation angle of α; K(α), l(α), and m(α) are proportional constants; and n(α) is the intercept. Although the intercept n(α) is essentially zero, it can have a very small value due to the slight tilt of the strain gauge. Since F _X , F _Y , and W are unknown, the three-dimensional first-order simultaneous equations are derived from Eq(1) at three different rotation angles αi (i=1-3), and the following values are obtained:

The values of F _X , F _Y , and W can be found by solving the above equations for them. The friction coefficient μ is then calculated by dividing the square root of the sum of the squares of F _X and F _Y by W, as follows:

However, the selected rotation angle combination α _i (i=1,2,3) results in extremely poor conditions for the simultaneous equations. In this case, no accurate solution can be obtained. Therefore, in the present invention, the values of the experimental constants k(α), l(α), m(α) and n(α) are obtained in a calibration experiment, and at the same time, the appropriate rotation angle combination α _i (i=1,2,3) is determined based on the condition number C of the two modules of the first coefficient matrix on the right side of formula (2), as described below.

Table 3 Mean and standard deviation of the slope and intercept of the fitted straight line

5. Friction coefficient measurement experiment

5.1. Determination of experimental constants

The experimental constants k(α), l(α), m(α), and n(α) in formula (1) are determined by the calibration experiment of the smooth acrylic force plate, as shown in Table 4. As mentioned in the previous chapter, the strain of the tire sidewall can be expressed by a linear equation of the circumferential load F _X , the width load F _Y , and the vertical load W. Therefore, there is no need to use multiple contact surfaces with different friction coefficients. The experimental constants can be determined by linearly approximating the experimental results of different load ratios F _X , F _Y , and W on a single contact surface through formula (1).

The experimental conditions used to determine the constants are listed in Table 4. Under each vertical load, the direction of the friction load was changed in six directions, and the strain induced on the sidewall was measured as the tire rotated. Each experiment listed in Table 4 was performed twice.

Based on the measurement results under six conditions, the experimental constants k(α), l(α), m(α) and n(α) at each degree of rotation angle α in formula (1) were obtained by multivariate linear approximation. The experimental constants determined by formula (1) are shown in Figure 6. As can be seen from the figure, all experimental constants are larger near the rotation angle α = 180°, which is the farthest from the contact surface, and smaller at α = 0° and 360°. In addition, all experimental constants show a sudden change at the tire rotation angle of 180° and nearby. This is because when the tire contacts the ground at 180° and near the rotation angle, the strain changes suddenly near this angle, as shown in Figure 4. The repeatability of this significant change has been verified in multiple experiments, and it has also been confirmed that other tires also show similar trends.

5.2. Determine the appropriate rotation angle combination

The friction coefficient can be measured simultaneously by using the strain generated on the sidewall at three different tire rotation angles α _i (i=1-3). In this section, a method for determining a combination of rotation angles α _i suitable for measuring the friction coefficient is described. First, the friction coefficient is measured using the experimental constants shown in Figure 6, and the strain is measured in an experiment with triaxial load variation using a smooth acrylic force plate as the contact surface, as shown in Table 4. In the present invention, the friction coefficient is measured using the measured strain corresponding to the rotation angle α in the range of 0-360° with a step size of 10°. The friction coefficient of all groups is measured at the rotation angle.

Table 4 Experimental conditions for determining experimental constants

On this basis, the three-dimensional simulation equation group derived from formula (1) was numerically analyzed, and the conditions C of the two norms of the matrix corresponding to the rotation angle set were calculated. As an example, Figure 7 shows the change of the condition number when one rotation angle used for measurement is fixed at α = 190°, and the combination of the remaining two rotation angles changes. As shown in Figure 7, the number of conditions representing the suitability of the numerical analysis solution of the simulation formula (2) is different depending on the selected rotation angle combination. Factors that cause the rotation angle combination to lead to poor conditions include small strain values at any selected rotation angle and similar relationships between strain and load at the selected rotation angle. The rotation angle combinations that lead to good working conditions are shown in Figure 7. They include a combination with a rotation angle α of 180°, a combination with a large strain at the strain gauge attachment position close to the ground surface, a combination with a difference of 10° from another rotation angle, and a combination with a rotation angle α of 360°, which will result in a relatively different relationship between strain and load. The relationship between the mean square error Er calculated from the friction coefficient measured by the method of the present invention and the friction coefficient measured by the force plate and the condition number c is shown in Table 5. As can be seen from Table 5, the closer the condition number is to 1, the better the three sets of rotation angles selected. And the better the measurement accuracy of the friction coefficient. Since the actual sliding friction coefficient of the vehicle on the road surface is 0.5-1.0 for dry asphalt, 0.3-0.9 for wet asphalt, 0.2-0.5 for snowy road surface, and 0.1-0.2 for icy road surface, a resolution of 0.2 or lower for the mean value measurement of the friction coefficient is considered acceptable. The present invention selects a set of rotation angles (the blue part in Figure 7) that meet the condition 1≤C≤20 to measure the friction coefficient, and the mean square error Er is less than 0.2.

5.3. Measurement and verification of friction coefficient

In order to evaluate the accuracy of the proposed method for measuring the friction coefficient, the present invention uses four plates with different friction coefficients (aluminum plate, smooth acrylic force plate, polytetrafluoroethylene plate, oiled smooth acrylic force plate) as the contact surface, as shown in Table 6. The other experimental conditions are as follows. The target values of the vertical load W are 1500, 2000 and 2500N, respectively. In order to change the values of the friction loads F _X and F _Y , the friction load direction θ is adjusted to about 0, 30, 150, 180, 210 and 330°, and the friction speed is set to about 30 mm/s. The tire rotates at a speed of 400°, and the measurement values are obtained at all intervals except for the 20° intervals at the beginning and end of the rotation. Each experiment is performed twice.

Based on the above experimental results, the friction loads F _X , F _Y , W and the friction coefficient μ are calculated using the method proposed in Section 5. The obtained values are then compared with the true values measured using the force plate.

Figure 8 shows the relationship between F _X , F _Y , W and μ obtained by this method and the measured value of the force plate. These data were obtained at rotation angles α = 20°, 130° and 190°, as shown in Figure 7, because the measurement accuracy of this set of rotation angles is the best when the condition number C = 12.5. Figures 8 (a), (b), (c) and (d) show the results of tire circumferential friction load F _X , tire width direction friction load F _Y , vertical load W and friction coefficient μ. The vertical axis represents the value measured using the proposed method, and the horizontal axis represents the true value measured using the force plate. Figure 8 (d) of the friction coefficient μ also shows the measurement results under biaxial loading conditions without lateral load, which is obtained using the average strain of the tire for one rotation in the reference.

Table 5 Relationship between the mean value of quadratic mean square law error _Er and the condition number C

Table 6 Experimental conditions when the vertical load W is approximately 1500N, 2000N and 2500N

Figures 8(a), (b), and (c) show that the friction load can be accurately measured as a whole. In addition, according to Figure 8(c), a good vertical load can be measured. As shown in Figure 8(d), the accuracy of the friction coefficient measured by the present invention under triaxial loading is lower than that of the friction coefficient measured by the previous study under biaxial loading. However, in the above results, the mean square error of μ obtained in the present invention and the value measured using the force plate is about 0.07. Therefore, the proposed triaxial loading method is expected to fully identify dry asphalt and snow road conditions.

5.4. Analysis and discussion

The present invention studies the use of the strain induced on the tire sidewall to measure the triaxial load acting on the tire contact surface and determine the friction coefficient between the tire and the road surface. The relationship between the measured value and the true value of the strain induced on the tire sidewall is shown in Figure 8.

Under the action of vertical load and tangential load of about 2kN on the tire contact surface, the strain gauge reaches about 1000με. In addition, it is confirmed that the strain of the longitudinal, lateral and vertical loads of the tire contact surface is almost linearly generated under each load. Therefore, the relationship between the load acting on the tire contact surface and the strain generated on the sidewall can be expressed by a simple linear equation. By deterring-mining the coefficients involved in the experimental equation, the loads acting on the tire contact surface in three directions can be obtained from a simultaneous equation using the strains at three locations on the tire sidewall. Unlike the inner surface of the tire tread used traditionally, the tire sidewall strain can be measured from the outside of the tire, and the strain gauge will not fall off easily due to the unevenness of the road surface. The strain generated is relatively large and tends to change linearly with respect to the triaxial load of the tire contact surface, so it is relatively easy to measure using this strain. In addition, the present invention confirms that for several tires of different types, the same form of experimental formula (2) can be determined, and the ground load acting on the tire can be measured with the same accuracy. Therefore, the proposed measurement method has strong practicality. However, the experimental equation is only obtained under full slip conditions. In addition, the tire rotation speed used in the present invention is low and the experiments were conducted at room temperature. Therefore, in the future, the present invention will study whether the proposed method can be applied to various slip ratios. In addition, experiments will be conducted on actual vehicles to study the measurement accuracy under actual driving conditions. In addition, the experimental equipment used in the present invention can withstand a maximum vertical load of 2.5 kN, which is suitable for small vehicles. Since the vertical load of large vehicles can reach about 4 kN, this is considered to change the contact area of the tire and affect the relationship between the sidewall strain and the contact load.

As shown in FIG9 and FIG10 , the tire-road friction coefficient measurement method provided by the embodiment of the present invention includes:

S1, the friction loads F _X , F _Y and the vertical load W are varied independently and the sidewall strain is measured.

S2, using different friction coefficients of the contact surface to change the load F _X , F _Y and w independently, the contact surface is a rubber plate, aluminum plate, patterned acrylic force plate or polytetrafluoroethylene plate;

S3, assumes that the strain induced in the sidewall is proportional to each load acting on the tire and is the linear sum of the strains caused by each load.

S4, use the measured value of the intermediate strain ε _m to determine the various loads acting on the tire.

S5, by solving the equations for F _X , F _Y and W to obtain their values, and then dividing the square root of the sum of the squares of F _X and F _Y by W to calculate the friction coefficient μ.

An application embodiment of the present invention provides a computer device, which includes a memory and a processor. The memory stores a computer program. When the computer program is executed by the processor, the processor executes the steps of the tire-road friction coefficient measurement method.

An application embodiment of the present invention provides a computer-readable storage medium storing a computer program. When the computer program is executed by a processor, the processor executes the steps of a tire-road friction coefficient measurement method.

Friction coefficient measurement experiment-application example

1. Determination of experimental constants

The experimental constants k(α), l(α), m(α), and n(α) in formula (1) are determined by the calibration experiment of the smooth acrylic force plate, as shown in Table 4. As mentioned in the previous chapter, the strain of the tire sidewall can be expressed by a linear equation of the circumferential load F _X , the width load F _Y , and the vertical load W. Therefore, there is no need to use multiple contact surfaces with different friction coefficients. The experimental constants can be determined by linearly approximating the experimental results of different load ratios F _X , F _Y , and W on a single contact surface through formula (1).

The experimental conditions used to determine the constants are listed in Table 4. Under each vertical load, the direction of the friction load was changed in six directions, and the strain induced on the sidewall was measured as the tire rotated. Each experiment listed in Table 4 was performed twice.

Based on the measurement results under six conditions, the experimental constants k(α), l(α), m(α) and n(α) at each degree of rotation angle α in formula (1) were obtained by multivariate linear approximation. The experimental constants determined by formula (1) are shown in Figure 6. As can be seen from the figure, all experimental constants are larger at the rotation angle α=180° and its vicinity, which is the farthest from the contact surface, and smaller at α=0° and 360°. In addition, all experimental constants show a sudden change at the tire rotation angle near 180°. This is because when the tire contacts the ground near the rotation angle of 180°, the strain changes suddenly near this angle, as shown in Figure 4. The repeatability of this significant change has been verified in multiple experiments, and it has also been confirmed that other tires also show similar trends.

2. Determine the appropriate rotation angle combination

The friction coefficient can be measured simultaneously by using the strain generated on the sidewall at three different tire rotation angles α _i (i=1-3). In this section, a method for determining a combination of rotation angles α _i suitable for measuring the friction coefficient is described. First, the friction coefficient is measured using the experimental constants shown in Figure 6, and the strain is measured in an experiment with triaxial load variation using a smooth acrylic force plate as the contact surface, as shown in Table 7. In the present invention, the friction coefficient is measured using the measured strain corresponding to the rotation angle α in the range of 0-360° with a step size of 10°. The friction coefficient of all groups is measured at the rotation angle.

Table 7 Experimental conditions for determining experimental constants

On this basis, the three-dimensional simulation equation group derived from formula (1) was numerically analyzed, and the conditions C of the two norms of the matrix corresponding to the rotation angle set were calculated. As an example, Figure 7 shows the change of the condition number C when one rotation angle used for measurement is fixed at α = 190°, and the combination of the remaining two rotation angles is changed. As shown in Figure 7, the number of conditions representing the suitability of the numerical analysis solution of the simulation formula (2) is different depending on the selected rotation angle combination. Factors that lead to poor conditions for the rotation angle combination include small strain values at any selected rotation angle and similar relationships between strain and load at the selected rotation angle. The rotation angle combinations that lead to good working conditions are shown in Figure 7. They include a combination with a rotation angle α of 180°, which produces a large strain at the strain gauge attachment position close to the ground surface, a combination with a difference of 10° from another rotation angle, and a combination with a rotation angle α of 360°, which will result in a relatively different relationship between strain and load.

The relationship between the mean square error Er calculated by the friction coefficient measured by the method and the friction coefficient measured by the force plate and the condition number C is shown in Table 8. It can be seen from Table 8 that the closer the condition number C is to 1, the better the three sets of rotation angles selected. And the better the measurement accuracy of the friction coefficient. Since the actual sliding friction coefficient of the vehicle on the road surface is 0.5-1.0 for dry asphalt, 0.3-0.9 for wet asphalt, 0.2-0.5 for snowy road surface, and 0.1-0.2 for icy road surface, the resolution of the mean value measurement of the friction coefficient is 0.2 or lower, which is considered acceptable. The present invention selects a set of rotation angles that meet the condition 1≤C≤20 (the blue part in Figure 7) to measure the friction coefficient, and the mean square error Er is less than 0.2.

3. Measurement and verification of friction coefficient

In order to evaluate the accuracy of the method proposed in Section 5 for measuring the friction coefficient, the present invention uses four plates with different friction coefficients (aluminum plate, smooth acrylic plate, polytetrafluoroethylene plate, oiled smooth acrylic plate) as the contact surface, as shown in Table 9. The other experimental conditions are as follows. The target values of the vertical load W are 1500, 2000 and 2500N, respectively. In order to change the values of the friction loads F _X and F _Y , the friction load direction θ is adjusted to about 0, 30, 150, 180, 210 and 330°, and the friction speed is set to about 30 mm/s. The tire rotates at a speed of 400°, and measurement values are obtained at all intervals except for the 20° intervals at the beginning and end of the rotation. Each experiment is performed twice.

Based on the above experimental results, the friction loads F _X , F _Y , W and the friction coefficient μ are calculated using the method proposed in Chapter 5. The obtained values are then compared with the true values measured using the force plate.

Figure 8 shows the relationship between F _X , F _Y , W and μ obtained by this method and the measured value of the force plate. These data were obtained at rotation angles α = 20°, 130° and 190°, as shown in Figure 7, because the measurement accuracy of this set of rotation angles is the best when the condition number C = 12.5. Figures 8 (a), (b), (c) and (d) show the results of tire circumferential friction load F _X , tire width direction friction load F _Y , vertical load W and friction coefficient μ. The vertical axis represents the value measured using the proposed method, and the horizontal axis represents the true value measured using the force plate. Figure 8 (d) of the friction coefficient μ also shows the measurement results under biaxial loading conditions without lateral load, which are obtained using the average strain of tire rotation.

Table 8 Relationship between the mean value of quadratic mean square law error _Er and the condition number C

Table 9 Experimental conditions when the vertical load W is approximately 1500N, 2000N and 2500N

Many studies have been conducted to form a method for measuring the road friction coefficient using the strain on the inner surface of the tire tread. The sensor installed on the inner surface of the tire tread is easy to fall off or be damaged because the protrusions on the road surface will be significantly deformed locally. Therefore, the present invention proposes a method for measuring the road friction coefficient using the strain on the tire sidewall. The present invention uses the sidewall of the tire instead, which can obtain stable measurement results because the sidewall of the tire is more difficult to deform locally than the inner surface of the tire tread. First, using an experimental device that simulates the full slip state of the tire, the present invention measures the relationship between the triaxial load acting on the tire ground and the strain generated on the tire sidewall. Subsequently, the present invention establishes an experimental formula to express this relationship and designs a method for measuring the road friction coefficient. The results confirm that even under the action of triaxial loads, the friction coefficient of multiple friction surfaces can be accurately measured using the method proposed in this article. The measurement of the tire adhesion coefficient under low speed and full slip conditions is achieved with high accuracy. From this perspective, the technical difficulties in measuring the tire-road adhesion coefficient are solved.

The general technical route for the tire-road adhesion coefficient is mainly based on estimation, such as visual estimation, Kalman filter estimation, fusion estimation, etc.; there is no low-cost, convenient direct or indirect measurement method. This technical solution improves the sensor measurement solution, and changes the sensor measurement method installed inside the tire to the tire sidewall through a lower-cost strain gauge method. Combined with the independently invented tire test bench (Figure 3) and the derived formula, it can quickly measure the corresponding strain value changes under different adhesion coefficient roads and different rotation angles, improve the measurement accuracy of the tire-road adhesion coefficient, and reduce the measurement cost. Figures 8(a), (b) and (c) show that the friction load can be accurately measured as a whole. In addition, according to Figure 8(c), a better vertical load can be measured. As shown in Figure 8(d), the friction coefficient accuracy measured by the present invention under triaxial load is lower than the friction coefficient accuracy measured by the previous study under biaxial load. However, in the above results, the mean square error between μ obtained in the present invention and the value measured using the force plate is about 0.07. Therefore, the proposed triaxial loading method is expected to fully identify dry asphalt and snow road conditions.

In the description of the present invention, unless otherwise specified, "plurality" means two or more than two; the orientations or positional relationships indicated by the terms "upper", "lower", "left", "right", "inner", "outer", "front end", "rear end", "head", "tail", etc. are based on the orientations or positional relationships shown in the drawings, and are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, be constructed and operate in a specific orientation, and therefore cannot be understood as limiting the present invention. In addition, the terms "first", "second", "third", etc. are only used for descriptive purposes and cannot be understood as indicating or implying relative importance.

The working principle of the tire-road friction coefficient measurement method provided by the present invention is mainly based on mechanical principles and strain measurement technology. The following is the detailed working principle:

First, you need to understand the friction behavior of tires on the road. When a tire rolls or slides on the road, it is subject to friction and vertical loads from the road. These forces will produce strains on the sidewalls of the tire, which can be detected by specialized measurement equipment.

In step S1, the friction loads F _X , F _Y and the vertical load W are changed independently, and the strains on the tire sidewalls caused by these changes are measured. The purpose of this is to establish the relationship between load and strain.

In step S2, different road conditions are simulated using contact surfaces with different friction coefficients (such as rubber plates, aluminum plates, patterned acrylic force plates, or polytetrafluoroethylene plates). For each contact surface, the loads F _X , F _Y , and W are independently changed, and the corresponding strains are measured. In this way, a series of load-strain data under different road conditions can be collected.

Step S3 is based on an assumption that the strain generated on the sidewall is proportional to each load acting on the tire and is the linear sum of the strains caused by each load. This assumption allows the complex friction behavior to be simplified into a linear model, making it easier to analyze and calculate.

In step S4, the measured value of the intermediate strain ε _m is used to determine the various loads acting on the tire. This is achieved by comparing the actual measured strain with the data collected in steps S1 and S2. In this way, the friction load and vertical load on the tire under the current road conditions can be estimated.

Finally, in step S5, the exact values of F _X , F _Y and W are obtained by solving their equations. Then, the friction coefficient μ is calculated by dividing the square root of the sum of the squares of F _X and F _Y by W. This friction coefficient reflects the friction performance of the tire under the current road conditions and is an important indicator for evaluating tire performance and safety.

The tire-road friction coefficient measurement method provided by the present invention accurately evaluates the friction performance of the tire by measuring and analyzing the strain and load data of the tire under different road conditions. This method has high flexibility and accuracy, can adapt to different road conditions and tire types, and provides an important reference for tire design and use.

Based on the provided tire-road friction coefficient measurement method, two specific embodiments can be designed to demonstrate how to apply this method to measure the friction coefficient under different conditions.

###Example 1: Measurements on a dry aluminum plate

1) Preparation stage:

Select a flat, dry aluminum plate as the ground plane.

Make sure the contact surface between the tire and the aluminum plate is clean and free of oil or other substances.

2) Measurement steps:

S1: In a controlled laboratory environment, the friction loads F _X (along the tire rolling direction) and F _Y (perpendicular to the rolling direction), as well as the vertical load W (the force of the tire pressing on the aluminum plate) are independently varied using a dedicated force measuring device. At the same time, the strain of the tire sidewall is measured using a strain gauge.

S2: Change the loads F _X , F _Y and W on the aluminum plate independently and record the data under different conditions.

S3: Based on the assumption that strain is proportional to load, the sidewall strain data is analyzed to confirm its relationship with each load.

S4: Using the measured intermediate strain ε _m value, an algorithm is used to determine the precise values of F _X , F _Y and W.

S5: Based on the values of F _X , F _Y and W, calculate the friction coefficient μ (the square root of the sum of the squares of F _X and F _Y divided by W) by a mathematical formula.

###Example 2: Measurement on a slippery PTFE plate

1) Preparation stage:

A polytetrafluoroethylene plate was used as the contact surface for the test and an appropriate amount of water was sprayed on it to simulate a wet condition.

Make sure the tire type is the same as in Example 1 in order to compare the friction coefficient under different road conditions.

2) Measurement steps:

S1: In a laboratory setting, the friction loads F _X , F _Y and the vertical load W are adjusted independently. The strain values are recorded by a strain measuring device on the tire sidewall.

S2: On the prepared wet PTFE plate, change the loads _FX , _FY and W borne by the tire and record the data under different friction conditions.

S3: Analyze the tire sidewall strain data to determine how they are proportional to the individual loads and find their linear sum.

S4: Based on the measured value of the sidewall strain ε _m , calculate the exact value of each load acting on the tire.

S5: Use these load values to calculate the friction coefficient μ, based on the ratio of the square root of the sum of the squares of F _X and F _Y divided by W.

The two examples show the application of the method to measure the friction coefficient between the tire and the road under different road conditions (dry aluminum plate and wet polytetrafluoroethylene plate). This method can provide important data support for tire design, safety analysis and performance testing.

It should be noted that the embodiments of the present invention can be implemented by hardware, software, or a combination of software and hardware. The hardware part can be implemented using dedicated logic; the software part can be stored in a memory and executed by an appropriate instruction execution system, such as a microprocessor or dedicated design hardware. It can be understood by a person of ordinary skill in the art that the above-mentioned devices and methods can be implemented using computer executable instructions and/or contained in a processor control code, such as a carrier medium such as a disk, CD or DVD-ROM, a programmable memory such as a read-only memory (firmware), or a data carrier such as an optical or electronic signal carrier. Such code is provided on the carrier medium. The device and its modules of the present invention can be implemented by hardware circuits such as very large-scale integrated circuits or gate arrays, semiconductors such as logic chips, transistors, etc., or programmable hardware devices such as field programmable gate arrays, programmable logic devices, etc., can also be implemented by software executed by various types of processors, and can also be implemented by a combination of the above-mentioned hardware circuits and software, such as firmware.

The above description is only a specific implementation mode of the present invention, but the protection scope of the present invention is not limited thereto. Any modifications, equivalent substitutions and improvements made by any technician familiar with the technical field within the technical scope disclosed by the present invention and within the spirit and principle of the present invention should be covered by the protection scope of the present invention.

Claims (5)

1. A method for measuring a friction coefficient of a tire road surface, comprising:

S1, respectively and independently changing a friction load F _X、F_Y and a vertical load W, and measuring the strain of a side wall;

S2, adopting ground planes with different friction coefficients to respectively and independently change loads F _X、F_Y and W, wherein the ground planes are a rubber plate, an aluminum plate, a pattern sub-gram force measuring plate or a polytetrafluoroethylene plate;

s3, assuming that the strain generated on the sidewall is proportional to each load acting on the tire and is the linear sum of the strain induced by each load;

S4, determining each load acting on the tire by using the measured value of the intermediate strain epsilon _m;

S5, obtaining values of the F _X、F_Y and the W by solving an equation of the F _X、F_Y and the W, and then dividing the square root of the sum of the square of the F _X and the square of the F _Y by the W to calculate a friction coefficient mu;

the relationship between sidewall strain and each load in S4 is defined as follows:

ε_m(α)＝k(α)·F_X+l(α)·F_Y+m(α)·W+n(α) (1)

wherein k (alpha), l (alpha), m (alpha) and n (alpha) are experimental constants when the rotation angle alpha is equal to the rotation angle alpha; k (alpha), l (alpha), m (alpha) are proportionality constants; and n (α) is the intercept, although the intercept n (α) is substantially zero, there is a small value due to the slight tilting of the strain gauge;

Since F _X、F_Y, W are unknown in S5, three-dimensional first-order simultaneous equations are derived from Eq (1) at three different rotation angles α _i, i=1, 2,3, yielding the following values:

By solving the equations for F _X、F_Y and W, their values can be obtained, and then the square root of the sum of F _X and F _Y is divided by W to calculate the coefficient of friction μ, as follows:

However, the combination of selected rotation angles α _i, i=1, 2,3, results in extremely poor simultaneous equation conditions; in this case, an accurate solution is not obtained; the values of the experimental constants k (α), l (α), m (α) and n (α) are obtained in a calibration experiment, while the appropriate rotation angle combination α _i, i=1, 2,3 is determined according to the condition number C of the two modes of the first term coefficient matrix on the right side of equation (2).

2. A tire road surface friction coefficient measuring apparatus for realizing a tire road surface friction coefficient measuring method as set forth in claim 1, characterized by comprising a two-degree-of-freedom translation mechanism for applying a vertical load and a friction load to the tire, a driving unit for rotating the tire, a ground contact surface, and a force measuring plate for measuring three axial loads between the tire and the ground contact surface; the translation mechanism vertically moves the ground plane in the z-axis direction relative to the coordinate system O-XYZ and horizontally moves the ground plane in the X-axis direction; when the tire rotates, the tangential velocity with respect to the ground contact surface is in the Y-axis direction, the rotation angle of the tire is denoted by α, and the direction of the frictional load acting on the ground contact surface of the tire is denoted by θ.

3. The tire road surface friction coefficient measuring device according to claim 2, wherein the tire road surface friction coefficient measuring device applies a vertical load W on the tire, pushing the force-receiving plate up to the bottom surface in the z-axis direction; in this case, when the tire rotates, a longitudinal friction load F _X acts on the tire ground-contact surface; when the force-receiving plate moves horizontally along the Y-axis direction, a lateral friction load F _Y acts on the surface of the tire; the ratio of the value F _X to the value F _Y can be changed by changing the rotating speed of the tire and the horizontal movement speed of the loading device of the translation mechanism; the direction of the friction load F, calculated as the square root of the sum of the squares of F _X and F _Y, can be adjusted; the friction coefficient of the tire ground contact surface can be adjusted by changing the material of the top plate on the force measuring plate.

4. A computer device comprising a memory and a processor, the memory storing a computer program that, when executed by the processor, causes the processor to perform the steps of the tire road friction coefficient measuring method according to claim 1.

5. A computer-readable storage medium storing a computer program which, when executed by a processor, causes the processor to perform the steps of the tire road surface friction coefficient measuring method according to claim 1.