TIRE CORNERING STIFFNESS ESTIMATION SYSTEM AND METHOD

Field of the Invention

The invention relates generally to tire monitoring systems and methods for collecting measured tire parameter data during vehicle operation and, more particularly, to systems and methods utilizing such tire sensor-based data in vehicle control systems.

Background of the Invention

It is desirable to ascertain cornering stiffness of a vehicle tire in order to optimize control commands (active front/rear steering input, yaw control command) to achieve vehicle stability and safety without degrading driver intentions. Heretofore, a robust and high fidelity system and method for determining tire cornering stiffness in real time has not been achieved. Accordingly, there remains a need for a tire cornering stiffness determination system and method that is both robust and accurate and which can adapt to changes to tire conditions during operation of a vehicle.

Summary of the Invention

The invention relates to a system in accordance with claim 1 and to a method in accordance with claim 6.

Dependent claims refer to preferred embodiments of the invention.

In one aspect of the invention, a tire cornering stiffness estimation system and method is provided for a supportive tire to a vehicle, the tire having multiple tire-specific measureable parameters. The system employs a multiple tire-affixed sensors mounted to the tire for operably measuring the tire-specific parameters and generating tire-specific information. One or more accelerometer(s) are mounted to the hub supporting the tire to generate a hub accelerometer signal. A model-based tire cornering stiffness estimator is included to generate a model-derived tire cornering stiffness estimation based upon the hub accelerometer signal adapted by the tire-specific information.

In another aspect of the invention, the cornering stiffness estimation system may conduct a frequency domain spectral analysis of the hub accelerometer signal by the model-based tire cornering stiffness estimator.

According to a further aspect of the invention, the tire cornering stiffness estimator may employ as estimator inputs: a load estimation for the object vehicle tire; temperature of the vehicle tire, air pressure within a cavity of the vehicle tire, a tire ID identifying the vehicle tire by tire type and a wear estimation on a tread of the vehicle tire.

The tire cornering stiffness estimation system and method, in another aspect, of the invention may obtain the hub accelerometer signal from the vehicle CAN bus.

Definitions

"ANN" or "Artificial Neural Network" is an adaptive tool for non-linear statistical data modeling that changes its structure based on external or internal information that flows through a network during a learning phase. ANN neural networks are nonlinear statistical data modeling tools used to model complex relationships between inputs and outputs or to find patterns in data.

"Axial" and "axially" means lines or directions that are parallel to the axis of rotation of the tire.

"Circumferential" means lines or directions extending along the perimeter of the surface of the annular tread perpendicular to the axial direction.

"Dugoff Model" is an empirical tire model providing analytical relations for the longitudinal and lateral forces as functions of the slip angle and slip ratio. It accounts for the coupling between the side and longitudinal forces.

"Equatorial Centerplane (CP)" means the plane perpendicular to the tire's axis of rotation and passing through the center of the tread.

"Inboard side" means the side of the tire nearest the vehicle when the tire is mounted on a wheel and the wheel is mounted on the vehicle.

"Lateral" means an axial direction.

"Outboard side" means the side of the tire farthest away from the vehicle

"Piezoelectric Film Sensor" a device in the form of a film body that uses the piezoelectric effect actuated by a bending of the film body to measure pressure, acceleration, strain or force by converting them to an electrical charge.

"Radial" and "radially" means directions radially toward or away from the axis of rotation of the tire.

Brief Description of the Drawings

The invention will be described by way of example and with reference to the accompanying drawings in which:

• FIG. 1 is a two degree of freedom (DOF) bicycle vehicle model and state-space representation of the model describing lateral and yaw dynamics.
• FIGS. 2A and 2B are graphs showing cornering stiffness dependency on tire load and tread wear for two respective inflation pressures.
• FIGS. 2C and 2D are additional graphs showing cornering stiffness dependency on tire load and tread wear for two additional inflation pressures. FIG. 3 is a graph showing cornering stiffness dependency on tire temperature.
• FIG. 4 is a chart summary of cornering stiffness sensitivities to load, pressure, tire wear state and temperature.
• FIG. 5 is an adaptation model for determining a cornering stiffness estimation.
• FIG. 6A through 6D are graphs showing goodness of fit of the model in estimating cornering stiffness at four inflation pressures.
• FIG. 7 is a table showing model coefficients for different four inflation levels.
• FIG. 8 is a graph showing model fitting, adapting model coefficients to inflation pressure changes for a coefficient p00 vs. pressure.
• FIG. 9 is a model fitting graph for a coefficient p10 vs. pressure.
• FIG. 10 is a model fitting graph for a coefficient p01 vs. pressure.
• FIG. 11 is a model fitting graph for a coefficient p20 vs. pressure.
• FIG. 12 is a model fitting graph for a coefficient p11 vs. pressure.
• FIG. 13 is a model fitting graph for a coefficient p02 vs. pressure.
• FIG. 14 is a model fitting graph for a coefficient p21 vs. pressure.
• FIG. 15 is a model fitting graph for a coefficient p12 vs. pressure.
• FIG. 16 is a model fitting graph for a coefficient p03 vs. pressure.
• FIG. 17 is a table showing model fitting coefficients determinations.
• FIGS. 18A through 18D are graphs showing cornering stiffness dependency on tire wear state and load at four different tire inflation levels.
• FIGS. 19A through 19C are test result graphs of cornering stiffness, peak grip level, and mean temperature in a cold to hot test temperature variation test.
• FIG. 20 is a graph showing cornering stiffness - temperature variation model fit.

Detailed Description of Example Embodiments of the Invention

Referring to FIG. 1, a two degree of freedom (DOF) bicycle vehicle model and state-space expression for the model describing lateral and yaw dynamics is shown. The expression of FIG. 1 follows the definitional key where u is the vehicle forward speed, v the vehicle lateral speed, r the yaw rate, m the vehicle mass, I_zz the yaw moment of inertia, C_af and C_ar are the front and rear cornering stiffness (per axle), δ_f the front wheel steering angle, and a and b are the distances from the vehicle center of gravity to front and rear axles, respectively.

By way of background, the subject invention is directed to a tire force model adaptation to tire-based information obtained from tire-attached sensors in order to make a tire cornering stiffness estimation. As seen in the FIG. 5, schematic representation of the subject cornering stiffness estimation system and method 10. The system includes a vehicle 12 supported by one or more tires 14. The purpose of the system 10 is to dynamically estimate cornering stiffness for each tire 14 supporting the vehicle 12. The tire 14 is of conventional build, having a tire tread 16, a pair of sidewalls 18 and an air containing cavity 22. A tire-attached sensor 20 is affixed to the inner liner defining cavity 22 as shown. The sensor 20, referred to herein as a tire pressure monitoring sensor is a package of sensors and transponders intended to measure tire temperature and cavity pressure. In addition, a tire identification transponder is present, programmed to provide a unique tire-specific identification. Such sensors and transponders are commercially available and may be attached to the tire 14 by suitable means such as adhesive.

The cornering stiffness estimation system 10 develops an estimate of the loading on the tire 14 by means of a load estimation method 23. The load estimation 23 is based upon a dynamic tire load estimator configured as presented in US-A-2014/0278040, hereby incorporated herein in its entirety. In addition, the system 10 uses as an adaptive input a wear estimation method 24 based upon vehicle-based sensors provided from the CAN bus 25 of the vehicle 12. The CAN bus 25 input of vehicle-based information into the wear estimation method 24 results in an estimation of tire wear state of the tire tread 16. A suitable wear estimation method, referred herein as an "indirect" wear state estimation method, is found US-A-2014/0366618, hereby incorporated by reference in its entirety herein. The "indirect" tire wear state estimation algorithm is used to generate tread depth estimation indirectly; that is, without the use of tire mounted tread depth measuring sensors. As such the difficulty of implementing and maintaining accurate tire-based sensor tread depth measurement is avoided. The indirect tire wear state estimation algorithm utilizes a hub acceleration signal which is accessible via the vehicle CAN bus 25 from vehicle based sensors. The hub acceleration signal is analyzed and an estimation is made as to tread depth or wear. The tread depth used may be the percentage tread wear left or a quantitative value of tread wear depth left on the tire.

The collective information provided by the tire-based sensors and transponders, referred to as tire-based information, constitute adaptation inputs 26 into a tire cornering stiffness adaptation model 28 that outputs the object cornering stiffness estimation 30. Operation of the model 28 and adaptation are based upon cornering stiffness dependency on the inputs 26 as will be explained below.

With reference to FIG. 1, vehicle control systems are based on tire characteristics (cornering stiffness, peak grip level). However these characteristics fluctuate under varying operating conditions of the tire (temperature change, pressure change, tire wear state change, load change) which affects the accuracy of the vehicle stability control. The availability of a high fidelity tire model with suitable adaptation terms would facilitate the online computation of the optimized control commands such as active front/rear steering input, yaw control to achieve vehicle stability and safety without degrading driver intentions. The subject method and system provides such an adaptation model for the cornering stiffness parameter by using inflation pressure, tire wear state, load, and tire temperature as adaptation inputs.

The subject system uses information from tire-attached sensors and transducers 20 and utilizes different tire-affixed sensor within a sensor fusion framework. A model 32 describing the motion of the vehicle is selected, such as that shown in FIG. 1, known as the "bicycle model" which includes tire cornering stiffness parameters. These parameters describe the tire-road contact and are unknown and time-varying. Hence, in order to fully make use of the single track or bicycle model, the parameters affecting corning stiffness are used. Following is a state-space representation 34 of the model: $$\left[\begin{array}{c}\dot{\upsilon }\\ \dot{r}\end{array}\right]=\left[\begin{array}{cc}\frac{-\left(C_{\alpha \mathrm{f}}+C_{\alpha \mathrm{r}}\right)}{\mathit{mu}}& \frac{b{C}_{\alpha \mathrm{r}}-a{C}_{\alpha \mathrm{f}}}{\mathit{mu}}-u\\ \frac{b{C}_{\alpha \mathrm{r}}-a{C}_{\alpha \mathrm{f}}}{I_{\mathit{zz}}u}& \frac{-\left(a^2{C}_{\alpha \mathrm{f}}+b^2{C}_{\alpha \mathrm{r}}\right)}{I_{\mathit{zz}}u}\end{array}\right]\left[\begin{array}{c}\upsilon \\ r\end{array}\right]+\left[\begin{array}{c}\frac{C_{\alpha \mathrm{f}}}{m}\\ \frac{a{C}_{\alpha \mathrm{f}}}{I_{\mathit{zz}}}\end{array}\right]{\mathrm{\delta }}_{\mathrm{f}}$$

The dependency of cornering stiffness in a tire to tire wear state and tire load is demonstrated graphically by test results in FIGS. 2A through 2D showing cornering stiffness vs. load for 33, 37, 41, and 45 psi inflation pressure (1 psi = 9895 Pa). Full 60 percent and 30 percent of tread depth were used in the tests and their respective effect on cornering stiffness were examined under the four inflation pressures selected. A 35 percent change in the tire cornering stiffness was measured for the three different tread depths evaluated. It will further be noted by a comparison of the four graphs to each other that cornering stiffness changes both with changes in the tire inflation pressure and changes in load as evidenced by the plots.

In FIG. 3, the dependency of cornering stiffness to tire temperature is seen. A sweep was conducted varying temperature between 35°C and 60°C. The effect of the change in temperature on the measured cornering stiffness Cy is shown. A 30 percent drop in cornering stiffness was measured between 35°C and 60°C.

The test results and sensitivities are summarized in FIG. 4. As seen, cornering stiffness is a function of load, pressure, tire wear state and temperature and such dependencies are important in a cornering stiffness estimation system and method. Regarding load, a 10 percent increase in cornering stiffness from a 200 pound increase in load is noted. For inflation pressure, a 10 percent increase in cornering stiffness for a 4 psi decrease in inflation pressure. A 15 percent increase in cornering stiffness occurs with a 3 mm decrease in tread depth and a 30 percent drop with a 25°C increase in tire temperature.

The subject model capturing the dependencies between the tire cornering stiffness, tire wear state and tire load is shown below. A Polynomial model (third order in load and second order in tread depth) results in a good fit as shown in FIGS. 6A through 6D. The tests were conducted at inflation pressures of 33, 37, 41 and 45 psi. Goodness of fit resultant correlation coefficient R was 0.998 at 33 psi, 0.998 at 37 psi, 0.999 at 41 psi and 0.999 at 45 psi.

• Model Fit:

  • fit result (x,y) = p00 + p10*x + p01 *y + p20*x^2 + p11 *x*y + p02*y^2 + p21 *x^2*y + p12*x*y^2 + p03*y^₃
  • Coeff = [p00 p10 p01 p20 p11 p02 p21 p12 p03];
  • Coeff_33 = [-23.23 -179.5 0.9513 13.93 0.01817 -0.0001009 -0.00324 1.946e-06 2.744e-09];
  • Coeff_37 = [126.6 -178.9 0.7611 15.81 0.001912 -5.894e-05 -0.00316 3.107e-06 5.617e-10];
  • Coeff_41=[98.89 -128.8 0.6958 12.82 -0.01452 -4.279e-05 -0.002379 3.565e-06 - 1.006e-10];
  • Coeff_45=[-107.9 -98.23 0.7392 11.84 -0.02464 -4.481 e-05 -0.001773 3.464e-06 1.883e-10];

The model thus is seen to give a good fit for all pressure conditions.

The expression used in the model for cornering stiffness Cy is as follows: $$\mathrm{Cy}=\left(\mathrm{p}\mathrm{20}+\mathrm{p}\mathrm{21}*\mathrm{load}\right)*\mathrm{tread}{\mathrm{depth}}^{\wedge }\mathrm{2}+\left(\mathrm{p}\mathrm{10}+\mathrm{p}\mathrm{11}*\mathrm{load}+\mathrm{p}\mathrm{12}*{\mathrm{load}}^{\wedge }\mathrm{2}\right)*\mathrm{tread\; depth}+\left(\mathrm{p}\mathrm{00}+\mathrm{p}\mathrm{01}*\mathrm{load}+\mathrm{p}\mathrm{02}*{\mathrm{load}}^{\wedge }\mathrm{2}+\mathrm{p}\mathrm{03}*{\mathrm{load}}^{\wedge }\mathrm{3}\right)$$

The table shown in FIG. 7 summarizes the model coefficients for each of the four pressure levels evaluated. The model coefficients verify the dependency of cornering stiffness estimation to tire pressure.

Model fitting through the adaptation of coefficients to inflation pressure changes is further demonstrated by the coefficient-against-pressure graphs of FIG. 8, 9, 10, 11, 12, 13, 14, 15, and 16. Model fit is expressed as follows: $$\mathrm{Cy}=\left(\mathrm{p}\mathrm{20}+\mathrm{p}\mathrm{21}*\mathrm{load}\right)*\mathrm{tread}{\mathrm{depth}}^{\wedge }\mathrm{2}+\left(\mathrm{p}\mathrm{10}+\mathrm{p}\mathrm{11}*\mathrm{load}+\mathrm{p}\mathrm{12}*{\mathrm{load}}^{\wedge }\mathrm{2}\right)*\mathrm{tread\; depth}+\left(\mathrm{p}\mathrm{00}+\mathrm{p}\mathrm{01}*\mathrm{load}+\mathrm{p}\mathrm{02}*{\mathrm{load}}^{\wedge }\mathrm{2}+\mathrm{p}\mathrm{03}*{\mathrm{load}}^{\wedge }\mathrm{3}\right)$$ where x is normalized by mean 39 and standard deviation 5.164.

As seen, coefficients defined are: p1, p2, p3, and p4.

• FIG. 8
  
  

  % p00

  • p1 = -0.5523
  • p2 = -148.6
  • p3 = -35.69
  • p4 = 135

• FIG. 9
  
  

  % p10

  • p1 = -24.75
  • p2 = 12.49
  • p3 = 68.39
  • p4 = -155.7

• FIG. 10
  
  

  % p01

  • p1 = -0.005809
  • p2 = 0.09733
  • p3 = -0.08343
  • p4 = 0.7138

• FIG. 11
  
  

  % p20

  • p1 = 2.467
  • p2 = -1.192
  • p3 = -4.23
  • p4 = 14.49

• FIG. 12
  
  

  % p11

  • p1 = 0.0002326
  • p2 = 0.0002558
  • p3 = -0.02156
  • p4 = -0.006688

• FIG. 13
  
  

  % p02

  • p1 = 2.74e-06
  • p2 = -1.833e-05
  • p3 = 2.044e-05
  • p4 = -4.812e-05

• FIG. 14
  
  

  % p21

  • p1 = -0.0003141
  • p2 = 0.0002192
  • p3 = 0.001055
  • p4 = 0.002802

• FIG. 15
  
  

  % p12

  • p1 = 5.164e-08
  • p2 = -5.258e-07
  • p3 = 5.835e-07
  • p4 = 3.145e-06

• FIG. 16
  
  

  % p03

  • p1 =-2.04e-10
  • p2 =1.03e-09
  • p3 = -8.244e-10
  • p4 = 7.61 e-11

FIG. 17 shows in tabular form the coefficients for an estimation of cornering stiffness subject to the following expression: $$\mathrm{Cy}=\left(\mathrm{p}\mathrm{20}+\mathrm{p}\mathrm{21}*\mathrm{load}\right)*\mathrm{tread}{\mathrm{depth}}^{\wedge }\mathrm{2}+\left(\mathrm{p}\mathrm{10}+\mathrm{p}\mathrm{11}*\mathrm{load}+\mathrm{p}\mathrm{12}*{\mathrm{load}}^{\wedge }\mathrm{2}\right)*\mathrm{tread\; depth}+\left(\mathrm{p}\mathrm{00}+\mathrm{p}\mathrm{01}*\mathrm{load}+\mathrm{p}\mathrm{02}*{\mathrm{load}}^{\wedge }\mathrm{2}+\mathrm{p}\mathrm{03}*{\mathrm{load}}^{\wedge }\mathrm{3}\right)$$ where the coefficients [p00, p10, p01, p20, p11, p02, p21, p12, p03] are pressure dependent and given by the following expression: $$\left[\mathrm{p}\mathrm{00}\mathrm{p}\mathrm{10}\mathrm{p}\mathrm{01}\mathrm{p}\mathrm{20}\mathrm{p}\mathrm{11}\mathrm{p}\mathrm{02}\mathrm{p}\mathrm{21}\mathrm{p}\mathrm{12}\mathrm{p}\mathrm{03}\right]=\mathrm{p}\mathrm{1}*{\mathrm{x}}^{\wedge }\mathrm{3}+\mathrm{p}\mathrm{2}*{\mathrm{x}}^{\wedge }\mathrm{2}+\mathrm{p}\mathrm{3}*\mathrm{x}+\mathrm{p}\mathrm{4}$$ Here x is normalized by mean 39 and standard deviation 5.164.

Model fitting results with pressure adapted coefficients are shown graphically in FIGS. 18A through 18D for the four pressure settings: 33, 37, 41, and 45 psi. Tread wear at full non-skid, 60 percent, 30 percent are plotted for both experimental and Model fit. The plotting of Cy vs. load is shown comparing experimental to Model fit and indicate the model is effective in predicting cornering stiffness Cy at different load, pressure, and tread wear.

In FIG. 19A, a cold to hot test results are shown graphically for a tested Mustang GT500 vehicle fitted with Goodyear P265/40R19 front tires. The cornering stiffness in the cold to hot test is shown. In FIG. 19B, peak grip level variation for the cold to hot test is graphed. In FIG. 19C, temperature variation for the test is shown graphically. FIG. 20 shows the graph of cornering stiffness during the test as temperature is varied.

The dependence of cornering stiffness on the tire temperature can be captured by introducing a polynomial scaling factor as follows.

• Model Fit: $$\mathrm{f}\left(\mathrm{x}\right)=\mathrm{p}\mathrm{1}*{\mathrm{x}}^{\mathrm{2}}*\mathrm{p}\mathrm{2}*\mathrm{x}+\mathrm{p}\mathrm{3}$$
• Coefficients (with 95 percent confidence bounds): $$\mathrm{p}\mathrm{1}=\mathrm{1.761}\left(\mathrm{0.04273},\mathrm{3.48}\right)$$ $$\mathrm{p}\mathrm{2}=-\mathrm{356.5}\left(-\mathrm{629.8},-\mathrm{88.09}\right)$$ $$\mathrm{p}\mathrm{3}=\mathrm{1.983}\mathrm{e}+\mathrm{0.4}\left(\mathrm{8978},\mathrm{3.067}\mathrm{e}+\mathrm{04}\right)$$
• Cornering stiffness adaptation model thus becomes as follows: $$\mathrm{Cy}=\left(\mathrm{p}\mathrm{20}+\mathrm{p}\mathrm{21}*\mathrm{load}\right)*\mathrm{tread}{\mathrm{depth}}^{\wedge }\mathrm{2}+\left(\mathrm{p}\mathrm{10}+\mathrm{p}\mathrm{11}*\mathrm{load}+\mathrm{p}\mathrm{12}*{\mathrm{load}}^{\wedge }\mathrm{2}\right)*\mathrm{tread\; depth}+\left(\mathrm{p}\mathrm{00}+\mathrm{p}\mathrm{01}*\mathrm{load}+\mathrm{p}\mathrm{02}*{\mathrm{load}}^{\wedge }\mathrm{2}+\mathrm{p}\mathrm{03}*{\mathrm{load}}^{\wedge }\mathrm{3}\right)*\mathrm{Temperature\; Scaling\; Factor}$$

From the foregoing and in reference to FIG. 5, the subject tire cornering stiffness estimation system and method 10 is provided for analyzing and estimating cornering stiffness for each supportive tire 14 to a vehicle 12. The tire has multiple tire-specific measureable parameters of tire inflation pressure, tire ID (required for using tire-specific model coefficients), tire load, tire wear state and tire temperature. The tire ID is recognized by a reading of a tire-mounted transducer and the coefficients for that particular tire are then used by the model in making its estimation.

The system employs a multiple tire-affixed sensors 20 mounted to the tire for operably measuring the tire-specific parameters and generating tire-specific information. The tire inflation pressure, load, temperature and tire ID information is available from a tire attached TPMS sensor 20 equipped with tire ID information. One or more accelerometer(s) are mounted to the hub supporting the tire to generate a hub accelerometer signal. The model-based tire cornering stiffness estimator generates a model-derived tire cornering stiffness estimation based upon the hub accelerometer signal (used to estimate loading) and adapted by the tire-specific information (tire ID, pressure, temperature, and wear state).

Tire wear state is derived by doing a frequency domain/spectral analysis of the suspension hub-mounted accelerometer signal as taught in US-A-2014/0366618.

The tire cornering stiffness estimator for Cy employs as estimator inputs 26: a load estimation for the object vehicle tire, temperature of the vehicle tire, air pressure within a cavity of the vehicle tire and the tire ID used to generate model coefficients by recognition of tire-type, and a wear estimation on a tread of the vehicle tire. The hub accelerometer signal is obtained from the vehicle CAN-bus.