Method for determining tire slip state

Abstract

The present invention relates to a method for determining a tire slip state, which includes the following steps: detecting rotational fluctuations of a power transmission member and a wheel body of a wheel; determining whether the vibration mode of the wheel body and the tire is an elastic slip mode or a sliding slip mode based on an amplitude ratio between the rotational fluctuation amplitude of the wheel body and the rotational fluctuation amplitude of the power transmission member and a phase delay of the rotational fluctuation of the wheel body relative to the rotational fluctuation of the power transmission member; and determining that the tire is in a sliding slip state when the vibration mode is the sliding slip mode. The amplitude ratio and the phase delay are calculated by using the effective rolling radius in a region where the relationship between the dynamic load radius and the effective rolling radius is linear as the tire driving radius.

Description

Technical Field

[0001] The present invention relates to a method for determining the slip state of a tire. Background Art

[0002] When a tire grips the ground, torsional vibration of the drive shaft is generated. When the tire slips, the slip of the tire causes the torsion of the drive shaft to be released and the torsional vibration of the drive shaft disappears. JP2019 - 31112A discloses a running control method that detects the rotational fluctuation of a differential device and the rotational fluctuation of a wheel body connected to the drive shaft via the differential device, sets a slip identification amount based on the amplitude ratio and phase delay of the rotational fluctuation amplitude of the wheel body with respect to the rotational fluctuation amplitude of the differential device, and controls the driving force of the tire so that the slip identification amount does not exceed a slip identification amount threshold corresponding to the elastic slip limit of the tire with respect to the road surface.

[0003] In JP2019 - 31112A, the dynamic radius of the tire is used to calculate the amplitude ratio and phase delay of the rotational fluctuation amplitude of the wheel body with respect to the rotational fluctuation amplitude of the differential device. The dynamic radius of the tire is considered to be the dynamic load radius, which represents the distance between the ground contact surface and the wheel axle when a load is applied to the tire. The dynamic load radius may be affected by the vertical load and tire pressure. Therefore, the frictional torque generated at the ground contact surface, the viscous resistance between the tire and the ground contact surface, and the tire stiffness calculated based on the dynamic radius of the tire tend to fluctuate due to the influence of the vertical load and tire pressure. Summary of the Invention

[0004] In view of the above background art, the main object of the present invention is to provide a method for determining the slip state of a tire with less influence from the vertical load and tire pressure.

[0005] To achieve the above object, an aspect of the present invention provides a method for determining the slip state of a tire of a wheel relative to a road surface, wherein the wheel is connected to a drive source via a power transmission member, and the method includes the following steps: detecting the rotational fluctuation of the power transmission member and the rotational fluctuation of the wheel body of the wheel; based on the amplitude ratio of the rotational fluctuation amplitude of the wheel body to the rotational fluctuation amplitude of the power transmission member and the phase delay of the rotational fluctuation of the wheel body relative to the rotational fluctuation of the power transmission member, determining whether the vibration mode of the wheel body and the tire is an elastic slip mode in which the vibration mode of the wheel body and the tire represents the frequency response in an elastic slip state, or a sliding slip mode in which the vibration mode of the wheel body and the tire represents the frequency response in a sliding slip state; and when the vibration mode of the wheel body and the tire is the sliding slip mode, determining that the tire is in the sliding slip state, wherein the amplitude ratio and the phase delay are calculated by using the effective rolling radius in a region where the relationship between the dynamic load radius and the effective rolling radius is linear as the tire drive radius, the dynamic load radius is the distance between the central axis of the wheel and the road surface, and the effective rolling radius is a value obtained by dividing the distance traveled by the tire in one rotation by 2π.

[0006] According to this aspect, a method for determining the slip state of a tire with less influence from vertical load and tire pressure is provided. Compared with the dynamic load radius, the effective rolling radius is less affected by vertical load and tire pressure.

[0007] Preferably, in a region where the relationship between the dynamic load radius and the effective rolling radius is linear, the correlation coefficient between the dynamic load radius and the effective rolling radius is 0.99 or higher.

[0008] Preferably, the tire drive radius is the effective rolling radius in the 1G state.

[0009] Preferably, the tire drive radius is the effective rolling radius when the vertical load applied to the wheel is in the range of 2000N to 6500N.

[0010] Preferably, the effective rolling radius is calculated by dividing the driving distance of the vehicle detected based on the GNSS signal within a predetermined period by the number of rotations of the tire within the predetermined period.

[0011] According to the above configuration, a method for determining the slip state of a tire with less influence from vertical load and tire pressure can be provided. Description of the Drawings

[0012] Figure 1 is a configuration diagram of a vehicle equipped with a vehicle control system;

[0013] Figure 2 is a graph showing the relationship between the slip ratio and the driving torque;

[0014] Figures 3A to 3D is an explanatory diagram showing the driving radius of the tire;

[0015] Figure 4 is an explanatory diagram showing the dynamic model of the driving wheel;

[0016] Figure 5A is a graph showing the characteristics of the rotational fluctuation transmission between the differential device and the driving wheel;

[0017] Figure 5B is an explanatory diagram showing the relationship between the frequency and the vibration mode;

[0018] Figure 6 is a graph showing the root locus in the elastic slip mode and the sliding slip mode;

[0019] Figure 7 is a graph with the X-axis representing the vertical load Fz and the Y-axis representing the dynamic load radius DLR;

[0020] Figure 8 is a graph with the X-axis representing the vertical load Fz and the Y-axis representing the effective rolling radius ERR;

[0021] Figure 9 is a graph with the X-axis representing the vehicle speed, the Y-axis representing the tire radius, and the tire pressure being 200 kPa;

[0022] Figure 10 is a graph with the X-axis representing the vehicle speed, the Y-axis representing the tire radius, and the tire pressure being 240 kPa;

[0023] Figure 11 is a graph with the X-axis representing the vehicle speed, the Y-axis representing the tire radius, and the tire pressure being 280 kPa;

[0024] Figure 12 is a graph with the X-axis representing the tire pressure and the Y-axis representing the tire radius when the vertical load is 500 N, and this tire radius is normalized by the tire radius when the vertical load is 6500 N;

[0025] Figure 13 is a graph with the X-axis representing the vehicle speed, the Y-axis representing DLR / ERR, and the tire pressure being 200 kPa;

[0026] Figure 14 is a graph with the X-axis representing the vehicle speed, the Y-axis representing DLR / ERR, and the tire pressure being 240 kPa;

[0027] Figure 15 is a graph with the vehicle speed represented on the X-axis, DLR / ERR represented on the Y-axis, and a tire pressure of 280 kPa;

[0028] Figure 16 is an explanatory diagram showing the shape change of the tire corresponding to the change in the vertical load;

[0029] Figure 17 is a graph showing the relationship between the effective rolling radius ERR and the dynamic load radius DLR;

[0030] Figure 18 is a graph showing the relationship between the dynamic load radius DLR and the ground contact surface length GPL;

[0031] Figure 19 is a graph showing the relationship between the dynamic load radius DLR and the ground contact surface length GPL;

[0032] Figure 20 is a graph showing the relationship between the effective rolling radius ERR and the ground contact surface length GPL;

[0033] Figure 21 is a graph showing the relationship between the ground contact surface length GPL and the ground contact angle GPA;

[0034] Figure 22 is a graph showing the relationship between the ground contact angle GPA and the effective rolling radius ERR;

[0035] Figure 23 is a graph with the vertical load represented on the X-axis, the dynamic load radius DLR represented on the first Y-axis, and the ratio represented on the second Y-axis;

[0036] Figure 24 is a graph with the vertical load represented on the X-axis, the effective rolling radius ERR represented on the first Y-axis, and the ratio represented on the second Y-axis; and

[0037] Figure 25 is a flowchart for obtaining the tire driving radius during vehicle travel. DETAILED DESCRIPTION

[0038] Hereinafter, a method for determining the tire slip state according to an embodiment of the present invention and a driving control system for executing the method for determining the tire slip state will be described with reference to the accompanying drawings. As Figure 1 shown, the vehicle 1 is a four-wheel motor vehicle having a vehicle body 2 and four wheels 3 provided on the vehicle body 2. The wheels 3 include two front wheels 3F as driving wheels and two rear wheels 3R as non-driving wheels. Each wheel 3 has a wheel body W and a tire T mounted on the wheel body W.

[0039] Vehicle 1 has a drive source 5 for driving the front wheels 3F. The drive source 5 can be an internal combustion engine or an electric motor. The drive source 5 can include a speed reducer and a differential device. In the present embodiment, the drive source 5 is configured by an internal combustion engine 5A, a speed reducer 5B, and a differential device 5C (DN). The differential device 5C of the drive source 5 is connected to each front wheel 3F via a power transmission member 6. The power transmission member 6 can be a drive shaft.

[0040] Vehicle 1 has a braking device 8 for braking each wheel 3. Each braking device 8 includes a hydraulic supply device 8A and a disc brake 8B, and the disc brake 8B is provided in the wheel body W of each wheel 3 to be actuated by the hydraulic pressure from the hydraulic supply device 8A.

[0041] Vehicle 1 has a driving control system 10 for controlling the drive source 5 and the braking device 8. The driving control system 10 includes a control device 14 that controls the drive source 5 and the braking device 8 based on signals from a driving operation element 11 and a vehicle sensor 12. The driving operation element 11 includes: a steering wheel 11A for receiving a steering operation of the driver; an accelerator pedal 11B for receiving an acceleration operation of the driver; and a brake pedal 11C for receiving a deceleration operation of the driver.

[0042] The vehicle sensor 12 includes: left and right front wheel speed sensors 12A that respectively detect the rotational speeds of the left and right front wheels; left and right rear wheel speed sensors 12B that respectively detect the rotational speeds of the left and right rear wheels; a drive source rotational speed sensor 12C that detects the rotational speed of the output end of the drive source 5; and an acceleration sensor 12D that detects the longitudinal acceleration and lateral acceleration of the vehicle body 2. The front wheel speed sensors 12A and the rear wheel speed sensors 12B each detect the rotational speed of the corresponding wheel body W. The left and right rear wheel speed sensors 12B and the acceleration sensor 12D serve as a vehicle body speed acquisition unit to acquire information related to the vehicle body speed.

[0043] The drive source rotational speed sensor 12C detects the rotational speed of the main drive gear of the differential device of the drive source 5. The vehicle sensor 12 further includes: a steering angle sensor 12E that detects the steering angle of the steering wheel 11A; an accelerator pedal sensor 12F that detects the operation amount of the accelerator pedal 11B; a brake pedal sensor 12G that detects the operation amount of the brake pedal 11C; and an engine rotational speed sensor 12H that detects the rotational speed of the internal combustion engine 5A. In addition, the vehicle sensor 12 includes a vertical acceleration sensor 12K that detects the vertical acceleration of the vehicle body 2. It is preferable to provide a vertical acceleration sensor 12K for each wheel 3. The vertical acceleration sensor 12K can be provided on a suspension arm (not shown in the figure) that supports each wheel 3. The acceleration sensor 12D and the vertical acceleration sensor 12K can be configured as a common 3-axis or 6-axis acceleration sensor. The output torque of the internal combustion engine 5A is estimated by the control device 14, as described later.

[0044] The vehicle sensor 12 further includes a distance sensor 12L that measures the distance from the vehicle to an object around the vehicle and an inclination sensor 12M that measures the inclination angle of the vehicle. The distance sensor 12L is preferably a millimeter-wave radar, an ultrasonic sensor, a lidar, etc. The inclination sensor 12M is preferably a microelectromechanical system (MEMS) inertial sensor, etc.

[0045] The control device 14 is an electronic control unit (ECU) composed of a CPU, a ROM, a RAM, etc. The control device 14 performs various vehicle controls by executing computational processing according to a program using the CPU. The control device 14 includes an estimation unit 14A, a control unit 14B, and a torque acquisition unit 14C (torque acquisition device). The estimation unit 14A determines the slip state of the tire based on at least the rotational speed of the drive source 5, the rotational speed of the wheel body W, the vehicle body speed, and the torque applied to the wheel body W. The control unit 14B controls at least one of the drive source 5 and the braking device 8 based on the slip state of the tire.

[0046] The torque acquisition unit 14C acquires the output torque of the internal combustion engine 5A. For example, the torque acquisition unit 14C preferably estimates the output torque of the internal combustion engine 5A based on the intake air amount and the negative pressure in the intake manifold. In addition, when the drive source 5 is an electric motor, it is preferable to estimate the output torque of the electric motor based on the phase current supplied to the electric motor. Note that in another embodiment, a torque sensor for detecting the output torque may be provided on the internal combustion engine 5A or the electric motor. In addition, the torque acquisition unit 14C estimates the braking torque applied to the wheel body W based on the control amount of the control unit 14B for the braking device 8.

[0047] The control device 14 is connected to the navigation device 15. The navigation device 15 determines the position of the vehicle 1 based on GNSS (Global Navigation Satellite System) signals. The navigation device 15 has map information. The map information preferably includes information related to the characteristics of the road surface such as the shape, inclination (bank angle), and curvature of each road.

[0048] Hereinafter, a method for determining the tire slip state by the estimation unit 14A will be described. The estimation unit 14A determines the tire slip state by executing a program configured based on the theory shown below.

[0049] Since the wheel body W is made of a metal such as aluminum or steel, the stiffness of the wheel body W is sufficiently high compared to the tire T made of rubber. When a driving torque is applied to the wheel body W, the sidewall portion and the tread portion of the tire T undergo elastic deformation. Therefore, here it is assumed that the wheel body W and the tread of the tire T are represented by a rigid body mass, and a spring force acts in a direction to suppress the torsion between the wheel body W and the tread of the tire T. At the contact portion between the tire T and the road surface, the tire T is deformed due to the mass of the vehicle 1, so that the tire T contacts the road surface (ground contact surface) with a certain constant width (ground contact width). At the ground contact surface, a frictional force F acts between the tire and the road surface, and this frictional force F is expressed by the following formula.

[0050] F = μN (1)

[0051] Here, μ is the road surface friction coefficient, that is, the friction coefficient between the tire T and the road surface; N is the wheel load, that is, the ground contact load of the tire T. The change in the road surface friction coefficient μ depends on the air pressure and aging degree of the tire T, the road surface, the weather, the climate, etc. The magnitude of the frictional force F needs to match the magnitude of the driving force, which is the force that causes the vehicle 1 to travel (accelerate, decelerate, or travel at a constant speed) against the driving resistance.

[0052] At the moment when the driving torque is applied to the wheel body W, the torque has not yet been transmitted to the tire T, and the tire T has not yet started to roll. At this time, the tire T undergoes elastic deformation, and a torsional angle is generated between the wheel body W and the tire T. In this state, the tire T is in a static torsional state, in which a torsional angle proportional to the driving torque of the wheel body W is generated. When the torsional angle is generated, the torque is transmitted to the tire T as its reaction force, and the tire T starts to roll. As the tire T rolls, one element of the tire T that has undergone elastic deformation leaves the ground contact surface, and the elastic strain is released. At this time, the reaction force for transmitting the driving torque of the wheel body W becomes insufficient, and the amount of this insufficiency is the magnitude corresponding to the released elastic strain. Therefore, the rolling of the tire T will temporarily stop. However, instead of an element of the tire T leaving the ground contact surface, a new element of the tire T comes into contact with the road surface and generates elastic strain, thereby restoring the lost reaction force, and the tire T rolls again. The boundary conditions for individual elements are not unique for each element and move as the element moves. Such a situation is specifically referred to as a moving boundary. When the actual tire T continues to roll, the above phenomena occur successively. Therefore, the rolling angle of the tire T decreases at a constant rate with respect to the rotation angle of the wheel body W. Since the rotation angle of the wheel body W per unit time is proportional to the rotational speed (angular velocity of rotation), the rolling angle of the tire T per unit time also relatively decreases proportionally to the rotational speed of the wheel body W, and a constant rotational transmission loss occurs. This phenomenon is called elastic slip because an apparent slip occurs between the wheel body W and the road surface due to elastic deformation. Since the amount of elastic slip is generated at a constant rate with respect to the rotational speed of the wheel body W, the rotational speed loss Δω due to slip and the rotational speed ω 轮 of the wheel body W r The ratio S

[0053] Sr = Δω / ω 轮 (2)

[0054] The elastic slip characteristics of the tire T are as Figure 2 shown. Because there is a limit to the frictional force between the tire T and the road surface, as the driving torque of the wheel body W increases, the ground contact surface between the tire T and the road surface starts to slip. This is called sliding slip to distinguish it from elastic slip. Therefore, as the driving torque of the wheel body W increases, the elastic slip state changes to the sliding slip state. The boundary between the elastic slip state and the sliding slip state is called the elastic slip limit or adhesion limit, and the driving force (torque) corresponding to the adhesion limit is called the adhesion limit driving force (torque).

[0055] In the elastic slip state, when a torsional angle φE appears between the wheel body W and the tire T due to elastic deformation and the ground contact surface moves by the length of the ground contact surface, the strain energy generated due to elastic deformation Stored in the ground contact surface before rolling and the strain energy is released due to rolling. This strain energy has no effect on the driving of the vehicle 1. Therefore, in this state, it can be considered that the driving energy from the wheel body W is dissipated through the cycle of strain accumulation and release. When understanding that this energy dissipation occurs due to apparent slip (elastic slip), the following formula can be obtained using the frictional force F acting on the ground contact surface.

[0056]

[0057] That is, the energy dissipation can be replaced by the virtual work calculated from the frictional force and the apparent slip, as shown in Formula 3, where k T is the torsional stiffness of the tire T [Nm / rad], R is the driving radius of the tire T [m], and T f is the frictional torque [Nm] generated at the ground contact surface. If when the tire T rolls according to the torsional angle and the rotation angle of the wheel body W including the torsional angle is then based on the geometric relationship, the slip speed ratio S r is represented by the following Formula 4.

[0058]

[0059] According to Formula 2 and Formula 4, is represented by the following Formula 5.

[0060]

[0061] By substituting it into Formula 3, the following Formula 6 can be obtained.

[0062]

[0063] As expressed in Formula 6, the frictional torque T f is represented by the viscous resistance, which is proportional to the slip (rotation speed loss) Δω occurring between the wheel body W and the road surface. Here, c T is the friction damping coefficient between the tire and the road surface [Nm / (rad / s)], corresponding to the viscosity coefficient, and is proportional to the tire torsional stiffness k T proportional.

[0064] Here, as the driving radius R of the tire T used in Equation 3, the effective rolling radius ERR in the region where the relationship between the dynamic load radius DLR and the effective rolling radius ERR is linear is used. In the region where the relationship between the dynamic load radius DLR and the effective rolling radius ERR is linear, the correlation coefficient between the dynamic load radius DLR and the effective rolling radius ERR is 0.99 or higher. Alternatively, as the driving radius R of the tire T used in Equation 3, the effective rolling radius ERR when the vertical load applied to the tire T is 1G can be used.

[0065] As Figures 3A to 3D shown, the radius of the tire T generally includes the unloaded radius OD, the static load radius SLR, the dynamic load radius DLR, and the effective rolling radius ERR. As Figure 3A shown, the unloaded radius OD is the distance from the central axis of the wheel to the outer peripheral surface of the tire in a state where the wheel is not in contact with the road surface, the wheel is not rotating, and no load is applied to the central axis of the wheel. As Figure 3B shown, the static load radius SLR is the distance from the central axis of the wheel to the road surface in a state where the wheel is in contact with the road surface, the wheel is not rotating, and a load is applied to the central axis of the wheel. As Figure 3C shown, the dynamic load radius DLR is the distance from the central axis of the wheel to the road surface in a state where the wheel is in contact with the road surface, the wheel is rotating, and a load is applied to the central axis of the wheel. As Figure 3D shown, the effective rolling radius ERR is a value obtained by dividing the distance traveled by the tire in one rotation by 2π in a state where the wheel is in contact with the road surface, the wheel is rotating, and a load is applied to the central axis of the wheel.

[0066] It is possible to represent the dynamic model from the drive source 5 to the contact surface as Figure 4 shown. Based on this model, the state equation is represented by Equation 7 below. Equation 7 is obtained for one of the left and right front wheels of the vehicle 1, which constitutes an FF vehicle in which an internal combustion engine is mounted in its front part to drive the front wheels via a transmission.

[0067]

[0068] Here, θ DN is the rotational angle disturbance [rad] of the ring gear of the differential device DN (output shaft of the drive source 5), θ W is the rotational angle disturbance [rad] of the wheel body, θ T is the rotational angle disturbance [rad] of the tire, I w is the moment of inertia [kgm 2 of the wheel body, I T is the moment of inertia [kgm 2 of the tire, and k Dis the torsional stiffness [Nm / rad] of the power transmission member 6 (drive shaft).

[0069] By making Equation 7 dimensionless using the following Equation 8, the state variable (vector) represented by Equation 9 can be represented by Equation 10.

[0070]

[0071]

[0072]

[0073] The frequency response of the rotational fluctuation of the wheel body W obtained from Equation 10 to the rotational fluctuation of the differential device DN can be as Figure 5A shown. Figure 5A Shown are the amplification ratio (amplitude ratio m) of the rotational fluctuation amplitude of the wheel body W to the rotational fluctuation amplitude of the differential device DN and the phase delay (phase delay Ψ1) of the rotational fluctuation of the wheel body W with respect to the rotational fluctuation of the differential device DN, with respect to frequency.

[0074] According to Equation 6, as the friction damping coefficient c T value decreases, the slip state approaches the slip-sliding state. In Figure 5A , (a) represents the response in the elastic slip state, and (c) represents the response in the slip-sliding state. Additionally, (b) represents the boundary (adhesion limit) between the two slip states. When Figure 5A the graphs (a) and (c) representing the amplitude ratio in are compared with each other, it can be seen that when entering the slip-sliding state, a new peak appears on the low-frequency side, and the peak on the high-frequency side moves towards the higher-frequency side. The vibration mode corresponding to the peak on the high-frequency side will be referred to as the elastic slip mode, and the vibration mode corresponding to the peak on the low-frequency side will be referred to as the slip-sliding mode.

[0075] Figure 5B shows the existence ranges of the elastic slip mode and the slip-sliding mode with respect to frequency and the friction damping coefficient c T . In Figure 5B , the existence ranges of the elastic slip mode and the slip-sliding mode are represented by solid lines.

[0076] In the elastic slip mode, since the driving force is transmitted to the road surface due to the elastic deformation of the tire T, the elastic force generated by the tire torsional stiffness k T acts as a reaction force on the wheel body W. Therefore, the wheel body W receives the combination of the elastic forces generated by the drive shaft stiffness k D and the tire torsional stiffness k T , causing the wheel body W to vibrate. In Figure 5A and Figure 5BThe elastic slip mode can be seen on the high-frequency side. As Figure 5B shown, as the friction damping coefficient c T decreases, the elastic slip mode shifts to the higher-frequency side, that is, the slip state approaches the sliding slip state from the elastic slip state. This corresponds to Figure 5A the phenomenon in the graph showing the amplitude ratio (i.e., when the state transitions to the sliding slip state, the peak on the high-frequency side moves toward the higher-frequency side).

[0077] In the sliding slip mode, due to the dynamic slip between the tire T and the road surface, the elastic force generated by the tire torsional stiffness k T is released due to the slip, and the reaction force acting on the wheel body W also disappears. Therefore, the wheel body W and the tire T become integrated and only receive the elastic force generated by the drive shaft stiffness k D and thus vibrate in phase. The sliding slip mode can be seen on the low-frequency side in Figure 5A and Figure 5B . As Figure 5B shown, when the friction damping coefficient c T is less than a constant (i.e., when the slip state becomes the sliding slip state), the sliding slip mode appears and does not appear in the elastic slip state. This corresponds to Figure 5A the phenomenon in the graph showing the amplitude ratio (i.e., when the slip state changes to the sliding slip state, a new peak appears on the low-frequency side).

[0078] As described above, when the slip state transitions from the elastic slip state to the sliding slip state, the sliding slip mode appears. Therefore, the adhesion limit can be determined by monitoring the appearance of the sliding slip mode. However, as seen from the amplitude ratio in Figure 5A , the peak on the low-frequency side cannot be confirmed at the adhesion limit. That is, the appearance of the sliding slip mode cannot be strictly determined only by simply observing the vibration waveform. Therefore, attention is focused on the dimensionless quantity ζ 2 representing the damping state of the system. As shown in Equation 8, the dimensionless quantity ζ 2 is a dimensionless quantity composed of the friction damping coefficient c T and the tire torsional stiffness k T and uniquely represents the damping state of the system without being affected by various factor changes. If the current dimensionless quantity ζ 2 can be estimated, then by comparing it with the threshold corresponding to the adhesion limit, the occurrence of the sliding slip can be strictly determined. In addition, since the deviation between the dimensionless quantity ζ 2 and the aforementioned threshold can be used as the basis for determining the margin before the occurrence of the sliding slip, it is useful to know the dimensionless quantity ζ 2 . In the following, first, the method for obtaining the dimensionless quantity ζ 2 will be described.

[0079] Torque fluctuations often occur in the internal combustion engine serving as the drive source 5 of the vehicle 1, and such torque fluctuations are also transmitted from the differential device DN to the tires. As a cause of the torque fluctuations, in the case of an internal combustion engine, there are fluctuations in the in-cylinder pressure, while in the case of an electric motor, there is cogging torque attributable to the number of poles. In the differential device DN, rotational fluctuations attributable to the input torque fluctuations occur simultaneously. Here, the rotational fluctuations of the differential device DN are expressed by the following formula 11.

[0080]

[0081] Formula 11 can be regarded as a forced excitation under boundary conditions. A 1 is the amplitude of the rotational fluctuations of the differential device DN [m], Ω is the angular frequency [rad / s] of the excitation force (torque fluctuations of the internal combustion engine E), and t is the time [s]. In this state of forced excitation, the state equation represented by formula 10 becomes the following equation.

[0082]

[0083] In formula 12, B represents the external force (excitation input), and the natural vibration mode (hereinafter referred to as the natural mode) possessed by the original system is determined by the Jacobian matrix A. The parameters that determine the Jacobian matrix A are ρ, ω 1 、ω 2 and ζ 2 , where ρ and ω 1 are design specifications (known values). Therefore, once the dimensionless quantity ω 2 corresponding to the slip identification quantity and the dimensionless quantity ζ 2 are known, the natural mode can be known. In formula 7, there are two leading equations and two unknown dimensionless quantities (i.e., ω 2 and ζ 2 ), so it should be possible to uniquely determine ω 2 、ζ 2 . Note that since the dimensionless quantity ω 2 is obtained based on the tire torsional stiffness k T , and the dimensionless quantity ζ 2 is obtained based on the friction damping coefficient c T and the tire torsional stiffness k T , it is possible to determine the dimensionless quantities ω 2 、ζ 2 , which is equivalent to being able to determine the friction damping coefficient c T and the tire torsional stiffness k T .

[0084] Assume that the periodic solution of formula 12 is expressed as follows.

[0085]

[0086] By substituting the periodic solution of Equation (13) into Equation (12) and determining the coefficients based on the Galerkin method, the following relational expressions are obtained.

[0087]

[0088] Here, m is the amplification ratio (amplitude ratio) of the rotational fluctuation amplitude of the wheel body to the rotational fluctuation amplitude of the differential device DN, and Ψ1 is the phase delay of the rotational fluctuation of the wheel body relative to the rotational fluctuation of the differential device DN. Therefore, by measuring the rotational fluctuations of the differential device DN and the wheel body, the dimensionless quantity ω can be obtained according to Equation (14). 2 and ζ 2 .

[0089] Next, if the current dimensionless quantities ω 2 and ζ 2 have been obtained according to Equation (14), then a method for describing the relationship between the obtained dimensionless quantity ζ 2 and the natural mode will be described. The dimensionless quantity ω 2 reflects the change in the tire torsional stiffness k T . However, since there is no significant change under the same conditions, the relationship between the dimensionless quantity ζ T and the natural mode will be described assuming that the tire torsional stiffness k 2 is a constant. Therefore, the dimensionless quantity ζ 2 uniquely corresponds to the friction damping coefficient c T . The behavior of the natural mode can be described by obtaining the eigenvalues λ of the Jacobian matrix A. Figure 6 Shows the behavior (root locus) of the eigenvalues λ corresponding to the above-mentioned slip-sliding mode. Figure 6 (a) to (b) of Figure 5A corresponds to (a) to (c) of T . Note that if the tire torsional stiffness k Figure 6 changes, the frequency of the vibration mode also changes. Therefore, the scale of the root locus of 2 also changes, but the main characteristics described below do not change. Additionally, in this case, the dimensionless quantity ω T in the current situation is already known (therefore the tire torsional stiffness k

[0090] In Figure 6 , the horizontal axis represents the real axis, the vertical axis represents the imaginary axis, and the imaginary part represents the vibration solution. In the elastic slip state (see Figure 6(a)), there is a pair of roots on the real axis, which means there is no oscillatory solution. That is, no vibration corresponding to the stick-slip mode is generated. On the other hand, when the slip state becomes the stick-slip state (see Figure 6 (c)), the roots have an imaginary part, which means that vibration is generated. That is, it can be understood that when the dimensionless quantity ζ 2 becomes less than ζ C (see Figure 6 (c)), the stick-slip mode appears. Therefore, based on the value of the dimensionless quantity ζ C , the slip state can be determined as follows:

[0091] When the dimensionless quantity ζ 2 > ζ C , the slip state is the elastic slip state;

[0092] When the dimensionless quantity ζ 2 = ζ C , the slip state is the adhesion limit; and

[0093] When the dimensionless quantity ζ 2 < ζ C , the slip state is the stick-slip state,

[0094] where ζ C is a value that varies according to the design specifications. In Figure 6 , the numerical values of ζ 2 and the friction damping coefficient c T are exemplarily shown in the case where ζ C is 0.86. Once the dimensionless quantity ζ C is known, the friction damping coefficient c Tc when the slip state becomes the elastic slip limit can be obtained according to Equation 8.

[0095] Subsequently, the importance of calculating the amplitude ratio m and the phase delay Ψ 1 by using the effective rolling radius ERR as the tire driving radius R in the region where the relationship between the dynamic load radius DLR and the effective rolling radius ERR is linear will be described. The dynamic load radius DLR tends to be affected by the vertical load and the tire air pressure. Therefore, the driving radius R of the tire T affects the frictional torque T f occurring on the ground contact surface, and also affects the friction damping coefficient c T and the tire torsional stiffness k T .

[0096] In the following, the results of measuring the dynamic load radius (DLR) and the effective rolling radius (ERR) using a flat belt type tire tester are shown. The flat belt type tire tester includes a rotatable annular flat belt and a wheel support portion that supports the central axis of the wheel and supports the wheel on the flat belt. The wheel support portion can apply an arbitrary vertical load to the wheel. In the test, the DLR and the ERR are measured while changing the vertical load, the air pressure of the tire T (tire air pressure), and the vehicle speed. The vertical load is changed from 500 N to 6500 N at intervals of 500 N. The vehicle speed is changed from 20 kph to 80 kph. The tire air pressures are 200 kPa, 240 kPa, and 280 kPa. The DLR is obtained by measuring the distance between the central axis of the wheel and the upper surface of the flat belt. The ERR is obtained by obtaining the traveling distance per rotation of the wheel based on the vehicle speed and the wheel rotation speed and dividing the traveling distance per rotation of the wheel by 2π.

[0097] Figure 7 is a graph in which the X-axis represents the vertical load Fz [N] and the Y-axis represents the dynamic load radius DLR [m]. Figure 8 is a graph in which the X-axis represents the vertical load Fz [N] and the Y-axis represents the effective rolling radius ERR [m]. In Figure 7 and Figure 8 the vehicle speed is 80 kph in both cases, and the air pressures of the tire T are 200 kPa, 240 kPa, and 280 kPa. From Figure 7 it can be seen that as the vertical load Fz increases, the DLR decreases. It can also be seen that as the tire air pressure decreases, the DLR decreases. Similarly, from Figure 8 it can be seen that as the vertical load Fz increases, the ERR decreases. It can also be seen that as the tire air pressure decreases, the ERR decreases. From Figure 7 and Figure 8 it can be seen that even when the vertical load Fz, the vehicle speed, and the tire air pressure are the same, the ERR and the DLR have different values. Moreover, it can be seen that the rate of change of the ERR with respect to the vertical load is smaller than the rate of change of the DLR with respect to the vertical load. Therefore, it can be seen that the ERR is less affected by the vertical load and the tire air pressure than the DLR.

[0098] Figure 9 is a graph in which the X-axis represents the vehicle speed [km / h], the Y-axis represents the tire radius [m], and the tire air pressure is 200 kPa. Figure 10 is a graph in which the X-axis represents the vehicle speed [km / h], the Y-axis represents the tire radius [m], and the tire air pressure is 240 kPa. Figure 11It is a curve graph where the X-axis represents the vehicle speed [km / h], the Y-axis represents the tire radius [m], and the tire pressure is 280 kPa. From Figures 9 to 11 it can be seen that as the vehicle speed increases, the effective rolling radius ERR and the dynamic load radius DLR increase. It can also be seen that when the vertical load, tire pressure, and vehicle speed are the same, the effective rolling radius ERR is greater than the dynamic load radius DLR. When the tire pressure and vehicle speed are constant, if the vertical load changes from 500 N to 6500 N, the effective rolling radius ERR decreases by approximately 2%. On the other hand, when the tire pressure and vehicle speed are constant, if the vertical load changes from 500 N to 6500 N, the dynamic load radius DLR decreases by approximately 8% to 17%.

[0099] Figure 12 It is a curve graph where the X-axis represents the tire pressure [Pa] and the Y-axis represents the tire radius when the vertical load is 500 N, and this tire radius is normalized by the tire radius when the vertical load is 6500 N (i.e., the ratio of the tire radius when the vertical load is 500 N to the tire radius when the vertical load is 6500 N). Specifically, Figure 12 it shows that when the vehicle speed is 20 km / h and when the vehicle speed is 80 km / h, the effective rolling radius ERR and the dynamic load radius DLR when the vertical load is 500 N are normalized by the corresponding radii when the vertical load is 6500 N. As Figure 12 shown, when the tire pressure changes from 200 kPa to 280 kPa, the change amount of the normalized effective rolling radius ERR is less than the change amount of the normalized dynamic load radius DLR. The change rate of the effective rolling radius ERR is less than or equal to 1%. From the above, it can be known that the effective rolling radius ERR is less affected by the tire pressure than the dynamic load radius DLR.

[0100] Figure 13 It is a curve graph where the X-axis represents the vehicle speed [km / h], the Y-axis represents DLR / ERR, and the tire pressure is 200 kPa. Figure 14 It is a curve graph where the X-axis represents the vehicle speed [km / h], the Y-axis represents DLR / ERR, and the tire pressure is 240 kPa. Figure 15 It is a curve graph where the X-axis represents the vehicle speed [km / h], the Y-axis represents DLR / ERR, and the tire pressure is 280 kPa. DLR / ERR is the ratio of the dynamic load radius DLR to the effective rolling radius ERR. From Figures 13 to 15 it can be seen that the greater the vertical load, the greater the difference between the effective rolling radius ERR and the dynamic load radius DLR.

[0101] From Figures 7 to 15It can be seen that the effective rolling radius ERR is less affected by the vertical load, tire pressure, and vehicle speed compared to the dynamic load radius DLR. When the vertical load varies from 500 N to 6500 N while the tire pressure and vehicle speed are constant, the effective rolling radius ERR decreases by approximately 2%. On the other hand, when the vertical load varies from 500 N to 6500 N while the tire pressure and vehicle speed are constant, the dynamic load radius DLR decreases by approximately 8% to 17%. In the elastic slip region, since the slip ratio is approximately 10%, it is difficult to detect the elastic slip region if the detection error of the slip ratio becomes 10% or higher. Since the change rate of the effective rolling radius ERR under the tire usage conditions is 2%, the effective rolling radius ERR can be used to detect the tire slip ratio in the elastic slip region. The effective rolling radius ERR can improve the detection accuracy of the tire slip ratio compared to the dynamic load radius DLR.

[0102] Figure 16 is an explanatory diagram showing the shape change of the tire corresponding to the change in the vertical load. As Figure 16 shown, when the vertical load increases, the tire T presses against the road surface, and the tire contracts in the vertical direction and expands in the horizontal direction. As a result, the ground contact surface length GPL, which is the length of the ground contact surface between the tire T and the road surface, becomes longer. In addition, the ground contact angle GPA is defined as the angle formed between a first line segment passing through the front end of the ground contact surface and the central axis of the wheel in the front-rear direction (wheel rotation direction) and a second line segment passing through the rear end of the ground contact surface and the central axis of the wheel. The length of each of the first line segment and the second line segment corresponds to the effective rolling radius ERR. The ground contact angle GPA increases as the vertical load increases. Here, the ground contact surface length GPL and the ground contact angle GPA are expressed as follows using the effective rolling radius ERR and the dynamic load radius DLR.

[0103] GPL = 2 * (ERR 2 − DLR 2 ) 1 / 2

[0104] GPA = 2 * cos -1 (DLR / ERR)

[0105] Figure 17 is a graph showing the relationship between the effective rolling radius ERR and the dynamic load radius DLR. In Figure 17 it, the vehicle speed is 20 km / h or 80 km / h, the tire pressure is 200 kPa, 240 kPa, or 280 kPa, and the vertical load is 500 N to 6500 N. From Figure 17It can be seen that the effective rolling radius ERR and the dynamic load radius DLR have a low correlation. In addition, the change amount of the effective rolling radius ERR is less than that of the dynamic load radius DLR.

[0106] Figure 18 is a curve graph showing the relationship between the dynamic load radius DLR and the ground contact surface length GPL. In Figure 18 , the vehicle speed is 20 km / h or 80 km / h, the tire pressure is 200 kPa, 240 kPa or 280 kPa, and the vertical load is from 500 N to 6500 N. From Figure 18 it can be seen that the dynamic load radius DLR and the ground contact surface length GPL have a first-order correlation. The correlation coefficient between the dynamic load radius DLR and the ground contact surface length GPL is 0.99 or higher.

[0107] Figure 19 is a curve graph showing the relationship between the dynamic load radius DLR and the ground contact surface length GPL. In Figure 19 , the vehicle speed is 20 km / h or 80 km / h, the tire pressure is 200 kPa, 240 kPa or 280 kPa, and the vertical load is from 4000 N to 6500 N. By extracting the part with a vertical load from 4000 N to 6500 N from the curve graph of Figure 18 to obtain Figure 19 . From Figure 19 it can be seen that the dynamic load radius DLR and the ground contact surface length GPL have a first-order correlation. The correlation coefficient between the dynamic load radius DLR and the ground contact surface length GPL is 0.998 or higher. When the vertical load is from 4000 N to 6500 N, the correlation coefficient between the dynamic load radius DLR and the ground contact surface length GPL is higher than that when the vertical load is from 500 N to 6500 N.

[0108] Figure 20 is a curve graph showing the relationship between the effective rolling radius ERR and the ground contact surface length GPL. In Figure 20 , the vehicle speed is 20 km / h or 80 km / h, the tire pressure is 200 kPa, 240 kPa or 280 kPa, and the vertical load is from 4000 N to 6500 N. From Figure 20 it can be seen that the effective rolling radius ERR and the ground contact surface length GPL have a first-order correlation. As shown in Figure 19 and Figure 20 , the change amount of the effective rolling radius ERR with respect to the ground contact surface length GPL is less than that of the dynamic load radius DLR with respect to the ground contact surface length GPL.

[0109] Figure 21 is a graph showing the relationship between the ground contact surface length GPL and the ground contact angle GPA. From Figure 21 it can be seen that the ground contact surface length GPL and the ground contact angle GPA have a first-order correlation. Figure 22 is a graph showing the relationship between the ground contact angle GPA and the effective rolling radius ERR. From Figure 22 it can be seen that the effective rolling radius ERR decreases as the ground contact angle GPA increases, and in the region where the ground contact angle GPA is about 30 degrees or more, the ground contact angle GPA and the effective rolling radius ERR have a first-order correlation.

[0110] As Figure 7 and Figure 8 shown, the ratio of the change in the effective rolling radius ERR to the change in the vertical load is smaller than the ratio of the change in the dynamic load radius DLR to the change in the vertical load. Therefore, by using the effective rolling radius ERR instead of the dynamic load radius DLR when calculating the amplitude ratio and phase delay, the calculation is less affected by the vertical load, tire pressure, and vehicle speed. When the vertical load increases, the ratio of the change in the effective rolling radius ERR to the change in the vertical load becomes smaller. Therefore, it is preferable to use the effective rolling radius ERR in the range of 2500 N to 6500 N for the vertical load, more preferably in the range of 3500 N to 6500 N for the vertical load, and further preferably in the range of 4000 N to 6500 N for the vertical load. In the case of a normal passenger car, the weight of the vehicle is about 1428 kg. In this case, the load applied to each front wheel as a driving wheel in a 1G state is about 4000 N. Therefore, the tire driving radius is preferably the effective rolling radius ERR in a 1G state.

[0111] According to Figure 17 , when the range of the vertical load is from 500 N to 6500 N, the first-order correlation coefficient between the effective rolling radius ERR and the dynamic load radius DLR is about 0.82. On the other hand, when the range of the vertical load is from 2500 N to 6500 N, the first-order correlation coefficient between the effective rolling radius ERR and the dynamic load radius DLR is about 0.96. It can also be seen that in the region where the first-order correlation coefficient between the effective rolling radius ERR and the dynamic load radius DLR is high, even if the dynamic load radius DLR changes greatly, the effective rolling radius ERR changes slightly.

[0112] Figure 23 is a graph with the X-axis representing the vertical load, the first Y-axis representing the dynamic load radius DLR, and the second Y-axis representing the ratio. Figure 23 The curve 231 of Figure 23The curve 232 represents the dynamic load radius DLR at a tire pressure of 200 kPa and a vehicle speed of 20 km / h. Figure 23 The curve 233 in represents the dynamic load radius DLR when the tire pressure is 280 kPa and the vehicle speed is 80 km / h, which is normalized by the dynamic load radius DLR at a vertical load of 6000 N (or the ratio of the dynamic load radius DLR represented by curve 231 to the dynamic load radius DLR at a vertical load of 6000 N). Figure 23 The curve 234 in represents the ratio of curve 231 to curve 232. Figure 23 The curve 235 in represents the value obtained by multiplying curve 233 by curve 234 for each vertical load.

[0113] Figure 24 It is a graph where the X-axis represents the vertical load, the first Y-axis represents the effective rolling radius ERR, and the second Y-axis represents the ratio. Figure 24 The curve 241 in represents the effective rolling radius ERR when the tire pressure is 280 kPa and the vehicle speed is 80 km / h. Figure 24 The curve 242 in represents the effective rolling radius ERR when the tire pressure is 200 kPa and the vehicle speed is 20 km / h. Figure 24 The curve 243 in represents the effective rolling radius ERR when the tire pressure is 280 kPa and the vehicle speed is 80 km / h, which is normalized by the effective rolling radius ERR at a vertical load of 6000 N (or the ratio of the effective rolling radius ERR represented by curve 241 to the effective rolling radius ERR at a vertical load of 6000 N). Figure 24 The curve 244 in represents the ratio of curve 241 to curve 242. Figure 24 The curve 245 in represents the value obtained by multiplying curve 243 by curve 244 for each vertical load.

[0114] From Figure 23 and Figure 24It can be seen that compared with the dynamic load radius (DLR), the effective rolling radius (ERR) is less affected by the vertical load, tire pressure, and speed. The greater the vertical load, the less the ERR is affected by the vertical load, tire pressure, and speed. In the 1G state of an ordinary vehicle with a weight of 1428 kg, the change rate of the DLR is approximately 5.3% (the vertical load applied to each front wheel as a driving wheel is 4000 N). On the other hand, in the 1G state of an ordinary vehicle with a weight of 1428 kg, the change rate of the ERR is approximately 0.6% (the vertical load applied to each front wheel as a driving wheel is 4000 N). Therefore, by using the ERR as the tire radius in the 1G state, the detection accuracy of the tire slip ratio can be improved.

[0115] A method for obtaining the tire driving radius during vehicle travel will be described below. Figure 25 It is a flowchart for obtaining the tire driving radius during vehicle travel. Figure 25 The program shown is executed by the control device 14. The control device 14 first sets a measurement section (S1). The measurement section includes the start and end points of the measurement section, the section distance measured along the road from the start point to the end point, and information related to the characteristics of the section. Preferably, the control device 14 obtains information related to the measurement section from the map information in the navigation device 15. Additionally, the control device 14 can obtain the section distance based on the signal from the distance sensor 12L. The characteristics of the section include the inclination angle of the road surface. Preferably, the control device 14 obtains the characteristics of the section based on the signal from the inclination sensor 12M and the map information in the navigation device 15.

[0116] Subsequently, the control device 14 obtains the rotation numbers of each wheel 3 from reaching the start point to reaching the end point (S2).

[0117] Subsequently, the control device 14 calculates the rotation number difference between the left and right wheels 3, i.e., the left - right rotation number difference, based on the rotation numbers of each wheel 3 obtained in step S2, and determines whether the left - right rotation number difference is less than or equal to a first determination value (S3). The left - right rotation number difference can be the rotation number difference between the left and right front wheels, or can be the rotation number difference between the left and right rear wheels. When the left - right rotation number difference is not less than or equal to the first determination value, the control flow returns to step S1. When the left - right rotation number difference is less than or equal to the first determination value, the control flow proceeds to step S4.

[0118] In step S4, the control device 14 calculates the front-rear rotation number difference, which is the rotation number difference between the drive wheels and the non-drive wheels, based on the rotation speed of each wheel 3 obtained in step S2, and determines whether the front-rear rotation number difference is less than or equal to a second determination value. The drive wheels can be the front wheels or the rear wheels. The rotation number of the front wheels can be the rotation number of one of the left front wheel and the right front wheel, or can be the average of the rotation numbers of the left front wheel and the right front wheel. The rotation number of the rear wheels can be the rotation number of one of the left rear wheel and the right rear wheel, or can be the average of the rotation numbers of the left rear wheel and the right rear wheel. When the front-rear rotation number difference is not less than or equal to the second determination value, the control flow returns to step S1. When the front-rear rotation number difference is less than or equal to the second determination value, the control flow proceeds to step S5.

[0119] In step S5, the tire drive radius is obtained based on the cross-sectional distance and the rotation number of each wheel. The tire drive radius is the effective rolling radius ERR and is calculated by dividing the cross-sectional distance by 2π and the rotation number of the wheel.

[0120] The specific embodiments of the present invention have been described above, but the present invention is not limited to the above embodiments and can be modified or changed in various ways. For example, the present invention is not limited to four-wheel vehicles, but can be applied to two-wheel vehicles.

Claims

1. A method for determining a tire slip state, which is used to determine the slip state of a tire of a wheel relative to a road surface, wherein the wheel is connected to a drive source via a power transmission member, and the method for determining the tire slip state comprises the following steps: detecting a rotational fluctuation of the power transmission member and a rotational fluctuation of a wheel body of the wheel; determining whether the vibration mode of the wheel body and the tire is an elastic slip mode in which the vibration mode of the wheel body and the tire represents a frequency response in an elastic slip state, or a sliding slip mode in which the vibration mode of the wheel body and the tire represents a frequency response in a sliding slip state, based on an amplitude ratio of an amplitude of the rotational fluctuation of the wheel body to an amplitude of the rotational fluctuation of the power transmission member and a phase delay of the rotational fluctuation of the wheel body relative to the rotational fluctuation of the power transmission member; and when the vibration mode of the wheel body and the tire is the sliding slip mode, determining that the tire is in the sliding slip state, wherein the amplitude ratio and the phase delay are calculated by using the effective rolling radius in a region where the relationship between the dynamic load radius and the effective rolling radius is linear as the tire drive radius, the dynamic load radius is the distance between the central axis of the wheel and the road surface, and the effective rolling radius is a value obtained by dividing the distance traveled by the tire in one rotation by 2π.

2. The method for determining a tire slip state according to claim 1, wherein in a region where the relationship between the dynamic load radius and the effective rolling radius is linear, a correlation coefficient between the dynamic load radius and the effective rolling radius is 0.99 or higher.

3. The method for determining a tire slip state according to claim 1, wherein the tire drive radius is the effective rolling radius in a 1G state.

4. The method for determining a tire slip state according to claim 1, wherein the tire drive radius is the effective rolling radius when a vertical load applied to the wheel is in a range of 2000 N to 6500 N.

5. The method for determining a tire slip state according to any one of claims 1 to 4, wherein the effective rolling radius is calculated by dividing a driving distance of a vehicle detected based on a GNSS signal within a predetermined period by a number of rotations of the tire within the predetermined period.

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