Method, system, and program for calculating tire wear performance value

The method addresses the issue of load fluctuations in tire wear evaluation by correcting friction energy based on load corrections, resulting in more accurate tire wear performance calculations.

JP7783033B2Active Publication Date: 2025-12-09TOYO TIRE CORP
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Patent Information

Application Number
JP2021196647
Authority / Receiving Office
JP · JP
Patent Type
Patents
Current Assignee / Owner
Filing Date
2021-12-03
Publication Date
2025-12-09
Estimated Expiration
2041-12-03

AI Technical Summary

Technical Problem

Existing methods for evaluating tire wear performance do not adequately account for fluctuations in load acting on tires, which affect frictional energy calculations.

Method used

A method that calculates tire wear performance by acquiring and classifying vehicle acceleration data in multiple directions, setting driving modes, calculating frequency, and correcting friction energy based on load fluctuations using load correction amounts to convert it into a more accurate tire wear value.

Benefits of technology

Improves the accuracy of tire wear evaluation by accounting for load fluctuations, enhancing the precision of tire wear performance assessment.

✦ Generated by Eureka AI based on patent content.

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Abstract

To provide a method for calculating a tire wear performance value in consideration of variation of loads acting on a tire.SOLUTION: A plurality of pieces of measurement data having acceleration in two directions of a longitudinal direction and a lateral direction of a vehicle is obtained, and a plurality of travelling modes constituted of combinations of sections in the two directions is set. The plurality of pieces of measurement data is sorted into any travelling modes of the plurality of travelling modes and frequencies of the travelling modes are calculated based on the number of the measurement data sorted into the travelling modes respectively and the number of all measurement data. For the travelling modes, first friction energy is obtained from acceleration in the longitudinal direction, acceleration in the lateral direction and loads during rest. First and second load correction amounts are calculated based on the acceleration in the longitudinal and lateral directions. The first friction energy is corrected to be converted into second friction energy on the basis of the first and second load correction amounts and the loads during rest. A tire wear performance value is calculated based on the second friction energy in the travelling modes and the frequencies of the modes.SELECTED DRAWING: Figure 2
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Description

[Technical Field]

[0001] The present disclosure relates to a method, system, and program for calculating a tire wear performance value. [Background technology]

[0002] A known method for evaluating the wear performance value of a tire is to calculate friction energy based on the front-rear and left-right acceleration of a vehicle, and then calculate the wear performance value of the tire from the friction energy (see, for example, Patent Document 1). [Prior art documents] [Patent documents]

[0003] [Patent Document 1] Japanese Patent Application Laid-Open No. 2011-149879 Summary of the Invention [Problem to be solved by the invention]

[0004] The load acting on the tires fluctuates while the vehicle is running, and the load fluctuations affect the frictional energy, so it is desirable to take the load fluctuations acting on the tires into consideration.

[0005] The present disclosure provides a method, system, and program for calculating a tire wear performance value that takes into account fluctuations in load acting on a tire. [Means for solving the problem]

[0006] The tire wear performance value calculation method of the present disclosure is a method executed by one or more processors, which acquires a plurality of measurement data having acceleration in at least two directions, i.e., the longitudinal direction and the lateral direction of the vehicle, measured by an acceleration sensor while the vehicle is traveling, sets a plurality of subdivided sections for each of the at least two directions of acceleration, sets a plurality of driving modes consisting of combinations of the sections in at least two directions, classifies each of the acquired plurality of measurement data into one of the plurality of driving modes, and for each driving mode, calculates the frequency of each driving mode based on the number of classified measurement data and the number of all measurement data. For the driving modes in which the measured data has been calculated and classified, a first friction energy is obtained from the longitudinal acceleration, the lateral acceleration, and the load at rest, and for the driving modes in which the first friction energy has been obtained, a first load correction amount based on the longitudinal acceleration and a second load correction amount based on the lateral acceleration are calculated for the driving modes in which the first friction energy has been obtained, and the first friction energy is corrected based on the first load correction amount, the second load correction amount, and the load at rest to convert the first friction energy into a second friction energy that takes into account load fluctuations in the longitudinal and lateral directions, and a tire wear performance value is calculated based on the second friction energy and the frequency for each driving mode. [Brief explanation of the drawings]

[0007] [Figure 1] FIG. 1 is a block diagram showing a system according to an embodiment of the present invention. [Figure 2] 4 is a flowchart showing a method for calculating a tire wear evaluation value. [Figure 3] FIG. 10 is an explanatory diagram of acceleration frequency distribution data. [Figure 4] FIG. 10 is an explanatory diagram relating to a modified example of acceleration frequency distribution data. DETAILED DESCRIPTION OF THE INVENTION

[0008] Hereinafter, an embodiment of the present disclosure will be described with reference to the drawings.

[0009] [system] The system 1 of this embodiment calculates frictional energy and calculates the tire wear performance value based on the calculated frictional energy.

[0010] As shown in FIG. 1, the system 1 includes a measurement data acquisition unit 10, an acceleration frequency distribution data generation unit 11, a first friction energy acquisition unit 15, a first load correction amount calculation unit 16, a second load correction amount calculation unit 17, a conversion unit 18, and a tire wear performance value calculation unit 19. The acceleration frequency distribution data generation unit 11 includes a driving mode setting unit 12, a data classification unit 13, and a frequency calculation unit 14. These units (10-19) are realized by software and hardware working together when the processor 1a executes a processing routine shown in FIG. 2 that is pre-stored in a computer equipped with a processor 1a, memory 1b, various interfaces, etc. In this embodiment, each unit is realized by the processor 1a in a single device, but this is not limited to this. For example, the units may be distributed using a network, with multiple processors executing the processing of each unit. In other words, one or more processors execute the processing. The memory 1b stores measurement data, acceleration frequency distribution data, first friction energy for each driving mode, first load correction amount for each driving mode, second load correction amount for each driving mode, second friction energy for each driving mode, tire wear performance values, etc.

[0011] The measurement data acquisition unit 10 acquires a plurality of pieces of measurement data. The measurement data includes acceleration measured by a three-axis acceleration sensor 20 provided on the vehicle 2 while the vehicle 2 is traveling. The measurement data includes acceleration in three directions of the vehicle 2, that is, acceleration Ax in the front-rear direction of the vehicle 2, acceleration Ay in the left-right direction, and acceleration Az in the up-down direction. The unit of acceleration is [m / s 2]. The measurement data includes data that can be converted into distance or is associated with data that can be converted into distance. In this embodiment, the measurement data is measured at a constant sampling time (measurement interval, for example, 0.1 seconds (10 Hz)). The speed and sampling time can be converted into distance. Therefore, the measurement data has speed as data that can be converted into distance. The measurement data is also associated with the sampling time (sampling frequency) as data that can be converted into distance (for example, if the speed is 16 m / s and the sampling time is 0.1 seconds (10 Hz), the distance per measurement data can be calculated as 16 ÷ 10 = 1.6 m). The speed can be calculated based on the position information, obtained based on the wheel rotation speed, or obtained using the ground speed meter 21.

[0012] The measurement data acquiring unit 10 may acquire the measurement data from the acceleration sensor 20 by any means as long as it can acquire the measurement data. For example, the measurement data may be stored in a storage medium of a computer installed in the vehicle, and after the vehicle has completed traveling, the storage medium may be attached to a reading device of the system 1, and the measurement data may be acquired from the reading device. Alternatively, the measurement data acquiring unit 10 may receive the measurement data via wireless communication from the computer including the acceleration sensor 20 of the vehicle.

[0013] In this embodiment, the plurality of measurement data are generated by measuring the acceleration of the acceleration sensor 20 while the vehicle 2 travels along a predetermined travel course. For example, the acceleration sensor 20 measures the acceleration as the vehicle accelerates from a stopped state at the start of the travel course, decelerates before a curve, turns the curve, accelerates again, and then repeats acceleration, deceleration, and turns until the vehicle stops at the finish line of the travel course.

[0014] In this embodiment, the measurement data includes speed measured at regular time intervals, but is not limited to this. For example, the measurement data may include location information as data that can convert location information into distance, or may be associated with location information as data that can convert location information into distance. Location information can be acquired at regular time intervals by various location information acquisition devices, including a GPS receiver that acquires satellite location information based on GPS. Furthermore, the measurement data may be measured each time the vehicle 2 travels a certain distance, rather than at regular time intervals. In this case, the measurement data itself is associated with distance. The measurement data is stored in memory 1b.

[0015] The acceleration frequency distribution data generating unit 11 generates acceleration frequency distribution data. The acceleration distribution data has a plurality of driving modes and the frequency of each driving mode. As shown schematically in FIG. 3, a plurality of sections are set by subdividing (dividing) each of the three directions of acceleration. In FIG. 3, one side of one box corresponds to one section. One driving mode can be represented by one box as shown in FIG. 3. One box (driving mode) is made up of a combination of sections (sides) in three directions. In this embodiment, each of the three directions is divided into 0.05 m / s 2 Therefore, the acceleration range (width of the side) of one driving mode (box) is 0.05 m / s 2 The width of the section is 0.05 m / s 2 Therefore, the representative value for each driving mode is +0.10 [m / s 2 ],+0.05[m / s 2 ],0[m / s 2 ],-0.05[m / s 2 ],-0.10[m / s 2]. As shown in FIG. 3, a certain driving mode M1 has a representative value of longitudinal acceleration Ax, a representative value of lateral acceleration Ay, a representative value of vertical acceleration Az, and a frequency (frequency value: 0.1). Similarly, a certain driving mode M2 ​​has a representative value of longitudinal acceleration Ax, a representative value of lateral acceleration Ay, a representative value of vertical acceleration Az, and a frequency (frequency value: 0.01). The frequency value indicates how often that driving mode appears in all the measurement data. In the example of FIG. 3, the frequency value is expressed as a decimal, so that adding up the frequency values ​​of all the driving modes results in 1.0. As shown in FIG. 3, the measured acceleration includes not only positive values ​​(+) but also negative values ​​(-). For example, the longitudinal acceleration Ax of driving mode M1 is 0 [m / s 2 ], the lateral acceleration Ay is a positive value, and the vertical acceleration Az is a positive value. In driving mode M2, the longitudinal acceleration Ax is a negative value, the lateral acceleration Ay is a negative value, and the vertical acceleration Az is a positive value. In this way, the acceleration values ​​in the three directions in each driving mode are different. Note that the longitudinal acceleration Ax is a positive value at the front of vehicle 2 and a negative value at the rear of vehicle 2. The lateral acceleration Ay is a positive value at the right side of vehicle 2 and a negative value at the left side of vehicle 2. The vertical acceleration Az is a positive value at the bottom of vehicle 2 and a negative value at the top of vehicle 2.

[0016] The acceleration frequency distribution data shown in Fig. 3 has 11 sections in the forward / backward direction, 11 sections in the left / right direction, and 6 sections in the up / down direction, and there are 11 x 11 x 6 = 726 driving modes, but the number of sections is the resolution and can be set arbitrarily. For example, the number of driving modes may be (41 x 41 x 41).

[0017] The driving mode setting unit 12 sets a plurality of subdivided sections for each of the three acceleration directions, and sets a plurality of driving modes formed by combinations of the sections in the three directions, as shown in Fig. 3. In this embodiment, the sizes of the plurality of sections are uniform, but they do not have to be uniform.

[0018] The data classification unit 13 classifies each of the multiple measurement data acquired by the measurement data acquisition unit 10 into one of the multiple driving modes set by the driving mode setting unit 12. The measurement data is classified into a driving mode in which the acceleration in each direction matches. For example, if the longitudinal acceleration Ax is 0.12 m / s 2 In this case, the typical value is 0.10 m / s 2 and the acceleration range is 0.075~0.125m / s 2 As a result, measurement data is always classified into one of the driving modes. There are cases where no measurement data is classified in a driving mode, and the number of measurement data classified also varies.

[0019] The frequency calculation unit 14 calculates the frequency of each driving mode based on the number of classified measurement data and the number of all measurement data for each driving mode. The frequency (frequency value) can be calculated by dividing the number of classified measurement data by the number of all measurement data. If there are N driving modes, the frequency calculation is performed N times. As a result, acceleration frequency distribution data is generated. In this embodiment, measurements are taken at regular intervals, so the measurement data is expressed in units of time, and the frequency calculated simply using the number of measurement data points is the frequency in units of time. Frictional energy is preferably calculated based on distance units corresponding to the number of contacts between the tire and the road surface. Therefore, in this embodiment, a process is performed to convert the data from units of time to units of distance. Specifically, the travel distance in each driving mode is calculated based on the speed and time in that driving mode, and the frequency of the travel distance in each driving mode relative to the total travel distance is calculated. Of course, if the measurement data is measured every time a certain distance is traveled, the data is already in units of distance, so the frequency may be calculated based on the number of measurement data.

[0020] The first friction energy acquisition unit 15 acquires first friction energy from the longitudinal acceleration, lateral acceleration, and stationary load for the driving mode in which the measurement data has been classified. The friction energy can be calculated by multiplying the shear force acting between the tire and the road surface by the amount of slippage. The first friction energy is friction energy generated in a state in which longitudinal acceleration and lateral acceleration occur, assuming that the stationary load is the same as the stationary load. Because the first friction energy is calculated using the stationary load, load fluctuations due to vertical acceleration are not taken into account. The first friction energy can be acquired based on computer simulations such as FEM (finite element method) or experimentally measured values, and is well known, so a detailed description will be omitted. For example, the first friction energy may be output by inputting the longitudinal acceleration, lateral acceleration, and stationary load in each driving mode into an existing friction energy simulation system. The friction energy simulation system, for example, applies a specified load (the input stationary load) to a tire model and brings it into contact with the road surface, rolls the tire model to achieve specified conditions (longitudinal acceleration and lateral acceleration), and simulates the longitudinal shear force, longitudinal slip displacement, lateral shear force, and lateral slip displacement that occur at any node on the tire tread surface. The friction energy can be calculated from the longitudinal and lateral shear forces and the amount of slip displacement. For example, the longitudinal acceleration, lateral acceleration, and stationary load in each driving mode may be input to a tire testing machine, and the first friction energy calculated based on the obtained measurement results may be output. The tire testing machine, for example, applies a specified load (the input stationary load) to a road surface and causes the tire to contact the road surface and roll under specified conditions (longitudinal acceleration and lateral acceleration). At this time, based on a pressure sensor and a motor on the road surface, measures longitudinal shear force, longitudinal slippage, lateral shear force, and lateral slippage generated at a given point on the tire tread surface. The friction energy in each direction can be calculated from the longitudinal and lateral shear force and the amount of slippage.

[0021] The first load correction amount calculation unit 16 calculates the first load correction amount based on the acceleration in the longitudinal direction for the driving mode in which the first frictional energy is acquired. Specifically, the first load correction amount is calculated using equation (1). First load correction amount = 0.5×(m·ax·h) / Wb…(1) where m is the vehicle mass [kg], ax is the longitudinal acceleration [m / s 2 ], h is the height of the vehicle's center of gravity [m], and Wb is the wheelbase [m].

[0022] The second load correction amount calculation unit 17 calculates the second load correction amount based on the lateral acceleration for the driving mode in which the first friction energy is acquired. Specifically, the second load correction amount is calculated using equation (2). Second load correction amount = (m·ay·h) / Tr…(2) where m is the vehicle mass [kg] and ay is the lateral acceleration [m / s 2 ], h indicates the height of the center of gravity of the vehicle [m], and Tr indicates the distance between the left and right wheels [m].

[0023] The conversion unit 18 corrects the first friction energy based on the first load correction amount, the second load correction amount, and the load at rest, and converts the first friction energy into second friction energy that takes into account load fluctuations in the front-rear and left-right directions, for the traveling mode in which the first friction energy is acquired, because shear force is proportional to the load. Specifically, the process of converting the first frictional energy into the second frictional energy is calculated using the following formula (3): This conversion process is executed for each driving mode, and therefore the number of times the conversion process is executed is equal to the number of driving modes. Second friction energy = First friction energy × (load at rest + first load correction amount + second load correction amount) / load at rest ... (3) This makes it possible to convert, at the friction energy level, the first friction energy, which does not take into account load fluctuations due to acceleration in the forward / backward direction and acceleration in the left / right direction, into the second friction energy, which takes into account load fluctuations due to acceleration in the forward / backward direction and acceleration in the left / right direction.

[0024] The tire wear performance value calculation unit 19 calculates the tire wear performance value based on the second friction energy and frequency of each driving mode. One example is to multiply the second friction energy by a weighting corresponding to the frequency of each driving mode and add up the result (see, for example, Japanese Patent Application Laid-Open No. 2015-123941). Calculating a tire wear performance value from friction energy is well known, so a detailed description will be omitted. The tire wear performance value may be a value that allows tires to be compared as the amount of wear across the entire tire, or may be a value that allows the amount of wear of each part of a tire (for example, a tread block) to be compared using the second friction energy and additional data.

[0025] [Calculation method for tire wear performance value] The method for calculating the tire wear performance value will be explained with reference to FIG.

[0026] First, in step ST1, the acceleration sensor 20 measures the acceleration of the vehicle in three directions (front-rear, left-right, and up-down) multiple times while the vehicle is running. In this embodiment, the measurement is performed once every 0.1 seconds (10 Hz). In step ST2, the measurement data acquisition unit 10 acquires a plurality of measurement data containing accelerations in three directions, namely, the front-rear direction, the left-right direction, and the up-down direction of the vehicle. In step ST3, the driving mode setting unit 12 sets a plurality of subdivided sections for each of the three directions of acceleration, and sets a plurality of driving modes formed by combinations of the sections in the three directions. In step ST4, the data classification unit 13 classifies each of the acquired multiple pieces of measurement data into one of multiple driving modes. In step ST5, the frequency calculation unit 14 calculates the frequency of each driving mode based on the number of classified measurement data and the total number of measurement data for each driving mode. In step ST6, the first frictional energy acquiring unit 15 acquires the first frictional energy from the longitudinal acceleration, the lateral acceleration, and the load when stationary for the driving mode in which the measurement data has been classified. In step ST7, the first load correction amount calculation section 16 calculates the first load correction amount based on the acceleration in the front-rear direction. In step ST8, the second load correction amount calculation section 17 calculates the second load correction amount based on the acceleration in the left-right direction. In step ST9, the conversion unit 18 corrects the first friction energy based on the first load correction amount, the second load correction amount, and the load at rest for the driving mode in which the first friction energy was acquired, and converts the first friction energy into second friction energy that takes into account load fluctuations in the forward / backward and left / right directions. In step ST10, the tire wear performance value calculation unit 19 calculates the tire wear performance value based on the second friction energy and frequency of each driving mode.

[0027] As described above, the method for calculating tire wear performance values ​​according to this embodiment is a method executed by one or more processors, and includes acquiring a plurality of measurement data having acceleration in at least two directions, i.e., the longitudinal direction and the lateral direction of the vehicle, measured by the acceleration sensor 20 while the vehicle is traveling, setting a plurality of subdivided sections for each of the at least two directions of acceleration, setting a plurality of driving modes each consisting of a combination of sections in at least two directions, classifying each of the acquired plurality of measurement data into one of the plurality of driving modes, and determining, for each driving mode, the number of classified measurement data and the total number of measurement data. The frequency of driving modes may be calculated, and for the driving modes for which the measurement data has been classified, first friction energy may be obtained from the longitudinal acceleration, the lateral acceleration, and the load at rest; for the driving mode for which the first friction energy has been obtained, a first load correction amount based on the longitudinal acceleration and a second load correction amount based on the lateral acceleration may be calculated; the first friction energy may be corrected based on the first load correction amount, the second load correction amount, and the load at rest to convert the first friction energy into second friction energy that takes into account load fluctuations in the longitudinal and lateral directions; and a tire wear performance value may be calculated based on the second friction energy and frequency of each driving mode. In this way, the first friction energy obtained from the longitudinal acceleration, lateral acceleration and stationary load is converted into second friction energy that takes into account tire load fluctuations due to longitudinal and lateral acceleration using first and second load correction amounts based on the longitudinal and lateral acceleration and the stationary load.This makes it possible to take into account tire load fluctuations while utilizing the existing configuration for obtaining the first friction energy, thereby improving the accuracy of the tire wear evaluation value.

[0028] Although not particularly limited, as in this embodiment, the first load correction amount may be calculated using formula (1), the second load correction amount may be calculated using formula (2), and the second frictional energy may be calculated using formula (3). In this way, correction can be realized using a simple correction formula.

[0029] The program according to this embodiment is a program that causes one or more computers to execute the above method. By executing these programs, it is possible to obtain the effects of the above-mentioned methods.

[0030] Although the embodiments of the present disclosure have been described above with reference to the drawings, the specific configurations should not be considered to be limited to these embodiments. The scope of the present disclosure is defined not only by the description of the above embodiments but also by the claims, and further includes all modifications within the meaning and scope of the claims.

[0031] The structures employed in the above-described embodiments can be employed in any other embodiment. The specific configurations of the components are not limited to the above-described embodiments, and various modifications are possible within the scope of the present disclosure.

[0032] For example, the order of execution of each process, such as operations, procedures, steps, and stages, in the devices, systems, programs, and methods shown in the claims, specifications, and drawings, can be implemented in any order, as long as the output of a previous process is not used in a subsequent process. Even if the flow in the claims, specifications, and drawings is described using terms such as "first" and "next" for convenience, this does not mean that the processes must be executed in this order.

[0033] (1) In the above embodiment, the acceleration sensor 20 measures acceleration in three directions, namely, forward / backward, left / right, and up / down. However, it is sufficient if it can measure acceleration in two directions, namely, forward / backward and left / right.

[0034] (2) In the above embodiment, as shown in Fig. 3, the acceleration frequency distribution data is subdivided (divided) into a plurality of sections in each of the three directions of acceleration, and one driving mode is set by combining the sections (edges) in the three directions. However, this is not limited to this. For example, as shown in Fig. 4, two directions, the forward / backward direction and the left / right direction, may be subdivided (divided) into a plurality of sections, and one driving mode may be set by combining the sections (edges) in the two directions. In this case, the measurement data may include acceleration in three directions or may include acceleration in two directions.

[0035] 1 are realized by executing a predetermined program on one or more processors, but each unit may also be configured with a dedicated memory or dedicated circuit. In the system 1 of the above embodiment, each unit is implemented in the processor 1a of a single computer, but each unit may be distributed and implemented on multiple computers or in the cloud. In other words, the above method may be executed on one or more processors.

[0036] System 1 includes a processor 1 a. For example, processor 1 a can be a central processing unit (CPU), a microprocessor, or other processing unit capable of executing computer-executable instructions. System 1 also includes memory 1 b for storing data for system 1. In one example, memory 1 b includes computer storage media, such as RAM, ROM, EEPROM, flash memory or other memory technology, CD-ROM, DVD or other optical disk storage, magnetic cassette, magnetic tape, magnetic disk storage or other magnetic storage device, or any other medium that can be used to store desired data and that can be accessed by system 1. [Explanation of symbols]

[0037] 1...system, 10...measurement data acquisition unit, 11...acceleration frequency distribution data generation unit, 12...driving mode setting unit, 13...data classification unit, 14...frequency calculation unit, 15...first friction energy acquisition unit, 16...first load correction amount calculation unit, 17...second load correction amount calculation unit, 18...conversion unit, 19...tire wear performance value calculation unit.

Claims

1. 1. A method executed by one or more processors, comprising: acquiring a plurality of pieces of measurement data having acceleration in at least two directions, i.e., the forward / backward direction and the left / right direction, of the vehicle measured by an acceleration sensor while the vehicle is traveling; A plurality of sections are set in at least two directions of acceleration, and a plurality of driving modes are set, each of which is formed by a combination of the sections in at least two directions; classifying each of the acquired plurality of measurement data into one of a plurality of driving modes; For each driving mode, calculate the frequency of each driving mode based on the number of classified measurement data and the number of all measurement data; For the driving mode in which the measurement data has been classified, a first friction energy is obtained from the longitudinal acceleration, the lateral acceleration, and the load at a standstill; calculating a first load correction amount based on longitudinal acceleration using Equation (1) for the driving mode in which the first frictional energy is acquired; Calculating a second load correction amount based on the acceleration in the lateral direction using equation (2); The first friction energy is converted into a second friction energy that takes into account load fluctuations in the front-rear direction and the left-right direction using equation (3), A method for calculating a tire wear performance value, the method comprising: calculating a tire wear performance value based on the second friction energy and the frequency of each driving mode. First load correction amount = 0.5×(m・ax・h) / Wb…(1) Second load correction amount = (m・ay・h) / Tr…(2) Second friction energy = First friction energy × (Load at rest + First load correction amount + Second load correction amount) / Load at rest (3) where m is the vehicle mass [kg], ax is the longitudinal acceleration [m / s2], ay is the lateral acceleration [m / s2], h is the height of the vehicle's center of gravity [m], Wb is the wheelbase [m], and Tr is the distance between the left and right wheels [m].

2. A system comprising one or more processors for executing the method of claim 1.

3. A program causing one or more processors to execute the method of claim 1.

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