A method and system for measuring wheel polygons based on multi-point chord measurement, and a storage medium.

Abstract

This invention discloses a method and system for measuring wheel polygons based on multi-point chord measurement, as well as a storage medium. The method includes the following steps: determining the basic configuration of the multi-point chord system, including the chord reference length L, sampling interval Δs, order n, and measurement point position k; constructing the multi-point chord measurement system measurement matrix H based on the measurement point positions; constructing the multi-point chord measurement system inversion model operator; calculating the wheel polygon chord measurement value G based on the gap sensor data of the wheel polygon multi-point chord measurement system; and outputting the wheel polygon reconstruction waveform. This invention can simultaneously meet the static or dynamic measurement requirements of wheel polygons. This invention is the first to use the multi-point chord measurement principle to completely measure the wheel polygon waveform, including the polygon order, polygon wavelength, and polygon amplitude; it has high measurement efficiency, good stability, good repeatability, resistance to external environmental vibration interference, and good environmental adaptability.

Description

Technical Field

[0001] This invention relates to the field of wheel polygon measurement technology, specifically to a wheel polygon measurement method and system based on multi-point chord measurement, and a storage medium. Background Technology

[0002] The wheel is a key component of the railway wheel-rail system. Its long-term, continuous rolling contact with the rail forms the link between the vehicle and track systems. Factors such as wheel manufacturing processes, wheel materials, wheel-rail contact surface roughness, track structure vibration characteristics, and bogie vibration characteristics can influence wheel bending resonance modes. When the characteristic wavelength matching the operating speed is divisible by the wheel circumference, non-uniform wear is prone to occur along the wheel circumference. This wear has a wide wavelength distribution, ranging from a few centimeters to the entire wheel circumference. Polygonal wear of the wheel worsens the wheel-rail interaction, significantly increasing the amplitude and frequency of the force between the wheel and rail. This leads to fatigue damage to key vehicle and track components, such as rail surface spalling, rail surface spots, wheel tread spalling, and fastener breakage. This greatly reduces the service life of critical components in the wheel-rail system and, in severe cases, threatens operational safety.

[0003] Uneven wear with polygonal shapes is a common phenomenon in wheel systems and a pressing engineering problem that needs to be addressed. Due to the complexity of its inducing factors and the lack of a clear mechanism, it is impossible to fundamentally solve the problem of wheel polygonal wear. Currently, wheel resurfacing is an effective measure to eliminate wheel polygonal wear and reduce the damage to critical components of the vehicle-track system caused by the wide-band vibrations excited by wheel non-roundness. Therefore, rapid and accurate measurement of wheel polygonal wear is a crucial prerequisite for guiding scientific wheel resurfacing.

[0004] Existing wheel polygon detection methods are broadly categorized into static and dynamic detection. Static detection utilizes specialized instruments such as wheel roughness measuring instruments (e.g., laser profile measuring instruments, contact profile measuring instruments) when the train is stationary. This method offers high accuracy but suffers from low efficiency and high cost. Dynamic wheel polygon detection is further divided into trackside and onboard detection. Trackside detection involves installing acceleration sensors or strain gauges on the rail web or base, cleaning and performing time-frequency domain analysis on the measurement data to identify the order and amplitude of the wheel polygon. Since the wheel tread circumference is approximately 2.9m, the sensor layout area for trackside detection must be at least equal to the wheel tread circumference to cover the entire tread area. Onboard wheel polygon measurement based on axle box acceleration is susceptible to interference from short-wave irregularities on the rail surface, which correspond to the typical wavelength of the wheel polygon, as well as bogie vibration interference. This complicates the wheel polygon identification algorithm based on axle box acceleration data and also results in a complex measurement system. All of the aforementioned dynamic measurement methods struggle to measure the complete waveform of the wheel polygon, offering only approximate estimates of its order and amplitude. Therefore, there is an urgent need for a rapid measurement technology that can simultaneously satisfy both static and dynamic measurements of the complete waveform of the wheel polygon. Summary of the Invention

[0005] To address the problems existing in the prior art, this invention provides a wheel polygon measurement method and system based on the multi-point chord measurement method, as well as a storage medium, which enables rapid and accurate measurement of the real waveform of the train wheel polygon, while simultaneously satisfying both static and dynamic measurement of the wheel polygon, providing data support for the precise turning of the wheel polygon, and solving the problems mentioned in the background art.

[0006] To achieve the above objectives, the present invention provides the following technical solution: a wheel polygon measurement method based on multi-point chord measurement, the wheel polygon measurement method comprising the following steps:

[0007] S101. Determine the basic configuration of the multi-point chord system, including the chord reference length L, sampling interval Δs, order n, and measurement point position k;

[0008] S102. Construct the measurement matrix H of the multi-point chord measurement system based on the location of the measuring points;

[0009] S103. Constructing the inversion model operator for a multi-point chord measurement system.

[0010] S104. Calculate the chord measurement value G of the wheel polygon based on the gap sensor data of the wheel polygon multi-point chord measurement system.

[0011] S105, Output the polygonal waveform of the wheel.

[0012] Further, in step S102, the chord reference length L is divided according to the sampling interval Δs to obtain the number of measurement point positions n-1. The i-th measurement point divides the chord reference length L into two parts: the left length of the i-th measurement point is i*Δs, and the right length of the i-th measurement point is (ni)*Δs. The measurement matrix H corresponding to the i-th measurement point... i The expression is as follows:

[0013]

[0014] Wherein, γ is the proportion of the length to the right of the i-th measuring point to the length L of the chord reference. is the proportion of the length on the left side of the i-th measuring point to the length of the chord reference; N is the number of points discretely representing the total length of the measured object according to the sampling interval Δs; n is the order of the chord reference.

[0015]

[0016] Based on the location of each measuring point, a multi-point chord measurement system measurement matrix H is constructed, which is expressed as follows:

[0017]

[0018] Furthermore, in step S103, based on the measurement point position k, a multi-point chord measurement system inversion model operator is constructed. The formula is expressed as follows:

[0019]

[0020] in, is the mathematical summation operator; T is the matrix transpose operator; β is the regularization coefficient, generally ranging from 0.001 to 0.005; I is the identity matrix.

[0021] Furthermore,

[0022] In step S104, based on the gap sensor data of the wheel polygon multi-point chord measurement system, the i-th chord measurement value G(i) corresponding to the wheel polygon chord measurement value is calculated, and the formula is expressed as follows:

[0023] H i Z = G(i);

[0024] Z = [z0, z1, ..., z N-1 ] T ;

[0025] Where Z is the original waveform of the wheel polygon, discretized at sampling intervals Δs, with a length of N, and the amplitude of each discrete point is represented by z. j T represents the matrix transpose operation;

[0026] The set of chord measurements from all measuring points on the chord reference, i.e., the formula for the chord measurement G of the wheel polygon, is as follows:

[0027]

[0028] Furthermore, in step S105, the chord measurement value G of the wheel polygon is used as the input to the inversion model, and then processed by the inversion model operator. After processing, the final measurement result is obtained, and the waveform of the restored wheel polygon is output. The formula is expressed as follows:

[0029]

[0030] Among them, Z * The waveform is the restored polygon of the wheel.

[0031] In addition, to achieve the above objectives, the present invention also provides the following technical solution: a wheel polygon measurement system based on the multi-point chord measurement method, the measurement system comprising:

[0032] Sensing layer deployment module: Using the polygonal shape of the wheel circumference as the measurement object of the multi-point chord measurement system, it is equipped with a gap sensor to sense the distance from the wheel tread.

[0033] Data acquisition card module: An encoder is closely attached to the wheel tread. When the wheel rotates, the encoder, which is closely attached to the wheel tread, rotates synchronously. The encoder triggers the data acquisition card to record the gap value of the gap sensor of the multi-point chord measurement system.

[0034] Data transmission module: Uses UDP / TCP protocol to transmit data collected by the gap sensor to the host computer via wireless or wired transmission;

[0035] Data post-processing module: Processes the data collected by the gap sensor based on the multi-point chord measurement method and outputs the complete polygonal waveform of the wheel.

[0036] In addition, to achieve the above objectives, the present invention also provides the following technical solution: an electronic device, the electronic device comprising: a processor; and a memory for storing one or more programs;

[0037] When the one or more programs are executed by the processor, the processor performs the wheel polygon measurement method.

[0038] In addition, to achieve the above objectives, the present invention also provides the following technical solution: a computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the wheel polygon measurement method.

[0039] The beneficial effects of this invention are: the method of this invention can simultaneously meet the static or dynamic measurement requirements of wheel polygons; this invention is the first to use the multi-point chord measurement principle to completely measure the waveform of wheel polygons, including polygon order, polygon wavelength, and polygon amplitude; it has high measurement efficiency, good stability, good repeatability, resistance to external environmental vibration interference, and good environmental adaptability. Attached Figure Description

[0040] Figure 1 This is a schematic diagram of the module composition of the chord measurement method system;

[0041] Figure 2 This is a schematic diagram showing the positions of each measuring point in a multi-point chord system.

[0042] Figure 3 A schematic diagram of a multi-point chord reference;

[0043] Figure 4 This is a schematic diagram of the wheel polygon measurement process based on the multi-point chord measurement method;

[0044] Figure 5 This is a schematic diagram of the installation of a wheel polygon measurement system based on the multi-point chord measurement method.

[0045] Figure 6 This is a schematic diagram illustrating the steps of a wheel polygon measurement method based on the multi-point chord measurement method.

[0046] Figure 7 This is a schematic diagram of the measured data of the 9th-order polygonal wheel of the EMU in Example 2;

[0047] Figure 8 This is a schematic diagram of the multi-point chord measurement system configuration in Example 2;

[0048] Figure 9 This is a schematic diagram of the measurement of the chord reference at a certain position on the wheel in Example 2;

[0049] Figure 10 A schematic diagram comparing the measurement results with the original waveform for two-point chord measurement;

[0050] Figure 11 This is a schematic diagram of a wheel polygon measurement system module based on the multi-point chord measurement method.

[0051] Figure 12 This is a schematic diagram of the electronic device structure;

[0052] In the diagram, 110 is the sensor layer deployment module; 120 is the data acquisition card module; 130 is the data transmission module; 140 is the data post-processing module; 210 is the processor; and 220 is the memory. Detailed Implementation

[0053] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0054] Example 1

[0055] In wheel-rail systems, the chordal survey method is used to measure track irregularities. The chordal survey method consists of a measurement model and an inversion model, such as... Figure 1 As shown, in the measurement model, the measured object is represented as Y, which serves as the input to the chord measurement system. After being processed by the chord reference convolution kernel h, the chord measurement value g is obtained and used as the inversion model h. r The input yields the restored waveform Y. * This is the final measurement result of the chord measurement method.

[0056] To improve the robustness of the chordal measurement system and ensure the measurement accuracy of wheel polygons, this invention provides a wheel polygon measurement method based on multi-point chordal measurement, such as... Figure 6 As shown, the specific steps are as follows:

[0057] S101. Determine the basic configuration of the multi-point chord system, including the chord reference length L, sampling interval Δs, order n, and measurement point position k;

[0058] S102. Construct the measurement matrix H of the multi-point chord measurement system based on the location of the measuring points;

[0059] S103. Constructing the inversion model operator for a multi-point chord measurement system.

[0060] S104. Calculate the chord measurement value G of the wheel polygon based on the gap sensor data of the wheel polygon multi-point chord measurement system.

[0061] S105, Output the polygonal waveform of the wheel.

[0062] Furthermore, in step S101, the wavelength components of the wheel polygon range from a few centimeters to the wheel circumference. For example, the wavelength corresponding to a first-order non-circular wheel is the wheel circumference, which is close to 3 meters. To completely measure the wavelength components of the wheel polygon, the chord reference length L is approximately one-tenth of the maximum wavelength, about 30 cm, and the sampling interval can be 1 mm. Therefore, the wavelength range for chord reference measurement is 2 mm to 3000 mm, corresponding to a multi-point chord system order n of 301. Considering both the measurement accuracy and device development cost of the multi-point chord measurement system, it is recommended to use 2 to 5 intermediate measurement points in addition to the two measurement points at the ends of the chord reference, and to sample 2 to 5 points at all chord reference division points. This results in the following possible operating conditions: k = 2 to 5.

[0063] The chord reference length L is divided according to the sampling interval Δs to obtain the number of measurement point positions. The chord reference length L is further divided according to the sampling interval Δs to obtain the number of measurement point positions n-1. The i-th measurement point is as follows: Figure 2 As shown, the i-th measuring point divides the chord reference length L into two parts. The length on the left side of the i-th measuring point is i*Δs, and the length on the right side of the i-th measuring point is (ni)*Δs. The measurement matrix H corresponding to the i-th measuring point is... i ;

[0064] The measurement matrix H of the multi-point chord measurement system is:

[0065]

[0066] The chord reference uses a multi-point chord, for example as follows: Figure 3 As shown, the chord length L is divided into m equal parts according to the sampling interval Δs, with an order of 7, and the number of measurement points in the full configuration is 5:

[0067]

[0068] Figure 3 The measurement system convolution kernel h corresponds to the 5 measurement points. i i = 1, 2, ..., 5, represented as:

[0069]

[0070] In the formula, γ i , This indicates the proportion by which measuring point i divides the chord reference.

[0071]

[0072] Figure 4 The process of multi-point chord measurement of a wheel polygon is illustrated. Taking the circumferential polygon of the wheel as the measurement object, the measurement matrix of the multi-point chord measurement system is constructed to obtain intermediate measurement results, namely the wheel polygon chord measurements, which are used as inputs to the inverse system (inversion model) of the measurement system. After processing by the inversion model operator, the final measurement result is obtained, and the restored waveform of the wheel polygon is output.

[0073] by Figure 3 Taking a multi-point chord measurement configuration as an example, the multi-point chord system measurement model can be regarded as an independent combination of the measurement processes of each measurement point {#1,#2,#3,#4,#5}, and the measurement system convolution kernel h corresponding to measurement point i. i See equation (2), forming a single-point measurement matrix H. i Then the set of measurement equations related to measurement point i can be expressed as:

[0074] H iZ = G(i), i = 1, 2, ..., 5 (4)

[0075] In the formula, H i Let Z be the measurement matrix for measurement point i, Z be the column vector of the wheel polygon, and G(i) be the i-th row matrix of the chord measurement matrix G, which can be represented as:

[0076]

[0077] Z = [z0, z1, ..., z N-1 ] T (6)

[0078] G(i)=[g i,0 ,g i,1 ,…,g i,N-n-1 ] T (7)

[0079] Wherein, γ is the proportion of the length to the right of the i-th measuring point to the length L of the chord reference. is the proportion of the length to the left of the i-th measuring point to the length of the chord reference; N is the number of points discretely representing the total length of the measured object according to the sampling interval Δs; n is the order of the chord reference.

[0080] Next, the global optimization model is transformed into a combinatorial optimization model, expressed as:

[0081]

[0082] In the formula, Z represents the objective function for optimization.

[0083] The solution Z of the inversion model of the multi-point string system * It can be represented as:

[0084]

[0085] but Figure 4 Inversion model operator for multi-point string measurement system for:

[0086]

[0087] Furthermore, in S103, based on the measurement point location k, the corresponding inversion model operator is constructed using equation (10).

[0088]

[0089] Furthermore, in step S104, by Figure 5 The clearance sensor data of the wheel polygon measuring device is used to calculate the set of chord measurements of all measuring points mounted on the chord reference according to equation (4), i.e., the wheel polygon chord measurement value G.

[0090]

[0091] Furthermore, based on the inversion model operator of the wheel polygonal chord measurement system Chord measurements G are used as input to the inversion model, which is then processed by the inversion model operator. After processing, the final measurement result is obtained, and the restored waveform of the wheel polygon is output, thus obtaining the final measurement result of the wheel polygon:

[0092]

[0093] Example 2

[0094] like Figure 7 As shown, Figure 7 The measured data of a 9th-order polygonal wheel of a certain EMU is used as... Figure 4 The object being measured by the measuring device. The basic configuration of the chord reference includes a chord length of 30cm, a sampling interval of 1mm, and two measurement positions, as shown below. Figure 8 As shown.

[0095] The convolution kernel h1 corresponding to measurement point #1:

[0096]

[0097] In the formula, element 1 is located at position 101, and all other elements are 0.

[0098] The convolution kernel h2 corresponding to measurement point #2:

[0099]

[0100] In the formula, element 1 is located at position 150, and all other elements are 0.

[0101] Next, the measurement matrix H is constructed according to equations (5) and (8).

[0102] Based on chord Taking the polygonal measurement of a wheel by rotating it around the wheel as an example... Figure 9 This is a schematic diagram of the measurement of the chord reference at a certain position on the wheel. The diagram only shows the calculation of the chord measurement value at measuring point 1#. The distance between sensor 1# and chord reference o1 is represented as a = 10cm, and the distance between sensor 1# and chord reference o2 is represented as b = 20cm. The chord measurement value g in the diagram is calculated as follows:

[0103]

[0104] In the formula, s1 is the distance between the position sensor at measuring point #1 and the wheel tread; s o1 s is the distance between the chord reference endpoint o1 and the wheel tread;o2 The distance between the reference endpoint o2 of the chord and the wheel tread is given.

[0105] It is particularly important to note that the gap sensor is installed at an angle perpendicular to the chord reference.

[0106] chord reference The device rotates around the wheel once, and the final measurement result is compared with the original waveform. Figure 10 As shown, the two-point chord measurement results can accurately identify the order of the wheel polygon, with only a deviation in amplitude. This deviation can be suppressed by increasing the number of measurement points, such as increasing the number of measurement points to 5, until the measurement results meet the measurement accuracy requirements.

[0107] Example 3

[0108] Based on the same inventive concept as the above-described method embodiments, this application also provides a wheel polygon measurement system based on the multi-point chordal measurement method, used to implement the wheel polygon measurement method based on the multi-point chordal measurement method described in the above embodiments, such as... Figure 6 and Figure 11 As shown, the measurement system specifically includes:

[0109] Sensing layer deployment module 110: Using the polygonal shape of the wheel circumference as the measurement object of the multi-point chord measurement system, it is equipped with a gap sensor to sense the distance from the wheel tread.

[0110] Data acquisition card module 120: An encoder is closely attached to the wheel tread. When the wheel rotates, the encoder that is closely attached to the wheel tread rotates synchronously. The encoder triggers the data acquisition card to record the gap value of the gap sensor of the multi-point chord measurement system.

[0111] Data transmission module 130: Uses UDP / TCP protocol to transmit data collected by the gap sensor to the host computer via wireless or wired transmission;

[0112] Data post-processing module 140: Processes the data collected by the gap sensor based on the multi-point chord measurement method and outputs the complete polygonal waveform of the wheel.

[0113] The wheel polygon measurement method based on multi-point chord measurement includes the following steps:

[0114] Determine the basic configuration of the multi-point chord system, including the chord reference length L, sampling interval Δs, order n, and measurement point position k;

[0115] Based on the location of the measuring points, construct the measurement matrix H of the multi-point chord measurement system;

[0116] Constructing operators for inversion models of multi-point chord measurement systems

[0117] Calculate the chord measurement value G of the wheel polygon based on the gap sensor data of the wheel polygon multi-point chord measurement system;

[0118] Output the polygonal waveform of the wheel.

[0119] Based on the same inventive concept as the above-described method embodiments, this application also provides an electronic device, such as... Figure 12 As shown, the device includes: a processor 210; and a memory 220 for storing one or more programs;

[0120] When the one or more programs are executed by the processor 210, the processor performs the wheel polygon measurement method.

[0121] The method for measuring the polygon of a wheel includes the following steps:

[0122] Determine the basic configuration of the multi-point chord system, including the chord reference length L, sampling interval Δs, order n, and measurement point position k;

[0123] Based on the location of the measuring points, construct the measurement matrix H of the multi-point chord measurement system;

[0124] Constructing operators for inversion models of multi-point chord measurement systems

[0125] Calculate the chord measurement value G of the wheel polygon based on the gap sensor data of the wheel polygon multi-point chord measurement system;

[0126] Output the polygonal waveform of the wheel.

[0127] Based on the same inventive concept as the above-described method embodiments, this application also provides a computer-readable storage medium storing a computer program thereon, which, when executed by processor 210, implements the wheel polygon measurement method.

[0128] The method for measuring the polygon of a wheel includes the following steps:

[0129] Determine the basic configuration of the multi-point chord system, including the chord reference length L, sampling interval Δs, order n, and measurement point position k;

[0130] Based on the location of the measuring points, construct the measurement matrix H of the multi-point chord measurement system;

[0131] Constructing operators for inversion models of multi-point chord measurement systems

[0132] Calculate the chord measurement value G of the wheel polygon based on the gap sensor data of the wheel polygon multi-point chord measurement system;

[0133] Output the polygonal waveform of the wheel.

[0134] The method of this invention can simultaneously meet the static or dynamic measurement requirements of wheel polygons. For the first time, it adopts the multi-point chord measurement principle to completely measure the waveform of wheel polygons, including polygon order, polygon wavelength, and polygon amplitude. It has high measurement efficiency, good stability, good repeatability, resistance to external environmental vibration interference, and good environmental adaptability.

[0135] Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for measuring the polygonal shape of a wheel based on multi-point chord measurement, characterized in that, The method for measuring the polygon of a wheel includes the following steps: S101. Determine the basic configuration of the multi-point chord system, including the chord reference length L, sampling interval Δs, order n, and measurement point position k; S102. Based on the measurement point locations, construct the measurement matrix H of the multi-point chord measurement system; divide the chord reference length L according to the sampling interval Δs to obtain the number of measurement point locations n-1, where the i-th measurement point divides the chord reference length L into two parts, with the left length of the i-th measurement point being i*Δs and the right length of the i-th measurement point being (ni)*Δs. The measurement matrix H corresponding to the i-th measurement point... i The expression is as follows: Based on the location of each measuring point, a multi-point chord measurement system measurement matrix H is constructed, which is expressed as follows: S103. Constructing the inversion model operator for a multi-point chord measurement system. The formula is expressed as follows: in, `t` is the mathematical summation operator; `T` is the matrix transpose operator; `β` is the regularization coefficient, ranging from 0.001 to 0.005; `I` is the identity matrix. S104. Based on the gap sensor data of the wheel polygon multi-point chord measurement system, calculate the wheel polygon chord measurement value G; based on the gap sensor data of the wheel polygon multi-point chord measurement system, calculate the i-th chord measurement value G(i) corresponding to the wheel polygon chord measurement value, expressed by the following formula: H i ·Z=G(i); Z=[z0,z1,…,z N-1 ] T ; Where Z is the original waveform of the wheel polygon, discretized at sampling intervals Δs, with a length of N, and the amplitude of each discrete point is represented by z. j T represents the matrix transpose operation; The set of chord measurements from all measuring points on the chord reference, i.e., the formula for the chord measurement G of the wheel polygon, is as follows: S105. Output the restored waveform of the wheel polygon. Use the chord measurement value G of the wheel polygon as the input of the inversion model, and process it through the inversion model operator. After processing, the final measurement result is obtained, and the waveform of the restored wheel polygon is output. The formula is expressed as follows: Among them, Z * The waveform is the restored polygon of the wheel.

2. A measurement system for a wheel polygon measurement method based on multi-point chord measurement as described in claim 1, characterized in that: The measurement system includes: Sensing layer deployment module (110): Using the circumferential polygon of the wheel as the measurement object of the multi-point chord measurement system, it is equipped with a gap sensor to sense the distance from the wheel tread. Data acquisition card module (120): The encoder is closely attached to the wheel tread. The rotation of the wheel drives the encoder closely attached to the wheel tread to rotate synchronously. The encoder triggers the data acquisition card to record the gap value of the gap sensor of the multi-point chord measurement system. Data transmission module (130): Using UDP / TCP protocol, it transmits the data collected by the gap sensor to the host computer via wireless or wired transmission; Data post-processing module (140): Processes the data collected by the gap sensor based on the multi-point chord measurement method and outputs the complete polygonal waveform of the wheel.

3. An electronic device, characterized in that: The electronic device includes: a processor (210); and a memory (220) for storing one or more programs; When the one or more programs are executed by the processor (210), the processor performs the wheel polygon measurement method as described in claim 1.

4. A computer-readable storage medium, characterized in that: It stores a computer program that, when executed by a processor (210), implements the wheel polygon measurement method as described in claim 1.

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