Method for measuring equivalent cornering stiffness of each shaft of articulated train based on steady-state steering experiment

Abstract

The invention provides a method for measuring equivalent cornering stiffness of each axis of an articulated train based on a steady-state steering experiment, and relates to the technical field of articulated trains, comprising the following steps: collecting train motion data, and performing anomaly detection processing on the train motion data by using a sliding window dynamic threshold method; calculating the side slip angle of the axle of the test train according to the geometric and dynamic relationship, and fitting the movement track of the axle in the movement process by combining the side slip angle of the axle of the test train and utilizing a weighted average mode; determining the motion radius of the test train, and obtaining the lateral deviation force of the test train through the transverse kinetic equation; and calculating the cornering stiffness of the test train based on the cornering force of the test train and the slip angle of the axle of the test train. A whole vehicle experiment method is adopted, the motion state parameters of vehicle motion during steady-state steering are measured, the sideslip force is obtained through a whole vehicle transverse kinetic equation, the sideslip angle is obtained through front and rear axle tracks of the vehicle in the steady state, the sensor is simpler, and the cost is lower.

Description

Technical Field

[0001] This invention relates to the field of articulated train technology, and more particularly to a method for measuring the equivalent lateral stiffness of each axle of an articulated train based on a steady-state steering experiment. Background Technology

[0002] The construction of vehicle dynamics models is an important part of active safety design for automobiles, and lateral stiffness is an important parameter in vehicle dynamics models.

[0003] The lateral stiffness of most vehicles is primarily obtained through testing using specialized tire testing machines. While this method provides accurate lateral stiffness data, the testing equipment is complex and expensive. Furthermore, during vehicle cornering, the vertical loads on the left and right wheels dynamically change with the vehicle's attitude and suspension system characteristics. This variation can significantly impact the estimation of actual lateral forces, a change that is even more pronounced in articulated trains.

[0004] Therefore, traditional lateral stiffness testing methods have the following problems, including: high cost and great influence from vehicle suspension characteristics and lateral roll.

[0005] No effective solutions have yet been proposed to address the problems in the relevant technologies. Summary of the Invention

[0006] In view of this, the present invention provides a method for measuring the equivalent lateral stiffness of each axle of an articulated train based on a steady-state steering experiment, in order to solve the aforementioned problems.

[0007] To solve the above problems, the specific technical solution adopted by the present invention is as follows: A method for measuring the equivalent lateral stiffness of each axle of an articulated train based on steady-state steering experiments includes the following steps: S1. Use sensors pre-installed on the test train to collect train motion data, and use the sliding window dynamic threshold method to perform anomaly detection processing on the train motion data to obtain a standardized dataset. S2. Based on the standardized dataset, the sideslip angle of the test train axle is calculated through geometric and dynamic relationships. Combined with the sideslip angle of the test train axle, the final motion trajectory of the test train is determined by weighted averaging. S3. Based on the final trajectory of the test train, determine the radius of motion of the test train and obtain the lateral force of the test train through the lateral dynamics equation; S4. Calculate the lateral stiffness of the test train based on the lateral force of the test train and the lateral angle of the test train axle.

[0008] Preferably, the step of collecting train motion data using sensors pre-installed on the test train and performing anomaly detection processing on the train motion data using a sliding window dynamic threshold method to obtain a standardized dataset includes the following steps: S11. Based on a pre-set steering test strategy, a steering test is conducted on the test train, and the train motion data is collected by sensors installed on the test train; the test train consists of two sets of vehicles connected by an articulation. S12. Based on the preset time window, calculate the mean and standard deviation of train motion data within each time window, and determine the dynamic threshold range based on the mean and standard deviation of train motion data. S13. Compare each data point in the train motion data with the dynamic threshold range. If the data point exceeds the dynamic threshold range, the data point is judged as an abnormal value; otherwise, the data point is judged as a normal value. S14. Use interpolation or discarding methods to process outlier data points in train motion data, and use the outlier-processed train motion data as a standardized dataset.

[0009] Preferably, the process of determining the trajectory of the test train based on a standardized dataset using the Laplacian operator matrix, and then calculating the sideslip angle of the test train axle based on the trajectory, includes the following steps: S21. Based on the train motion data in the standardized dataset, fit the motion trajectory of the test train axle, and based on the initial motion trajectory of the test train axle, S22. Based on the Laplace operator matrix, the initial motion trajectory of the test train axle is smoothed by combining the weighted average method to obtain the final motion trajectory of the test train.

[0010] S23. Based on the final motion trajectory of the test train, the sideslip angle of the test train axle is calculated to obtain the sideslip angle of the test train axle.

[0011] Preferably, the process of smoothing the initial trajectory of the test train axle based on the Laplace operator matrix and using a weighted average method to obtain the final trajectory of the test train includes the following steps: S221. Based on each data point in the initial motion trajectory, construct the adjacency matrix and degree matrix respectively; S222. Determine the Laplace matrix of the motion trajectory based on the adjacency matrix and degree matrix; S223. The motion trajectory data points of the test train are iteratively adjusted using the weighted average method and the Laplace smoothing term to obtain the final motion trajectory of the test train.

[0012] Preferably, determining the radius of motion of the test train based on its final trajectory and obtaining the lateral force of the test train through the lateral dynamics equation includes the following steps: S31. The final trajectory of the test train, determining the radius of motion of the test train, and determining the angle between the two groups of vehicles in the test train based on the radius of motion; S32. Based on the force and moment balance of the vehicle in the axial direction, construct a set of lateral dynamic equations; S33. Based on the fact that the interaction forces at the connection points of the two sets of vehicles in the test train are the same in magnitude and opposite in direction, and combined with the angular relationship between the two sets of vehicles, construct a set of Newton's second equations for the interaction forces between the two vehicles. S34. The lateral and longitudinal forces of the tires of each axle of the two sets of vehicles in the test train are converted into the lateral and longitudinal forces of each axle through the relationship of the steering angle, and the coordinate axis transformation equations are obtained. S35. Based on the relationship between the rolling resistance coefficient and the vertical force of each axle, construct a set of friction force equations; S36. Solve the lateral dynamics equations, the Newton's second equations for the interaction forces between the two vehicles, the coordinate axis transformation equations, and the friction equations to obtain the lateral force.

[0013] Preferably, the expression for the transverse dynamic equations is: ; In the formula, F x11 This represents the longitudinal force on the first axle of the first vehicle. F x12 This represents the longitudinal force on the second axle of the first vehicle. F J21x This indicates the second car relative to the first car. x Force acting in the axial direction, F y11 This represents the lateral force on the first axle of the first vehicle. F y12 This represents the lateral force on the second axle of the first vehicle. F J21y This indicates the second car relative to the first car. y Force acting in the axial direction, L 11 This indicates the front wheelbase of the first vehicle. L 12 This indicates the rear wheelbase of the first vehicle. L 13 This represents the distance from the center of mass of the first vehicle to the hinge point between the two vehicles. F x21 This represents the longitudinal force on the first axle of the second vehicle. F x22This represents the longitudinal force on the second axle of the second vehicle. F J12x This indicates the first car's relationship to the second car. x Force acting in the axial direction, F y21 This represents the lateral force on the first axle of the second vehicle. F y22 This represents the lateral force on the second axle of the second vehicle. F J12y This indicates the first car's relationship to the second car. y Force acting in the axial direction, L 21 This indicates the front wheelbase of the second vehicle. L 22 This indicates the rear wheelbase of the second vehicle. L 23 This represents the distance from the center of mass of the second vehicle to the hinge point between the two vehicles. m 1 represents the mass of one vehicle. a x1 This represents the longitudinal acceleration of vehicle 1. a y1 This represents the lateral acceleration of vehicle 1. m 2 indicates the mass of the 2 vehicles. a x2 This indicates the longitudinal acceleration of the two vehicles. a y2 This indicates the lateral acceleration of the two vehicles.

[0014] Preferably, the expression for the Newton's second equations governing the interaction forces between the two vehicles is: ; In the formula, F J12x This indicates the first car's relationship to the second car. x Force acting in the axial direction, F J21x This indicates the second car relative to the first car. x Force acting in the axial direction, F J21y This indicates the second car relative to the first car. y Force acting in the axial direction, F J12y This indicates the first car's relationship to the second car. y Force acting in the axial direction, F J21y This indicates the second car relative to the first car. y Force acting in the axial direction, F J21x This indicates the second car relative to the first car. x Force acting in the axial direction, f This indicates the angle between two sets of vehicles in the test train.

[0015] Preferably, the expression for the coordinate axis transformation equation system is: ; In the formula, F x11 This represents the longitudinal force on the first axle of the first vehicle. F tx11 This represents the longitudinal force on the first axle tire of the first vehicle. F ty11 This represents the lateral force of the tire on the first axle of the first vehicle. F x12 This represents the longitudinal force on the second axle of the first vehicle. F tx12 This represents the longitudinal force on the tire of the second axle of the first vehicle. F ty12 This indicates the lateral force of the tire on the second axle of the first vehicle. F x21 This represents the longitudinal force on the first axle of the second vehicle. F tx21 This represents the longitudinal force on the tire of the first axle of the second vehicle. F ty21 This indicates the lateral force of the tire on the first axle of the second vehicle. F x22 This represents the longitudinal force on the second axle of the second vehicle. F tx22 This represents the longitudinal force on the tire of the second axle of the second vehicle. F ty22 This indicates the lateral force of the tire on the second axle of the second vehicle. d 11 This indicates the rotation angle of the first axle of the first vehicle. d 12 This indicates the rotation angle of the second axle of the first vehicle. d 21 This indicates the rotation angle of the first axle of the second vehicle. d 22 This indicates the rotation angle of the second axle of the second vehicle.

[0016] Preferably, the expression for the friction force equation is: ; In the formula, F tx12 This represents the longitudinal force on the tire of the second axle of the first vehicle. F tx21 This represents the longitudinal force on the tire of the first axle of the second vehicle. F tx22 This represents the longitudinal force on the tire of the second axle of the second vehicle. f This represents the coefficient of rolling resistance of tires on the ground.G 12 This represents the vertical force on the second axle of the first vehicle. G 21 This represents the vertical force on the first axle of the second vehicle. G 22 This represents the vertical force on the second axle of the second vehicle.

[0017] Preferably, the calculation of the lateral stiffness of the test train based on the lateral force and the lateral angle of the test train axle includes the following steps: S41. Based on the lateral force of the test train and the lateral angle of the test train axle, determine the linear relationship between the lateral angle and the lateral force, and establish a set of equations to obtain the lateral stiffness by calculating the ratio between the lateral force and the lateral angle. S42. Solve for the lateral stiffness according to the equations of lateral stiffness to obtain the lateral stiffness of the test train.

[0018] The beneficial effects of this invention are as follows: 1. This invention greatly simplifies the experimental design and implementation process by conducting experiments under steady-state conditions, solves the applicability problem of existing methods in articulated vehicle platforms, and provides new ideas and methods for testing the lateral stiffness of articulated vehicles.

[0019] 2. Under steady-state circular motion conditions, this invention obtains the radius of motion by fitting the vehicle's trajectory and uses an IMU to measure the vehicle's lateral acceleration. The lateral force is then derived from the lateral dynamics equation. This method offers significant cost advantages and greatly simplifies the measurement of relevant physical quantities under steady-state conditions. Identifying the lateral stiffness of a single-track model through steady-state steering tests avoids complex real-time data calculations and costly sensor configurations, demonstrating high practical value. Considering the unique characteristics of automobile trains, the steady-state steering-based experimental method can provide stable and accurate lateral stiffness estimates without relying on complex real-time calculations, providing strong support for automobile train research and applications. Therefore, the method for identifying the lateral stiffness of a single-track model based on steady-state steering tests has high practical value.

[0020] 3. This invention adopts a whole-vehicle experimental method to measure the motion state parameters of the vehicle during steady-state steering. The lateral force is obtained through the lateral dynamics equation of the whole vehicle, and the lateral angle is obtained from the front and rear axle trajectories of the vehicle during steady-state. The sensor is simpler and the cost is lower. Moreover, the lateral stiffness data obtained from the experiment is the equivalent lateral stiffness, which is a parameter that reflects the motion state of the whole vehicle, making it more conducive to the practical use of the experiment. Attached Figure Description

[0021] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly described below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort. In the drawings: Figure 1 This is a flowchart of a method for measuring the equivalent lateral stiffness of each axle of an articulated train based on a steady-state steering experiment, according to an embodiment of the present invention. Figure 2 This is a schematic diagram of the sensor installation position in the method for measuring the equivalent lateral stiffness of each axle of an articulated train based on a steady-state steering experiment according to an embodiment of the present invention. Figure 3 This is a schematic diagram illustrating the calculation of the sideslip angle in the method for measuring the equivalent sideslip stiffness of each axle of an articulated train based on a steady-state steering experiment, according to an embodiment of the present invention. Figure 4 This is a schematic diagram of the lateral force calculation in the method for measuring the equivalent lateral stiffness of each axle of an articulated train based on a steady-state steering experiment according to an embodiment of the present invention. Detailed Implementation

[0022] To enable those skilled in the art to better understand the technical solutions in this application, the technical solutions in the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of the embodiments. Based on the embodiments in this application, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of this application.

[0023] According to an embodiment of the present invention, a method for measuring the equivalent lateral stiffness of each axle of an articulated train based on a steady-state steering experiment is provided.

[0024] The present invention will now be further described in conjunction with the accompanying drawings and specific embodiments, such as... Figure 1 As shown, the method for measuring the equivalent lateral stiffness of each axle of an articulated train based on a steady-state steering experiment according to an embodiment of the present invention includes the following steps: S1. Use sensors pre-installed on the test train to collect train motion data, and use the sliding window dynamic threshold method to perform anomaly detection processing on the train motion data to obtain a standardized dataset. It should be noted that sensors need to be installed on the test train before testing. The master and slave antennas of the two Real-Time Kinematic (RTK) receivers need to be installed at the front and rear axle positions of cars 1 and 2 respectively, and the two Inertial Measurement Units (IMUs) need to be installed at the center of mass positions of the front and rear axles respectively. Figure 2 As shown, in Figure 2 In the diagram, (1) is the main antenna of RTK1, (2) is IMU1, (3) is the slave antenna of RTK1, (4) is the main antenna of RTK2, (5) is IMU2, and (6) is the slave antenna of RTK1.

[0025] In a preferred embodiment, the step of collecting train motion data using sensors pre-installed on the test train and performing anomaly detection processing on the train motion data using a sliding window dynamic threshold method to obtain a standardized dataset includes the following steps: S11. Based on a pre-set steering test strategy, a steering test is conducted on the test train, and the train motion data is collected by sensors installed on the test train; the test train consists of two sets of vehicles connected by an articulation. Specifically, when conducting steering experiments on a test train based on a pre-set steering experiment strategy and collecting train motion data using sensors installed on the test train, the following steps are included: The test train was made to circle the tires three times at a speed of 15 km / h along a circle with a radius of 30 m. On a track with a radius of 30m, starting with car 1, maintain a steady circular motion at a speed of 5km / h. Once stable, start recording data. Stop recording data after three laps and store the data in a CSV file. Then test at 10 / 15 / 20 / 25km / h in the same way.

[0026] On a track with a radius of 30m, two cars are used as the lead cars to maintain a steady circular motion at a speed of 5km / h. Once stable, data is recorded. After three laps, data recording stops and the data is stored in a CSV file. The same method is then used to test speeds of 10 / 15 / 20 / 25km / h.

[0027] On a track with a radius of 20m, starting with car 1, a steady-state circular motion is performed at a speed of 5km / h. Once stable, data is recorded. Data recording stops after three laps. Anomalies are handled and classified using a sliding window dynamic threshold method, and the data is stored in a CSV file. The same method is then used to test speeds of 10 / 15 / 20 / 25km / h.

[0028] On a track with a radius of 20m, two cars are used as the lead cars to maintain a steady circular motion at a speed of 5km / h. After stabilization, data is recorded. Data recording stops after three laps and is stored in a CSV file (the relevant data is recorded and written to the CSV file using embedded development software). The same method is then used to test speeds of 10 / 15 / 20 / 25km / h.

[0029] S12. Based on the preset time window, calculate the mean and standard deviation of train motion data within each time window, and determine the dynamic threshold range based on the mean and standard deviation of train motion data. S13. Compare each data point in the train motion data with the dynamic threshold range. If the data point exceeds the dynamic threshold range, the data point is judged as an abnormal value; otherwise, the data point is judged as a normal value. S14. Use interpolation or discarding methods to process outlier data points in train motion data, and use the outlier-processed train motion data as a standardized dataset.

[0030] It is important to note that the detection and handling of outlier data is a crucial step in the experiment. During the experiment, as the vehicle travels around the track at different speeds (e.g., 5 km / h, 10 km / h, 15 km / h, 20 km / h, and 25 km / h), data fluctuations or significant deviations from the normal range may occur due to sensor accuracy, environmental noise, or other uncontrollable factors. These outliers may manifest as sudden speed fluctuations, excessively high or low acceleration values, or even extreme values ​​caused by measurement system malfunctions. To accurately identify and correct these outliers, appropriate data processing is essential. Therefore, a sliding window dynamic threshold method was adopted as the core method for outlier data processing. The sliding window method processes continuous data streams by setting a fixed-size time window. Within each window, the mean and standard deviation of the data are first calculated. The mean reflects the central tendency of the data, while the standard deviation reveals the dispersion of the data. Based on this, a dynamic threshold is set to determine whether a data point is outlier. If the value of a data point exceeds twice the standard deviation of the mean within the current window, then this data point is marked as an outlier. The advantage of the sliding window method's dynamic threshold is that it can automatically adjust the detection standard as the data changes, thus adapting to different experimental data characteristics.

[0031] Once outlier data is detected, it needs to be processed. Common processing methods include interpolation and discarding. Interpolation is typically used to correct isolated outlier data points caused by sensor malfunctions or other unexpected events. By linearly interpolating normal data points before and after the outlier, reasonable values ​​can be calculated to fill in these outlier data. Another processing method is discarding, which is particularly suitable when outliers deviate significantly from the normal range. If a data point clearly exceeds a reasonable physical range, it can be discarded directly to avoid adversely affecting the entire dataset. In experiments, especially when there are few data points, discarding is an effective and simple choice, but this requires that the frequency of outlier data is relatively low; otherwise, it will affect the overall representativeness of the data.

[0032] After data cleaning and outlier handling, the experimental data will be stored as CSV files to ensure data persistence and ease of subsequent analysis. Each CSV file contains multiple fields, such as timestamp, vehicle speed, acceleration, angular velocity, and displacement, which comprehensively describe the vehicle's motion on the circular track.

[0033] S2. Based on the standardized dataset, the sideslip angle of the test train axle is calculated through geometric and dynamic relationships. Combined with the sideslip angle of the test train axle, the final motion trajectory of the test train is determined by weighted averaging. In a preferred embodiment, the process of determining the motion trajectory of the test train based on a standardized dataset using the Laplacian operator matrix, and then calculating the sideslip angle of the test train axle based on the motion trajectory, includes the following steps: S21. Based on the train motion data in the standardized dataset, fit the motion trajectory of the test train axle, and based on the initial motion trajectory of the test train axle, S22. Based on the Laplace operator matrix, the initial motion trajectory of the test train axle is smoothed by combining the weighted average method to obtain the final motion trajectory of the test train.

[0034] S23. Based on the final motion trajectory of the test train, the sideslip angle of the test train axle is calculated to obtain the sideslip angle of the test train axle.

[0035] In a preferred embodiment, the process of smoothing the initial trajectory of the test train axle based on the Laplace operator matrix and using a weighted average method to obtain the final trajectory of the test train includes the following steps: S221. Based on each data point in the initial motion trajectory, construct the adjacency matrix and degree matrix respectively; S222. Determine the Laplace matrix of the motion trajectory based on the adjacency matrix and degree matrix; S223. The motion trajectory data points of the test train are iteratively adjusted using the weighted average method and the Laplace smoothing term to obtain the final motion trajectory of the test train.

[0036] It should be noted that, in order to fit the trajectory of the axle, the relationship between steering angle, wheelbase, and vehicle speed must first be derived using a kinematic model (a kinematic model is the kinematic model of a vehicle, which is basic knowledge in the industry and existing technology, so it will not be elaborated on here). Through geometric and dynamic relationships, the sideslip angle of each axle can be obtained, thereby calculating the trajectory of the axle during the movement.

[0037] Then, after obtaining the trajectory of the axle during its movement, the Laplacian algorithm is used to introduce a weighted average among the data points. This ensures that the value of each data point considers not only its own value but also its relationship with neighboring data points, thereby smoothing out irregular fluctuations in the trajectory. This smoothing process is achieved by solving the Laplacian matrix, which effectively eliminates errors caused by noise and yields a smoother, more stable trajectory.

[0038] Furthermore, the Laplacian operator is a mathematical operator used to smooth curves by introducing a weighted average among data points. Using the Laplacian operator, noise is reduced by weighting the relationship between each data point and its neighboring data points, thus smoothing irregular fluctuations. The specific steps are as follows: (1) Construct a relation matrix between data points. Usually, an adjacency matrix or a distance matrix is ​​used to define the relationship between data points.

[0039] (2) By applying the Laplacian smoothing operator to each data point, its value is made to consider not only the current value of the point, but also the weighted relationship with the adjacent data points. The weights are usually determined based on the distance or similarity between the data points.

[0040] (3) By using the optimized result of the Laplacian operator, a smoother and more stable trajectory can be obtained, and the influence of noise can be removed.

[0041] The Laplacian matrix is ​​a matrix that describes the relationships between data points, and is usually represented as: L = D − A; Where D is the degree matrix (a diagonal matrix representing the degree of each node, i.e., the number of connections), and A is the adjacency matrix (describing the connection relationships between data points). Based on this, the specific steps for solving the Laplacian matrix are as follows: Calculate the degree matrix D and adjacency matrix A for each data point, and construct the Laplacian matrix L.

[0042] Then, the trajectory data is smoothed using the Laplacian matrix, that is, by solving the eigenvalue problem of the Laplacian matrix or by iterative optimization methods, the position of the data points is adjusted to make the trajectory smoother.

[0043] In this way, fluctuations in the trajectory can be effectively eliminated, the impact of noise can be reduced, and a more stable trajectory can be obtained in the end.

[0044] Using the methods described above, steering angle, wheelbase, vehicle speed, and the Laplacian smoothing method can effectively describe and optimize the vehicle's motion trajectory.

[0045] Additionally, when solving for the sideslip angle: Fitting the axle trajectories of each vehicle R ij ,in, i =1, 2, j =1, 2, the same below i The corresponding 1 and 2 refer to car 1 and car 2, j The corresponding 1 and 2 refer to the 1st axle (front axle) and the 2nd axle (rear axle) of the vehicle. L wi The wheelbase of car 1 and car 2. d ij For each axis rotation angle, then calculate the side slip angle of each axis. α ij .

[0046] Figure 3 middle R 11 , R 12 and wheelbase L wi Forming a triangle shape, according to the Law of Cosines, we can obtain... R 12 The angle corresponding to the edge is: ; According to the rotational properties of a rigid body, the normal to the instantaneous velocity of a particle points towards the center of the circle. Therefore, the velocity direction along axis 1 is perpendicular to the direction of rotation. R 11 Vertical, that is: ; Therefore, the skid angle is derived: ; In the formula, R 11 This represents the trajectory of the first axle of the first vehicle. R 12 This represents the trajectory of the second axle of the first vehicle. L w1 This indicates the wheelbase of the first vehicle. d 11 This indicates the rotation angle of the first axle of the first vehicle. α 11 This indicates the side slip angle of the first axle of the first vehicle.

[0047] The remaining sideslip angle can be obtained through the same derivation process, and the specific set of equations is as follows: ; In the formula, R 11 This represents the trajectory of the first axle of the first vehicle.R 12 This represents the trajectory of the second axle of the first vehicle. L w1 This indicates the wheelbase of the first vehicle. d 11 This indicates the rotation angle of the first axle of the first vehicle. α 11 This indicates the slip angle of the first axle of the first vehicle; L w2 This indicates the wheelbase of the second vehicle. α 12 This indicates the side slip angle of the second axle of the first vehicle; α 22 This indicates the side slip angle of the second axle of the second vehicle; α 21 This indicates the side slip angle of the second axle of the second vehicle; R 22 This represents the trajectory of the second axle of the second vehicle. R 21 This represents the trajectory of the first axle of the second vehicle. d 12 This indicates the rotation angle of the second axle of the first vehicle. d 21 This indicates the rotation angle of the first axle of the second vehicle. d 22 This indicates the rotation angle of the second axle of the second vehicle.

[0048] S3. Based on the final trajectory of the test train, determine the radius of motion of the test train and obtain the lateral force of the test train through the lateral dynamics equation; It should be noted that the IMU collects acceleration information based on... Figure 2 As shown, the lateral force needs to be solved by solving the equation. f The rolling resistance coefficient of the tires on the ground. G ij For the first i Cart j Vertical force on the axle F xij For the first i Cart j Longitudinal force of the axle, F yij For the first i Cart j Lateral force on the axle F txij For the first i Cart j The longitudinal force of the axle and tires, F tyij For the first i Cart jLateral forces on the axle and tires, F Jijx for i car pair j The car is j car x Force acting in the axial direction, F Jijy for i car pair j The car is j car y Force acting in the axial direction, L i1 The front wheelbase is where L i2 Rear wheelbase L i3 This is the distance from the vehicle's center of mass to the hinge point. f The angle between the two workshops is an acute angle. Each car body is in... x Axial direction and y The axial force balance and moment balance yield the lateral dynamic equations. The interaction forces at the vehicle body connection points are equal in magnitude and opposite in direction; combining this with the angular relationship between the vehicle bodies, we can obtain the Newton's Second Law equations for the interaction forces between the two vehicles. The lateral and longitudinal forces of the tires on each axle are converted into the lateral and longitudinal forces of each axle through the relationship of the steering angle, resulting in coordinate axis transformation equations. The longitudinal force of the tires can be calculated using the rolling resistance coefficient and the relationship between the vertical forces of each axle, yielding the friction force equations. Solving the above equations yields the lateral force.

[0049] As a preferred embodiment, such as Figure 4 As shown, determining the radius of motion of the test train based on its final trajectory and obtaining its lateral force through the lateral dynamics equation includes the following steps: S31. The final trajectory of the test train, determining the radius of motion of the test train, and determining the angle between the two groups of vehicles in the test train based on the radius of motion; S32. Based on the force and moment balance of the vehicle in the axial direction, construct a set of lateral dynamic equations; S33. Based on the fact that the interaction forces at the connection points of the two sets of vehicles in the test train are the same in magnitude and opposite in direction, and combined with the angular relationship between the two sets of vehicles, construct a set of Newton's second equations for the interaction forces between the two vehicles. S34. The lateral and longitudinal forces of the tires of each axle of the two sets of vehicles in the test train are converted into the lateral and longitudinal forces of each axle through the relationship of the steering angle, and the coordinate axis transformation equations are obtained. S35. Based on the relationship between the rolling resistance coefficient and the vertical force of each axle, construct a set of friction force equations; S36. Solve the lateral dynamics equations, the Newton's second equations for the interaction forces between the two vehicles, the coordinate axis transformation equations, and the friction equations (the lateral force can be obtained by elimination when solving these four equations).

[0050] In a preferred embodiment, the expression for the transverse dynamic equations is: ; In the formula, F x11 This represents the longitudinal force on the first axle of the first vehicle. F x12 This represents the longitudinal force on the second axle of the first vehicle. F J21x This indicates the second car relative to the first car. x Force acting in the axial direction, F y11 This represents the lateral force on the first axle of the first vehicle. F y12 This represents the lateral force on the second axle of the first vehicle. F J21y This indicates the second car relative to the first car. y Force acting in the axial direction, L 11 This indicates the front wheelbase of the first vehicle. L 12 This indicates the rear wheelbase of the first vehicle. L 13 This represents the distance from the center of mass of the first vehicle to the hinge point between the two vehicles. F x21 This represents the longitudinal force on the first axle of the second vehicle. F x22 This represents the longitudinal force on the second axle of the second vehicle. F J12x This indicates the first car's relationship to the second car. x Force acting in the axial direction, F y21 This represents the lateral force on the first axle of the second vehicle. F y22 This represents the lateral force on the second axle of the second vehicle. F J12y This indicates the first car's relationship to the second car. y Force acting in the axial direction, L 21 This indicates the front wheelbase of the second vehicle. L 22 This indicates the rear wheelbase of the second vehicle. L 23 This represents the distance from the center of mass of the second vehicle to the hinge point between the two vehicles. m 1 represents the mass of one vehicle.a x1 This represents the longitudinal acceleration of vehicle 1. a y1 This represents the lateral acceleration of vehicle 1. m 2 indicates the mass of the 2 vehicles. a x2 This indicates the longitudinal acceleration of the two vehicles. a y2 This represents the lateral acceleration of the two vehicles.

[0051] In a preferred embodiment, the expression for the Newton's second equations governing the interaction forces between the two vehicles is as follows: ; In the formula, F J12x This indicates the first car's relationship to the second car. x Force acting in the axial direction, F J21x This indicates the second car relative to the first car. x Force acting in the axial direction, F J21y This indicates the second car relative to the first car. y Force acting in the axial direction, F J12y This indicates the first car's relationship to the second car. y Force acting in the axial direction, F J21y This indicates the second car relative to the first car. y Force acting in the axial direction, F J21x This indicates the second car relative to the first car. x Force acting in the axial direction, f This indicates the angle between two sets of vehicles in the test train.

[0052] In a preferred embodiment, the expression for the coordinate axis transformation equations is: ; In the formula, F x11 This represents the longitudinal force on the first axle of the first vehicle. F tx11 This represents the longitudinal force on the first axle tire of the first vehicle. F ty11 This represents the lateral force of the tire on the first axle of the first vehicle. F x12 This represents the longitudinal force on the second axle of the first vehicle. F tx12 This represents the longitudinal force on the tire of the second axle of the first vehicle. F ty12 This indicates the lateral force of the tire on the second axle of the first vehicle.F x21 This represents the longitudinal force on the first axle of the second vehicle. F tx21 This represents the longitudinal force on the tire of the first axle of the second vehicle. F ty21 This indicates the lateral force of the tire on the first axle of the second vehicle. F x22 This represents the longitudinal force on the second axle of the second vehicle. F tx22 This represents the longitudinal force on the tire of the second axle of the second vehicle. F ty22 This indicates the lateral force of the tire on the second axle of the second vehicle. d 11 This indicates the rotation angle of the first axle of the first vehicle. d 12 This indicates the rotation angle of the second axle of the first vehicle. d 21 This indicates the rotation angle of the first axle of the second vehicle. d 22 This indicates the rotation angle of the second axle of the second vehicle.

[0053] In a preferred embodiment, the expression for the friction force equation is: ; In the formula, F tx12 This represents the longitudinal force on the tire of the second axle of the first vehicle. F tx21 This represents the longitudinal force on the tire of the first axle of the second vehicle. F tx22 This represents the longitudinal force on the tire of the second axle of the second vehicle. f This represents the coefficient of rolling resistance of tires on the ground. G 12 This represents the vertical force on the second axle of the first vehicle. G 21 This represents the vertical force on the first axle of the second vehicle. G 22 This represents the vertical force on the second axle of the second vehicle.

[0054] S4. Calculate the lateral stiffness of the test train based on the lateral force of the test train and the lateral angle of the test train axle.

[0055] In a preferred embodiment, calculating the lateral stiffness of the test train based on the lateral force and the lateral angle of the test train axle includes the following steps: S41. Based on the lateral force of the test train and the lateral angle of the test train axle, determine the linear relationship between the lateral angle and the lateral force, and establish a set of equations to obtain the lateral stiffness by calculating the ratio between the lateral force and the lateral angle. S42. Solve for the lateral stiffness according to the equations of lateral stiffness to obtain the lateral stiffness of the test train.

[0056] Equivalent lateral stiffness is an important parameter in vehicle lateral behavior, used to describe the relationship between the lateral force generated by the tire and the wheel slip angle during vehicle steering. Lateral force is generated by the friction between the tire and the ground, while slip angle is the angle of the tire relative to the longitudinal direction of the vehicle. Equivalent lateral stiffness can be obtained by calculating the ratio between lateral force and slip angle.

[0057] It should be noted that within a small range of sideslip angles, the sideslip angle and sideslip force exhibit a linear relationship. The sideslip stiffness can be calculated from the obtained sideslip force and sideslip angle, expressed by the following equations: k ij = F tyij / α ij .

[0058] In the formula, k ij Indicates lateral stiffness, F tyij Indicates lateral force. α ij Indicates the sideslip angle.

[0059] In summary, by utilizing the above-mentioned technical solutions of this invention, the present invention greatly simplifies the experimental design and implementation process by conducting experiments under steady-state conditions, solves the applicability problem of existing methods in articulated vehicle platforms, and provides a new approach and method for testing the lateral stiffness of articulated vehicles. Under steady-state circular motion conditions, this invention obtains the motion radius by fitting the vehicle's motion trajectory and uses an IMU to measure the vehicle's lateral acceleration, obtaining the vehicle's lateral force through the lateral dynamic equation. This method has significant cost advantages and can greatly simplify the measurement of relevant physical quantities under steady-state conditions. Identifying the lateral stiffness of a single-rail model through steady-state steering tests avoids complex real-time data calculations and high-cost sensor configurations, possessing high practical value. Considering the special characteristics of automobile trains, the experimental method based on steady-state steering can provide stable and accurate lateral stiffness estimation without relying on complex real-time calculations, providing strong support for the research and application of automobile trains. Therefore, the method for identifying the lateral stiffness of a single-rail model based on steady-state steering tests has high practical value. This invention employs a whole-vehicle experimental method to measure the motion state parameters of the vehicle during steady-state steering. The lateral force is obtained through the vehicle's lateral dynamics equation, and the lateral angle is obtained from the vehicle's front and rear axle trajectories during steady-state operation. The sensors are simpler and less expensive. Furthermore, the lateral stiffness data obtained from the experiment is equivalent lateral stiffness, which reflects the motion state of the whole vehicle and is more conducive to practical experimental use.

[0060] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, optical storage, etc.) containing computer-usable program code.

[0061] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above descriptions are merely specific embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for measuring the equivalent lateral stiffness of each axle of an articulated train based on a steady-state steering experiment, characterized in that, Includes the following steps: S1. Use sensors pre-installed on the test train to collect train motion data, and use the sliding window dynamic threshold method to perform anomaly detection processing on the train motion data to obtain a standardized dataset. S2. Based on the standardized dataset, the sideslip angle of the test train axle is calculated through geometric and dynamic relationships. Combined with the sideslip angle of the test train axle, the final motion trajectory of the test train is determined by weighted averaging. S3. Based on the final trajectory of the test train, determine the radius of motion of the test train and obtain the lateral force of the test train through the lateral dynamics equation; S4. Calculate the lateral stiffness of the test train based on the lateral force of the test train and the lateral angle of the test train axle.

2. The method for measuring the equivalent lateral stiffness of each axle of an articulated train based on a steady-state steering experiment according to claim 1, characterized in that, The process of collecting train motion data using sensors pre-installed on the test train and performing anomaly detection processing on the train motion data using a sliding window dynamic threshold method to obtain a standardized dataset includes the following steps: S11. Based on a pre-set steering test strategy, a steering test is conducted on the test train, and the train motion data is collected by sensors installed on the test train; the test train consists of two sets of vehicles connected by an articulation. S12. Based on the preset time window, calculate the mean and standard deviation of train motion data within each time window, and determine the dynamic threshold range based on the mean and standard deviation of train motion data. S13. Compare each data point in the train motion data with the dynamic threshold range. If the data point exceeds the dynamic threshold range, the data point is judged as an abnormal value; otherwise, the data point is judged as a normal value. S14. Use interpolation or discarding methods to process outlier data points in train motion data, and use the outlier-processed train motion data as a standardized dataset.

3. The method for measuring the equivalent lateral stiffness of each axle of an articulated train based on a steady-state steering experiment according to claim 1, characterized in that, The process of determining the trajectory of the test train based on a standardized dataset using the Laplacian operator matrix, and then calculating the sideslip angle of the test train axle based on the trajectory, includes the following steps: S21. Based on the train motion data in the standardized dataset, fit the motion trajectory of the test train axle, and based on the initial motion trajectory of the test train axle, S22. Based on the Laplace operator matrix, the initial motion trajectory of the test train axle is smoothed by combining the weighted average method to obtain the final motion trajectory of the test train. S23. Based on the final motion trajectory of the test train, the sideslip angle of the test train axle is calculated to obtain the sideslip angle of the test train axle.

4. The method for measuring the equivalent lateral stiffness of each axle of an articulated train based on a steady-state steering experiment according to claim 3, characterized in that, The process of smoothing the initial trajectory of the test train axle based on the Laplace operator matrix and using a weighted average method to obtain the final trajectory of the test train includes the following steps: S221. Based on each data point in the initial motion trajectory, construct the adjacency matrix and degree matrix respectively; S222. Determine the Laplace matrix of the motion trajectory based on the adjacency matrix and degree matrix; S223. The motion trajectory data points of the test train are iteratively adjusted using the weighted average method and the Laplace smoothing term to obtain the final motion trajectory of the test train.

5. The method for measuring the equivalent lateral stiffness of each axle of an articulated train based on a steady-state steering experiment according to claim 1, characterized in that, The process of determining the radius of motion of the test train based on its final trajectory and obtaining its lateral force through the lateral dynamics equation includes the following steps: S31. The final trajectory of the test train, determining the radius of motion of the test train, and determining the angle between the two groups of vehicles in the test train based on the radius of motion; S32. Based on the force and moment balance of the vehicle in the axial direction, construct a set of lateral dynamic equations; S33. Based on the fact that the interaction forces at the connection points of the two sets of vehicles in the test train are the same in magnitude and opposite in direction, and combined with the angular relationship between the two sets of vehicles, construct a set of Newton's second equations for the interaction forces between the two vehicles. S34. The lateral and longitudinal forces of the tires of each axle of the two sets of vehicles in the test train are converted into the lateral and longitudinal forces of each axle through the relationship of the steering angle, and the coordinate axis transformation equations are obtained. S35. Based on the relationship between the rolling resistance coefficient and the vertical force of each axle, construct a set of friction force equations; S36. Solve the lateral dynamics equations, the Newton's second equations for the interaction forces between the two vehicles, the coordinate axis transformation equations, and the friction equations to obtain the lateral force.

6. The method for measuring the equivalent lateral stiffness of each axle of an articulated train based on a steady-state steering experiment according to claim 5, characterized in that, The expression for the transverse dynamic equations is: ； In the formula, F x11 This represents the longitudinal force on the first axle of the first vehicle. F x12 This represents the longitudinal force on the second axle of the first vehicle. F J21x This indicates the second car relative to the first car. x Force acting in the axial direction, F y11 This represents the lateral force on the first axle of the first vehicle. F y12 This represents the lateral force on the second axle of the first vehicle. F J21y This indicates the second car relative to the first car. y Force acting in the axial direction, L 11 This indicates the front wheelbase of the first vehicle. L 12 This indicates the rear wheelbase of the first vehicle. L 13 This represents the distance from the center of mass of the first vehicle to the hinge point between the two vehicles. F x21 This represents the longitudinal force on the first axle of the second vehicle. F x22 This represents the longitudinal force on the second axle of the second vehicle. F J12x This indicates the first car's relationship to the second car. x Force acting in the axial direction, F y21 This represents the lateral force on the first axle of the second vehicle. F y22 This represents the lateral force on the second axle of the second vehicle. F J12y This indicates the first car's relationship to the second car. y Force acting in the axial direction, L 21 This indicates the front wheelbase of the second vehicle. L 22 This indicates the rear wheelbase of the second vehicle. L 23 This represents the distance from the center of mass of the second vehicle to the hinge point between the two vehicles. m 1 represents the mass of 1 vehicle. a x1 This represents the longitudinal acceleration of vehicle 1. a y1 This represents the lateral acceleration of vehicle 1. m 2 indicates the mass of the 2 vehicles. a x2 This indicates the longitudinal acceleration of the two vehicles. a y2 This indicates the lateral acceleration of the two vehicles.

7. The method for measuring the equivalent lateral stiffness of each axle of an articulated train based on a steady-state steering experiment according to claim 6, characterized in that, The expression for the Newton's second equations governing the interaction force between the two vehicles is: ； In the formula, F J12x This indicates the first car's relationship to the second car. x Force acting in the axial direction, F J21x This indicates the second car relative to the first car. x Force acting in the axial direction, F J21y This indicates the second car relative to the first car. y Force acting in the axial direction, F J12y This indicates the first car's relationship to the second car. y Force acting in the axial direction, F J21y This indicates the second car relative to the first car. y Force acting in the axial direction, F J21x This indicates the second car relative to the first car. x Force acting in the axial direction, φ This indicates the angle between two sets of vehicles in the test train.

8. The method for measuring the equivalent lateral stiffness of each axle of an articulated train based on a steady-state steering experiment according to claim 6, characterized in that, The expression for the coordinate axis transformation equation system is: ； In the formula, F x11 This represents the longitudinal force on the first axle of the first vehicle. F tx11 This represents the longitudinal force on the tire of the first axle of the first vehicle. F ty11 This represents the lateral force of the tire on the first axle of the first vehicle. F x12 This represents the longitudinal force on the second axle of the first vehicle. F tx12 This represents the longitudinal force on the tire of the second axle of the first vehicle. F ty12 This indicates the lateral force of the tire on the second axle of the first vehicle. F x21 This represents the longitudinal force on the first axle of the second vehicle. F tx21 This represents the longitudinal force on the tire of the first axle of the second vehicle. F ty21 This indicates the lateral force of the tire on the first axle of the second vehicle. F x22 This represents the longitudinal force on the second axle of the second vehicle. F tx22 This represents the longitudinal force on the tire of the second axle of the second vehicle. F ty22 This indicates the lateral force of the tire on the second axle of the second vehicle. δ 11 This indicates the rotation angle of the first axle of the first vehicle. δ 12 This indicates the rotation angle of the second axle of the first vehicle. δ 21 This indicates the rotation angle of the first axle of the second vehicle. δ 22 This indicates the rotation angle of the second axle of the second vehicle.

9. The method for measuring the equivalent lateral stiffness of each axle of an articulated train based on a steady-state steering experiment according to claim 6, characterized in that, The expression for the friction force equation is: ； In the formula, F tx12 This represents the longitudinal force on the tire of the second axle of the first vehicle. F tx21 This represents the longitudinal force on the tire of the first axle of the second vehicle. F tx22 This represents the longitudinal force on the tire of the second axle of the second vehicle. f This represents the rolling resistance coefficient of tires on the ground. G 12 This represents the vertical force on the second axle of the first vehicle. G 21 This represents the vertical force on the first axle of the second vehicle. G 22 This represents the vertical force on the second axle of the second vehicle.

10. The method for measuring the equivalent lateral stiffness of each axle of an articulated train based on a steady-state steering experiment according to claim 1, characterized in that, The calculation of the lateral stiffness of the test train based on the lateral force and lateral angle of the test train axle includes the following steps: S41. Based on the lateral force of the test train and the lateral angle of the test train axle, determine the linear relationship between the lateral angle and the lateral force, and establish a set of equations to obtain the lateral stiffness by calculating the ratio between the lateral force and the lateral angle. S42. Solve for the lateral stiffness according to the equations of lateral stiffness to obtain the lateral stiffness of the test train.

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