A method for estimating vertical force of heavy-load tires based on circumferential strain analysis

Abstract

The present invention belongs to the field of vehicle engineering technology, and specifically relates to a method for estimating the vertical force of a heavy-loaded tire based on circumferential strain analysis. Step 1: Establish a finite element model of a heavy-loaded tire; Step 2: Use the finite element model of the heavy-loaded tire established in step 1 to simulate static load conditions under different vertical forces, analyze the static load grounding characteristics of the heavy-loaded tire and the static load circumferential strain of the heavy-loaded tire, and estimate the ground contact angle based on the circumferential strain of the inner liner; Step 3: On the basis of step 2, establish a heavy-loaded tire vertical force estimation model, extract vertical force-ground contact angle simulation data under different static loads to train and test the heavy-loaded tire vertical force estimation model, and then predict the vertical force. The present invention reduces the influence of model errors and method errors caused by complex tire formulas, and the estimation process is simpler and more efficient, and the estimation results are more accurate and reliable.

Description

Technical Field

[0001] The present invention belongs to the technical field of vehicle engineering, and in particular relates to a method for estimating the vertical force of a heavy-load tire based on circumferential strain analysis. Background Art

[0002] Tires are the sole contributor to the forces required for vehicle operation, aside from the effects of air flow. They are also the only component of a vehicle that comes into contact with the road. Information on tire-road interaction plays a crucial role in improving vehicle performance indicators such as ride comfort, handling stability, dynamics, and braking. Tire vertical force influences the vehicle's vertical vibration characteristics and is crucial for controlling ride comfort and estimating vehicle parameters.

[0003] Tire force information is crucial for vehicle control systems, but dynamic measurement of tire forces during driving is difficult to achieve due to technical and cost constraints. Previously, domestic and international researchers have established various vehicle dynamics models to estimate tire forces, including the widely used LuGre model and Brush tire model [6,7] in analytical models, and the Rill model and Burckhardt tire model [8,9] in empirical models. However, because empirical models cannot describe dynamic and nonlinear characteristics, and analytical models suffer from incomplete characterization of influencing factors and significant limitations on their scope of application, it is difficult to achieve real-time tire force estimation based solely on vehicle dynamics models.

[0004] With the significant advancements in sensor technology, intelligent tires integrated with these technologies have provided new approaches for sensing and acquiring tire dynamic information. Sensors measure actual tire dynamic data, and then use algorithmic analysis to estimate tire state and parameters. In recent years, several researchers have conducted research on tire vertical force estimation algorithms. One researcher designed a three-axis MEMS acceleration test system, analyzed and extracted acceleration signal features, and established a vertical force estimation algorithm using a BP neural network. Other researchers used a ring model to analyze the relationship between contact angle and vertical force, and combined this with innerliner acceleration data to estimate vertical force. Other researchers established corresponding empirical models by analyzing tire acceleration functions and tire state. Based on these empirical models, a peak synchronization algorithm, and an extended Kalman filter, a tire state observer (TSE) was constructed to estimate tire vertical force. Other researchers used acceleration signals to estimate contact length and used polynomial fitting to study the relationship between vertical force, contact length, and tire pressure to estimate tire vertical force. Accelerometers are lightweight, inexpensive, and compact, making them widely used in smart tires. However, they suffer from significant noise interference and a complex array of acceleration signals, making feature extraction difficult. Strain sensors, on the other hand, offer the advantages of being lightweight, compact, and inexpensive, while also providing a more singular and pure signal. With the development of flexible sensing technology, strain sensors are finding greater application in smart tires.

[0005] However, the current tire information acquisition method still has the following problems:

[0006] (1) Intelligent tire force monitoring based on acceleration signals is susceptible to interference.

[0007] The acceleration signal contains rotation, vibration and gravitational acceleration. It is difficult to extract the characteristics of the acceleration signal. In addition, the acceleration signal is very sensitive to the noise generated by the road surface. It is easy to mistakenly extract features that have little or no correlation with the research object, which has a negative impact on the overall sensitivity and credibility of the characteristic signal, thereby reducing the estimation accuracy of tire force.

[0008] (2) The intelligent recognition algorithm has the problem of unclearly revealing the relationship between tire force and deformation.

[0009] Current research on tire forces based on intelligent recognition algorithms primarily involves acquiring test signals from sensors and then estimating tire forces using algorithms and empirical or analytical tire models, replacing the forces observed from vehicle signals. This is essentially an indirect method for obtaining tire forces. Both empirical and analytical tire models are highly simplified, have significant limitations, and focus on a single area of ​​research. The tire model's formulas and approximate parameters differ from actual tire behavior, making it difficult to express a clear relationship between tire force and deformation. This results in a lack of precise basis for research on tire mechanical properties, significantly hindering the accurate estimation of tire forces. Summary of the Invention

[0010] To address these issues, this paper proposes a method for estimating the vertical force of a heavy-duty tire based on circumferential strain analysis. Using a 16.00R20 heavy-duty tire as the research object, this paper establishes a tire finite element model and performs finite element simulations under different static load conditions. The tire's contact characteristics and the influence of the innerliner's circumferential strain are investigated, and a contact angle characterization metric is proposed. A strain-vertical force dataset is obtained through finite element simulation. The estimated contact angle and contact length are selected as characteristic indicators. A support vector machine (SVM) based on the Grey Wolf algorithm is used to perform regression prediction of the tire's vertical force.

[0011] In order to achieve the above object, the technical solution adopted by the present invention is as follows:

[0012] A method for estimating vertical force of a heavy-load tire based on circumferential strain analysis includes:

[0013] Step 1: Establish a finite element model of heavy-duty tire;

[0014] Step 2: Use the heavy-duty tire finite element model established in Step 1 to simulate static load conditions under different vertical forces. Then, analyze the heavy-duty tire's static ground contact characteristics and static circumferential strain curve, and estimate the contact angle based on the inner liner's circumferential strain.

[0015] Step 3: Based on step 2, a heavy-load tire vertical force estimation model is established. The vertical force-ground angle simulation data under different static loads are extracted to train and test the heavy-load tire vertical force estimation model, and then the vertical force is predicted.

[0016] Preferably, the step 1 comprises:

[0017] Step 1.1: Use finite element software to establish a finite element model of the heavy-duty tire;

[0018] Step 1.2: Conduct a heavy-duty tire loading test using a heavy-duty tire mechanical vibration test system to obtain the contact patch shape and tire sinkage under different static loads. Verify the contact patch characteristics and vertical stiffness by comparing them with the finite element model simulation results from step 1.1. Conduct a modal test using a modal test system to obtain the first eight radial vibration mode shapes and frequencies of the heavy-duty tire rim in the free state. Verify the vibration characteristics by comparing them with the finite element model simulation results from step 1.1.

[0019] Preferably, the step 2 is specifically as follows:

[0020] Step 2.1: Use the heavy-duty tire finite element model from Step 1 to simulate static load conditions under different vertical forces. Obtain tire contact stress cloud maps and tread center point circumferential strain datasets under different loads. Analyze the heavy-duty tire's static contact characteristics and obtain simulation datasets of front and rear contact angles and contact lengths under different static loads.

[0021] Step 2.2: Use the heavy-duty tire finite element model to simulate and analyze the inner liner circumferential strain curves of tires with standard tire pressure and different static load conditions;

[0022] Step 2.3: Based on the analysis of steps 2.1 and 2.2, the ground contact angle is estimated based on the circumferential strain of the liner, a ground contact angle characterization index is proposed, and the ground contact length is estimated by combining the ground contact length calculation formula.

[0023] Preferably, the step 3 is specifically as follows:

[0024] Step 3.1: Establish a vertical force estimation model based on a support vector regression machine and establish the optimal solution formula for the vertical force estimation model based on the support vector regression machine through transformation. The error penalty coefficient C and the kernel function parameter γ are key factors affecting the model's prediction performance. The error penalty coefficient C and the kernel function parameter γ are optimized using the gray wolf algorithm.

[0025] Step 3.2: Combine the strain data set, ground contact angle characterization index, and ground contact length calculation formula in step 2 to obtain a feature set with ground contact angle and ground contact length as input and vertical load as output. Use 28 of the 56 data sets in the feature set as the model training set and input them into the vertical force estimation model in step 3.1 for training. Adjust the model's penalty coefficient C and kernel function parameter γ. Then, use the remaining 28 test set data sets to test the prediction performance of the vertical force estimation model and realize the prediction of vertical force.

[0026] Preferably, the process of establishing the optimal solution formula of the vertical force estimation model of the support vector regression machine in step 3.1 is:

[0027] Step 3.1.1.1: Use support vector regression machine to make vertical force regression prediction, and define the training set as: D = {(x1,Fz1), (x2,Fz2),…, (x m ,Fz m )},Fz i ∈R, Then the vertical force estimation model is:

[0028] f z (x) = w T Φ(x)+b (2)

[0029] Where, i∈(1,2,3…,m), m is the number of training sets, f z (x) is the predicted value of vertical force, Fz i is the finite element simulation value of vertical force, φ fi 、φ ri is the finite element simulation value of the front and rear contact angles, L i is the finite element simulation value of the front and rear contact angles, w is the weight vector, b is the bias vector, and Φ(x) represents the value of x i Feature vector after mapping to high-dimensional feature space;

[0030] Step 3.1.1.2: Introduce slack variable ξ i * and ξ i , transforming the support vector regression machine regression prediction problem into a minimum optimization problem:

[0031]

[0032] In the formula, C is the penalty coefficient, ε is the insensitivity coefficient, Fz i is the finite element simulation value of vertical force;

[0033] Step 3.1.1.3: Introduce the Lagrange coefficient and transform the minimum optimization problem in step 3.1.2 into a dual problem:

[0034]

[0035] Where, a i , a j is the Lagrange multiplier, K(x i ,x j ) is the kernel function;

[0036] The kernel function is:

[0037]

[0038] Where γ is the kernel function parameter;

[0039] Step 3.1.1.4: Establish the optimal solution formula of the vertical force estimation model of the support vector regression machine according to formula (4):

[0040]

[0041] Preferably, the step 3.1 of optimizing the error penalty coefficient C and the kernel function parameter γ by the gray wolf algorithm includes:

[0042] (1) Parameter set hierarchical stratification: randomly generating parameter clusters in the search space Then, the three parameter sets with the best fitness in the parameter cluster are marked as and The rest is divided equally into The grading process is repeated after each iteration;

[0043] Where, is the generated parameter set of the i-th group of penalty coefficient C and kernel function coefficient γ, k is the number of generated parameter sets, α, β, and δ are the three best parameters in the contemporary parameter set, and the degree of optimality of the three decreases in turn; ω is the other parameter set after removing α, β, and δ; is the i-th set of penalty coefficients and kernel function parameters in ω; n = k-3;

[0044] (2) Searching for the optimal parameter set: Before obtaining the optimal parameter set, its position is determined first. The search mode and search direction of the optimal parameter set are adjusted by the coordination coefficient vectors μ and B, and the random vectors r1 and r2. When |μ|>1, the parameter cluster performs a global search; when |μ|<1, the parameter cluster performs a local search in a certain area.

[0045] D=|BX p (t)-X(t)| (7)

[0046] X(t+1)=X p (t)-μD (8)

[0047] μ=2ar2-a (9)

[0048] B=2r1 (10)

[0049] Where: D is the distance between the current parameter set and the optimal parameter set; X p (t) is the position vector of the optimal parameter set of the tth generation; X(t) is the position vector of the current parameter set of the tth generation; a decreases linearly from 2 to 0 during the entire iteration process; r1 and r2 are random vectors in [0, 1];

[0050] (3) Optimal acquisition: parameter clusters after iteration and The three parameter sets are closest to the optimal parameter set, and the three parameter sets use the distance between themselves and the optimal parameter set to jointly guide the other Parameter set adjustment position to obtain the optimal,

[0051]

[0052]

[0053]

[0054] Where: D α 、D β 、D δ are the distances between the α, β, δ parameter sets and the current parameter set respectively; B1, B2, B3 are random vectors; X1, X2, X3 are the position vectors of the current parameter set after the movement guided by the α, β, δ parameter sets respectively; X(t+1) defines the final position of the current parameter set.

[0055] Compared with the prior art, the present invention has the following beneficial effects:

[0056] With the help of strain sensors, circumferential strain signals with less noise interference and relatively simple signals are obtained, which makes signal processing simpler and more accurate; combined with the strain curve, the contact angle and contact length are more accurately estimated. The vertical force estimation algorithm based on the Grey Wolf Support Vector Regression Machine with contact angle and contact length as input feature indicators can accurately estimate the vertical force of the tire; the circumferential strain signal obtained by the strain sensor can more directly estimate the vertical force, reducing the influence of model errors and method errors caused by complex tire formulas. The estimation process is simpler and more efficient, and the estimation results are more accurate and reliable.

[0057] (1) The ground contact angle can be estimated more accurately by combining the characteristic indexes of the spacing angle of the zero-order, first-order, and second-order derivatives of the strain curve;

[0058] (2) The vertical force estimation algorithm based on the Gray Wolf Support Vector Regression Machine has a good estimation effect. The error between the estimated value and the finite element simulation value is within 1.8%, which can accurately estimate the tire vertical force. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] The accompanying drawings are used to provide further understanding of the present invention and constitute a part of the specification. They are used to explain the present invention together with the embodiments of the present invention and do not constitute a limitation of the present invention.

[0060] In the attached figure:

[0061] Figure 1 It is the finite element model of heavy-duty tire;

[0062] Figure 2 Figure 1 shows the heavy-duty tire loading test verification: (a) Heavy-duty tire mechanical vibration test system, (b) contact patch shape comparison, and (c) tire sinkage result comparison.

[0063] Figure 3 Validation of the heavy-duty tire modal experiment: (a) Schematic diagram of the modal test system, (b) comparison of free modal data;

[0064] Figure 4 is a flow chart of the method of the present invention;

[0065] Figure 5 The influence of static load on grounding characteristics: (a) grounding stress cloud diagram under different vertical forces, (b) grounding stress curve under different vertical forces, (c) relationship between grounding stress and vertical force;

[0066] Figure 6 is the change of ground contact length with vertical force;

[0067] Figure 7 The influence of vertical force on circumferential strain: (a) Circumferential strain curve of liner under different vertical forces, (b) Change of circumferential strain characteristic value under different vertical forces;

[0068] Figure 8 This is a comparison diagram of the angle difference of the characteristic points of the circumferential strain curve of the liner and the ground contact angle;

[0069] Figure 9 Model training results: (a) GWO-SVM convergence curve, (b) changes in circumferential strain eigenvalues ​​under different vertical forces;

[0070] Figure 10 The vertical force estimation result. DETAILED DESCRIPTION

[0071] The preferred embodiments of the present invention are described below with reference to the accompanying drawings. It should be understood that the preferred embodiments described herein are only used to illustrate and explain the present invention, and are not used to limit the present invention.

[0072] Example:

[0073] Refer to the attached Figure 1-10 As shown, a method for estimating the vertical force of a heavy-load tire based on circumferential strain analysis includes:

[0074] Step 1: Establish a finite element model of the heavy-duty tire.

[0075] Step 1.1: Use finite element software to create a finite element model of the heavy-duty tire. Specifically, after using CAD software to draw and create the heavy-duty tire's 2D structural model, use HYPERMESH software to mesh the 2D structural model and complete the remaining pre-processing steps for the tire's 2D finite element modeling.

[0076] Then refer to the center reference point and edit the heavy-duty tire two-dimensional finite element model through the inp file command Figure 1 (a) Rotation to heavy-duty tire 3D model Figure 1 (b). Considering that there are large gradients in stress distribution and strain levels in different parts of the tire during operation, and the impact on the tire analysis results is also quite different, if the rotation step size adopts a single size, the node signal can be obtained at a constant sampling frequency, which improves the calculation accuracy of the model to a certain extent and avoids stress mutations caused by step size changes. In finite element simulation, the finer the grid, the higher the simulation accuracy, but it increases the amount of calculation, resource consumption and reduces the convergence rate. Since the main area of ​​change of tire strain is before and after the contact area, the accuracy requirements for deformation and strain in the non-contact area are not high. When this embodiment rotates the two-dimensional model to generate a three-dimensional model, a variable rotation step size method is adopted, and the mesh is only refined near the contact area. While reducing the calculation cost and saving resources, it more realistically simulates the actual behavior of the tire contact area and improves the accuracy of the strain signal in the contact area.

[0077] Step 1.2: Use a heavy-duty tire mechanical vibration test system to conduct a heavy-duty tire loading test to obtain the contact patch shape and tire sinkage under different static loads, and compare the contact patch characteristics and vertical stiffness with the finite element model simulation results in step 1.1. Specifically:

[0078] Tire vertical stiffness is a key parameter characterizing tire performance, significantly impacting a vehicle's load-bearing capacity and ride comfort. A tire's contact patch directly influences its service life, wear, and force characteristics, significantly impacting vehicle safety.

[0079] This embodiment uses a heavy-load tire mechanical vibration test system Figure 2 (a) A heavy-duty tire loading test was conducted. The heavy-duty tire mechanical vibration test system is an existing device and will not be described here. The contact patch shape and tire sinkage under different static loads of the heavy-duty tire were obtained. The contact patch characteristics and vertical stiffness were verified by comparing with the finite element simulation results. The results are shown in Figure 2 (b) and (c) show that the shapes of the tire contact patch under each load are similar between the test and simulation. The tire sinkage changes in the same trend as the load increases, with the maximum error being 7.79%.

[0080] A modal test system was used to conduct modal testing to obtain the first eight radial vibration modes and frequencies of the heavy-duty tire rim in the free state, and the vibration characteristics were verified by comparing them with the finite element model simulation results in step 1.1. The details are as follows:

[0081] The modal parameters of a tire can characterize its vibration characteristics and are directly related to the tire's inflation pressure and constraint conditions. This embodiment builds a heavy-duty tire modal test system, such as Figure 3 (a) shows the heavy-duty tire modal test system, which is an existing device and will not be described in detail here. The modal test system includes: tire support device, force hammer and charge amplifier, data test system and PC computer. The modal test system is used to perform a force hammer test on the tire in the free state of the rim, and the first 8 radial vibration modes of the tire are extracted. The experimental test modal results are compared with the analytical modal results of the finite element simulation, as shown in Figure 2. Figure 3 (b), it is found that the order of the two vibration modes is consistent, and the maximum error of the characteristic frequencies corresponding to the same vibration mode is 5.49%.

[0082] The above experimental results show that the vertical stiffness and modal parameters of the heavy-duty tire finite element model established in step 1.1 are highly consistent with those of the actual tire, and can reliably reflect the true mechanical properties of the tire. The accuracy and authenticity of the model meet the conditions for subsequent experiments.

[0083] Step 2: During vehicle operation, only the tire tread is in direct contact with the ground. Sensors installed on the tread provide the most intuitive signal representation of tire deformation and stress. However, tread sensor signals are highly susceptible to external interference, resulting in a complex signal curve. Furthermore, sensor installation is challenging. Given that tire forces and deformation under static load and linear rolling are symmetrical about the tread centerline, the center of the tread was selected as the strain sensor mounting point.

[0084] The heavy-load tire finite element model established in step 1 is used to simulate static load conditions under different vertical forces. The tire ground contact stress cloud map and tread center point circumferential strain data set under different loads are obtained. The static load ground contact characteristics and static load circumferential strain of the heavy-load tire are analyzed, and the contact angle is estimated based on the circumferential strain of the inner liner.

[0085] Step 2.1: Use the heavy-duty tire finite element model of step 1 to simulate the static load conditions under different vertical forces, and obtain the tire ground stress cloud diagram under different loads ( Figure 5 a) and the tread center point circumferential strain data set, the static load ground contact characteristics of heavy-duty tires are analyzed. Specifically:

[0086] The heavy-duty tire finite element model in step 1 is used to simulate the static load conditions under different vertical forces, and the ground stress of the tire tread centerline is extracted and analyzed. The results are shown in Figure 5 .

[0087] from Figure 5 It can be seen that: as the vertical force increases, the shape of the contact patch changes from elliptical to rectangular, the tire contact patch length continues to increase, and the contact width basically stops changing after it grows to close to the tread width; the contact stress at the center point of the contact area and the maximum contact stress both increase rapidly and then slowly decrease, reaching a maximum when the vertical force is 28 kN; when the vertical force is greater than 47 kN, the maximum contact stress and the center point contact stress begin to differ significantly, and the contact stress curve changes from an upward convex parabola to a saddle shape, with the maximum contact stress point shifting from the center point to both sides.

[0088] Extracting the front and rear contact angles φ of heavy-duty tires based on the characteristics of the contact stress curve f and φ r The angle data set is combined with the ground contact length calculation formula (1) to obtain the ground contact length L data set under each vertical force, and compared with the finite element simulation value. The results are shown in Figure 6 The maximum error between the calculated results of the ground contact length formula and the simulation results is 1.3%, which shows high consistency. As the vertical force increases from 5kN to 80kN, the ground contact length and ground contact angle increase continuously, but the growth rate decreases continuously.

[0089] L=R·(sinφ f +sinφ r ) (1)

[0090] Where: R is the radius of the tire in the free state after inflation; the front and rear contact angles are equal in the static load state, φ f =φ r .

[0091] Step 2.2: Use the heavy-duty tire finite element model to simulate and analyze the inner liner circumferential strain curves of tires with standard tire pressure and different static load conditions. Specifically:

[0092] Finite element simulation analysis was performed on the circumferential strain curve of the inner liner of a tire with a standard tire pressure of 0.8 MPa and different static load conditions. The results are as follows: Figure 7As shown in the figure, it can be seen that when the vertical force increases from 5KN to 80KN, the baseline value of the circumferential strain curve does not change significantly due to the fact that the force in the non-contact area remains basically unchanged. As the vertical force increases, the valley value and the valley spacing angle of the curve both show a decreasing increase.

[0093] Combine Figure 5 (c) and Figure 7 (b) The curve peak value changes with vertical force in a similar manner to the ground stress, first rapidly increasing to a maximum value before slowly decreasing. As the vertical force increases from 5 kN to 28 kN, both the strain curve and the ground stress curve experience rapid growth. When the vertical force increases between 28 kN and 47 kN, the ground stress begins to decrease with the vertical force, while the strain curve peak increases only slightly. When the vertical force exceeds 47 kN, the strain peak begins to slowly decrease, and the strain curve near the contact center also develops a saddle shape. Under various vertical forces, the tire innerliner circumferential strain curve and the ground stress curve within the contact area are highly similar in shape.

[0094] Step 2.3: Analyzing Steps 2.1 and 2.2, it was found that the angle between adjacent valleys in the tire innerliner's circumferential strain curve, the tire contact patch angle, and the contact patch length all showed a positive correlation with vertical force, and the three curves showed similar trends. Therefore, the tire contact patch angle is closely related to the angle between valleys in the circumferential strain curve, and the tire contact patch angle can be characterized by characteristic parameters of the circumferential strain curve.

[0095] The finite element simulation results under 0.8 MPa standard pressure and static load conditions were extracted, and the contact angle was compared with the characteristic point spacing angle of the zero-order, first-order, and second-order derivative curves of the circumferential strain. The results of the characteristic point spacing angle of the strain curve under different vertical forces are shown in Table 1.

[0096] Table 1 Characteristic point spacing angles of strain curves under different vertical forces

[0097]

[0098] It can be seen that the valley spacing angle of the circumferential strain curve and the peak spacing angle of the second-order strain derivative are both greater than the ground contact angle, while the peak-to-valley spacing angle of the first-order strain curve is smaller than the ground contact angle. Furthermore, the error angle increases with increasing vertical force. Since it is difficult to accurately characterize the ground contact angle using only one type of strain curve, the average of multiple spacing angles is used as a ground contact angle characterization metric. Because the ground contact angle lies between the spacing angles of the zero-order, second-order, and first-order strain characteristic points, a ground contact angle characterization metric is proposed. Combined with the ground contact length calculation formula, ground contact lengths CA1, CA2, and CA3 are estimated, with errors from the ground contact angle being δ1, δ2, and δ3, respectively.

[0099]

[0100]

[0101]

[0102] Fz / KN <![CDATA[δ1 / %]]> <![CDATA[δ2 / %]]> <![CDATA[δ3 / %]]> 10 7.69 7.69 5.12 20 5.88 6.67 5.88 30 7.5 5.00 6.67 40 6.52 4.34 5.79 50 5.77 3.85 5.12 60 8.93 1.78 7.14 70 6.45 3.22 5.38

[0103] Table 2 shows that CA1, CA2, and CA3 all provide good characterization of contact angle. The errors of CA1 and CA3 are relatively stable under varying vertical forces, generally within the 5%-7% range. CA2 maintains an error within 4% under high loads, but exhibits a higher error under low loads. The main reason for the CA2 error variation is that under low loads, the contact angle and the characteristic angle of the first-order derivative of strain are relatively small, amplifying the effect of the model mesh accuracy on the angle. Given the standard load of a 16.0020 heavy-duty tire, which is 63,700 N, CA2 is a more suitable characterization of contact angle.

[0104] Step 3: Based on step 2, a heavy-load tire vertical force estimation model is established, and vertical force-ground angle simulation data under different static loads are extracted to train and test the heavy-load tire vertical force estimation model, thereby predicting the vertical force. Specifically:

[0105] Step 3.1: Establish a vertical force estimation model based on support vector regression machine, and establish the optimal solution formula of the vertical force estimation model based on support vector regression machine through transformation. The error penalty coefficient C and kernel function parameter γ are the key factors affecting the model prediction performance. The error penalty coefficient C and kernel function parameter γ are optimized by the gray wolf algorithm.

[0106] The process of establishing the optimal solution formula of the vertical force estimation model of the support vector regression machine in step 3.1 is as follows:

[0107] Step 3.1.1.1: Use support vector regression machine to make vertical force regression prediction, and define the training set as: D = {(x1,Fz1), (x2,Fz2),…, (x m ,Fz m )},Fz i ∈R, Then the vertical force estimation model is:

[0108] f z (x) = w T Φ(x)+b (2)

[0109] Where, i∈(1,2,3…,m), m is the number of training sets, f z (x) is the predicted value of vertical force, Fz i is the finite element simulation value of vertical force, φ fi 、φ ri is the finite element simulation value of the front and rear contact angles, L iis the finite element simulation value of the front and rear contact angles, w is the weight vector, b is the bias vector, and Φ(x) represents the value of x i Feature vector after mapping to high-dimensional feature space;

[0110] Step 3.1.1.2: Introduce slack variable ξ i * and ξ i , transforming the support vector regression machine regression prediction problem into a minimum optimization problem:

[0111]

[0112] In the formula, C is the penalty coefficient, ε is the insensitivity coefficient, Fz i is the finite element simulation value of vertical force;

[0113] Step 3.1.1.3: Introduce the Lagrange coefficient and transform the minimum optimization problem in step 3.1.2 into a dual problem:

[0114]

[0115] Where, a i , a j is the Lagrange multiplier, K(x i ,x j ) is the kernel function;

[0116] The kernel function is:

[0117]

[0118] Where γ is the kernel function parameter;

[0119] Step 3.1.1.4: Establish the optimal solution formula of the vertical force estimation model of the support vector regression machine according to formula (4):

[0120]

[0121] The step 3.1 optimizes the error penalty coefficient C and the kernel function parameter γ through the gray wolf algorithm. The parameter set is first hierarchically layered, with the first three high-level parameter sets α, β, and δ leading the low-level parameter sets. Each iteration will re-classify. After the hierarchy is established, the optimal parameter set is searched and surrounded. The positions of the high-level parameter sets α, β, and δ are first established, and then the positions of other parameter sets are updated according to the positions of the high-level parameter sets to surround the optimal parameter set. During the surrounding process, the optimal parameter set is searched by adjusting μ and B. In the continuous hierarchical surrounding search, each generation of α is the optimal solution in the current parameter set, and guides the next generation of parameter sets to approach the optimal parameter set. When the iteration reaches the maximum, the last generation of α parameter set is the optimal set of all generated parameter sets, achieving optimal acquisition. Specifically:

[0122] (1) Parameter set hierarchical stratification: randomly generating parameter clusters in the search space Then, the three parameter sets with the best fitness in the parameter cluster are marked as and The rest is divided equally into The grading process is repeated after each iteration;

[0123] Where, is the generated parameter set of the i-th group of penalty coefficient C and kernel function coefficient γ, k is the number of generated parameter sets, α, β, and δ are the three best parameters in the contemporary parameter set, and the degree of optimality of the three decreases in turn; ω is the other parameter set after removing α, β, and δ; is the i-th set of penalty coefficients and kernel function parameters in ω; n = k-3;

[0124] (2) Searching for the optimal parameter set: Before obtaining the optimal parameter set, its position is determined first. The search mode and search direction of the optimal parameter set are adjusted by the coordination coefficient vectors μ and B, and the random vectors r1 and r2. When |μ|>1, the parameter cluster performs a global search; when |μ|<1, the parameter cluster performs a local search in a certain area.

[0125] D=|BX p (t)-X(t)| (7)

[0126] X(t+1)=X p (t)-μD (8)

[0127] μ=2ar2-a (9)

[0128] B=2r1 (10)

[0129] Where: D is the distance between the current parameter set and the optimal parameter set; X p(t) is the position vector of the optimal parameter set of the tth generation; X(t) is the position vector of the current parameter set of the tth generation; a decreases linearly from 2 to 0 during the entire iteration process; r1 and r2 are random vectors in [0, 1];

[0130] (3) Optimal acquisition: parameter clusters after iteration and The three parameter sets are closest to the optimal parameter set, and the three parameter sets use the distance between themselves and the optimal parameter set to jointly guide the other Parameter set adjustment position to obtain the optimal,

[0131]

[0132]

[0133]

[0134] Where: D α 、D β 、D δ are the distances between the α, β, δ parameter sets and the current parameter set respectively; B1, B2, B3 are random vectors; X1, X2, X3 are the position vectors of the current parameter set after the movement guided by the α, β, δ parameter sets respectively; X(t+1) defines the final position of the current parameter set.

[0135] Step 3.2: Combine the strain data set, the ground contact angle characterization index CA2, and the ground contact length calculation formula in step 2 to obtain a feature set with the ground contact angle and ground contact length as input and the vertical load as output. 28 of the 56 data sets in the feature set are used as model training sets and input into the vertical force estimation model in step 3.1 for training. The penalty coefficient C and kernel function parameter γ of the model are adjusted. The prediction performance of the vertical force estimation model is then tested using the remaining 28 test set data to achieve the prediction of vertical force.

[0136] In summary, this paper established a finite element model of a 16.00R20 heavy-duty tire, and verified the vertical stiffness and vibration characteristics of the model through loading tests and modal experiments. The influence of rolling speed and load on the circumferential strain curve of the tire inner liner was analyzed using finite element simulation. A touchdown angle characterization index was proposed, and its reliability was verified by comparing the finite element simulation results. Using the estimated values ​​of touchdown angle and touchdown length as identification features, a vertical force estimation model was established by combining the Grey Wolf optimization algorithm and support vector regression machine.

[0137] The results show that the contact angle and contact length decrease with increasing vertical force; the spacing between extreme points of the circumferential strain curve is sensitive to vertical force changes, and the greater the vertical force, the larger the spacing; it is feasible to use the average of the spacing angles of the characteristic points of the zero-order, first-order, and second-order derivatives of the circumferential strain as a characterization indicator of the tire contact angle, and the average of the first-order and second-order spacing angles is the most effective characterization indicator; the vertical force estimation model using tire contact angle and contact length as identification features of the support vector machine has an estimated vertical force error within 2%, and can accurately estimate the vertical force.

[0138] The basic principles, main features, and advantages of the present invention are shown and described above. Those skilled in the art should understand that the present invention is not limited to the foregoing embodiments. The foregoing embodiments and descriptions are merely illustrative of the principles of the present invention. Various changes and modifications may be made to the present invention without departing from the spirit and scope of the present invention. Such changes and modifications are intended to fall within the scope of the present invention. The scope of protection claimed in the present invention is defined by the appended claims and their equivalents.

Claims

1. A method for estimating the vertical force of a heavy-duty tire based on circumferential strain analysis, characterized by: include: Step 1: Establish a finite element model of heavy-duty tire; Step 2: Use the heavy-duty tire finite element model established in Step 1 to simulate static load conditions under different vertical forces. Then, analyze the heavy-duty tire's static ground contact characteristics and static circumferential strain curve, and estimate the contact angle based on the inner liner's circumferential strain. The step 2 is specifically as follows: Step 2.1: Use the heavy-duty tire finite element model from Step 1 to simulate static load conditions under different vertical forces. Obtain tire contact stress cloud maps and tread center point circumferential strain datasets under different loads. Analyze the heavy-duty tire's static contact characteristics and obtain simulation datasets of front and rear contact angles and contact lengths under different static loads. Step 2.2: Use the heavy-duty tire finite element model to simulate and analyze the inner liner circumferential strain curves of tires with standard tire pressure and different static load conditions; Step 2.3: Based on the analysis of steps 2.1 and 2.2, the ground contact angle is estimated based on the circumferential strain of the liner, and a ground contact angle characterization index is proposed. The ground contact length is estimated by combining the ground contact length calculation formula; Step 3: Based on step 2, a heavy-load tire vertical force estimation model is established. Vertical force-ground angle simulation data under different static loads are extracted to train and test the heavy-load tire vertical force estimation model, thereby predicting the vertical force. The step 3 is specifically as follows: Step 3.1: Establish a vertical force estimation model based on a support vector regression machine and establish the optimal solution formula for the vertical force estimation model based on the support vector regression machine through transformation. The error penalty coefficient C and the kernel function parameter γ are key factors affecting the model's prediction performance. The error penalty coefficient C and the kernel function parameter γ are optimized using the gray wolf algorithm. Step 3.2: Combine the strain data set, ground contact angle characterization index, and ground contact length calculation formula in step 2 to obtain a feature set with ground contact angle and ground contact length as input and vertical load as output. Use 28 of the 56 data sets in the feature set as the model training set and input them into the vertical force estimation model in step 3.1 for training. Adjust the model's penalty coefficient C and kernel function parameter γ. Then, use the remaining 28 test set data sets to test the prediction performance of the vertical force estimation model and realize the prediction of vertical force.

2. The method for estimating the vertical force of a heavy-load tire based on circumferential strain analysis according to claim 1, characterized in that: The step 1 comprises: Step 1.1: Use finite element software to establish a finite element model of the heavy-duty tire; Step 1.2: Conduct a heavy-duty tire loading test using a heavy-duty tire mechanical vibration test system to obtain the contact patch shape and tire sinkage under different static loads. Verify the contact patch characteristics and vertical stiffness by comparing them with the finite element model simulation results from step 1.

1. Conduct a modal test using a modal test system to obtain the first eight radial vibration mode shapes and frequencies of the heavy-duty tire rim in the free state. Verify the vibration characteristics by comparing them with the finite element model simulation results from step 1.

1.

3. The method for estimating the vertical force of a heavy-load tire based on circumferential strain analysis according to claim 2, characterized in that: The process of establishing the optimal solution formula of the vertical force estimation model of the support vector regression machine in step 3.1 is as follows: Step 3.1.1.1: Use support vector regression machine to make vertical force regression prediction, and define the training set as: D = {(x1,Fz1), (x2,Fz2),…, (x m ,Fz m )},Fz i ∈R, Then the vertical force estimation model is: f z (x)=w T Φ(x)+b (2) Where, i∈(1,2,3…,m), m is the number of training sets, f z (x) is the predicted value of vertical force, Fz i is the finite element simulation value of vertical force, φ fi 、φ ri is the finite element simulation value of the front and rear contact angles, L i is the finite element simulation value of the front and rear contact angles, w is the weight vector, b is the bias vector, and Φ(x) represents the value of x i Feature vector after mapping to high-dimensional feature space; Step 3.1.1.2: Introduce slack variable ξ i * and ξ i , transforming the support vector regression machine regression prediction problem into a minimum optimization problem: In the formula, C is the penalty coefficient, ε is the insensitivity coefficient, Fz i is the finite element simulation value of vertical force; Step 3.1.1.3: Introduce Lagrange multipliers to transform the minimum optimization problem in step 3.1.2 into solving the dual problem: Where, a i , a j is the Lagrange multiplier, K(x i ,x j ) is the kernel function; The kernel function is: Where γ is the kernel function parameter; Step 3.1.1.4: Establish the optimal solution formula of the vertical force estimation model of the support vector regression machine according to formula (4):

4. The method for estimating the vertical force of a heavy-load tire based on circumferential strain analysis according to claim 3, characterized in that: The step 3.1 of optimizing the error penalty coefficient C and the kernel function parameter γ by the gray wolf algorithm includes: (1) Parameter set hierarchical stratification: randomly generating parameter clusters in the search space Then, the three parameter sets with the best fitness in the parameter cluster are marked as and The rest is divided equally into The grading process is repeated after each iteration; Where, is the generated parameter set of the i-th group of penalty coefficient C and kernel function coefficient γ, k is the number of generated parameter sets, α, β, and δ are the three best parameters in the contemporary parameter set, and the degree of optimality of the three decreases in turn; ω is the other parameter set after removing α, β, and δ; is the i-th set of penalty coefficients and kernel function parameters in ω; n = k-3; (2) Searching for the optimal parameter set: Before obtaining the optimal parameter set, its position is determined first. The search mode and search direction of the optimal parameter set are adjusted by the coordination coefficient vectors μ and B, and the random vectors r1 and r2. When |μ|>1, the parameter cluster performs a global search; when |μ|<1, the parameter cluster performs a local search in a certain area. D=|BX p (t)-X(t)| (7) X(t+1)=X p (t)-μD (8) μ=2ar2-a (9) B＝2r1 (10) Where: D is the distance between the current parameter set and the optimal parameter set; X p (t) is the position vector of the optimal parameter set of the tth generation; X(t) is the position vector of the current parameter set of the tth generation; a decreases linearly from 2 to 0 during the entire iteration process; r1 and r2 are random vectors in [0, 1]; (3) Optimal acquisition: parameter clusters after iteration and The three parameter sets are closest to the optimal parameter set, and the three parameter sets use the distance between themselves and the optimal parameter set to jointly guide the other Parameter set adjustment position to obtain the optimal, Where: D α 、D β 、D δ are the distances between the α, β, δ parameter sets and the current parameter set respectively; B1, B2, B3 are random vectors; X1, X2, X3 are the position vectors of the current parameter set after the movement guided by the α, β, δ parameter sets respectively; X(t+1) defines the final position of the current parameter set.

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