Combined estimation method of tire vertical force and cornering force based on in-utero strain analysis

Abstract

The application discloses a combined estimation method for tire vertical force and side force based on in-utero strain analysis, and comprises the following steps: S1, establishing a tire finite element three-dimensional model; S2, calculating a tire grounding angle φ and a grounding length L based on the tire finite element three-dimensional model established in the step S1 according to in-utero strain; S3, estimating a tire vertical force F based on the tire grounding angle φ and the grounding length L calculated in the step S2 by using a support vector regression machine; S4, simulating and calculating a tire side deflection working condition by using the tire finite element three-dimensional model, taking a last valley value h2 of a side deflection circumferential strain difference curve as a characteristic of a side deflection force F ; S5, establishing a combined estimation model for the vertical force and the side deflection force based on the characteristic h2 of the tire vertical force F and the side deflection force F, and estimating an actual side deflection force of the tire. c c z y z y The application is applicable to static load, rolling and side deflection working conditions, can accurately estimate the vertical force and the side deflection force, and the error between an estimated value and a finite element simulation value is less than 3%.​​​​​

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of tire cornering force calculation, and particularly relates to a tire vertical force and cornering force combined estimation method based on tire internal strain analysis. BACKGROUND

[0002] As the only component directly contacting with the road surface, the tire transmits most of the forces acting on the vehicle to the whole vehicle during the running process, and its mechanical properties directly affect the performance indicators of the vehicle, such as the operation stability, the smoothness, the braking performance, the passability and the like, and are an important guarantee for the safe and efficient driving of the vehicle. Therefore, real-time acquisition of the tire force information is of great significance to the vehicle dynamics control. However, at present, the tire is still only used as a passive component, and cannot directly realize the measurement and acquisition of the force acting thereon.

[0003] Many scholars previously deduced and estimated the tire force through the vehicle dynamics model, and described and characterized the tire mechanical behavior by combining the empirical model or the analytical model. However, these methods are essentially indirect acquisition of the tire force, and both the empirical model and the analytical model are tire models with high simplification degree, large use limitation and single research emphasis. The expression formula and the approximate acquisition of the formula parameters of such tire models are different from the actual behavior of the tire, it is difficult to express the clear relationship between the tire force and the deformation, and the research on the mechanical properties of the tire lacks accurate basis, which greatly hinders the accurate estimation of the tire force.

[0004] In recent years, with the rapid development of electronic information technology and sensor technology, some scholars at home and abroad use sensors to acquire tire dynamic information, and realize real-time estimation of the tire force by combining estimation algorithms. Wang Guolin, Ding Junjie and the like divide the tire force signal sensitivity response area by using the sobol sensitivity analysis method, and establish a tire longitudinal and lateral force estimation model based on the radial basis neural network with displacement and acceleration signals as inputs; Zhao Jian, Lu Yanhui and the like establish a three-axis MEMS acceleration test system to analyze and extract the acceleration signal characteristics, and realize the estimation of the vertical and longitudinal forces by combining the BP neural network. Tuononen combines optical sensors to realize the tire body deflection measurement, and proposes a tire three-direction force estimation algorithm through linear regression. The acceleration sensor is small in size, compact in structure, less affected by temperature, and is widely used in intelligent tires, but the acceleration signal is very sensitive to the noise generated by the road surface, and it is difficult to accurately extract the acceleration signal characteristics; the optical sensor is low in price and strong in anti-interference performance, but its installation and calibration process is complex and troublesome, and it is easily affected by dust, which reduces the signal accuracy.

[0005] The strain sensor also has the advantages of flexibility, compactness, low price and easy installation, and the signal is more simple and pure. With the development of flexible sensing technology, the patch type strain sensor has low hardness and high ductility, and can almost adapt to all strains, and has great application space in the development of intelligent tires. SUMMARY

[0006] In order to solve the above problems, the present application provides a tire vertical force and cornering force combined estimation method based on intra-tire strain analysis, which is suitable for static load, rolling and cornering conditions and can accurately estimate the vertical force and cornering force.

[0007] In order to achieve the above-mentioned purpose, the technical solution adopted by the present application is as follows:

[0008] The tire vertical force and cornering force combined estimation method based on intra-tire strain analysis comprises the following steps:

[0009] S1: Establish a tire finite element three-dimensional model;

[0010] S2: Based on the tire finite element three-dimensional model established in step S1, calculate the tire grounding angle φ c and the grounding length L based on intra-tire strain;

[0011] S3: Based on the tire grounding angle φ c and the grounding length L calculated in step S2, use support vector regression machine to estimate the tire vertical force F z ;

[0012] S4: Perform simulation calculation on the tire cornering condition through the tire finite element three-dimensional model, and take the last valley value h2 of the tire side circumferential strain difference curve as the characteristic feature of the cornering force F y ;

[0013] S5: Based on the tire vertical force F z in step S3 and the characteristic feature h2 of the cornering force F y in step S4, establish a vertical force and cornering force combined estimation model to estimate the actual cornering force of the tire.

[0014] Further, the specific operation of step S1 comprises the following steps:

[0015] S101: Use CAD to construct a tire finite element two-dimensional cross-section structure model;

[0016] S102: Rotate the tire finite element two-dimensional cross-section structure model around the center reference point to a tire three-dimensional model, and in the rotation process, use the variable rotation step method to refine the tire contact area grid;

[0017] S103: Verify the grounding footprint characteristics and vertical stiffness of the tire three-dimensional model established in step S102.

[0018] Further, the specific operation of step S2 comprises the following steps:

[0019] S201: Obtain the linear circumferential strain signal in the inner liner of the tire under static load by finite element, and perform data processing;

[0020] S202: Calculate the average angle φ of the peak interval angle of the zero order and the first order of the circumferential strain c As a representation index of the ground contact angle, φ c =(φ2+φ3) / 2, wherein φ2 is the peak interval angle of the zero order of the circumferential strain, and φ3 is the peak interval angle of the first order;

[0021] S203: Calculate the tire ground contact length L according to the ground contact angle

[0022] L=R·(sinφ f +sinφ r )

[0023] wherein R is the free state radius of the tire after inflation, φ f and φ r are the ground contact angles before and after the static load state respectively, the ground contact angles before and after the static load state are equal, and φ f =φ r .

[0024] Further, the calculation method of the tire vertical force F z in step S3 is as follows:

[0025] Let D={(x1, F z1 ), (x2, F z2 ), …, (x m , F zm )}

[0026] wherein, F zi is the finite element simulation value of the vertical force, i∈(1, 2, 3…, m); is the estimated value of the front and rear ground contact angles, is the estimated value of the ground contact length, and m is the number of training sets;

[0027] The estimated regression model of the tire vertical force F z is

[0028] f z (x)=w T Φ(x)+b

[0029] wherein w is a feature weight vector, f z (x) is a vertical force prediction value, b is a bias vector, and Φ(x) represents a feature vector after x i is mapped to a high-dimensional feature space.

[0030] Further, the specific operation of step S3 includes the following steps,

[0031] S301: Obtain multiple sets of circumferential strain and load data of the inner liner in the tread under static load, rolling, and cornering conditions through finite element simulation, and calculate the ground contact angle φ c and the ground contact length L, and establish the ground contact angle φ c and the ground contact length L-load data set;

[0032] S302: Identify the ground contact angle φ c and the ground contact length L as input features, and use the support vector regression machine to predict the vertical force F z of the tire as the estimated output; z

[0033] S303: Divide the data sets in the data set into a training set and a test set, use the data sets in the training set for model training, and then detect the prediction performance of the support vector regression machine through the data sets in the test set to realize the estimation of the vertical force F z .

[0034] Further, the specific operation of step S4 includes the following steps,

[0035] S401: Perform simulation calculation on the tire cornering condition through the finite element three-dimensional model of the tire, and extract and analyze the tire model ground stress cloud map and cornering characteristics;

[0036] S402: Extract and analyze the inner liner strain of the tire tread, shoulder, and sidewall under the cornering condition, and determine the part most sensitive to circumferential strain response under the cornering state of the tire;

[0037] S403: Extract and analyze the circumferential strain difference curve of the symmetric point of the inner liner of the tire sidewall under different loads and different cornering angles, and determine the last valley value h2 of the circumferential strain difference curve of the sidewall as the characteristic feature of the cornering force F y ;

[0038] S404: Normalize and compare the characteristic values h2 under different loads.

[0039] Further, the vertical force and cornering force joint estimation model in step S5 is:

[0040]

[0041]

[0042] In the formula, h b2 is the unit characteristic value after processing h2 combined with the vertical force F z ; k3 is the normalized proportion of the characteristic value h2 under the 3t load; F yb is the unit cornering force. ​

[0043] Further, the specific operation of step S5 comprises the following steps,

[0044] S501: Obtain multiple sets of characteristic values h2 and vertical forces F by finite element simulation z According to the formula Convert the characteristic values h2 and the vertical forces F z Into unit characteristic values h b2 ;

[0045] S502: Construct a [h b2 , F yb ] data set, input a support vector regression machine, and calculate the cornering force F y by the support vector regression machine.

[0046] S503: Divide the data sets in the data set into a training set and a test set, use the data sets in the training set to train a vertical force and cornering force combined estimation model, and then detect the prediction performance of the model by the data sets in the test set to realize estimation of the cornering force F y .

[0047] The beneficial effects of the present application are:

[0048] 1. In the present application, the tire vertical force and cornering force combined estimation method based on tire inner strain analysis first establishes a tire finite element three-dimensional model and verifies the effectiveness of the model from the vertical stiffness and vibration characteristics; based on the analysis of the circumferential strain signal of the tire inner liner, the ground contact angle and the ground contact length are characterized by the peak spacing angle of the circumferential strain curve, and the characterization accuracy under static load, rolling and cornering conditions is compared; through the analysis of the circumferential strain of the symmetric point in the tire, the cornering force characterization features are extracted, and the linear relationship between the vertical force and the cornering force characterization features is analyzed; a vertical force and cornering force combined estimation model is established by using a support vector regression machine, the ground contact angle and the ground contact length are first used as input identification features to estimate the vertical force, and then the cornering force is estimated by combining the vertical force estimation with the cornering force characterization features, and the estimation accuracy of the model is verified by finite element test. The results show that: the characterization error of the average of the peak spacing angle of the zero-order and first-order strain curves on the ground contact angle and the ground contact length is within 4.5%; the vertical force and cornering force combined estimation method based on tire inner strain analysis is applicable to static load, rolling and cornering conditions, and can accurately estimate the vertical force and cornering force, and the error between the estimated value and the finite element simulation value is less than 3%.

[0049] 2、The tire vertical force and side force combined estimation method based on intrauterine strain analysis in the application is more economical than the existing side slip angle estimation method, the strain difference can be measured through the patch type strain gauge, the operation is simple; the black box system is adopted, the side slip angle is directly estimated through the input and output relationship of the support vector machine, the influence of the model error and method error caused by the complex tire formula is reduced, and the estimation process is more simple and efficient. BRIEF DESCRIPTION OF DRAWINGS

[0050] Figure 1 It is a schematic diagram of the tire finite element model of the application.

[0051] Figure 2 It is a tire footprint shape comparison chart of the application.

[0052] Figure 3 It is a heavy load tire modal shape chart of the application.

[0053] Figure 4 It is a comparison chart of the circumferential strain peak angle difference of the inner liner and the ground angle of the application.

[0054] Figure 5 It is a ground parameter representation effect curve chart under different loads of the application.

[0055] Figure 6 It is a vertical force estimation flow chart of the application.

[0056] Figure 7 It is a vertical force estimation effect curve of the application.

[0057] Figure 8 It is a side slip tire ground stress nephogram of the application.

[0058] Figure 9 It is a curve chart of the relationship between the side slip characteristics and the side slip angle of the application.

[0059] Figure 10 It is a multi-point strain chart of the side slip state tire of the application.

[0060] Figure 11 It is a curve chart of the influence of the side slip angle on the circumferential strain difference of the tire side.

[0061] Figure 12 It is a histogram of the correlation coefficient of the strain characteristic value and the side slip force of the application.

[0062] Figure 13 It is a curve chart of the variation law of the characteristic value h2 and the side slip force with the side slip angle of the application.

[0063] Figure 14 It is a normalized comparison curve chart of the characteristic value h2 under different loads of the application.

[0064] Figure 15 This is a flowchart illustrating the combined estimation of vertical force and lateral force according to the present invention.

[0065] Figure 16 This is the result of the lateral force estimation in this invention. Detailed Implementation

[0066] To enable those skilled in the art to better understand the technical solutions of the present invention, the technical solutions of the present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0067] The method for jointly estimating tire vertical force and lateral force based on in-tire strain analysis includes the following steps.

[0068] S1: Establish a finite element 3D model of the tire;

[0069] Specifically, S101: Construct a two-dimensional finite element cross-sectional structure model of a tire using CAD; select an appropriate element density using HYPERMESH to divide the structural model, and then import it into ABAQUS software to assign material properties, element types, boundary conditions, etc. to complete the establishment of the finite element tire cross-sectional model.

[0070] S102: Using the inp file command, the two-dimensional finite element cross-sectional structure model of the tire is rotated around the central reference point to form a three-dimensional tire model; taking a 16.00R20 heavy-duty tire as the research object, the finite element model of the heavy-duty tire is attached. Figure 1 As shown, (a) is a two-dimensional cross-sectional model of the tire, and (b) is a three-dimensional model of the tire. Since the accuracy requirement for strain signals in the docking area is much higher than that in the non-docking area, a variable rotation step size method is used during rotation to refine the mesh in the docking area, thereby obtaining more accurate and distinct docking area signals.

[0071] S103: Verify the ground imprint characteristics and vertical stiffness of the tire three-dimensional model established in step S102.

[0072] More specifically, this invention employs a heavy-duty tire mechanical vibration testing system to conduct static loading tests on heavy-duty tires. The ground contact patch characteristics and vertical stiffness of the finite element model are verified through ground contact and subsidence measurements. The test tire pressure is the standard tire pressure of 0.79 MPa. The comparison results of the finite element simulation and experimental results of the tire ground contact patch are attached. Figure 2 As shown in Table 1 below, the results of the subsidence comparison are as follows.

[0073] Table 1 Comparison of Tire Sinking Amount

[0074]

[0075] From the appendix Figure 2As can be seen from Table 1, the tire footprint test results under different loads are consistent with the simulation results; the maximum error of the tire sinking amount results is 7.2%, and the model can accurately describe the tire ground characteristics.

[0076] Then, the hammering experiment is carried out on the tire in the free state of the rim through the heavy-duty tire modal test system, the first 8 orders of radial vibration modal shapes and frequencies of the tire are extracted, and the vibration characteristics of the model are verified by comparing the finite element calculation results, and the results are shown in Table 2 and the following Figure 3 From Table 2 and the following Figure 3 , it can be found that the test results and the simulation results are consistent in the vibration mode sequence, and the modal frequency error corresponding to the same vibration mode is less than 6%.

[0077] Table 2 Tire modal characteristic frequency

[0078]

[0079] The above experimental results show that the simulation results of the ground characteristics and the vibration characteristics of the tire finite element three-dimensional model are consistent with the experimental results of the real tire, the finite element three-dimensional model has high precision and good effectiveness, and can accurately represent the real mechanical characteristics of the tire.

[0080] Further, S2: calculating the tire ground angle φ c and the ground length L based on the strain in the tire according to the tire finite element three-dimensional model established in step S1.

[0081] Specifically, S201: obtaining the circumferential strain signal of the inner liner of the tire under static load through finite element, and performing data processing, first-order derivation and second-order derivation on the axial strain, and the results are shown in the following Figure 4 From the following Figure 4 , it can be seen that the actual ground angle φ1 of the tire is located between the circumferential strain zero order and the signal characteristic angle of the strain first-order and second-order derivatives, therefore, the average angle φ c between the circumferential strain zero order and the first-order peak value interval angle is selected as the representation index of the ground angle.

[0082] S202: calculating the average angle φ c between the circumferential strain zero order and the first-order peak value interval angle as the representation index of the ground angle, φ c = (φ2+φ3) / 2, wherein φ2 is the circumferential strain zero-order peak value interval angle, and φ3 is the first-order peak value interval angle.

[0083] S203: calculating the tire ground length L

[0084] L = R·(sinφ f +sinφ r )

[0085] In the formula, R is the radius of the tire in its free state after inflation, and φ f and φ r These are the grounding angles before and after the static load state, respectively, and the grounding angles before and after the static load state are equal, φ. f =φ r .

[0086] Obtain the simulated value φ1 and the characterized value φ of the grounding angle under different loads. c Calculate the grounding lengths L1 and L2 using the grounding length calculation formula. c The results are attached. Figure 5 As shown, the comparison reveals the characteristic angle φ c The average error is 1.7%, and the grounding length characterization value L1 and the finite element simulation value L c The maximum error is 1.2%, φ c and L c It has good characterization accuracy.

[0087] Furthermore, to investigate the influence of rolling and lateral slip conditions on tire contact characteristics, finite element analysis was used to simulate and analyze the combined conditions of different rolling speeds and lateral slip angles under a 5t load and a 0.8MPa tire pressure, obtaining the simulated value φ1 and the characterized value φ of the tire centerline contact angle. c The results are shown in Table 3 below.

[0088] Table 3. Grounding Angle of Tire Tread Centerline

[0089]

[0090] As shown in Table 3, during the process of changing the rolling speed from 30km / h to 100km / h and the slip angle from 1° to 10°, the contact angle of the tread centerline showed a very small change. The simulated value φ1 and the characterized value φ c The maximum errors for the two under static loads are 3.8% and 1% respectively, so φ c The centerline grounding angle can also accurately characterize lateral slip and rolling conditions.

[0091] Furthermore, S3: Based on the tire contact angle φ calculated in step S2 c Given the ground contact length L, the vertical force F of the tire is calculated using a support vector regression machine. z Make an estimate;

[0092] Specifically, from the appendix Figure 5 It can be seen that the vertical force has a nonlinear relationship with the grounding angle and grounding length. Support vector regression converges faster and approximates the nonlinear function better than polynomial fitting. The vertical force estimation process is shown in the attached figure. Figure 6 As shown, the specific steps include:

[0093] S301: Obtain 60 sets of inner liner midline circumferential strain and load data of the tire tread under static load, rolling, and cornering conditions through finite element simulation, calculate the ground angle φ c and the ground length L, and establish the ground angle φ c , the ground length L-load data set;

[0094] S302: Identify the ground angle φ c and the ground length L as input features, and the tire vertical force F z as the estimated output, and use support vector regression (SVR) to predict the tire vertical force F z ;

[0095] The calculation method of the tire vertical force F z is:

[0096] Let D = {(x1, F z1 ), (x2, F z2 ), …, (x m , F zm )}

[0097] In the formula, F zi is the vertical force finite element simulation value, i ∈ (1, 2, 3…, m); is the estimated value of the front and rear ground angle, is the estimated value of the ground length, and m is the number of training sets;

[0098] The estimated regression model of the tire vertical force F z is

[0099] f z (x) = w T Φ(x) + b

[0100] In the formula, w is the feature weight vector, f z (x) is the vertical force prediction value, b is the bias vector, and Φ(x) represents the feature vector after mapping x i to a high-dimensional feature space.

[0101] S303: Divide the data sets in the data set into training sets and test sets, where the training sets contain 30 data sets and the test sets contain 30 data sets. Use the 30 data sets in the training set for model training, and then use the remaining 30 data sets in the test set to detect the prediction performance of the support vector regression machine to estimate the vertical force F z . The model prediction effect is shown in the attached Figure 7 . As can be seen from the attached Figure 7 , the root mean square error of the test set is 0.2987 KN, the maximum absolute error is 1.31%, and the determination coefficient reaches 0.9998, which can accurately estimate the tire vertical force.

[0102] Furthermore, S4: The tire sidewall condition is simulated and calculated using a three-dimensional finite element model of the tire, and the last valley value h2 of the circumferential strain difference curve of the tire sidewall is taken as the sidewall force F. y Characteristic features;

[0103] Specifically, S401: Simulate the tire side slip condition using a finite element 3D model of the tire, and extract and analyze the ground stress cloud map and side slip characteristics of the tire model.

[0104] Appendix Figure 8 The tire ground contact stress cloud diagrams for a 5t load, a rolling speed of 70km / h, and different sideslip angles show that when the tire slips, the shape of the ground contact mark changes from rectangular to triangular. The area of ​​maximum ground stress shifts from the center area to the tire shoulder area as the sideslip angle increases. Under small sideslip angle conditions, the ground contact area decreases significantly and the ground stress increases rapidly as the sideslip angle increases. After the sideslip angle reaches 5°, the shape of the ground contact mark is fixed as triangular, and the distribution of ground stress area, ground shape, and ground contact mark area basically no longer change. The ground stress shows a trend of first increasing and then decreasing within a small range as the sideslip angle increases.

[0105] Appendix Figure 9 This diagram illustrates the relationship between sideslip characteristics and sideslip angle. (a) shows the curve relating lateral force to sideslip angle, and (b) shows the curve relating aligning moment to sideslip angle. (From the attached diagram...) Figure 9 As can be seen, the lateral force initially increases nearly linearly with the increase of the sideslip angle, then the rate of increase decreases rapidly after the sideslip angle reaches 4°, and it basically reaches a saturation value at a sideslip angle of 6°. After that, the rate of increase tends to 0, and the lateral force basically no longer changes. Under the condition of a constant friction coefficient, the saturation value of the lateral force increases proportionally with the increase of the load, while the sideslip angle required to reach saturation is not affected by the load. The self-aligning torque increases rapidly to a peak value with the increase of the sideslip angle, then decreases and eventually tends to 0. The self-aligning torque reaches its maximum value when the sideslip angle reaches 2.5°. At the same sideslip angle, the self-aligning torque increases with the increase of the load, and the steering maneuverability decreases.

[0106] S402: To study the strain-sensitive areas of the tire, strain analysis was performed on the inner liner layers of three parts: the tire tread, shoulder, and sidewall, under lateral slip conditions. The results are shown in the attached figure. Figure 10 As shown, (a) represents the strain of the inner liner at the tire cross-section strain extraction point, (b) represents the tire circumferential strain, and (c) represents the tire radial strain. (See attached diagram.) Figure 10As shown in (b) and (c), under tire sideslip conditions, the amplitudes of both circumferential and radial strains on the opposite side of the sideslip are greater than those at other points; the closer to the tire tread centerline, the smaller the peak-to-valley difference in the strain curve; the circumferential strain on the sidewall, both in terms of single-point strain amplitude and strain difference at symmetrical points, is greater than that of the radial strain. Therefore, under sideslip conditions, the sidewall is more sensitive to strain response than other parts, especially to circumferential strain.

[0107] S403: Extract and analyze the circumferential strain difference curves of symmetrical points in the tire sidewall liner under different loads and sideslip angles, and determine the last valley value h2 of the sidewall circumferential strain difference curve as the sideslip force F. y Characteristic features;

[0108] Based on the strain sensitivity analysis results, the circumferential strain of the tire sidewall, which exhibits high sensitivity in the lateral force sensitive response, was selected as the research object. Considering the significant asymmetry between the left and right tire sides after being subjected to lateral force, the circumferential strain difference curves at symmetrical points of the tire sidewall liner under different loads, rolling speeds of 70 km / h, and different sideslip angles were extracted and analyzed, as shown in the attached figure. Figure 11 As shown.

[0109] From the appendix Figure 11 As can be seen, there are significant differences in the circumferential strain difference curves at different tire sidewall locations under different loads. Near the 180° contact center area, the curve changes from a convex peak to a concave valley shape as the load increases. With the increase of the side slip angle, the left-right asymmetry of the tire sidewall becomes more pronounced, and the absolute value of the valley value of the circumferential strain difference curve continues to increase. The baseline h0, the first valley h1, and the last valley h2 of the circumferential strain difference curve under different loads are related to the side slip force F. y All showed a significant correlation, and the coefficients of determination are shown in the attached figure. Figure 12 As shown, the determination coefficients of h1 and h2 are both higher than 0.9996, and the amplitude of h2 changes more significantly compared to h1. Therefore, h2 is selected as the lateral force F. y The characterization features.

[0110] Appendix Figure 13 The curves showing the relationship between the eigenvalue h2 and the lateral force as a function of the lateral slip angle are shown in the attached figure. Figure 13 As can be seen from this, before the lateral force curve reaches saturation, the lateral force F corresponding to different lateral angles S under the same load is... y Both the eigenvalue and strain eigenvalue h2 are unique, and the lateral force and lateral angle can be estimated using the eigenvalue h2; however, the lateral force F corresponding to the eigenvalue h2 varies under different loads. y There are multiple possible sideslip angles S.

[0111] S404: A normalized comparative study and analysis of the eigenvalue h2 under different loads was conducted, and the results are attached. Figure 14 As shown.

[0112] Appendix Figure 14 The variation trends of tire lateral force with the increase of lateral angle under different loads are highly similar. There is a significant correlation between the lateral force variation curves of 1t, 3t, and 5t, which can characterize each other. Moreover, the ratio of the normalized proportions of the three is k1∶k3∶k5≈1∶3∶5, which is linearly related to the load.

[0113] Furthermore, S5: Based on the tire vertical force F in step S3 z And the lateral force F in step S4 y Based on the characterization feature h2, a joint estimation model of vertical force and lateral force is established to estimate the actual lateral force of the tire.

[0114] Analysis of the circumferential strain characteristics of the tire sidewall revealed that, given a clear vertical force, the lateral force can be estimated using the strain characteristic value h2. This invention combines a support vector regression machine, obtains a dataset through finite element simulation, establishes an estimation model, and predicts the lateral force after estimating the vertical force, achieving joint estimation of vertical and lateral forces. The estimation process is attached. Figure 15 As shown.

[0115] Based on the vertical force and the characteristic value h2 and the lateral force F y The influence law, combining h2 with vertical force F z Processed unit eigenvalue h b2 As input features to the model, the unit lateral force F is calculated. yb Then, based on the vertical force F z Calculate the actual lateral force F y It should be noted that, according to h b2 Solve for the unit lateral force F yb The method and the vertical force F of the tire z The solution method is similar, also using a support vector machine to calculate h. b2 As input to the support vector machine, F yb As the output of the support vector machine model, the training sample set is first defined as D = {h b2(1) F yb1 ), (h b2(2) F yb2 ), ..., (h b2(m) F ybm If f )}, then the lateral force estimation model is f yb (x)=w T Φ(h b2 )+b, where w is the feature weight vector, m is the number of training sets, and f yb (x) is the predicted value of the unit lateral force, F ybm Here is the finite element simulation value of the unit lateral force, b is the bias vector, and Φ(h) is the bias vector.b2 represents the characteristic vector after h b2 is mapped to a high-dimensional feature space.

[0116] That is, the vertical force and side force combined estimation model is:

[0117]

[0118]

[0119] In the formula, h b2 is the unit characteristic value after h2 combined with the vertical force F z ; k3 is the normalized proportion of the characteristic value h2 under 3t load; F yb is the unit side force.

[0120] The specific operation of this step includes the following steps,

[0121] S501: Obtain a plurality of sets of characteristic values h2 and vertical forces F z by finite element simulation, and convert the characteristic values h2 and the vertical forces F z into unit characteristic values h b2 according to the formula ;

[0122] S502: Construct a [h b2 , F yb ] data set, input a support vector regression machine, calculate the side force F y by the support vector regression machine, and obtain the side force F y according to the formula .

[0123] S503: Divide the data sets in the data set into a training set and a test set, use the data sets in the training set to train the vertical force and side force combined estimation model, and then detect the prediction performance of the model by the data sets in the test set, to realize the estimation of the side force F y .

[0124] Since the characteristic value h2 under 3t load has high correlation with the 1t and 5t curves, the determination coefficient R 2 exceeds 0.993, 21 sets of [h b2 , F yb ] data sets under 3t load are selected as the training set to train the side force estimation model; and 40 sets of data under 1t and 5t loads are used as the test set to detect the prediction performance of the vertical force estimation model.

[0125] The model test results are shown in the attached Figure 16As shown, the maximum absolute error of the test set is less than 3%, and the determination coefficient reaches 0.999, with good estimation accuracy. It can be considered that the vertical force and cornering force joint estimation method based on the analysis of the circumferential strain of the tire side is feasible.

[0126] In summary, the present application takes 16.00R20 heavy-duty tires as the research object, based on the finite element tire model, carries out the vertical force and cornering force estimation research based on the analysis of the circumferential strain, and draws the following conclusions:

[0127] (1) The average value of the peak distance angle of the zero-order and first-order curves of the circumferential strain of the tire inner liner has good characterization effect on the tire ground angle under static load, rolling and cornering conditions.

[0128] (2) The determination coefficient R2 between the valley value characteristics of the circumferential strain difference curve of the tire side and the cornering force is greater than 0.999, and has significant correlation; under the same cornering angle, the valley value of the circumferential strain difference curve of the tire side and the vertical force are linearly related.

[0129] (3) The vertical force and cornering force joint estimation model based on the analysis of the circumferential strain can accurately estimate the vertical force under static load, rolling and cornering conditions of heavy-duty tires and the tire cornering force under different vertical forces, and the vertical force estimation error of the force estimation model is less than 2% by using finite element simulation, and the cornering force estimation accuracy is greater than 97%, with good estimation effect.

[0130] The above shows and describes the basic principles, main features and advantages of the present application. It should be understood by those skilled in the art that the present application is not limited by the above examples, and the above examples and descriptions in the specification are only to illustrate the principles of the present application, and various changes and improvements can be made without departing from the spirit and scope of the present application, and these changes and improvements all fall within the scope of the claimed present application. The scope of protection of the present application is defined by the appended claims and their equivalents.

Claims

1. A method for combined estimation of tire vertical and cornering forces based on in-utero strain analysis, characterized in that, The method comprises the following steps, S1: establishing a finite element three-dimensional model of the tire; S2: Calculate the tire contact angle and contact length L based on the strain in the tire according to the finite element three-dimensional model of the tire established in step S1 and contact length L; S3: estimating the tire vertical force F based on the tire ground angle and the ground length L calculated in step S2 using a support vector regression machine z ; S4: through the finite element three-dimensional model of the tire, the tire cornering condition is simulated and calculated, and the last valley value h2 of the cornering circumferential strain difference curve is taken as the cornering force characteristic of the tire ; S5: based on the tire vertical force F z and the lateral force in step S4 characteristic h2, a vertical force and lateral force combined estimation model is established to estimate the actual lateral force of the tire; The vertical force and cornering force joint estimation model is: ； ； wherein h2 is the characteristic value of the vertical force k3 is the normalized proportion of the characteristic value h2 under the 3t load; is the unit lateral force The specific operation of step S5 comprises the following steps, S501: Obtain multiple sets of characteristic values h2 and vertical forces F by finite element simulation z , according to the formula Convert the characteristic values h2 and the vertical forces F z into unit characteristic values ; S502: construct a dataset, input the support vector regression machine, and calculate the side force by the support vector regression machine , ] data set, input the support vector regression machine, and calculate the side force by the support vector regression machine ; S503: The data sets in the data set are divided into training set and test set, the data sets in the training set are used for vertical force and side force combined estimation model training, and then the data sets in the test set are used for detecting the prediction performance of the model, so as to realize the estimation of the side force .

2. The method of claim 1, wherein, The specific operation of step S1 comprises the following steps, S101: constructing a finite element two-dimensional cross-section structure model of the tire by using CAD; S102: rotating the finite element two-dimensional cross-section structure model of the tire around a center reference point into a three-dimensional model of the tire, and in the rotating process, a variable rotating step method is adopted to refine the mesh in the joint area; S103: verifying the footprint characteristics and vertical stiffness of the three-dimensional model of the tire established in step S102.

3. The method of claim 2, wherein, The specific operation of step S2 comprises the following steps, S201: obtaining a linear circumferential strain signal of the inner liner of the tire under static load by using finite element, and performing data processing; S202: Calculate the average of the circumferential strain zero-order and first-order peak interval angle angle As a representation index of grounding angle, , wherein, is the circumferential strain zero-order peak interval angle, is the first-order peak interval angle; S203: calculating the tire footprint length L according to the ground angle ； wherein R is the free state radius after the tire is inflated, and are the contact angles before and after the static load state, respectively, and the contact angles before and after the static load state are equal, .

4. The method of claim 3, wherein, In step S3, the vertical force F of the tire z The calculation method is as follows: Let ; In the formula, , F zi is the vertical force finite element simulation value, ; , is the front and rear grounding angle estimation value, is the grounding length estimation value, and m is the number of training sets. Then the vertical force F of the tire z The estimated regression model for ； In the formula, w is the feature weight vector. Here, b is the predicted vertical force value, and b is the bias vector. Indicates will The feature vector after mapping to a high-dimensional feature space.

5. The method of claim 4, wherein, The specific operation of step S3 comprises the following steps, S301: Obtain multiple sets of inner liner midline circumferential strain and load data under static load, rolling, and cornering conditions through finite element simulation, calculate the ground contact angle and the ground contact length L, establish the ground contact angle , the ground contact length L-load data set; S302: with the grounding angle and the grounding length L as input recognition features, the tire vertical force F z As an estimation output, the tire vertical force F z is predicted using a support vector regression machine; S303: The data sets in the data set are divided into training set and test set, the data sets in the training set are used for model training, and the data sets in the test set are used for detecting the prediction performance of the support vector regression machine, so as to realize the estimation of the vertical force F z .

6. The method of claim 5, wherein, The specific operation of step S4 comprises the following steps, S401: performing simulation calculation on the tire cornering working condition by using the finite element three-dimensional model of the tire, and extracting and analyzing the tire model ground stress nephogram and cornering characteristics; S402: extracting and analyzing the inner liner strain of the tire tread, shoulder and sidewall under the tire cornering working condition, and determining the most sensitive part of the tire in the circumferential strain response under the cornering state; S403: Extract the difference curve of the circumferential strain of the tire sidewall inner liner at different loads and different cornering angles, and determine the last valley value h2 of the sidewall circumferential strain difference curve as the characterization feature of cornering force ; S404: performing normalization comparison on the characteristic values h2 under different loads.

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