A method for analyzing the asymmetry of rolling contact of heavy-duty tires based on boundary analysis

Abstract

The present invention discloses a method for analyzing the asymmetric rolling contact of heavy-duty tires based on boundary analysis. The method takes heavy-duty tires with large aspect ratio as the research object, takes the flexible carcass model based on elastic foundation as the basis, considers the coupling relationship between the radial deformation and the tangential deformation of the carcass ring, establishes a two-dimensional tire low-frequency dynamic model of flexible ring based on analytical elastic foundation, and uses the ground boundary solution method to explore the asymmetric characteristics of the ground contact angle and the ground contact mark during the ground contact rolling process of the tire, and conducts nonlinear experimental verification of the tire ground contact stiffness and ground contact mark. The results show that: (1) the ground boundary solution can realize accurate calculation of both the ground contact angle and the ground contact mark; (2) the ground contact mark estimation method based on the tire internal strain sensor can realize indirect measurement of the ground contact mark during the tire rolling process.

Description

Technical Field

[0001] The invention belongs to the technical field of vehicle engineering, and in particular relates to a method for analyzing the rolling ground contact asymmetry of a heavy-duty tire based on boundary analysis. Background Art

[0002] The tire transmits the wheel-ground force to the vehicle, relieves the impact and vibration caused by the unevenness of the road surface, and is the only element in contact with the ground during vehicle driving. Therefore, the characteristics of the tire affect the performance indicators of the vehicle such as power, smoothness, braking and handling stability. Therefore, an accurate tire dynamics model becomes critical, especially the tire dynamics model based on structural flexibility. As a typical representative of the tire structure model, the flexible carcass tire model simplifies the tire into a flexible carcass on an elastic basis. The elastic basis is distributed along the circumference radially and tangentially to simulate the sidewall-carcass force and inflation preload effect. The tire carcass is in direct contact with the road surface, and the sidewall is the connection and force transmission component between the carcass and the rim. Its mechanical characteristics and vibration characteristics affect the transmission characteristics between the carcass and the rim. Therefore, how to accurately describe the carcass, sidewall flexible structure vibration and tire ground contact characteristics has always been the focus and difficulty in tire dynamics research. Scholars at home and abroad have studied different carcass flexibility modeling methods and proposed flexible carcass models from one dimension to three dimensions, including string models, beam models, plate models, ring models, shell models and distributed mass models based on elastic foundations. For the description of the mechanical properties of the sidewall, scholars at home and abroad have also proposed one-dimensional radial stiffness, two-dimensional radial / tangential stiffness, and a three-dimensional stiffness model that considers the lateral characteristics of the tire surface based on radial and tangential springs. Tire-ground contact modeling, as the key to tire force generation, is the core of tire dynamics modeling. The rolling smoothness analysis is carried out using the flexible ring model, and the high-order deformation of the carcass is taken into account using the flexible body dynamics modeling method. The numerical integration method is used to iteratively solve the carcass contact mark and the vertical response of the rim under the action of road roughness. P.Zegelaar and Gong used the elastic-based flexible ring model, introduced radial springs between the flexible ring and the ground to simulate the compression effect of the tire body, and used the modal expansion method to explore the ground contact and rim response of the tire at different rolling speeds and loads on flat roads; Zuo Shuguang from Tongji University used the LuGre model to analyze the longitudinal ground contact characteristics of the tire based on Gong's flexible ring ground contact analysis, and established a dynamic tire ground contact model based on the flexible ring tire ground contact analysis; Guan Dihua from Tsinghua University used the modal parameters of the tire in the free state to characterize the high-order flexibility characteristics of the tire body, and used the integral method of modal coordinates and The moving load method was used to derive a time domain model for simulating the dynamic characteristics of tires on uneven roads, and the model was used to simulate transient responses of tires such as starting and braking. Huang Haibo from Ningbo University used an elastic-based ring model to analyze the effects of different structural parameters, rotation speeds and damping on the asymmetry of tire contact marks, and used the Euler beam and lateral slicing methods to simulate the lateral deformation of the tire, and established an analytical solution for the three-dimensional contact characteristics of the tire based on the driving torque and the rolling torque. Based on Gong's elastic-based flexible ring model, Korean scholars Kim et al. considered the tangential deformation of the tire ring during the contact process and analyzed the contact pressure distribution of the drive wheel and the brake wheel. RabieMeftah

[20] Based on the elastic foundation flexible ring theory, the Green integral method is used to solve the vibration response of the tire facing the road surface unevenness excitation; R J.Pinnington uses the flexible carcass model and the point load in the elastic half-space to solve the vibration response of the rim based on a given ground contact mark; Chunjian Wang uses the elastic foundation layer ring theory, considers the compression effect of the tread ring, and based on the force balance condition, uses the proportional feedback correction method to solve the vibration response of the layer ring under arbitrary road surface unevenness excitation.

[0003] The carcass of a heavy-load tire is a typical circular ring structure, and there is a coupling relationship between the radial deformation and tangential deformation of the carcass points. Traditional ground contact characteristics are mostly solved by iterative methods based on ground springs, which are difficult to converge and have a long calculation time. Therefore, this patent, based on a flexible ring two-dimensional tire low-frequency dynamic model based on analytical elasticity, proposes a heavy-load tire rolling ground contact asymmetry calculation based on boundary analysis and an experimental method based on an in-tire strain sensor, which are used to explore the asymmetric characteristics of the ground contact angle and ground contact mark during the tire's ground contact rolling process. Summary of the invention

[0004] In view of the above problems, the present invention proposes a heavy-duty tire rolling contact asymmetry analysis method based on boundary analysis, which is characterized by comprising the following steps:

[0005] Step 1: Establish a flexible ring tire model based on elastic foundation;

[0006] Step 2: Establish a steady-state tire dynamics model

[0007] Step 201: Express the carcass inextensibility assumption as:

[0008] v′+w=0 (3);

[0009] Step 202: Substitute equation (3) into the flexible ring tire model established in step 1 to obtain a tire steady-state dynamic model:

[0010]

[0011] Step 3: Obtain the tire carcass width, tire effective radius and carcass linear density through tire dissection test;

[0012] Step 4: Based on the width, effective radius and carcass linear density obtained in step 3, the tire modal parameters are identified through a heavy-load tire vibration modal test to obtain the tire sidewall radial stiffness, sidewall tangential stiffness and carcass bending stiffness;

[0013] Step 5: Solve the tire steady-state dynamics model based on the parameter values ​​obtained in steps 3 and 4, derive the front and rear contact angle expressions, and obtain the conditions that the contact angle must satisfy, thereby deriving the front and rear contact angles corresponding to different tire rolling speeds under different tire pressure flatness, and obtain the change trend of the front and rear contact angle asymmetry coefficient with rolling speed based on the obtained front and rear contact angles;

[0014] Step 6: Conduct a heavy-load tire ground contact characteristic experiment to verify the tire rolling ground contact asymmetry results and obtain the ground contact footprint estimation method of the tire in-tire strain sensor.

[0015] Furthermore, the specific steps of step 4 are:

[0016] Step 41: Based on the assumption that the carcass is inextensible, the rim is fixed, and the tire speed is 0, transform equation (5) into equation (11):

[0017]

[0018] Substituting formula (3) into formula (11), formula (11) is transformed into:

[0019]

[0020] Step 42: Based on equation (5), the carcass ring is deformed tangentially Substituting into equation (12), we get the angular velocity in radians:

[0021]

[0022] Then, the tire modal resonance frequency based on the assumption that the carcass is inextensible is:

[0023]

[0024] Here, the ± sign indicates that the tire has two resonant frequencies at each modal order, which are opposite to each other;

[0025] Step 43: Construct a heavy-duty tire vibration modal test system, use formula (14) to obtain the test modal results of each order of the tire, and use the undetermined coefficient method to calculate the tire sidewall radial stiffness, sidewall tangential stiffness and carcass bending stiffness.

[0026] Furthermore, the specific steps of step 5 are:

[0027] Step 51: Solve equation (5), the characteristic root is:

[0028]

[0029] Step 52: The general solution of equation (5) consists of two parts: tire carcass deformation caused by the front contact angle and tire flexible carcass deformation caused by the rear contact angle. The carcass ring radial deformation w is expressed as:

[0030]

[0031] in, The angle between the line connecting the contact point and the center of the tire and the vertical line between the center of the tire and the ground is positive in the counterclockwise direction (away from the front end of the contact area) and negative in the clockwise direction (away from the rear end of the contact area); B 1 , B 2 is a dimensionless term related to external loads and geometric boundaries; 1 and λ 2 is the characteristic root;

[0032] Step 53: Define the front and rear contact angles of the tires as and And the radial deformation of the tire before entering the contact angle is an increasing function The radial deformation of the tread after the contact area is

[0033] Step 54: Establish the front and rear contact angles of the tires and The continuity conditions of deformation and rotation angle of the contact area and non-contact area are expressed as:

[0034]

[0035] Step 55: Based on equation (7) and the contact area between the tire and the road surface meets the plane foundation constraint condition, the expressions for the conditions satisfied by the front and rear contact angles are obtained as follows:

[0036]

[0037] Step 56: Substitute equation (5) into equations (c) and (d) in equation (9) respectively, and solve the linear equation system to obtain the front and rear contact angles corresponding to different tire rolling speeds under different tire flattening conditions.

[0038] Furthermore, the heavy-load tire vibration modal experimental system established in step 43 includes a tire support device, a force hammer and a charge amplifier, a data testing system and a PC computer. The experimental principle is: the force hammer sensor transmits the force hammer excitation signal to the DEWE-43 high-speed data acquisition device after conditioning by the charge amplifier. At the same time, the vibration response generated by the tire under the excitation of the force hammer is collected by the acceleration sensor and transmitted to DEWE-43. The computer performs spectral analysis on the acquired excitation signal and acceleration vibration response, and calculates the vibration transfer function of the tire.

[0039] Furthermore, the heavy-load tire contact mark verification test described in step 6 builds a heavy-load tire mechanical vibration experimental system, which includes a heavy-load tire to be tested, a tire fixing fixture (used to limit the vertical freedom of the tire so that the tire moves vertically), an MTS hydraulic servo excitation device, a displacement sensor, a force sensor and an acceleration sensor.

[0040] Furthermore, the experimental principle of the heavy-loaded tire mechanical vibration experimental system is as follows: the heavy-loaded tire is connected to the gantry and the excitation head equipment of the platform through tooling, and the MTS hydraulic servo excitation is used as the excitation source of the system to apply static excitation; the hydraulic excitation end is equipped with displacement and force sensors, and the displacement and loading force signals of the heavy-loaded tire are sampled through the computer data acquisition system to monitor the tire loading force and deformation. At the same time, the ink method is used to measure the ground contact mark of the heavy-loaded tire, and the loading is performed at equal intervals. The tire body is equivalent to a flexible ring, and the influence of the lateral direction of the tire body on the tire ground contact characteristics is ignored, and the length of the tire ground contact mark is obtained for analysis.

[0041] Furthermore, step 6 performs a heavy-duty tire contact characteristic experiment, and the results obtained by analyzing the length of the tire contact mark include:

[0042] 1) The tire exhibits symmetrical ground contact characteristics during steady-state ground contact, and the tire rolling causes an asymmetrical ground contact angle and ground contact mark;

[0043] 2) According to the rolling speed and contact patch length of the tire, the effective rolling radius of the tire at different rolling speeds can be calculated. Therefore, the tire rolling deformation characteristics should be estimated based on the strain sensor signal inside the tire body during the experiment.

[0044] 3) The rolling of the tire causes the maximum radial deformation point of the tire body to move backward, resulting in an asymmetric contact patch area. As the rolling speed increases, the nonlinear characteristics of the tire contact patch become obvious, and its vertical contact force peak increases.

[0045] Furthermore, the contact patch estimation method of the tire strain sensor described in step 6 is: the deformation of the tire body is divided into points A, B, C, D and E, point B is the front contact point of the tire body, point D is the rear contact point of the tire body, point C is the midpoint of the contact patch, point A and point E are the deformation points of the tire body, wherein the distance between point B and point D can represent the contact patch length of the tire body, and the time interval between point A and point F is the time for the tire to roll one circle, which can be used to calculate the rolling speed of the tire. In addition, according to the rolling speed of the tire and the contact patch length, the effective rolling radius of the tire at different rolling speeds can be calculated.

[0046] The beneficial effects of the present invention are:

[0047] The present invention proposes a method for analyzing the rolling ground contact asymmetry of heavy-load tires based on boundary analysis. The heavy-load tire with a large aspect ratio is taken as the research object. Based on the flexible carcass model based on the elastic foundation, the low-frequency dynamic modeling and ground contact rolling asymmetry analysis of the heavy-load tire are carried out. The main aspects include: (1) considering the coupling relationship between the radial deformation and the tangential deformation of the carcass ring, a flexible ring two-dimensional tire low-frequency dynamic model based on the analytical elastic foundation is established, and the model parameters are solved based on the experimental modal parameters; (2) the ground contact boundary solution method is used to explore the relationship between the tire ground contact angle and the tire flattening amount and the rolling speed; the tire ground contact stiffness and ground contact mark nonlinearity are experimentally verified, and the ground contact mark estimation method based on the tire internal strain sensor is obtained. The simulation experiment shows that the method proposed by the present invention overcomes the shortcomings of the prior art that the method based on the ground spring iteration solution method is used in the prior art, which is not easy to converge and has a long calculation time. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Figure 1 It is a flexible ring tire model based on elastic foundation;

[0049] Figure 2 (a) is the electrical connection diagram of the modal test system; Figure 2 (b) is the modal test result;

[0050] Figure 3 (a)-(d) are the analysis of the influence of different rolling speeds on the asymmetric characteristics of the front and rear contact angles;

[0051] Figure 4 The trend diagram of the asymmetric coefficient of the front and rear contact angles changing with the rolling speed under different flattening amounts;

[0052] Figure 5 (a)-(b) are heavy-duty tire rolling test systems based on in-body sensing technology. Figure 5 (a) is the strain sensor inside the tire body, Figure 5 (b) The mechanical body and electrical system of the heavy-load tire rolling test system;

[0053] Figure 6 (a)-(b) are heavy-duty tire loading tests, where Figure 6 (a) the mechanical part of the test system, Figure 6 (b) is the contact footprint of heavy-duty tires with different loading forces;

[0054] Figure 7 This is a comparison diagram of carcass strain signal filtering based on empirical mode decomposition;

[0055] Figure 8 (a)-(d) are the quasi-static rolling deformation characteristic diagrams of heavy-duty tires with standard inflation pressure and 4 tons load. Figure 8(a) is the carcass tangential strain (one cycle), Figure 8 (b) is a schematic diagram of tire body deformation. Figure 8 (c) is the carcass tangential strain (contact area), Figure 8 (d) is the rate of change of carcass tangential strain;

[0056] Fig. 9 (a) is the tangential strain curve of the heavy-duty tire flexible carcass under load-dependent tangential strain, and Fig. 9(b) is the contact patch length based on the carcass strain sensor signal;

[0057] Fig.10 Figure 3 is the carcass tangential strain diagram of heavy-load tire at different rolling speeds. DETAILED DESCRIPTION

[0058] In order to enable those skilled in the art to better understand the technical solution of the present invention, the technical solution of the present invention is further described below in conjunction with the accompanying drawings and embodiments.

[0059] 1. Dynamic modeling of flexible carcass ring

[0060] The tire-rim system is equivalent to a system consisting of a two-dimensional spring, a flexible ring and a disk. The radial and tangential springs connect the flexible ring and the disk, as shown in Figure 1 As shown in the figure. The disk simulates the rim mass, the flexible ring represents the belt and the carcass connected to the crown, and the two-dimensional linear spring represents the sidewall and inflation effect. The flexible ring model based on elastic foundation is studied from three aspects: dynamic modeling, model structure parameter identification and modal vibration analysis.

[0061] (1) Flexible ring tire model based on elastic foundation

[0062] Formula (1) is a complete tire model, including the radial and tangential vibration equations of the tire ring and the vertical, horizontal and rotational vibration equations of the rim disk, and taking into account the rim degree of freedom and rotation effect. In the formula, The preload force generated by the inflation pressure and the centrifugal force of the ring Right now:

[0063]

[0064] Where, E: section modulus of carcass ring beam, I: section inertia of carcass ring beam, w: radial deformation of carcass ring, v: tangential deformation of carcass ring, θ: rotation angle of carcass ring relative to hub disk; x: displacement of hub disk in X direction, y: displacement of hub disk in Y direction, k w : Radial spring stiffness, k v Tangential spring stiffness, P 0 : rated air pressure, ρ: equivalent density of circular beam, Ω: angular velocity of the disk, qw : radial distributed load, q v : Tangential distributed load, I w : moment of inertia of the disk, γ: rotation angle of the disk.

[0065] Then, the tire model of the tire flexible ring in the rotating state is:

[0066]

[0067] The radial tire carcass is composed of composite materials such as steel wire and rubber, and the steel wire is along the meridian direction of the tire, and its circumferential tensile stiffness is large. In the 400Hz frequency range, the modal vibration mode of the GL073 radial tire is the bending vibration mode in the carcass surface, and the breathing vibration mode related to the carcass tensile stiffness does not appear in this frequency range, which verifies the validity of the "carcass inextensibility assumption". The "carcass inextensibility assumption" describes the characteristic that the circumferential length of the carcass ring neutral surface remains unchanged during the deformation process, which is expressed as:

[0068] v′+w=0 (3)

[0069] Substitute equation (3) into equation (2), take the derivative of equation (b), subtract equation (a) from (b), set the time term in the equation to 0, and consider the influence of tire damping. The steady-state dynamic equation of the tire considering the tire proportional damping effect is established, as shown in equation (4).

[0070]

[0071] Among them, c w is the radial spring damping coefficient; c v is the tangential spring damping coefficient;

[0072] (2) Ground boundary analysis

[0073] The tire contact angle under rolling conditions is solved by using the boundary continuity conditions of the tire contact area and non-contact area. There is no external force in the tire non-contact area, so the tire steady-state dynamic equation is:

[0074]

[0075] The characteristic root of equation (5) is:

[0076]

[0077] Then, the general solution of equation (5) consists of two parts, the tire carcass deformation caused by the front contact angle and the tire flexible carcass deformation caused by the rear contact angle, which can be expressed as:

[0078]

[0079] in, The angle between the line connecting the contact point and the center of the tire and the vertical line between the center of the tire and the ground; counterclockwise is positive (away from the front end of the contact area); clockwise is negative (away from the rear end of the contact area); B 1 , B 2 It is a dimensionless term, which is related to the external load and geometric boundary;

[0080] According to the rolling deformation characteristics of the tire, when entering the contact area, the rolling deformation of the tire increases from 0, and when leaving the rear end of the contact area, the rolling deformation of the tire decreases to 0. The definition is: the front and rear contact angles of the tire are and Therefore, the radial deformation of the tire before entering the contact angle is an increasing function, which is The radial deformation of the tread after the contact area is

[0081] In addition, the contact area between the tire and the road surface meets the plane foundation constraint condition, which is:

[0082]

[0083] Among them, w c is the deformation of the point in the contact area; d 0 The amount of tire flatness.

[0084] Establish the front and rear tire contact angles respectively The continuity conditions of deformation and rotation angle of the contact area and non-contact area are:

[0085]

[0086] Substituting equations (7) to (8) into equation (9), the front / rear contact angles must satisfy:

[0087]

[0088] 2. Tire model parameter identification based on experimental modal

[0089] There are unknown variables in the tire dynamics model (Formula (5)) based on the "carcass inextensibility assumption", including: bending stiffness EI, sidewall radial stiffness k w , sidewall tangential stiffness k v and carcass density ρA;

[0090] Based on the "carcass inextensibility assumption", the rim is fixed, and the tire speed is 0, then the flexible ring tire model based on elastic foundation is transformed into:

[0091]

[0092] Substituting equation (3) into equation (11), the equation is transformed into:

[0093]

[0094] Using the mechanical model based on the "carcass inextensibility assumption", the carcass radial deformation in the previous formula is Substituting into the dynamic equation (12), we get:

[0095]

[0096] Then, the tire modal resonance frequency based on the "carcass inextensibility assumption" is:

[0097]

[0098] Among them, the ± symbol indicates that the tire has two resonant frequencies at each modal order, which are opposite to each other. This is caused by the symmetrical structure of the tire. There are two vibration modes in the clockwise and counterclockwise direction along the circumferential direction. The present invention focuses on the modal frequencies corresponding to multiple vibration modes in a single direction.

[0099] The vibration modal parameters of the tire are directly related to the inflation pressure of the tire and the constraints of the tire. In order to carry out detailed experimental analysis of the vibration modal of the heavy-duty tire, the inflation pressure and the constraints of the tire are taken into consideration. A heavy-duty tire modal test system is built, including: tire support device, force hammer and charge amplifier, data test system and PC computer. Figure 2 (a) shows the electrical connection diagram of the modal test system. Figure 2 (b) is the modal test result.

[0100] The hammer sensor transmits the hammer excitation signal to the DEWE-43 high-speed data acquisition device after conditioning by the charge amplifier. At the same time, the vibration response of the tire under the excitation of the hammer is collected by the acceleration sensor and transmitted to DEWE-43. The computer performs spectral analysis on the acquired excitation signal and acceleration vibration response to calculate the vibration transfer function of the tire.

[0101] The width of the tire, the effective radius of the tire and the linear density of the tire are the test results of the tire anatomy test, and the tire inflation pressure is a known inflation condition. In view of the problem that the radial / tangential stiffness of the sidewall and the bending stiffness of the tire are unknown, the radial / tangential stiffness of the sidewall and the bending stiffness of the tire are calculated by the undetermined coefficient method using formula (23) and the experimental modal results of each order of the tire. The calculation results are shown in Table 1.

[0102] Table 1 GL073A heavy-duty tire geometry and structural parameters (including identification results)

[0103]

[0104] 3. Analysis of tire rolling contact asymmetry results

[0105] Substitute equation (5) into (c) and (d) in equation (9) and solve the nonlinear equation system. Figure 3 The tire flattening amount d is given 0 The front and rear contact angles corresponding to different tire rolling speeds under the conditions of 0.25m, 0.05m, 0.75 and 0.1m respectively. Figure 4 The variation trend of the asymmetric coefficient of the front and rear contact angles with rolling speed under different flattening amounts is given (the asymmetric coefficient of the contact angle is the ratio of the contact angle under different rolling speeds to the steady-state contact angle). The results in the figure show that: (1) As the tire rolling speed increases, the front contact angle φ of the tire body increases. f Increase, ground clearance angle φ r The contact patch area is asymmetric with respect to the vertical axis. (2) The greater the tire flattening, the slower the trend of the contact angle asymmetry coefficient changing with rolling speed. Figure 4 shown.

[0106] 4. Heavy-load tire ground contact characteristics test

[0107] (1) Tire rolling test system

[0108] The tire is the part that is in direct contact with the road surface. The forces and torques acting on the vehicle are all generated in the contact area. Therefore, accurate analysis and testing of tire deformation in the contact area and the contact characteristics between the tire and the road surface are the key points of tire experimental research. At the same time, real-time monitoring of tire dynamic information, evaluation of tire motion status, and prediction of tire-road friction characteristics can be used to grasp the motion status of the vehicle, implement accurate vehicle control, and ultimately achieve the purpose of improving vehicle automation and driving safety. The present invention uses a method of arranging sensors in the tire body to detect tire rolling deformation and tire-road contact information. Figure 5 (a) is a schematic diagram of the tire body sensing technology based on strain gauge sensors. Figure 5 (b) is the schematic diagram of the mechanical body and electrical connection system of the heavy-load tire rolling test system. The tire deformation and tire-road contact information are obtained through sensors inside the tire body, and the sensor signals are transmitted to the acquisition system through mechanical slip rings to achieve the purpose of sensor data collection, recording and analysis.

[0109] (2) Heavy-load tire contact mark verification test

[0110] Build a heavy-duty tire mechanical vibration experimental system based on MTS hydraulic servo excitation device, such as Figure 6(a) shows the mechanical body of the system. The system includes: the heavy-load tire to be tested, the tire fixing fixture (used to limit the vertical freedom of the tire and make the tire move vertically), the MTS hydraulic servo excitation device, the displacement sensor, the force sensor and the acceleration sensor, etc. The heavy-load tire is connected to the gantry and the excitation head equipment of the platform through the fixture. The MTS hydraulic servo excitation is the excitation source of the system, and the excitation static excitation is applied; the hydraulic excitation end is equipped with displacement and force sensors, and the displacement and loading force signals of the heavy-load tire are sampled through the computer data acquisition system to realize the monitoring of the tire loading force and deformation. At the same time, the ink method is used to measure the ground contact mark of the heavy-load tire, and the loading is equal to 1t, 2t, 3t, 4t, 5t and 6t respectively. The tire body is equivalent to a flexible ring, and the influence of the lateral direction of the tire body on the tire ground contact characteristics is ignored. The main analysis is on the length of the tire ground contact mark. Next, the analysis and discussion are carried out from the following aspects:

[0111] First, preprocessing of intra-fetal strain signals:

[0112] In order to characterize the deformation characteristics of the flexible carcass under quasi-static conditions, an indoor low-speed rolling test method was adopted. The carcass strain signal was collected by running at a constant speed of 3 km / h in a straight line. Figure 7 As shown in the figure, since the strain signal is easily interfered by the 50Hz AC signal, the empirical mode decomposition method is used for filtering during the experiment. Figure 7 The initial signal and filtered signal of the strain sensor are compared. The comparison results show that the tire body strain filtering method based on modal analysis can effectively filter out the 50Hz AC signal. In addition, theoretical analysis shows that the tire presents symmetrical grounding characteristics during steady-state grounding, and the tire rolling causes an asymmetrical grounding angle and grounding mark. Figure 7 The strain peaks at midpoint A and point E are different, indicating that the low-speed rolling test can reflect the quasi-static deformation characteristics of the tire to a certain extent, but cannot fully characterize the static deformation characteristics of the tire.

[0113] Second, grounding footprint estimation based on intra-fetal strain signals:

[0114] In order to illustrate the effectiveness of deformation analysis based on tire body strain sensor, Figure 8(b) The deformation diagram of the tire body is used to analyze the deformation characteristics of the tire body. The deformation of the tire body is divided into points A, B, C, D and E, point B is the front contact point of the tire body, point D is the rear contact point of the tire body, point C is the midpoint of the contact mark, point A and point E are the deformation points of the tire body, and the distance between point B and point D can represent the contact mark length of the tire body. At the same time, the time interval between point A and point F is the time for the tire to roll one circle, which can be used to calculate the rolling speed of the tire. In addition, according to the rolling speed of the tire and the contact mark length, the effective rolling radius of the tire at different rolling speeds can be calculated. Therefore, based on the strain sensor signal in the tire body, the estimation of the rolling deformation characteristics of the tire can be realized.

[0115] Third, analysis of the impact of load on grounding characteristics

[0116] Fig. 9 The tangent strain curves of the heavy-duty tire flexible carcass under different load conditions are listed, and the contact patch length estimation results based on the strain sensor signal inside the carcass are compared with the tire mechanical test results ( Figure 6 (b)) is compared to verify the effectiveness of the contact patch length estimation based on the strain sensor signal inside the tire body.

[0117] Fourth, rolling nonlinear verification analysis

[0118] Fig.10 The carcass tangential strain diagrams of heavy-load tires at rolling speeds of 5, 10 and 15 km / h are listed. The results show that the rolling of the tire causes the maximum radial deformation point of the carcass to move backward, resulting in an asymmetric contact print area. As the rolling speed increases, the nonlinear characteristics of the tire contact print become obvious, and its vertical print force peak increases.

[0119] The above shows and describes the basic principles, main features and advantages of the present invention. It should be understood by those skilled in the art that the present invention is not limited to the above embodiments, and the above embodiments and descriptions are only for explaining the principles of the present invention. Without departing from the spirit and scope of the present invention, the present invention may have various changes and improvements, which fall within the scope of the present invention to be protected. The scope of protection of the present invention is defined by the attached claims and their equivalents.

Claims

1. A heavy-duty tire rolling contact asymmetry analysis method based on boundary analysis, characterized in that: The following steps are involved: Step 1: Establish a flexible ring tire model based on elastic foundation; Step 2: Establish a steady-state tire dynamics model Step 201: Express the carcass inextensibility assumption as: v′+w=0 (3); Step 202: Substitute equation (3) into the flexible ring tire model established in step 1 to obtain a tire steady-state dynamic model: Step 3: Obtain the tire carcass width, tire effective radius and carcass linear density through tire dissection test; Step 4: Based on the width, effective radius and carcass linear density obtained in step 3, the tire modal parameters are identified through a heavy-load tire vibration modal test to obtain the tire sidewall radial stiffness, sidewall tangential stiffness and carcass bending stiffness; Step 5: Solve the tire steady-state dynamics model based on the parameter values ​​obtained in steps 3 and 4, derive the front and rear contact angle expressions, and obtain the conditions that the contact angle must satisfy, thereby deriving the front and rear contact angles corresponding to different tire rolling speeds under different tire pressure flatness, and obtain the change trend of the front and rear contact angle asymmetry coefficient with rolling speed based on the obtained front and rear contact angles; Step 6: Conduct a heavy-load tire ground contact characteristic experiment to verify the tire rolling ground contact asymmetry results and obtain the ground contact footprint estimation method of the tire in-tire strain sensor.

2. The method for analyzing the asymmetry of rolling contact of heavy-duty tires based on boundary analysis according to claim 1, characterized in that: The specific steps of step 4 are: Step 41: Based on the assumption that the carcass is inextensible, the rim is fixed, and the tire speed is 0, transform equation (5) into equation (11): Substituting formula (3) into formula (11), formula (11) is transformed into: Step 42: Based on equation (5), the carcass ring is deformed tangentially Substituting into equation (12), we get the angular velocity in radians: Then, the tire modal resonance frequency based on the assumption that the carcass is inextensible is: Here, the ± sign indicates that the tire has two resonant frequencies at each modal order, which are opposite to each other; Step 43: Construct a heavy-duty tire vibration modal test system, use formula (14) to obtain the test modal results of each order of the tire, and use the undetermined coefficient method to calculate the tire sidewall radial stiffness, sidewall tangential stiffness and carcass bending stiffness.

3. The method for analyzing the asymmetry of rolling contact of heavy-duty tires based on boundary analysis according to claim 1, characterized in that: The specific steps of step 5 are: Step 51: Solve equation (5), Its characteristic root is: Step 52: The general solution of equation (5) consists of two parts: tire carcass deformation caused by the front contact angle and tire flexible carcass deformation caused by the rear contact angle. The carcass ring radial deformation w is expressed as: in, The angle between the line connecting the contact point and the tire center and the vertical line between the center and the ground is positive in the counterclockwise direction and negative in the clockwise direction. B1 and B2 are dimensionless terms related to the external load and geometric boundaries. λ1 and λ2 are characteristic roots. Step 53: Define the front and rear contact angles of the tires as and And the radial deformation of the tire before entering the contact angle is an increasing function The radial deformation of the tread after the contact area is Step 54: Establish the front and rear contact angles of the tires and The continuity conditions of deformation and rotation angle of the contact area and non-contact area are expressed as: Step 55: Based on equation (7) and the contact area between the tire and the road surface meets the plane foundation constraint condition, the expressions for the conditions satisfied by the front and rear contact angles are obtained as follows: Step 56: Substitute equation (5) into equations (c) and (d) in equation (9) respectively, and solve the linear equation system to obtain the front and rear contact angles corresponding to different tire rolling speeds under different tire flattening conditions.

4. A heavy-duty tire rolling contact asymmetry analysis method based on boundary analysis as claimed in claim 3, characterized in that: The heavy-load tire vibration modal experimental system established in step 43 includes a tire support device, a force hammer and a charge amplifier, a data testing system and a PC computer. The experimental principle is: the force hammer sensor transmits the force hammer excitation signal to the DEWE-43 high-speed data acquisition device after conditioning by the charge amplifier. At the same time, the vibration response generated by the tire under the excitation of the force hammer is collected by the acceleration sensor and transmitted to DEWE-43. The computer performs spectral analysis on the acquired excitation signal and acceleration vibration response, and calculates the vibration transfer function of the tire.

5. The method for analyzing the asymmetry of rolling contact of heavy-duty tires based on boundary analysis according to claim 1, characterized in that: The heavy-load tire contact mark verification test described in step 6 builds a heavy-load tire mechanical vibration experimental system, which includes a heavy-load tire to be tested, a tire fixing fixture, an MTS hydraulic servo excitation device, a displacement sensor, a force sensor and an acceleration sensor.

6. The method for analyzing the asymmetry of rolling contact of heavy-duty tires based on boundary analysis according to claim 5, characterized in that: The experimental principle of the heavy-load tire mechanical vibration experimental system is as follows: the heavy-load tire is connected to the gantry and the excitation head equipment of the platform through the tooling, and the MTS hydraulic servo excitation is used as the excitation source of the system to apply static excitation; the hydraulic excitation end is equipped with displacement and force sensors, and the displacement and loading force signals of the heavy-load tire are sampled through the computer data acquisition system to realize the monitoring of the tire loading force and deformation, and the ink method is used to measure the ground contact mark of the heavy-load tire at the same time, the loading is performed at equal intervals, the tire body is equivalent to a flexible ring, and the influence of the lateral direction of the tire body on the tire ground contact characteristics is ignored, and the length of the tire ground contact mark is obtained for analysis results.

7. A heavy-duty tire rolling contact asymmetry analysis method based on boundary analysis as claimed in claim 6, characterized in that: Step 6: Conduct a heavy-duty tire ground contact characteristic test and analyze the length of the tire ground contact mark to obtain the following results: 1) The tire exhibits symmetrical ground contact characteristics during steady-state ground contact, and the tire rolling causes an asymmetrical ground contact angle and ground contact mark; 2) According to the rolling speed and contact patch length of the tire, the effective rolling radius of the tire at different rolling speeds can be calculated. Therefore, the tire rolling deformation characteristics should be estimated based on the strain sensor signal inside the tire body during the experiment. 3) The rolling of the tire causes the maximum radial deformation point of the tire body to move backward, resulting in an asymmetric contact patch area. As the rolling speed increases, the nonlinear characteristics of the tire contact patch become obvious, and its vertical contact force peak increases.

8. The method for analyzing the asymmetry of rolling contact of heavy-duty tires based on boundary analysis according to claim 7, characterized in that: The method for estimating the contact patch of the tire strain sensor described in step 6 is as follows: the deformation of the tire body is divided into points A, B, C, D and E, point B is the front contact point of the tire body, point D is the rear contact point of the tire body, point C is the midpoint of the contact patch, point A and point E are the deformation points of the tire body, the distance between point B and point D can represent the contact patch length of the tire body, and the time interval between point A and point F is the time it takes for the tire to roll one circle, which can be used to calculate the rolling speed of the tire. In addition, according to the rolling speed of the tire and the contact patch length, the effective rolling radius of the tire at different rolling speeds can be calculated.

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