A method for indirectly measuring the stiffness of the carcass and tread

Abstract

The present invention provides a method for indirectly measuring the stiffness of a carcass and a tread, comprising the following steps: S100: respectively performing longitudinal, lateral and torsional stiffness tests on the tire, and collecting test data when the tire deforms; S200: extracting generalized forces and generalized displacements based on the collected test data, and calculating the test data by means of parameter identification to obtain the tread stiffness k s , the tread stiffness k f , the extreme value F of the generalized frictional force c and the offset Δx between the actual value and the test value of the displacement; S300: calculating the overall stiffness K of the tire according to the carcass stiffness k s and the tread stiffness k f . The present invention performs parameter identification on a new relationship model between generalized forces and generalized displacements through test data, can separate the carcass and tread rigidities, and calculates the overall static stiffness of the tire, realizing the decoupling of the stiffness of tire components and separating the carcass and tread rigidities. At the same time, since the measurement method disclosed in this patent takes into account the influence of road surface friction and the offset of the testing machine at zero point, the measurement of the tire static stiffness is more accurate.

Description

Technical Field

[0001] The present invention relates to the technical field of tire static stiffness measurement, and particularly relates to a method for indirectly measuring the stiffness of a tire carcass and a tread. Background Art

[0002] In the prior art, the test methods for obtaining the static stiffness of a tire mostly intercept the data near zero displacement, and take the slope of the secant line between two points or the fitting straight line of the data segment as the static stiffness value. The applicable condition of this test method is that the linearity of the selected data segment is good. However, due to the influence of road surface friction in the test, the tire deformation is large, and the larger the tire deformation, the worse the linearity of its static test data. At the same time, many testing machines have the problem of zero drift, that is, the data error when the displacement is zero is large, which will also affect the reliability of the static stiffness calculation. Therefore, the prior art can only obtain the overall static stiffness of the tire and cannot obtain the static stiffness values of the various components of the tire. However, obtaining the static stiffness values of the various components of the tire, such as the tread and the carcass, is of great significance for studying the dynamic behavior of the tire. Research shows that: the stiffness of the tread in the lateral and longitudinal directions significantly affects the cornering stiffness and longitudinal slip stiffness of the tire respectively, the stiffness of the carcass in the lateral and longitudinal directions affects the lateral relaxation length and longitudinal relaxation length of the tire respectively, and the torsional stiffness of the carcass affects the effective cornering angle of the tire and the self-aligning characteristics of the tire.

[0003] In the national standard, GB / T23663-2009 defines the longitudinal and lateral stiffness as follows:

[0004] Longitudinal stiffness: the ratio of the increment of the longitudinal force to the increment of the longitudinal displacement;

[0005] Lateral stiffness: the ratio of the increment of the lateral force to the increment of the lateral displacement.

[0006] In the industry standard, there is no definition of torsional stiffness, and its definition is being formulated. However, in each enterprise standard, the definition of the national standard is basically followed, and the longitudinal, lateral, and torsional stiffness are all defined as the ratio of the increment of the generalized force to the increment of the generalized displacement.

[0007] In the national standard, there is no test method for torsional stiffness. The test methods for longitudinal and lateral stiffness in GB / T23663-2020 are as follows:

[0008] Method A:

[0009] L x =(F x2 -F x1 ) / (δ x2 -δ x1 )

[0010] L y =(F y2 -F y1) / (δ y2 -δ y1 )

[0011] L x 、L y are the longitudinal and transverse stiffnesses respectively, F x2 、F x1 、δ x2 、δ x1 are the longitudinal force and longitudinal displacement at two selected points respectively, F y2 、F y1 、δ y2 、δ y1 are the transverse force and transverse displacement at two selected points respectively. The two selected points are located at ±250 N of 30% of the vertical load.

[0012] Method B:

[0013] Extract the data segment of 30% - 60% of the vertical force in the curve, and use the least squares method to fit a unary linear equation. Take the slope of the straight line as the longitudinal or transverse rigidity of the tire.

[0014] Assume the fitting equation:

[0015] y = a0 + a1x

[0016] Solve:

[0017]

[0018] From the values of the minimum a0 and a1, obtain the normal equations:

[0019]

[0020] Solve for a0 and a1.

[0021] In the formula:

[0022] a1 - longitudinal or transverse stiffness;

[0023] y - longitudinal or transverse force;

[0024] x - longitudinal or transverse displacement.

[0025] Each enterprise standard generally adopts one of these methods, and the difference lies in intercepting data segments at different positions.

[0026] However, the existing calculation methods have the following disadvantages: 1. In the existing standards, the definition of stiffness is the ratio of the increment of force to displacement, but it does not specify where the force and displacement are, which makes the enterprises have great arbitrariness in using the standards; 2. In the existing test methods, there are mainly two methods. One is to select two points on the test curve to take the slope, and the other is to take a section of data for linear fitting. However, both of these methods have obvious deficiencies. First, both of these methods are approximate estimations. Using the data segment outside the zero point to estimate the zero point is easily affected by the road surface friction coefficient and tire unevenness. Second, the offset of the test data at the zero point affects the calculation result; 3. The existing technology can only obtain the overall static stiffness of the tire and cannot obtain the static stiffness values of each component of the tire. Summary of the Invention

[0027] The present invention provides a method for indirectly measuring the rigidity of the carcass and tread of a tire, covering a large amount of test data. Starting from the mechanical properties of the tire, considering the influence of road surface friction and the offset of test data at the zero point, a corresponding model and calculation process are established, and the tread rigidity, carcass rigidity and overall static stiffness of the tire can be accurately obtained. This measurement method is applicable to the longitudinal, lateral and torsional directions.

[0028] In order to solve the above technical problems, the present invention adopts the following technical solutions:

[0029] A method for indirectly measuring the stiffness of the carcass and tread of a tire, comprising the following steps:

[0030] S100: Conduct longitudinal, lateral and torsional stiffness tests of the tire respectively, and collect test data when the tire deforms;

[0031] S200: Extract the generalized force and generalized displacement based on the collected test data, and calculate the test data by means of parameter identification to obtain the tread stiffness k s , the tread stiffness k f , the extreme value F of the generalized frictional force c and the offset Δx between the actual value and the test value of the displacement;

[0032] S300: Calculate the overall stiffness K of the tire according to the carcass stiffness k s and the tread stiffness k f .

[0033] Preferably, the tire camber angle in the step S100 is set to zero, and the test stops when the tire slips.

[0034] Preferably, the test data includes the test time m, the tire pressure p and the vertical load force n.

[0035] Preferably, the generalized force includes a lateral force c, a longitudinal force v, and a torsional force t; the generalized displacement includes a lateral displacement l1, a longitudinal displacement l2, and a torsional angle θ.

[0036] Preferably, the calculation formula for parameter identification in step S200 is as follows:

[0037] In the formula, F is the generalized frictional force, and x is the generalized displacement.

[0038] Preferably, the calculation formula for the overall tire stiffness is as follows:

[0039] K -1 = k f -1 + k s -1 .

[0040] From the above technical solutions, it can be seen that the present invention has the following beneficial effects: Based on the Dahl friction model and the assumption of rigid series connection between the carcass and the tread, the present invention derives a new relationship model between the generalized force and the generalized displacement in the tire static stiffness test, and proposes a method for indirectly measuring the rigidities of the carcass and the tread of the tire in the longitudinal, lateral, and torsional directions based on this model. By identifying the parameters of the new relationship model through test data, the rigidities of the carcass and the tread can be separated, and the overall static stiffness of the tire can be calculated, realizing the decoupling of the stiffness of the tire components and separating the rigidities of the carcass and the tread. At the same time, since the measurement method disclosed in this patent takes into account the influence of road surface friction and the offset at the zero point of the testing machine, the measurement of the tire static stiffness is more accurate. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1 is a flowchart of an alternative embodiment of the present invention;

[0042] Figure 2 is a schematic diagram of the force on the tire at any moment during the longitudinal, lateral, and torsional static stiffness tests;

[0043] Figure 3 is a flowchart for fitting the generalized force;

[0044] FIG. 4 is a comparison curve graph of the torsional stiffness test and the fitted data of an alternative embodiment of the present invention;

[0045] FIG. 5 is a comparison curve graph of the lateral stiffness test and the fitted data of an alternative embodiment of the present invention;

[0046] FIG. 6 is a comparison curve graph of the longitudinal stiffness test and the fitted data of an alternative embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0047] The following is a detailed description of a preferred embodiment of the present invention in conjunction with the accompanying drawings.

[0048] As Figure 1 shown, the embodiment of the present invention provides a method for indirectly measuring the carcass and tread stiffness of a tire in the longitudinal, lateral, and torsional directions, including the following steps:

[0049] S100: Conduct longitudinal, lateral, and torsional stiffness tests on a tire static stiffness testing machine.

[0050] Specifically, install the tire to be tested on the static stiffness testing machine, set the test parameters, set the tire camber angle to zero, set the tire air pressure p and the vertical load force n to the corresponding test values, set the displacement loading speed to a relatively small value, generally set the displacement loading speed to 50 mm / min. After the above parameters are set, conduct longitudinal, lateral, and torsional stiffness tests in sequence, control the loading speed to make the tire approach the quasi-steady state, and the test ends when the tire slips. The test data at least includes time m, tire air pressure p, vertical force, generalized forces (lateral force c, longitudinal force v, torsional force t), and generalized displacements (lateral displacement l1, longitudinal displacement l2, torsional angle θ).

[0051] S200: Extract the generalized forces and generalized displacements from the collected test data, and calculate the test data through parameter identification to obtain the carcass stiffness k s , the tread stiffness k f , the extreme value of the generalized friction force F c and the offset Δx between the actual displacement value and the test value. The calculation formulas for the parameters to be identified are as follows:

[0052]

[0053] S300: Calculate the overall tire stiffness K according to the carcass stiffness k s and the tread stiffness k f . The calculation formula is as follows:

[0054] K -1 =k f -1 +k s -1 .

[0055] In this embodiment, both the generalized force and the generalized displacement can be directly obtained from the test data. By substituting the values of the generalized force and the generalized displacement into the calculation formula and using the parameter identification method, the values of F c , Δx, k f , k s can be obtained. The derivation process of the calculation formula is as follows:

[0056] The Dahl model assumes that before the maximum friction force is reached, the contact peaks between interfaces will produce deformations similar to spring behavior. This model was proposed by Dahl in the late 1960s. It regards the friction characteristics in the stagnant state as a dynamic friction model similar to spring characteristics, so there will be a small slip (pre-sliding displacement). To describe the relationship between the friction force and displacement, the Dahl model uses a differential equation to describe:

[0057]

[0058] In the model, F represents the generalized friction force, F c represents the extreme value that the generalized friction force can reach, x represents the generalized displacement, k represents the stiffness coefficient, and α determines the shape of the curve, generally 1. The larger α is, the greater the curvature of the curve.

[0059] In the longitudinal, lateral, and torsional stiffness tests, the change of the applied generalized displacement is very slow, similar to a steady-state process. The force diagram of the tire at any moment can be obtained from Figure 2 as shown:

[0060] The whole tire is regarded as a series connection between the carcass and the friction between the tread and the ground. The carcass stiffness is expressed as k s , the displacement is x1, and the tread stiffness is expressed as k f , the displacement is x2. Since the longitudinal, lateral, and torsional stiffness tests are steady-state tests, the tire is in overall force balance, that is, the force at the rim and the friction force between the tread and the ground are both F, and the resultant force at the connection between the tread and the carcass is zero.

[0061] Since the tire is a series connection of the carcass and the tread, the overall tire stiffness K can be calculated by the following formula:

[0062] K -1 =k f -1 +k s -1 (2)

[0063] The Dahl model can be used to describe the friction between the tread and the ground. Since the change direction of the generalized force is the same as the slip direction, υ in formula (1) is taken as positive, and α = 1, and it is expressed as follows:

[0064]

[0065] This expression is a first-order differential equation. The boundary condition is that when x = 0, F = 0, and the solution is:

[0066]

[0067] The deformation law of the carcass satisfies Hooke's law, i.e.:

[0068] F = k s x1 (5)

[0069] Considering the equipment error in the experiment, Δx is introduced to represent the offset between the actual value and the experimental value of the displacement, i.e.:

[0070] x = x0 - Δx (6)

[0071] x is the measured value of the generalized displacement of the tire in the experiment, and x0 is the actual value of the generalized displacement of the tire.

[0072] The actual value of the generalized displacement of the tire is the superposition of the displacements of the carcass and the tread, then:

[0073] x0 = x1 + x2 (7)

[0074] Substituting formulas (5), (6), and (7) into formula (4), we get:

[0075]

[0076] In this way, we can identify the parameters through the experimental data and obtain the carcass stiffness k s and the tread stiffness k f values.

[0077] Select a sample tire to conduct lateral, longitudinal, and torsional static stiffness tests to obtain the generalized force and generalized displacement data at low and high loads for each test. Using the experimental data and formula (8), the numerical values of the identified parameters can be obtained. Substituting the identified carcass stiffness k s and the tread stiffness k f into formula (2), the overall stiffness K of the tire can be obtained.

[0078] The identification results are shown in Table 1. It can be seen from Table 1 that the tread stiffness k f increases with the increase of the load, while the carcass stiffness k s does not change with the load in the torsional and longitudinal stiffness tests and decreases with the load in the lateral stiffness test. At the same time, in the lateral and longitudinal stiffness tests, the carcass stiffness k s is much smaller than the tread stiffness k f , so its overall stiffness is mainly affected by the carcass stiffness k s ; while in the torsional stiffness test, the carcass stiffness k s and the tread stiffness k f are of the same order of magnitude, so its overall stiffness is jointly affected by the carcass stiffness k s and the tread stiffness k f .

[0079] In Equation (8), F and x are the generalized force and generalized displacement obtained from test data, and F c , Δx, k f , k s are the parameters to be identified.

[0080] The least squares method is used to define the error:

[0081]

[0082] F sim is the fitted value of the generalized force, and F test is the measured value of the generalized force.

[0083] By programming to solve for the minimum error value ε, the values of F c , Δx, k f , k s can be identified, thus obtaining the complete Equation (8).

[0084] Equation (8) is an implicit function of the generalized force F and the generalized displacement x, belonging to a transcendental equation, for which an analytical solution cannot be obtained, and only a numerical solution can be obtained.

[0085] The iterative method can be used to find the fitted value F sim of the generalized force. To ensure the convergence of the iterative sequence, Equation (8) is rewritten as

[0086]

[0087] Since the test data is near the exact iterative solution, the test data is used as the initial value of the iteration.

[0088] The specific iterative process is as shown in Figure 3 .

[0089] Figure 3 where δ is the accuracy of the fitted value of the controlled generalized force relative to the test value.

[0090] Through the above calculation rules, the fitted value F sim of the generalized force corresponding to each generalized displacement x can be obtained.

[0091] Using the test data, the identified parameters, and the iterative method, the fitted value of the generalized force corresponding to the generalized displacement can be obtained. Comparing with the original test data, as shown in Figures 4, 5, and 6.

[0092] The fitting error between the fitted value of the generalized force and the original test data is shown in Table 2.

[0093] As can be seen from FIGS. 4, 5, 6 and Table 2, the fitting error between the fitting values of the generalized forces and the original test data is very small, and the fitting effect is very good, verifying the correctness of the identified parameters, that is, the tread and carcass stiffnesses separated by the indirect measurement method proposed in this patent are appropriate.

[0094] Table 1

[0095]

[0096] Table 2

[0097]

[0098] The above-described embodiments are only descriptions of the preferred embodiments of the present invention, and do not limit the scope of the present invention. Without departing from the design spirit of the present invention, various deformations and improvements made by those of ordinary skill in the art to the technical solutions of the present invention shall fall within the protection scope determined by the claims of the present invention.

Claims

1. An indirect method for measuring the stiffness of the carcass and tread, characterized in that, It includes the following steps: S100: Conduct longitudinal, lateral and torsional stiffness tests on the tire respectively, and collect the test data when the tire deforms; S200: Extract the generalized force and generalized displacement based on the collected test data, and calculate the test data through parameter identification to obtain the tread stiffness k s , the tread stiffness k f , the extreme value F of the generalized friction force c and the offset Δx between the actual displacement value and the test value. The calculation formula for the parameter identification is as follows: where F is the generalized frictional force and x is the generalized displacement; S300: Calculate the overall tire stiffness K based on the carcass stiffness k s and the tread stiffness k f .

2. The indirect method for measuring the stiffness of the carcass and tread according to claim 1, characterized in that, In step S100, the tire camber angle is set to zero, and the test stops when the tire slips.

3. The indirect method for measuring the stiffness of the carcass and tread according to claim 2, characterized in that, The test data includes the test time m, the tire pressure p and the vertical load force n.

4. The indirect method for measuring the stiffness of the carcass and tread according to claim 3, characterized in that, The generalized forces include the lateral force c, the longitudinal force v and the torsional force t; the generalized displacements include the lateral displacement l1, the longitudinal displacement l2 and the torsional angle θ.

5. The indirect method for measuring the stiffness of the carcass and tread according to claim 4, characterized in that, The calculation formula for the overall stiffness of the tire is as follows: K -1 = k f -1 + k s -1 .

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