Tire relaxation characteristics test method

Abstract

The present invention discloses a tire relaxation characteristic testing method, which belongs to the field of tire performance evaluation. It includes the steps of calculating the initial steady-state mechanical response mean F0, calculating the steady-state mean of the mechanical response, calculating the delay time error T of the test system, and calculating the delay time error T of the test system. e , determine the function fitting start time T s Steps, data interception steps, determine the numerical fitting start time T s The present invention is applied to tire performance evaluation and solves the problem in related arts that relaxation characteristic test curves cannot accurately obtain the starting calculation time of the mechanical response. It has the characteristics of being able to accurately determine the time constant starting time and function fitting starting time of transient angular step data obtained by different test methods, test equipment, or simulation methods, and obtain accurate time constants. The calculation method can be programmed to reduce human errors, improve the accuracy of tire relaxation characteristic characterization, and provide method guidance for quickly and automatically obtaining tire relaxation characteristic parameters.

Description

Technical Field

[0001] The invention belongs to the field of tire performance evaluation, and in particular relates to a tire relaxation characteristic testing method. Background Art

[0002] Radial tires are vehicle load-bearing components made of a composite of carbon black-filled rubber and reinforcing materials. Due to the nonlinear mechanical properties of rubber composites, the tire exhibits a delayed mechanical response to transient angle (or slip rate, displacement, etc.) inputs. This phenomenon is characterized in the tire industry by relaxation characteristics. For example, the delayed response of lateral force to a transient side slip angle input is called lateral relaxation, and the delayed response of longitudinal force to a transient longitudinal slip input is called longitudinal relaxation. Research results show that in vehicle handling evaluation, by adding a parametric representation of the tire's lateral relaxation characteristics, the gain attenuation of indicators such as the vehicle's transient yaw rate and lateral acceleration under steering wheel angle step input conditions can be significantly improved. Therefore, a complete and correct expression of tire relaxation characteristics is essential for tuning the transient performance of the vehicle chassis.

[0003] In vehicle-tire dynamics, tire relaxation length is the primary indicator for characterizing tire relaxation characteristics. It is defined as the distance a tire rolls within the time (time constant) required to reach 63.2% of its steady-state response force value after a transient input. The calculation method is shown in the following formula.

[0004]

[0005] L=0.277778·V·T A (2)

[0007] Where, F(t)—transient response force, N; F t —mean value of steady-state mechanical response, N; L—relaxation length, m; τ—time constant, s; T A —Relaxation characteristic response time (the sum of the time constant and the test system delay response error), s; V—tire running speed, km / h.

[0008] In recent years, Qiu Changfeng, Li Fei, CN 109556891 B, CN 112414728 B and CN115096612A have published tire lateral relaxation length measurement methods and data processing methods; CN109612748B, CN 111504663 B and others have published tire longitudinal relaxation length measurement methods and data processing methods; W Luty and Wei Chongfeng calculated the relaxation length using tire finite element relaxation simulation analysis results. Although these documents describe the identification calculation method or formula function of the relaxation length, they do not specify the specific processing method of the test data, nor do they consider the uncertainty of the initial calculation time point of the mechanical response time constant (such as Figure 1 This error has little impact on low speeds or parking conditions, but it can lead to larger calculation errors due to increased speed in high-speed conditions such as double lane changes, steering wheel angle steps, and transient acceleration or braking.

[0009] At the same time, Qingdao Sentury Tire announced the test method and software identification method for the lateral relaxation length of tires. However, the literature pointed out that the relaxation length data processing process is cumbersome and the use of numerical analysis software for identification is prone to errors or non-convergence of calculations; there is also the relaxation length characterization error caused by the uncertainty of the mechanical response data truncation interval and the initial calculation time point of the time constant, which affects the convergence of the dynamic model calculation.

[0010] about Figure 1 , F0: initial steady-state rolling dynamic response mean; F T2 : force value corresponding to the time constant; F T3 :90%F t Corresponding force value; T e : Test system delay time; T0: transient input time point; T1: time constant theoretical starting time; T2: time constant (τ); T3: 90% F t Corresponding time; T s : Function fitting starting time (cut-off time point); T t :End time, it should be noted that:

[0011] (1) Transient input part

[0012] The transient input table in the figure shows that a tire dynamic mechanical testing machine (such as the Flat Trac CT III testing machine from MTS in the United States) applies an angle (or slip rate, displacement, etc.) to the tire in 0.1s or less. Due to the minimum response accuracy limit of the equipment sensor itself and the response delay of the control circuit driving the operating mechanism, there will be a time error between the test program command input and the equipment action, that is, the test system delay time T e .

[0013] (2) Mechanical response part

[0014] During the rolling process, the tire will produce a corresponding mechanical response to the transient input of the test equipment. Due to the nonlinear stress-strain of the tire rubber, the mechanical response cannot respond immediately like a metal part with a high elastic modulus, resulting in a nonlinear mechanical response in area A. First, the tire rolls freely, and the steady-state response force values in all directions on the ground surface remain stable. The average of the steady-state response forces during the free rolling time can be obtained to obtain the initial steady-state rolling dynamic response mean F0. Afterwards, when the test program command is issued at time T0, the control circuit drives the operating mechanism to control the tire to produce transient deformation, and the tire ground surface mechanics responds to the deformation with a lag, that is, T0~T in the figure. s The nonlinear interval between the first drop and then rise. Then the tire response force value gradually increases until the force value fluctuation is small and reaches a relatively stable state. The average value of the steady-state response force within a specified time can be obtained to obtain the steady-state mechanical response mean F t Since T0~T s The curve is nonlinear, so the test data needs to be eliminated to accurately calculate the time constant and find the numerical fitting start time (cutoff time point) T of the mechanical response. s , and then determine the time constant starting time T1 through formula (1), but T s Special data processing is required to obtain it, but the relevant literature fails to provide a specific method description, resulting in large differences in relaxation length values when processing data for different test equipment, test methods, or simulation methods, affecting the characterization accuracy of the transient part of the tire dynamics model. Summary of the Invention

[0015] In view of the shortcomings of the existing technology, the technical problem to be solved by the present invention is that the relaxation characteristic test curve in the related technology cannot accurately obtain the starting calculation time of the mechanical response. A data processing method for the field of tires and their evaluation is proposed, and specifically a tire relaxation characteristic test method is provided. It can accurately determine the time constant starting time and function fitting starting time of transient angular step data obtained by different test methods or test equipment or simulation methods to obtain an accurate time constant. The calculation method can be programmed to reduce human errors, improve the accuracy of tire relaxation characteristic characterization, and provide method guidance for quickly and automatically obtaining tire relaxation characteristic parameters.

[0016] In order to solve the technical problem, the technical solution adopted by the present invention is:

[0017] The present invention provides a tire relaxation characteristic testing method, comprising the steps of calculating an initial steady-state mechanical response mean value F0, calculating a steady-state mechanical response mean value F t Step 1: Calculate the test system delay time error T e , determine the function fitting start time Ts Steps, data interception steps, determine the numerical fitting start time T s Steps, and relaxation length calculation steps;

[0018] The relaxation length calculation step is to numerically fit the starting time T s As the starting point of curve fitting, T1 is taken as the theoretical starting point of the time constant. The mechanical response data is fitted based on the following formula to obtain the time constant τ:

[0019]

[0020] Then, the relaxation length is calculated according to the following formula:

[0021] L=0.277778·V·T A .

[0022] Preferably, the step of calculating the initial steady-state mechanical response mean F0 includes:

[0023] For test or simulation analysis data, specify a time interval before the corresponding time of the transient input, calculate the mean value of the mechanical response in this time interval, and obtain the F0; or

[0024] A program calculation method is used to specify a transient input time point, and the program automatically calculates the mean force value corresponding to each time point in the interval from time zero to the transient input time point T0. When the mean value reaches the minimum and the length of the corresponding time interval is not less than 20% of T0, the mean mechanical response value of this time interval is obtained to obtain the said F0;

[0025] If F0 is a non-zero value, the mechanical response curve is vertically translated as a whole to set F0 to zero, and the mechanical response curve is horizontally translated as a whole to set T0 to zero.

[0026] Preferably, the step of calculating the steady-state mean of the mechanical response includes: specifying a steady-state force value time point, calculating the mean to obtain F t ;or

[0027] The program calculates the time automatically from the end time T t Recursively forward, calculate each time point to T t The force value is the mean value. When the mean value reaches the maximum and the corresponding time interval length is not less than 20% (T t -T3), calculate the mean mechanical response of this time interval and get F t .

[0028] Preferably, the calculation test system delay time error T eIt includes: taking more than two data points near 50% of the transient input and feedback peak, calculating the corresponding time response errors and taking the average; if the input and feedback values are not equal, linear fitting can be used to calculate the time corresponding to the same transient input value to obtain the delay time error; for finite element simulation method calculations, there is no need to consider the system delay time error.

[0029] Preferably, the determination function fitting start time T s The steps include:

[0030] F t -F(t)=K·e -m·t

[0031] Wherein, the left side is the difference between the mean value of the steady-state mechanical response and the response force value at each moment, the right side is the power function, and K is the amplitude of the power function. The linear equation is obtained by taking the logarithm with a base greater than zero and not equal to 1 on both sides of the above equation and simplifying it.

[0032] Preferably, the determination function fitting start time T s The steps include:

[0033] F t -F(t)=K·e -m·t

[0034] Wherein, the left part is the difference between the mean value of the steady-state mechanical response and the response force value at each moment, the right side is the power function, and K is the amplitude of the power function;

[0035] Take the base 10 logarithm of both sides of the above equation, that is

[0036] log 10 (F t -F(t))=log 10 (K·e -m·t )

[0037] Simplify, and we get

[0038] log 10 (F t -F(t))=log 10 (K)-0.434294·m·t

[0039] Get the slope of -0.434294m, log 10 (K) is the equation of the line with the intercept.

[0040] Preferably, the data interception step includes: intercepting data between the transient input time T0 and the time when the steady-state mechanical response is reached, which is 63.2%-90% of the mean value of the mechanical response.

[0041] Preferably, the determination of the numerical fitting start time Ts The steps include: eliminating T0~T s After the nonlinear interval data between the two points are obtained, linear fitting is performed on the valid data points;

[0042] The principle of data elimination is: monitor the change of curve fitting accuracy during the elimination process, and the fitting accuracy is calculated as follows:

[0043]

[0044] Where RSQ is the fitting accuracy, the closer to 1 the better; P s,i is the curve fitting value at point i, i=1,2…,n; P t,i is the test or simulation value at point i; P t,avg is the test or simulation mean;

[0045] When the fitting accuracy reaches above 99%, the data exclusion interval can be obtained. The time corresponding to the last set of data in the exclusion interval is the function fitting start time T s .

[0046] Preferably, the time corresponding to the last set of data in the excluded data interval is the function fitting start time T s Need to ensure T s Less than 25% F t The corresponding time.

[0047] Preferably, during the data processing, after the steady-state mechanical response value is calculated, a normalized processing method is adopted, that is,

[0048] make

[0049]

[0050] Take the base 10 logarithm of both sides, that is

[0051]

[0052] Simplify, and we get

[0053]

[0054] The data processing process removes data points that make the logarithmic function invalid and ensures that the independent variable of the logarithmic function is greater than zero.

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

[0056] The present invention provides a tire relaxation characteristic testing method, which not only takes into account the influence of the relaxation characteristic mechanical response curve on the relaxation length, but also takes into account the influence of the delayed response error of the test equipment or the test method itself, thereby improving the accuracy of relaxation length calculation and the calculation universality between different test equipment, and can quickly and accurately obtain the relaxation length calculation result. The calculation process does not require a tedious data processing process, and the test or simulation data is fitted by a linear equation, so there is no problem of data fitting calculation failure; a method for intercepting the effective data interval of the relaxation characteristic mechanical response curve is proposed, and the interception range of the effective data interval of the mechanical response curve is defined, which solves the problem of the time interception method that has not been proposed or solved in relevant technical documents; the method is suitable for data processing of the mechanical response curve of the tire after transient input in the tire industry, and tire relaxation characteristic parameters can be quickly obtained by using simple data calculation, avoiding the problems of unsatisfactory data processing, errors between different test equipment or test methods, and data calculation failure. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] Figure 1 Schematic diagram of tire transient input and its mechanical response;

[0058] Figure 2 This is a schematic diagram of the tire mechanical response data capture;

[0059] Figure 3 Linear fitting intention for tire mechanical response data;

[0060] Figure 4 Linear fitting intention for valid data points of tire mechanical response;

[0061] Figure 5 This is the original data graph of the test of Example 1;

[0062] Figure 6 This is a translation diagram of the lateral force response curve of Example 1;

[0063] Figure 7 This is a schematic diagram of the delay time error calculation of the test system in Example 1;

[0064] Figure 8 0~63.2%F of Example 1 t Schematic diagram of mechanical response in logarithmic interval;

[0065] Figure 9 This is a schematic diagram of the mechanical response in the logarithmic range of 0-90% Ft of Example 1;

[0066] Figure 10 is T of Example 1 s = Schematic diagram of the fitting results of the effective data points of the relaxation characteristics after 0.203125s;

[0067] Figure 11 is T of Example 1 s = Schematic diagram of the fitting results of the effective data points of the relaxation characteristics after 0.1875s;

[0068] Figure 12 This is the original data curve of the longitudinal force simulation of Example 2;

[0069] Figure 13 This is the curve of the original data of the longitudinal force simulation of Example 2 after horizontal movement for 0.15s;

[0070] Figure 14 0~63.2%F of Example 2 t Logarithmic interval mechanical response curve;

[0071] Figure 15 This is the fitting curve of the effective data points of the longitudinal relaxation characteristics of Example 2. DETAILED DESCRIPTION

[0072] The following is a detailed and complete description of the technical solutions in the specific embodiments of the present invention, with reference to the accompanying drawings. It should be understood that the described embodiments are merely some specific implementations of the overall technical solution of the present invention, and are not exhaustive. All other implementations derived by those skilled in the art based on the overall concept of the present invention are intended to fall within the scope of protection of the present invention.

[0073] The present invention provides a tire relaxation characteristic testing method, comprising the steps of calculating an initial steady-state mechanical response mean value F0, calculating a steady-state mechanical response mean value F t Step 1: Calculate the test system delay time error T e , determine the function fitting start time T s Steps, data interception steps, determine the numerical fitting start time T s Steps, and relaxation length calculation steps;

[0074] The relaxation length calculation step is to numerically fit the starting time T s As the starting point of curve fitting, T1 is taken as the theoretical starting point of the time constant. The mechanical response data is fitted based on the following formula to obtain the time constant τ:

[0075]

[0076] Then, the relaxation length is calculated according to the following formula:

[0077] L=0.277778·V·T A (2)

[0078] Since the theoretical starting time T1 of the power function time constant cannot be determined, and the time T0 is the zero time of the mechanical response curve, a time offset is added to equation (1), and the model is modified to (7). This method not only takes into account the influence of the relaxation characteristic mechanical response curve on the relaxation length, but also takes into account the influence of the delayed response error of the test equipment or test method itself, thereby improving the accuracy of the relaxation length calculation and the calculation universality between different test equipment. It can quickly and accurately obtain the relaxation length calculation result. The calculation process does not require a tedious data processing process, and the test or simulation data is fitted by a linear equation, without the problem of data fitting calculation failure. A method for intercepting the effective data interval of the relaxation characteristic mechanical response curve is proposed, and the interception range of the effective data interval of the mechanical response curve is defined, solving the problem of the time interception method that has not been proposed or solved in the relevant technical literature. This method is suitable for the tire industry for data processing of the tire mechanical response curve after transient input. It can quickly obtain the tire relaxation characteristic parameters by using simple data calculation, avoiding the problems of unsatisfactory data processing, errors between different test equipment or test methods, and data calculation failure.

[0079] In a preferred embodiment, the step of calculating the initial steady-state mechanical response mean F0 includes:

[0080] For test or simulation analysis data, specify a time interval before the corresponding time of the transient input, calculate the mean value of the mechanical response in this time interval, and obtain the F0; or

[0081] A program calculation method is used to specify a transient input time point, and the program automatically calculates the mean force value corresponding to each time point in the interval from time zero to the transient input time point T0. When the mean value reaches the minimum and the length of the corresponding time interval is not less than 20% of T0, the mean mechanical response value of this time interval is obtained to obtain the said F0;

[0082] If F0 is a non-zero value, the mechanical response curve is vertically translated as a whole, and F0 is set to zero. Since the relaxation characteristics only focus on the mechanical response part, the mechanical response curve is horizontally translated as a whole, and T0 is set to zero.

[0083] In a preferred embodiment, the step of calculating the steady-state mean of the mechanical response is similar to the step of calculating F0, including: specifying the steady-state force value time point, calculating the mean to obtain F t ;or

[0084] The program calculates the time automatically from the end time T t Recursively forward, calculate each time point to T t The force value is the mean value. When the mean value reaches the maximum and the corresponding time interval length is not less than 20% (T t -T3), calculate the mean mechanical response of this time interval and get F t .

[0085] In a preferred embodiment, the calculation test system delay time error T e It includes: taking more than two data points near 50% of the transient input and feedback peak, calculating the corresponding time response errors and taking the average; if the input and feedback values are not equal, linear fitting can be used to calculate the time corresponding to the same transient input value to obtain the delay time error; for finite element simulation method calculations, there is no need to consider the system delay time error.

[0086] In a preferred embodiment, the determination function fitting start time T s The steps include:

[0087] F t -F(t)=K·e -m·t (3)

[0088] Wherein, the left side is the difference between the mean value of the steady-state mechanical response and the response force value at each moment, the right side is the power function, and K is the amplitude of the power function. The linear equation is obtained by taking the logarithm with a base greater than zero and not equal to 1 on both sides of the above equation and simplifying it.

[0089] In a preferred embodiment, the determination function fitting start time T s The steps include: From formula (1), it can be seen that the mechanical response curve is a power function with the natural constant e as the base, let

[0090] F t -F(t)=K·e -m·t (3)

[0091] Wherein, the left part is the difference between the mean value of the steady-state mechanical response and the response force value at each moment, the right side is the power function, and K is the amplitude of the power function;

[0092] Take the base 10 logarithm of both sides of the above equation, that is

[0093] log 10 (F t -F(t))=log 10 (K·e -m·t ) (4)

[0094] Simplify, and we get

[0095] log 10 (F t -F(t))=log 10 (K)-0.434294·m·t(5)

[0096] Get the slope of -0.434294m, log 10(K) is the equation of the line with the intercept. Because the mechanical response curve may contain all negative values, the absolute values of the left and right sides of the function should be taken before taking the logarithm to ensure that the logarithmic function can take certain values. The data processing process removes independent variable values that make the logarithmic function invalid.

[0097] In a preferred embodiment, the data interception step includes: intercepting data between the transient input time T0 and the time when the steady-state mechanical response reaches 63.2%-90% of the mean value. Figure 2 The data between T0 and T2 or T0 and T3. The sub-interval of the data selection interval must contain the mechanical response data corresponding to T0 to T2, otherwise it will affect the starting time (cutoff time point) of the numerical fitting. s The selection and linear fitting accuracy can ensure that there are enough data samples and the data interval corresponding to the time constant is included. Figure 2 The data processed according to formula (4) and the data interception position diagram are shown. Where, T0: transient input time point; T1: time constant starting time; T2: time constant; T3: 90% F t Corresponding time. As can be seen from the figure, on the mechanical response curve, the data curve at time T0 gradually decreases from the approximate horizontal level, mainly because T0~T s The force value is nonlinear between the two periods; the data fluctuate greatly after time T3, which has a great impact on the accuracy of the linear fitting based on formula (5). This is because the force data tends to a steady-state value and the independent variables of some logarithmic functions tend to zero.

[0098] In a preferred embodiment, the determination of the numerical fitting start time T s The steps include: eliminating T0~T s After the nonlinear interval data between the two points are obtained, linear fitting is performed on the valid data points;

[0099] The principle of data elimination is: monitor the change of curve fitting accuracy during the elimination process, and the fitting accuracy is calculated as follows:

[0100]

[0101] Where RSQ is the fitting accuracy, the closer to 1 the better; P s,i is the curve fitting value at point i, i=1,2…,n; P t,i is the test or simulation value at point i; P t,avg is the test or simulation mean.

[0102] When the fitting accuracy reaches above 99%, the data exclusion interval can be obtained. The time corresponding to the last set of data in the exclusion interval is the function fitting start time T s .

[0103] like Figure 3 The figure shows the linear fitting diagram of the intercepted data according to formula (5). Among them, 1 is the overall linear fitting of the intercepted data interval; 2 is the linear fitting of the valid data points. The fitting line 1 (blue) in the figure is the fitting result of all the intercepted data. It can be seen that the overall curve is affected by T0~T s The nonlinear interval between the two leads to poor fitting accuracy and large errors. Figure 4 The fitted straight line 2 (green) is shown as Figure 3 The enlarged diagram of the fitted straight line 2 is the result of eliminating T0~T s After the nonlinear interval data between the two points (the black point data in the enlarged figure in the figure), the effective data points (the red point data in the enlarged figure in the figure) are linearly fitted. Figure 4 It can be seen that the effective data point fitting curve is generally close to the response data, with a small error. s Principle of eliminating nonlinear data: Monitor the change of curve fitting accuracy during the elimination process. The fitting accuracy calculation is shown in formula (6). When the fitting accuracy reaches more than 99%, the elimination data interval can be obtained. The time corresponding to the last set of data in the elimination data interval is the function fitting start time (truncation time point) T s , and at the same time, T s Less than 25% F t The corresponding time is used to ensure that the relaxation length fit has sufficient data interval.

[0104] In a preferred embodiment, during the data processing, after the steady-state mechanical response value is calculated, a normalized processing method is adopted, that is,

[0105] make

[0106]

[0107] Take the base 10 logarithm of both sides, that is

[0108]

[0109] Simplify, and we get

[0110]

[0111] The data processing process removes data points that make the logarithmic function invalid and ensures that the independent variable of the logarithmic function is greater than zero.

[0112] In order to more clearly and in detail introduce the tire relaxation characteristics testing method provided by the embodiment of the present invention, it will be described below in conjunction with specific embodiments.

[0113] Example 1

[0114] Take the lateral relaxation length test data processing of the passenger car radial tire 215 / 60R17 94V DH16S as an example

[0115] 1. Test plan design

[0116] The tire lateral relaxation characteristics were tested using the Flat-Trac CT III six-component force test bench from MTS, USA. The test method is shown in Table 1.

[0117] Table 1 Rotational slip angle step test method

[0118]

[0119] Note: The starting time of step 5 in the table corresponds to the starting time point T0 of the transient input of the test equipment.

[0120] 2. Data Analysis

[0121] According to the test conditions shown in Table 1, the test raw data curve obtained from step 4 is as follows: Figure 5 As shown, the data processing and calculation process is as follows:

[0122] (1) Calculate the initial steady-state rolling dynamic response mean F0. Calculate the mean lateral force in the first 5 seconds (0 to T0 time interval) and obtain F0 = 97.8419N. Perform an overall vertical translation of the mechanical response curve, set F0 to zero, and horizontally translate the data after T0, taking T0 as the zero time of the curve, as shown in the following example: Figure 6 shown.

[0123] (2) Calculate the mean steady-state response force F t .Pick Figure 6 The average lateral force in the 3-5s time interval is obtained as F t =-1400.1435N.

[0124] (3) Calculate the test system delay time T e . Take three input and feedback data points at the 50% sideslip angle peak, such as Figure 7 Among them, A1(0.046875,0.4386233), A2(0.054688,0.5555694), A3(0.0625,0.6697971), B1(0.109375,0.4025187), B2(0.117188,0.517275), B3(0.125,0.6367611), linear fitting is performed on A1, A2, A3 and B1, B2, B3 respectively, as shown Figure 7 As shown, 1 is the fitting curve of the sideslip angle input value, y = 14.795x-0.2544, R 2≈1; 2 is the fitting curve of the sideslip angle feedback value, y=14.992x-1.238, R 2 =0.9999. The corresponding time is calculated respectively with the input side deflection angle as input, and the final time response error mean T is calculated. e =0.064890s, as shown in Table 2.

[0125] Table 2 Calculation of test system response delay error

[0126]

[0127] (4) Data capture. Get 0~63.2%F respectively t and 0~90%F t The data between the two are processed using the logarithm with base 10 of the left part of formula (5), as follows: Figure 8 and Figure 9 shown.

[0128] (5) Linear fitting. Gradually remove data from time zero and calculate the linear fitting accuracy of the removed data. When the fitting accuracy reaches more than 99%, the removal can be stopped and the time point corresponding to the last removal of data can be recorded to obtain the function fitting start time (truncation time point) T s . Figure 8 and Figure 9 In the figure, linear fitting is performed on the valid data after removing the data (black data points) to obtain the goodness of fit R 2 are 0.9974 and 0.9932 respectively, T s They are 0.203125s and 0.1875s respectively, both less than 25% F t The corresponding time is 0.3125s.

[0129] 3. Results and Discussion

[0130] (1) Numerical fitting of relaxation characteristics. In this implementation case, the steady-state response force value F t As a parameter to be fitted for the relaxation characteristic, it is used to determine the difference between the numerically fitted steady-state response force value and the initial steady-state response mean value.

[0131] Establish the target optimization function as shown in formula (7), Figure 6 The effective data points in the numerical optimization were used to obtain the time constants of 0.47295s and 0.4752s, and the steady-state lateral forces were -1397.0720N and -1397.2748N. The fitting results are shown in Figure 2. Figure 10 and Figure 11 As shown in the figure, the fitting results show that the difference between the steady-state lateral force obtained by the program fitting and the initial steady-state response mean is very small, and the fitting accuracy is above 0.99, approaching 1.

[0132] (2) Relaxation length calculation results. According to formula (2), the relaxation lengths at a running speed of 5 km / h are 0.7467 m and 0.75012 m, respectively. It can be seen that the size of the data interception interval has a slight effect on the relaxation length, but the data interval selection method of this patent has little effect on the relaxation length calculation results.

[0133] Example 2

[0134] Take the simulation data processing of the longitudinal relaxation length of the passenger car radial tire 215 / 60R17 94V DH16S as an example

[0135] 1. Simulation analysis solution

[0136] The Korean VTIRE finite element analysis system is used to simulate the tire longitudinal relaxation characteristics. The analysis step settings are shown in Table 3.

[0137] Table 3 Rotation slip angle step simulation analysis steps

[0138]

[0139] Note: The starting time of step 2 in the table corresponds to the starting time point T0 of the simulation transient slip input.

[0140] 2. Data Analysis

[0141] According to the analysis conditions shown in Table 3, the original data curve of the longitudinal force response is obtained, as shown in Figure 12 As shown in the figure, it can be seen that there are large numerical oscillations in the initial stage of the simulation, which will be removed during data processing. The data processing and calculation process are as follows:

[0142] (1) Calculate the initial steady-state rolling dynamic response mean F0. Remove Figure 12 The data of the numerical oscillation region from 0 to 0.075s is used to calculate the average longitudinal force from 0.075 to 0.15s, and the result is F0 = -45.167443 N. For the vertical translation curve, F0 is set to zero, and for the horizontal translation curve, T0 is set to zero, as shown in the following example: Figure 13 shown.

[0143] (2) Calculate the mean steady-state response force F t .calculate Figure 13 The average longitudinal force in the time interval of 0.4s to 0.55s is F t =3269.5341N.

[0144] (3) Determine the function fitting start time (truncation time point) T s This implementation case only intercepts 0~63.2%F tThe data between the two are processed by the logarithm with base 10 of the left part of formula (5), and Ts = 0.055947s is obtained, which is less than 25% of F t The corresponding time is 0.0664s, such as Figure 14 shown.

[0145] 3. Results and Discussion

[0146] (1) Time constant calculation results. Figure 13 Eliminate T s = The data before 0.055947s, retain the valid data points and use formula (7) for numerical optimization, and the time constant is 0.07402s and the steady-state longitudinal force is 3292.6277N. Figure 15 The figure shows the fitting results of the effective data points of the longitudinal relaxation characteristics. The fitting results show that the fitting accuracy reaches 0.99722, and the difference between the steady-state longitudinal force obtained by the system fitting and the calculated steady-state response mean is only 23.09362N, with an error of less than 1%.

[0147] (2) Relaxation length calculation results. The implementation case is a simulation calculation result, and the system delay time error does not need to be considered. Therefore, according to formula (2), the longitudinal relaxation length at a running speed of 60 km / h is 1.2337 m.

Claims

1. A tire relaxation characteristics testing method, characterized in that: Including calculation of the initial steady-state mechanical response mean F Step 0, calculate the steady-state mean value of the mechanical response, calculate the delay time error of the test system T e , determine the function fitting start time T s Steps, data interception steps, determine the starting time of numerical fitting T s Steps, and relaxation length calculation steps; The relaxation length calculation step is to numerically fit the starting time T s is the starting point of curve fitting, T 1 is the theoretical starting point of the time constant. The mechanical response data is fitted based on the following formula to obtain the time constant τ : Then, the relaxation length is calculated according to the following formula: ； Determining the function fitting start time T s The steps include: Where the left side is the difference between the mean value of the steady-state mechanical response and the response force value at each moment, the right side is a power function, and K is the amplitude of the power function. Take the logarithm with a base greater than zero and not equal to 1 on both sides of the above equation and simplify it to obtain the linear equation. The data interception step includes: intercepting the transient input moment in the mechanical response data T Data between 0 and 63.2%-90% of the mean value of steady-state mechanical response; Determining the function fitting start time T s Steps include: Elimination T 0- T s After the nonlinear interval data between the two points are obtained, linear fitting is performed on the valid data points; The principle of data elimination is: monitor the change of curve fitting accuracy during the elimination process, and the fitting accuracy is calculated as follows: Where, RSQ For fitting accuracy, the closer to 1 the better; P s,i is the curve fitting value at point i, i =1, 2…, n; P t,i is the test or simulation value at point i; P t,avg is the test or simulation mean; When the fitting accuracy reaches 99% or more, the data exclusion interval can be obtained. The time corresponding to the last set of data in the exclusion interval is the starting time of the function fitting. T s .

2. The tire relaxation characteristics testing method according to claim 1, characterized in that: The calculation of the initial steady-state mechanical response mean F The 0 steps include: For test or simulation analysis data, specify the time interval before the transient input corresponding time, calculate the mean value of the mechanical response in this time interval, and obtain the F 0; or Use program calculation method to specify the transient input time point, and the program will automatically calculate the time from zero to the transient input time point T Each time point in the interval 0 to T The force value corresponding to 0 is the mean value. When the mean value reaches the minimum and the length of the corresponding time interval is not less than 20%, T At 0, the mean mechanical response of this time interval is obtained, and the F 0; like F 0 is a non-zero value, the mechanical response curve is vertically translated as a whole. F 0 is set to zero, and the mechanical response curve is horizontally shifted as a whole. T 0 is set to zero.

3. The tire relaxation characteristics testing method according to claim 1, wherein: The step of calculating the steady-state mean value of the mechanical response includes: specifying a steady-state force value time point, calculating the mean value, and obtaining F t ;or The program calculates the time automatically from the end time. T t Recursively forward, calculate each time point to T t The force value is average, when the average value reaches the maximum and the corresponding time interval length is not less than 20% ( T t - T 3), calculate the mean mechanical response of this time interval and get F t .

4. The tire relaxation characteristics testing method according to claim 1, characterized in that: The calculation test system delay time error T e It includes: taking more than two data points near 50% of the transient input and feedback peak, calculating the corresponding time response errors and taking the average; if the input and feedback values are not equal, linear fitting can be used to calculate the time corresponding to the same transient input value to obtain the delay time error; for finite element simulation method calculations, there is no need to consider the system delay time error.

5. The tire relaxation characteristics testing method according to claim 1, characterized in that: Determining the function fitting start time T s The steps include: Wherein, the left part is the difference between the mean value of the steady-state mechanical response and the response force value at each moment, the right side is the power function, and K is the amplitude of the power function; Take the base 10 logarithm of both sides of the above equation, that is Simplify, and we get Get the slope of -0.434294m, log 10 (K) is the equation of the line with the intercept.

6. The tire relaxation characteristics testing method according to claim 1, characterized in that: The time corresponding to the last set of data in the excluded data interval is the function fitting start time T s Need for guarantee T s Less than 25% F t The corresponding time.

7. The tire relaxation characteristics testing method according to claim 1, characterized in that: In the data processing process, after the steady-state mechanical response value is calculated, the normalization method is adopted, that is, make Take the base 10 logarithm of both sides, that is Simplify, and we get The data processing process removes data points that make the logarithmic function invalid and ensures that the independent variable of the logarithmic function is greater than zero.

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