Method and device for testing coating rigidity of non-pneumatic tire

Abstract

The invention relates to the technical field of tire testing, in particular to a non-pneumatic tire coating rigidity testing method and device.The non-pneumatic tire coating rigidity testing method comprises the steps that coating force data and coating displacement data generated in the coating testing process are collected through a rigidity testing machine, and complete motion period testing data are formed; dividing the data points into a plurality of feature intervals according to a test load proportion; performing cubic polynomial fitting on the data in each feature interval to generate a fitting function; performing derivation operation on the fitting function to obtain a function expression that the coating rigidity changes along with displacement; and extracting a coating rigidity value corresponding to the characteristic displacement point from the expression as a node, and generating a coating rigidity characteristic curve through curve fitting. According to the method, through multi-stage data acquisition, refined interval division and mathematical model construction, accurate quantitative characterization of the coating rigidity of the non-pneumatic tire is realized, the reliability and engineering applicability of a test result are improved, and data support is provided for tire performance evaluation and structure optimization.

Description

Technical Field

[0001] This invention relates to the field of tire testing technology, and in particular to a method and apparatus for testing the sheath stiffness of a non-pneumatic tire. Background Technology

[0002] Currently, non-pneumatic tire sheath stiffness testing and vehicle tire performance evaluation technologies face the following technical challenges: As a new type of puncture-proof and explosion-proof product, non-pneumatic tires lack standardized testing methods for sheath stiffness. This results in the inability to obtain continuous and reliable load-displacement data in tire mechanical property measurements, thus affecting performance analysis during the tire development stage. For example, in vehicle tire performance evaluation scenarios, due to the lack of sheath stiffness testing, it is difficult to quantify the stiffness changes of the tire during forward loading and reverse unloading processes, which may cause distortion in the assessment of vehicle handling stability and increase safety risks. Summary of the Invention

[0003] To address the shortcomings of existing technologies, this invention provides a method and apparatus for testing the stiffness of non-pneumatic tire sheathing, solving the technical problem that the lack of relevant testing methods for the stiffness of non-pneumatic tire sheathing makes it impossible to accurately measure and analyze the mechanical properties of tires.

[0004] To solve the above-mentioned technical problems, the specific contents of the present invention are as follows: In a first aspect, the present invention provides a method for testing the stiffness of a non-pneumatic tire sheath, comprising: Step 1: Obtain the wrapping force data and wrapping displacement data generated by the non-pneumatic tire during the wrapping test to form test data for the complete motion cycle including the forward loading segment, the forward unloading segment, the reverse loading segment, and the reverse unloading segment; Step 2: For the test data, divide the data points into multiple characteristic intervals according to the proportion of the test load, wherein the characteristic intervals correspond to the 20%-40%, 40%-60%, and 60%-80% range of the load in each motion segment; Step 3: For each feature interval after division, perform cubic polynomial fitting using the covering force data and covering displacement data within the interval to generate the fitting function for each feature interval. Step 4: Differentiate the fitted function to obtain the functional expression of the change of the covering stiffness with displacement; Step 5: Extract the wrapping stiffness values ​​corresponding to the feature displacement points from the function expression as nodes, and use the nodes to generate the wrapping stiffness characteristic curve through curve fitting.

[0005] Furthermore, in the non-pneumatic tire sheath stiffness test method of the present invention, step 1 includes: A vertical load is applied to a non-pneumatic tire at a constant rate using the hydraulic servo system of a stiffness testing machine. When the vertical load reaches the first preset value, the protrusion device on the tire contact surface is activated simultaneously to apply the second load, causing the protrusion to displace. During the loading process, the correspondence between the covering force data and the covering displacement data is recorded at a set sampling frequency; After loading is complete, the unloading process is executed at the same rate, and the covering force data and covering displacement data during the unloading phase are collected. By changing the direction of force application and repeating the loading and unloading process, test data were obtained for four motion stages: forward loading, forward unloading, reverse loading, and reverse unloading.

[0006] Furthermore, in the non-pneumatic tire sheath stiffness test method of the present invention, step 2 includes: Using the test data, a scatter plot is generated with the displacement of the covering as the abscissa and the covering force as the ordinate. Based on the percentage range of the test load, the data points in the scatter plot are divided into three characteristic segments; The three characteristic zones correspond to the 20%-40% load range, the 40%-60% load range, and the 60%-80% load range, respectively.

[0007] Furthermore, in the non-pneumatic tire sheath stiffness test method of the present invention, step 3, performing cubic polynomial fitting, includes: Filter data points within the feature interval to remove outlier data points; The coefficients of the fitted curve are calculated using the least squares method; During the calculation process, a first weight is assigned to data points in the central region of the interval, and a second weight is assigned to data points in the edge region, wherein the first weight is greater than the second weight. The cubic polynomial fitting function is obtained by weighted calculation.

[0008] Furthermore, in the non-pneumatic tire sheath stiffness test method of the present invention, step 4 includes: The derivative function is obtained by calculating the first derivative of the cubic polynomial fitting function; The derivative function is used as an expression for the change of the covering stiffness with displacement; Select the characteristic displacement point and calculate the corresponding wrapping stiffness value; The stiffness values ​​of all feature displacement points are summarized to form a stiffness value dataset.

[0009] Furthermore, in the non-pneumatic tire sheath stiffness test method of the present invention, step 5 includes: Select the wrapping stiffness value corresponding to the feature displacement point from the stiffness value dataset obtained in step 4 as the key node; Based on the key nodes, determine the range of the overlapping area at the boundary of adjacent feature intervals; The weighted average of the covering stiffness values ​​within the overlapping region is calculated. The weighted averaged cladding stiffness value is used as input, and a spline interpolation algorithm is used for curve fitting to generate a curve showing the relationship between cladding stiffness and displacement.

[0010] Furthermore, in the non-pneumatic tire sheath stiffness test method of the present invention, step 1 further includes: When the forward loading section reaches the preset load Fz1, the bulging device is simultaneously activated to apply the second load Fz2; The change in the displacement S of the bump is monitored by a displacement sensor, and the change in the covering force is recorded synchronously. During the unloading phase, unloading is performed at the same rate as during loading, and the covering force data of the tire separating from the contact surface is collected.

[0011] Furthermore, in the non-pneumatic tire sheath stiffness test method of the present invention, step 2 further includes: Identify the boundary locations of adjacent feature intervals and determine the extent of the overlapping area on both sides of the boundary; Calculate the distance of data points within the overlapping area from the boundary, and determine the weighting coefficient based on the distance; A weighted average is calculated for the data points within the overlapping area using weighting coefficients. The data points after weighted average are used as the final data points at the boundary.

[0012] Furthermore, the non-pneumatic tire sheath stiffness test method of the present invention further includes: Input the coating stiffness characteristic curve into the vehicle dynamics simulation system; The mechanical response of tires under different operating conditions was analyzed using a simulation system. Adjust tire structure parameters or vehicle control parameters based on the analysis results.

[0013] Secondly, the present invention provides a non-pneumatic tire sheath stiffness testing device, applied to the non-pneumatic tire sheath stiffness testing method as described above, comprising: The data acquisition module is used to acquire the covering force data and covering displacement data generated by the non-pneumatic tire during the covering test, forming test data of the complete motion cycle including the forward loading segment, the forward unloading segment, the reverse loading segment, and the reverse unloading segment; The interval division module is used to divide the test data into multiple characteristic intervals according to the proportion of the test load, wherein the characteristic intervals correspond to the 20%-40%, 40%-60%, and 60%-80% range of the load in each motion segment; The fitting module is used to perform cubic polynomial fitting on each feature interval after division, using the covering force data and covering displacement data within the interval, to generate a fitting function for each feature interval. The differentiation module is used to perform differentiation on the fitted function to obtain a functional expression for the change of the covering stiffness with displacement; The curve generation module is used to extract the wrapping stiffness values ​​corresponding to the feature displacement points from the function expression as nodes, and to generate the wrapping stiffness characteristic curve by curve fitting using the nodes.

[0014] Beneficial effects of this invention; This invention effectively solves the technical problems of inaccurate tire mechanical property measurement and difficult analysis caused by the lack of standardized testing methods by adopting a systematic non-pneumatic tire wrap stiffness testing method. By acquiring test data of the complete motion cycle and dividing the characteristic interval based on the load ratio, combined with cubic polynomial fitting and differentiation, a smooth and continuous wrap stiffness characteristic curve is generated, which significantly improves the accuracy and reliability of stiffness measurement and provides reliable data support for tire performance evaluation and structural optimization. At the same time, nonlinear abrupt changes are eliminated through segmented processing and boundary optimization, enhancing the engineering applicability of the test results. Attached Figure Description

[0015] To more clearly illustrate the technical solution of the present invention, the drawings used in the embodiments will be briefly introduced below. Obviously, for those skilled in the art, other drawings can be obtained based on the drawings without creative effort.

[0016] Figure 1 This is a flowchart illustrating a non-pneumatic tire sheath stiffness test method provided by the present invention.

[0017] Figure 2 This is a schematic diagram of a non-pneumatic tire sheath stiffness testing device provided by the present invention. Detailed Implementation

[0018] To make the technical solution of the present invention clearer, the present invention will be clearly and completely described below with reference to specific embodiments and corresponding drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention. The present invention provided by various embodiments will be described in detail below with reference to the accompanying drawings. To better understand the purpose of the present invention, the present invention will be described in further detail below.

[0019] Please see Figure 1The present invention provides a method for testing the stiffness of a non-pneumatic tire sheath, comprising: Step 1: Obtain the wrapping force data and wrapping displacement data generated by the non-pneumatic tire during the wrapping test to form test data for the complete motion cycle including the forward loading segment, the forward unloading segment, the reverse loading segment, and the reverse unloading segment; Step 2: For the test data, divide the data points into multiple characteristic intervals according to the proportion of the test load, wherein the characteristic intervals correspond to the 20%-40%, 40%-60%, and 60%-80% range of the load in each motion segment; Step 3: For each feature interval after division, perform cubic polynomial fitting using the covering force data and covering displacement data within the interval to generate the fitting function for each feature interval. Step 4: Differentiate the fitted function to obtain the functional expression of the change of the covering stiffness with displacement; Step 5: Extract the wrapping stiffness values ​​corresponding to the feature displacement points from the function expression as nodes, and use the nodes to generate the wrapping stiffness characteristic curve through curve fitting.

[0020] This invention provides a method for testing the stiffness of non-pneumatic tire sheathing, achieving accurate measurement of the sheathing stiffness of non-pneumatic tires through a systematic data processing workflow. The method first involves acquiring test data for the complete motion cycle. During the sheathing test, a vertical load is applied to the non-pneumatic tire at a constant rate via the hydraulic servo system of a stiffness testing machine. When the vertical load reaches a first preset value, a second load is simultaneously applied to the protrusion device on the tire contact surface, causing displacement of the protrusion. The correspondence between sheathing force data and sheathing displacement data is recorded at a set sampling frequency. After loading is completed, an unloading process is performed at the same rate, and the direction of force application is changed, repeating the operation. This forms a test data matrix including a forward loading segment, a forward unloading segment, a reverse loading segment, and a reverse unloading segment, providing a basis for subsequent analysis.

[0021] For the test data, the method divides the data points into multiple characteristic intervals according to the proportion of the test load. Each characteristic interval corresponds to a specific proportion range of the load in each motion segment. Using the test data, a scatter plot is generated with the overlay displacement as the abscissa and the overlay force value as the ordinate. Based on the percentage range of the test load, the data points are divided into three characteristic segments. Each motion segment corresponds to the low-proportion, medium-proportion, and high-proportion load ranges, respectively. This division method can accurately capture the nonlinear variation characteristics of non-pneumatic tires under different stress states.

[0022] For each segmented feature interval, a cubic polynomial fitting is performed using the covering force and covering displacement data within the interval to generate a fitting function for each feature interval. The fitting process includes filtering data points within the feature interval to remove outliers, calculating the coefficients of the fitted curve using the least squares method, and assigning higher weights to data points in the central region and lower weights to data points in the peripheral region during the calculation. The cubic polynomial fitting function is obtained through weighted calculation, thereby improving the fitting accuracy and reducing boundary effects.

[0023] The fitted function is differentiated to obtain a functional expression for the change of covering stiffness with displacement. The differentiation operation includes calculating the first derivative of the cubic polynomial fitted function to obtain the derivative function. This derivative function is used as the expression for the change of covering stiffness with displacement. The corresponding covering stiffness values ​​are calculated at characteristic displacement points, and the covering stiffness values ​​at all characteristic displacement points are summarized to form a stiffness value dataset, providing nodal data for the generation of the stiffness characteristic curve.

[0024] The system extracts the wrapping stiffness values ​​corresponding to feature displacement points from the function expression as nodes, and uses these nodes to generate a wrapping stiffness characteristic curve through curve fitting. The curve generation process includes selecting the wrapping stiffness values ​​corresponding to feature displacement points from the stiffness value dataset as key nodes, determining the overlapping region at the boundary of adjacent feature intervals based on the key nodes, calculating a weighted average of the wrapping stiffness values ​​within the overlapping region, and using the weighted averaged wrapping stiffness values ​​as input to perform curve fitting using a spline interpolation algorithm. Finally, a smooth and continuous wrapping stiffness versus displacement curve is generated, accurately representing the stiffness characteristics of non-pneumatic tires.

[0025] During the data acquisition process in step 1, the hydraulic servo system of the stiffness testing machine applies a vertical load to the non-pneumatic tire at a constant rate. This constant rate is achieved through closed-loop control of the servo valve to maintain the stability of the loading process. When the vertical load reaches a first preset value, the control system synchronously triggers the protrusion device on the tire contact surface to apply a second load, causing the protrusion to displace. The displacement is monitored in real time by a linear displacement sensor. The data acquisition unit records the correspondence between the covering force data and the covering displacement data at a set sampling frequency. The sampling frequency is selected based on the signal frequency response characteristics to capture dynamic changes. After the loading stage is completed, the hydraulic system performs the unloading process at the same rate, with the unloading direction opposite to the loading direction, ensuring the integrity of the force-displacement curve. By changing the direction of force application and repeating the loading and unloading operations, test data matrices for four motion stages—forward loading, forward unloading, reverse loading, and reverse unloading—are obtained, providing a basis for subsequent analysis.

[0026] Step 2, the segmentation of characteristic intervals, involves generating a scatter plot using test data, with the displacement on the x-axis and the covering force on the y-axis. The scatter plot is then visualized using data processing software. Based on the percentage range of the test load, the data points in the scatter plot are automatically divided into three characteristic segments. These segments are based on the load ranges of 20%-40%, 40%-60%, and 60%-80% within each motion segment. The load percentage is calculated by normalizing to the maximum test load. A threshold recognition algorithm is used to identify the boundary points of each percentage interval and classify the data points falling within those intervals. The three characteristic segments correspond to the low-load, medium-load, and high-load intervals, respectively. This segmentation method focuses on the data characteristics of the tire at different deformation stages, reducing overall fitting errors.

[0027] Step 3, the cubic polynomial fitting, first filters the data points within the feature interval. A sliding window method is used to identify and remove outlier data points caused by noise or equipment vibration, improving data quality. The coefficients of the fitted curve are calculated using the least squares method, which optimizes fitting accuracy by minimizing the sum of squared residuals. During the calculation, a weighting strategy assigns higher weights to data points in the central region of the interval and lower weights to data points in the peripheral regions. The weight values ​​are calculated inversely proportional to the distance of each data point from the center of the interval. A cubic polynomial fitting function is obtained through weighted least squares. The function is a cubic polynomial of the covering force with respect to the covering displacement. The weighting enhances the contribution of data from the central region and suppresses boundary effects.

[0028] Step 4 involves calculating the first derivative of the cubic polynomial fitting function using analytical differentiation, directly differentiating the polynomial terms to obtain the derivative function. This derivative function is then used as an expression for the change in covering stiffness with respect to displacement, where covering stiffness is defined as the rate of change of covering force with respect to covering displacement. Characteristic displacement points are selected, including interval boundary points and center points, and their corresponding covering stiffness values ​​are calculated by substituting them into the derivative function. The covering stiffness values ​​from all characteristic displacement points are then compiled into a stiffness value dataset, arranged in displacement order, providing nodal data for curve generation.

[0029] Step 5 generates the covering stiffness characteristic curve by selecting the covering stiffness values ​​corresponding to feature displacement points from the stiffness value dataset as key nodes. The selection of key nodes is based on the displacement distribution density and stiffness change gradient. Based on the key nodes, the overlapping region at the boundary of adjacent feature intervals is determined. The overlapping region is the displacement interval on both sides of the boundary, and its width is adaptively adjusted according to the data point distribution. A weighted average is calculated for the covering stiffness values ​​within the overlapping region. The weighting coefficient is inversely proportional to the distance of the data point from the boundary, and the weighted average eliminates abrupt boundary changes. The processed covering stiffness values ​​are used as input, and a spline interpolation algorithm is used for curve fitting. Spline interpolation ensures the second-order continuity of the curve, generating a smooth covering stiffness versus displacement curve.

[0030] The data acquisition also includes simultaneously activating the bulge device to apply a second load Fz2 when the preset load Fz1 is reached during the forward loading phase. The ratio of Fz1 to Fz2 is preset according to the tire specifications. Changes in the bulge displacement S are monitored by displacement sensors, which can be inductive or optical displacement gauges. The changes in the covering force are recorded synchronously, and sampling synchronization is ensured by a timing controller. During the unloading phase, unloading is performed at the same rate as loading, with the hydraulic system maintaining a constant rate. Covering force data during the tire-contact surface separation process is collected, and the separation point is identified using a force threshold.

[0031] The process of defining feature intervals also includes identifying the boundary positions of adjacent feature intervals. The boundary positions are determined using a load percentage threshold, defining the overlapping area on both sides of the boundary. This overlapping area is typically defined as the displacement range within 15% of the boundary. The distance from the data points within the overlapping area to the boundary is calculated using the Euclidean distance method, with weighting coefficients determined based on whether the distance is linear or non-linear. A weighted average is then calculated using these weighting coefficients, and the coefficients are normalized. The weighted average data points are used as the final data points at the boundary, and these final data points are used for subsequent fitting to improve the smoothness of the interval transition.

[0032] This also includes inputting the tire stiffness characteristic curve into the vehicle dynamics simulation system, with the input interface using standard data formats such as CSV or MAT files. The simulation system analyzes the tire's mechanical response under different operating conditions, including straight-line driving, cornering, and braking scenarios. Based on the analysis results, tire structural parameters or vehicle control parameters are adjusted. Tire structural parameters include tread stiffness and support structure geometry, while vehicle control parameters include suspension stiffness and ESP threshold, to optimize overall vehicle performance.

[0033] Secondly, the present invention provides a non-pneumatic tire sheath stiffness testing device, applied to the non-pneumatic tire sheath stiffness testing method as described above, comprising: The data acquisition module is used to acquire the covering force data and covering displacement data generated by the non-pneumatic tire during the covering test, forming test data of the complete motion cycle including the forward loading segment, the forward unloading segment, the reverse loading segment, and the reverse unloading segment; The interval division module is used to divide the test data into multiple characteristic intervals according to the proportion of the test load, wherein the characteristic intervals correspond to the 20%-40%, 40%-60%, and 60%-80% range of the load in each motion segment; The fitting module is used to perform cubic polynomial fitting on each feature interval after division, using the covering force data and covering displacement data within the interval, to generate a fitting function for each feature interval. The differentiation module is used to perform differentiation on the fitted function to obtain a functional expression for the change of the covering stiffness with displacement; The curve generation module is used to extract the wrapping stiffness values ​​corresponding to the feature displacement points from the function expression as nodes, and to generate the wrapping stiffness characteristic curve by curve fitting using the nodes.

[0034] This invention solves the technical problem of inaccurate measurement and analysis of tire mechanical properties due to the lack of standardized testing methods by establishing a systematic test method for the stiffness of non-pneumatic tire wrapping. The method first collects complete motion cycle data of the non-pneumatic tire during the wrapping test using a stiffness testing machine, including the forward loading, forward unloading, reverse loading, and reverse unloading phases. A hydraulic servo system applies a vertical load at a constant rate. When the vertical load reaches a preset value, a second load is simultaneously applied to the protrusion device on the tire contact surface, causing displacement of the protrusion. The correspondence between wrapping force data and wrapping displacement data is recorded at a set sampling frequency. This comprehensive data acquisition method covers the tire's changes in different force directions, providing a complete dataset for subsequent analysis.

[0035] Based on the collected test data, the data points were divided into multiple characteristic intervals according to the proportion of the test load. These intervals correspond to the low-proportion, medium-proportion, and high-proportion ranges of the load in each motion segment. This division strategy is based on the nonlinear mechanical characteristics exhibited by non-pneumatic tires during the wrapping process, accurately capturing the changing characteristics under different stress states and avoiding errors caused by overall fitting. For each divided characteristic interval, a cubic polynomial fitting was performed using the wrapping force data and wrapping displacement data within the interval to generate a fitting function for each interval. During the fitting process, outliers were removed from the data points, and the least squares method was used to calculate the coefficients. Higher weights were assigned to data points in the central region of the interval, and lower weights were assigned to data points in the peripheral regions. This weighted calculation improved the fitting accuracy.

[0036] Then, the fitted function is differentiated to obtain a functional expression for the change of covering stiffness with displacement. After differentiation, the covering stiffness values ​​corresponding to characteristic displacement points are extracted from the functional expression as nodes. These nodes are then used to generate a covering stiffness characteristic curve through curve fitting. During curve generation, the overlapping region at the boundary of adjacent characteristic intervals is determined based on key nodes. A weighted average of the covering stiffness values ​​within the overlapping region is calculated, and a spline interpolation algorithm is used for curve fitting to generate a smooth and continuous curve relating covering stiffness and displacement. This piecewise processing combined with boundary optimization effectively eliminates abrupt stiffness changes and ensures physical continuity.

[0037] Ultimately, the overlay stiffness characteristic curve can be input into a vehicle dynamics simulation system to analyze the tire's mechanical response under different operating conditions, thereby providing data support for adjusting tire structural parameters or vehicle control parameters. This method, through multi-stage data acquisition, refined interval division, mathematical model construction, and curve reconstruction, achieves accurate quantitative characterization of the overlay stiffness of non-pneumatic tires, solving the technical problems of inaccurate measurement and analysis.

[0038] As a novel product for puncture and explosion protection, non-pneumatic tires lack standardized testing methods for measuring their mechanical properties. This results in the inability to obtain continuous and reliable load-displacement data, affecting performance analysis during tire development and assessment of vehicle handling stability. This invention provides a method and apparatus for testing the sheath stiffness of non-pneumatic tires, addressing the technical gap in sheath stiffness testing.

[0039] For detailed implementation methods, please refer to Figure 2 The non-pneumatic tire sheath stiffness test method applies a vertical load to the non-pneumatic tire at a constant rate using the hydraulic servo system of a stiffness testing machine. When the vertical load reaches a first preset value, a second load is simultaneously applied to the protrusion device on the tire contact surface, causing displacement of the protrusion. During the loading process, the correspondence between sheath force data and sheath displacement data is recorded at a set sampling frequency. After loading is completed, an unloading process is performed at the same rate, and sheath force data and sheath displacement data are collected during the unloading phase. The loading and unloading process is repeated by changing the direction of force application to obtain test data for the complete motion cycle, including the forward loading segment, forward unloading segment, reverse loading segment, and reverse unloading segment.

[0040] Based on the test data, the data points were divided into multiple characteristic intervals according to the proportion of the test load. These intervals correspond to the 20%-40%, 40%-60%, and 60%-80% load ranges in each motion segment. A scatter plot was generated using the test data, with the covering displacement as the x-axis and the covering force as the y-axis. The data points in the scatter plot were then divided into three characteristic segments based on the percentage range of the test load: 20%-40% load, 40%-60% load, and 60%-80% load, respectively. When dividing the characteristic intervals, the boundary positions of adjacent intervals were identified, the overlapping area on both sides of the boundary was determined, and the distance from the data points within the overlapping area to the boundary was calculated. A weighting coefficient was determined based on the distance, and a weighted average was calculated using this coefficient. The weighted average data point was then used as the final data point at the boundary.

[0041] For each segmented feature interval, a cubic polynomial fitting is performed using the covering force and covering displacement data within the interval to generate a fitting function for each feature interval. Data points within the feature interval are filtered to remove outliers, and the coefficients of the fitted curve are calculated using the least squares method. During the calculation, a first weight is assigned to data points in the central region of the interval, and a second weight is assigned to data points in the edge region. The first weight is greater than the second weight, and the cubic polynomial fitting function is obtained through weighted calculation.

[0042] Differentiating the fitted function yields a functional expression for the change in covering stiffness with displacement. The first derivative of the cubic polynomial fitted function is calculated to obtain the derivative function, which is then used as the expression for the change in covering stiffness with displacement. Feature displacement points are selected, and the corresponding covering stiffness values ​​are calculated. The covering stiffness values ​​for all feature displacement points are then summarized to form a stiffness value dataset.

[0043] The wrapping stiffness values ​​corresponding to feature displacement points are extracted from the function expression and used as nodes. These nodes are then used to generate a wrapping stiffness characteristic curve through curve fitting. From the stiffness value dataset, the wrapping stiffness values ​​corresponding to feature displacement points are selected as key nodes. Based on these key nodes, the overlapping region at the boundary of adjacent feature intervals is determined. A weighted average of the wrapping stiffness values ​​within the overlapping region is calculated. The weighted averaged wrapping stiffness value is then used as input, and a spline interpolation algorithm is employed for curve fitting to generate a curve relating wrapping stiffness to displacement. This wrapping stiffness characteristic curve can be input into a vehicle dynamics simulation system. The simulation system analyzes the tire's mechanical response under different operating conditions, and tire structural parameters or vehicle control parameters are adjusted based on the analysis results.

[0044] The non-pneumatic tire overlay stiffness testing device includes a data acquisition module, an interval division module, a fitting module, a differentiation module, and a curve generation module. The data acquisition module acquires the overlay force and displacement data generated by the non-pneumatic tire during the overlay test, forming test data for a complete motion cycle. The interval division module divides the test data into multiple characteristic intervals according to the proportion of the test load. The fitting module performs a cubic polynomial fitting on each of the divided characteristic intervals to generate a fitting function for each interval. The differentiation module performs differentiation on the fitting function to obtain a functional expression for the overlay stiffness as a function of displacement. The curve generation module extracts the overlay stiffness values ​​corresponding to characteristic displacement points from the functional expression as nodes and generates an overlay stiffness characteristic curve through curve fitting. This method, through multi-stage data acquisition, refined interval division, mathematical model construction, and curve reconstruction, achieves accurate quantitative characterization of the overlay stiffness of non-pneumatic tires.

[0045] In Embodiment 1 of this invention, the non-pneumatic tire sheath stiffness test method is applied in a tire testing laboratory environment to meet the quantitative requirements of non-pneumatic tire sheath stiffness. Specifically, a vertical load is applied to the non-pneumatic tire at a constant rate using the hydraulic servo system of a stiffness testing machine. The constant rate is set to several millimeters per second to maintain stability during the loading process. When the vertical load reaches a first preset value, such as a specific percentage of the rated load, a second load is applied simultaneously to the protrusion device on the tire contact surface, causing displacement of the protrusion. The displacement is monitored in real time by a linear displacement sensor with a sampling frequency set to several kilohertz per second to capture dynamic changes. During the loading process, the correspondence between sheath force data and sheath displacement data is recorded, forming complete motion cycle test data including a forward loading segment, a forward unloading segment, a reverse loading segment, and a reverse unloading segment. The test data is then divided into multiple characteristic intervals according to the proportion of the test load. These characteristic intervals correspond to the 20%-40%, 40%-60%, and 60%-80% load ranges in each motion segment. During the division, a scatter plot is used to automatically identify boundaries, and overlapping area data is processed through weight calculation to eliminate nonlinear abrupt changes. For each feature interval, a cubic polynomial fitting is performed using the least squares method. During the fitting process, data points in the central region of the interval are assigned higher weights, while those in the peripheral regions are assigned lower weights. After generating the fitting function, the first derivative is calculated to obtain an expression for the change of the wrapping stiffness with displacement. Finally, the wrapping stiffness values ​​corresponding to the feature displacement points are extracted from the expression as nodes, and a smooth wrapping stiffness characteristic curve is generated using a spline interpolation algorithm. This curve can be directly input into a vehicle dynamics simulation system to analyze the mechanical response of the tire under straight-line driving or cornering conditions, providing data support for adjusting tire structural parameters such as tread stiffness, thereby improving the reliability and engineering applicability of the test results.

[0046] In Embodiment 2 of this invention, a non-pneumatic tire wrapping stiffness testing device is integrated into a standardized testing platform to implement the aforementioned method. The device includes a data acquisition module, an interval division module, a fitting module, a differentiation module, and a curve generation module. The data acquisition module collects wrapping force and displacement data of the non-pneumatic tire during the wrapping test using a hydraulic servo system and displacement sensors, forming complete motion cycle test data. Sampling synchronization is ensured by a timing controller. The interval division module automatically divides data points into characteristic intervals based on the test load ratio, identifies the boundaries of adjacent intervals during processing, and optimizes overlapping area data using a weighted average method. The fitting module performs cubic polynomial fitting on each characteristic interval, using weighted least squares to calculate coefficients to ensure fitting accuracy. The differentiation module performs analytical differentiation on the fitted function to generate a wrapping stiffness expression. The curve generation module extracts the stiffness values ​​of characteristic displacement points and generates a wrapping stiffness characteristic curve through spline interpolation. In practical applications, the device can interface with vehicle dynamics simulation systems, for example, by transmitting curve data through standard data formats such as CSV files, to simulate and analyze the mechanical behavior of tires under different loads, thereby optimizing vehicle control parameters such as suspension stiffness.

Claims

1. A method for testing the stiffness of a non-pneumatic tire sheath, characterized in that, include: Step 1: Obtain the wrapping force data and wrapping displacement data generated by the non-pneumatic tire during the wrapping test to form test data for the complete motion cycle including the forward loading segment, the forward unloading segment, the reverse loading segment, and the reverse unloading segment; Step 2: For the test data, divide the data points into multiple characteristic intervals according to the proportion of the test load, wherein the characteristic intervals correspond to the 20%-40%, 40%-60%, and 60%-80% range of the load in each motion segment; Step 3: For each feature interval after division, perform cubic polynomial fitting using the covering force data and covering displacement data within the interval to generate the fitting function for each feature interval. Step 4: Differentiate the fitted function to obtain the functional expression of the change of the covering stiffness with displacement; Step 5: Extract the wrapping stiffness values ​​corresponding to the feature displacement points from the function expression as nodes, and use the nodes to generate the wrapping stiffness characteristic curve through curve fitting.

2. The method for testing the stiffness of a non-pneumatic tire overlay according to claim 1, characterized in that, Step 1 includes: A vertical load is applied to a non-pneumatic tire at a constant rate using the hydraulic servo system of a stiffness testing machine. When the vertical load reaches the first preset value, the protrusion device on the tire contact surface is activated simultaneously to apply the second load, causing the protrusion to displace. During the loading process, the correspondence between the covering force data and the covering displacement data is recorded at a set sampling frequency; After loading is complete, the unloading process is executed at the same rate, and the covering force data and covering displacement data during the unloading phase are collected. By changing the direction of force application and repeating the loading and unloading process, test data were obtained for four motion stages: forward loading, forward unloading, reverse loading, and reverse unloading.

3. The method for testing the stiffness of a non-pneumatic tire overlay according to claim 2, characterized in that, Step 2 includes: Using the test data, a scatter plot is generated with the displacement of the covering as the abscissa and the covering force as the ordinate. Based on the percentage range of the test load, the data points in the scatter plot are divided into three characteristic segments; The three characteristic zones correspond to the 20%-40% load range, the 40%-60% load range, and the 60%-80% load range, respectively.

4. The method for testing the stiffness of a non-pneumatic tire overlay according to claim 3, characterized in that, Step 3 also includes: Filter data points within the feature interval to remove outlier data points; The coefficients of the fitted curve are calculated using the least squares method; During the calculation process, a first weight is assigned to data points in the central region of the interval, and a second weight is assigned to data points in the edge region, wherein the first weight is greater than the second weight. The cubic polynomial fitting function is obtained by weighted calculation.

5. The method for testing the stiffness of a non-pneumatic tire sheath according to claim 4, characterized in that, Step 4 includes: The derivative function is obtained by calculating the first derivative of the cubic polynomial fitting function; The derivative function is used as an expression for the change of the covering stiffness with displacement; Select the characteristic displacement point and calculate the corresponding wrapping stiffness value; The stiffness values ​​of all feature displacement points are summarized to form a stiffness value dataset.

6. The method for testing the stiffness of a non-pneumatic tire overlay according to claim 5, characterized in that, Step 5 includes: Select the wrapping stiffness value corresponding to the feature displacement point from the stiffness value dataset obtained in step 4 as the key node; Based on the key nodes, determine the range of the overlapping area at the boundary of adjacent feature intervals; The weighted average of the covering stiffness values ​​within the overlapping region is calculated. The weighted averaged cladding stiffness value is used as input, and a spline interpolation algorithm is used for curve fitting to generate a curve showing the relationship between cladding stiffness and displacement.

7. The method for testing the stiffness of a non-pneumatic tire overlay according to claim 6, characterized in that, Step 1 also includes: When the forward loading section reaches the preset load Fz1, the bulging device is simultaneously activated to apply the second load Fz2; The change in the displacement S of the bump is monitored by a displacement sensor, and the change in the covering force is recorded synchronously. During the unloading phase, unloading is performed at the same rate as during loading, and the covering force data of the tire separating from the contact surface is collected.

8. The method for testing the stiffness of a non-pneumatic tire overlay according to claim 7, characterized in that, Step 2 also includes: Identify the boundary locations of adjacent feature intervals and determine the extent of the overlapping area on both sides of the boundary; Calculate the distance of data points within the overlapping area from the boundary, and determine the weighting coefficient based on the distance; A weighted average is calculated for the data points within the overlapping area using weighting coefficients. The data points after weighted average are used as the final data points at the boundary.

9. The method for testing the stiffness of a non-pneumatic tire overlay according to claim 8, characterized in that, Also includes: Input the coating stiffness characteristic curve into the vehicle dynamics simulation system; The mechanical response of tires under different operating conditions was analyzed using a simulation system. Adjust tire structure parameters or vehicle control parameters based on the analysis results.

10. A non-pneumatic tire sheath stiffness testing apparatus, applied to the non-pneumatic tire sheath stiffness testing method as described in any one of claims 1 to 9, characterized in that, include: The data acquisition module is used to acquire the covering force data and covering displacement data generated by the non-pneumatic tire during the covering test, forming test data of the complete motion cycle including the forward loading segment, the forward unloading segment, the reverse loading segment, and the reverse unloading segment; The interval division module is used to divide the test data into multiple characteristic intervals according to the proportion of the test load, wherein the characteristic intervals correspond to the 20%-40%, 40%-60%, and 60%-80% range of the load in each motion segment; The fitting module is used to perform cubic polynomial fitting on each feature interval after division, using the covering force data and covering displacement data within the interval, to generate a fitting function for each feature interval. The differentiation module is used to perform differentiation on the fitted function to obtain a functional expression for the change of the covering stiffness with displacement; The curve generation module is used to extract the wrapping stiffness values ​​corresponding to the feature displacement points from the function expression as nodes, and to generate the wrapping stiffness characteristic curve by curve fitting using the nodes.

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