A method for predicting vertical stiffness of a spoke type non-pneumatic tire and applications thereof

Abstract

The application discloses a kind of spoke non-pneumatic tire vertical stiffness prediction method and its application, the prediction method includes: according to stress-strain curve to determine the constitutive model of outer tread material, determine the preselected spoke material constitutive model set and strain parameter set;According to entity tire size to establish tire geometric model;The constitutive model parameters of outer tread material are assigned to the outer tread component in geometric model, traverse the parameters in preselected spoke material constitutive model set and strain parameter set, obtain multiple tire simulation models of different spoke constitutive model and different fitting strain;Multiple tire simulation models are respectively simulated, and effective tire simulation model is determined according to the simulation curve of counterforce-displacement;The thickness and the number of spoke of effective simulation model are adjusted, and the relationship of the vertical stiffness of tire and the thickness and the number of spoke is obtained: according to the relationship, the vertical stiffness of non-pneumatic entity tire of different spoke thickness, spoke quantity is predicted.

Description

Technical Field

[0001] This invention belongs to the field of performance prediction technology for spoked non-pneumatic tires, and specifically relates to a method for predicting the vertical stiffness of spoked non-pneumatic tires and its application. Background Technology

[0002] After more than a century of development, pneumatic tires can be considered highly engineered composite structures among vehicle components. However, pneumatic tires have drawbacks such as susceptibility to blowouts, difficulty in maintaining tire pressure, and complex manufacturing processes. Non-pneumatic tires (NPTs) can overcome these disadvantages, achieving better suspension performance, handling, and driving comfort.

[0003] Spoke-type non-pneumatic tires: Tires with a spoke-like design that do not require inflation. Their structure consists of the following parts: elastic spokes, belt layers, shear bands, and tread. The spokes can be divided into three parts: the inner ring, the outer ring, and the spokes themselves. The spoke structure has the following characteristics: the material is a single isotropic material; the spoke shape includes a curved segment with a radius of curvature not less than 100 times the difference between the radii of the inner and outer rings; and the spokes are evenly distributed between the inner and outer rings.

[0004] The spokes of non-pneumatic tires play a crucial role in absorbing energy and providing tension. The form and structural parameters of the spokes also affect tire performance, such as load-bearing capacity (vertical stiffness). Current technologies primarily use simulation methods to study the impact of spoke form and structural parameters on tire performance.

[0005] Currently, for each type of non-pneumatic tire with different spoke parameters, a new finite element model needs to be established to determine its vertical stiffness. The modeling process is cumbersome and inefficient. Summary of the Invention

[0006] The purpose of this invention is to provide a method for predicting the vertical stiffness of spoked non-pneumatic tires, which can determine the numerical relationship between the tire's vertical stiffness and the thickness and number of spokes, and quickly predict the vertical stiffness of spoked non-pneumatic tires.

[0007] The present invention also discloses an application of a method for predicting the vertical stiffness of a spoked non-pneumatic tire, which can determine the spoke thickness and the number of spokes of the non-pneumatic tire based on the target value of the tire's vertical stiffness.

[0008] The technical solution provided by this invention is as follows:

[0009] A method for predicting the vertical stiffness of a spoked non-pneumatic tire includes:

[0010] Spoke samples are prepared by cutting samples from the spokes of a non-pneumatic solid tire; tread samples are prepared by cutting samples from the outer surface of the solid tire; the samples are tested to obtain stress-strain curves for the spokes and the tread, respectively.

[0011] The constitutive model of the tire tread material is determined based on the stress-strain curve, and the set of pre-selected constitutive models and strain parameters for the spoke materials are determined.

[0012] The pre-selected constitutive model set for spoke materials includes multiple constitutive models for spoke materials, and the set of strain parameters includes multiple spoke strain parameters.

[0013] Measure the dimensions of the actual tire and establish a tire geometric model based on the actual tire dimensions; assign the constitutive model parameters of the tread material to the tread component in the geometric model, traverse the parameters in the pre-selected constitutive model set of spoke material and strain parameter set to obtain multiple tire simulation models with different spoke constitutive models and different fitting strains.

[0014] Simulation tests were conducted on the multiple tire simulation models to obtain the reaction force-displacement simulation curves of the tire under different constitutive models and different fitting strains, and the effective tire simulation model was determined based on the reaction force-displacement simulation curves.

[0015] By adjusting the spoke thickness and number of spokes in the effective simulation model, multiple effective tire simulation models with different combinations of spoke thickness and number of spokes are obtained;

[0016] The vertical stiffness of the multiple effective tire simulation models was determined, and the relationship between the tire's vertical stiffness and the spoke thickness and number of spokes was obtained as follows:

[0017] K = α·(T·N) β ;

[0018] Where K represents the vertical stiffness of the tire; T represents the spoke thickness; N represents the number of spokes; α and β are fitting parameters;

[0019] The vertical stiffness of non-pneumatic solid tires with different spoke thicknesses and numbers of spokes can be predicted based on the aforementioned relationship.

[0020] Preferably, the method for determining an effective tire simulation model is as follows:

[0021] Obtain the reaction force-displacement curve when the tire is actually loaded, compare the reaction force-displacement simulation curve with the reaction force-displacement curve, and select the tire simulation model corresponding to the reaction force-displacement simulation curve with the smallest error as the effective tire simulation model.

[0022] Preferably, the error between the reaction force-displacement simulation curve of the effective tire simulation model and the reaction force-displacement curve is less than 5%.

[0023] Preferably, the stress-strain parameters of the tire tread material are input into finite element software to determine the constitutive model of the tire tread material as a Neo-hookean model.

[0024] Preferably, the pre-selected constitutive model set for spoke materials includes Neo-Hookean and Yeoh models.

[0025] Preferably, the strain parameters in the strain parameter set include 20%, 50%, and 80%.

[0026] Preferably, the method further includes the following steps before conducting simulation tests on the plurality of tire simulation models:

[0027] Mesh the components in the tire simulation model; use shell elements to simulate the spoke structure and wire layer, and use hybrid solid elements to simulate the tread and shear band.

[0028] An application of a method for predicting the vertical stiffness of a spoked non-pneumatic tire, used to determine the spoke thickness and the number of spokes of the non-pneumatic tire based on a target value for the tire's vertical stiffness.

[0029] The beneficial effects of this invention are:

[0030] The method for predicting the vertical stiffness of spoked non-pneumatic tires provided by this invention can determine the numerical relationship between the tire's vertical stiffness and the thickness and number of spokes, and quickly predict the vertical stiffness of spoked non-pneumatic tires.

[0031] The method for predicting the vertical stiffness of spoked non-pneumatic tires provided by this invention can be applied to tire spoke parameter design and can determine the spoke thickness and the number of spokes of a non-pneumatic tire based on the target value of the tire's vertical stiffness. Attached Figure Description

[0032] Figure 1 This is a structural diagram of a 12N16.5 X Tweel SSL all-terrain non-pneumatic tire.

[0033] Figure 2(a) is a schematic diagram of the deformation results of the finite element model when the tread rubber material is compressed.

[0034] Figure 2(b) is a comparison of the results of the compression test and simulation of the tread rubber material.

[0035] Figure 3(a) is a comparison of the fitted stress-strain curve and the experimental curve of the spoke polyurethane material under tensile test at 20% strain.

[0036] Figure 3(b) is a comparison of the fitted stress-strain curve and the experimental curve of the spoke polyurethane material under 50% strain in the tensile test.

[0037] Figure 3(c) is a comparison between the fitted stress-strain curve and the experimental curve of the spoke polyurethane material under 80% strain in the tensile test.

[0038] Figure 4 This is a schematic diagram of the finite element model for the radial stiffness test of a non-pneumatic tire established in the embodiment.

[0039] Figure 5 This is a schematic diagram of the constraints of the model in the embodiment.

[0040] Figure 6 The simulation curve of reaction force-displacement obtained in the example is shown.

[0041] Figure 7(a) is a comparison of the reaction force-displacement curves of the Yeoh constitutive simulation model and the actual tire.

[0042] Figure 7(b) is a comparison of the reaction force-displacement curves of the Neo-hookean constitutive simulation model and the actual tire.

[0043] Figure 8 The graph shows the fitted formula in the example. Detailed Implementation

[0044] The present invention will now be described in further detail with reference to the accompanying drawings, so that those skilled in the art can implement it based on the description.

[0045] This invention provides a method for predicting the vertical stiffness of spoked non-pneumatic tires, and the specific implementation process is as follows.

[0046] Spoke specimens are prepared by cutting samples from the spokes of a spoked non-pneumatic solid tire; tread specimens are prepared by cutting samples from the outer surface of the spoked non-pneumatic solid tire. Uniaxial tensile and compression tests are performed on the spoke specimens to obtain the parameters (stress-strain curves); uniaxial tensile and compression tests are performed on the tread specimens to obtain the parameters (stress-strain curves) of the tread.

[0047] The constitutive model of the tire tread material is determined based on the stress-strain curve, and a pre-selected set of constitutive models and strain parameters for the spoke materials are determined. The pre-selected set of constitutive models for the spoke materials includes multiple spoke material constitutive models, and the set of strain parameters includes multiple spoke strain parameters.

[0048] In one embodiment, the stress-strain parameters of the tire tread material are input into finite element software to determine that the constitutive model of the tire tread material is a Neo-hookean model.

[0049] In one embodiment, the preselected set of constitutive models for spoke materials includes Neo-Hookean and Yeoh models.

[0050] In one embodiment, the strain parameters in the strain parameter set include 20%, 50%, and 80%.

[0051] The dimensions of a spoked, non-pneumatic solid tire are measured, and a tire geometric model is established based on these dimensions. Constitutive model parameters of the tread material are assigned to the tread components in the geometric model. The parameters in a pre-selected set of spoke material constitutive models and strain parameters are iterated through to obtain multiple tire simulation models with different spoke constitutive models and different fitted strains.

[0052] In the finite element method's mesh module, the various components of the tire simulation model are meshed. Shell elements are used to simulate the spoke structure and the steel wire layer. Considering the typical incompressible properties of rubber, hybrid solid elements are used to simulate the tread and shear band. Four-node shell elements (S4R) with linear reduced integrals are used for the spokes. Surface elements (SFM3D4R) are used to simulate the steel wire layer. Octahedral hybrid solid elements (C3D8H) and hexahedral hybrid solid elements (C3D6H) are used to simulate the tread. The shear band is simulated using hexahedral hybrid solid elements (C3D8H).

[0053] Two displacement boundary conditions were applied to the tire simulation model: (1) To facilitate the calculation of the pressure of the rigid surface on the tire, the nodes of the inner ring of the spoke were set to fixed, that is, the inner ring of the spoke was fully constrained. (2) The rigid analytical surface representing the ground was specified to move towards the tread along its own normal direction, with a displacement value of 25mm. The contact type between the tread and the shear band, and the contact type between the shear band and the outer ring of the spoke were defined as Tie, and the contact type between each steel wire layer and the shear band was defined as Embedded region.

[0054] Simulation tests were conducted on the multiple tire simulation models to obtain the reaction force-displacement simulation curves of the tires under different constitutive models and different fitting strains. A tire vertical stiffness test was performed on a physical tire using a tire testing machine to obtain the reaction force-displacement curves of the tire under actual load. The curves obtained from the tests and simulations were compared, and the constitutive model with the smallest error was selected. If the error is less than 5%, the model is considered effective (as a valid simulation model) and can be used to predict the vertical stiffness of this type of non-pneumatic wheel.

[0055] By adjusting the spoke thickness and number of spokes in the effective simulation model, multiple effective tire simulation models with different combinations of spoke thickness and number of spokes are obtained. The vertical stiffness of these multiple effective tire simulation models is calculated in finite element software, and the correspondence between the tire's vertical stiffness and the spoke thickness and number of spokes is obtained. The fitted formula for the relationship between the tire's vertical stiffness and the spoke thickness and number of spokes is as follows:

[0056] K = α·(T·N) β ;

[0057] Where K represents the vertical stiffness of the tire, in N / mm; T represents the spoke thickness, in mm; and N represents the number of spokes. α and β are fitting parameters, with parameter α in N / mm. (1+β) The parameter β is a dimensionless parameter.

[0058] Then, the aforementioned relationship can be used to predict the vertical stiffness of non-pneumatic solid tires with different spoke thicknesses and numbers of spokes.

[0059] The method for predicting the vertical stiffness of spoked non-pneumatic tires provided by this invention can also be applied to designing key spoke design parameters according to load-bearing requirements. Specifically, it is used to determine the spoke thickness and the number of spokes of a non-pneumatic tire based on the target value of the tire's vertical stiffness. For example, in the design stage of a spoked non-pneumatic tire, if the tire's load-bearing performance does not meet the requirements, the relationship between the tire's vertical stiffness and the spoke thickness and number of spokes can be used to guide the optimized design of the product's spoke parameters.

[0060] Example

[0061] In this embodiment, the operating environment for the software is Windows 10 Professional, version 21H2. The research object of this embodiment is the Michelin-developed commercial 12N16.5 X Tweel SSL all-terrain non-pneumatic tire, with the structure as follows: Figure 1 As shown.

[0062] According to ASTM D412, dumbbell-shaped specimens were cut and prepared from the tire spokes, and according to ASTM D575, cylindrical specimens were cut and prepared from the tire tread. Uniaxial tensile and compression tests were performed on the specimens using an Instron 5969 multi-testing machine. The test results are the material parameters (i.e., stress-strain curves) of the tire tread and spoke components.

[0063] Select a suitable constitutive model for the tread rubber material. Input the experimentally obtained tread material parameters into the simulation software Abaqus 2016 (or later) and fit them into a Neo-hookean form. Verify the effectiveness of the model: such as... Figures 2(a)-2(b)This paper compares the compression test data of the tire tread material with the simulation data using the Neo-Hooke constitutive model. The results show that the accuracy of the simulation using the Neo-Hooke constitutive model is over 95%, therefore, this constitutive model is an effective constitutive model for the tread material.

[0064] A suitable constitutive model was selected for the polyurethane spoke material. To accurately simulate the deformation of the spokes during tire loading, a comparative study of the Neo-Hookean and Yeoh constitutive models for polyurethane was conducted. The influence of uniaxial tensile test data under different strain ranges on the fitting parameters was considered. Strain ranges of 20%, 50%, and 80% were selected for fitting, and the fitting parameters of different models under different strains were recorded for subsequent finite element model establishment.

[0065] Neo-Hookean and Yeoh fitting curves under different strain ranges are as follows Figures 3(a)-3(c) As shown in the figure. The recorded fitting parameters are shown in Table 1.

[0066] Table 1

[0067]

[0068] Establish a finite element model for the radial stiffness test of a non-pneumatic tire in Abaqus 2016 (or later), such as... Figure 4-6 As shown. The modeling process includes:

[0069] 1. Establish the geometric model. In the part module, establish the geometric model of the spokes, steel wire layer, shear band and tire tread. Establish a rigid analytical plane to simulate the road surface, whose size (400mm×1000mm) is significantly larger than the possible contact area between the road surface and the tire tread.

[0070] 2. Select the constitutive model for each component. In the property module, assign the parameters of the selected spoke constitutive model to each component.

[0071] III. Meshing. Mesh each component in the mesh module, using shell elements to simulate the spoke structure and wire layer. Considering the typical incompressible properties of rubber, hybrid solid elements are used to simulate the tread and shear band. Four-node shell elements (S4R) with linear reduced integral are used for the spokes. Surface elements (SFM3D4R) are used to simulate the wire layer. Octahedral hybrid solid elements (C3D8H) and hexahedral hybrid solid elements (C3D6H) are used to simulate the tread. Hexahedral hybrid solid elements (C3D8H) are used to simulate the shear band.

[0072] IV. Component Boundary Conditions and Contact Types. Two displacement boundary conditions are applied to the model: (1) To facilitate the calculation of the pressure of the rigid surface on the tire, the nodes of the inner ring of the spoke are set to fixed, that is, the inner ring of the spoke is fully constrained. (2) The rigid analytical surface representing the ground is specified to move towards the tread along its own normal, with a displacement value of 25mm. The contact type between the tread and the shear band, and the contact type between the shear band and the outer ring of the spoke are defined as Tie, and the contact type between each steel wire layer and the shear band is defined as Embedded region.

[0073] The above modeling process was completed in Abaqus 2016 (or later). The simulation task was submitted to calculate the reaction force-displacement curve (i.e., the reaction force-displacement simulation curve) during the wheel deformation process. The fitting parameters were changed according to the selected strain range (20%, 50%, 80%) to obtain simulation curves for different constitutive models under different fitting strains.

[0074] Vertical stiffness tests were conducted on physical tires using an Ektron PL-2003 tire testing machine to obtain the reaction force-displacement curves under actual load. The test and simulation curves were compared, and the constitutive model with the smallest error was selected. If the error is less than 5%, the model is considered valid and can be used to predict the vertical stiffness of this type of non-pneumatic tire.

[0075] The results of the comparison between the actual tire test and the simulation curve are as follows: Figures 7(a)-7(b) As shown, the NPT model that fits the Yeoh constitutive parameters under experimental data with a strain range of 80% has the smallest error. Its vertical stiffness in finite element analysis is 920.3 N / mm, and the approximate error with the experimental result (887.0 N / mm) is 3.75%. Therefore, this model is effective.

[0076] This embodiment establishes an effective finite element model for testing the vertical stiffness of non-pneumatic tires. This model should meet two basic conditions: 1. High simulation accuracy (the simulation results should not differ from the actual results by more than 5%); 2. The number and thickness of spokes in the model can be adjusted. Simulation models established by other methods can also be used if they meet the above conditions.

[0077] Adjust the values ​​of spoke thickness and number to obtain several sets of finite element models. Use the simulation software Abaqus2016 (or later) to calculate the vertical stiffness and obtain several sets of data, as shown in Table 2 (spoke thickness T, number of spokes N, vertical stiffness K).

[0078] Table 2. Relationship between Vertical Stiffness and Spoke Thickness and Number of Spokes

[0079]

[0080] Fit these data into the following relationship using Origin 2021 (or later):

[0081] K = α·(T·N) β

[0082] Here, α and β are two fitting parameters, and the fitting accuracy can be measured by the coefficient of determination R. 2 To reflect (R) 2 A value greater than 0.95 indicates that the formula is effective. The values ​​of the above three parameters can be obtained through fitting.

[0083] In this embodiment, the obtained fitting curve is as follows: Figure 8 As shown, the fitting result is: α = 61.86 N / mm (1+β) β=0.476, R 2 =0.9869>0.95, that is

[0084] K = 61.86 (T·N) 0.476 R 2 =0.9869.

[0085] The vertical stiffness of this type of non-pneumatic tire can be quickly predicted using the fitted formula. Taking the Michelin 12N16.5 X Tweel SSL all-terrain non-pneumatic tire as an example, with T = 5.8 mm and N = 50, the formula yields K = 919.4 N / mm, which has an error of approximately 3.65% compared to the actual tire test result of 887.0 N / mm. This demonstrates that the prediction method provided by this invention has high accuracy. Similarly, it can also be used for the rapid design of key spoke design parameters given a load-bearing capacity.

[0086] Although embodiments of the present invention have been disclosed above, they are not limited to the applications listed in the specification and embodiments. They can be applied to various fields suitable for the present invention. For those skilled in the art, other modifications can be easily made. Therefore, without departing from the general concept defined by the claims and their equivalents, the present invention is not limited to the specific details and illustrations shown and described herein.

Claims

1. A method for predicting the vertical stiffness of a spoked non-pneumatic tire, characterized in that, include: Spoke samples are prepared by cutting samples from the spokes of a non-pneumatic solid tire; tread samples are prepared by cutting samples from the outer surface of the solid tire. The specimens were tested, and the stress-strain curves of the spokes and the outer tire tread were obtained respectively. The constitutive model of the tire tread material is determined based on the stress-strain curve, and the set of pre-selected constitutive models and strain parameters for the spoke materials are determined. The pre-selected constitutive model set for spoke materials includes multiple constitutive models for spoke materials, and the set of strain parameters includes multiple spoke strain parameters. Measure the dimensions of the actual tire and establish a tire geometric model based on the actual tire dimensions; assign the constitutive model parameters of the tread material to the tread component in the geometric model, traverse the parameters in the pre-selected constitutive model set of spoke material and strain parameter set to obtain multiple tire simulation models with different spoke constitutive models and different fitting strains. Simulation tests were conducted on the multiple tire simulation models to obtain the reaction force-displacement simulation curves of the tire under different constitutive models and different fitting strains, and the effective tire simulation model was determined based on the reaction force-displacement simulation curves. By adjusting the spoke thickness and number of spokes of the effective tire simulation model, multiple effective tire simulation models with different combinations of spoke thickness and number of spokes are obtained. The vertical stiffness of the multiple effective tire simulation models was determined, and the relationship between the tire's vertical stiffness and the spoke thickness and number of spokes was obtained as follows: K=α·(T·N) β ; Where K represents the vertical stiffness of the tire; T represents the spoke thickness; N represents the number of spokes; α and β are fitting parameters; The vertical stiffness of non-pneumatic solid tires with different spoke thicknesses and numbers of spokes can be predicted based on the aforementioned relationship.

2. The method for predicting the vertical stiffness of a spoked non-pneumatic tire according to claim 1, characterized in that, The method for determining an effective tire simulation model is as follows: Obtain the reaction force-displacement curve when the tire is actually loaded, compare the reaction force-displacement simulation curve with the reaction force-displacement curve, and select the tire simulation model corresponding to the reaction force-displacement simulation curve with the smallest error as the effective tire simulation model.

3. The method for predicting the vertical stiffness of a spoked non-pneumatic tire according to claim 2, characterized in that, The error between the reaction force-displacement simulation curve of the effective tire simulation model and the reaction force-displacement curve is less than 5%.

4. The method for predicting the vertical stiffness of a spoked non-pneumatic tire according to claim 3, characterized in that, The stress-strain parameters of the tire tread material were input into the finite element software, and the constitutive model of the tire tread material was determined to be the Neo-hookean model.

5. The method for predicting the vertical stiffness of a spoked non-pneumatic tire according to claim 4, characterized in that, The pre-selected constitutive model set for spoke materials includes Neo-Hookean and Yeoh models.

6. The method for predicting the vertical stiffness of a spoked non-pneumatic tire according to claim 5, characterized in that, The strain parameters in the strain parameter set include 20%, 50%, and 80%.

7. The method for predicting the vertical stiffness of a spoked non-pneumatic tire according to claim 1 or 6, characterized in that, Before conducting simulation tests on the multiple tire simulation models, the following steps are also included: Mesh the components in the tire simulation model; use shell elements to simulate the spoke structure and wire layer, and use hybrid solid elements to simulate the tread and shear band.

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