Gradient negative Poisson's ratio non-pneumatic tire rigidity prediction method

Abstract

The invention discloses a gradient negative Poisson's ratio non-pneumatic tire rigidity prediction method which comprises the following steps: creating a negative Poisson's ratio non-pneumatic tire model in finite element simulation analysis software, setting material attributes of a negative Poisson's ratio non-pneumatic tire, carrying out grid division on the model, establishing a static force general analysis step in an analysis step module of the software, and carrying out static force general analysis on the negative Poisson's ratio non-pneumatic tire. Setting load and boundary conditions; carrying out static simulation analysis on the non-pneumatic tire, and researching the influence of structural parameters on the performance of the negative Poisson's ratio non-pneumatic tire; carrying out sensitivity analysis on the rigidity of the tire according to four structural parameters of the tire, namely the gradient of the support body, the thickness of the support body, the thickness of the tread and the thickness of the reinforcing layer; establishing a BP neural network model to predict the radial rigidity of the tire; according to the method, the relationship between the structural parameters of the negative Poisson's ratio non-pneumatic tire and the radial stiffness of the tire is searched by utilizing the BP neural network, the radial stiffness value can be quickly and accurately predicted, the step of finite element simulation analysis and calculation is omitted, and the efficiency is greatly improved.

Description

Technical Field

[0001] The invention relates to the technical field of automobiles, in particular to a method for predicting the stiffness of a gradient negative Poisson's ratio non-pneumatic tire. Background Art

[0002] Tires are an important part of the vehicle chassis and the only medium for the vehicle to contact and interact with the road surface. They have an important impact on the safety, stability, economy, and comfort of the vehicle. Traditional pneumatic tires have safety hazards such as puncture, deflation, and blowout, which seriously threaten the safety and reliability of vehicle driving. In order to improve or overcome the shortcomings of traditional pneumatic tires, major tire manufacturers and research institutes have gradually increased their investment in the research and development of non-pneumatic tire technology. Non-pneumatic tires use elastic supports or fillers to replace the inflatable structure, fundamentally overcoming the shortcomings of pneumatic tires such as easy puncture and blowout. However, due to factors such as stress concentration, high temperature, variable load, variable working conditions, large disturbances and impacts during its service, the overall and key component performance will inevitably degrade. Once the component performance degradation causes final failure, it will still have a huge impact on vehicle safety.

[0003] With the continuous innovation and development of industrial technology, the requirements for material performance of products in various industries are becoming more and more stringent. Ordinary materials can no longer meet the needs of many industries. The development of new materials with superior performance has become an inevitable trend. The advent of metamaterials has provided a new direction for the development of new materials. In the study of mechanical metamaterials, scientists discovered the abnormal mechanical phenomenon of negative Poisson's ratio. Mechanical metamaterials with negative Poisson's ratio characteristics usually have light weight, high damping, good sound absorption and heat insulation properties, and also have specific elastic modulus, shear modulus, indentation resistance and energy absorption. Negative Poisson's ratio materials have good application development potential in many industries such as aviation, shipbuilding and automobile industries due to their special deformation mechanism and good mechanical properties.

[0004] The most commonly used method for predicting tire stiffness today is an empirical model based on experimental data: this method uses a large amount of experimental data to establish an empirical relationship between tire stiffness and various parameters (such as tire size, air pressure, load, etc.). For example, tire inflation pressure, related dimensions, load (vertical / lateral / torsional), displacement (vertical / lateral / torsional) and other data can be obtained through tire stiffness testing, and then the lateral stiffness, torsional stiffness and damping of the tire are calculated using empirical formulas. This method relies on a large amount of experimental data. However, the acquisition of experimental data may be limited by cost, time and resources, and the experimental conditions may not fully simulate the actual driving conditions, so the prediction accuracy of these models may be affected. Summary of the invention

[0005] In view of the above problems and / or the problems existing in the existing non-pneumatic tire prediction technology, the present invention is proposed.

[0006] Therefore, the problem to be solved by the present invention is that the acquisition of experimental data in the prior art may be limited by cost, time and resources, thus affecting the prediction accuracy. The present invention uses a BP neural network to find the relationship between the structural parameters of a negative Poisson's ratio non-pneumatic tire and the radial stiffness of the tire, which can quickly and accurately predict the radial stiffness value, eliminating the finite element simulation analysis and calculation steps, and greatly improving efficiency.

[0007] In order to solve the above technical problems, the present invention provides the following technical solutions: a method for predicting the stiffness of a gradient negative Poisson's ratio non-pneumatic tire, comprising the following steps:

[0008] Create a negative Poisson's ratio non-pneumatic tire model in the finite element simulation analysis software, set the material properties of the negative Poisson's ratio non-pneumatic tire, mesh the non-pneumatic tire model, establish a static general analysis step in the analysis step module of the software, and set the load and boundary conditions;

[0009] Conduct static simulation analysis on the designed non-pneumatic tire to study the influence of structural parameters on the performance of negative Poisson's ratio non-pneumatic tire;

[0010] The sensitivity analysis of tire stiffness was conducted on four tire structural parameters, namely, support body gradient, support body thickness, tread thickness and reinforcement layer thickness;

[0011] A BP neural network model is established to predict the radial stiffness of the tire. If the radial stiffness does not reach the set stiffness threshold, return to the first step, otherwise, output the result.

[0012] As a preferred solution of a method for predicting stiffness of a gradient negative Poisson's ratio non-pneumatic tire in the present invention, the specific steps of setting loads and boundary conditions are as follows:

[0013] In the interaction module, a reference point is established at the center of the non-pneumatic tire. The tire center reference point is coupled with the wheel hub using coupling constraints. The reinforcement layer and the tread are constrained by built-in area constraints. The deformation of the ground during the simulation analysis is ignored. The ground is regarded as a rigid plane and a reference point is established. The reference point is constrained with the rigid ground through rigid body constraints. The contact between the tread of the non-pneumatic tire and the ground is set to hard contact in the normal direction.

[0014] The static mechanics analysis step is divided into two static general analysis steps, which are the first analysis step and the second analysis step. The first analysis step is to fix the reference point at the center of the non-pneumatic tire, constrain the five degrees of freedom of the rigid ground except the vertical displacement, and move the rigid ground vertically for a small displacement until it contacts the tread; the second analysis step is to keep the rigid ground and the tread in contact with each other, release the vertical degrees of freedom of the reference point at the center of the non-pneumatic tire, and apply a downward force of 4000N to the reference point.

[0015] As a preferred solution of a method for predicting stiffness of a gradient negative Poisson's ratio non-pneumatic tire in the present invention, when the BP neural network model predicts the radial stiffness of the tire, several groups of structural parameter samples collected from the previous data are extracted, and the structural parameter samples are processed. According to the processed sample data, a finite element model of the negative Poisson's ratio non-pneumatic tire is established using finite element software, and finite element simulation analysis is performed respectively under the vertical load of the same magnitude of 4000N.

[0016] As a preferred solution of a method for predicting stiffness of a gradient negative Poisson's ratio non-pneumatic tire in the present invention, a BP neural network is used to predict the radial stiffness of the negative Poisson's ratio non-pneumatic tire, the BP neural network includes an input layer, a hidden layer and an output layer, the support body gradient, support body thickness, tread thickness and reinforcement layer thickness are used as inputs of the neural network, and the sinkage of the negative Poisson's ratio non-pneumatic tire is used as the output of the neural network.

[0017] As a preferred solution of a gradient negative Poisson's ratio non-pneumatic tire stiffness prediction method in the present invention, wherein: during the training process of the BP neural network, the data is randomly divided into a 70% training set and a 30% test set.

[0018] As a preferred solution of a method for predicting stiffness of a non-pneumatic tire with a gradient negative Poisson's ratio in the present invention, when processing the structural parameter samples, the n-dimensional vector space D∈R n The sampling of m points is taken as an example, including the following steps:

[0019] Divide the sample space of each dimension into m equal parts. The probability of each interval being drawn is the same. Convert the interval of each dimension to [0,1]. Then the m intervals of each dimension are

[0020]

[0021] Randomly sample m intervals in each dimension and get Where j is the number of the dimension

[0022] The data obtained after the above two steps are randomly combined and matched again. The data that has been used in the combination process cannot be used again. All data values ​​can only be used once. Finally, n-dimensional sample data with m sampling points in each dimension is obtained.

[0023] As a preferred solution of a gradient negative Poisson's ratio non-pneumatic tire stiffness prediction method in the present invention, wherein: the number of nodes l in the hidden layer satisfies the following formula, Among them, n is the number of input layer nodes, m is the number of output layer nodes, and a is a constant between 0 and 10.

[0024] As a preferred solution of a method for predicting stiffness of a non-pneumatic tire with a gradient negative Poisson's ratio in the present invention, when setting material properties, a third-order Ogden model is selected to describe the mechanical properties of tire polyurethane and rubber materials, and the strain energy density function of the Ogden model is:

[0025]

[0026] In the formula, μ j , α j are material constants, and n is the number of expansion terms.

[0027] The beneficial effects of the present invention are as follows: the present invention first obtains which structural parameters have the greatest influence on the radial stiffness of a non-pneumatic tire through finite element simulation analysis, and then uses these structural parameters as input of a BP neural network to predict the radial stiffness of the non-pneumatic tire through the BP neural network, with high prediction accuracy, and can be applied to predict the radial stiffness of a negative Poisson's ratio non-pneumatic tire, providing a feasible research method for optimizing the stiffness characteristics of non-pneumatic tires; the proxy model for predicting the radial stiffness of the negative Poisson's ratio non-pneumatic tire structural parameters established in the present invention can substitute other level values ​​of the studied structural parameters into the proxy model, and can quickly and accurately predict the radial stiffness value, eliminating the calculation steps of the finite element simulation analysis and improving efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following briefly introduces the drawings required for describing the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative labor. Among them:

[0029] Figure 1 A flowchart of the invention.

[0030] Figure 2 It is a schematic structural diagram of a non-pneumatic tire in the present invention;

[0031] Among them, 1 is the tread, 2 is the reinforcement layer, 3 is the support body, and 4 is the wheel hub.

[0032] Figure 3 It is a relationship diagram between load and sinking amount under different support body gradients of the non-pneumatic tire of the present invention.

[0033] Figure 4 It is a stress cloud diagram of the non-pneumatic tire support body with a gradient of -6° in the present invention.

[0034] Figure 5 The figure is a relationship diagram between load and sinking amount under different support body thickness of the non-pneumatic tire of the present invention.

[0035] Figure 6 Graph showing the relationship between load and sinking amount at different tread thicknesses of the non-pneumatic tire of the present invention.

[0036] Figure 7 The figure is a relationship diagram between load and sinking amount under different reinforcing layer thicknesses of the non-pneumatic tire of the present invention.

[0037] Figure 8 This is a neural network model diagram for predicting tire sinkage in the present invention.

[0038] Fig. 9 It is a regression diagram of the neural network training in the present invention.

[0039] Fig.10 It is a performance diagram of the neural network training in the present invention. DETAILED DESCRIPTION

[0040] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the specific implementation methods of the present invention are described in detail below in conjunction with the accompanying drawings.

[0041] In the following description, many specific details are set forth to facilitate a full understanding of the present invention, but the present invention may also be implemented in other ways different from those described herein, and those skilled in the art may make similar generalizations without violating the connotation of the present invention. Therefore, the present invention is not limited to the specific embodiments disclosed below.

[0042] Secondly, the term "one embodiment" or "embodiment" as used herein refers to a specific feature, structure, or characteristic that may be included in at least one implementation of the present invention. The term "in one embodiment" that appears in different places in this specification does not necessarily refer to the same embodiment, nor does it refer to a separate or selective embodiment that is mutually exclusive with other embodiments.

[0043] Example 1

[0044] Reference Figure 1 to Figure 4, which is the first embodiment of the present invention, provides a gradient negative Poisson's ratio non-pneumatic tire stiffness prediction method, which can improve the efficiency of negative Poisson's ratio non-pneumatic tire stiffness prediction.

[0045] A method for predicting the stiffness of a gradient negative Poisson's ratio non-pneumatic tire comprises the following steps:

[0046] Step 1,

[0047] 1.1) Create a negative Poisson's ratio non-pneumatic tire model in ABAQUS software;

[0048] 1.2) Set the material properties of the negative Poisson's ratio non-pneumatic tire, and use the third-order Ogden model to describe the mechanical properties of tire polyurethane and rubber materials. The strain energy density function of the Ogden model is:

[0049]

[0050] In the formula, μ j , α j are all material constants, n is the number of expansion terms;

[0051] 1.3) Mesh the non-pneumatic tire model. After meshing, define boundary conditions and loads in other modules of ABAQUS.

[0052] 1.4) Set the load and boundary conditions, specifically, establish a static general analysis step in the ABAQUS software analysis step module, establish a reference point at the center of the non-pneumatic tire in the interaction module, and use coupling constraints to couple the tire center reference point with the wheel hub, so that the reference point effectively simulates the role of the wheel hub in static analysis, and constrains the reinforcement layer and the tread through built-in area constraints. Ignore the deformation of the ground during the simulation analysis process, regard the ground as a rigid plane, and establish a reference point. Constrain the reference point and the rigid ground through rigid body constraints. Set the contact of the non-pneumatic tire tread in the normal direction to hard contact, and ignore the influence of tangential contact;

[0053] The static mechanics analysis step is divided into two general static analysis steps: In the first analysis step, the reference point at the center of the non-pneumatic tire is fixed, the five degrees of freedom of the rigid ground except the vertical displacement are constrained, and the rigid ground is moved vertically for a small distance until it contacts the tread; In the second analysis step, the rigid ground and the tread are kept in contact with each other, the vertical degrees of freedom of the reference point at the center of the non-pneumatic tire are released, and a downward force of 4000N is applied to the reference point;

[0054] Step 2, performing static simulation analysis on the designed non-pneumatic tire to study the influence of structural parameters on the performance of the negative Poisson's ratio non-pneumatic tire;

[0055] In view of the current research on non-pneumatic tires, this application evaluates negative Poisson's ratio non-pneumatic tires from two aspects:

[0056] (1) Radial stiffness: evaluates load-bearing capacity;

[0057] (2) Maximum ground stress and ground contact area: to evaluate braking and grip performance;

[0058] The safety performance, load-bearing performance and dynamic performance of non-pneumatic tires are all indirectly or directly affected by their stiffness characteristics. The smaller the radial stiffness of a non-pneumatic tire, the better its cushioning and shock absorption, which means that the non-pneumatic tire has good ride comfort, thus ensuring that the driver has a good driving experience when the car is driving; when the radial stiffness is large, it indicates that the tire has a strong load-bearing capacity, so it is very important to have appropriate radial stiffness. The radial stiffness is obtained by solving the ratio of the vertical load increment to the center sink increment. The solution formula is as follows:

[0059]

[0060] Where: Gz is the radial stiffness; dFz is the increment of vertical load; dz is the increment of sinking;

[0061] Through the structural analysis of the negative Poisson's ratio non-pneumatic tire, the support body gradient, support body thickness, tread thickness and reinforcement layer thickness are selected as the main objects affecting the performance, and the two evaluation indicators of sinkage and maximum ground stress are used as benchmarks to analyze the influencing rules.

[0062] Step 3, performing sensitivity analysis on tire stiffness of four tire structural parameters, namely, support body gradient, support body thickness, tread thickness and reinforcement layer thickness;

[0063] Different structural parameters have different effects on the radial stiffness of non-pneumatic tires. Orthogonal tests are used to analyze the sensitivity of structural parameters to radial stiffness. Through the sensitivity analysis of the structural parameters of negative Poisson's ratio non-pneumatic tires to radial stiffness, it can be known which structural parameter of the tire has the greatest influence on the radial stiffness of the negative Poisson's ratio non-pneumatic tire; when the radial stiffness of the negative Poisson's ratio non-pneumatic tire meets the design requirements, the structural parameters that have the greatest influence on the radial stiffness are optimized first, thereby improving the design efficiency and accuracy.

[0064] Step 4: Establish a BP neural network model to predict tire radial stiffness, specifically,

[0065] Extract several groups of structural parameter samples collected from the previous data, process the structural parameter samples, and process the structural parameter samples in the n-dimensional vector space D∈R n The sampling of m points is taken as an example, including the following steps:

[0066] Divide the sample space of each dimension into m equal parts. The probability of each interval being drawn is the same. Convert the interval of each dimension to [0,1]. Then the m intervals of each dimension are

[0067]

[0068] Randomly sample m intervals in each dimension and get Where j is the number of the dimension

[0069] The data obtained after the above two steps are randomly combined and matched again. The data that has been used in the combination process cannot be used again. All data values ​​can only be used once. Finally, n-dimensional sample data with m sampling points in each dimension is obtained.

[0070] According to the processed sample data, the finite element model of the negative Poisson's ratio non-pneumatic tire was established using finite element software, and finite element simulation analysis was performed under the vertical load of the same magnitude of 4000N to complete the data collection;

[0071] A neural network including an input layer, a hidden layer and an output layer is used to predict the radial stiffness of a non-pneumatic tire with a negative Poisson's ratio. The support body gradient, support body thickness, tread thickness and reinforcement layer thickness are used as inputs of the neural network. The sinkage of the non-pneumatic tire with a negative Poisson's ratio is used as the output of the neural network. If the predicted radial stiffness is less than the set stiffness threshold, return to step 1. Otherwise, output the result to complete the prediction of the radial stiffness of the non-pneumatic tire.

[0072] The number of nodes l in the hidden layer satisfies the following formula, Among them, n is the number of input layer nodes, m is the number of output layer nodes, and a is a constant between 0 and 10; during the training process of the BP neural network, the data is randomly divided into 70% training set and 30% test set.

[0073] Example 2

[0074] Reference Figure 5 to Figure 7 , which is the second embodiment of the present invention. This embodiment is based on the previous embodiment. The difference between this embodiment and embodiment 1 is that, taking a gradient negative Poisson's ratio non-pneumatic tire as an example, it verifies the technical effect of the present invention through the technical means of specific parameter simulation verification. Other types of non-pneumatic tires can also refer to the method proposed in the present invention.

[0075] The non-pneumatic tire comprises a wheel hub, a support body with a concave hexagonal honeycomb structure is fixed on the outer edge of the wheel hub, a reinforcement layer is fixed on the outer edge of the support body, and the outer edge of the reinforcement layer is a tread.

[0076] Step 1:

[0077] 1.1) Non-pneumatic tire structure design and finite element model establishment

[0078] The support structure of the negative Poisson's ratio non-pneumatic tire adopts a concave hexagonal honeycomb structure as shown in the figure above. The structure has reliable overall stiffness and excellent deformation rebound characteristics. Since the concave hexagonal honeycomb support structure of the negative Poisson's ratio non-pneumatic tire is an irregular shape, if solid shape modeling is used, the number of meshes obtained during subsequent mesh division will be too large and the mesh quality will be poor, resulting in large errors in the simulation analysis results. That is, when establishing the tire model in ABAQUS, the shell shape is used to establish the support structure, and then the shell is given a corresponding thickness. Create a negative Poisson's ratio non-pneumatic tire model in the ABAQUS software component function, as shown in Figure 2 shown.

[0079] 1.2) Material property settings

[0080] The constitutive model refers to the relationship between strain and stress when a material is stretched and compressed. Since there are many factors affecting polyurethane materials, it is difficult to accurately describe its mechanical properties. This paper uses the third-order Ogden model to describe the mechanical properties of tire polyurethane and rubber materials. The strain energy density function of the Ogden model is:

[0081]

[0082] In the formula, μ j , α j are material constants; n is the number of expansion terms.

[0083] The tread of the negative Poisson's ratio non-pneumatic tire is made of rubber material, the support body is made of polyurethane material, and the reinforcement layer and wheel hub are both made of rigid material. The material parameters are shown in Table 1.1 and Table 1.2.

[0084] Table 1.1 Rubber material parameters

[0085]

[0086]

[0087] Table 1.2 Polyurethane material parameters

[0088]

[0089] 1.3) Mesh Generation

[0090] The Mesh module of ABAQUS is used to mesh the non-pneumatic tire model, where the mesh seed size of the tread, reinforcement layer and hub is 10mm, the mesh seed size of the supporting structure is 5mm, the mesh unit shape of the tread and hub is mainly hexahedron, and the neutral axis algorithm (which is the existing technology) is adopted. The reinforcement layer and the supporting structure are built from the shell shape in the ABAQUS software component module. The unit shape of the reinforcement layer and the supporting structure is mainly quadrilateral, and the advanced algorithm (which is the existing technology) is adopted. After the mesh division is completed, as shown in Table 2.3, the boundary conditions and loads are defined in other modules of ABAQUS.

[0091] 1.4) Set loads and boundary conditions

[0092] A static general analysis step is established in the ABAQUS software analysis step module. A reference point is established at the center of the non-pneumatic tire in the interaction module. The tire center reference point is coupled with the wheel hub using coupling constraints, so that the reference point effectively simulates the role of the wheel hub in static analysis. The reinforcement layer and the tread are constrained by built-in area constraints. The deformation of the ground during the simulation analysis is ignored. The ground is regarded as a rigid plane and a reference point is established. The reference point is constrained with the rigid ground through rigid body constraints. The part of the non-pneumatic tire tread that contacts the ground is set to hard contact in the normal direction, and the influence of tangential contact is ignored.

[0093] The static mechanics analysis step can be divided into two general static analysis steps: in the first analysis step, the reference point at the center of the non-pneumatic tire is fixed, the five degrees of freedom of the rigid ground except the vertical displacement are constrained, and the rigid ground is moved vertically for a small distance until it contacts the tread; in the second analysis step, the rigid ground and the tread are kept in contact with each other, the vertical degrees of freedom of the reference point at the center of the non-pneumatic tire are released, and a downward force of 4000N is applied to the reference point.

[0094] Step 2: Perform static simulation analysis on the designed non-pneumatic tire to study the influence of structural parameters on the performance of negative Poisson's ratio non-pneumatic tire.

[0095] Negative Poisson's ratio non-pneumatic tires are evaluated from two aspects:

[0096] (1) Radial stiffness: evaluates load-bearing capacity;

[0097] (2) Maximum ground contact stress and ground contact area: evaluate braking and grip performance.

[0098] The safety performance, load-bearing performance and dynamic performance of non-pneumatic tires are all indirectly or directly affected by their stiffness characteristics. The smaller the radial stiffness of a non-pneumatic tire, the better its cushioning and shock absorption, which means that the non-pneumatic tire has good ride comfort, thus ensuring that the driver has a good driving experience when the car is driving; when the radial stiffness is large, it indicates that the tire has a strong load-bearing capacity, so it is very important to have appropriate radial stiffness. The radial stiffness is obtained by solving the ratio of the vertical load increment to the center sink increment, and the solution formula is as follows:

[0099]

[0100] Where: Gz is the radial stiffness; dFz is the increment of vertical load; dz is the increment of sinking.

[0101] Through the structural analysis of the negative Poisson's ratio non-pneumatic tire, the support body gradient, support body thickness, tread thickness and reinforcement layer thickness are selected as the main objects affecting the performance, and the two evaluation indicators of sinkage and maximum ground stress are used as benchmarks to analyze the influencing rules.

[0102] 2.1 Effect of support body gradient on non-pneumatic tire performance

[0103] This section will analyze the influence of changing the support body gradient on the performance of negative Poisson's ratio non-pneumatic tires. The support body gradient sizes are shown in Table 2.1, which are -4°, -5°, and -6° respectively.

[0104] Table 2.1 Support gradient scheme

[0105]

[0106] 2.1.1 Effect of support gradient on radial stiffness

[0107] Figure 3 It can be seen that when the gradient is -4°, the load and the sinking amount show a linear relationship, which means that it has a good damping effect and better driving comfort. Figure 3 It is found that the slope of the curve of the negative Poisson's ratio non-pneumatic tire with a support gradient of -6° suddenly increases when the vertical load is greater than 3000N. According to the simulated stress cloud diagram Figure 4 As shown in the figure, the support body of the non-pneumatic tire with a negative Poisson's ratio is in a state of structural instability, indicating that when the support body gradient is -6°, the vertical load cannot be greater than 3000N. Table 2.2 shows the radial stiffness values ​​under different support body gradients after data processing. It can be seen from the table that as the support body gradient decreases, the radial stiffness of the non-pneumatic tire shows a trend of first decreasing and then increasing. Correspondingly, the load-bearing capacity of the non-pneumatic tire also shows the characteristics of first weakening and then strengthening.

[0108] Table 2.2 Radial stiffness values ​​under different support gradients

[0109]

[0110] 2.1.2 Effect of support gradient on grounding performance

[0111] The contact patch and contact stress of a non-pneumatic tire have an important influence on its service life and driving performance. The static mechanical properties of a non-pneumatic tire with a negative Poisson's ratio also change under different sizes of the support gradient structure. This paper explores the effect of changing only the support gradient size on the static mechanical properties of a non-pneumatic tire with a negative Poisson's ratio.

[0112] Table 2.3 Maximum ground stress under different support gradients

[0113]

[0114] Table 2.3 shows the maximum ground contact stress generated on the tread of a negative Poisson's ratio non-pneumatic tire with different support body gradients under the same vertical force. The maximum ground contact stress of a negative Poisson's ratio non-pneumatic tire with different support body gradients from A1 to A3 is 1.064MPa, 1.161MPa and 1.095MPa. It can be seen that when the support body gradient decreases, the maximum ground contact stress and contact area of ​​the tire tread first increase and then decrease, the tread wear of the negative Poisson's ratio non-pneumatic tire first increases and then decreases, and the braking performance of the tire first increases and then weakens.

[0115] 2.2 Effect of support thickness on non-pneumatic tire performance

[0116] This section will analyze the influence of the thickness of the support body on the performance of the negative Poisson's ratio non-pneumatic tire. The thickness of the support body is shown in Table 2.4, which is 4mm, 6mm, and 8mm respectively.

[0117] Table 2.4 Support thickness scheme

[0118]

[0119] 2.2.1 Effect of support body thickness on radial stiffness

[0120] Figure 5 It is a curve diagram of load and sinking under different support body thickness. After data processing, the radial stiffness values ​​of negative Poisson's ratio non-pneumatic tires under different support body thicknesses are listed in Table 2.5. It is easy to see from Table 2.5 that the radial stiffness of non-pneumatic tires is positively correlated with the support body thickness. When the support body thickness increases, the radial stiffness of the tire increases, and correspondingly, the load-bearing capacity of negative Poisson's ratio non-pneumatic tires is enhanced.

[0121] Table 2.5 Radial stiffness values ​​at different support thicknesses

[0122]

[0123] 2.2.2 Effect of support thickness on grounding performance

[0124] The static mechanical properties of negative Poisson's ratio non-pneumatic tires established with different thicknesses of support bodies are also different.

[0125] Table 2.6 shows the maximum ground stress generated by negative Poisson's ratio non-pneumatic tires with different support body thicknesses under a vertical load of 4000N. According to Table 2.6, from Scheme B1 to Scheme B3, the maximum ground stress of negative Poisson's ratio non-pneumatic tires is 1.064MPa, 1.036MPa, and 1.023MPa, respectively. It is easy to see that with the increase in support body thickness, the maximum ground stress of negative Poisson's ratio non-pneumatic tires shows a downward trend, that is, the degree of wear of the tread of negative Poisson's ratio non-pneumatic tires shows a downward trend.

[0126] Table 2.6 Maximum ground stress under different support thickness

[0127]

[0128] 2.3 Effect of tread thickness on non-pneumatic tire performance

[0129] This section analyzes the influence of changing the tread thickness on the performance of negative Poisson's ratio non-pneumatic tires. The tread thickness is shown in Table 2.7, which are 19mm, 22mm, and 25mm respectively.

[0130] Table 2.7 Tread thickness scheme

[0131]

[0132] 2.3.1 Effect of tread thickness on radial stiffness

[0133] Figure 6 The graph of the load and sinkage of a non-pneumatic tire with a negative Poisson's ratio under different tread thicknesses shows a linear change in the load and sinkage of a non-pneumatic tire under different tread thicknesses. Through data processing, the radial stiffness values ​​under different tread thicknesses are calculated, as shown in Table 2.8. From the data in the table, it can be seen that with the increase in tread thickness, the radial stiffness of the non-pneumatic tire with a negative Poisson's ratio gradually increases, and the load-bearing capacity is enhanced.

[0134] Table 2.8 Radial stiffness values ​​at different tread thicknesses

[0135]

[0136] 2.3.2 Effect of tread thickness on ground contact performance

[0137] Different tread thicknesses will also affect the static mechanical properties of the negative Poisson's ratio non-pneumatic tire, and thus affect the ground contact performance of the negative Poisson's ratio non-pneumatic tire.

[0138] Table 2.9 Maximum ground contact stress at different tread thicknesses

[0139]

[0140] Table 2.9 shows the maximum ground stress of negative Poisson's ratio non-pneumatic tires under 4000N vertical load with different tread thicknesses. It can be seen from Table 2.9 that the maximum ground stress of negative Poisson's ratio non-pneumatic tires with tread thicknesses of 19mm, 22mm, and 25mm are 1.064MPa, 1.012MPa, and 0.9441MPa, respectively. It can be seen that with the increase of tread thickness, the maximum ground stress of negative Poisson's ratio non-pneumatic tires gradually decreases, and the maximum wear degree of the tread also decreases.

[0141] 2.4 Effect of reinforcement layer thickness on non-pneumatic tire performance

[0142] The reinforcement layer is a material layer that tightens the tread and plays a role in mitigating impact. Its thickness will also affect the performance of negative Poisson's ratio non-pneumatic tires. This section studies the effect of changing the thickness of the reinforcement layer on the performance of negative Poisson's ratio non-pneumatic tires. The thickness of the reinforcement layer is shown in Table 2.10, which is 4mm, 5mm, and 6mm respectively.

[0143] Table 2.10 Reinforcement layer thickness scheme

[0144]

[0145] 2.4.1 Effect of reinforcement layer thickness on radial stiffness

[0146] Table 2.11 Radial stiffness values ​​at different reinforcement layer thicknesses

[0147]

[0148] Figure 7 The curve diagram of the relationship between load and sinking under different reinforcement layer thicknesses. After data processing, the radial stiffness values ​​of negative Poisson's ratio non-pneumatic tires under different reinforcement layer thicknesses are shown in Table 2.11. It can be seen that as the thickness of the reinforcement layer increases, the radial stiffness increases, and the load-bearing capacity of the negative Poisson's ratio non-pneumatic tire increases.

[0149] 2.4.2 Effect of reinforcement layer thickness on grounding performance

[0150] Table 2.12 shows the maximum ground stress of a negative Poisson's ratio non-pneumatic tire under a vertical load of 4000N under three reinforcement layer thickness schemes.

[0151] From Table 2.12, we know that the maximum ground stress of the negative Poisson's ratio non-pneumatic tire with a reinforcement layer thickness of 4mm, 5mm, and 6mm is 1.064MPa, 1.048MPa, and 1.036MPa, respectively. It is known that the maximum ground stress gradually decreases with the increase of the reinforcement layer thickness. According to the ground footprint diagram, it can be seen that the negative Poisson's ratio non-pneumatic ground footprints of the three reinforcement layer thicknesses are almost the same, and the ground stress distribution is also almost the same.

[0152] Table 2.12 Maximum ground stress under different reinforcement layer thickness

[0153]

[0154] The above results show that:

[0155] (1) By reducing the support body gradient, it can be observed that under the rated vertical load, the tire sinking first decreases and then increases, and the load-bearing capacity shows a trend of first increasing and then decreasing;

[0156] (2) As the thickness of the support body increases, it is observed that under the rated vertical load, the tire sinking amount decreases and the tire load-bearing capacity is enhanced; as the thickness of the support body increases, the ground contact stress shows a downward trend and the tire's grip performance decreases;

[0157] (3) After increasing the tread thickness, the tire sinking amount under the same load is reduced, and the tire load-bearing capacity is enhanced;

[0158] (4) With the increase of the thickness of the reinforcement layer, under the same load, the tire sinking amount is observed to decrease, thereby enhancing the tire load-bearing capacity; the ground stress shows a downward trend and the degree of tire wear is reduced.

[0159] Step 3, the sensitivity analysis of the tire stiffness was performed on the four tire structural parameters of support body gradient, support body thickness, tread thickness and reinforcement layer thickness.

[0160] Different structural parameters have different effects on the radial stiffness of non-pneumatic tires. Orthogonal tests can be used to analyze the sensitivity of structural parameters to radial stiffness. Through the sensitivity analysis of the structural parameters of negative Poisson's ratio non-pneumatic tires to radial stiffness, it can be known which structural parameter of the tire has the greatest influence on the radial stiffness of the negative Poisson's ratio non-pneumatic tire. When the radial stiffness of the negative Poisson's ratio non-pneumatic tire meets the design requirements, the structural parameters that have the greatest influence on the radial stiffness are optimized first, thereby improving the design efficiency and accuracy.

[0161] The following is a detailed analysis and calculation of the orthogonal test method, so as to obtain a design scheme for analyzing the sensitivity of structural parameters to the radial stiffness of non-pneumatic tires. The standard orthogonal test design scheme process is as follows:

[0162] (1) Clarify the purpose of the experiment and determine the evaluation indicators;

[0163] After a series of simulations and calculations, a sensitivity analysis of the structural parameters on the radial stiffness of the non-pneumatic tire was carried out, and the evaluation criterion was the center sinkage of the non-pneumatic tire.

[0164] (2) Determine the factors and factor levels that affect the indicators;

[0165] According to the designed negative Poisson's ratio non-pneumatic tire model, the structural parameters that affect the radial stiffness of the non-pneumatic tire are determined, which are the support body gradient, support body thickness, tread thickness and reinforcement layer thickness. In this orthogonal test, each structural parameter only takes three levels: the support body gradient is -4, -5, and -6; the support body thickness is 4mm, 6mm, and 8mm; the tread thickness is 19mm, 22mm, and 25mm; the reinforcement layer thickness is 4mm, 5mm, and 6mm. The test factors and levels are shown in Table 3.1.

[0166] Table 3.1 Orthogonal test factors and levels

[0167]

[0168] (3) Select the orthogonal test table

[0169] From the above, we can see that this test is 4 factors and 3 levels, so according to L9(3 4 ) The test scheme of the orthogonal test table is used to analyze the sensitivity of the structural parameters of the negative Poisson's ratio non-pneumatic tire to the radial stiffness. There are 9 groups of orthogonal tests in total, and the total number of test schemes is 81 groups, which reduces the workload by nearly 88.9%, significantly improves the work efficiency, and can ensure the accuracy of the test results. The design scheme of the orthogonal test is shown in Table 3.2. Then, the finite element simulation analysis and calculation of the negative Poisson's ratio non-pneumatic tire under the same vertical force are carried out according to the scheme. The simulation results of the 9 groups of orthogonal test schemes are shown in Table 3.3.

[0170] Table 3.2 Orthogonal test table

[0171]

[0172] This test uses the tire center sinkage as the orthogonal test evaluation standard. Table 3.3 shows the test results of this orthogonal test design. According to the results of the orthogonal test, the sinkage range is calculated. The specific data results are listed in Table 3.4. The sinkage ranges of the four structural parameters of support body gradient, support body thickness, tread thickness and reinforcement layer thickness are 0.3687mm, 9.4598mm, 1.5313mm, and 2.3536mm respectively. The influence degree is R(B)>R(D)>R(C)>(A). The sinkage range of support body thickness is the largest, while the sinkage range of support body gradient is the smallest. This shows that the support body thickness has the most significant effect on the sinkage of negative Poisson's ratio non-pneumatic tires, followed by the reinforcement layer thickness, followed by the tread thickness, and the support body gradient has the smallest effect. According to the relationship between radial stiffness and sinkage in the above text, it is also concluded that the support body thickness has the greatest effect on the radial stiffness of negative Poisson's ratio non-pneumatic tires, followed by the reinforcement layer thickness, followed by the tread thickness, and the support body gradient has the smallest effect. It can be seen that when the radial stiffness value of the designed negative Poisson's ratio non-pneumatic tire meets the design requirements, the structural parameter of the support body thickness can be optimized first, followed by the reinforcement layer thickness, then the tread thickness, and finally the structural parameter of the support body gradient can be optimized to make the radial stiffness of the designed negative Poisson's ratio non-pneumatic tire meet the requirements.

[0173] Table 3.3 Orthogonal test results

[0174]

[0175]

[0176] Table 3.4 Extreme difference in sinking

[0177]

[0178] Step 4: Establish a BP neural network model to predict tire radial stiffness.

[0179] The present invention studies the influence of four structural parameters of negative Poisson's ratio non-pneumatic tire, namely support body gradient, support body thickness, tread thickness and reinforcement layer thickness, on the radial stiffness of negative Poisson's ratio non-pneumatic tire. A total of 25 groups of structural parameter samples were extracted using the Latin hypercube sampling method. The Latin hypercube sampling method is an experimental design scheme that can generate random sample points to ensure that the randomly selected sample points have the characteristics of being able to represent all points in the vector space. In the n-dimensional vector space D∈R n In the case of sampling m points, the idea of ​​Latin hypercube sampling is explained. The detailed process is as follows:

[0180] Divide the sample space of each dimension into m equal parts, and the probability of each interval being drawn is the same. Convert the interval of each dimension to [0,1], then the m intervals of each dimension are

[0181] Randomly sample m intervals in each dimension and get Where j is the number of the dimension

[0182] The data obtained after the two steps of stratification and sampling are then randomly combined and matched. The data that has been used in the combination process cannot be used again. All data values ​​can only be used once. Finally, n-dimensional sample data with m sampling points in each dimension is obtained.

[0183] Table 4.1 Sampling results

[0184]

[0185] The sampling results of this application are shown in Table 4.1. Based on the obtained structural parameter sample data, the finite element model of the negative Poisson's ratio non-pneumatic tire was established using ABAQUS finite element software, and finite element simulation analysis was performed under the vertical load of the same magnitude of 4000N. After finite element simulation analysis, the results obtained are shown in Table 4.2, and the data collection is completed.

[0186] Table 4.2 Subsidence results

[0187]

[0188]

[0189] A three-layer BP neural network is used to predict the radial stiffness of a negative Poisson's ratio non-pneumatic tire. The three layers are the input layer, the hidden layer, and the output layer. The structural parameters (support body gradient, support body thickness, tread thickness, and reinforcement layer thickness) that affect the radial stiffness of a negative Poisson's ratio non-pneumatic tire are used as the input of the neural network, and the sinking amount of the negative Poisson's ratio non-pneumatic tire is used as the output of the neural network. In the BP neural network, the number of its hidden layer nodes has a significant impact on the prediction accuracy of the BP neural network: if the number of its hidden layer nodes is too small, the neural network cannot fully explore the complex characteristics of the input data, resulting in the need to increase the number of training times for the neural network, and the training accuracy of the neural network is also affected, and its training results may be limited; on the other hand, if the number of hidden layer nodes of the BP neural network is too large, it may increase the training time of the neural network and may cause the neural network to easily fall into overfitting. Therefore, it is crucial to choose an appropriate number of hidden layer nodes. The number of hidden layer nodes is selected according to the following formula:

[0190]

[0191] The BP neural network model for predicting radial stiffness of non-pneumatic tire with negative Poisson's ratio is as follows: Figure 8 As shown, the input layer has 4 nodes, including four structural parameters: support body gradient, support body thickness, tread thickness and reinforcement layer thickness; the hidden layer has 10 nodes; and the output layer has only 1 node, which is the sinking amount of the non-pneumatic tire.

[0192] The 25 sets of structural parameter samples and sinking result data obtained in the previous data collection were randomly divided into 70% training set and 30% test set during the training process. Before the BP neural network starts training, the data to be studied must be processed accordingly. The processing of each data mainly includes: randomly shuffling the data to be studied, dividing the shuffled data into the training set data and test set data of the neural network, and normalizing the data to be studied.

[0193] The training regression diagram is as follows Fig. 9 The training performance graph is shown in Figure 10. The values ​​of regression coefficient R and mean square error MSE in the training, validation and testing stages are shown in Table 4.3. Fig. 9 It can be seen that in the regression analysis of training, the regression coefficient R of each indicator is greater than 0.9, indicating that the data set is highly correlated. In the BP neural network training performance analysis, if the verification curve is closer to the training curve and the test curve, and the value is closer to 0, the training effect is better. Fig.10 In the figure, the green circle represents the number of iterations corresponding to the best goodness of fit, so the verification performance is best at the 4th iteration. From Table 4.3, it can be seen that the proxy model established by the BP neural network to predict the radial stiffness of non-pneumatic tires has a high prediction accuracy, and this BP neural network can be used to predict the radial stiffness of non-pneumatic tires with negative Poisson's ratio.

[0194] Table 4.3 Mean square error MSE and regression coefficient R

[0195]

[0196] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solutions of the present invention can be modified or replaced by equivalents without departing from the spirit and scope of the technical solutions of the present invention, which should all be included in the scope of the technical solutions of the present invention.

Claims

1. A method for predicting the stiffness of a non-pneumatic tire with a gradient negative Poisson's ratio, characterized in that: The following steps are included: Create a negative Poisson's ratio non-pneumatic tire model in the finite element simulation analysis software, set the material properties of the negative Poisson's ratio non-pneumatic tire, mesh the non-pneumatic tire model, establish a static general analysis step in the analysis step module of the software, and set the load and boundary conditions; Conduct static simulation analysis on the designed non-pneumatic tire to study the influence of structural parameters on the performance of negative Poisson's ratio non-pneumatic tire; The sensitivity analysis of tire stiffness was conducted on four tire structural parameters, namely, support body gradient, support body thickness, tread thickness and reinforcement layer thickness; A BP neural network model is established to predict the radial stiffness of the tire. If the radial stiffness does not reach the set stiffness threshold, return to the first step, otherwise, output the result.

2. A method for predicting stiffness of a gradient negative Poisson's ratio non-pneumatic tire as claimed in claim 1, characterized in that: The specific steps for setting loads and boundary conditions are as follows: In the interaction module, a reference point is established at the center of the non-pneumatic tire. The tire center reference point is coupled with the wheel hub using coupling constraints. The reinforcement layer and the tread are constrained by built-in area constraints. The deformation of the ground during the simulation analysis is ignored. The ground is regarded as a rigid plane and a reference point is established. The reference point is constrained with the rigid ground through rigid body constraints. The contact between the tread of the non-pneumatic tire and the ground is set to hard contact in the normal direction. The static mechanics analysis step is divided into two static general analysis steps, which are the first analysis step and the second analysis step. The first analysis step is to fix the reference point at the center of the non-pneumatic tire, constrain the five degrees of freedom of the rigid ground except the vertical displacement, and move the rigid ground vertically for a small displacement until it contacts the tread; the second analysis step is to keep the rigid ground and the tread in contact with each other, release the vertical degrees of freedom of the reference point at the center of the non-pneumatic tire, and apply a downward force of 4000N to the reference point.

3. A method for predicting stiffness of a gradient negative Poisson's ratio non-pneumatic tire as claimed in claim 2, characterized in that: When the BP neural network model predicts the radial stiffness of the tire, several groups of structural parameter samples collected from the previous data are extracted and processed. According to the processed sample data, the finite element model of the negative Poisson's ratio non-pneumatic tire is established using finite element software, and finite element simulation analysis is performed under the vertical load of the same magnitude of 4000N.

4. A method for predicting the stiffness of a gradient negative Poisson's ratio non-pneumatic tire as claimed in claim 3, characterized in that: A BP neural network is used to predict the radial stiffness of a negative Poisson's ratio non-pneumatic tire. The BP neural network includes an input layer, a hidden layer and an output layer. The support body gradient, support body thickness, tread thickness and reinforcement layer thickness are used as the input of the neural network, and the sinkage of the negative Poisson's ratio non-pneumatic tire is used as the output of the neural network.

5. The method for predicting the stiffness of a non-pneumatic tire with a gradient negative Poisson's ratio as claimed in claim 3, characterized in that: During the training process of the BP neural network, the data is randomly divided into 70% training set and 30% test set.

6. A method for predicting stiffness of a gradient negative Poisson's ratio non-pneumatic tire as claimed in claim 4 or 5, characterized in that: When processing the structural parameter samples, we use the n-dimensional vector space D∈R n The sampling of m points is taken as an example, including the following steps: Divide the sample space of each dimension into m equal parts. The probability of each interval being drawn is the same. Convert the interval of each dimension to [0,1]. Then the m intervals of each dimension are Randomly sample m intervals in each dimension and get Where j is the number of the dimension The data obtained after the above two steps are randomly combined and matched again. The data that has been used in the combination process cannot be used again. All data values ​​can only be used once. Finally, n-dimensional sample data with m sampling points in each dimension is obtained.

7. A method for predicting stiffness of a gradient negative Poisson's ratio non-pneumatic tire according to any one of claims 1 to 3, characterized in that: The number of nodes l in the hidden layer satisfies the following formula: Among them, n is the number of input layer nodes, m is the number of output layer nodes, and a is a constant between 0 and 10.

8. A method for predicting stiffness of a gradient negative Poisson's ratio non-pneumatic tire according to any one of claims 1 to 6, characterized in that: When setting material properties, the third-order Ogden model is used to describe the mechanical properties of tire polyurethane and rubber materials. The strain energy density function of the Ogden model is: In the formula, μ j , α j are material constants, and n is the number of expansion terms.

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