A non-pneumatic tire and its multi-scale parallel topology optimization design method

Abstract

The present invention discloses a non-pneumatic tire and a multi-scale parallel topology optimization design method thereof, which relates to the field of wheel design technology. It solves technical problems existing in traditional single-scale tire topology optimization design methods, such as limited design space, high computational cost, and poor connectivity of connected structures. The key point of its technical solution is to map the tire annular design domain to a rectangular design domain through coordinate transformation, thereby reducing optimization costs. Multiple types of microstructures are introduced into the multi-scale optimization of the structure, and a multi-scale parallel topology optimization design model for the non-pneumatic tire structure is constructed based on the SIMP method and the energy homogenization method. This also effectively solves the topology optimization design problem of the mechanical properties of the continuum structure considering the non-design domain, and realizes the parallel topology optimization of the non-pneumatic tire macrostructure and microscopic unit cell configuration, so as to give full play to the advantages of the porous structure, so that the non-pneumatic tire has the characteristics of high specific stiffness, impact energy absorption, light weight, and designability.

Description

Technical Field

[0001] The present application relates to the technical field of wheel design, and in particular to a non-pneumatic tire and a multi-scale parallel topology optimization design method thereof. Background Art

[0002] Tires are the only part of a vehicle that comes into contact with the ground, so their performance directly impacts the stability and safety of the entire vehicle. Compared to traditional pneumatic tires, non-pneumatic tires fundamentally eliminate the possibility of blowouts. Their materials are also more environmentally friendly, meeting the needs of the future automotive industry.

[0003] Since the design of non-pneumatic tires mainly relies on engineers' experience and heuristic methods, the design cycle is long and there is little room for improvement in structural performance. In recent years, relevant scholars have performed topological optimization of tires based on bidirectional progressive structural optimization methods, obtained innovative structural forms, and improved material utilization efficiency. However, the traditional single-scale topological optimization method based on homogeneous materials can no longer meet the increasingly stringent tire performance requirements, and the degree of lightweighting is limited. In order to fully tap the potential of materials and comprehensively improve the overall performance of tires, multi-scale parallel topological design theory has become an inevitable trend in the design of the next generation of new lightweight tire structures. In addition, when performing topological optimization on the structure, the influence of certain local features on the mechanical properties of the structure is rarely considered, and the superiority of the topological optimization method in lightweight design is not fully utilized. Therefore, it is necessary to consider the contribution coefficient of the certain non-design area to the overall performance of the structure to provide more detailed guidance for the detailed design of the structure.

[0004] For engineering applications, how to introduce a material distribution optimization model in the multi-scale topology optimization design of non-pneumatic tires, reasonably distribute the multiple types of microstructures of the macrostructure, and improve the target performance of the tire structure with the three core optimization elements of "macrostructure topology", "microstructure topology" and "microstructure distribution" remains an urgent problem to be solved. Summary of the Invention

[0005] The present application provides a non-pneumatic tire and a multi-scale parallel topology optimization design method thereof. The technical purpose is to perform parallel topology optimization design of the tire's macrostructure and micro unit cell configuration, reduce the tire's weight, improve the tire's load-bearing capacity, shorten the production cycle, and achieve the purpose of energy conservation and emission reduction.

[0006] The above technical objectives of this application are achieved through the following technical solutions:

[0007] A non-pneumatic tire comprising, from the inside out, a hub, spokes, an inner ring, a shear band, an outer ring, and a tread; 24 cross bars are provided in each of the spokes, one end of each cross bar being connected to the hub and the other end being connected to the inner ring; a first diagonal bar and a second diagonal bar are provided between adjacent cross bars; the inner ring, adjacent cross bars, and the first diagonal bars constitute a first hole microstructure; the adjacent cross bars, the first diagonal bars, the second diagonal bars, and the outer surface of the hub constitute a second hole microstructure; and the cross bars, the second diagonal bars, and the outer surface of the hub constitute a third hole microstructure; the cross bars, the first diagonal bars, and the second diagonal bars are all composed, from the inside out, of a first density material, a second density material, and a third density material; the second density material and the third density material are evenly distributed with numerous micropore structures, and the distance between adjacent micropore structures is 0.01 mm;

[0008] In the crossbar, the area of ​​the first density material is much larger than the area of ​​the second density material and the third density material;

[0009] In the first oblique rods and the second oblique rods, the area of ​​the first density material is smaller than the area of ​​the second density material and the third density material.

[0010] A multi-scale parallel topology optimization design method for a non-pneumatic tire, comprising:

[0011] S1: Convert the structure of the non-pneumatic tire from the Cartesian coordinate system (x, y) to the translational periodic structure in the polar coordinate system (r, θ), expressed as:

[0012]

[0013] Then the macroscopic coordinates (r,θ) and microscopic coordinates in the polar coordinate system are It is associated with the characteristic length δ and expressed as:

[0014] S2: Define the initial macro and micro design parameters of the tire, including: the number of tire rotation cycles is 24, the tire pressure is 4900N, the hub area meets the Dirichlet boundary condition, the tire structure size L×H is defined as 180mm×116mm, and the design domain spoke is L d ×H d Defined as 180mm×100mm; L represents the length corresponding to the rotation of θ degrees around the center of the tire, 0.5mm is equivalent to 1 degree, tanθ=y / x, θ∈[0°,360°]; H represents the length from the hub to the tread, H=ρ, ρ 2 =x 2 +y 2In the finite element analysis, the macrostructure is discretized into 180×116 finite elements, and the size of each macrostructure finite element is 1mm; multiple types of microstructures are discretized into 100×100 finite elements through finite element analysis, and the size of each microstructure finite element is 0.01mm;

[0015] S3: Constructing a material topology optimization model based on the macro-micro initial design parameters and the improved SIMP method, optimizing the material distribution of the tire based on the material topology optimization model, and obtaining a regional material density unit distribution map;

[0016] The material topology optimization model is expressed as:

[0017]

[0018] Among them, X d and X n They represent the design domain topology variable vector and the non-design domain topology variable vector respectively; i represents the unit number, or When it is equal to 1, it means that unit i belongs to the design domain. represents the topological variable of the i-th design domain; or When it is equal to 0, it means that unit i belongs to the non-design domain. represents the i-th non-design domain topological variable; ρ min represents the minimum value of the design variable; ρ represents the design variable vector, the total number is N e ; C represents the compliance of the non-pneumatic tire structure; F represents the load borne by the macrostructure; U represents the displacement field within the macrostructure; K represents the global stiffness matrix of the macrostructure; K0 represents the global stiffness matrix of the solid element; U e represents the displacement field of the solid element; G d represents the volume constraint for material distribution optimization; V d Indicates the maximum allowable material usage; v0 indicates the volume fraction of the solid element;

[0019] S4: Based on the macro-micro initial design parameters and the regional material density unit distribution, a parallel topology optimization design model for the macrostructure and multiple types of microstructures is constructed using SIMP and energy homogenization, and the macro design variables and micro design variables of the parallel topology optimization design model are updated until the optimal structural topology configuration of the macrostructure and multiple types of microstructures is obtained, and a homogenized equivalent elastic matrix corresponding to the optimal structural topology configuration is obtained;

[0020] The parallel topology optimization design model is expressed as:

[0021]

[0022] Where C' represents the multi-scale optimization objective function, which is defined by the compliance C of the non-pneumatic tire structure; Ω M represents the macro design domain; Ω m represents the micro-design domain; N M Represents the total number of macro design variables; N m represents the total number of micro-design variables; ρ M and ρ m Represent the unit density at macro scale and micro scale respectively; G M represents the overall volume constraint for multi-scale topology optimization; V M Indicates the maximum allowable material usage of the macrostructure; G m represents the volume constraint for microstructure topology optimization; V m Indicates the maximum allowable material usage in the material microstructure; and Represent the minimum values ​​of macro unit density and micro unit density respectively; u M represents the macroscopic displacement field; v M represents the virtual displacement field within the macrostructure, which allows H in the dynamic displacement field within the macrostructure per Take any value; u m represents the microscopic displacement field; v m represents the virtual displacement field within the microstructure, which allows the dynamic displacement field within the microstructure to be Take any value; a represents the energy bilinear function; l represents the load unilinear function;

[0023] S5: Convert the homogenized equivalent elastic matrix in the polar coordinate system to the Cartesian coordinate system, expressed as:

[0024]

[0025] Among them, D H represents the homogenized equivalent elastic matrix in the polar coordinate system; represents the homogenized elastic tensor matrix in the Cartesian coordinate system; M represents the rotation matrix of the second-order tensor;

[0026]

[0027] S6: Obtaining a mapping structure in a Cartesian coordinate system through coordinate transformation, and performing multi-scale topological optimal design of a non-pneumatic tire through the mapping structure;

[0028] Among them, the mapping structure is expressed as:

[0029]

[0030] The beneficial effects of the present application are as follows: the non-pneumatic tire and its multi-scale parallel topology optimization design method described in the present application solve the problems of limited design space, high computational cost, and poor connectivity of connected structures existing in traditional single-scale tire topology optimization methods. Through coordinate transformation, the tire circular design domain is mapped to a rectangular design domain, reducing optimization costs. Multiple types of microstructures are introduced into the structural multi-scale optimization, and based on the SIMP method and energy homogenization method, a non-pneumatic tire multi-scale parallel topology optimization design model is constructed. This also effectively solves the topology optimization design problem of the mechanical properties of continuum structures considering non-design domains, and realizes the parallel topology optimization of the macrostructure and microscopic unit cell configuration of the non-pneumatic tire, so as to give full play to the advantages of the porous structure, so that the non-pneumatic tire has high specific stiffness, impact energy absorption, heat insulation and heat release, vibration and noise reduction, light weight, and designability. The optimization efficiency of tire structure / structural multi-scale topology optimization considering multiple types of microstructures is faster than that of the single-type microstructure model, which is more conducive to improving the target performance of the tire and does not have the connectivity problem between microstructures. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] Figure 1 A diagram of the non-pneumatic tire structure designed for multi-scale parallel topology optimization in this application;

[0032] Figure 2 Schematic diagram of coordinate changes of non-pneumatic tire model;

[0033] Figure 3 Schematic diagram of the initial model structure of a non-pneumatic tire;

[0034] Figure 4 Schematic diagram of the equivalent structure of the multi-scale topology optimization model of a non-pneumatic tire;

[0035] Figure 5 It is a schematic diagram of the density unit distribution of continuous materials;

[0036] Figure 6 This is a schematic diagram of regional material density unit distribution;

[0037] Figure 7 Schematic diagram of the optimal topological configuration of the macrostructure of a non-pneumatic tire;

[0038] Figure 8 Iteration graph of objective function and global volume fraction for non-pneumatic tire;

[0039] Figure 9 Design a flow chart for multi-scale parallel topology optimization of non-pneumatic tires;

[0040] In the figure: 1-hub; 2-spoke; 3-tread; 4-inner ring; 5-shear band; 6-outer ring; 7-cross bar; 8-first diagonal bar; 9-second diagonal bar; 10-first hole microstructure; 11-second hole microstructure; 12-third hole microstructure; 13-microhole structure. DETAILED DESCRIPTION

[0041] The technical solution of this application will be described in detail below with reference to the accompanying drawings.

[0042] like Figure 1 and Figure 3 As shown, the non-pneumatic tire described in the present application includes a hub, spokes, an inner ring, a shear band, an outer ring and a tread from the inside out, and 24 cross bars are provided in the spokes, one end of the cross bar is connected to the hub and the other end is connected to the inner ring, and a first diagonal bar and a second diagonal bar are provided between adjacent cross bars, the inner ring, adjacent cross bars and the first diagonal bar constitute a first hole microstructure, the adjacent cross bars, the first diagonal bar, the second diagonal bar and the outer surface of the hub constitute a second hole microstructure, and the cross bars, the second diagonal bar and the outer surface of the hub constitute a third hole microstructure; the cross bars, the first diagonal bar and the second diagonal bar are all composed of a first density material, a second density material and a third density material from the inside out, and countless micropore structures are evenly distributed on the second density material and the third density material, and the distance between adjacent micropore structures is 0.01 mm.

[0043] In the crossbar, the area of ​​the first density material is much larger than the area of ​​the second density material and the third density material.

[0044] In the first oblique rods and the second oblique rods, the area of ​​the first density material is smaller than the area of ​​the second density material and the third density material.

[0045] As a specific embodiment, the first oblique rod and the second oblique rod are approximately parallel, both ends of the first oblique rod are respectively connected to adjacent cross rods, and one end of the second oblique rod is connected to the cross rod and the other end is connected to the wheel hub.

[0046] As a specific example, the area of ​​a non-pneumatic tire is 33580.8mm 2 , the area of ​​the spoke is 2135πmm 2 The microstructure area of ​​the first hole is 513.04 mm 2 The microstructure area of ​​the second hole is 373.12 mm 2 The microstructure area of ​​the third hole is 46.64mm 2 , the microporous structure area is 4×10 -5 mm 2 .

[0047] As a specific embodiment, the relative density of the first density material is 100%, the relative density of the second density material is 70%, the relative density of the third density material is 50%, and the relative densities of the first hole microstructure, the second hole microstructure and the third hole microstructure are all 0%.

[0048] As a specific embodiment, the sum of the areas of the first hole microstructure, the second hole microstructure and the third hole microstructure accounts for 40.11% of the spoke, the area of ​​the first density material accounts for 43.1% of the spoke, the area of ​​the second density material accounts for 14.31% of the spoke, and the area of ​​the third density material accounts for 2.43% of the spoke.

[0049] like Figure 9 As shown, the multi-scale parallel topology optimization design method for the non-pneumatic tire of the present application includes:

[0050] S1: If Figure 2 As shown in Figure 1, the special periodic structure of the non-pneumatic tire with cyclic symmetry along the circumferential direction is mapped to the translational periodic design domain, that is, the structure of the non-pneumatic tire is converted from the Cartesian coordinate system (x, y) to the translational periodic structure in the polar coordinate system (r, θ), which is expressed as:

[0051]

[0052] Then the macroscopic coordinates (r,θ) and microscopic coordinates in the polar coordinate system are It is associated with the characteristic length δ and expressed as:

[0053] S2: Define the macro and micro initial design parameters of the tire.

[0054] Specifically, when a vehicle is driving on the road, the pressure on the non-pneumatic tire from the road is actually an unevenly distributed load. However, in finite element analysis, a node set is established on the surface of the non-pneumatic tire, and the pressure on the non-pneumatic tire from the ground is applied through this node set. At this time, the pressure received by the non-pneumatic tire can be simulated by a uniformly distributed load. Assume that the number of tire rotation cycles is 24 and the pressure on the tire is 4900N. In addition, it is assumed that the deformation of the wheel hub is very small and can be ignored, that is, the wheel hub is deemed to meet the Dirichlet boundary condition. Then the equivalent model is as follows Figure 4 As shown, a vertical downward force of 4900N is applied every 15 (360° / 24=15) unit nodes at the upper boundary of the tread.

[0055] The structural dimensions of the tire are defined as 180mm×116mm, and the design domain is L d ×H dDefined as 180mm×100mm; L represents the length corresponding to the rotation of θ degrees around the center of the tire, 0.5mm is equivalent to 1 degree, tanθ=y / x, θ∈[0°,360°]; H represents the length from the hub to the tread, H=ρ, ρ 2 =x 2 +y 2 In the finite element analysis, the macrostructure is discretized into 180×116 finite elements, and the size of each macrostructure finite element is 1mm. Various types of microstructures are discretized into 100×100 finite elements through finite element analysis, and the size of each microstructure finite element is 0.01mm. The size of the microstructure finite element is much smaller than the macroscale, which meets the application conditions of the homogenization theory. In the distributed material optimization design, the maximum allowable material amount G in its volume constraint is d Defined as 50%.

[0056] Figure 3 The material parameters of each component of the non-pneumatic tire are shown in Table 1.

[0057] Part number Material Thickness (mm) <![CDATA[Density (kg / m 3 )]]> Young's modulus (GPa) Poisson's ratio 1-Wheel Hub aluminum alloy 5 2800 72 0.33 2-spoke polyurethane 9 1100 32 0.49 3-Tread synthetic rubber 5 1043 11.9 0.49 4,6-inner ring, outer ring high-strength steel 0.5 7800 210 0.29 5-Shear band polyurethane 9 1100 32 0.49

[0058] Table 1

[0059] S3: To optimize the material density unit distribution of the tire macrostructure, a material topology optimization model is constructed based on the macro-micro initial design parameters and the improved SIMP method. The material distribution of the tire is optimized based on the material topology optimization model to obtain a regional material density unit distribution.

[0060] The SIMP method is used to construct a material topology optimization model, taking into account both the design domain and the non-design domain. The material topology optimization model includes the calculation of finite element analysis F=KU and structural flexibility C. The material topology optimization model is expressed as:

[0061]

[0062] Among them, ρ represents the design variable vector, the total number is N e ; i represents the unit number; E d and E n They represent the design domain unit number array and the non-design domain unit number array respectively; ρ min represents the minimum value of the design variable; C represents the compliance of the non-pneumatic tire structure; F represents the load borne by the macrostructure; U represents the displacement field within the macrostructure; K represents the global stiffness matrix of the macrostructure; K0 represents the global stiffness matrix of the solid element; U e represents the displacement field of the solid element; G d represents the volume constraint for material distribution optimization; V dIndicates the maximum allowable material usage; v0 represents the volume fraction of the solid element.

[0063] Extract the non-design domain unit number and use the non-design domain identification array and design domain identification array to identify the non-design unit and design unit respectively; define the array R d and R n ,when or When it is equal to 1, it means that unit i belongs to the design domain; when or When it is equal to 0, it means that the element i belongs to the non-design domain. Based on the design domain element number array E d and the non-design element number array E n , the design domain identification array and the non-design domain identification array are determined by FOR loop. Therefore, the improved material topology optimization model is expressed as:

[0064]

[0065] Among them, X d and X n They represent the design domain topology variable vector and the non-design domain topology variable vector respectively; represents the topological variable of the i-th design domain, represents the i-th non-design domain topological variable.

[0066] Specifically, step S3 includes:

[0067] S31: In material distribution optimization, the first-order differential of the objective function and the volume function with respect to the macro design variable, that is, the sensitivity analysis of the material topology optimization model is performed to obtain the material density unit, which is expressed as:

[0068]

[0069] Where p represents the penalty parameter; c = 1e -9 Represents a constant to avoid singularity in the stiffness matrix; Ω M represents the macrostructure design domain; G M represents the overall volume constraint for multi-scale topology optimization; D H represents the homogenized equivalent elastic matrix in the polar coordinate system; u M represents the macroscopic displacement field.

[0070] S32: Based on the Kuhn-Tucker condition, the optimal criterion method OC is used to update the material density unit, which is expressed as:

[0071]

[0072] Among them, κ represents the number of κ-th iteration steps; and represent the design variables for the κth iteration step The iteration factor of ; μ represents a very small constant value close to 0, which is used to avoid the denominator being 0; represents the update factor in the κ step when optimizing the material distribution, based on the two-way method. Solve and update.

[0073] The density unit distribution of macrostructure continuous material is as follows Figure 5 As shown in the figure, within the entire macrostructure, the material density unit varies continuously in space, and there are a large number of intermediate density units. If this continuous material density unit distribution is used for subsequent parallel topology optimization design, the intermediate density in each finite element will correspond to a microstructure. Therefore, in the subsequent parallel topology optimization design, a large number of microstructures and macrostructures will be optimized simultaneously, which will greatly increase the time cost of parallel topology optimization design.

[0074] S33: Determine whether the material density unit has converged. If not, go to step S2; otherwise, go to step S34.

[0075] S34: Regularize the material density unit and output the regional material density unit distribution, including: if the initial continuous material density distribution needs to be divided into Θ categories, that is, the macro structure needs to be divided into Θ sub-regions, the corresponding regularization mechanism is expressed as:

[0076]

[0077] in, represents the density of the i'th unit of the ξth class; and represents the upper and lower boundaries of the ξth class; N ξ represents the total number of units in the ξth class; represents the regularized density of all units in the ξ-th class.

[0078] Based on formula (6), the density value of each group of units after regularization is equal to the average density value of all units in the group. The regularized material density units are distributed in a regional pattern in the rectangular design space. Each region is represented by a color, and each region is composed of a uniform distribution of density units. Based on this regional material density unit, it is used to describe the subsequent material microstructure regional pattern. At the same time, each region is uniformly distributed with only one microstructure. The macro material density unit determines the maximum material usage of the subsequent microstructure design.

[0079] against Figure 5The continuous material density unit distribution shown is mainly divided into four groups, namely [0, 0.2), [0.4, 0.6), [0.6, 0.8), and [0.8, 1]. Based on formula (6), the normalized density value of each group of units is equal to the average density value of all units in the group. To simplify the numerical calculation, when the density unit belongs to [0.8, 1], the normalized unit density value is assumed to be 1; when the density unit belongs to [0, 0.2), the normalized unit density value is assumed to be 0.

[0080] like Figure 6 As shown in the figure, the regularized material density elements are distributed in a zone-like pattern within the rectangular design space. Each zone is represented by a color, and each zone is composed of a uniform distribution of elements of a single density. Compared to the initial continuous material density element distribution, this zone-based material density element distribution contains only three densities and two intermediate densities. From the perspective of the entire zone-based material density element distribution, the entire macrostructure is divided into three zones, each containing only one element density. This zone-based material density element distribution is used to describe the subsequent zone-based pattern of the material microstructure, with each zone consisting of only one microstructure uniformly and periodically distributed. The macroscopic material element density determines the maximum material usage in the subsequent microstructure design. Therefore, based on this zone-based material density element distribution, only two microstructures are required in the subsequent macro-microstructure parallel topology optimization design: a density of 0 represents a pore microstructure, a density of 1 represents a solid microstructure, dark gray represents a microstructure with a density of 0.7, and light gray represents a microstructure with a density of 0.5.

[0081] S4: Based on the macro-micro initial design parameters and the regional material density unit distribution, a parallel topology optimization design model for the macrostructure and multiple types of microstructures is constructed using SIMP and energy homogenization, and the macro design variables and micro design variables of the parallel topology optimization design model are updated until the optimal structural topology configuration of the macrostructure and multiple types of microstructures is obtained, and a homogenized equivalent elastic matrix corresponding to the optimal structural topology configuration is obtained;

[0082] The parallel topology optimization design model is expressed as:

[0083]

[0084] Where C' represents the multi-scale optimization objective function, which is defined by the compliance C of the non-pneumatic tire structure; Ω M represents the macro design domain; Ω m represents the micro-design domain; N M Indicates the total number of macro design variables; N m represents the total number of micro-design variables; ρ M and ρm Represent the unit density at macro scale and micro scale respectively; G M represents the overall volume constraint for multi-scale topology optimization; V M Indicates the maximum allowable material usage of the macrostructure; G m represents the volume constraint for microstructure topology optimization; V m Indicates the maximum allowable material usage in the material microstructure; and Represent the minimum values ​​of macro unit density and micro unit density respectively; u M represents the macroscopic displacement field; v M represents the virtual displacement field within the macrostructure, which allows the dynamic displacement field within the macrostructure to Take any value; u m represents the microscopic displacement field; v m represents the virtual displacement field within the microstructure, which allows the dynamic displacement field within the microstructure to be Take any value; a represents the energy bilinear function; l represents the load unilinear function.

[0085] Specifically, step S4 includes:

[0086] S41: On a macroscopic scale, the line equilibrium state equation is constructed by the principle of virtual work, and the line equilibrium state equation is used to calculate v M and v m Solve it, and the line equilibrium state equation is expressed as:

[0087]

[0088] Where f represents the volume force within the macrostructure; h represents the Neumann boundary Γ of the macrostructure m Boundary traction on D M Represents the elastic tensor matrix of the macrostructure, D m The elastic tensor matrix representing the microstructure, D M and D m It is defined by material interpolation in SIMP, as shown in Equation (9):

[0089]

[0090] Where D0 represents the constitutive elastic tensor of the material;

[0091] Then the homogenized equivalent elastic matrix D is obtained H , expressed as:

[0092]

[0093] S42: According to the homogenized equivalent elastic matrix D HA multi-scale stiffness sensitivity analysis is performed on the parallel topology optimization design model to obtain the objective function and volume function of the parallel topology optimization design model. The first-order differentials of the objective function and volume function with respect to the macro design variables, i.e., the macro unit density, are expressed as follows:

[0094]

[0095] The first-order differential of the objective function and volume function with respect to the microscopic design variable, i.e., the microscopic element density, is expressed as:

[0096]

[0097] Then the homogenized equivalent elastic matrix D H The first derivative with respect to the microscopic element density is expressed as:

[0098]

[0099] S43: According to the Kuhn-Tucker condition, the macro-design variables and micro-design variables are updated by the optimal criterion method OC, which is expressed as:

[0100]

[0101] in, represents the macro design variable in the κth iteration step The iteration factor of represents the micro-design variable in the κth iteration step The iteration factor of represents the update factor at step κ for parallel topology optimization macro design; represents the update factor at step κ for parallelized topology optimization micro-design;

[0102] S44: Determine whether the updated macro-design variables and micro-design variables have converged. If not, go to step S41. Otherwise, output the optimal structural topology configuration of the macro structure and multiple types of micro structures.

[0103] S5: Convert the homogenized equivalent elastic matrix in the polar coordinate system to the Cartesian coordinate system, expressed as:

[0104]

[0105] Among them, D H represents the homogenized equivalent elastic matrix in the polar coordinate system; represents the homogenized elastic tensor matrix in the Cartesian coordinate system; M represents the rotation matrix of the second-order tensor;

[0106]

[0107] S6: Obtaining a mapping structure in a Cartesian coordinate system through coordinate transformation, and performing multi-scale topological optimal design of a non-pneumatic tire through the mapping structure;

[0108] Among them, the mapping structure is expressed as:

[0109]

[0110] Topology optimization design is performed simultaneously for both macrostructure and microstructure. Figure 7 As shown in Figure 2, the optimal topological design of the macrostructure is given, which determines the specific location of various microstructures within the macrostructure. It can be seen that the macrostructure topology has smooth boundaries and clear material boundaries. Next, the optimal numerical structures for the three microstructures are shown in Table 2, which mainly include the volume fraction of each microstructure, the optimal topological configuration, the 10×10 periodic distribution, and its homogenized elastic tensor matrix. Similar to the macrostructure topology, the optimal microstructure topological design also has relatively smooth boundaries and clear material boundaries.

[0111] Table 2

[0112]

[0113] Based on the optimal macroscopic material distribution, optimal microstructure topology and optimal macrostructure topology of the above four types of microstructures, the optimal structure of the multi-scale design of non-pneumatic tire structure is as follows: Figure 1 shown.

[0114] It can be seen that unlike traditional topology optimization design, the optimized macrostructure is divided into four sub-regions, each represented by a color, and each sub-region is composed only of the periodically repeated arrangement of its corresponding microstructure. From the perspective of the topology of the entire macrostructure and microstructure, the microstructures are symmetrical about the coordinate axis. This is mainly due to the axial symmetry of the positions where the macro load and boundary conditions are applied. The two middle types of microstructures also have good topological continuity. This is mainly because the macrostructure topology and the two microstructures are optimized simultaneously in the parallel topology optimization design model. In order to ensure the reasonable transferability of the macro load force within its structural design domain, the continuity of the boundaries must also be guaranteed when the different microstructures are distributed in different macro regions. Only in this way can the entire optimization have reasonable physical meaning.

[0115] Figure 8Iteration plots for the objective function and global volume fraction are presented, along with the corresponding iteration plots for the objective function of the entire macrostructure. Throughout the iterative process, the objective function and volume fraction remain numerically stable, with the primary changes occurring in the first 20 iterations. This is due to the extensive changes in the macrostructure's topology during these steps. In the subsequent dozens of iterations, the macrostructure's topology remains unchanged, primarily contributing to shape optimization, which continuously optimizes the target performance and ultimately leads to the optimal solution. This overall optimization process demonstrates the effectiveness of this model.

[0116] The present invention proposes a multi-scale parallel topology optimization design method and structure for non-pneumatic tires based on conformal mapping, which relates to the field of wheel design technology and solves the problems of limited design space, high computational cost, and poor connectivity of connected structures in traditional single-scale tire topology optimization design methods. Through coordinate transformation, the tire annular design domain is mapped to a rectangular design domain, reducing the optimization cost. In the multi-scale optimization of the structure, multiple types of microstructures are introduced, and based on the SIMP method and the energy homogenization method, a multi-scale stiffness topology optimization design model for the non-pneumatic tire structure is constructed. This also effectively solves the topology optimization design problem of the mechanical properties of the continuum structure considering the non-design domain, and realizes the parallel topology optimization of the macroscopic structure and microscopic unit cell configuration of the non-pneumatic tire, so as to give full play to the advantages of the porous structure, so that the non-pneumatic tire has the characteristics of high specific stiffness, impact energy absorption, light weight and designability.

[0117] The above embodiments are preferred embodiments of the present invention, but the present invention is not limited to the above embodiments. Any obvious improvements, substitutions or modifications that can be made by those skilled in the art without departing from the essence of the invention are within the scope of protection of the present invention.

Claims

1. A non-pneumatic tire comprising, from the inside out, a hub, spokes, an inner ring, a shear band, an outer ring, and a tread, characterized in that: Each of the spokes is provided with 24 cross bars, one end of which is connected to the hub and the other end is connected to the inner ring. A first oblique bar and a second oblique bar are provided between adjacent cross bars. The inner ring, adjacent cross bars and the first oblique bars constitute a first hole microstructure, the adjacent cross bars, the first oblique bars, the second oblique bars and the outer surface of the hub constitute a second hole microstructure, and the cross bars, the second oblique bars and the outer surface of the hub constitute a third hole microstructure. The cross bars, the first oblique bars and the second oblique bars are all composed of a first density material, a second density material and a third density material from the inside out. Numerous micropore structures are evenly distributed on the second density material and the third density material, and the distance between adjacent micropore structures is 0.01 mm. In the crossbar, the area of ​​the first density material is much larger than the area of ​​the second density material and the third density material; In the first oblique rods and the second oblique rods, the area of ​​the first density material is smaller than the area of ​​the second density material and the third density material.

2. The non-pneumatic tire according to claim 1, wherein: The first oblique rod and the second oblique rod are approximately parallel, both ends of the first oblique rod are respectively connected to adjacent cross rods, and one end of the second oblique rod is connected to the cross rod and the other end is connected to the wheel hub.

3. The non-pneumatic tire according to claim 1, wherein: The area of ​​a non-pneumatic tire is 33580.8mm 2 , the area of ​​the spoke is 2135πmm 2 The microstructure area of ​​the first hole is 513.04 mm 2 The microstructure area of ​​the second hole is 373.12 mm 2 The microstructure area of ​​the third hole is 46.64mm 2 , the microporous structure area is 4×10 -5 mm 2 .

4. The non-pneumatic tire according to claim 1, wherein: The relative density of the first density material is 100%, the relative density of the second density material is 70%, the relative density of the third density material is 50%, and the relative densities of the first hole microstructure, the second hole microstructure and the third hole microstructure are all 0%.

5. The non-pneumatic tire according to claim 1, wherein: The sum of the areas of the first, second and third pore microstructures accounts for 40.11% of the spokes, the area of ​​the first density material accounts for 43.1% of the spokes, the area of ​​the second density material accounts for 14.31% of the spokes, and the area of ​​the third density material accounts for 2.43% of the spokes.

6. A multi-scale parallel topology optimization design method for a non-pneumatic tire, characterized in that: include: S1: Convert the structure of the non-pneumatic tire from the Cartesian coordinate system (x, y) to the translation periodic structure in the polar coordinate system (r, θ), expressed as: Then the macroscopic coordinates (r,θ) and microscopic coordinates in the polar coordinate system are It is associated with the characteristic length δ and expressed as: S2: Define the initial macro and micro design parameters of the tire, including: the number of tire rotation cycles is 24, the tire pressure is 4900N, the hub area meets the Dirichlet boundary condition, the tire structure size L×H is defined as 180mm×116mm, and the design domain spoke is L d ×H d Defined as 180mm×100mm; L represents the length corresponding to the rotation of θ degrees around the center of the tire, 0.5mm is equivalent to 1 degree, tanθ=y / x, θ∈[0°,360°]; H represents the length from the hub to the tread, H=ρ, ρ 2 =x 2 +y 2 In the finite element analysis, the macrostructure is discretized into 180×116 finite elements, and the size of each macrostructure finite element is 1mm; multiple types of microstructures are discretized into 100×100 finite elements through finite element analysis, and the size of each microstructure finite element is 0.01mm; S3: Constructing a material topology optimization model based on the macro-micro initial design parameters and the improved SIMP method, optimizing the material distribution of the tire based on the material topology optimization model, and obtaining a regional material density unit distribution map; The material topology optimization model is expressed as: Among them, X d and X n They represent the design domain topology variable vector and the non-design domain topology variable vector respectively; i represents the unit number, or When it is equal to 1, it means that unit i belongs to the design domain. represents the topological variable of the i-th design domain; or When it is equal to 0, it means that unit i belongs to the non-design domain. represents the i-th non-design domain topological variable; ρ min represents the minimum value of the design variable; represents the design variable vector, the total number is; C represents the compliance of the non-pneumatic tire structure; F represents the load borne by the macrostructure; U represents the displacement field within the macrostructure; K represents the global stiffness matrix of the macrostructure; K0 represents the global stiffness matrix of the solid element; U e represents the displacement field of the solid element; G d represents the volume constraint for material distribution optimization; V d Indicates the maximum allowable material usage; v0 indicates the volume fraction of the solid element; S4: Based on the macro-micro initial design parameters and the regional material density unit distribution, a parallel topology optimization design model for the macrostructure and multiple types of microstructures is constructed using SIMP and energy homogenization, and the macro design variables and micro design variables of the parallel topology optimization design model are updated until the optimal structural topology configuration of the macrostructure and multiple types of microstructures is obtained, and a homogenized equivalent elastic matrix corresponding to the optimal structural topology configuration is obtained; The parallel topology optimization design model is expressed as: Where C' represents the multi-scale optimization objective function, which is defined by the compliance C of the non-pneumatic tire structure; Ω M represents the macro design domain; Ω m represents the micro-design domain; N M Indicates the total number of macro design variables; N m represents the total number of micro-design variables; ρ M and ρ m Represent the unit density at macro scale and micro scale respectively; G M represents the overall volume constraint for multi-scale topology optimization; V M Indicates the maximum allowable material usage of the macrostructure; G m represents the volume constraint for microstructure topology optimization; V m Indicates the maximum allowable material usage in the material microstructure; and Represent the minimum values ​​of macro unit density and micro unit density respectively; u M represents the macroscopic displacement field; v M represents the virtual displacement field within the macrostructure, which allows the dynamic displacement field within the macrostructure to Take any value; u m represents the microscopic displacement field; v m represents the virtual displacement field within the microstructure, which allows the dynamic displacement field within the microstructure to be Take any value; a represents the energy bilinear function; l represents the load unilinear function; S5: Convert the homogenized equivalent elastic matrix in the polar coordinate system to the Cartesian coordinate system, expressed as: Among them, D H represents the homogenized equivalent elastic matrix in the polar coordinate system; represents the homogenized elastic tensor matrix in the Cartesian coordinate system; M represents the rotation matrix of the second-order tensor; S6: Obtaining a mapping structure in a Cartesian coordinate system through coordinate transformation, and performing multi-scale topological optimal design of a non-pneumatic tire through the mapping structure; Among them, the mapping structure is expressed as:

7. The method according to claim 6, wherein Step S3 includes: S31: Perform sensitivity analysis on the material topology optimization model to obtain the material density unit, which is expressed as: Where p represents the penalty parameter; p represents a constant to avoid the occurrence of singularity in the stiffness matrix; S32: Based on the Kuhn-Tucker condition, the optimal criterion method OC is used to update the material density unit, which is expressed as: Among them, κ represents the number of κ-th iteration steps; and represent the design variables for the κth iteration step The iteration factor of ; μ represents a very small constant value close to 0; represents the update factor at step κ when optimizing the material distribution; S33: Determine whether the material density unit has converged. If not, go to step S2; otherwise, go to step S34. S34: Regularize the material density unit and output the regional unit density distribution, including: if the initial continuous material density distribution needs to be divided into Θ categories, that is, the macro structure needs to be divided into Θ sub-regions, the corresponding regularization mechanism is expressed as: in, represents the density of the i'th unit of the ξth class; and represents the upper and lower boundaries of the ξth class; N ξ represents the total number of units in the ξth class; represents the regularized density of all units in the ξ-th class.

8. The method according to claim 7, wherein Step S4 includes: S41: On a macroscopic scale, the line equilibrium state equation is constructed by the principle of virtual work, and the line equilibrium state equation is used to calculate v M and v m Solve it, and the line equilibrium state equation is expressed as: Where f represents the volume force within the macrostructure; h represents the Neumann boundary Γ of the macrostructure m Boundary traction on D M represents the elastic tensor matrix of the macrostructure; D m elastic tensor matrix representing the microstructure; Where D0 represents the constitutive elastic tensor of the material; Then the homogenized equivalent elastic matrix D is obtained H , expressed as: S42: According to the homogenized equivalent elastic matrix D H A multi-scale stiffness sensitivity analysis is performed on the parallel topology optimization design model to obtain the objective function and volume function of the parallel topology optimization design model. The first-order differentials of the objective function and volume function with respect to the macro design variables, i.e., the macro unit density, are expressed as follows: The first-order differential of the objective function and volume function with respect to the microscopic design variable, i.e., the microscopic element density, is expressed as: Then the homogenized equivalent elastic matrix D H The first derivative with respect to the microscopic element density is expressed as: S43: According to the Kuhn-Tucker condition, the macro-design variables and micro-design variables are updated by the optimal criterion method OC, which is expressed as: in, represents the macro design variable in the κth iteration step The iteration factor of represents the micro-design variable in the κth iteration step The iteration factor of represents the update factor at step κ for parallel topology optimization macro design; represents the update factor at step κ for parallelized topology optimization micro-design; S44: Determine whether the updated macro-design variables and micro-design variables have converged. If not, go to step S41; otherwise, output the optimal structural topology configuration of the macro-structure and multiple types of micro-structures.

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