A spoke structure optimization method for improving the lateral stiffness of honeycomb non-pneumatic tires

Abstract

The present invention discloses a spoke structure optimization method for improving the lateral stiffness of a honeycomb non-pneumatic tire, relates to the technical field of wheel design, and solves the problem of handling stability of non-pneumatic tires during driving. The key point of its technical solution is to perform multi-objective optimization design by dividing the NPT model at equal intervals in the tire width direction to set different spoke structure thickness gradients. It aims to adjust the thickness of each divided spoke structure of the NPT to maintain the original radial stiffness while striving to reduce the lateral stiffness of the NPT, thereby achieving a coordinated optimization of the stiffness performance of the two. Latin hypercube sampling is used to generate sample points, and a radial basis function RBF proxy model is constructed. The non-dominated sorting genetic algorithm NSGA‑II is used to solve the multi-objective optimization problem. The optimized NPT achieves a better balance between lateral stiffness and radial stiffness, while also achieving better performance in terms of lightweighting and maximum spoke stress, providing a valuable reference and reference for the design of non-pneumatic tires.

Description

Technical Field

[0001] The present invention relates to a non-pneumatic tire, in particular to a spoke structure optimization method for improving the lateral stiffness of a honeycomb non-pneumatic tire, belonging to the technical field of vehicle tires. Background Art

[0002] Tires are the only part of a vehicle that comes into contact with the road, and they play a vital role in driving. Traditional pneumatic tires offer advantages in terms of low lateral stiffness, low energy loss, low mass, and low radial stiffness, but they also present potential risks such as air leakage, unstable tire pressure, and blowouts. According to statistics, approximately 46% of traffic accidents are caused by tire failure, with blowouts accounting for as much as 70%. Compared to traditional pneumatic tires, non-pneumatic tires (NPT) rely on spoke structures instead of the air pressure of pneumatic tires to perform load-bearing, cushioning, and force-generating functions, thus avoiding the risks of blowouts and air leakage.

[0003] While extensive research has examined the response characteristics of non-pneumatic tires in terms of load-deflection relationships, wheel-ground contact pressure distribution, vibration modes, rolling resistance, temperature distribution, and spoke and tread stresses, limited research has examined their out-of-plane properties. Honeycomb spoke structures (NPTs) are composed of individual polygonal units. Modifying the unit arrangement, wall thickness, or length can influence the overall performance of the NPT, leading to the discovery that honeycomb structures have great potential for application in non-pneumatic tires. However, honeycomb NPTs exhibit significant in-plane and out-of-plane mechanical properties, particularly lateral stiffness. This leads to significant differences in their multi-stiffness performance and ground contact behavior compared to pneumatic tires, severely hindering the development of non-pneumatic tires as alternatives to traditional pneumatic tires. Furthermore, changes in honeycomb spoke structural parameters can significantly impact the mechanical properties of the NPT, leading to changes in the tire's multi-stiffness properties. Therefore, the key scientific challenge is to optimize the NPT spoke structure parameters while minimizing radial stiffness while simultaneously reducing lateral stiffness and achieving synergistic optimization of stiffness and performance. Summary of the Invention

[0004] Purpose of the Invention: To address the shortcomings of the existing technology, the present invention provides a spoke structure optimization method for improving the lateral stiffness of a honeycomb non-pneumatic tire. This method divides the honeycomb spoke structure into evenly spaced segments across the tire width and sets different thickness gradients for each segment. Subsequently, while adjusting the honeycomb NPT spoke structure parameters to maintain tire radial stiffness, the method also aims to reduce the excessive lateral stiffness of the NPT. This achieves a synergistic optimization of the stiffness performance of both spokes, significantly enhancing the performance of the non-pneumatic tire.

[0005] Technical solution: A spoke structure optimization method for improving the lateral stiffness of a honeycomb non-pneumatic tire, comprising:

[0006] S1. Establishing a honeycomb non-pneumatic tire model according to tire width, tire sidewall height, and rim diameter;

[0007] S2. Using finite element simulation software, a radial load is applied to the honeycomb non-pneumatic tire model. The tire remains stationary in the lateral direction and a lateral displacement is applied to the road surface. Simulation results are obtained to extract the radial displacement U2 and the lateral force RF3 of the honeycomb non-pneumatic tire.

[0008] S3. Obtain a stress distribution cloud map of the spoke bottom of the honeycomb non-pneumatic tire based on the simulation results, select a path with significant Mises stress changes on the spoke bottom cross section, and divide it into even-numbered equidistant segments along the tire width direction;

[0009] Along the tire width direction, the segmented bodies that show symmetrical distribution characteristics are set as a set, and a total of i sets are set. The sets are named L from the outside to the inside. i (i=1, 2, ..., i), and set the corresponding spoke thickness parameter for each set, and the corresponding spoke thickness parameter range is 2mm to 4mm;

[0010] The criterion for determining a significant stress change is that the Mises stress first increases and then decreases to its initial value along the path length;

[0011] S4. Import the obtained simulation results into a multidisciplinary multi-objective optimization tool. Using the i sets of spoke thickness parameters in the width direction of the honeycomb non-pneumatic tire as independent variables, the lateral stiffness of the honeycomb non-pneumatic tire as the target response, and the radial stiffness of the honeycomb non-pneumatic tire as a constraint, perform the following steps:

[0012] S4.1. Perform a Latin super test to generate sample points;

[0013] S4.2. Establish a surrogate model, import sample point data, use the sample point data to simulate the relationship between the design variables and the target response, and test the prediction accuracy of the surrogate model through cross-validation;

[0014] S4.3. Using a multi-objective optimization algorithm, set the minimization of lateral stiffness as the target response and radial stiffness as the constraint, and set the weights of the optimization objective and constraint, i.e., lateral force RF3 and radial displacement U2, to generate a Pareto optimal solution set. Select the optimal solution that satisfies the radial displacement constraint and minimizes the lateral force from the solution set.

[0015] The S1 is specifically:

[0016] The tire width is 215 mm, the sidewall height is 129 mm, which is 60% of the width, and the rim diameter is 16 inches. A three-dimensional numerical simulation model of the honeycomb non-pneumatic tire is constructed.

[0017] The S2 is specifically:

[0018] The radial load applied to the tire is fixed at 4000N; the tire remains stationary in the lateral direction, and the lateral displacement applied to the road surface is fixed at 7mm.

[0019] The S3 is specifically:

[0020] Ten symmetrically distributed equidistant segments are made along the width of the tire. Two segments symmetrically distributed along the longitudinal centerline of the tire are grouped together. The group is named L from outside to inside. i (i=1, 2, 3, 4, 5), the initial thickness of L1 to L5 of the honeycomb non-pneumatic tire is set to 3 mm.

[0021] The S4.1 is specifically:

[0022] Through the Latin hypertest, 100 sample points are generated.

[0023] The S4.2 is specifically:

[0024] Radial basis function (RBF) is used to construct proxy models of spoke thickness parameters and lateral stiffness corresponding to the five sets. The prediction accuracy of the RBF proxy model is tested through cross-validation. If the accuracy does not meet the requirements, the sample size is increased and the RBF model is rebuilt and the accuracy is verified again until the prediction accuracy of the RBF proxy model meets the requirements.

[0025] The cross-validation method is as follows: 90 sample points in the sample are used to build the model, and the remaining 10 sample points are used to verify the accuracy of the model;

[0026] Select root mean square error RMSE, determination coefficient R 2 As an evaluation index for the prediction accuracy of the validation model, if R 2 >0.9 and RMSE <0.2, the accuracy meets the requirements.

[0027] The S4.3 is specifically:

[0028] Multi-objective optimization is performed using the non-dominated sorting genetic algorithm NSGA-II. The optimization objective is the minimum lateral force RF3 with a weight of 0.6; the tire radial displacement U2 is constrained with a weight of 0.4. Through multi-objective optimization, a Pareto optimal solution set is obtained.

[0029] Beneficial effects: The present invention optimizes the structural design of the spoke by performing equal-interval divisions in the spoke width direction and setting a thickness gradient according to the stress distribution when subjected to lateral force; the thickness of each segment is kept consistent in the spoke height direction, ensuring the consistency of the tire structure and the uniformity of strength; this design method not only improves the overall stability of the tire, but also optimizes the mechanical properties of the spoke, so that the tire exhibits better performance under the same working conditions.

[0030] By dividing the honeycomb spoke structure into equal intervals along the tire width and setting different thickness gradients, a multi-objective optimization design method based on the RBF surrogate model and the non-dominated sorting genetic algorithm (NSGA-II) is proposed. This method significantly reduces the lateral stiffness of the tire without significantly affecting the radial stiffness, thereby improving the tire's handling and comfort, and achieving synergistic optimization of the two stiffness properties.

[0031] The optimized honeycomb non-pneumatic tire has demonstrated better handling, comfort and durability in practical applications, providing a reliable technical solution and valuable reference, and offering new ideas and effective solutions for the design and development of non-pneumatic tires. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are merely embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying any creative work.

[0033] Figure 1 Technology roadmap for multi-objective optimization design.

[0034] Figure 2 It is a honeycomb NPT model.

[0035] Figure 3 Diagram of the design setup for gradient optimization of spoke structures.

[0036] Figure 4 Diagram of the design setup for gradient optimization of spoke structures.

[0037] Figure 5 Select a plot for the stress distribution and path of the NPT bottom spoke.

[0038] Figure 6 Mises stress plot for the selected path at the base of an NPT spoke.

[0039] Figure 7 A two-dimensional graph showing the data derived from the Pareto optimal solution set generated by Isight. DETAILED DESCRIPTION

[0040] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0041] In the description of the present invention, it should be understood that the terms "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inside", "outside", etc., indicating directions or positional relationships, are based on the directions or positional relationships shown in the accompanying drawings, and are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific direction, be constructed and operated in a specific direction, and therefore should not be understood as limiting the present invention.

[0042] In the present invention, unless otherwise expressly specified or limited, a first feature being "above" or "below" a second feature may include the first and second features being in direct contact, or may include the first and second features being in contact not directly but through another feature between them. Furthermore, a first feature being "above," "above," and "above" a second feature may include the first feature being directly above or obliquely above the second feature, or may simply mean that the first feature is higher in level than the second feature. A first feature being "below," "below," and "below" a second feature may include the first feature being directly below or obliquely below the second feature, or may simply mean that the first feature is lower in level than the second feature.

[0043] like Figures 1 to 7 As shown, a spoke structure optimization method for improving the lateral stiffness of a honeycomb non-pneumatic tire includes:

[0044] S1. Establish a honeycomb non-pneumatic tire model based on tire width, tire sidewall height, and rim diameter; specifically:

[0045] The tire width is 215 mm, the sidewall height is 129 mm, which is 60% of the width, and the rim diameter is 16 inches. A three-dimensional numerical simulation model of a honeycomb non-pneumatic tire was constructed. The specific result parameters and material parameters are shown in Tables 1 and 2.

[0046] Table 1 Non-pneumatic tire structural parameters

[0047]

[0048] Table 2 Material parameters of aluminum alloy and high-strength steel and polyurethane and synthetic rubber

[0049]

[0050] S2. Using finite element simulation software, a radial load is applied to the honeycomb non-pneumatic tire model. The tire remains stationary in the lateral direction and a lateral displacement is applied to the road surface. Simulation results are obtained to extract the radial displacement U2 and the lateral force RF3 of the honeycomb non-pneumatic tire. Specifically:

[0051] The radial load applied to the tire is fixed at 4000N; the tire remains stationary in the lateral direction, and the lateral displacement applied to the road surface is fixed at 7mm.

[0052] S3. Obtain a stress distribution cloud map of the spoke bottom of the honeycomb non-pneumatic tire based on the simulation results, select a path with significant Mises stress changes on the spoke bottom cross section, and divide it into even-numbered equidistant segments along the tire width direction;

[0053] Along the tire width direction, the segmented bodies that show symmetrical distribution characteristics are set as a set, and a total of i sets are set. The sets are named L from the outside to the inside. i (i=1, 2, ..., i), and set the corresponding spoke thickness parameter for each set, and the corresponding spoke thickness parameter range is 2mm to 4mm;

[0054] The criterion for determining a significant stress change is the region along the path length where the Mises stress first increases and then decreases to its initial value; specifically:

[0055] Areas of concentrated stress distribution appear as darker colors, and the stress values ​​in these areas are significantly higher than those in the surrounding areas. Based on the cloud map, a path with relatively concentrated stress on the spoke bottom section was selected for specific analysis. The uneven distribution of Mises stress intuitively reflects the stress differences in various areas along the spoke width. Therefore, a section with significant initial stress changes was selected as the benchmark, and 10 symmetrically distributed equidistant segments were divided along the tire width.

[0056] Two segments symmetrically distributed along the longitudinal centerline of the tire are grouped together, and the group is named L from outside to inside. i (i=1, 2, 3, 4, 5), the initial thickness of L1 to L5 of the honeycomb non-pneumatic tire is set to 3 mm; the radial displacement U2 when the tire is subjected to a radial load of 4000 N is 21.3 mm; and the lateral force exerted on the tire is 3144 N.

[0057] S4. Import the obtained simulation results into a multidisciplinary multi-objective optimization tool. Using the i sets of spoke thickness parameters in the width direction of the honeycomb non-pneumatic tire as independent variables, the lateral stiffness of the honeycomb non-pneumatic tire as the target response, and the radial stiffness of the honeycomb non-pneumatic tire as a constraint, perform the following steps:

[0058] S4.1. Perform a Latin super test to generate 100 sample points.

[0059] S4.2. Establish a surrogate model, import sample point data, use the sample point data to simulate the relationship between the design variables and the target response, and test the prediction accuracy of the surrogate model through cross-validation; specifically:

[0060] Radial basis function (RBF) is used to construct proxy models of spoke thickness parameters and lateral stiffness corresponding to the five sets. The prediction accuracy of the RBF proxy model is tested through cross-validation. If the accuracy does not meet the requirements, the sample size is increased and the RBF model is rebuilt and the accuracy is verified again until the prediction accuracy of the RBF proxy model meets the requirements.

[0061] The cross-validation method is as follows: 90 sample points in the sample are used to build the model, and the remaining 10 sample points are used to verify the accuracy of the model;

[0062] Select root mean square error RMSE, determination coefficient R 2 As an evaluation index for the prediction accuracy of the validation model, if R 2 >0.9, RMSE <0.2, the accuracy meets the requirements, as shown in Table 3;

[0063] Table 3 Accuracy of RBF model

[0064]

[0065] S4.3. Using a multi-objective optimization algorithm, set the minimization of lateral stiffness as the target response, radial stiffness as the constraint, and set the weights of the optimization objective and constraint, i.e., lateral force RF3 and radial displacement U2, to generate a Pareto optimal solution set. From the solution set, select the optimal solution that satisfies the radial displacement constraint and minimizes the lateral force. Specifically:

[0066] Multi-objective optimization is performed using the non-dominated sorting genetic algorithm NSGA-II. The optimization objective is the minimum lateral force RF3 with a weight of 0.6; the tire radial displacement U2 is constrained with a weight of 0.4. Through multi-objective optimization, a Pareto optimal solution set is obtained.

[0067] Since the radial displacement U2 of the honeycomb non-pneumatic tire is 21.3mm and the lateral force RF3 is 3144N, in order to keep its radial stiffness within the allowable range and optimize the lateral stiffness to the maximum extent, the radial displacement U2 of the optimization target is constrained to be controlled within 21mm~22mm, and the solution with the minimum lateral force RF3 is selected from the solution set. The design model of the multi-objective optimization is expressed as:

[0068]

[0069] Among them L i , U2, and RF3 are the thickness of the spoke in the spoke segment, the displacement of the tire under radial load, and the lateral force acting on the tire, respectively.

[0070] This approach ensures that the radial stiffness remains within an appropriate range while reducing the lateral stiffness, thereby improving the overall performance of the non-pneumatic tire.

[0071] According to the working conditions, a design scheme of the honeycomb non-pneumatic tire with the best comprehensive consideration is selected from the Pareto optimal solution set, and the results are compared and analyzed with the initial honeycomb non-pneumatic tire. The optimization results are shown in Table 4.

[0072] Table 4 Comparison of results before and after optimization (initial tire: NPT-1 optimized tire: NPT-OP)

[0073]

[0074] The optimized NPT showed significant changes in multiple parameters. The optimized spoke thickness (L1 to L5) changed significantly, with the thickness of L1, L3, and L4 decreasing, while the thickness of L2 and L5 increased, indicating that increasing the thickness in specific areas can better disperse stress and reduce stress concentration. The radial stiffness decreased from 240.83N / mm before optimization to 232.05N / mm. Although it decreased by about 3.64%, it was still within the allowable range, indicating that other performance properties were improved without significantly affecting the radial stiffness. The lateral stiffness decreased from 449.17N / mm to 410.95N / mm, a decrease of about 8.51%, significantly improving the vehicle's handling and steering precision, and enhancing the driving experience. The spoke mass decreased from 2.78kg to 2.74kg, a decrease of about 0.04kg. This small mass reduction helps to improve the energy efficiency and lightweight of the tire while ensuring other performance indicators. The maximum spoke stress decreased by approximately 0.17 MPa, from 4.92 MPa to 4.75 MPa. This lower maximum stress indicates that the optimized spokes offer improved load-bearing capacity and durability, helping to extend the tire's service life. Through multi-objective optimization design, the overall performance of the NPT has been significantly improved. While maintaining appropriate radial stiffness, the optimized NPT significantly reduces lateral stiffness, improving handling and comfort. Furthermore, the reduction in spoke mass and maximum stress further enhances the tire's energy efficiency and durability. In summary, the optimized design achieves a better balance and improvement in multiple aspects of NPT performance.

[0075] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. Reference can be made to the common and similar parts between the various embodiments. For the devices disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the description is relatively simple, and the relevant parts can be referred to the method description.

[0076] The above description of the disclosed embodiments is intended to enable one skilled in the art to implement or use the present invention. Various modifications to these embodiments will be readily apparent to one skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention is not limited to the embodiments shown herein but is intended to conform to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A spoke structure optimization method for improving the lateral stiffness of a honeycomb non-pneumatic tire, characterized in that: include: S1. Establishing a honeycomb non-pneumatic tire model according to tire width, tire sidewall height, and rim diameter; S2. Using finite element simulation software, a radial load is applied to the honeycomb non-pneumatic tire model. The tire remains stationary in the lateral direction and a lateral displacement is applied to the road surface. Simulation results are obtained to extract the radial displacement U2 and the lateral force RF3 of the honeycomb non-pneumatic tire. S3. Obtain a stress distribution cloud map of the spoke bottom of the honeycomb non-pneumatic tire based on the simulation results, select a path with significant Mises stress changes on the spoke bottom cross section, and divide it into even-numbered equidistant segments along the tire width direction; Along the tire width direction, the segmented bodies that show symmetrical distribution characteristics are set as a set, and a total of i sets are set. The sets are named L from the outside to the inside. i (i=1, 2, ..., i), and set the corresponding spoke thickness parameter for each set, and the corresponding spoke thickness parameter range is 2mm to 4mm; The criterion for determining a significant stress change is that the Mises stress first increases and then decreases to its initial value along the path length; S4. Import the obtained simulation results into a multidisciplinary multi-objective optimization tool. Using the i sets of spoke thickness parameters in the width direction of the honeycomb non-pneumatic tire as independent variables, the lateral stiffness of the honeycomb non-pneumatic tire as the target response, and the radial stiffness of the honeycomb non-pneumatic tire as a constraint, perform the following steps: S4.

1. Perform a Latin super test to generate sample points; S4.

2. Establish a surrogate model, import sample point data, use the sample point data to simulate the relationship between the design variables and the target response, and test the prediction accuracy of the surrogate model through cross-validation; S4.

3. Using a multi-objective optimization algorithm, set the minimization of lateral stiffness as the target response and radial stiffness as the constraint, and set the weights of the optimization objective and constraint, i.e., lateral force RF3 and radial displacement U2, to generate a Pareto optimal solution set. Select the optimal solution that satisfies the radial displacement constraint and minimizes the lateral force from the solution set.

2. The spoke structure optimization method for improving the lateral stiffness of a honeycomb non-pneumatic tire according to claim 1, characterized in that: The S1 is specifically: The tire width is 215 mm, the sidewall height is 129 mm, which is 60% of the width, and the rim diameter is 16 inches. A three-dimensional numerical simulation model of the honeycomb non-pneumatic tire is constructed.

3. The spoke structure optimization method for improving the lateral stiffness of a honeycomb non-pneumatic tire according to claim 1, characterized in that: The S2 is specifically: The radial load applied to the tire is fixed at 4000N; the tire remains stationary in the lateral direction, and the lateral displacement applied to the road surface is fixed at 7mm.

4. The spoke structure optimization method for improving the lateral stiffness of a honeycomb non-pneumatic tire according to claim 1, characterized in that: The S3 is specifically: Ten symmetrically distributed equidistant segments are made along the width of the tire. Two segments symmetrically distributed along the longitudinal centerline of the tire are grouped together. The group is named L from outside to inside. i (i=1, 2, 3, 4, 5), the initial thickness of L1 to L5 of the honeycomb non-pneumatic tire is set to 3 mm.

5. The spoke structure optimization method for improving the lateral stiffness of a honeycomb non-pneumatic tire according to claim 1, characterized in that: The S4.1 is specifically: Through the Latin hypertest, 100 sample points are generated.

6. The spoke structure optimization method for improving the lateral stiffness of a honeycomb non-pneumatic tire according to claim 5, characterized in that: The S4.2 is specifically: Radial basis function (RBF) is used to construct proxy models of spoke thickness parameters and lateral stiffness corresponding to the five sets. The prediction accuracy of the RBF proxy model is tested through cross-validation. If the accuracy does not meet the requirements, the sample size is increased and the RBF model is rebuilt and the accuracy is verified again until the prediction accuracy of the RBF proxy model meets the requirements. The cross-validation method is as follows: 90 sample points in the sample are used to build the model, and the remaining 10 sample points are used to verify the accuracy of the model; Select root mean square error RMSE, determination coefficient R 2 As an evaluation index for the prediction accuracy of the validation model, if R 2 >0.9 and RMSE <0.2, the accuracy meets the requirements.

7. The spoke structure optimization method for improving the lateral stiffness of a honeycomb non-pneumatic tire according to claim 1, characterized in that: The S4.3 is specifically: Multi-objective optimization is performed using the non-dominated sorting genetic algorithm NSGA-II. The optimization objective is the minimum lateral force RF3 with a weight of 0.6; the tire radial displacement U2 is constrained with a weight of 0.

4. Through multi-objective optimization, a Pareto optimal solution set is obtained.

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