Optimization of Airless Tires Composed of Fiber/Rubber Composites for High-Speed
Vehicles Using ANN and Computational Analyses
Optimization of Airless Tires Composed of Fiber/Rubber Composites for High-Speed
Vehicles Using ANN and Computational Analyses| Optimization of Airless Tires Composed of Fiber/Rubber Composites for High-Speed |
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Title: "Optimization of Airless Tires Composed of Fiber/Rubber Composites for High-Speed
Vehicles Using ANN and Computational Analyses"| Title: | Optimization of Airless Tires Composed of Fiber/Rubber Composites for High-Speed <br> Vehicles Using ANN and Computational Analyses |
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Type of Manuscript: Article 稿件类型: 文章
Running Title: 运行标题:
Abstract 抽象
An artificial neural network is employed to predict the hyper-elastic mechanical properties of glass-fiber/rubber composites used for airless tires. The training data are generated through FEA for representative volume elements. All data are split into training, validation, and testing sets in a ratio of 0.7:0.15:0.15. The comparison between FEA and ANN reveals an error margin of approximately 7.0%7.0 \%, indicating good accuracy. Additionally, the sensitivity analysis based on the response surface methodology is conducted to identify critical design variables influencing the shape and thickness of the spoke and tread of airless tires. An innovative airless tire model has been created using key design variables: fiber volume fractions in the spokes and tread, and thicknesses of the upper and lower spoke sections. The goal-attain multi-objective optimization is performed to optimize four stiffness of the tire. To validate the effectiveness of the optimization, a 3D FE tire model is constructed with optimal design parameters and subjected to deformation analyses to compute four types of static tire stiffness. The discrepancies in stiffness between the two methods range from 0.11%0.11 \% to 7.59%7.59 \%. Finally, the optimized model of the tire undergoes dynamic analyses to assess its vibrational performance, resulting in significantly decaying reaction forces. 采用人工神经网络来预测用于无气轮胎的玻璃纤维/橡胶复合材料的超弹性机械性能。训练数据是通过 FEA 为代表性体积元素生成的。所有数据都按照 0.7:0.15:0.15 的比例拆分为训练集、验证集和测试集。FEA 和 ANN 之间的比较显示误差范围约为 7.0%7.0 \% ,表明精度良好。此外,还进行了基于响应面方法的敏感性分析,以确定影响无气轮胎辐条和胎面形状和厚度的关键设计变量。使用关键设计变量创建了一个创新的无气轮胎模型:辐条和胎面中的纤维体积分数,以及上下辐条截面的厚度。执行目标实现多目标优化以优化轮胎的四个刚度。为了验证优化的有效性,使用最佳设计参数构建了 3D FE 轮胎模型,并进行了变形分析,以计算四种类型的静态轮胎刚度。两种方法之间的刚度差异范围为 0.11%0.11 \% 到 7.59%7.59 \% 。最后,轮胎的优化模型进行动态分析以评估其振动性能,从而导致反作用力显着衰减。
Optimization of Airless Tires Composed of Fiber/Rubber Composites for High-Speed Vehicles Using ANN and Computational Analyses 使用 ANN 和计算分析优化用于高速车辆的纤维/橡胶复合材料无气轮胎
Kelvin Lee Hanyong ^(1)*{ }^{1} \cdot Heung Soap Choi ^(2){ }^{2} •Cheol Kim ^(1){ }^{1} Kelvin Lee Hanyong ^(1)*{ }^{1} \cdot 香皂 Choi ^(2){ }^{2} •Cheol Kim ^(1){ }^{1}(Received date ; Revised date ; Accepted date ) (接收日期 ;修订日期 ;接受日期 )
Abstract 抽象
An artificial neural network is employed to predict the hyper-elastic mechanical properties of glassfiber/rubber composites used for airless tires. The training data are generated through FEA for representative volume elements. All data are split into training, validation, and testing sets in a ratio of 0.7:0.15:0.15. The comparison between FEA and ANN reveals an error margin of approximately 7.0%, indicating good accuracy. Additionally, the sensitivity analysis based on the response surface methodology is conducted to identify critical design variables influencing the shape and thickness of the spoke and tread of airless tires. An innovative airless tire model has been created using key design variables: fiber volume fractions in the spokes and tread, and thicknesses of the upper and lower spoke sections. The goalattain multi-objective optimization is performed to optimize four stiffness of the tire. To validate the effectiveness of the optimization, a 3D FE tire model is constructed with optimal design parameters and subjected to deformation analyses to compute four types of static tire stiffness. The discrepancies in stiffness between the two methods range from 0.11%0.11 \% to 7.59%7.59 \%. Finally, the optimized model of the tire undergoes dynamic analyses to assess its vibrational performance, resulting in significantly decaying reaction forces. 采用人工神经网络来预测用于无气轮胎的玻璃纤维/橡胶复合材料的超弹性机械性能。训练数据是通过 FEA 为代表性体积元素生成的。所有数据都按照 0.7:0.15:0.15 的比例拆分为训练集、验证集和测试集。FEA 和 ANN 之间的比较显示误差范围约为 7.0%,表明精度良好。此外,还进行了基于响应面方法的敏感性分析,以确定影响无气轮胎辐条和胎面形状和厚度的关键设计变量。使用关键设计变量创建了一个创新的无气轮胎模型:辐条和胎面中的纤维体积分数,以及上下辐条截面的厚度。执行 goalattain 多目标优化以优化轮胎的四个刚度。为了验证优化的有效性,使用最佳设计参数构建了 3D FE 轮胎模型,并进行了变形分析,以计算四种类型的静态轮胎刚度。两种方法之间的刚度差异范围为 0.11%0.11 \% 到 7.59%7.59 \% 。最后,轮胎的优化模型进行动态分析以评估其振动性能,从而导致反作用力显着衰减。
Pneumatic tires are crucial for vehicles, providing a balance of traction, load support, and performance through air pressure. They are the only contact between the vehicle and the road, aiding in steering and cushioning against road imperfections for a smoother ride (Genoverse et al., 2021). Despite these advantages, pneumatic tires are prone to punctures, leaks, and blowouts, which pose safety risks, cause inconvenience, and result in financial costs. This has led to the exploration of alternative airless tires. To tackle these challenges, the concept of non-pneumatic tires designed to completely eliminate reliance on air pressure has emerged as a revolutionary alternative to traditional options. Airless tires, with their innovative design and material choices, aim to provide a robust, low-vibration, and puncture-resistant solution that can withstand significant external forces during high-speed travel for various vehicles. 充气轮胎对车辆至关重要,它通过气压提供牵引力、负载支撑和性能的平衡。它们是车辆与道路之间的唯一接触,有助于转向和缓冲道路缺陷,以实现更平稳的行驶(Genoverse 等人,2021 年)。尽管有这些优点,但充气轮胎容易被刺穿、泄漏和爆裂,这会带来安全风险,造成不便,并导致财务成本。这导致了对替代无气轮胎的探索。为了应对这些挑战,旨在完全消除对气压依赖的非充气轮胎概念已成为传统选择的革命性替代品。无气轮胎采用创新的设计和材料选择,旨在提供一种坚固、低振动和抗穿刺的解决方案,该解决方案可以在各种车辆的高速行驶中承受巨大的外力。
To date, researchers have put forth diverse design proposals and conducted investigations into the mechanical performance for non-pneumatic tires (NPTs), aiming to either match or surpass the performance of current pneumatic tires. Researchers have tried to find the key design variables - such as material, geometry and configuration of airless tires - that influence critical performance characteristics like structural strength, stiffness, durability, and rolling resistance. Several advantages of using honeycomb structures in NPTs, as a replacement for air, have been reported, particularly regarding load-bearing and energy absorption for lowspeed vehicles (Liu et al., 2022; Liang et al., 2021). While NPTs have shown some potential for slow-speed mobility applications, they are still in the early stages of research for high-speed uses. Besides mechanical performance factors like vibration, stiffness and strength, their practical use is restricted by the design of the exposed supporting spokes, which are vulnerable to vibration and damage from debris and mud accumulation, further reducing tire performance, especially in rough terrains (Deng et al., 2023). The durability of NPTs developed thus far lags behind that of current pneumatic tires, highlighting the need for extensive optimization research from multiple angles. This study seeks to advance the non-pneumatic tire technology by 迄今为止,研究人员已经提出了不同的设计方案,并对非充气轮胎 (NPT) 的机械性能进行了调查,旨在达到或超过当前充气轮胎的性能。研究人员试图找到影响结构强度、刚度、耐久性和滚动阻力等关键性能特征的关键设计变量,例如无气轮胎的材料、几何形状和配置。据报道,在 NPT 中使用蜂窝结构作为空气替代品的几个优势,特别是在低速车辆的承重和能量吸收方面(Liu 等人,2022 年;Liang et al., 2021)。虽然 NPT 已显示出一些低速移动应用的潜力,但它们仍处于高速应用研究的早期阶段。除了振动、刚度和强度等机械性能因素外,它们的实际使用还受到外露支撑辐条设计的限制,这些辐条容易受到振动以及碎屑和泥浆堆积的损坏,进一步降低轮胎性能,尤其是在崎岖地形中(邓等人,2023 年)。迄今为止开发的 NPT 的耐用性落后于当前的充气轮胎,这凸显了从多个角度进行广泛优化研究的必要性。本研究旨在通过以下方式推进非充气轮胎技术
tackling these challenges and refining them for high-speed vehicle applications. 应对这些挑战并针对高速车辆应用进行改进。
This research has led to the development of new computational frameworks for designing innovative airless tires made from hyper-elastic fiber/rubber composite materials. These frameworks use artificial neural networks (ANN) to predict the nonlinear properties of the composite materials, apply response surface methodology (RSM) and goal-attainment optimization to determine the four ideal tire stiffnesses, and include dynamic performance analyses for high-speed driving. As a result, a new optimized airless tire design is proposed based on these advanced frameworks. 这项研究导致了新的计算框架的开发,用于设计由超弹性纤维/橡胶复合材料制成的创新无气轮胎。这些框架使用人工神经网络 (ANN) 来预测复合材料的非线性特性,应用响应面法 (RSM) 和目标实现优化来确定四种理想的轮胎刚度,并包括高速驾驶的动态性能分析。因此,基于这些先进的框架提出了一种新的优化无气轮胎设计。
2. MECHANICAL PROPERTIES OF FIBER/RUBBER COMPOSITES 2. 纤维/橡胶复合材料的机械性能
The airless tire used in this study will be developed using glass fiber reinforced rubber composite materials. These fiber/rubber composites have complex behaviors due to their hyper-elastic nature, anisotropic properties, and microstructural variability. Initially, we gather partial nonlinear stress-strain data through the finite element analysis (FEA) of the representative volume element (RVE). We then employ ANN machine learning to determine the effective elastic moduli for different composite mixture scenarios. 本研究中使用的无气轮胎将使用玻璃纤维增强橡胶复合材料开发。这些纤维/橡胶复合材料由于其超弹性、各向异性和微观结构可变性而具有复杂的行为。最初,我们通过代表性体积单元 (RVE) 的有限元分析 (FEA) 收集部分非线性应力-应变数据。然后,我们采用 ANN 机器学习来确定不同复合材料混合物场景的有效弹性模量。
2.1 FEA on RVEs 2.1 RWE 的 FEA
A unit cell is commonly used to compute numerically composite material properties. To develop a RVE model, it is essential to create a unit cell that accurately represents the composite element. To simulate infinite periodic behavior across the unit cell, periodic boundary conditions (PBCs), as illustrated in Fig. 1 are often applied. This approach involves applying boundary conditions to the faces of the RVE so that it behaves as though it is part of an infinite material. Essentially, any displacement ( UU ), stress, or strain applied to the RVE is replicated periodically, mimicking an infinite lattice of identical RVEs. By using PBCs, researchers can study the RVE in isolation, enabling them to derive effective material properties and understand the macroscopic behavior of the heterogeneous material. In this context, a square array unit cell is employed for the RVE model, as depicted in Fig. 2 and described in Table 1. The fiber-to-rubber volume fraction is adjusted in 2.5%2.5 \% increments, from 10%10 \% to 60%60 \%. Correspondingly, the fiber diameters are determined as shown in Table 1. 晶胞通常用于计算数值复合材料的属性。要开发 RVE 模型,必须创建一个准确表示复合单元的晶胞。为了模拟整个晶胞的无限周期性行为,通常采用周期性边界条件 (PBC),如图 1 所示。这种方法涉及将边界条件应用于 RVE 的面,使其行为就像它是无限材料的一部分。从本质上讲,施加到 RVE 的任何位移 ( UU )、应力或应变都会定期复制,模拟相同 RVE 的无限晶格。通过使用 PBC,研究人员可以孤立地研究 RVE,使他们能够获得有效的材料特性并了解异质材料的宏观行为。在这种情况下,RVE 模型采用方形阵列晶胞,如图 2 所示,如表 1 所示。纤维与橡胶的体积分数以 2.5%2.5 \% 增量方式调整,从 10%10 \% 到 60%60 \% 。相应地,纤维直径的确定如表 1 所示。
In this study, the neo-Hookean model (Rivlin and Saunders, 1951; Ogden, 1972; Yeoh, 1993) is used in modeling the nonlinear elastic behaviors as follows: 在这项研究中,新胡克模型(Rivlin 和 Saunders,1951 年;Ogden, 1972;Yeoh,1993 年)用于对非线性弹性行为进行建模,如下所示:
where WW is a specific strain-energy density function; C_(10)C_{10} is the shear modulus; D_(1)D_{1} is the material’s incompressible parameter; bar(I)_(1)\bar{I}_{1} is the first invariant of the deformation tensor. If the material is assumed to be incompressible, J=1J=1 and the second term becomes zero. 其中 WW 是特定的应变-能量密度函数; C_(10)C_{10} 是剪切模量; D_(1)D_{1} 是材质的不可压缩参数; bar(I)_(1)\bar{I}_{1} 是变形张量的第一个不变量。如果假设材料是不可压缩的, J=1J=1 则第二项变为零。
Natural rubbers with different composition of chemicals such as carbon black, silica, stearic acid, zinc oxide, MBT (Methylene Bis Thiocayanate) and sulphur are used in this study (Shahzad et al., 2015) and their neo-Hookean constants are listed in Table 2. The other two data are 本研究使用了具有不同化学成分的天然橡胶,如炭黑、二氧化硅、硬脂酸、氧化锌、MBT(亚甲基双硫代酸盐)和硫磺(Shahzad等人,2015 年),它们的新胡克常数列于表 2 中。其他两个数据是
Cheol Kim kimchul@knu.ac.kr ^(1){ }^{1} Department of Mechanical Engineering, Kyungpook National University, Daegu 41566, Korea ^(1){ }^{1} 庆北大学 机械工程系, 韩国 大邱 41566 ^(2){ }^{2} Department of Mechanical and Design Engineering, Hongik University, Sejong 30016, Korea ^(2){ }^{2} 弘益大学 机械与设计工程系, 韩国 世宗 30016