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Cite this: DOI: 10.1039/d4dd00169a
引用此文：DOI: 10.1039/d4dd00169a
Received 20th June 2024 2024 年 6 月 20 日收到
Accepted 23rd September 2024
2024 年 9 月 23 日接受
DOI: 10.1039/d4dd00169a
rsc.li/digitaldiscovery

Machine learning-assisted analysis of dry and lubricated tribological properties of Al − Co − Cr − Al − Co − Cr − Al-Co-Cr-\mathrm{Al}-\mathrm{Co}-\mathrm{Cr}- Fe − Ni Fe − Ni Fe-Ni\mathrm{Fe}-\mathrm{Ni} high entropy alloy
机器学习辅助分析 Al − Co − Cr − Al − Co − Cr − Al-Co-Cr-\mathrm{Al}-\mathrm{Co}-\mathrm{Cr}- Fe − Ni Fe − Ni Fe-Ni\mathrm{Fe}-\mathrm{Ni} 高熵合金的干燥和润滑摩擦学特性

Saurabh Vashistha, abc abc  ^("abc "){ }^{\text {abc }} Bashista Kumar Mahanta, ab ab  ^("ab "){ }^{\text {ab }} Vivek Kumar Singh, d d  ^("d "){ }^{\text {d }} Neha Sharma, b b  ^("b "){ }^{\text {b }} Anjan Ray, e e ^(e){ }^{e} Saurabh Dixit f f ^(f){ }^{f} and Shailesh Kumar Singh (1) *abc
Saurabh Vashistha、 abc abc  ^("abc "){ }^{\text {abc }} Bashista Kumar Mahanta、 ab ab  ^("ab "){ }^{\text {ab }} Vivek Kumar Singh、 d d  ^("d "){ }^{\text {d }} Neha Sharma、 b b  ^("b "){ }^{\text {b }} Anjan Ray、 e e ^(e){ }^{e} Saurabh Dixit f f ^(f){ }^{f} 和 Shailesh Kumar Singh (1) *abc

Abstract 摘要

This study marks a notable advancement in tribology by thoroughly investigating the tribological properties of a high-entropy alloy under both lubricated and dry conditions. The research encompasses a detailed evaluation of the alloy’s wear behavior, utilizing a data-driven modeling approach that employs an evolutionary framework to build and validate a predictive model. The findings offer critical insights into the tribological performance of high-entropy alloys under diverse operational and lubrication conditions. Specifically, the Al − Co − Cr − Fe − Ni Al − Co − Cr − Fe − Ni Al-Co-Cr-Fe-Ni\mathrm{Al}-\mathrm{Co}-\mathrm{Cr}-\mathrm{Fe}-\mathrm{Ni} alloy exhibits exceptional tribological properties, with a coefficient of friction ranging from 0.0165 to 0.6024 and surface roughness between 0.261 and 1.11. A data-driven methodology was employed to develop a predictive model with an accuracy exceeding 94%, effectively capturing the precise trends in lubrication behavior and providing in-depth information on surface characteristics for future experimental endeavors and data extraction. Additionally, the study underscores the profound impact of lubricant chemical composition on the wear behavior of the alloy, highlighting the crucial importance of selecting appropriate lubricants for specific tribological applications.
这项研究通过深入研究一种高熵合金在润滑和干燥条件下的摩擦学特性，标志着摩擦学取得了显著进展。研究详细评估了合金的磨损行为，利用数据驱动的建模方法，采用进化框架建立并验证了一个预测模型。研究结果为了解高熵合金在不同操作和润滑条件下的摩擦学性能提供了重要见解。具体来说， Al − Co − Cr − Fe − Ni Al − Co − Cr − Fe − Ni Al-Co-Cr-Fe-Ni\mathrm{Al}-\mathrm{Co}-\mathrm{Cr}-\mathrm{Fe}-\mathrm{Ni} 合金具有优异的摩擦学性能，摩擦系数在 0.0165 到 0.6024 之间，表面粗糙度在 0.261 到 1.11 之间。研究采用数据驱动方法开发了一个准确率超过 94% 的预测模型，有效捕捉了润滑行为的精确趋势，并为未来的实验工作和数据提取提供了有关表面特征的深入信息。此外，研究还强调了润滑剂化学成分对合金磨损行为的深远影响，突出了为特定摩擦学应用选择适当润滑剂的重要性。

1. Introduction 1.导言

High entropy alloys (HEAs) have emerged as a revolutionary alternative to traditional alloys in recent years. Unlike alloys that contain only one or two core components, HEAs require multiple constituents and provide a wide range of benefits that cater to different needs. In contrast, HEAs consist of four or more principal elements, with several elements present in concentrations ranging from 5 % 5 % 5%5 \% to 35 % . 1 35 % . 1 35%.^(1)35 \% .^{1} This increased configurational entropy reaches a certain level and results in the formation of a single-phase solid solution. This characteristic helps prevent the precipitation of intermetallic compounds, which is a primary factor in reducing mechanical performance. The HEA alloy is an important material for structural and functional purposes due to its outstanding mechanical strength, resilience to corrosion, and stability under elevated temperatures. 2 , 3 2 , 3 ^(2,3){ }^{2,3} The surface properties of a material play a vital role in determining its overall service life in most applications.
近年来，高熵合金（HEAs）已成为传统合金的革命性替代品。与只包含一种或两种核心成分的合金不同，高熵合金需要多种成分，并能提供满足不同需求的多种优势。相比之下，HEA 由四种或四种以上的主要元素组成，其中几种元素的浓度从 5 % 5 % 5%5 \% 到 35 % . 1 35 % . 1 35%.^(1)35 \% .^{1} 这种增加的构型熵达到一定水平后会形成单相固溶体。这一特性有助于防止金属间化合物的析出，而金属间化合物是降低机械性能的主要因素。HEA 合金具有出色的机械强度、抗腐蚀性和高温稳定性，是一种重要的结构性和功能性材料。 2 , 3 2 , 3 ^(2,3){ }^{2,3} 在大多数应用中，材料的表面特性对决定其整体使用寿命起着至关重要的作用。
While the bulk properties are important, it is the surface that directly interacts with the environment, leading to various forms of degradation, wear, and corrosion. Therefore, optimizing and maintaining favourable surface properties is crucial for ensuring the longevity and performance of a material. One way to increase the service life of a material is by reducing the coefficient of friction at its mating surface, which leads to a decrease in the wear rate. Surface treatment processes, such as bronzing, are often used to improve the hardenability and wear resistance of materials like Ni, Al, Fe, Co, and Ti-based alloys. 4 4 ^(4){ }^{4} However, these processes can be costly. An alternative approach to achieve similar results without undergoing surface treatment is to use lubricating oils on the contacting surface. Lubricants are substances that are applied between two surfaces in relative motion to reduce friction and wear. They can be in the form of oils, greases, or solid lubricants. By using appropriate lubricating oils, a protective film is formed on the mating surfaces, which reduces direct metal-to-metal contact and minimizes friction and wear. The lubricating film acts as a barrier, providing a smooth surface that separates the mating materials. This helps to decrease the wear rate and increase the service life of the materials. It’s important to select the right type of lubricating oil based on factors such as the operating conditions, temperature, load, and compatibility with the mating materials. Different lubricants have different properties and viscosities, which make them suitable for specific applications.
材料的整体性能固然重要，但直接与环境发生作用，导致各种形式降解、磨损和腐蚀的却是材料的表面。因此，优化和保持良好的表面特性对于确保材料的使用寿命和性能至关重要。提高材料使用寿命的方法之一是降低其配合表面的摩擦系数，从而降低磨损率。青铜化等表面处理工艺通常用于提高镍、铝、铁、钴和钛基合金等材料的淬透性和耐磨性。 4 4 ^(4){ }^{4} 然而，这些工艺的成本可能很高。另一种无需进行表面处理即可达到类似效果的方法是在接触面上使用润滑油。润滑油是涂抹在相对运动的两个表面之间以减少摩擦和磨损的物质。其形式可以是油、脂或固体润滑剂。通过使用适当的润滑油，可在配合表面形成一层保护膜，从而减少金属与金属之间的直接接触，将摩擦和磨损降至最低。润滑油膜就像一道屏障，提供了一个光滑的表面，将配合材料隔离开来。这有助于降低磨损率，延长材料的使用寿命。根据工作条件、温度、负载以及与配合材料的兼容性等因素选择正确的润滑油类型非常重要。不同的润滑油具有不同的特性和粘度，因此适用于特定的应用。
The lack of knowledge about the tribological behavior of High-Entropy Alloys (HEAs) can be attributed to several factors.
对高熵合金 (HEA) 的摩擦学行为缺乏了解可归因于几个因素。
Firstly, the number of alloy systems that have been thoroughly studied is still relatively small, resulting in limited available data. To address this, a broader range of HEA systems should be investigated to expand the knowledge base. Secondly, the tribological behavior of HEAs is significantly influenced by their microstructural and compositional characteristics, which makes it challenging to draw generalized conclusions. Therefore, it is important to conduct systematic studies that take into account various microstructural features and alloy compositions to better understand their impact on tribological properties. Thirdly, although several lubricants have been tested on HEAs, the number of studies conducted in this area is still relatively limited. To alleviate this limitation, more study should be performed to investigate how different lubricants affect the level of friction and wear encountered by HEAs. Furthermore, most research on HEAs has primarily focused on their mechanical properties, with only a few studies dedicated to tribology. To enhance our understanding of the tribological behavior of HEAs, it is crucial to place greater emphasis on conducting tribological investigations alongside the characterization of mechanical properties.
首先，经过深入研究的合金系统数量仍然相对较少，导致可用数据有限。为此，应研究更广泛的 HEA 系统，以扩大知识库。其次，HEA 的摩擦学行为受其微观结构和成分特征的显著影响，这使得得出一般性结论具有挑战性。因此，必须进行系统研究，将各种微观结构特征和合金成分考虑在内，以更好地了解它们对摩擦学特性的影响。第三，虽然已经在 HEA 上测试了几种润滑剂，但在这一领域开展的研究数量仍然相对有限。为缓解这一局限性，应开展更多研究，探讨不同润滑剂如何影响 HEA 的摩擦和磨损水平。此外，大多数关于 HEA 的研究主要集中在其机械性能上，只有少数研究专门针对摩擦学。为了加深我们对 HEA 摩擦学行为的了解，在研究机械性能特征的同时，必须更加重视开展摩擦学研究。
In order to address these knowledge gaps, studies should prioritize three main areas. Firstly, there should be a focus on examining the impact of different lubricants on the wear and friction behaviour of HEAs. This will provide valuable insights into the optimal lubrication strategies for HEA applications. Secondly, it is important to explore the effect of microstructural and compositional attributes on the tribological properties of HEAs. By systematically varying these parameters, researchers can uncover correlations and establish guidelines for designing HEAs with tailored tribological properties. Lastly, in conjunction with the development of new HEA systems, tribological studies should be integrated to better understand the lubrication behavior of these materials. This interdisciplinary approach will ensure that both mechanical and tribological aspects are comprehensively addressed in HEA research. By addressing these factors and conducting further research in these areas, a deeper understanding of the tribological behavior of HEAs can be achieved, enabling their broader application in industries where friction and wear properties are critical.
为了填补这些知识空白，研究应优先考虑三个主要领域。首先，应重点研究不同润滑剂对 HEA 磨损和摩擦行为的影响。这将为 HEA 应用的最佳润滑策略提供有价值的见解。其次，必须探索微结构和成分属性对 HEA 摩擦学特性的影响。通过系统地改变这些参数，研究人员可以发现相关性，并为设计具有定制摩擦学特性的 HEA 制定指导方针。最后，在开发新的 HEA 系统的同时，应结合摩擦学研究，以更好地了解这些材料的润滑行为。这种跨学科方法将确保在 HEA 研究中全面涉及机械和摩擦学两个方面。通过解决这些因素并在这些领域开展进一步的研究，可以更深入地了解 HEA 的摩擦学行为，从而使其在摩擦和磨损特性至关重要的行业中得到更广泛的应用。
High Entropy Alloys (HEAs) have gained significant attention in recent years due to their exceptional mechanical properties, corrosion resistance, and high-temperature stability. However, understanding the tribological behavior of HEAs, particularly the Al − Co − Cr − Fe − Ni Al − Co − Cr − Fe − Ni Al-Co-Cr-Fe-Ni\mathrm{Al}-\mathrm{Co}-\mathrm{Cr}-\mathrm{Fe}-\mathrm{Ni} system, remains limited. Yuan Yu et al. 5 5 ^(5){ }^{5} investigated the tribological properties of Al − Co − Cr − Fe − Ni Al − Co − Cr − Fe − Ni Al-Co-Cr-Fe-Ni\mathrm{Al}-\mathrm{Co}-\mathrm{Cr}-\mathrm{Fe}-\mathrm{Ni} and Al − Co − Cr − Al − Co − Cr − Al-Co-Cr-\mathrm{Al}-\mathrm{Co}-\mathrm{Cr}- Fe-Ni-Ti0.5 HEAs using gear oil and multiple alkylated cyclopentanes (MACs). The study showed that the Al-Co-Cr-Fe-NiTi0.5 alloy exhibited superior tribological properties compared to the Al − Co − Cr − Fe − Ni Al − Co − Cr − Fe − Ni Al-Co-Cr-Fe-Ni\mathrm{Al}-\mathrm{Co}-\mathrm{Cr}-\mathrm{Fe}-\mathrm{Ni} alloy when adequately lubricated with gear oil. Heat treatment resulted in a uniform grain structure for Al- Co − Cr − Fe − Ni Co − Cr − Fe − Ni Co-Cr-Fe-Ni\mathrm{Co}-\mathrm{Cr}-\mathrm{Fe}-\mathrm{Ni} alloy, while the dendrite structure was retained in the Al − Co − Cr − Fe − Ni − Ti 0.5 Al − Co − Cr − Fe − Ni − Ti 0.5 Al-Co-Cr-Fe-Ni-Ti0.5\mathrm{Al}-\mathrm{Co}-\mathrm{Cr}-\mathrm{Fe}-\mathrm{Ni}-\mathrm{Ti} 0.5 alloy. Young Liu et al. 6 6 ^(6){ }^{6} studied the influence of normal loads on the friction and wear behaviours of AlCrCuFeNi 2 AlCrCuFeNi 2 AlCrCuFeNi_(2)\mathrm{AlCrCuFeNi}_{2} HEA against Si 3 N 4 Si 3 N 4 Si_(3)N_(4)\mathrm{Si}_{3} \mathrm{~N}_{4} ceramic balls under different conditions (dry, simulated rainwater, and deionized water). The study found that simulated rainwater affected tribological
近年来，高熵合金（HEAs）因其优异的机械性能、耐腐蚀性和高温稳定性而备受关注。然而，人们对 HEA 的摩擦学行为，尤其是 Al − Co − Cr − Fe − Ni Al − Co − Cr − Fe − Ni Al-Co-Cr-Fe-Ni\mathrm{Al}-\mathrm{Co}-\mathrm{Cr}-\mathrm{Fe}-\mathrm{Ni} 系统的了解仍然有限。Yuan Yu 等人 5 5 ^(5){ }^{5} 使用齿轮油和多烷基化环戊烷 (MAC) 研究了 Al − Co − Cr − Fe − Ni Al − Co − Cr − Fe − Ni Al-Co-Cr-Fe-Ni\mathrm{Al}-\mathrm{Co}-\mathrm{Cr}-\mathrm{Fe}-\mathrm{Ni} 和 Al − Co − Cr − Al − Co − Cr − Al-Co-Cr-\mathrm{Al}-\mathrm{Co}-\mathrm{Cr}- Fe-Ni-Ti0.5 HEAs 的摩擦学特性。研究表明，与 Al − Co − Cr − Fe − Ni Al − Co − Cr − Fe − Ni Al-Co-Cr-Fe-Ni\mathrm{Al}-\mathrm{Co}-\mathrm{Cr}-\mathrm{Fe}-\mathrm{Ni} 合金相比，Al-Co-Cr-Fe-NiTi0.5合金在齿轮油的充分润滑下表现出更优越的摩擦学特性。热处理使 Al- Co − Cr − Fe − Ni Co − Cr − Fe − Ni Co-Cr-Fe-Ni\mathrm{Co}-\mathrm{Cr}-\mathrm{Fe}-\mathrm{Ni} 合金具有均匀的晶粒结构，而 Al − Co − Cr − Fe − Ni − Ti 0.5 Al − Co − Cr − Fe − Ni − Ti 0.5 Al-Co-Cr-Fe-Ni-Ti0.5\mathrm{Al}-\mathrm{Co}-\mathrm{Cr}-\mathrm{Fe}-\mathrm{Ni}-\mathrm{Ti} 0.5 合金则保留了枝晶结构。Young Liu 等人 6 6 ^(6){ }^{6} 研究了在不同条件（干燥、模拟雨水和去离子水）下，法向载荷对 AlCrCuFeNi 2 AlCrCuFeNi 2 AlCrCuFeNi_(2)\mathrm{AlCrCuFeNi}_{2} HEA 与 Si 3 N 4 Si 3 N 4 Si_(3)N_(4)\mathrm{Si}_{3} \mathrm{~N}_{4} 陶瓷球的摩擦和磨损行为的影响。研究发现，模拟雨水对摩擦学
behavior through processes such as passive film formation, lubrication, cooling, cleaning, and corrosion, resulting in adhesive, abrasive, and corrosive wear. Haitao Duan et al. 7 7 ^(7){ }^{7} studied the lubricated tribological properties of an Al − Co − Cr − Fe − Ni − Cu Al − Co − Cr − Fe − Ni − Cu Al-Co-Cr-Fe-Ni-Cu\mathrm{Al}-\mathrm{Co}-\mathrm{Cr}-\mathrm{Fe}-\mathrm{Ni}-\mathrm{Cu} highentropy alloy (HEA) utilising pin-on-disc testing. The results showed that by lubricating the HEA with a hydrogen peroxide solution ( 90 % ) ( 90 % ) (90%)(90 \%) and oil, the friction and wear resistance of the HEA was significantly enhanced or improved as compared to using only conventional lubricating oil. The coefficient of friction was lower after a grinding stage. These studies demonstrate the importance of different lubricants in influencing the tribological behaviour of Al − Co − Cr − Fe − Ni Al − Co − Cr − Fe − Ni Al-Co-Cr-Fe-Ni\mathrm{Al}-\mathrm{Co}-\mathrm{Cr}-\mathrm{Fe}-\mathrm{Ni} HEAs. Gear oil and MACs were found to enhance the tribological properties of Al − Co − Cr − Fe − Ni − Ti 0.5 Al − Co − Cr − Fe − Ni − Ti 0.5 Al-Co-Cr-Fe-Ni-Ti0.5\mathrm{Al}-\mathrm{Co}-\mathrm{Cr}-\mathrm{Fe}-\mathrm{Ni}-\mathrm{Ti} 0.5 alloy, while simulated rainwater and hydrogen peroxide solution showed positive effects on wear and friction reduction. These findings highlight the need to explore and optimize lubrication strategies for HEAs, considering specific working conditions and lubricant characteristics. The influence of normal loads on the tribological properties of HEAs was also emphasized. Simulated rainwater, for instance, induced complex wear mechanisms, including adhesive, abrasive, and corrosive wear. Understanding these effects is crucial for predicting the wear behaviour of HEAs in practical applications. The literature survey highlights the scarcity of studies on the tribological behaviour of HEAs, indicating the need for further research in this field. Furthermore, the utilization of machine learning-based approaches for validating experimental data has emerged as a promising avenue for advancing our understanding of HEA tribology. 8 − 12 8 − 12 ^(8-12){ }^{8-12} In the present context, ANNbased modeling approaches have emerged as highly efficient techniques for capturing the intricate trends inherent in complex datasets. Their ability to handle nonlinearity and adapt to diverse data structures makes them particularly suited for modeling phenomena with multifaceted dependencies. ANN models excel in identifying underlying patterns without the need for explicit mathematical formulations, offering a robust solution for processing and interpreting complex data. This flexibility and precision enable ANN-based models to accurately predict behaviors across a wide range of applications, making them a powerful tool for data-driven analysis and modeling in complex systems. 13 − 15 13 − 15 ^(13-15){ }^{13-15} This work represents a notable progress in the field of tribology as it provides a comprehensive analysis of the tribological behaviour of a high-entropy alloy (HEA) under both lubricated and dry conditions. By examining the wear characteristics of the alloy, the research contributes to a better understanding of its performance in real-world applications.
通过被动成膜、润滑、冷却、清洁和腐蚀等过程，产生粘着磨损、磨料磨损和腐蚀磨损。段海涛等人 7 7 ^(7){ }^{7} 利用针盘试验研究了一种 Al − Co − Cr − Fe − Ni − Cu Al − Co − Cr − Fe − Ni − Cu Al-Co-Cr-Fe-Ni-Cu\mathrm{Al}-\mathrm{Co}-\mathrm{Cr}-\mathrm{Fe}-\mathrm{Ni}-\mathrm{Cu} 高熵合金 (HEA) 的润滑摩擦学特性。结果表明，用过氧化氢溶液 ( 90 % ) ( 90 % ) (90%)(90 \%) 和油润滑高熵合金，与仅使用传统润滑油相比，高熵合金的摩擦和耐磨性显著增强或改善。磨削阶段后的摩擦系数更低。这些研究表明，不同的润滑剂对 Al − Co − Cr − Fe − Ni Al − Co − Cr − Fe − Ni Al-Co-Cr-Fe-Ni\mathrm{Al}-\mathrm{Co}-\mathrm{Cr}-\mathrm{Fe}-\mathrm{Ni} HEA 的摩擦学特性具有重要影响。研究发现，齿轮油和 MACs 可增强 Al − Co − Cr − Fe − Ni − Ti 0.5 Al − Co − Cr − Fe − Ni − Ti 0.5 Al-Co-Cr-Fe-Ni-Ti0.5\mathrm{Al}-\mathrm{Co}-\mathrm{Cr}-\mathrm{Fe}-\mathrm{Ni}-\mathrm{Ti} 0.5 合金的摩擦学特性，而模拟雨水和过氧化氢溶液则对磨损和摩擦降低有积极影响。这些发现突出表明，有必要在考虑特定工作条件和润滑剂特性的情况下，探索和优化 HEA 的润滑策略。正常负载对 HEA 摩擦学特性的影响也得到了强调。例如，模拟雨水诱发了复杂的磨损机制，包括粘着磨损、磨蚀磨损和腐蚀磨损。了解这些影响对于预测 HEA 在实际应用中的磨损行为至关重要。文献调查显示，有关 HEA 摩擦学行为的研究很少，这表明需要在这一领域开展进一步的研究。此外，利用基于机器学习的方法来验证实验数据已成为促进我们对 HEA 摩擦学理解的一条大有可为的途径。 8 − 12 8 − 12 ^(8-12){ }^{8-12} 在当前背景下，基于 ANN 的建模方法已成为捕捉复杂数据集内在复杂趋势的高效技术。它们能够处理非线性问题并适应各种数据结构，因此特别适合对具有多方面依赖关系的现象进行建模。ANN 模型在识别潜在模式方面表现出色，无需明确的数学公式，为处理和解释复杂数据提供了强大的解决方案。这种灵活性和精确性使基于 ANN 的模型能够准确预测各种应用中的行为，使其成为复杂系统中数据驱动分析和建模的强大工具。 13 − 15 13 − 15 ^(13-15){ }^{13-15} 这项工作代表了摩擦学领域的一个显著进步，因为它对高熵合金 (HEA) 在润滑和干燥条件下的摩擦学行为进行了全面分析。通过研究合金的磨损特性，这项研究有助于更好地了解合金在实际应用中的性能。

2. Materials and methodology
2.材料和方法

The granules of aluminum, cobalt, chromium, iron, and nickel with high level of purity (purity > 99.9 wt % 99.9 wt % 99.9wt%99.9 \mathrm{wt} \% ) have been employed to fabricate the Al-Co-Cr-Fe-Ni High Entropy Alloy (HEA) utilizing the method of vacuum induction melting. The resultant cast component was a rectangular ingot characterized by dimensions of 115 × 135 × 170 mm 115 × 135 × 170 mm 115 xx135 xx170mm115 \times 135 \times 170 \mathrm{~mm}. The cylindrical specimens measuring 6 mm in diameter and 20 mm in length were extracted from the as-cast ingot through the process of Wire Cut Electrode Discharge Machining (EDM) to conduct the
采用高纯度（纯度 > 99.9 wt % 99.9 wt % 99.9wt%99.9 \mathrm{wt} \% ）的铝、钴、铬、铁和镍颗粒，利用真空感应熔炼法制造了铝-钴-铬-铁-镍高熵合金（HEA）。由此获得的铸件是矩形铸锭，尺寸为 115 × 135 × 170 mm 115 × 135 × 170 mm 115 xx135 xx170mm115 \times 135 \times 170 \mathrm{~mm} 。直径为 6 毫米、长度为 20 毫米的圆柱形试样是通过线切割放电加工 (EDM) 工艺从铸锭中提取的，以便进行
Table 1 Chemical composition (%) of HEA
表 1 HEA 的化学成分（百分比
Element 要素 Al Co Cr Fe 铁 Ni 倪
at% 20.1 20.0 19.3 18.7 21.8
wt % wt % wt%\mathrm{wt} \% 10.7 23.4 19.9 20.7 25.4
Element Al Co Cr Fe Ni at% 20.1 20.0 19.3 18.7 21.8 wt% 10.7 23.4 19.9 20.7 25.4| Element | Al | Co | Cr | Fe | Ni | | :--- | :--- | :--- | :--- | :--- | :--- | | at% | 20.1 | 20.0 | 19.3 | 18.7 | 21.8 | | $\mathrm{wt} \%$ | 10.7 | 23.4 | 19.9 | 20.7 | 25.4 |
Table 2 Physicochemical property of lubricants
表 2 润滑油的物理化学特性
Property 财产 Mineral oil 矿物油 Synthetic oil 合成机油 Vegetable oil 植物油
Density ( g cm − 3 ) g cm − 3 (gcm^(-3))\left(\mathrm{g} \mathrm{cm}^{-3}\right) 密度 ( g cm − 3 ) g cm − 3 (gcm^(-3))\left(\mathrm{g} \mathrm{cm}^{-3}\right) 0.848 0.856 0.859
Viscosity ( cst ) ( cst ) (cst)(\mathrm{cst}) 粘度 ( cst ) ( cst ) (cst)(\mathrm{cst}) 18.24 18.56 18.78
Property Mineral oil Synthetic oil Vegetable oil Density (gcm^(-3)) 0.848 0.856 0.859 Viscosity (cst) 18.24 18.56 18.78| Property | Mineral oil | Synthetic oil | Vegetable oil | | :--- | :---: | :---: | :---: | | Density $\left(\mathrm{g} \mathrm{cm}^{-3}\right)$ | 0.848 | 0.856 | 0.859 | | Viscosity $(\mathrm{cst})$ | 18.24 | 18.56 | 18.78 |
Fig. 1 Test samples used in experiments.
图 1 实验中使用的测试样品。
experiment. The nominal composition of the high entropy alloy is given below in Table 1.
实验。表 1 列出了高熵合金的标称成分。

2.1 Test sample and experimental test conditions
2.1 试验样品和试验条件

The test specimens were in the form of circular plates and cylindrical pins. The test specimens have the following specification:
试样采用圆板和圆柱销的形式。试样规格如下：
(i) Metallic disc: EN-31 alloy steel circular plate of 50 mm diameter with hardness 680 Hv .
(i) 金属圆盘：EN-31 合金钢圆板，直径 50 毫米，硬度 680 Hv。
(ii) HEA pin: cylindrical pins of 6 mm diameter and 20 mm length having hardness 338 Hv .
(ii) HEA 销针：圆柱形销针，直径 6 毫米，长 20 毫米，硬度 338 Hv。
(iii) Lubricants: mineral oil, synthetic oil, vegetable oil and their physicochemical properties are shown Table 2 below. The vegetable oil was synthesized in the laboratory using Karanja oil. The mineral oil and synthetic oil were purchased from the market and the base oils used were SN 150 and polyalphaolefin (PAO 200) respectively.
(iii) 润滑剂：矿物油、合成油和植物油及其理化特性见下表 2。植物油是在实验室使用卡兰贾油合成的。矿物油和合成油是从市场上购买的，使用的基础油分别是 SN 150 和聚α烯烃（PAO 200）。
The image of test samples used in the experiments is shown in Fig. 1. The experiments were carried out on a pin on disc tribo-tester with a constant rotational speed, under varied test settings with varying load, over a set period of time. The Table 3 shows the experimental test conditions for pin on disc experiment. The scanning electron microscopy (SEM) was done to analyze the worn surface morphologies of the samples after test. Also, a Coherence Correlation Interferometry (CCI) optical profilometer was used to find the average values of surface roughness and 3D roughness maps of the samples after experiment.
实验中使用的测试样本图像如图 1 所示。实验是在圆盘销轴三维测试仪上进行的，测试仪的转速恒定，在不同的测试设置下，载荷变化，并持续一段时间。表 3 列出了圆盘销钉实验的测试条件。扫描电子显微镜（SEM）分析了测试后样品的磨损表面形态。此外，还使用了相干干涉仪（CCI）光学轮廓仪来测定样品表面粗糙度的平均值和实验后的三维粗糙度图。

2.2 Experimental Setup 2.2 实验装置

Experiments were conducted to investigate the tribological properties of an Al − Co − Cr − Fe − Ni Al − Co − Cr − Fe − Ni Al-Co-Cr-Fe-Ni\mathrm{Al}-\mathrm{Co}-\mathrm{Cr}-\mathrm{Fe}-\mathrm{Ni} high entropy alloy. The R-tec USA tribo-tester (Fig. 2) is used to evaluate material tribological properties. The tribo-tester comprises of a revolving stage that may be modified to rotate at the fixed rpm. A disc bearing a test specimen is fastened to the stage, while a friction arm is held motionless above the stage. At the end of the friction arm is a fixture with a mating pin test specimen which has an offset of 20 mm from the centre of the disc. A lubricant or oil can be filled around the disc to submerge it, and a sensor is put on the friction arm to measure frictional resistance when the disc is spun. A servomotor is used to load the test specimens, and computer-controlled software runs the test apparatus, continuously monitoring and recording the friction encountered.
实验研究了 Al − Co − Cr − Fe − Ni Al − Co − Cr − Fe − Ni Al-Co-Cr-Fe-Ni\mathrm{Al}-\mathrm{Co}-\mathrm{Cr}-\mathrm{Fe}-\mathrm{Ni} 高熵合金的摩擦学特性。R-tec 美国摩擦试验机（图 2）用于评估材料的摩擦学特性。摩擦试验机由一个旋转台组成，旋转台可以修改为以固定转速旋转。承载试样的圆盘固定在平台上，摩擦臂在平台上方静止不动。摩擦臂的末端是一个夹具，夹具上有一个与圆盘中心偏移 20 毫米的插销试样。可在圆盘周围注入润滑剂或油，使其浸没，并在摩擦臂上安装一个传感器，以测量圆盘旋转时的摩擦阻力。伺服电机用于加载测试样本，计算机控制的软件运行测试设备，持续监测和记录所遇到的摩擦。
Table 3 Experimental test conditions
表 3 实验测试条件
S. No. S.编号 Normal force (N) 法向力（牛顿） Condition 条件 Test duration (min) 测试时间（分钟） RPM Temperature ( ∘ C ) ∘ C (^(@)C)\left({ }^{\circ} \mathrm{C}\right) 温度 ( ∘ C ) ∘ C (^(@)C)\left({ }^{\circ} \mathrm{C}\right)
1 50 Dry 干燥 30 200 25 ± 2 25 ± 2 25+-225 \pm 2
2 100 Dry 干燥 30 200 25 ± 2 25 ± 2 25+-225 \pm 2
3 150 Dry 干燥 30 200 25 ± 2 25 ± 2 25+-225 \pm 2
4 200 Dry 干燥 30 200 25 ± 2 25 ± 2 25+-225 \pm 2
5 50 Mineral oil 矿物油 30 200 25 ± 2 25 ± 2 25+-225 \pm 2
6 100 Mineral oil 矿物油 30 200 25 ± 2 25 ± 2 25+-225 \pm 2
7 150 Mineral oil 矿物油 30 200 25 ± 2 25 ± 2 25+-225 \pm 2
8 200 Mineral oil 矿物油 30 200 25 ± 2 25 ± 2 25+-225 \pm 2
9 50 Synthetic oil 合成机油 30 200 25 ± 2 25 ± 2 25+-225 \pm 2
10 100 Synthetic oil 合成机油 30 200 25 ± 2 25 ± 2 25+-225 \pm 2
11 150 Synthetic oil 合成机油 30 200 25 ± 2 25 ± 2 25+-225 \pm 2
12 200 Synthetic oil 合成机油 30 200 25 ± 2 25 ± 2 25+-225 \pm 2
13 50 Vegetable oil 植物油 30 200 25 ± 2 25 ± 2 25+-225 \pm 2
14 100 Vegetable oil 植物油 30 200 25 ± 2 25 ± 2 25+-225 \pm 2
15 150 Vegetable oil 植物油 30 200 25 ± 2 25 ± 2 25+-225 \pm 2
16 200 Vegetable oil 植物油 30 200 25 ± 2 25 ± 2 25+-225 \pm 2
S. No. Normal force (N) Condition Test duration (min) RPM Temperature (^(@)C) 1 50 Dry 30 200 25+-2 2 100 Dry 30 200 25+-2 3 150 Dry 30 200 25+-2 4 200 Dry 30 200 25+-2 5 50 Mineral oil 30 200 25+-2 6 100 Mineral oil 30 200 25+-2 7 150 Mineral oil 30 200 25+-2 8 200 Mineral oil 30 200 25+-2 9 50 Synthetic oil 30 200 25+-2 10 100 Synthetic oil 30 200 25+-2 11 150 Synthetic oil 30 200 25+-2 12 200 Synthetic oil 30 200 25+-2 13 50 Vegetable oil 30 200 25+-2 14 100 Vegetable oil 30 200 25+-2 15 150 Vegetable oil 30 200 25+-2 16 200 Vegetable oil 30 200 25+-2| S. No. | Normal force (N) | Condition | Test duration (min) | RPM | Temperature $\left({ }^{\circ} \mathrm{C}\right)$ | | :---: | :---: | :---: | :---: | :---: | :---: | | 1 | 50 | Dry | 30 | 200 | $25 \pm 2$ | | 2 | 100 | Dry | 30 | 200 | $25 \pm 2$ | | 3 | 150 | Dry | 30 | 200 | $25 \pm 2$ | | 4 | 200 | Dry | 30 | 200 | $25 \pm 2$ | | 5 | 50 | Mineral oil | 30 | 200 | $25 \pm 2$ | | 6 | 100 | Mineral oil | 30 | 200 | $25 \pm 2$ | | 7 | 150 | Mineral oil | 30 | 200 | $25 \pm 2$ | | 8 | 200 | Mineral oil | 30 | 200 | $25 \pm 2$ | | 9 | 50 | Synthetic oil | 30 | 200 | $25 \pm 2$ | | 10 | 100 | Synthetic oil | 30 | 200 | $25 \pm 2$ | | 11 | 150 | Synthetic oil | 30 | 200 | $25 \pm 2$ | | 12 | 200 | Synthetic oil | 30 | 200 | $25 \pm 2$ | | 13 | 50 | Vegetable oil | 30 | 200 | $25 \pm 2$ | | 14 | 100 | Vegetable oil | 30 | 200 | $25 \pm 2$ | | 15 | 150 | Vegetable oil | 30 | 200 | $25 \pm 2$ | | 16 | 200 | Vegetable oil | 30 | 200 | $25 \pm 2$ |
Fig. 2 Experimental Setup.
图 2 实验装置
The test specimens (pin and disc) were coded and then inspected to ensure that the surfaces were consistent. The specimens were forced together for 3-5 minutes under a weight of 25 − 30 N 25 − 30 N 25-30N25-30 \mathrm{~N} to obtain a full contact area between the pin and plates. Following that, the parts were cleaned with a solvent and dried in an oven to remove grease, oil, and dirt. Finally, the specimens were weighed to the fourth decimal place of a gram in the laboratory. The pins and plates were reinstalled and full area contact was verified. Once contact was established, the pins were loaded and the experiments were carried out under the specified conditions. Following completion, the pins and plates were removed, cleaned with a solvent, and placed in an oven to eliminate any remaining wear debris. The specimens were then weighed on laboratory weighing machine to elucidate their weight loss and wear rate. Data acquisition software was used to monitor and record the friction force. Each experiment was carried out three times to verify data repeatability and reproducibility.
对测试样本（针和圆盘）进行编码，然后进行检查，以确保表面一致。在 25 − 30 N 25 − 30 N 25-30N25-30 \mathrm{~N} 重量的作用下，将试样压在一起 3-5 分钟，以获得针和盘之间的完整接触区域。然后，用溶剂清洗部件，并在烘箱中烘干，以去除油脂、油渍和污垢。最后，在实验室对试样进行称重，精确到小数点后第四位。重新安装销钉和板，并验证全面积接触。一旦建立了接触，就装上销钉，并在规定的条件下进行实验。实验结束后，取下插销和插板，用溶剂清洗干净，然后放入烘箱中，以消除任何残留的磨损碎屑。然后在实验室称重机上对试样进行称重，以确定其重量损失和磨损率。数据采集软件用于监测和记录摩擦力。每个实验进行三次，以验证数据的重复性和再现性。

2.3 ANN based modelling 2.3 基于 ANN 的建模

The ANN model was developed using experimental data from a pin-on-disc tribo-tester, and it was then optimised using a Genetic Algorithm (GA), with the ANN model serving as the objective function. Experiments were carried out in order to determine the optimal lubricant for a particular HEA alloy by examining the coefficient of friction and roughness of
ANN 模型是利用针盘摩擦试验机的实验数据建立的，然后利用遗传算法（GA）对其进行优化，并将 ANN 模型作为目标函数。为了确定适用于特定 HEA 合金的最佳润滑剂，我们进行了实验，检查了 HEA 合金的摩擦系数和粗糙度。
computationally developed lubricants. The ANN-based Evolutionary Neural Network (EvoNN) 16 , 17 16 , 17 ^(16,17){ }^{16,17} is used in this work. EvoNN uses a population of neural networks as inputs and genetically evolves the weights and connections through Predator Prey Genetic Algorithm (PPGA) and Linear Least Square (LLSQ) method. 18 18 ^(18){ }^{18} A neural network is an interconnected layer of nodes that resembles neurons in our brain network. The layers are input, hidden, and output layers. The nodes in the layers are interconnected with each other through synapses. The synapses take the value from their input, multiply it with specific weights and biases, and pass the output to different layers. The entire process is repeated until the desired output from the output layer is obtained. The network’s efficiency is determined by the number of connections and nodes it has. A neural network’s hidden layer utilises a transfer/activation function to determine whether or not a neuron should be activated. Depending on the complexity of the problem, there may be numerous hidden layers. These layers use the transfer/activation function to calculate the values needed to determine whether or not to activate the neuron. 19 19 ^(19){ }^{19} The structure of EvoNN can be seen in Fig. 3. In EvoNN, the weights and connections between input and hidden layers were evolved genetically by PPGA. The weights and connections between the hidden and output layers were trained by the LLSQ method to ensure convergence. EvoNN employs a training methodology that computes a Pareto front between network training error and network complexity for a population of networks/models. This allows for a trade-off
计算开发的润滑剂。本研究采用了基于 ANN 的进化神经网络（EvoNN） 16 , 17 16 , 17 ^(16,17){ }^{16,17} 。EvoNN 使用神经网络群体作为输入，并通过捕食者-猎物遗传算法（PPGA）和线性最小平方法（LLSQ）对权重和连接进行遗传进化。 18 18 ^(18){ }^{18} 神经网络是一层层相互连接的节点，类似于我们大脑网络中的神经元。层分为输入层、隐藏层和输出层。层中的节点通过突触相互连接。突触从输入中获取数值，与特定的权重和偏置相乘，然后将输出传递到不同的层。整个过程不断重复，直到从输出层获得所需的输出。网络的效率取决于其连接和节点的数量。神经网络的隐藏层利用传递/激活函数来决定是否激活某个神经元。根据问题的复杂程度，可能会有许多隐藏层。这些层使用传递/激活函数计算所需的值，以确定是否激活神经元。 19 19 ^(19){ }^{19} 图 3 显示了 EvoNN 的结构。在 EvoNN 中，输入层和隐藏层之间的权重和连接是通过 PPGA 基因进化而来的。隐层和输出层之间的权重和连接通过 LLSQ 方法进行训练，以确保收敛。EvoNN 采用的训练方法可以计算出网络训练误差与网络复杂性之间的帕累托前沿。这样就可以权衡
Fig. 3 Structure of evolutionary neural network.
图 3 演化神经网络的结构。
between these two parameters in order to select optimum model. The training is done separately for all objectives, and the optimum final model is chosen using the AICc criterion. 20 20 ^(20){ }^{20}
以选择最佳模型。对所有目标分别进行训练，并使用 AICc 准则选择最优的最终模型。 20 20 ^(20){ }^{20}

3. Results and discussion
3.结果和讨论

After loading the test specimens in the tribotester, the experiments were conducted at different loads and conditions with
在摩擦试验机中对试样加载后，在不同的载荷和条件下进行了试验，试验条件为
time duration and rotational speed of 30 minutes and 200 rpm respectively. The data acquisition system continuously monitors and records the coefficient of friction values during the test. The results obtained during the experiments like friction, wear and surface roughness are discussed in the sections given below.
时间长度和转速分别为 30 分钟和 200 转/分钟。数据采集系统在试验过程中持续监测和记录摩擦系数值。下文将讨论实验过程中获得的摩擦、磨损和表面粗糙度等结果。

3.1 Friction and wear behaviour
3.1 摩擦和磨损行为

Fig. 4 shows the coefficient of friction (COF) curves of Al-CO- Cr − Fe − Ni Cr − Fe − Ni Cr-Fe-Ni\mathrm{Cr}-\mathrm{Fe}-\mathrm{Ni} based high entropy alloy against EN31 steel disc at four loads varying from 50 N to 200 N for dry condition, vegetable oil, mineral oil, and synthetic oil, respectively. It is observed that the COF curves are more fluctuating for the dry condition compared to the three lubricated conditions. This suggests that the presence of lubricants helps in reducing the fluctuations and stabilizing the frictional behavior between the HEA and steel disc. In a general context, the coefficient of friction (COF) exhibits an elevation to a maximal value during the preliminary phases (running-in period) before reaching a steady state. The phenomenon known as the running-in-period can be attributed to the rupture of mechanical bonds or localized welding occurring between the asperities of two interfacing surfaces. 21 − 23 21 − 23 ^(21-23){ }^{21-23} Thus, initially the coefficient of friction remains high in the running period and after sometime it becomes steady as the experiment runs and the average value of the coefficient of friction in the steady state was calculated for each test condition which was known to be steady state average
图 4 显示了基于 Al-CO- Cr − Fe − Ni Cr − Fe − Ni Cr-Fe-Ni\mathrm{Cr}-\mathrm{Fe}-\mathrm{Ni} 的高熵合金与 EN31 钢圆盘在干态、植物油、矿物油和合成油条件下分别承受 50 N 至 200 N 四种载荷时的摩擦系数 (COF) 曲线。据观察，与三种润滑条件相比，干燥条件下的 COF 曲线波动更大。这表明，润滑剂的存在有助于减少波动并稳定 HEA 和钢制圆盘之间的摩擦行为。一般来说，摩擦系数（COF）在达到稳定状态之前的初始阶段（磨合期）会升高到最大值。这种被称为磨合期的现象可归因于机械结合的断裂或两个交界面表面凸面之间发生的局部焊接。 21 − 23 21 − 23 ^(21-23){ }^{21-23} 因此，起初摩擦系数在磨合期保持较高水平，一段时间后随着实验的进行，摩擦系数逐渐趋于稳定。
Fig. 4 Friction coefficient curves of HEA alloy at (50-200 N) for dry condition (a), vegetable oil (b), mineral oil © and synthetic oil (d).
图 4 HEA 合金在（50-200 N）干燥条件下（a）、植物油（b）、矿物油 © 和合成油（d）的摩擦系数曲线。
Fig. 5 Steady state average coefficient of friction (COF) vs. load for each test condition.
图 5 每种测试条件下的稳态平均摩擦系数 (COF) 与负载的关系。
coefficient of friction (CoF). The CoF values reached in steady state after approximately 120-180 s for different test conditions. The steady state average COF is the average of 5000 to 5500 cycles. Fig. 5 presents the steady state average COFs at loads varying from 50 N to 200 N for all four conditions. From this figure, it can be inferred that synthetic oil provides the lowest coefficient of friction across all loads for the HEA and steel disc tribopair. On the other hand, the highest coefficient of friction is observed in the dry condition, where no lubricant is used. Among the lubricants, vegetable oil manifests the highest COF values at all loads.
摩擦系数（CoF）。在不同的测试条件下，CoF 值在大约 120-180 秒后达到稳定状态。稳态平均 COF 是 5000 至 5500 次循环的平均值。图 5 显示了所有四种条件下在 50 N 至 200 N 载荷变化时的稳态平均 COF。从图中可以推断出，在所有负载下，合成油对 HEA 和钢盘摩擦空气的摩擦系数最低。另一方面，在不使用润滑剂的干燥条件下，摩擦系数最高。在所有润滑油中，植物油在所有载荷下的摩擦系数值最高。
In dry conditions, Fig. 6(a) of SEM micrographs shows mild scratches at a load of 50 N . However, at a load of 100 N (Fig. 6(b)), deeper grooves are visible, accompanied by the presence of wear debris being pulled out. This increased wear and debris generation contribute to a higher coefficient of friction (COF) value at the 100 N load. The reason for the increase in COF value with an increase in load is explained as follows: when the load increases, there is a higher quantity of wear debris generated, which is unable to compress adequately between the two mating surfaces. This inability to compress leads to the phenomenon of abrasion and micro cutting, which contribute to increased friction and a higher COF value. This information is supported by ref. 24. However, Fig. 5 shows a decrease in COF values at loads of 150 N and 200 N for all conditions. This decrease can be attributed to the following factors: Increased load results in higher pressure between the mating surfaces. This increased pressure causes more shear strain on the surfaces, which, in turn, leads to an increase in the strength of the material. As a result of this higher strength, there is a decrease in the real area of contact between the surfaces, which leads to a lower COF value. Ref. 25 supports this explanation. With an increase in load, there is also an increase in the temperature between the mating surfaces, generating more frictional heat. The higher temperature contributes to better compression of wear debris. This improved compression
在干燥条件下，SEM 显微照片图 6(a) 显示了 50 N 负载下的轻微划痕。 然而，在 100 N 负载下（图 6(b)），可以看到更深的沟槽，并伴有磨损碎屑被拉出。磨损的加剧和碎屑的产生导致 100 N 负载时摩擦系数 (COF) 值升高。摩擦系数值随载荷增加而增加的原因如下：载荷增加时，产生的磨损碎屑数量增加，无法在两个配合表面之间充分压缩。这种无法压缩的现象会导致磨损和微切削，从而增加摩擦力，提高 COF 值。参考文献 24 证实了这一点。不过，图 5 显示，在所有条件下，当负载为 150 N 和 200 N 时，COF 值都有所下降。这种下降可归因于以下因素：载荷增加导致配合表面之间的压力增加。压力增加会导致表面上的剪切应变增加，进而导致材料强度增加。由于强度增加，表面之间的实际接触面积减小，导致 COF 值降低。参考文献25 支持这一解释。随着载荷的增加，配合表面之间的温度也会升高，从而产生更多的摩擦热。较高的温度有助于更好地压缩磨损碎屑。这种改进的压缩
leads to a reduction in the COF value. Ref. 26 provides support for this statement.
导致 COF 值降低。参考文献26 为这一说法提供了支持。
The primary wear mechanisms observed varies depending on the load and lubrication conditions. In dry conditions, the primary wear mechanism at 50 N and 100 N loads is identified as abrasive wear, as evidenced by Fig. 6(a and b) showing mild scratches and deeper grooves, respectively. However, at 150 N and 200 N loads, the dominant wear mechanism in the dry condition shifts to adhesive wear, which is confirmed by the presence of macroscopic chunks in Fig. 6(c and d). The COF values for all conditions are lower at 150 N and 200 N loads compared to 100 N load. This can be attributed to the increased load causing better compaction of wear debris on the surface. As the load increases, the wear debris becomes more compressed, resulting in reduced friction and lower COF values. Extreme states of sliding contact that eliminate any superficial layers of metal oxide and lubricating films produce metal surfaces that can give rise for substantial adhesion and thus adhesion comes into picture after disruption of oxide films between the sliding surfaces in case of lubricants. 27 27 ^(27){ }^{27} In lubricating conditions, the main wear mechanism observed for all loads is abrasive wear. This is confirmed by the SEM images of worn surfaces for vegetable oil (Fig. 6(e-h)), mineral oil (Fig. 7(a-d)), and synthetic oil (Fig. 7(e-h)). The presence of abrasive wear indicates that the lubricants are not fully preventing direct contact between the mating surfaces, leading to abrasive interactions. In summary, the wear mechanisms observed include abrasive wear and adhesive wear, with the dominant mechanism depending on the load and lubrication conditions. Abrasive wear is prevalent in lubricating conditions, while adhesive wear becomes dominant in the dry condition at higher loads. The compacting of wear debris with increasing load contributes to lower COF values.
观察到的主要磨损机制因载荷和润滑条件而异。图 6（a 和 b）分别显示了轻微的划痕和较深的沟槽，证明在干燥条件下，50 N 和 100 N 载荷的主要磨损机制是磨料磨损。然而，在 150 N 和 200 N 负载下，干燥条件下的主要磨损机制转变为粘着磨损，图 6（c 和 d）中出现的大块磨损证实了这一点。与 100 N 负载相比，150 N 和 200 N 负载下所有条件下的 COF 值都较低。这可能是由于载荷增加导致磨损碎片在表面的压实效果更好。随着载荷的增加，磨损碎屑被压缩得更厉害，从而导致摩擦力减小，COF 值降低。在滑动接触的极端状态下，金属氧化物表层和润滑油膜都会消失，产生的金属表面会产生很大的附着力，因此在润滑油的情况下，滑动表面之间的氧化物膜被破坏后，附着力就会出现。 27 27 ^(27){ }^{27} 在润滑条件下，所有负载的主要磨损机制都是磨料磨损。植物油（图 6(e-h)）、矿物油（图 7(a-d)）和合成油（图 7(e-h)）磨损表面的 SEM 图像证实了这一点。磨料磨损的出现表明，润滑油并没有完全阻止配合表面之间的直接接触，从而导致磨料相互作用。总之，观察到的磨损机制包括磨料磨损和粘着磨损，主要机制取决于载荷和润滑条件。磨料磨损在润滑条件下较为普遍，而粘着磨损则在较高负载的干燥条件下占主导地位。 磨损碎屑随着载荷的增加而压缩，导致 COF 值降低。
Wear tests were conducted for different durations to evaluate wear rates. For the lubricating conditions, the tests were initially performed for 30 minutes, and no wear was reported during this time. To determine the wear rate, extended tests were carried out for 1 hour in dry condition as well as using lubricating oils for 100 N and 200 N loads. The wear rates for mineral oil and vegetable oil for both the loads were found to be almost same i.e. 0.0038 g for 100 N and 0.013 g for 200 N . The wear measurements reported for dry condition and synthetic oil are as follows:
进行了不同持续时间的磨损测试，以评估磨损率。在润滑条件下，测试最初进行了 30 分钟，在此期间没有出现任何磨损。为确定磨损率，在干燥条件下进行了 1 小时的延长试验，并使用润滑油进行了 100 N 和 200 N 负载试验。发现矿物油和植物油在两种负载下的磨损率几乎相同，即 100 N 时为 0.0038 g，200 N 时为 0.013 g。干燥状态和合成油的磨损测量结果如下：
Dry condition: 干燥状态
  • Wear at 100 N load: 0.004 g .
    100 N 负载下的磨损：0.004 g .
  • Wear at 200 N load: 0.016 g .
    200 N 负载时的磨损：0.016 g .
Synthetic oil lubricant: 合成油润滑剂：
  • Wear at 100 N load: 0.003 g .
    100 N 负载下的磨损：0.003 g .
  • Wear at 200 N load: 0.005 g .
    200 N 负载时的磨损：0.005 g .
Based on these measurements, it is clear that the wear values are higher in the dry condition compared to the synthetic oil lubricant for both 100 N and 200 N loads. When comparing the percentage increase in wear from 100 N to 200 N load, the dry condition shows a 300 % 300 % 300%300 \% increase in wear (from 0.004 g to 0.016 g ) g ) g)\mathrm{g}). On the other hand, when using synthetic oil, the percentage increase in wear is 66 % 66 % 66%66 \% (from 0.003 g to 0.005 g ) when the load increases from 100 N to 200 N . These results indicate that the
根据这些测量结果，很明显，与合成油润滑剂相比，在 100 N 和 200 N 载荷下，干燥状态下的磨损值更高。在比较从 100 N 负载到 200 N 负载的磨损增加百分比时，干燥条件下的磨损增加 300 % 300 % 300%300 \% （从 0.004 g 增加到 0.016 g ) g ) g)\mathrm{g}) 。另一方面，使用合成油时，当载荷从 100 N 增加到 200 N 时，磨损百分比增加了 66 % 66 % 66%66 \% （从 0.003 g 增加到 0.005 g）。这些结果表明
Fig. 6 Worn surface morphologies of HEA samples at (50-200 N) for dry state (a-d) and vegetable oil (e-h).
图 6 在 50-200 N 条件下，干态（a-d）和植物油（e-h）HEA 样品的磨损表面形态。
lubricating effect of synthetic oil reduces the wear compared to the dry condition. Moreover, the percentage increase in wear is less pronounced with synthetic oil as the load increases, suggesting that the lubricant helps mitigate the wear rate as the load becomes higher.
与干燥状态相比，合成油的润滑效果降低了磨损。此外，随着载荷的增加，合成油的磨损增加百分比也没有那么明显，这表明随着载荷的增加，润滑油有助于降低磨损率。
The tribo-performance results of the lubricated conditions, as depicted in Fig. 4 and 5 suggests that the composition of the HEA alloy substrate plays a significant role in the interaction
如图 4 和图 5 所示，润滑条件下的三重性能结果表明，HEA 合金基材的成分在相互作用中起着重要作用。
between the alloy and different lubricating oils. The presence of metal elements from the d-block in the HEA alloy substrate, which possess extended covalency and vacant orbitals, tends to interact more strongly with synthetic oil compared to mineral and vegetable oil base stocks. This stronger interaction leads to a reduction in friction at the interface when synthetic oil is used as the lubricant. Furthermore, based on the molecular structure of synthetic oil, which is composed of polymeric
合金与不同润滑油之间的相互作用。由于 HEA 合金基体中含有 d 块金属元素，它们具有扩展共价和空位轨道，因此与矿物油和植物油基础油相比，它们与合成油的相互作用更为强烈。当使用合成油作为润滑剂时，这种更强的相互作用可减少界面摩擦。此外，根据合成油的分子结构，它是由聚合物组成的

MINERAL OIL 矿物油

SYNTHETIC OIL 合成油
Fig. 7 Worn surface morphologies of HEA samples at (50-200 N) using mineral oil (a-d) and synthetic oil (e-h).
图 7 在 50-200 N 条件下使用矿物油（a-d）和合成油（e-h）的 HEA 样品的磨损表面形态。
olefins, it is inferred that a reverse micelle structure is formed with the transition elements Cr , Co Cr , Co Cr,Co\mathrm{Cr}, \mathrm{Co}, and Cu present in the HEA alloy. Synthetic oils with larger molecular size exhibit soft chemical nature and follow the HSAB (Hard-Soft Acid-Base) principle. As a result, soft-soft solid interactions occur, forming a stable lubricating film with synthetic oil. This property of synthetic oils, along with the soft-soft solid interactions and the stable lubricating film formation, leads to a clear
因此可以推断，HEA 合金中的过渡元素 Cr , Co Cr , Co Cr,Co\mathrm{Cr}, \mathrm{Co} 和 Cu 形成了反向胶束结构。分子较大的合成油具有软化学性质，遵循 HSAB（硬-软酸碱）原理。因此，会发生软-软固体相互作用，与合成油形成稳定的润滑油膜。合成油的这一特性，加上软-软固体相互作用和稳定润滑膜的形成，使合成油具有明显的润滑性能。
decreasing trend in the coefficient of friction (COF) with an increase in load. This implies that as the load increases, the COF values decrease when synthetic oil is used as the lubricant. The information provided is supported by ref. 28-30, which likely provide more in-depth explanations and details on the specific properties and interactions mentioned. Overall, the composition of the HEA alloy substrate and the molecular structure of synthetic oil contribute to the strong interaction
随着载荷的增加，摩擦系数（COF）呈下降趋势。这意味着当合成油用作润滑油时，随着载荷的增加，COF 值会降低。参考文献 28-30 提供的信息支持了这一结论，其中可能对所提及的具体特性和相互作用提供了更深入的解释和细节。总之，HEA 合金基材的成分和合成油的分子结构有助于产生强烈的相互作用。
and reduced friction at the interface, resulting in a stable lubricating film formation and a decreasing trend in COF with increasing load.
并减少界面摩擦，从而形成稳定的润滑膜，并使 COF 随负载的增加而呈下降趋势。
On the other hand, mineral oil, which consists of a mixture of Paraffins, Isoparaffins, Olefins, Napthenes, and Aromatics (PIONA), tends to form less stable lubricating films on the HEA alloy. This is attributed to weak interactions between the oil molecules and the alloy surface, as well as the presence of unsaturated sites in the oil composition. These weak interactions result in weaker adsorption of the lubricant on the alloy surface, leading to higher friction. The weak film formation with mineral oil becomes more prominent at higher loads due to the effects of frictional heating. Under increased temperatures, the weak interaction between the alloy and mineral oil can be offset by stronger adsorption of sulfur present in the base stock. The presence of sulfur enhances the lubricating properties by forming a stronger adsorbed layer on the surface, resulting in a reduction in friction as the load increases. This suggests that the unsaturated sites and sulfur in mineral oil can better withstand higher stresses compared to vegetable oils. In contrast, vegetable oil exhibits the highest friction when used as a lubricant with the HEA alloy. This can be attributed to the long chain and ester moieties present in vegetable oil, which tend to form weak interfacial films. As a result, the interaction between the vegetable oil and the HEA alloy is poor, leading to greater fluctuations in friction values with increasing load. The explanation provided sheds light on the differences in performance observed with different lubricants, including mineral oil and vegetable oil, when used with the HEA alloy. It highlights the importance of the composition and properties of the lubricating oils in influencing the interfacial interactions and friction behavior.
另一方面，由石蜡、异构烷烃、烯烃、环烷烃和芳烃（PIONA）混合物组成的矿物油往往无法在 HEA 合金上形成稳定的润滑膜。这归因于油分子与合金表面之间的微弱相互作用，以及油成分中不饱和位点的存在。这些微弱的相互作用导致润滑油在合金表面的吸附力减弱，从而导致摩擦力增大。由于摩擦加热的影响，矿物油的弱油膜形成在较高负载下变得更加突出。在温度升高的情况下，合金与矿物油之间的微弱相互作用会被基础油中的硫吸附力所抵消。硫的存在可在表面形成更强的吸附层，从而增强润滑性能，导致摩擦力随着负荷的增加而减小。这表明，与植物油相比，矿物油中的不饱和位点和硫能更好地承受更大的应力。相比之下，植物油在用作 HEA 合金的润滑剂时摩擦力最大。这可能是由于植物油中的长链和酯分子容易形成薄弱的界面膜。因此，植物油与 HEA 合金之间的相互作用较差，导致摩擦值随着负荷的增加而波动较大。所提供的解释说明了不同润滑油（包括矿物油和植物油）与 HEA 合金一起使用时的性能差异。它强调了润滑油的成分和特性在影响界面相互作用和摩擦行为方面的重要性。
The SEM micrographs of the wear obtained under lubricated conditions, as depicted in Fig. 6 and 7, provide valuable insights into the wear modes and film stability of the HEA substrate when lubricated with different oils. When the HEA substrate is lubricated with vegetable oil, the SEM micrographs suggest that a better film stability is achieved compared to mineral oil. Under increasing load conditions, mild abrasion is observed, indicating a smoother wear mode. On the other hand, when mineral oil is used as the lubricant, deep ploughing is observed under similar load conditions, indicating a more severe wear mode. This difference in wear behavior can be attributed to the alloy composition of the HEA, which forms a compatible lubricating film with vegetable oil compared to mineral oil. 31 , 32 31 , 32 ^(31,32){ }^{31,32} The compatibility of the HEA alloy with vegetable oil contributes to better film stability and reduces the severity of wear. In the case of synthetic oil, the SEM micrograph suggests that the film-forming ability of synthetic oil with the HEA substrate is stronger than mineral and vegetable oil. The synthetic oil exhibits strong adsorption over the HEA substrate, leading to reduced wear loss at the interface and demonstrating better antiwear performance under different load conditions. This indicates that synthetic oil offers excellent compatibility with the HEA substrate and forms a robust lubricating film, resulting in improved wear resistance. The wear attributes observed in the SEM micrographs align with the friction results obtained,
如图 6 和图 7 所示，在润滑条件下获得的磨损扫描电镜显微照片为了解 HEA 基底在使用不同油润滑时的磨损模式和油膜稳定性提供了宝贵的信息。用植物油润滑 HEA 基底时，SEM 显微照片表明，与矿物油相比，薄膜稳定性更好。在负载增加的条件下，可观察到轻微的磨损，表明磨损模式更平滑。另一方面，当使用矿物油作为润滑剂时，在类似的负载条件下会观察到深坑，表明磨损模式更为严重。磨损行为的这种差异可归因于 HEA 的合金成分，与矿物油相比，HEA 可与植物油形成兼容的润滑膜。 31 , 32 31 , 32 ^(31,32){ }^{31,32} HEA合金与植物油的相容性有助于提高油膜的稳定性，降低磨损的严重程度。就合成油而言，SEM 显微照片表明，合成油与 HEA 基材的成膜能力强于矿物油和植物油。合成油对 HEA 基底的吸附力很强，从而减少了界面处的磨损，并在不同负载条件下表现出更好的抗磨损性能。这表明合成油与 HEA 基底具有良好的兼容性，能形成坚固的润滑膜，从而提高耐磨性。在扫描电镜显微照片中观察到的磨损属性与获得的摩擦结果一致、
indicating a correlation between wear and friction performance. The compatibility and film-forming ability of the lubricants with the HEA substrate play a crucial role in determining the wear modes and overall performance. The information provided is supported by ref. 33 and 34 , which likely offer further details and explanations regarding the wear modes, film stability, and compatibility between lubricants and the HEA substrate. Overall, the SEM micrographs of the wear and the observed wear attributes validate the obtained friction results, highlighting the importance of lubricant compatibility and film formation in influencing the wear behavior of the HEA substrate.
表明磨损与摩擦性能之间存在关联。润滑油与 HEA 基底的兼容性和成膜能力在决定磨损模式和整体性能方面起着至关重要的作用。参考文献33 和 34 提供了更多有关磨损模式、薄膜稳定性以及润滑剂与 HEA 基底之间相容性的详细信息和解释。总之，磨损的 SEM 显微照片和观察到的磨损属性验证了获得的摩擦结果，突出了润滑剂兼容性和薄膜形成在影响 HEA 基底磨损行为方面的重要性。

3.2 Surface roughness 3.2 表面粗糙度

Surface roughness is the parameter that can affect the frictional values and the wear rate of the mating parts. Fig. 8 states that as the load increases from 50 N to 200 N , the average surface roughness (Ra) exhibits an increasing trend for all four conditions.
表面粗糙度是影响摩擦值和配合部件磨损率的参数。图 8 显示，当载荷从 50 牛增加到 200 牛时，所有四种条件下的平均表面粗糙度（Ra）都呈上升趋势。
The conditions mentioned include dry conditions, usage of synthetic oil, and vegetable oil. The highest values of surface roughness are reported for dry conditions, while the usage of synthetic oil yields the lowest values of average surface roughness for all four loads. Among the three lubricants mentioned, vegetable oil shows high values of surface roughness (Ra). Fig. 9 and 10 provide 3D roughness images of the HEA samples for all the conditions, which further support the observations made regarding surface roughness. When the average surface roughness is higher, the retention of wear debris on the surface increases, which is responsible for a decrease in the coefficient of friction. In other words, increased surface roughness can contribute to higher wear rates and affect the frictional behavior of the mating parts. 35 35 ^(35){ }^{35}
提到的条件包括干燥条件、使用合成油和植物油。干燥条件下的表面粗糙度值最高，而在所有四种负载条件下，使用合成油产生的平均表面粗糙度值最低。在上述三种润滑油中，植物油的表面粗糙度 (Ra) 值较高。图 9 和图 10 提供了 HEA 样品在所有条件下的三维粗糙度图像，进一步证实了有关表面粗糙度的观察结果。当平均表面粗糙度较高时，磨损碎片在表面上的滞留会增加，从而导致摩擦系数下降。换句话说，表面粗糙度的增加会导致更高的磨损率，并影响配合部件的摩擦行为。 35 35 ^(35){ }^{35}

4. ANN approach to validate the results
4.验证结果的 ANN 方法

An ANN-based approach known as EvoNN 36 − 38 36 − 38 ^(36-38){ }^{36-38} is used in the modelling work to generate the prediction model for the
在建模工作中，使用了一种称为 EvoNN 36 − 38 36 − 38 ^(36-38){ }^{36-38} 的基于 ANN 的方法来生成预测模型。
Fig. 8 Surface roughness (Ra) of HEA vs. load for each test condition.
图 8 每种测试条件下 HEA 的表面粗糙度 (Ra) 与载荷的关系。

DRY 干燥

VEGETABLE OIL 植物油
Fig. 9 3D surface roughness maps of HEA samples at ( 50 − 100 N ) ( 50 − 100 N ) (50-100N)(50-100 \mathrm{~N}) for dry state ( a − d ) ( a − d ) (a-d)(a-d) and vegetable oil (e-h).
图 9 干态 ( a − d ) ( a − d ) (a-d)(a-d) 和植物油（e-h）在 ( 50 − 100 N ) ( 50 − 100 N ) (50-100N)(50-100 \mathrm{~N}) 时 HEA 样品的三维表面粗糙度图。
objectives like COF and roughness for Al-Co-Cr-Fe-Ni high entropy alloy. The data are collected from the tribological experiment to generate a data-driven model. In the experiment process, 16 experiments are carried out at four different load and lubricating conditions. The load is between 50 to 200 N ,
高熵合金的 COF 和粗糙度等目标。从摩擦学实验中收集数据，生成数据驱动模型。在实验过程中，在四种不同的载荷和润滑条件下进行了 16 次实验。载荷在 50 到 200 N 之间、
and four other lubricating conditions, like dry, vegetable oil, mineral oil, and synthetic oils, are used in the process. The COF and Roughness values generated in this work are shown in Table 4.
和其他四种润滑条件，如干油、植物油、矿物油和合成油。表 4 列出了在这项工作中产生的 COF 值和粗糙度值。

MINERAL OIL 矿物油

SYNTHETIC OIL 合成油
Fig. 10 3D surface roughness maps of HEA samples at 50-200 N using mineral oil (a-d) and synthetic oil (e-h).
图 10 在 50-200 N 条件下使用矿物油（a-d）和合成油（e-h）的 HEA 样品的三维表面粗糙度图。
EvoNN employs an evolutionary training approach where key mechanisms such as crossover, mutation, and selection are pivotal in capturing precise data trends. This method excels in modeling small, highly nonlinear datasets due to its inherent self-evolution capabilities, which minimize error using a Pred-ator-Prey Genetic Algorithm (PPGA). This distinguishes EvoNN from conventional ANN-based algorithms by its ability to iteratively refine the model, ensuring superior accuracy in complex data scenarios. This approach is applied to all the data, where
EvoNN 采用了一种进化训练方法，其中交叉、突变和选择等关键机制在捕捉精确数据趋势方面起着举足轻重的作用。这种方法因其固有的自我进化能力而在小型、高度非线性数据集建模方面表现出色，它利用 "先行者-猎物 "遗传算法（PPGA）将误差最小化。EvoNN 有别于传统的基于 ANN 的算法，它能够迭代完善模型，确保在复杂的数据场景中保持卓越的准确性。这种方法适用于所有数据，其中
the COF and the surface roughness are played a significant role in the tribological application, where both the objectives play a major role and provide better lubricating conditions and
COF 和表面粗糙度在摩擦学应用中起着重要作用，这两个目标在摩擦学应用中都发挥着重要作用，并提供更好的润滑条件和更高的表面粗糙度。
Table 4 The COF and roughness results generate from the experiment
表 4 实验得出的 COF 和粗糙度结果
COF (Y1) Roughness (Y2) 粗糙度 (Y2)
0.0165 − 0.6024 0.0165 − 0.6024 0.0165-0.60240.0165-0.6024 0.261 − 1.11 0.261 − 1.11 0.261-1.110.261-1.11
COF (Y1) Roughness (Y2) 0.0165-0.6024 0.261-1.11| COF (Y1) | Roughness (Y2) | | :--- | :--- | | $0.0165-0.6024$ | $0.261-1.11$ |

Hidden Nodes 隐藏节点

Fig. 11 Neural network architecture.
图 11 神经网络架构
control the COF for better performance during the working condition. Two different models are generated by considering the above data. To generate the best model, the optimum parameters are considered. EvoNN is a tried and tested method used largely in the modelling process, basically in alloy design, chemical synthesis process, mechanical properties modelling, and deforming process. 39 39 ^(39){ }^{39} In the modelling process, neural networks are connected between inputs like load (X1) and lubricating condition (X2) and the hidden nodes. Different weightage values are given to each connection, varying between 0 and 1. The input process value transfers from input to hidden nodes and is stored in the hidden nodes where the error reduction occurs; the detailed working process is described elsewhere. 18 18 ^(18){ }^{18} The EvoNN evolution process is carried out in the lower part of the network, i.e., between the input and the hidden layer. The upper part of the algorithm linear list squired (LLSQ) method 19 19 ^(19){ }^{19} is used for convergence purpose. EvoNN uses a linear transfer function for output nodes. The optimized input from the lower portion significantly improves the output by gradientbased solver procedure. By using LLSQ, mathematical convergence is possible at the output stage. The detailed architecture of the network is shown in Fig. 11. Here, one hidden layer along with 7 optimum hidden nodes are considered to generate the optimum model.
控制 COF，以提高工作状态下的性能。根据上述数据生成了两个不同的模型。为了生成最佳模型，需要考虑最佳参数。EvoNN 是一种久经考验的建模方法，主要用于合金设计、化学合成过程、机械性能建模和变形过程。 39 39 ^(39){ }^{39} 在建模过程中，神经网络连接负载 (X1) 和润滑条件 (X2) 等输入和隐藏节点。输入的过程值从输入节点转移到隐藏节点，并存储在隐藏节点中，在隐藏节点中发生误差减小；详细的工作过程将在其他地方进行描述。 18 18 ^(18){ }^{18} EvoNN演化过程在网络下部进行，即在输入层和隐藏层之间。 19 19 ^(19){ }^{19} 算法的上半部分使用线性列表平方（LLSQ）方法进行收敛。EvoNN 对输出节点使用线性传递函数。通过基于梯度的求解程序，来自下部的优化输入可显著改善输出。通过使用 LLSQ，可以在输出阶段实现数学收敛。网络的详细结构如图 11 所示。在这里，一个隐藏层和 7 个最佳隐藏节点被视为生成最佳模型。
The optimum parameters are decided by considering necessary changes in the input side, i.e., in the lower part of the network, where evolution takes place. Evolution processes like selection, crossover, and mutation are carried out in each generation with the help of a predator-prey genetic algorithm. 39 39 ^(39){ }^{39} The RSME error of the objective changes in each generation, and finally, a Pareto trade-off is generated between accuracy and
最佳参数是通过考虑输入端（即网络下部）的必要变化来决定的，网络下部是进化发生的地方。在捕食者-猎物遗传算法的帮助下，每一代都会进行选择、交叉和变异等进化过程。 39 39 ^(39){ }^{39} 目标的 RSME 误差在每一代中都会发生变化，最后在精确度和目标之间进行帕累托权衡。
complexity. Multiple models are generated through this process, out of which one is chosen by considering the corrected Akaike information criterion 40 40 ^(40){ }^{40} into the account. The various input parameters like the number of generations, hidden nodes, killing interval, numbers of predators and prey, crossover, and mutation factors generate the number of models. 41 41 ^(41){ }^{41} The initial parameters for this work are shown in Table 5.
复杂性。通过这个过程会生成多个模型，在考虑修正后的 Akaike 信息准则 40 40 ^(40){ }^{40} 后从中选出一个模型。各种输入参数，如代数、隐藏节点、杀戮间隔、捕食者和猎物的数量、交叉和突变因子，都会产生模型的数量。 41 41 ^(41){ }^{41} 这项工作的初始参数如表 5 所示。
The process is continued with all the changes after number iteration and combination changes; a time will come when values are stagnated, and no more variation is noticed in error reduction results. These parameters are considered optimum parameters for the particular work. The optimum parameters with the best-fitted training error considered for this work are shown in Table 6.
迭代次数和组合变化后，继续进行所有变化；当数值停滞时，误差减小结果将不再有变化。这些参数被认为是特定工作的最佳参数。表 6 列出了本研究采用的具有最佳拟合训练误差的最佳参数。
After the output is modeled against such parameters and the training models are generated with respect to these inputs, the training curves are properly analyzed. The best training models, already described in the table, with COF value for the training model, is 0.02742 and for roughness is 0.0263 , having the best model with the least error and higher accuracy. The optimum
根据这些参数对输出进行建模并生成与这些输入相关的训练模型后，对训练曲线进行适当分析。最佳训练模型已在表中说明，训练模型的 COF 值为 0.02742，粗糙度的 COF 值为 0.0263，是误差最小、精度最高的最佳模型。最佳
Table 5 Training parameters used in the modelling work
表 5 模拟工作中使用的训练参数
Parameters 参数 EvoNN
Hidden nodes 隐藏节点 5 , 7 , 10 5 , 7 , 10 5,7,105,7,10
Max rank 最高等级 10 , 15 , 20 10 , 15 , 20 10,15,2010,15,20
Number of preys 猎物数量 500
Number of 数量 50
predators 掠食者
Grit size 砂粒大小 60 × 60 60 × 60 60 xx6060 \times 60
No of generations 世代数 50 , 75 , 100 50 , 75 , 100 50,75,10050,75,100
Parameters EvoNN Hidden nodes 5,7,10 Max rank 10,15,20 Number of preys 500 Number of 50 predators Grit size 60 xx60 No of generations 50,75,100| Parameters | EvoNN | | :--- | :--- | | Hidden nodes | $5,7,10$ | | Max rank | $10,15,20$ | | Number of preys | 500 | | Number of | 50 | | predators | | | Grit size | $60 \times 60$ | | No of generations | $50,75,100$ |
Table 6 Optimum parameters used in the training work
表 6 训练工作中使用的最佳参数
Model 模型 Generation 一代人 Model structure (hidden nodes)
模型结构（隐藏节点）		 COF (Y1)
EvoNN 100 7 0.02742
Model Generation Model structure (hidden nodes) COF (Y1) EvoNN 100 7 0.02742| Model | Generation | Model structure (hidden nodes) | COF (Y1) | | :--- | :--- | :--- | :--- | :--- | | EvoNN | 100 | 7 | 0.02742 |
training models are shown in Fig. 12 with a red circle in the Pareto front.
图 12 显示了帕累托前沿的红色圆圈。
One of the most significant works in the training process knows the input parameters’ exact behavior. Single Variable Response (SVR), 41 41 ^(41){ }^{41} which is incorporated into the algorithm, gives a clear idea regarding the individual response with respect to the output. The input-like load shows the effect on the output parameter like COF and the roughness with continuous changes in the input side. This provides a clear idea of + v e , − v e + v e , − v e +ve,-ve+v e,-v e, mixed, and no response criteria of individual objectives. The single-variable responses are shown in Fig. 13.
训练过程中最重要的工作之一是了解输入参数的确切行为。算法中的单变量响应（SVR） 41 41 ^(41){ }^{41} 清楚地显示了与输出相关的单个响应。类输入负载显示了输入端连续变化对 COF 和粗糙度等输出参数的影响。这让人清楚地了解到各个目标的 + v e , − v e + v e , − v e +ve,-ve+v e,-v e 、混合和无响应标准。单变量响应如图 13 所示。
The slope of fitting and the Root Mean Squared Error is vital to know the difference between experimental results and the prediction results generated from the trained models. The slope of fitting and the training results for the COF and roughness are shown in Fig. 14.
拟合斜率和均方根误差对于了解实验结果与训练模型生成的预测结果之间的差异至关重要。COF 和粗糙度的拟合斜率和训练结果如图 14 所示。
The training results, which are generated from the optimum models, are compared with the experimental results. The fitting slope between the experimental COF and the predicted COF is
由最优模型生成的训练结果与实验结果进行了比较。实验 COF 与预测 COF 的拟合斜率为
evaluated as 0.94 , and the slope between the experimental roughness and the predicted roughness is 0.98 . This slope of fitting and the training indicate that the results neither under fitting nor over fitting with the experimental data. The root mean squared error is calculated for COF and the roughness. The above results are shown in Tables 7 and 8.
这一拟合斜率和训练表明，结果与实验数据既没有拟合不足，也没有拟合过度。计算了 COF 和粗糙度的均方根误差。上述结果如表 7 和表 8 所示。
Based on the information provided, it can be concluded that the error between the experimental and predicted results is significantly low, indicating a high prediction accuracy of the model. The testing results closely align with the model’s predictions. The values used in the modelling process were generated under similar conditions to those in the experimental method. Furthermore, the behaviour of the coefficient of friction (COF) in both the experimental and modelling work followed a similar pattern. It increased up to a 100 N load and then decreased at 200 N . This similarity suggests that the model accurately captured the relationship between the COF and the load conditions. Similarly, the roughness responses observed in both the modelling and experimental processes exhibited
根据所提供的信息，可以得出结论：实验结果与预测结果之间的误差非常小，表明模型的预测准确度很高。测试结果与模型的预测结果非常吻合。建模过程中使用的数值是在与实验方法类似的条件下产生的。此外，摩擦系数（COF）在实验和建模过程中的表现也类似。摩擦系数在 100 牛顿载荷时增大，在 200 牛顿载荷时减小。这种相似性表明，模型准确地捕捉到了 COF 与负载条件之间的关系。同样，在建模和实验过程中观察到的粗糙度反应也表现出以下特征

Fig. 12 Training models generated by using optimal parameters.
图 12 使用最佳参数生成的训练模型。

Fig. 13 Single variable responses of output with the input.
图 13 输出与输入的单变量响应。
Fig. 14 Slope of fitting and the training results for the COF and roughness.
图 14 COF 和粗糙度的拟合斜率和训练结果。
Table 7 RMSE results evaluated for COF
表 7 COF 的均方根误差评估结果
Experimental COF 实验性 COF Predicted COF 预测 COF RMSE
0.2904 0.3436 0.0532
0.6024 0.5145 0.0879
0.348 0.3783 0.0303
0.4252 0.4334 0.0082
0.0459 0.0279 0.0180
0.1633 0.1988 0.0355
0.081 0.0626 0.0184
0.1327 0.1177 0.0150
0.0345 0.0267 0.0078
0.0987 0.1442 0.0455
0.0165 0.0080 0.0085
0.023 0.0631 0.0401
0.0833 0.1108 0.0275
0.2759 0.2817 0.0058
0.153 0.1455 0.0075
0.23 0.2006 0.0294
Average 平均
error = 0.02741 = 0.02741 =0.02741=0.02741 错误 = 0.02741 = 0.02741 =0.02741=0.02741
Experimental COF Predicted COF RMSE 0.2904 0.3436 0.0532 0.6024 0.5145 0.0879 0.348 0.3783 0.0303 0.4252 0.4334 0.0082 0.0459 0.0279 0.0180 0.1633 0.1988 0.0355 0.081 0.0626 0.0184 0.1327 0.1177 0.0150 0.0345 0.0267 0.0078 0.0987 0.1442 0.0455 0.0165 0.0080 0.0085 0.023 0.0631 0.0401 0.0833 0.1108 0.0275 0.2759 0.2817 0.0058 0.153 0.1455 0.0075 0.23 0.2006 0.0294 Average error =0.02741| Experimental COF | Predicted COF | RMSE | | :--- | :--- | :--- | | 0.2904 | 0.3436 | 0.0532 | | 0.6024 | 0.5145 | 0.0879 | | 0.348 | 0.3783 | 0.0303 | | 0.4252 | 0.4334 | 0.0082 | | 0.0459 | 0.0279 | 0.0180 | | 0.1633 | 0.1988 | 0.0355 | | 0.081 | 0.0626 | 0.0184 | | 0.1327 | 0.1177 | 0.0150 | | 0.0345 | 0.0267 | 0.0078 | | 0.0987 | 0.1442 | 0.0455 | | 0.0165 | 0.0080 | 0.0085 | | 0.023 | 0.0631 | 0.0401 | | 0.0833 | 0.1108 | 0.0275 | | 0.2759 | 0.2817 | 0.0058 | | 0.153 | 0.1455 | 0.0075 | | 0.23 | 0.2006 | 0.0294 | | | | Average | | | | error $=0.02741$ |
a similar pattern. The figures depicting these responses are shown in Fig. 13. Overall, the close alignment between the experimental and predicted results, as well as the similarities in the observed patterns for both the COF and roughness, indicate a high level of agreement between the model and the real-world behaviour of the system being studied.
类似的模式。图 13 显示了这些响应。总体而言，实验结果和预测结果之间的密切吻合，以及对 COF 和粗糙度的观察模式的相似性，表明模型与所研究系统的实际行为之间具有很高的一致性。
Table 8 RMSE results evaluated for roughness
表 8 粗糙度的 RMSE 评估结果
Experimental roughness 实验粗糙度 Predicted roughness 预测粗糙度 RMSE
0.843 0.8315 0.0115
0.889 0.9043 0.0153
1.08 1.0532 0.0268
1.11 1.1352 0.0252
0.436 0.4224 0.0136
0.521 0.5201 0.0009
0.738 0.7149 0.0231
0.793 0.8241 0.0311
0.261 0.2785 0.0175
0.36 0.4233 0.0633
0.689 0.6371 0.0519
0.731 0.7080 0.0230
0.488 0.4839 0.0041
0.693 0.6387 0.0543
0.778 0.8098 0.0318
0.817 0.8419 0.0249
Average 平均
error = 0.02614 = 0.02614 =0.02614=0.02614 错误 = 0.02614 = 0.02614 =0.02614=0.02614
Experimental roughness Predicted roughness RMSE 0.843 0.8315 0.0115 0.889 0.9043 0.0153 1.08 1.0532 0.0268 1.11 1.1352 0.0252 0.436 0.4224 0.0136 0.521 0.5201 0.0009 0.738 0.7149 0.0231 0.793 0.8241 0.0311 0.261 0.2785 0.0175 0.36 0.4233 0.0633 0.689 0.6371 0.0519 0.731 0.7080 0.0230 0.488 0.4839 0.0041 0.693 0.6387 0.0543 0.778 0.8098 0.0318 0.817 0.8419 0.0249 Average error =0.02614| Experimental roughness | Predicted roughness | RMSE | | :--- | :--- | :--- | | 0.843 | 0.8315 | 0.0115 | | 0.889 | 0.9043 | 0.0153 | | 1.08 | 1.0532 | 0.0268 | | 1.11 | 1.1352 | 0.0252 | | 0.436 | 0.4224 | 0.0136 | | 0.521 | 0.5201 | 0.0009 | | 0.738 | 0.7149 | 0.0231 | | 0.793 | 0.8241 | 0.0311 | | 0.261 | 0.2785 | 0.0175 | | 0.36 | 0.4233 | 0.0633 | | 0.689 | 0.6371 | 0.0519 | | 0.731 | 0.7080 | 0.0230 | | 0.488 | 0.4839 | 0.0041 | | 0.693 | 0.6387 | 0.0543 | | 0.778 | 0.8098 | 0.0318 | | 0.817 | 0.8419 | 0.0249 | | | | Average | | | | error $=0.02614$ |

5. Conclusion 5.结论

  • The research work aimed to investigate the tribological behavior of an Al − Co − Cr − Fe − Ni Al − Co − Cr − Fe − Ni Al-Co-Cr-Fe-Ni\mathrm{Al}-\mathrm{Co}-\mathrm{Cr}-\mathrm{Fe}-\mathrm{Ni} high entropy alloy in dry and different lubricating conditions.
    这项研究工作旨在调查一种 Al − Co − Cr − Fe − Ni Al − Co − Cr − Fe − Ni Al-Co-Cr-Fe-Ni\mathrm{Al}-\mathrm{Co}-\mathrm{Cr}-\mathrm{Fe}-\mathrm{Ni} 高熵合金在干燥和不同润滑条件下的摩擦学行为。
  • The study found that using synthetic oil as a lubricant provided better performance compared to other lubricating
    研究发现，与其他润滑油相比，使用合成油作为润滑油能提供更好的性能。
    conditions, as the coefficient of friction was minimized due to extended covalency and the presence of vacant orbitals, which interact strongly in synthetic oil.
    在合成油中，由于共价键的扩展和空位轨道的存在，摩擦系数降到了最低。
  • The study also observed that the wear rate under lubrication was lower compared to dry conditions when tested for 1 hour. The favourable wear resistance was achieved in synthetic oil due to abrasive wear alone and better surface roughness.
    研究还发现，在润滑条件下测试 1 小时，磨损率低于干燥条件下的磨损率。合成油具有良好的耐磨性，这主要归功于单独的磨料磨损和更好的表面粗糙度。
  • In this study an artificial neural network (ANN)-based modelling (EvoNN) is used to validate the results. The accuracy of the trained model for the coefficient of friction was more than 94 % 94 % 94%94 \%, and for roughness, it was 98 % 98 % 98%98 \%.
    本研究使用基于人工神经网络（ANN）的建模（EvoNN）来验证结果。经过训练的模型在摩擦系数方面的精确度大于 94 % 94 % 94%94 \% ，在粗糙度方面的精确度为 98 % 98 % 98%98 \% 。
  • The study concludes that synthetic oil is an important lubrication medium for the Al − Co − Cr − Fe − Ni Al − Co − Cr − Fe − Ni Al-Co-Cr-Fe-Ni\mathrm{Al}-\mathrm{Co}-\mathrm{Cr}-\mathrm{Fe}-\mathrm{Ni} high entropy alloy. All the tribological properties were achieved under loading conditions, and the synthetic oil performed better than other lubricating media.
    研究得出结论，合成油是 Al − Co − Cr − Fe − Ni Al − Co − Cr − Fe − Ni Al-Co-Cr-Fe-Ni\mathrm{Al}-\mathrm{Co}-\mathrm{Cr}-\mathrm{Fe}-\mathrm{Ni} 高熵合金的重要润滑介质。在加载条件下，所有摩擦学特性都得到了实现，而且合成油的性能优于其他润滑介质。
  • The results of this study provide valuable insights into the development of high-performance lubricants for HEAs. By highlighting the benefits of synthetic oil and demonstrating the effectiveness of an ANN-based modeling approach, the research paves the way for future advancements in lubricant design and optimization, ultimately enhancing the tribological performance of HEAs in various industrial applications. The findings derived from the friction coefficient analysis indicate that the neural predictive model possesses the capability to serve as an effective predictor for the frictional and lubrication phenomena observed in the experimental applications associated with the journal bearing. 42 42 ^(42){ }^{42}
    这项研究的结果为开发高性能 HEA 润滑油提供了宝贵的见解。通过强调合成油的优点和展示基于神经网络的建模方法的有效性，本研究为未来润滑油设计和优化的进步铺平了道路，最终提高了 HEA 在各种工业应用中的摩擦学性能。摩擦系数分析得出的结果表明，神经预测模型能够有效预测与轴颈轴承相关的实验应用中观察到的摩擦和润滑现象。 42 42 ^(42){ }^{42}

Data availability 数据可用性

The code which is used in the modelling work is known as newmaster code, can be found at https://github.com/bashista1A/ bashi_code with https://doi.org/10.1016/j.commatsci.2009.04.023, https://doi.org/10.1080/10426914.2014.984203, https://doi.org/ 10.2355/isijinternational.47.1195, https://doi.org/10.1201/ 9781003201045. The version of the code employed for this study is newmaster code. Data and processing scripts for this paper, including friction data are available at https://github.com/ bashista1A/bashi_code. This study is carried out using self experiment data which are generated from the rotating disc Tribo tester experiments only. The data are provided in the manuscript.
建模工作中使用的代码称为 newmaster 代码，可在 https://github.com/bashista1A/ bashi_code 与 https://doi.org/10.1016/j.commatsci.2009.04.023、https://doi.org/10.1080/10426914.2014.984203 、https://doi.org/ 10.2355/isijinternational.47.1195、https://doi.org/10.1201/ 9781003201045。本研究使用的代码版本为 newmaster 代码。本文的数据和处理脚本（包括摩擦数据）可从https://github.com/ bashista1A/bashi_code获取。本研究使用的自我实验数据仅来自旋转盘 Tribo 试验机实验。手稿中提供了这些数据。

Conflicts of interest 利益冲突

The authors declare that they have no conflict of interest.
作者声明他们没有利益冲突。

Acknowledgements 致谢

The Council of Scientific and Industrial Research, New Delhi, provided funding for the current work (HCP-0042). The authors would like to express their sincere gratitude for the generous support provided by the Council of Scientific and Industrial Research, New Delhi. The financial assistance received from CSIR India played a crucial role in facilitating and advancing
新德里科学与工业研究理事会为本研究工作提供了资助（HCP-0042）。作者对新德里科学与工业研究理事会提供的慷慨支持表示衷心感谢。印度科学与工业研究理事会提供的资金援助在促进和推动本研究工作方面发挥了重要作用。
this research project. The authors acknowledge that CSIR’s funding has been instrumental in conducting the study and has significantly contributed to the successful completion of this work.
作者感谢 CSIR 为本研究项目提供的资金。作者承认，CSIR 的资助对本研究的开展起到了重要作用，并为本工作的顺利完成做出了巨大贡献。

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11 F. Pettersson、A. Biswas、P. K. Sen、H. Saxén 和 N. Chakraborti，《Mater.工艺》，2009 年，24 期，320-330 页。
12 F. Pettersson, N. Chakraborti and H. A. Saxén, Appl. Soft Comput., 2007, 70, 387-397.
12 F. Pettersson、N. Chakraborti 和 H. A. Saxén，《应用软计算》，2007，70，387-397。
13 A. S. Mohammed, S. Dodla, J. K. Katiyar and M. A. Samad, Proc. Inst. Mech. Eng., Part J, 2023, 237(4), 943-953.
13 A. S. Mohammed, S. Dodla, J. K. Katiyar and M. A. Samad, Proc. Inst.Eng., Part J, 2023, 237(4), 943-953。
14 D. K. Prajapati, D. Ahmad, J. K. Katiyar, C. Prakash and R. M. Ajaj, Surf. Topogr.: Metrol. Prop., 2023, 11(3), 035006.
14 D. K.Prajapati, D.Ahmad, J. K.Katiyar, C. Prakash and R. M. Ajaj, Surf.Topogr：Metrol.2023, 11(3), 035006.
15 D. K. Prajapati, J. K. Katiyar and C. Prakash, Ind. Lubr. Tribol., 2023, 75(9), 1022-1030.
15 D. K.Prajapati, J. K.Katiyar and C. Prakash, Ind.Lubr.2023，75（9），1022-1030。
16 B. K. Mahanta and N. Chakraborti, Steel Res. Int., 2018, 89(9), 1800121.
16 B. K. Mahanta和N. Chakraborti，《国际钢铁研究》，2018，89（9），1800121。
17 N. Chakraborti, Applications of Metaheuristics in Process Engineering, Springer, Cham, 2014.
17 N. Chakraborti，《过程工程中的元求导应用》，Springer，Cham，2014。
18 B. K. Mahanta, S. Sarkar, P. K. Sen and N. Chakraborti, Can. Metall. Q., 2022, 61(1), 1-13.
18 B. K. Mahanta, S. Sarkar, P. K. Sen and N. Chakraborti, Can.Metall.Q., 2022, 61(1), 1-13.
19 A. Agarwal, F. Pettersson, A. Singh, C. S. Kong, H. Saxén, K. Rajan, S. Iwata and N. Chakraborti, Mater. Manuf. Processes, 2009, 24(3), 274-281.
19 A.Agarwal、F. Pettersson、A. Singh、C. S. Kong、H. Saxén、K. Rajan、S. Iwata 和 N. Chakraborti，Mater.工艺》，2009 年，24（3），274-281。
20 B. K. Mahanta and N. Chakraborti, Mater. Manuf. Processes, 2020, 35(6), 677-686.
20 B. K. Mahanta 和 N. Chakraborti，Mater.工艺》，2020，35（6），677-686。
21 J. K. Katiyar, S. K. Sinha and A. Kumar, Wear, 2016, 362-363, 199-208.
21 J. K. Katiyar、S. K. Sinha 和 A. Kumar，《磨损》，2016，362-363，199-208。
22 V. Goyal, S. K. Sharma and B. V. M. Kumar, Mater. Today: Proc., 2015, 2(4-5), 1082-1091.
22 V. Goyal、S. K. Sharma 和 B. V. M. Kumar，Mater.Today：Proc.，2015，2（4-5），1082-1091。
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23 E. Zanoria、S. Danyluk 和 M. McNallan，《磨损》，1995，181，784-789。
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24 S. Samion、M. I. Ibrahim、N. A. C. Sidik 和 M. N. M. Jaafar，J. Teknol.，2014，66（1），53。
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25 C. F. Tu 和 T. Fort，Tribol.Int.，2004，37（9），701-710。
26 T. C. Ing, A. K. Mohammed Rafiq, Y. Azli and S. Syahrullail, Tribol. Trans., 2012, 55(5), 539-548.
26 T. C. Ing、A. K. Mohammed Rafiq、Y. Azli 和 S. Syahrullail，Tribol.2012，55（5），539-548。
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27 A. W. Batchelor 和 G. W. Stachowiak，《材料加工中的摩擦学》，J. Mater.Process.Technol.，1995，48（1-4），503-515。
28 J. Yan, H. M. Lien and F. Mangolini, Orthoborate Ionic Liquids, 2023.
29 R. Lu, H. Nanao, K. Kobayashi, T. Kubo and S. Mori, J. Jpn. Pet. Inst., 2010, 53(1), 55-60.
29 R. Lu、H. Nanao、K. Kobayashi、T. Kubo 和 S. Mori，J. Jpn.宠物研究所》，2010 年，53（1），55-60。
30 S. M. Hsu, Tribol. Int., 2004, 37(7), 553-559.
30 S. M. Hsu, Tribol.Int.，2004，37（7），553-559。
31 J. M. Martin, C. Grossiord, K. Varlot, B. Vacher and J. Igarashi, Tribol. Lett., 2000, 8, 193-201.
31 J. M. Martin、C. Grossiord、K. Varlot、B. Vacher 和 J. Igarashi，Tribol.Lett., 2000, 8, 193-201.
32 S. M. Hsu and R. S. Gates, Tribol. Int., 2005, 38(3), 305-312.
32 S. M. Hsu 和 R. S. Gates，Tribol.Int., 2005, 38(3), 305-312.
33 S. Zhang, Y. Qiao, Y. Liu, L. Ma and J. Luo, Friction, 2019, 7, 372-387.
33 S. Zhang, Y. Qiao, Y. Liu, L. Ma and J. Luo, Friction, 2019, 7, 372-387。
34 A. A. Khan and M. S. Kaiser, Res. Eng. Struct. Mater., 2023, 9(1), 1-18.
34 A. A. Khan and M. S. Kaiser, Res. Eng.Struct.Mater., 2023, 9(1), 1-18.
35 P. L. Menezes and S. V. Kailas, J. Mater. Process. Technol, 2008, 208(1-3), 372-382.
35 P. L. Menezes 和 S. V. Kailas, J. Mater.Process.Technol，2008，208（1-3），372-382。
36 B. K. Mahanta, R. Jha and N. Chakraborti, in Machine Learning in Industry, Springer, Cham, 2022, 47-81.
36 B. K. Mahanta、R. Jha 和 N. Chakraborti，《工业中的机器学习》，Springer，Cham，2022，47-81。
37 N. Chakraborti in Computational Approaches to Materials Design: Theoretical and Practical Aspects, IGI Global, Hershey, 2016.
37 N. Chakraborti，材料设计的计算方法：理论与实践》，IGI Global，赫希，2016 年。
38 R. Jha, F. Pettersson, G. S. Dulikravich, H. Saxen and N. Chakraborti, Mater. Manuf. Processes, 2015, 30(4), 488510.
38 R. Jha、F. Pettersson、G. S. Dulikravich、H. Saxen 和 N. Chakraborti，《材料。Manuf. Processes, 2015, 30(4), 488510.
39 S. Roy, A. Dutta and N. Chakraborti, Comput. Mater. Sci., 2021, 190, 110258.
39 S. Roy, A. Dutta and N. Chakraborti, Comput.Mater.Sci.，2021，190，110258。
40 J. Tiwari, B. K. Mahanta, H. Krishnaswamy, S. Devadula and M. A. Amirthalingam, Met. Mater. Int., 2023, 29(8), 22872303.
40 J. Tiwari, B. K. Mahanta, H. Krishnaswamy, S. Devadula and M. A. Amirthalingam, Met.Mater.Int.，2023，29（8），22872303。
41 B. K. Mahanta, P. Gupta, I. Mohanty, T. K. Roy and N. Chakraborti, Digit. Chem. Eng., 2023, 7, 100094.
41 B. K. Mahanta、P. Gupta、I. Mohanty、T. K. Roy 和 N. Chakraborti，Digit.Chem.Eng.，2023，7，100094。
42 E. Durak, Ö. Salman and C. Kurbanoğlu, Ind. Lubr. Tribol., 2008, 60(6), 309-316.
42 E. Durak, Ö.Salman and C. Kurbanoğlu, Ind.Lubr.Tribol.，2008，60（6），309-316。
  1. a a ^(a){ }^{a} Climate Change and Data Science, CSIR - Indian Institute of Petroleum, Dehradun-248005, India. E-mail: sk.singh@iip.res.in; shailesh.csiriip@gmail.com
    a a ^(a){ }^{a} 气候变化与数据科学，CSIR - 印度石油研究所，印度德拉敦-248005。电子邮件：sk.singh@iip.res.in; shailesh.csiriip@gmail.com
    b b ^(b){ }^{b} Advanced Tribology Research Centre, CSIR - Indian Institute of Petroleum, Dehradun248005, India
    b b ^(b){ }^{b} 高级摩擦学研究中心，CSIR - 印度石油研究所，印度德拉敦 248005
    c c ^(c){ }^{c} Academy of Scientific and Innovative Research (AcSIR), Ghaziabad-201002, India
    c c ^(c){ }^{c} 科学与创新研究院（AcSIR），印度加济阿巴德-201002
    d d ^(d){ }^{d} Department of Mechanical Engineering, Indian Institute of Technology Bombay, Mumbai-400076, India
    d d ^(d){ }^{d} 印度孟买印度理工学院机械工程系，印度孟买-400076
    e e ^(e){ }^{e} CSIR - Indian Institute of Petroleum, Dehradun-248005, India
    e e ^(e){ }^{e} CSIR - 印度石油研究所，印度，德拉敦-248005
    f f ^(f){ }^{f} Mishra Dhatu Nigam Limited, Hyderabad-500058, India
    f f ^(f){ }^{f} Mishra Dhatu Nigam Limited, Hyderabad-500058, India