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Keywords = asperity contact model

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14 pages, 966 KiB  
Article
Investigation of the Thermal Conductance of MEMS Contact Switches
by Zhiqiang Chen and Zhongbin Xie
Micromachines 2025, 16(8), 872; https://doi.org/10.3390/mi16080872 - 28 Jul 2025
Viewed by 207
Abstract
Microelectromechanical system (MEMS) devices are specialized electronic devices that integrate the benefits of both mechanical and electrical structures. However, the contact behavior between the interfaces of these structures can significantly impact the performance of MEMS devices, particularly when the surface roughness approaches the [...] Read more.
Microelectromechanical system (MEMS) devices are specialized electronic devices that integrate the benefits of both mechanical and electrical structures. However, the contact behavior between the interfaces of these structures can significantly impact the performance of MEMS devices, particularly when the surface roughness approaches the characteristic size of the devices. In such cases, the contact between the interfaces is not a perfect face-to-face interaction but occurs through point-to-point contact. As a result, the contact area changes with varying contact pressures and surface roughness, influencing the thermal and electrical performance. By integrating the CMY model with finite element simulations, we systematically explored the thermal conductance regulation mechanism of MEMS contact switches. We analyzed the effects of the contact pressure, micro-hardness, surface roughness, and other parameters on thermal conductance, providing essential theoretical support for enhancing reliability and optimizing thermal management in MEMS contact switches. We examined the thermal contact, gap, and joint conductance of an MEMS switch under different contact pressures, micro-hardness values, and surface roughness levels using the CMY model. Our findings show that both the thermal contact and gap conductance increase with higher contact pressure. For a fixed contact pressure, the thermal contact conductance decreases with rising micro-hardness and root mean square (RMS) surface roughness but increases with a higher mean asperity slope. Notably, the thermal gap conductance is considerably lower than the thermal contact conductance. Full article
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22 pages, 4555 KiB  
Article
Elastic–Plastic Analysis of Asperity Based on Wave Function
by Zijian Xu, Min Zhu, Wenjuan Wang, Ming Guo, Shengao Wang, Xiaohan Lu and Ziwei Li
Materials 2025, 18(15), 3507; https://doi.org/10.3390/ma18153507 - 26 Jul 2025
Viewed by 195
Abstract
This paper proposes an improved wave function asperity elastic–plastic model. A cosine function that could better fit the geometric morphology was selected to construct the asperity, the elastic phase was controlled by the Hertz contact theory, the elastoplastic transition phase was corrected by [...] Read more.
This paper proposes an improved wave function asperity elastic–plastic model. A cosine function that could better fit the geometric morphology was selected to construct the asperity, the elastic phase was controlled by the Hertz contact theory, the elastoplastic transition phase was corrected by the hyperbolic tangent function, and the fully plastic phase was improved by the projected area theory. The model broke through the limitations of the spherical assumption and was able to capture the stress concentration and plastic flow phenomena. The results show that the contact pressure in the elastic phase was 22% higher than that of the spherical shape, the plastic strain in the elastoplastic phase was 52% lower than that of the spherical shape, and the fully plastic phase reduced the contact area error by 20%. The improved hyperbolic tangent function eliminated the unphysical oscillation phenomenon in the elastoplastic phase and ensured the continuity and monotonicity of the contact variables, with an error of <5% from the finite element analysis. Meanwhile, extending the proposed model, we developed a rough surface contact model, and it was verified that the wavy asperity could better match the mechanical properties of the real rough surface and exhibited progressive stiffness reduction during the plastic flow process. The model in this paper can provide a theoretical basis for predicting stress distribution, plastic evolution, and multi-scale mechanical behavior in the connection interface. Full article
(This article belongs to the Section Materials Simulation and Design)
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18 pages, 3602 KiB  
Article
Modeling and Analysis of Torsional Stiffness in Rehabilitation Robot Joints Using Fractal Theory
by Shuaidong Zou, Wenjie Yan, Guanghui Xie, Renqiang Yang, Huachao Xu and Fanwei Sun
Materials 2025, 18(12), 2866; https://doi.org/10.3390/ma18122866 - 17 Jun 2025
Viewed by 290
Abstract
The torsional stiffness of rehabilitation robot joints is a critical performance determinant, significantly affecting motion accuracy, stability, and user comfort. This paper introduces an innovative traction drive mechanism that transmits torque through friction forces, overcoming mechanical impact issues of traditional gear transmissions, though [...] Read more.
The torsional stiffness of rehabilitation robot joints is a critical performance determinant, significantly affecting motion accuracy, stability, and user comfort. This paper introduces an innovative traction drive mechanism that transmits torque through friction forces, overcoming mechanical impact issues of traditional gear transmissions, though accurately modeling surface roughness effects remains challenging. Based on fractal theory, this study presents a comprehensive torsional stiffness analysis for advanced traction drive joints. Surface topography is characterized using the Weierstrass–Mandelbrot function, and a contact mechanics model accounting for elastic–plastic deformation of micro-asperities is developed to derive the tangential stiffness of individual contact pairs. Static force analysis determines load distribution, and overall joint torsional stiffness is calculated through the integration of individual contact contributions. Parametric analyses reveal that contact stiffness increases with normal load, contact length, and radius, while decreasing with the tangential load and roughness parameter. Stiffness exhibits a non-monotonic relationship with fractal dimension, reaching a maximum at intermediate values. Overall system stiffness demonstrates similar parameter dependencies, with a slight decrease under increasing output load when sufficient preload is applied. This fractal-based model enables more accurate stiffness prediction and offers valuable theoretical guidance for design optimization and performance improvement in rehabilitation robot joints. Full article
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14 pages, 3948 KiB  
Article
Effect of Deposits on Micron Particle Collision and Deposition in Cooling Duct of Turbine Blades
by Shihong Xin, Chuqi Peng, Junchao Qi, Baiwan Su and Yan Xiao
Crystals 2025, 15(6), 510; https://doi.org/10.3390/cryst15060510 - 26 May 2025
Viewed by 344
Abstract
Aerospace engines ingest small particles when operating in a particulate-rich environment, such as sandstorms, atmospheric pollution, and volcanic ash clouds. These micron particles enter their cooling channels, leading to film-cooling hole blockage and thus thermal damage to turbine blades made of nickel-based single-crystal [...] Read more.
Aerospace engines ingest small particles when operating in a particulate-rich environment, such as sandstorms, atmospheric pollution, and volcanic ash clouds. These micron particles enter their cooling channels, leading to film-cooling hole blockage and thus thermal damage to turbine blades made of nickel-based single-crystal superalloy materials. This work studied the collision and deposition mechanisms between the micron particles and structure surface. A combined theoretical and numerical study was conducted to investigate the effect of deposits on particle collision and deposition. Finite element models of deposits with flat and rough surfaces were generated and analyzed for comparison. The results show that the normal restitution coefficient is much lower when a micron particle impacts a deposit compared to that of particle collisions with DD3 nickel-based single-crystal wall surfaces. The critical deposition velocity of a micron particle is much higher for particle–deposit collisions than for particle–wall collision. The critical deposition velocity decreases with the increase in particle size. When micron particles deposit on the wall surface of the structure, early-stage particle–wall collision becomes particle–deposit collision when the height of the deposits is greater than twice the particle diameter. For contact between particles and rough surface deposits, surfaces with a shorter correlation length, representing a higher density of asperities and a steeper surface, have a much longer contact time but a lower contact area. The coefficient of restitution of the particle reduces as the surface roughness of the deposits increase. The characteristic length of the roughness has little effect on the rebounding rotation velocity of the particle. Full article
(This article belongs to the Section Inorganic Crystalline Materials)
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27 pages, 11346 KiB  
Article
Heat Transfer Analysis in Double Diaphragm Preforming Process of Dry Woven Carbon Fibres
by Srikara Dandangi, Sadegh Ghanei, Mohammad Ravandi, Jamal Naser and Adriano Di Pietro
Energies 2025, 18(6), 1471; https://doi.org/10.3390/en18061471 - 17 Mar 2025
Viewed by 411
Abstract
Double diaphragm forming (DDF) represents an efficient manufacturing technique leveraging vacuum pressure and heat to form composite material stacks between flexible diaphragms. This study focuses on the critical role of thermal management during preforming, essential for material integrity, defect mitigation, and process efficiency. [...] Read more.
Double diaphragm forming (DDF) represents an efficient manufacturing technique leveraging vacuum pressure and heat to form composite material stacks between flexible diaphragms. This study focuses on the critical role of thermal management during preforming, essential for material integrity, defect mitigation, and process efficiency. A comprehensive three-dimensional finite element model (FEM) is developed to investigate the heat transfer dynamics in DDF, incorporating temperature-dependent material properties such as specific heat and thermal conductivity under compaction and varying density conditions. A novel approach is introduced to predict thermal contact conductance (TCC) across multilayer carbon fabric interfaces, validated using four laminate configurations. The resulting effective thermal conductivity of the laminates is applied in production-scale simulations, enabling accurate predictions of temperature distributions, which are corroborated by experimental data. The findings highlight the significant impact of mesoscale interactions, such as yarn-level deformation and surface asperities, on TCC variation. The study provides an enhanced understanding of heat transfer mechanisms in DDF, offering insights to optimise process parameters, improve product quality, and advance manufacturing capabilities for complex geometries. Full article
(This article belongs to the Special Issue Advanced Analysis of Heat Transfer and Energy Conversion 2024)
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29 pages, 1700 KiB  
Review
Cross-Scale Mechanical Contact Analysis from Asperities to Rough Surfaces: A Critical Review
by Ziwei Li, Ming Guo, Yilong Liu, Shengao Wang, Xiaohan Lu and Zijian Xu
Coatings 2025, 15(3), 333; https://doi.org/10.3390/coatings15030333 - 14 Mar 2025
Viewed by 2633
Abstract
Engineering equipment is an important material foundation for supporting national defense security and promoting the development of the national economy. Large and complex mechanical equipment has a complex structural composition and a large number of components, with a great deal of connection structures [...] Read more.
Engineering equipment is an important material foundation for supporting national defense security and promoting the development of the national economy. Large and complex mechanical equipment has a complex structural composition and a large number of components, with a great deal of connection structures such as bolts and flanges inside. Affected by long-term loading conditions, phenomena like the degradation of contact stiffness will occur at the connection interfaces between components. This, in turn, will affect the dynamic characteristics of the entire system and seriously impact the reliability and performance of the equipment. By combining the microscopic contact mechanism with the cross-scale modeling method, the proposed contact framework can study the contact behavior of the connection interfaces more comprehensively. This paper classifies and summarizes the research status of the asperity contact model from the perspective of geometric modeling, classifies and summarizes the research status of the statistical contact model of rough surfaces according to different height distributions of asperities, and looks ahead to the research directions of the cross-scale model of connection structures in the future. Full article
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16 pages, 6195 KiB  
Article
A Mechanics Model for Contact with Rough Surface Considering the Interaction of Micro-Asperity Bodies
by Yazhou Mao, Qingxin Hu, Yingying Yu, Shaolin Shi, Jiaming Pei, Zichen Li and Linyuan Wang
Lubricants 2025, 13(3), 96; https://doi.org/10.3390/lubricants13030096 - 20 Feb 2025
Viewed by 608
Abstract
In order to evaluate contact characteristics, a modified contact model was proposed considering the deformation characteristics of asperity bodies, and the variation rules of wear rate with fractal dimension, material property constant and debris probability were established. The results show that the actual [...] Read more.
In order to evaluate contact characteristics, a modified contact model was proposed considering the deformation characteristics of asperity bodies, and the variation rules of wear rate with fractal dimension, material property constant and debris probability were established. The results show that the actual contact area increases with an increase in load when the surface topography is constant, whereas the contact area decreases with an increase in characteristic scale coefficient if the fractal dimension or load is constant. For running-in wear, the wear rate increases with an increase in surface profile parameters under the same contact area. In addition, the wear rate increases with an increase in actual contact area when the surface profile parameter is constant. Regarding abrasive wear, the wear rate is the smallest when the fractal dimension is 1.6. The wear rate increases with an increase in contact area under the same characteristic scale coefficient, but decreases with an increase in the characteristic scale coefficient under the same contact area, and the smaller the material constant and the larger the probability constant, the higher the wear rate. The establishment of this model provides a basis for further study of the tribological properties of the contact surface. Full article
(This article belongs to the Special Issue Recent Advances in Lubricated Tribological Contacts)
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30 pages, 11075 KiB  
Article
The Elasto-Plastic Contact Models of Cylinder-Based and Sphere-Based Fractal Rough Surfaces
by Xiaohui Yang, Bo Bai and Shimin Mao
Appl. Sci. 2025, 15(4), 1994; https://doi.org/10.3390/app15041994 - 14 Feb 2025
Viewed by 716
Abstract
The elasto-plastic contact models of cylinder-based and sphere-based fractal rough surfaces are developed. In the two models, the critical contact areas of a single asperity are scale-dependent. With an increase in the contact load and contact area, a transition from elastic, elasto-plastic to [...] Read more.
The elasto-plastic contact models of cylinder-based and sphere-based fractal rough surfaces are developed. In the two models, the critical contact areas of a single asperity are scale-dependent. With an increase in the contact load and contact area, a transition from elastic, elasto-plastic to full plastic deformation takes place in this order. The truncated asperity size distribution functions of different frequency indexes in different contact zones are deduced. The relations between the total real contact area and total contact load for cylinder-based and sphere-based fractal rough surfaces are obtained. The pressure distributions in the contact zone are obtained. The results of elasto-plastic contact models show that the mechanical property of cylinder-based and sphere-based fractal rough surfaces depends on the range of the frequency index of asperities. When the first six frequency indexes are smaller than the elastic critical frequency index, the cylinder-based and sphere-based fractal rough surfaces approximately appear to have an elastic property in the complete contact process. When the minimum frequency index is greater than the elastic critical frequency index, elastic deformation first takes place in the rough surfaces. Then, elasto-plastic deformation takes place with an increase in the total contact load. In elastic deformation, the ratios of the peak pressures of present fractal models to those of Hertzian models are constant for a given range of frequency indexes. In inelastic deformation, the ratios of the peak pressures are inversely proportional to the total contact load. Full article
(This article belongs to the Special Issue Research on Friction and Lubrication: Surfaces, Bearings and Gears)
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11 pages, 3760 KiB  
Article
Analysis of Contact Noise Due to Elastic Recovery of Surface Asperities for Spherical Contact
by Bora Lee, Kyungseob Kim and Taewan Kim
Inventions 2025, 10(1), 17; https://doi.org/10.3390/inventions10010017 - 8 Feb 2025
Viewed by 850
Abstract
Contact noise, often arising from frictional vibrations in mechanical systems, significantly impacts performance and user experience. This study investigates the generation of contact noise due to the elastic recovery of surface asperities during spherical contact with rough surfaces. A numerical algorithm was developed [...] Read more.
Contact noise, often arising from frictional vibrations in mechanical systems, significantly impacts performance and user experience. This study investigates the generation of contact noise due to the elastic recovery of surface asperities during spherical contact with rough surfaces. A numerical algorithm was developed to model the noise produced by the elastic–plastic deformation of asperities, incorporating surface roughness and normal load effects. Gaussian-distributed rough surfaces with varying Ra values (0.01–5 μm) were generated to analyze the interaction between a rigid sphere and the rough surface. Contact pressure, asperity deformation, and the resulting acoustic emissions were calculated. The results indicate that, as surface roughness and applied load increase, noise levels within the audible frequency range also rise, exceeding 70 dB under certain conditions. The transition from elastic to plastic deformation significantly influences the noise characteristics. Surfaces with Ra ≥ 0.1 μm showed a 10–15 dB increase in noise compared to smoother surfaces. These findings offer insights into optimizing surface parameters for noise reduction in rolling contact applications, providing a foundation for designing low-noise mechanical systems. Future experimental validations are expected to enhance the practical applications of this analytical framework. Full article
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26 pages, 9714 KiB  
Article
Simulation Study on the Evolution Behaviour of Endogenous Third Bodies in the Rough Friction Interface During Braking and Their Impact
by Lu Jin, Shengfang Zhang, Guotao Ru, Jian Yin, Li Shi, Xin Li, Zhihua Sha and Yu Liu
Machines 2025, 13(2), 83; https://doi.org/10.3390/machines13020083 - 23 Jan 2025
Viewed by 697
Abstract
During braking, high-power wind turbine disc brake friction pairs experience thermo-mechanical interactions at the interface, which lead to both physical and chemical changes. The friction interface features asperities and embedded hard particles within the substrate. Wear debris from these asperities or dislodged hard [...] Read more.
During braking, high-power wind turbine disc brake friction pairs experience thermo-mechanical interactions at the interface, which lead to both physical and chemical changes. The friction interface features asperities and embedded hard particles within the substrate. Wear debris from these asperities or dislodged hard particles accumulates at the interface, continuing to participate in the friction process—a phenomenon known as the “endogenous third body”. Throughout braking, the microscopic morphology and contact conditions of the interface evolve dynamically. The stress–strain distribution and vibration behaviour of the friction system, influenced by the endogenous third body, also vary with braking parameters. This study employs the W-M fractal theory to develop a finite element model of a rough friction interface containing hard-particle endogenous third bodies. The model is validated through experimental testing. Based on the performance test parameters of high-power wind turbine disc brakes, a simulation is conducted to analyse the contact friction process involving the endogenous third body at the rough interface between the brake disc and brake pad. The simulation reproduces the formation process of the endogenous third body and reveals its evolutionary stages, including “ploughing”, “gap-filling”, and “aggregation”. Additionally, the study examines changes in the internal stress–strain and vibration states of the friction system under varying braking speeds (5 m/s to 35 m/s) and braking loads (3 MPa to 6 MPa). The findings demonstrate how different braking parameters influence the friction system containing the endogenous third body. The results showed that when the braking speeds were 5 m/s, 15 m/s, 25 m/s, and 35 m/s, and the braking load was 6 MPa, the average amplitude of the brake pads was the smallest, at 0.017 mm, 0.021 mm, 0.025 mm, and 0.020 mm, respectively. This research provides valuable insights into the three-body contact friction mechanism at the micro-braking interface, the formation of composite material third bodies, and the role of wear-stage third bodies in affecting the friction interface. Full article
(This article belongs to the Section Friction and Tribology)
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20 pages, 14822 KiB  
Article
Investigation of Basic Assumption for Contact Between Spheric Asperities in Rough Surface
by Caixia Guo, Feng Gao, Yangsen Mu, Yuewen Su, Canjun Wang and Xubo Li
Materials 2025, 18(1), 150; https://doi.org/10.3390/ma18010150 - 2 Jan 2025
Viewed by 695
Abstract
Accurate analyses of contact problems for rough surfaces are important but complicated. Some assumptions, namely that all asperities can be approximated by a hemisphere with the same radius and assuming a Gaussian distribution of the asperity heights, are convenient but may lead to [...] Read more.
Accurate analyses of contact problems for rough surfaces are important but complicated. Some assumptions, namely that all asperities can be approximated by a hemisphere with the same radius and assuming a Gaussian distribution of the asperity heights, are convenient but may lead to less accurate results. The purpose of this work is to investigate these assumptions and analyze the conditions under which they are valid. The finite element method is used to construct spherical asperity contact models with different radii and materials. The validity of the assumptions is assessed by comparatively analyzing the results of four models in terms of contact loads, contact radii, and average contact pressures under different yield strengths. The results show that these assumptions are fully applicable under elastic deformation. For plastic cases, the lower yield strength of the two contacting bodies is the dominant factor affecting the contact results. Assuming the same lower yield strength, the ratio of the yield strengths of two spheres has an influence on contact characteristics in the range from 1.2 to 3, but a negligible influence when the ratio is greater than 3. With an equivalent yield strength and yield ratio, the plastic contact of asperities can be analyzed in detail, which be conducive to clarifying the application scope of the above assumption. The work reported in this study provides some theoretical basis for an accurate contact model of rough surfaces. Full article
(This article belongs to the Section Materials Simulation and Design)
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20 pages, 9842 KiB  
Article
A Study of the Effect of Roughness on the Three-Body Wear Mechanism from a Microscopic Point of View: Asperity Peak Removal
by Tangshengjie Wei, Ziyi Zhou, Xue Ling, Minghao Lv, Yunfei Di, Kun Qin and Qin Zhou
Metals 2024, 14(12), 1385; https://doi.org/10.3390/met14121385 - 2 Dec 2024
Cited by 3 | Viewed by 1578
Abstract
The presence of particles leads to varying degrees of mass loss on a metal sealing surface, which severely affects the seal’s lifespan. Understanding the complex wear mechanism and optimizing the surface roughness morphology are particularly important in engineering. By characterizing the surface of [...] Read more.
The presence of particles leads to varying degrees of mass loss on a metal sealing surface, which severely affects the seal’s lifespan. Understanding the complex wear mechanism and optimizing the surface roughness morphology are particularly important in engineering. By characterizing the surface of the metal (SS 304) with different roughness parameters Ra, Rp, Rpk, Rpc and Rku, the variation mode of mass loss under abrasive wear conditions was revealed. Unlike traditional two-body wear, the involvement of abrasive particles significantly impacts surface Ra and other surface morphologies (asperity peak features). A contact model for metal rough surfaces, distinct from two-body contact, was established to clarify the changes in removal mechanisms. It was found that the change in the contact between the particle and the asperity peak led to a change in the mass loss and guided the appropriate metal roughness range: Ra 0.05 μm and Ra 0.6–0.8 μm. In addition, it was found that the removal of asperity peaks is holistic under low roughness, and only parts of asperity peaks are removed under high roughness. Notably, the metrological methods used in this study supplement existing roughness measurements. By exploring the complex removal mechanism of asperity peaks, micro-scale guidance for surface (texture) design, machining, and optimization is provided. Full article
(This article belongs to the Section Metal Failure Analysis)
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32 pages, 13420 KiB  
Article
A Mixed-Elastohydrodynamic Lubrication Model of a Capped-T-Ring Seal with a Sectioned Multi-Material Film Thickness in Landing Gear Shock Absorber Applications
by Aaron Feria Alanis, Ahmed A. Sheikh Al-Shabab, Antonis F. Antoniadis, Panagiotis Tsoutsanis and Martin Skote
Fluids 2024, 9(12), 271; https://doi.org/10.3390/fluids9120271 - 21 Nov 2024
Viewed by 1147
Abstract
Numerical investigations of capped T-ring (CTR) seals performance in reciprocating motion for landing gear shock absorber applications are presented. A lubrication model using the Elastohydrodynamic lubrication theory and deformation mechanics is developed in a multi-material contact zone, and a procedure for coupling fluid [...] Read more.
Numerical investigations of capped T-ring (CTR) seals performance in reciprocating motion for landing gear shock absorber applications are presented. A lubrication model using the Elastohydrodynamic lubrication theory and deformation mechanics is developed in a multi-material contact zone, and a procedure for coupling fluid and deformation mechanics is introduced. By conducting Finite Element Method (FEM) simulations, the static contact pressure is obtained, which subsequently is used within the model developed herein consisting of a modified Reynolds equation and an asperity contact model, to calculate the fluid film pressure, and the deformation of the fluid channel is determined using an elastic deformation model applied to a multi-component multi-mechanical property channel. These computational results are used for estimations of the seal leakage and friction under various conditions. In addition, the influence of asperity orientation is compared with other parameters, such as sealing pressure and piston velocity. A correlation between asperity orientation and leakage was found, and a general trend of reduced leakage with longitudinally oriented asperities was established. Full article
(This article belongs to the Section Mathematical and Computational Fluid Mechanics)
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33 pages, 9249 KiB  
Article
A Closure Contact Model of Self-Affine Rough Surfaces Considering Small-, Meso-, and Large-Scale Stage Without Adhesive
by Tao Zhang, Yiming Wu, Xian Liu and Kai Jiang
Fractal Fract. 2024, 8(10), 611; https://doi.org/10.3390/fractalfract8100611 - 18 Oct 2024
Cited by 2 | Viewed by 1202
Abstract
Contact interface is essential for the dynamic response of the bolted structures. To accurately predict the dynamic characteristics of bolted joint structures, a fractal extension of the segmented scale model, i.e., the JK model, is proposed in this paper to comprehensively analyze the [...] Read more.
Contact interface is essential for the dynamic response of the bolted structures. To accurately predict the dynamic characteristics of bolted joint structures, a fractal extension of the segmented scale model, i.e., the JK model, is proposed in this paper to comprehensively analyze the dynamic contact performance of engineering surfaces and revisit the multi-scale model based on the concept of asperities. The influence of asperity geometry, dimensionless material properties, and the elastic, elastoplastic, and full plastic mechanical models of a single asperity is established considering the asperity–substrate interaction. Then, a segmented scale contact model of rough surfaces is proposed based on the island distribution function in a strict sense. The mechanical contact process of determining rough surfaces is divided into small-scale, medium-scale, and large-scale stages. Moreover, cross-scale boundary conditions, i.e., al1′, al2′, and al3′, are provided through strict mathematical deduction. The results show that the real contact area and contact stiffness are positively correlated with fractal dimension and negatively correlated with fractal roughness. On a small scale, the contact damping decreases with an increase in load. In meso-scale and large-scale stages, the contact damping increases with the load. Finally, the reliability of the proposed model is verified by setting up three groups of modal vibration experiments. Full article
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19 pages, 5943 KiB  
Article
A Novel Normal Contact Stiffness Model of Bi-Fractal Surface Joints
by Pengsheng Xue, Lida Zhu and Xiangang Cao
Mathematics 2024, 12(20), 3232; https://doi.org/10.3390/math12203232 - 15 Oct 2024
Cited by 1 | Viewed by 925
Abstract
The contact stiffness of the mechanical joint usually becomes the weakest part of the stiffness for the whole machinery equipment, which is one of the important parameters affecting the dynamic characteristics of the engineering machinery. Based on the three-dimensional Weierstrass–Mandelbrot (WM) function, the [...] Read more.
The contact stiffness of the mechanical joint usually becomes the weakest part of the stiffness for the whole machinery equipment, which is one of the important parameters affecting the dynamic characteristics of the engineering machinery. Based on the three-dimensional Weierstrass–Mandelbrot (WM) function, the novel normal contact stiffness model of the joint with the bi-fractal surface is proposed, which comprehensively considers the effects of elastoplastic deformation of asperity and friction factor. The effect of various parameters (fractal dimension, scaling parameter, material parameter, friction factor) on the normal contact stiffness of the joint is analyzed by numerical simulation. The normal contact stiffness of the joint increases with an increase in the fractal dimension, normal load, and material properties and decreases with an increase in the scaling parameter. Meanwhile, the fractal parameters of the equivalent rough surface of the joint are calculated by the structural function method. The experimental results show that when the load is between 14 and 38 N∙m, the error of the model is within 20%. The normal contact stiffness model of the bi-fractal surface joint can provide a theoretical basis for the analysis of the dynamic characteristics of the whole machine at the design stage. Full article
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