Research on the loading–unloading fractal contact model between two three-dimensional spherical rough surfaces with regard to friction

Purpose This paper aims to propose a semi-analytical model to investigate the elastic-plastic contact between fractal rough surfaces. Parametric studies have been performed to analyze the dependencies between the contact properties and the scale-independent fractal parameters. Design/methodology/approach A modified two-variable Weierstrass-Mandelbrot function has been used to build the geometrical model of rough surfaces. The computation program was developed using software MATLAB R2015a. The results have been qualitatively validated by the existing theoretical and experimental results in the literature. Findings In most cases, a nonlinear relation between the load and the displacement of the rigid plane is found. Only under the condition of larger loads, an approximate linear relation can be seen for great D and small G values. (D: fractal dimension and G: fractal roughness). Originality/value The contact model of the cylindrical joints (conformal contact) with radial clearance is constructed by using the fractal theory and the Kogut-Etsion elastic-plastic contact model, which includes purely elastic, elastic-plastic and fully plastic contacts. The present method can generate a more reliable calculation result as compared with the Hertz contact model and a higher calculation efficiency as compared with the finite element method for the conformal contact problem.

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Damping in Lap Joints Due to Partial and Full Micro-Slip Using a Three Dimensional Elastic Contact of Rough Surfaces

Volume 11: Mechanical Systems and Control ◽

10.1115/imece2008-69077 ◽

2008 ◽

Author(s):

K. Farhang ◽

A. Sepehri ◽

D. Segalman ◽

M. Starr

Keyword(s):

Rough Surfaces ◽

Tangential Force ◽

Three Dimensional ◽

Elastic Interaction ◽

Lap Joints ◽

Joint Interface ◽

Flat Surfaces ◽

Mechanical Joints ◽

Statistical Sense ◽

Scale Roughness

Energy dissipation in mechanical joints occurs as a result of micro-slip motion between contacting rough surfaces. An account of this phenomenon is especially challenging due to the vast differences in the length and time scale differences between the macro-mechanical structure and the micron-scale events at the joint interface. This paper considers the contact between two nominally flat surfaces containing micron-scale roughness. The rough surface interaction is viewed as a multi-sphere elastic interaction subject to a periodic tangential force. It combines the Mindlin’s formulation [1, 2] for the elastic interaction of two spheres with the Greenwood and Williamson’s [3] statistical approach for the contact of two nominally flat rough surfaces so as to develop a model for multi-sphere problem in which sphere radii, contact load and the number of spheres in contact can only be known in a statistical sense and not deterministically.

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Validation of the Stress Predictions in Rolling EHL Contacts Having In-Line Roughness Using the Inverse Method

Journal of Tribology ◽

10.1115/1.2345396 ◽

2006 ◽

Vol 128 (4) ◽

pp. 745-752 ◽

Cited By ~ 1

Author(s):

C. J. Hooke ◽

K. Y. Li

Keyword(s):

Fluid Flow ◽

Inverse Method ◽

Rough Surfaces ◽

Three Dimensional ◽

Plane Flow ◽

Preliminary Results ◽

Rolling Contacts ◽

Out Of Plane ◽

Transverse Roughness

Using modern EHL programs it is relatively simple to determine the pressures and clearances in rough EHL contacts. The pressures may then be used to calculate the subsurface stresses in the two contacting components. However, the results depend on the assumptions made about the fluid’s rheology. While it is possible to measure the clearances using interferometric techniques, measurement of either the pressures or stresses is extremely difficult. However it is these, rather than the clearances, that determine the life of the contact. In previous papers the authors have described how the inverse method may be used to validate the stress predictions for contacts with transverse roughness. This type of contact has fluid flow in only one plane and it remained necessary to check the results for more general rough surfaces where the flow is three-dimensional. Accordingly, the inverse method is extended, in this paper, to a situation where out-of-plane flow is significant. The paper describes the approach and presents some preliminary results for rolling contacts.

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Reduced Rough-Surface Parametrization for Use With the Discrete-Element Model

Journal of Turbomachinery ◽

10.1115/1.2952379 ◽

2009 ◽

Vol 131 (2) ◽

Cited By ~ 5

Author(s):

Stephen T. McClain ◽

Jason M. Brown

Keyword(s):

Heat Transfer ◽

Rough Surface ◽

Surface Characterization ◽

Rough Surfaces ◽

Roughness Element ◽

Three Dimensional ◽

Element Model ◽

Discrete Element ◽

Diameter Distribution ◽

Discrete Element Model

The discrete-element model for flows over rough surfaces was recently modified to predict drag and heat transfer for flow over randomly rough surfaces. However, the current form of the discrete-element model requires a blockage fraction and a roughness-element diameter distribution as a function of height to predict the drag and heat transfer of flow over a randomly rough surface. The requirement for a roughness-element diameter distribution at each height from the reference elevation has hindered the usefulness of the discrete-element model and inhibited its incorporation into a computational fluid dynamics (CFD) solver. To incorporate the discrete-element model into a CFD solver and to enable the discrete-element model to become a more useful engineering tool, the randomly rough surface characterization must be simplified. Methods for determining characteristic diameters for drag and heat transfer using complete three-dimensional surface measurements are presented. Drag and heat transfer predictions made using the model simplifications are compared to predictions made using the complete surface characterization and to experimental measurements for two randomly rough surfaces. Methods to use statistical surface information, as opposed to the complete three-dimensional surface measurements, to evaluate the characteristic dimensions of the roughness are also explored.

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Analysis of Plastic Strain between Substrate and Micro-Cantilever under Different Deformation Characteristics

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.477-478.21 ◽

2013 ◽

Vol 477-478 ◽

pp. 21-24

Author(s):

Hui Kai Gao ◽

Jian Meng Huang

Keyword(s):

Plastic Strain ◽

Rough Surface ◽

Three Dimensional ◽

Equivalent Plastic Strain ◽

Adhesive Contact ◽

Contact Model ◽

Deformation Characteristics ◽

Element Analysis ◽

Flat Substrate ◽

Micro Cantilever

The contact between substrate and micro-cantilever simplified as an ideal flat substrate contact with a micro-cantilever rough surface. A three-dimensional adhesive contact model was established on isotropic rough surfaces exhibiting fractal behavior, and the equivalent plastic strain was discussed using the finite element analysis. The maximum equivalent plastic strain and its depth were presented with the different paths of rough solid when loading. The result show that the equivalent plastic strain versus different depth which at different locations showed different laws, in the top area of the asperities versus different depth, the maximum equivalent plastic strain occurs in the subsurface range about 0.5μm from the surface or on the surface. In addition, with different deformation characteristics, the degree of the equivalent plastic strain was different.. The contact model between micro-cantilever rough surface and flat substrate will lay a foundation to further research on the substance of the process of friction and wear.

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Spatial model of the gecko foot hair: functional significance of highly specialized non-uniform geometry

Interface Focus ◽

10.1098/rsfs.2014.0065 ◽

2015 ◽

Vol 5 (1) ◽

pp. 20140065 ◽

Cited By ~ 19

Author(s):

Alexander E. Filippov ◽

Stanislav N. Gorb

Keyword(s):

Functional Significance ◽

Spatial Model ◽

Rough Surfaces ◽

Three Dimensional ◽

Intermolecular Forces ◽

Dimensional Structure ◽

Fractal Surface ◽

Flexible Form ◽

Spatial Geometry ◽

Adhesive Contacts

One of the important problems appearing in experimental realizations of artificial adhesives inspired by gecko foot hair is so-called clusterization. If an artificially produced structure is flexible enough to allow efficient contact with natural rough surfaces, after a few attachment–detachment cycles, the fibres of the structure tend to adhere one to another and form clusters. Normally, such clusters are much larger than original fibres and, because they are less flexible, form much worse adhesive contacts especially with the rough surfaces. Main problem here is that the forces responsible for the clusterization are the same intermolecular forces which attract fibres to fractal surface of the substrate. However, arrays of real gecko setae are much less susceptible to this problem. One of the possible reasons for this is that ends of the seta have more sophisticated non-uniformly distributed three-dimensional structure than that of existing artificial systems. In this paper, we simulated three-dimensional spatial geometry of non-uniformly distributed branches of nanofibres of the setal tip numerically, studied its attachment–detachment dynamics and discussed its advantages versus uniformly distributed geometry.

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An Efficient and Accurate Contact Model for Rough Surfaces Considering of Microscopic Interaction

Proceedings of 5th International Conference on Vehicle, Mechanical and Electrical Engineering ◽

10.5220/0008855801970202 ◽

2019 ◽

Author(s):

Cheng Zhang ◽

Jianrun Zhang

Keyword(s):

Rough Surfaces ◽

Contact Model

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Three-dimensional data-tracking simulations of sprinting using a direct collocation optimal control approach

PeerJ ◽

10.7717/peerj.10975 ◽

2021 ◽

Vol 9 ◽

pp. e10975

Author(s):

Nicos Haralabidis ◽

Gil Serrancolí ◽

Steffi Colyer ◽

Ian Bezodis ◽

Aki Salo ◽

...

Keyword(s):

Experimental Data ◽

Reaction Force ◽

Three Dimensional ◽

Contact Model ◽

Model Parameters ◽

Ground Contact ◽

Control Approach ◽

Average Percentage ◽

Data Tracking ◽

The Individual

Biomechanical simulation and modelling approaches have the possibility to make a meaningful impact within applied sports settings, such as sprinting. However, for this to be realised, such approaches must first undergo a thorough quantitative evaluation against experimental data. We developed a musculoskeletal modelling and simulation framework for sprinting, with the objective to evaluate its ability to reproduce experimental kinematics and kinetics data for different sprinting phases. This was achieved by performing a series of data-tracking calibration (individual and simultaneous) and validation simulations, that also featured the generation of dynamically consistent simulated outputs and the determination of foot-ground contact model parameters. The simulated values from the calibration simulations were found to be in close agreement with the corresponding experimental data, particularly for the kinematics (average root mean squared differences (RMSDs) less than 1.0° and 0.2 cm for the rotational and translational kinematics, respectively) and ground reaction force (highest average percentage RMSD of 8.1%). Minimal differences in tracking performance were observed when concurrently determining the foot-ground contact model parameters from each of the individual or simultaneous calibration simulations. The validation simulation yielded results that were comparable (RMSDs less than 1.0° and 0.3 cm for the rotational and translational kinematics, respectively) to those obtained from the calibration simulations. This study demonstrated the suitability of the proposed framework for performing future predictive simulations of sprinting, and gives confidence in its use to assess the cause-effect relationships of technique modification in relation to performance. Furthermore, this is the first study to provide dynamically consistent three-dimensional muscle-driven simulations of sprinting across different phases.

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Forced Vibration of Elastic Structures With Friction Contacts

Volume 7B: 17th Biennial Conference on Mechanical Vibration and Noise ◽

10.1115/detc99/vib-8180 ◽

1999 ◽

Author(s):

Walter Sextro

Keyword(s):

Relative Motion ◽

Dry Friction ◽

Turbine Blades ◽

Three Dimensional ◽

Point Contact ◽

Normal Pressure ◽

Tangential Direction ◽

Contact Model ◽

Elastic Structures ◽

Normal Forces

Abstract In many technical contacts energy is dissipated because of dry friction and relative motion. This can be used to reduce the vibration amplitudes. For example, shrouds with friction interfaces are used to reduce the dynamic stresses in turbine blades. The three-dimensional motion of the blades results in a three-dimensional relative motion of the contact planes. The developed Point-Contact-Model is used to calculate the corresponding tangential and normal forces for each contact element. This Point-Contact-Model includes the roughness of the contact surfaces, the normal pressure distribution due to roughness, the stiffness in normal and tangential direction and dry friction. An experiment with two non-Hertzian contacts is used to verify the developed contact model. The comparison between measured and calculated frequency response functions for three-dimensional forced vibrations of the elastic structures shows a very good agreement.

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