scholarly journals The Elastic Contact of Rough Spheres Investigated Using a Deterministic Multi-Asperity Model

2019 ◽  
Vol 10 (01) ◽  
pp. 1841002 ◽  
Author(s):  
Vladislav A. Yastrebov
Keyword(s):  
Contact Area ◽  
Rough Surfaces ◽  
Contact Problems ◽  
Hertzian Contact ◽  
Contact Radius ◽  
Geometrical Shape ◽  
Elastic Contact ◽  
Deterministic Analysis ◽  
Asperity Model ◽  
Deformation Modes

In this paper, we use a deterministic multi-asperity model to investigate the elastic contact of rough spheres. Synthetic rough surfaces with controllable spectra were used to identify individual asperities, their locations and curvatures. The deterministic analysis enables to capture both particular deformation modes of individual rough surfaces and also statistical deformation regimes, which involve averaging over a big number of roughness realizations. Two regimes of contact area growth were identified: the Hertzian regime at light loads at the scale of a single asperity, and the linear regime at higher loads involving multiple contacting asperities. The transition between the regimes occurs at the load which depends on the second and the fourth spectral moments. It is shown that at light indentation the radius of circumference delimiting the contact area is always considerably larger than Hertzian contact radius. Therefore, it suggests that there is no scale separation in contact problems at light loads. In particular, the geometrical shape cannot be considered separately from the surface roughness at least for approaching greater than one standard roughness deviation.

Strongly Anisotropic Rough Surfaces

1979 ◽  
Vol 101 (1) ◽  
pp. 15-20 ◽  
Author(s):  
A. W. Bush ◽  
R. D. Gibson ◽  
G. P. Keogh
Keyword(s):  
Random Process ◽  
Rough Surface ◽  
Contact Area ◽  
Process Model ◽  
Rough Surfaces ◽  
Plasticity Index ◽  
Real Contact Area ◽  
Elastic Contact ◽  
Elastic Plastic ◽  
Real Contact

The statistics of a strongly anisotropic rough surface are briefly described. The elastic contact of rough surfaces is treated by approximating the summits of a random process model by parabolic ellipsoids and applying the Hertzian solution for their deformation. Load and real contact area are derived as functions of the separation and for all separations the load is found to be approximately proportional to the contact area. The limits of elastic/plastic contact are discussed in terms of the plasticity index.

Singularity Consideration in Numerical Solution of Contact Stress Problems

1982 ◽  
Vol 104 (3) ◽  
pp. 352-356 ◽  
Author(s):  
L. Nayak
Keyword(s):  
Numerical Methods ◽  
Numerical Solution ◽  
Contact Stress ◽  
Contact Area ◽  
Fundamental Equation ◽  
Elliptic Functions ◽  
Contact Problems ◽  
Hertzian Contact ◽  
Elastic Displacement ◽  
Proper Analysis

The paper gives an account of different approaches to deal with the weak singularity in numerical methods of contact stress problems when the methods are based on the fundamental equation relating the elastic displacement with pressure. Singularity consideration in a new method to simultaneously determine the shape of the contact area and the pressure distribution, particularly in non-Hertzian contact problems, has been dealt with using elliptic functions. Necessity of proper analysis of singularity is discussed and the final results when compared with Hertz solution have been shown to be satisfactory.

scholarly journals Elastic-contact-based tool-path planning for free-form surface in belt grinding

2019 ◽  
Vol 11 (1) ◽  
pp. 168781401881992 ◽  
Author(s):  
Junde Qi ◽  
Bing Chen
Keyword(s):  
Path Planning ◽  
Contact Area ◽  
Tool Path ◽  
Hertzian Contact ◽  
Free Form ◽  
Real Contact Area ◽  
Elastic Contact ◽  
Tool Path Planning ◽  
Belt Grinding ◽  
Free Form Surface

As for the fact that the majority of current researches take the technology of tool-path planning for free-form surface only as a geometrical problem, which is not suitable for belt grinding because of the elastic deformation of the grinding belt that leads to a variable contact, in this article, the tool-path planning method for belt grinding is developed from the elastic contact point of view. Based on the Hertzian contact theory and taking the grinding force into consideration, a calculation method of the contact area between the belt and the workpiece is presented. Then, a tool-path planning model is presented based on the real contact area to meet the full coverage. In addition, an optimization model based on the constant scallop-height is further developed to meet the high form accuracy of the workpiece. First, a modified model for the material removal depth is developed based on the Preston equation. Then, according to the curvature of the contact surface, three situations are analyzed and the calculation methods of the tool-path interval are given. Finally, experiments on the simulation blade are conducted, and the experimental results show the effectiveness of the method in this article.

Heat Transfer Between Colliding Surfaces and Particles

2011 ◽  
Vol 134 (1) ◽  
Author(s):  
Like Li ◽  
Renwei Mei ◽  
James F. Klausner ◽  
David W. Hahn
Keyword(s):  
Heat Transfer ◽  
Contact Area ◽  
Thermal Field ◽  
Initial Period ◽  
Asymptotic Methods ◽  
Hertzian Contact ◽  
Thermal Conductivity Ratio ◽  
Contact Radius ◽  
Two Dimensional ◽  
Fourier Number

Collisional heat transfer between two contacting curved surfaces is investigated computationally using a finite difference method and analytically using various asymptotic methods. Transformed coordinates that scale with the contact radius and the diffusion length are used for the computations. Hertzian contact theory of elasticity is used to characterize the contact area as a function of time. For an axisymmetric contact area, a two-dimensional self-similar solution for the thermal field during the initial period of contact is obtained, and it serves as an initial condition for the heat transfer simulation throughout the entire duration of collision. A two-dimensional asymptotic heat transfer result is obtained for small Fourier number. For finite Fourier numbers, local analytical solutions are presented to elucidate the nature of the singularity of the thermal field and heat flux near the contact point. From the computationally determined heat transfer during the collision, a closed-form formula is developed to predict the heat transfer as a function of the Fourier number, the thermal diffusivity ratio, and the thermal conductivity ratio of the impacting particles.

An incremental equivalent circular contact model for rough surfaces

2021 ◽  
pp. 1-16
Author(s):  
Gangfeng Wang ◽  
Xuan-Ming Liang ◽  
Yan Duo
Keyword(s):  
Contact Area ◽  
Rough Surfaces ◽  
Normal Load ◽  
Real Contact Area ◽  
Contact Radius ◽  
Surface Separation ◽  
Real Contact ◽  
Proposed Model ◽  
Geometrical Information ◽  
Circular Contact

Abstract The accurate calculation of real contact area between rough surfaces is a key issue in tribology. In this paper, based on the geometrical information of total contact area and the number of contact patches with respect to surface separation, a new method is proposed to determine the relation between real contact area and normal load. The contact of rough surfaces is treated as an accumulation of equivalent circular contacts with varying average contact radius. For a realistic range of separation, the proposed model predicts a linear relation between real contact area and load, and coincides well with direct finite element calculations. Moreover, this model is general and not confined to isotropic Gaussian surfaces.

Numerical Solution of Non-Hertzian Elastic Contact Problems

1974 ◽  
Vol 41 (2) ◽  
pp. 484-490 ◽  
Author(s):  
Krishna P. Singh ◽  
Burton Paul
Keyword(s):  
Integral Equation ◽  
Numerical Analysis ◽  
Numerical Solution ◽  
Arbitrary Shape ◽  
Contact Problems ◽  
Hertzian Contact ◽  
Elastic Contact ◽  
New Techniques ◽  
General Method

A general method for the numerical analysis of frictionless nonconformable non-Hertzian contact of bodies of arbitrary shape is developed. Numerical difficulties arise because the solution is extremely sensitive to the manner in which one discretizes the governing integral equation. The difficulties were overcome by utilizing new techniques, referred to as the method of redundant field points (RFP) and the method of functional regularization (FR). The accuracy and efficiency of the methods developed were tested thoroughly against known solutions of Hertzian problems. To illustrate the power of the methods, a heretofore unsolved non-Hertzian problem (corresponding to the case of rounded indentors with local flat spots) has been solved.

Modeling of the Elastic Properties of Contact Between Nominally Flat Rough Surfaces Using a New Multiple Point Asperity Model

Tribology ◽  
2006 ◽  
Author(s):  
A. Hariri ◽  
J. W. Zu ◽  
R. Ben Mrad
Keyword(s):  
Contact Problem ◽  
Numerical Models ◽  
Rough Surfaces ◽  
Multiple Point ◽  
Elastic Contact ◽  
Height Distribution ◽  
Asperity Contact ◽  
New Model ◽  
Flat Surfaces ◽  
Asperity Model

The asperities of rough surfaces have long been considered to be points higher than their immediate neighbors. Based on this concept, theories were developed for quantitatively understanding the nature of contact between rough surfaces. Recently it has been recognized that the above model for asperities is inadequate. Consequently, all the models that have been developed based on that model are inadequate as well. In this paper, based on a newly developed multiple-point asperity model, the elastic contact problem between nominally flat surfaces is reformulated. This leads to finding the deformed area, and load produced by the contact. The model is developed for the general form of isotropic rough surfaces with arbitrary height distribution and autocorrelation function (ACF). The microcontact areas generated by each asperity contact are considered to be circles. The Gaussian distribution of heights and exponential ACF are considered as a benchmark to compare the results of the new model with the existing models. Using results from numerical models developed by other groups, the new model is validated.

scholarly journals THE “SPORT” OF ROUGH CONTACTS AND THE FRACTAL PARADOX IN WEAR LAWS

2018 ◽  
Vol 16 (1) ◽  
pp. 65 ◽  
Author(s):  
Michele Ciavarella ◽  
Antonio Papangelo
Keyword(s):  
Contact Area ◽  
Rough Surfaces ◽  
Wear Loss ◽  
Length Scale ◽  
Elastic Contact ◽  
Contact Sport ◽  
Frictional Loss ◽  
Contact Models ◽  
Large Effort ◽  
The Times

In a recent paper in Science, namely, “The Contact Sport of Rough Surfaces”, Carpick summarizes recent efforts in a “contact challenge” to predict in detail an elastic contact between the mathematically defined fractal rough surfaces under (very little) adhesion. He also suggests the next steps that are needed to “fulfill da Vinci’s dream of understanding what causes friction”. However, this is disappointing as friction has been studied since the times of Leonardo and in 500 years, no predictive model has emerged, nor any significant improvement from rough contact models. Similarly, a very large effort we have spent on the “sport” of studying rough surfaces has not made us any closer to being able to predict the coefficient of proportionality between wear loss and friction dissipation which was already observed by Reye in 1860. Recent nice simulations by Aghababaei, Warner and Molinari have confirmed the criterion for the formation of debris of a single particle, proposed in 1958 by Rabinowicz, as well as Reye’s assumption for the proportionality with frictional loss, which is very close to Archard anyway. More recent investigations under variable loads suggest that Reye’s assumption is probably much more general than Archard’s law. The attempts to obtain exact coefficients with rough surfaces models are very far from predictive, essentially because for fractals most authors fail to recognize that resolution-dependence of the contact area makes the models very ill-defined. We also suggest that in the models of wear, rough contacts should be considered “plastic” and “adhesive” and introduce a new length scale in the problem.

Heat Transfer Between Colliding Surfaces and Particles

2011 ◽  
Author(s):  
Like Li ◽  
Renwei Mei ◽  
James F. Klausner ◽  
David W. Hahn
Keyword(s):  
Heat Transfer ◽  
Contact Area ◽  
Initial Period ◽  
Asymptotic Methods ◽  
Theory Of Elasticity ◽  
Hertzian Contact ◽  
Contact Radius ◽  
Asymptotic Result ◽  
Fourier Number ◽  
Entire Duration

Collisional heat transfer between two contacting curved surfaces is investigated computationally using the finite difference method and analytically using various asymptotic methods. Transformed coordinates that scale with the contact radius and the diffusion length are used for the computations. Hertzian contact theory of elasticity is used to characterize the contact area as a function of time. For an axisymmetric contact area, a two-dimensional self-similar solution for the thermal field during the initial period of contact is obtained and it serves as an initial condition for the heat transfer simulation throughout the entire duration of collision. A modified 2-D asymptotic result of heat transfer at small Fourier number is obtained. For finite Fourier numbers the heat transfer during the collision has been determined computationally. A closed-form formula is developed to predict the heat transfer as a function of the Fourier number, the thermal diffusivity ratio and conductivity ratio of the impacting particles.

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