Analytical Approximations in Modeling Contacting Rough Surfaces

1999 ◽  
Vol 121 (2) ◽  
pp. 234-239 ◽  
Author(s):  
Andreas A. Polycarpou ◽  
Izhak Etsion
Keyword(s):  
Closed Form ◽  
Gaussian Distribution ◽  
Rough Surfaces ◽  
Critical Examination ◽  
Height Distribution ◽  
Closed Form Solutions ◽  
Real Area Of Contact ◽  
Analytical Approximations ◽  
Classic Paper ◽  
Real Area

A critical examination of the analytical solution presented in the classic paper of Greenwood and Williamson (1966), (GW) on the statistical modeling of nominally flat contacting rough surfaces is undertaken in this study. It is found that using the GW simple exponential distribution to approximate the usually Gaussian height distribution of the asperities is inadequate for most practical cases. Some other exponential type approximations are suggested, which approximate the Gaussian distribution more accurately, and still enable closed form solutions for the real area of contact, the contact load, and the number of contacting asperities. The best-modified exponential approximation is then used in the case of elastic-plastic contacts of Chang et al. (1987) (CEB model), to obtain closed-form solutions, which favorably compare with the numerical results using the Gaussian distribution.

On the plastic contact of rough surfaces

1972 ◽  
Vol 327 (1569) ◽  
pp. 159-173 ◽  
Keyword(s):  
Flat Surface ◽  
Rough Surfaces ◽  
Material Constant ◽  
Unexpected Result ◽  
Height Distribution ◽  
Real Area Of Contact ◽  
Soft Surface ◽  
The Mean ◽  
Load Separation ◽  
Real Area

The treatment of plastic contact developed in this paper is based on three physical observations: that the total volume of metal is not changed by plastic deformation; that the mean indentation pressure is a well-defined material constant applicable to the whole range of likely asperity shapes; and that the displaced material reappears as a uniform rise in the non-contacting surface. An energy-balance argument is used to obtain dimensionless relations between the load, separation, and degree of contact, in terms of the height distribution of the surface. A fourth observation is then added: that the height distributions of many engineering surfaces are, to a good approximation, Gaussian. The relations are worked out in detail for this height distribution and compared with experimental observations. The treatment accurately predicts the behaviour up to extremely high loads; and accounts for the remarkable persistence of asperities on rough surfaces in plastic contact. The argument, and the main supporting experiments, were conceived in terms of the contact of a uniformly loaded nominally flat surface, but the extention to local indentations is quite straightforward. It is shown that for local indentations in homogeneous bodies the real area of contact is always one half of the nominal area. This unexpected result is in fact accurately confirmed by experiment. The treatment also discusses the effect of a hard or soft surface layer on the indented body, and again the predictions are supported by practical measurements.

Human Joint Performance and the Roughness of Articular Cartilage

1980 ◽  
Vol 102 (1) ◽  
pp. 50-56 ◽  
Author(s):  
T. R. Thomas ◽  
R. S. Sayles ◽  
I. Haslock
Keyword(s):  
Articular Cartilage ◽  
Heel Strike ◽  
Height Distribution ◽  
Normal Walking ◽  
Cartilage Surface ◽  
Real Area Of Contact ◽  
The Mean ◽  
Human Joints ◽  
Human Joint ◽  
Real Area

It is known that the surface of articular cartilage is rough and it has been suggested that this is likely to affect the lubrication of human joints. This paper describes the direct measurement of a cartilage surface with a stylus instrument. It is found that the height distribution is Gaussian with an inverse-square power spectrum. It is thus possible to calculate the elastic deflection of the surface under normal walking loads and it is shown that the mean separation of the cartilage surfaces in a human joint varies rather slowly with load. In one particular hip joint at heel strike the real area of contact was calculated to be about 1.3 cm2, the mean gap to be about 60 μm and the trapped volume to be about 80 percent of that when standing.

Contact Mechanics of Rough Surfaces in Tribology: Single Asperity Contact

1996 ◽  
Vol 49 (5) ◽  
pp. 275-298 ◽  
Author(s):  
Bharat Bhushan
Keyword(s):  
Friction And Wear ◽  
Rough Surfaces ◽  
Asperity Contact ◽  
Elastic Solids ◽  
Elastic Plastic ◽  
Single Asperity ◽  
Real Area Of Contact ◽  
Single Asperity Contact ◽  
Indentation Problem ◽  
Real Area

Contact modeling of two rough surfaces under normal approach and with relative motion is carried out to predict the real area of contact which affects friction and wear of an interface. The contact of two macroscopically flat bodies with microroughness is reduced to the contact at multiple asperities of arbitrary shapes. Most of deformation at the asperity contact can be either elastic or elastic-plastic. In this paper, a comprehensive review of modeling of a single asperity contact or an indentation problem is presented. Contact analyses for a spherical asperity/indenter on homogeneous and layered, elastic and elastic-plastic solids with and without tangential loading are presented. The analyses reviewed in this paper fall into two groups: (a) analytical solutions, primarily for elastic solids and (b) finite element solutions, primarily for elastic-plastic problems and layered solids. Implications of these analyses in friction and wear are discussed.

Analysis of transient amplification for a torsional system passing through resonance

2014 ◽  
Vol 229 (13) ◽  
pp. 2341-2354 ◽  
Author(s):  
Laihang Li ◽  
Rajendra Singh
Keyword(s):  
Closed Form ◽  
Analytical Solutions ◽  
Classical Problem ◽  
Peak Frequency ◽  
Empirical Formulas ◽  
Closed Form Solutions ◽  
Analytical Approximations ◽  
Numerical Predictions ◽  
Prior Literature ◽  
Run Up

The classical problem of vibration amplification of a linear torsional oscillator excited by an instantaneous sinusoidal torque is re-examined with focus on the development of new analytical solutions of the transient envelopes. First, a new analytical method in the instantaneous frequency (or speed) domain is proposed to directly find the closed-form solutions of transient displacement, velocity, and acceleration envelopes for passage through resonance during the run-up or run-down process. The proposed closed-form solutions are then successfully verified by comparing them with numerical predictions and limited analytical solutions as available in prior literature. Second, improved analytical approximations of maximum amplification and corresponding peak frequency are found, which are also verified by comparing them with prior analytical or empirical formulas. In addition, applicability of the proposed analytical solution is clarified, and their error bounds are identified. Finally, the utility of analytical solutions and approximations is demonstrated by application to the start-up process of a multi-degree-of-freedom vehicle driveline system.

Thermal Effects on Elasto-Plastic Contacts between Rough Surfaces

2006 ◽  
Vol 532-533 ◽  
pp. 801-804
Author(s):  
Geng Liu ◽  
Tian Xiang Liu ◽  
Qin Xie
Keyword(s):  
Steady State ◽  
Thermal Effects ◽  
Rough Surfaces ◽  
Frictional Heating ◽  
Stress Fields ◽  
Frictional Heat ◽  
Plastic Behavior ◽  
Contact Conditions ◽  
Real Area Of Contact ◽  
Real Area

The effects of the steady-state frictional heating on the contact performance of surface asperities and subsurface stress fields between rough surfaces are investigated in this paper. The asperity distortion caused by the temperature variation in a tribological process, micro plastic flow of surface asperities, and the coupled thermo-elasto-plastic behavior of the materials, with and without considering the strain-hardening property of the materials are studied. In addition, the contact pressure, real area of contact, and average gap of real rough surface with different frictional heat inputs under the thermal elasto-plastic contact conditions are analyzed and discussed.

Asperity persistence and the real area of contact between rough surfaces

1972 ◽  
Vol 327 (1569) ◽  
pp. 147-157 ◽  
Keyword(s):  
Rough Surfaces ◽  
Intrinsic Property ◽  
Surface Layers ◽  
The Real ◽  
Real Area Of Contact ◽  
Heavy Loads ◽  
The Individual ◽  
Hardened Surface ◽  
Hard Ball ◽  
Real Area

It is well known that even under very heavy loads the hills on rough surfaces are not completely flattened. Many workers have advanced possible reasons for this remarkable persistence of the surface asperities. The most commonly advocated mechanisms are examined, and it is demonstrated that none of them provides an adequate explanation of the phenomenon. The plastic indentation of a flat by a hard ball is then studied, and the real area of contact is measured directly using high resolution profilometry. It is concluded that asperity persistence does not depend on the particular metal in contact. Nor is it an intrinsic property of the individual hills on the surface; there is no evidence that work hardening during the crushing of asperities can form a hardened surface layer which leads to a smaller contact area, as is commonly supposed. It is shown that, for local indentations, the degree of contact, i. e. the ratio of real to nominal area, is in general independent of the load. Whenever the surface layers are harder than the bulk the degree of contact is typically between one quarter and one third. However, when the indented body has a uniform hardness the degree of contact was found to be accurately equal to one-half.

Fractal Model of Elastic-Plastic Contact Between Rough Surfaces

1991 ◽  
Vol 113 (1) ◽  
pp. 1-11 ◽  
Author(s):  
A. Majumdar ◽  
B. Bhushan
Keyword(s):  
Size Distribution ◽  
Rough Surfaces ◽  
Surface Profile ◽  
Scanning Tunneling ◽  
Roughness Parameters ◽  
The Real ◽  
Real Area Of Contact ◽  
Fractal Roughness ◽  
Contact Spots ◽  
Real Area

Roughness measurements by optical interferometry and scanning tunneling microscopy on a magnetic thin-film rigid disk surface have shown that its surface is fractal in nature. This leads to a scale-dependence of statistical parameters such as r.m.s height, slope and curvature, which are extensively used in classical models of contact between rough surfaces. Based on the scale-independent fractal roughness parameters, a new model of contact between isotropic rough surfaces is developed. The model predicts that all contact spots of area smaller than a critical area are in plastic contact. When the load is increased, these plastically deformed spots join to form elastic spots. Using a power-law relation for the fractal size-distribution of contact spots, the model shows that for elastic deformation, the load P and the real area of contact Ar are related as P~Ar(3−D)/2, where D is the fractal dimension of a surface profile which lies between 1 and 2. This result explains the origins of the area exponent which has been the focus of a number of experimental and theoretical studies. For plastic loading, the load and area are linearly related. The size-distribution of spots also suggests that the number of contact spots contributing to a certain fraction of the real area of contact remains independent of load although the spot sizes increase with load. The model shows that the load-area relation and the fraction of the real area of contact in elastic and plastic deformation are quite sensitive to the fractal roughness parameters.

The Effect of Nanoparticles on the Real Area of Contact, Friction, and Wear

2013 ◽  
Vol 135 (4) ◽  
Author(s):  
Hamed Ghaednia ◽  
Robert L. Jackson
Keyword(s):  
Friction And Wear ◽  
Silicon Nanoparticles ◽  
Rough Surfaces ◽  
Contact Friction ◽  
Body Contact ◽  
The Real ◽  
Real Area Of Contact ◽  
The Coefficient Of Friction ◽  
Real Area ◽  
Nanoparticle Additives

Although nanoparticle additives have been the topic of multiple studies recently, very little work has attempted to explicitly model the third body contact of nanoparticles. This work presents and uses a novel methodology to model nanoparticles in contact between rough surfaces. The model uses two submodels to handle different scales of contact, namely the nano-sized particles and micrometer-sized roughness features. Silicon nanoparticles suspended in conventional lubricant are modeled in contact between steel rough surfaces. The effect of the particles on contact force and real area of contact has been modeled. The model makes predictions of the coefficient of friction and wear using fundamental models. The results suggest that particles would reduce the real area of contact and, therefore, decrease the friction force. Also, particles could induce abrasive wear by scratching the surfaces. The implications of the model are also discussed, and the arguments and results have been linked to available experimental data. This work finds that particle size and distribution are playing a key role in tribology characteristics of the nanolubricants.

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