scholarly journals Penetration factor of the surfaces in fast algorithm of solution of contact problems for wheel and rail.

2015 ◽  
Vol 2015 (1) ◽  
pp. 46-51
Author(s):  
Владимир Сакало ◽  
Vladimir Sakalo ◽  
Алексей Сакало ◽  
Aleksey Sakalo
Keyword(s):  
Contact Area ◽  
Fast Algorithm ◽  
Contact Problems ◽  
Normal Contact ◽  
Contact Patch ◽  
Penetration Factor ◽  
Rolling Surface

Values of penetration factor of wheel and rail surfaces that is used on application of fast algorithm for solution of normal contact problems are defined. Three cases had been considered: contact area has not strongly expressed spatial character; contact patch is situated nearby middle of rail rolling surface, radii of curvature of wheel and rail profiles have close values; contact patch is situated on fillet sections of the profiles.

A General Three-Dimensional Numerical Technique for Determining the Contact Area of an Arbitrary Punch on an Elastic Half-Space

2016 ◽  
Vol 08 (01) ◽  
pp. 1650005 ◽  
Author(s):  
Jing Jin Shen ◽  
Feng Yu Xu ◽  
Guo Ping Jiang
Keyword(s):  
Numerical Method ◽  
Contact Area ◽  
Numerical Technique ◽  
Three Dimensional ◽  
Contact Problems ◽  
Linear Interpolation ◽  
Contact Boundary ◽  
Reciprocal Theorem ◽  
Normal Contact ◽  
Indentation Force

The paper presents a numerical method for determining the contact area in three-dimensional elastostatic normal contact without friction. The method makes use of the theorem developed by Barber, the contact area is that over which the total indentation force achieves its maximum value. By approximating the punch by linear interpolation, the analytical expression for the indentation force is derived by virtue of the reciprocal theorem. The physical meaning of the parameter which determines the contact boundary is discussed, and its feasible range corresponding to the contact area is found. Then, the numerical algorithm for determining the parameter is developed and applied to solve several normal contact problems. The results show that the proposed numerical method possesses a good property on accuracy and convergency.

An Extension of Hertz’s Theory in Contact Mechanics

2006 ◽  
Vol 74 (2) ◽  
pp. 373-374 ◽  
Author(s):  
Guanghui Fu
Keyword(s):  
Contact Area ◽  
General Procedure ◽  
Contact Problems ◽  
The Body ◽  
Polynomial Functions ◽  
Contact Pressure Distribution ◽  
Total Load ◽  
Normal Contact ◽  
Elastic Bodies ◽  
Hertz's Solution

Hertz’s theory, developed in 1881, remains the foundation for the analysis of most contact problems. In this paper, we consider the axisymmetric normal contact of two elastic bodies, and the body profiles are described by polynomial functions of integer and noninteger positive powers. It is an extension of Hertz’s solution, which concerns the contact of two elastic spheres. A general procedure on how to solve this kind of problem is presented. As an example, we consider the contact between a cone and a sphere. The relations among the radius of the contact area, the depth of the indentation, the total load, and the contact pressure distribution are derived.

Development and Experimental Validation of a Point Contact Model for Dynamical Problems With Friction

2001 ◽  
Author(s):  
Walter Sextro
Keyword(s):  
Pressure Distribution ◽  
Relative Motion ◽  
Contact Area ◽  
Point Contact ◽  
Contact Problems ◽  
Normal Pressure ◽  
Tangential Direction ◽  
Contact Model ◽  
Impact Oscillator ◽  
Normal Contact

Abstract The contact forces are dependent on many parameters, such as contact stiffnesses, surface profiles, material parameters, temperature distribution, relative motion and normal pressure distribution. These parameters can change within the contact area and from here, it is impossible to derive a general force law. The only possibility to overcome this problem is to discretize the contact areas, since in general the relative motion and the contact parameters are not constantly distributed within the contact surface. This leads to a point contact model, which has to include all main physical effects as described above, which are important, when simulating dynamical contact problems with friction. The friction model includes the main parameters such as the roughness of the contact surfaces, the nonlinear friction law, the contact stiffnesses in normal and tangential direction. The decreasing characteristic of the friction coefficient with respect to the relative velocity has to be modeled in a sufficient way. With respect to the dissipation of energy, the hysteretic behavior is studied with respect to the normal and tangential direction. Separation of the contact is included. This point contact model is be applied to real dynamical contact problems. In the first example, a simple impact oscillator with an elastic contact is used to check the overall modeling with respect to the elastic normal contact. Then, a self excited friction oscillator is investigated with respect to the tangential contact. Here, the modeling of surface waviness leads to high periodic solutions, which is also observed within the experiments. In both examples, the comparison of measurements and calculated phase plots is good. Furthermore, the influence of wear on to the surface profile, contact area and normal pressure distribution is investigated. From here, it follows, that friction leads to time dependent systems.

Interaction Model for “Shelled Particles” and Small-Strain Modulus of Granular Materials

2018 ◽  
Vol 85 (10) ◽  
Author(s):  
Shun-hua Zhou ◽  
Peijun Guo ◽  
Dieter F. E. Stolle
Keyword(s):  
Elastic Modulus ◽  
Contact Stiffness ◽  
Scaling Law ◽  
Interaction Model ◽  
Contact Problems ◽  
Hertzian Contact ◽  
Spherical Particles ◽  
Thin Coating ◽  
Normal Contact ◽  
Laboratory Test Results

The elastic modulus of a granular assembly composed of spherical particles in Hertzian contact usually has a scaling law with the mean effective pressure p as K∼G∼p1/3. Laboratory test results, however, reveal that the value of the exponent is generally around 1/2 for most sands and gravels, but it is much higher for reclaimed asphalt concrete composed of particles coated by a thin layer of asphalt binder and even approaching unity for aggregates consisting of crushed stone. By assuming that a particle is coated with a thin soft deteriorated layer, an energy-based simple approach is proposed for thin-coating contact problems. Based on the features of the surface layer, the normal contact stiffness between two spheres varies with the contact force following kn∼Fnm and m∈[1/3,  1], with m=1/3 for Hertzian contact, m=1/2 soft thin-coating contact, m=2/3 for incompressible soft thin-coating, and m=1 for spheres with rough surfaces. Correspondingly, the elastic modulus of a random granular packing is proportional to pm with m∈[1/3,  1].

A Strategy for Fine Mesh Resolution in Contact Mechanics

2021 ◽  
Author(s):  
Gaurav Chauda ◽  
Daniel J. Segalman
Keyword(s):  
Degrees Of Freedom ◽  
Contact Problems ◽  
Boundary Integral ◽  
System Of Equations ◽  
Element Mesh ◽  
Contact Patch ◽  
Linear System Of Equations ◽  
Fine Mesh ◽  
Stiffness Matrices ◽  
Analytic Expressions

Abstract To obtain detail in elastic, frictional contact problems involving contact many — at least tens, and more suitably hundreds [1] — of nodes are necessary over the contact patch. Generally, this fine discretization results in intractable numbers of system equations that must be solved, but this problem is greatly mitigated when the elasticity of the contacting bodies is represented by elastic compliance matrices rather than stiffness matrices. An examination of the classical analytic expressions for the contact of disks — an example of smooth contact — shows that for most standard engineering metals, such as brass, steel, or titanium, the pressures that would cause more than one degree of arc of contact would push the materials past the elastic limit. The discretization necessary to capture the interface tractions would be on the order of at least tens of nodes. With the resulting boundary integral formulation would involve several hundreds of nodes over the disk, and the corresponding finite element mesh would have tens of thousands. The resulting linear system of equations must be solved at each load step and the numerical problem becomes extremely difficult or intractable. A compliance method of facilitating extremely fine contact patch resolution can be achieved by exploiting Fourier analysis and the Michell solution. The advantages of this compliance method are that only degrees of freedom on the surface are introduced and those not in the region of contact are eliminated from the system of equations to be solved.

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.

Influence of the in-plan distribution of asperities on the normal contact of periodically rough surfaces

2016 ◽  
Vol 230 (9) ◽  
pp. 1382-1391
Author(s):  
K Houanoh ◽  
H-P Yin ◽  
J Cesbron ◽  
Q-C He
Keyword(s):  
Numerical Simulations ◽  
Half Space ◽  
Contact Area ◽  
Rough Surfaces ◽  
Elastic Half Space ◽  
Real Contact Area ◽  
Normal Contact ◽  
Real Contact ◽  
Full Contact ◽  
Rigid Surfaces

The present work aims to analyze the influence of the in-plan distribution of asperities on the contact between periodically rough surfaces. Square pattern and hexagonal pattern rigid surfaces are considered. Their contact with an elastic half-space is analyzed by numerical simulations. Three surfaces are generated with identical asperities periodically distributed in a plan according to different patterns. It follows from numerical results that when the load and the real contact area are small, the asperities act almost independently. However, the interaction between close asperities increases with the load becomes intensified and has a significant effect on the contact area when the situation is close to full contact.

Shakedown in Frictional Contact Problems

2007 ◽  
Author(s):  
J. R. Barber ◽  
A. Klarbring ◽  
M. Ciavarella
Keyword(s):  
Frictional Contact ◽  
Elastic System ◽  
Contact Problems ◽  
Sufficient Condition ◽  
Normal Contact ◽  
Linear Elastic ◽  
Periodic Loading ◽  
Continuum Formulation ◽  
Complete Contact ◽  
The Continuum

If a linear elastic system with frictional interfaces is subjected to periodic loading, any slip which occurs generally reduces the tendency to slip during subsequent cycles and in some circumstances the system ‘shakes down’ to a state without slip. It has often been conjectured that a frictional Melan’s theorem should apply to this problem — i.e. that the existence of a state of residual stress sufficient to prevent further slip is a sufficient condition for the system to shake down. Here we discuss recent proofs that this is indeed the case for ‘complete’ contact problems if there is no coupling between relative tangential displacements at the interface and the corresponding normal contact tractions. By contrast, when coupling is present, the theorem applies only for a few special two-dimensional discrete cases. Counter-examples can be generated for all other cases. These results apply both in the discrete and the continuum formulation.

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.

Material Considerations for High Temperature Tilting Pad Gas Bearings

1968 ◽  
Vol 90 (4) ◽  
pp. 818-828 ◽  
Author(s):  
S. F. Murray ◽  
M. B. Peterson
Keyword(s):  
High Temperature ◽  
Contact Area ◽  
High Speed ◽  
Contact Problems ◽  
Sliding Contact ◽  
Gas Bearings ◽  
Hydrodynamic Bearing ◽  
Tilting Pad ◽  
Short Time

This paper is concerned with the sliding contact problems encountered in tilting pad gas bearings operating at temperatures up to 1400 deg F. Both the pivots and the bearing surfaces are considered. Short time experimental evaluations of pivot damage are summarized. The results of start-stop and high-speed rub tests on a single tilting pad hydrodynamic bearing are also described. Based on the results obtained to date, damage-resistant coatings are available for use on the bearing surfaces at high temperature. There are also suitable pivot materials, but the pivot must be properly designed to minimize slip in the contact area.

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