A Contact Model of Nominally Flat Rough Surfaces Based on a Visco-Elasto-Adhesive Interaction

2009 ◽  
Vol 131 (4) ◽  
Author(s):  
W. Cheng ◽  
K. Farhang
Keyword(s):  
Closed Form ◽  
Contact Force ◽  
Rough Surfaces ◽  
Mathematical Formulation ◽  
Power Laws ◽  
Adhesive Interaction ◽  
Time Rate ◽  
Normal Contact ◽  
Normal Contact Force ◽  
Rate Dependent

Approximate closed-form equations are derived for normal contact force between nominally flat rough surfaces in dry contact. The formulation is based on the asperity-level interaction in which adhesive forces between two asperities and elastic and rate-dependent forces are included. The elastic and time rate-dependent portion of force is derived using a viscoelastic interaction of the two asperities. Statistical consideration of rough surfaces then furnishes the mathematical formulation of total normal force due to adhesion, elastic, and rate-dependent properties of the solids in contact. The probabilistic formulation of contact force leads to integral equations. From these are derived approximate closed-form expressions that relate the microscale properties of the surfaces to the macroscale behavior in the form of the total normal contact force between the surfaces. The approximate equations for visco-elasto-adhesive contact of rough surfaces illustrate the dependence of the contact force on the time rate of approach based on a combination of 1/6, 1/3, and 1 power laws.

Contact Model of Two Rough Surfaces Based on a Visco-Elasto-Adhesive Interaction

2010 ◽  
Author(s):  
Ali Sepehri ◽  
Kambiz Farhang
Keyword(s):  
Normal Force ◽  
Rough Surfaces ◽  
Mathematical Formulation ◽  
Contact Model ◽  
Force Component ◽  
Adhesive Interaction ◽  
Normal Contact ◽  
Rate Dependent ◽  
Statistical Consideration ◽  
Adhesive Forces

Mathematical formulae are derived for normal contact force component between two nominally flat rough surfaces. The development of the contact model is based on the asperity level interaction in which adhesive forces between two asperities as well as elastic and rate-dependent forces are included. Statistical consideration of rough surfaces yields the mathematical formulation of total normal force due to adhesion, elastic and rate-dependent properties of the surfaces in contact.

Experimental Validation of a Volumetric Planetary Rover Wheel/Soil Interaction Model

2013 ◽  
Author(s):  
Willem Petersen ◽  
John McPhee
Keyword(s):  
Contact Force ◽  
Interaction Model ◽  
Contact Model ◽  
Soil Parameters ◽  
Model Parameters ◽  
Force Model ◽  
Normal Contact ◽  
Planetary Rover ◽  
Normal Contact Force ◽  
Contact Force Model

For the multibody simulation of planetary rover operations, a wheel-soil contact model is necessary to represent the forces and moments between the tire and the soft soil. A novel nonlinear contact modelling approach based on the properties of the hypervolume of interpenetration is validated in this paper. This normal contact force model is based on the Winkler foundation model with nonlinear spring properties. To fully define the proposed normal contact force model for this application, seven parameters are required. Besides the geometry parameters that can be easily measured, three soil parameters representing the hyperelastic and plastic properties of the soil have to be identified. Since it is very difficult to directly measure the latter set of soil parameters, they are identified by comparing computer simulations with experimental results of drawbar pull tests performed under different slip conditions on the Juno rover of the Canadian Space Agency (CSA). A multibody dynamics model of the Juno rover including the new wheel/soil interaction model was developed and simulated in MapleSim. To identify the wheel/soil contact model parameters, the cost function of the model residuals of the kinematic data is minimized. The volumetric contact model is then tested by using the identified contact model parameters in a forward dynamics simulation of the rover on an irregular 3-dimensional terrain and compared against experiments.

Closed-Form Equations for Three Dimensional Elastic-Plastic Contact of Nominally Flat Rough Surfaces

2009 ◽  
Vol 131 (4) ◽  
Author(s):  
Ali Sepehri ◽  
Kambiz Farhang
Keyword(s):  
Closed Form ◽  
Contact Force ◽  
Rough Surfaces ◽  
Tangential Force ◽  
Three Dimensional ◽  
Tangential Direction ◽  
Asperity Contact ◽  
Force Component ◽  
Elastic Plastic ◽  
Functional Forms

Approximate closed-form equations governing the shoulder-shoulder contact of asperities are derived based on a generalization by Chang, Etsion, and Bogy. The work entails the consideration of asperity shoulder-shoulder contact in which the volume conservation is assumed in the plastic flow regime. Shoulder-shoulder asperity contact gives rise to a slanted contact force comprising tangential and normal components. Each force component comprises elastic and plastic terms, which upon statistical summation yields the force component for the elastic and plastic forces for the contact of two rough surfaces. Half-plane tangential force due to elastic-plastic contact is derived through the statistical summation of tangential force component along an arbitrary tangential direction. Two sets of equations are found. In the first set of equations the functional forms are simpler and provide approximation of contact force to within 9%. The second set is enhanced equations derived from the first set of approximate equations that achieve an accuracy of within 0.2%.

A Theoretical Model for the Normal Contact Force of Two Elastoplastic Ellipsoidal Bodies

2020 ◽  
Vol 88 (3) ◽  
Author(s):  
Verena Becker ◽  
Marc Kamlah
Keyword(s):  
Theoretical Model ◽  
Contact Force ◽  
General Description ◽  
Element Analysis ◽  
Normal Contact ◽  
Normal Contact Force ◽  
Static Contact ◽  
Elliptical Contact ◽  
Individual Grains ◽  
Force Displacement

Abstract To model the mechanical behavior of granular materials, a reliable description of the material properties is indispensable. Individual grains are usually not perfectly spherical. In batteries, for instance, lithium nickel manganese cobalt oxide (NMC) is a frequently used material, consisting out of particles with possibly ellipsoidal like shapes. As particles may plastically deform under increasing stresses, the paper presents a theoretical model for the normal contact force of elastoplastic ellipsoidal bodies for the use in the context of mechanical discrete element method (DEM). The model can be considered as extension of the elastic, elastic-plastic, fully plastic Thornton model by using a more general description to incorporate elliptical contact areas. The focus is on a normal contact force description as continuous function of time for all regimes, elastic, elastoplastic, and fully plastic loading, as well as unloading from elastoplastic loading, while the evolution of the plastic contact area is not considered here. All underlying formulae to describe the force-displacement relationship for the static contact problem are derived, partly based on finite element analysis (FEA). To verify the new model, FEAs are performed and their results compared with the model predictions.

Normal and Angular Motions at Rough Planar Contacts During Sliding With Friction

1992 ◽  
Vol 114 (3) ◽  
pp. 567-578 ◽  
Author(s):  
D. P. Hess ◽  
A. Soom
Keyword(s):  
Nonlinear Equations ◽  
Contact Force ◽  
Contact Area ◽  
Normal Contact ◽  
Frictional Contacts ◽  
Normal Contact Force ◽  
The Real ◽  
Real Area Of Contact ◽  
Real Area ◽  
Contact Vibrations

The planar dynamics of a rough block in nominally stationary or sliding contact with a counter-surface is studied in this work. Starting with the Greenwood-Williamson model of a rough surface, the analysis of elastic contact deflections is extended to accommodate angular as well as normal motions. The real area of contact and the normal contact force are obtained in terms of the relative approach and orientation of the surfaces. It is shown that angular and normal motions at frictional contacts are generally coupled. The contact area and normal contact force are shown to be nonlinearly related to the normal and angular motions. However, the contact area remains proportional to the normal load, even in the presence of angular motions. When the friction force is assumed to be proportional to the real area of contact, the coefficient of sliding friction will be unchanged by small relative rotations between the sliding bodies. Based on this contact and friction model, the nonlinear equations of motion that describe the planar contact vibrations of a sliding block can be written directly. Although a detailed analysis of the stability and response characteristics of these nonlinear equations is beyond the scope of the present work, a limited comparison of calculations and measurements taken on both stationary and sliding blocks indicate that the small amplitude contact vibrations are reasonably well captured by the model developed in this work.

Friction/Vibration Coupling Due to Viscoelastic Interaction of Rough Surfaces of Two Disks in Frictional Contact

2003 ◽  
Author(s):  
Kambiz Farhang ◽  
Aik-Liang Lim
Keyword(s):  
Contact Force ◽  
Dynamic Instability ◽  
Rough Surfaces ◽  
Normal Load ◽  
Mathematical Formulation ◽  
Negative Slope ◽  
Axial Position ◽  
Disk System ◽  
Macro Scale ◽  
Approximate Equations

Approximate equations describing contact of rough surfaces are implemented in the equations of motion for frictional interaction of two disks in relative rotational motion. The approximate equations are nonlinear functions of the relative axial position of the two disks and provide coupling between their compressive and rotary motion. A set of two coupled nonlinear ordinary differential equations is obtained. The mathematical formulation propounded in this paper connects the tribological events at micron-scale and the macroscopic scale vibration response of the two-disk system. This is accomplished by a visco-elastic account of interaction at the micron scale, its statistical quantification through the approximate analytical representation of the statistical expectation of contact force and the introduction of the contact force into the macro-scale dynamics of the two-disk system. Steady-state analysis of the system supports observed behavior of many mechanical systems with friction. It is shown that, as a result of coupling of the macro-system’s dynamics and contact, there are combinations of parameters at the microand macro-scale that yield negative slope in friction force/sliding speed, a well known source of dynamic instability. This results in an effective negative damping that tends to reduce with decrease in the normal load and/or increase in structural damping of the system.

Elastic-Plastic Finite-Element Analysis of Repeated, Two-Dimensional Wheel-Rail Rolling Contact under Time-Dependent Load

2006 ◽  
Vol 220 (5) ◽  
pp. 603-613 ◽  
Author(s):  
Z. F. Wen ◽  
X. S. Jin
Keyword(s):  
Finite Element ◽  
Residual Stresses ◽  
Contact Force ◽  
Rolling Contact ◽  
Time Dependent ◽  
Two Dimensional ◽  
Normal Contact ◽  
Normal Contact Force ◽  
Residual Strains ◽  
Harmonic Variation

A study was performed using a finite-element model to obtain stresses, strains, and deformations for repeated, two-dimensional rolling contact of a locomotive driving wheel and a rail under time-dependent load. An advanced cyclic plasticity model was used with a commercial finite element code via a material subroutine. The time-dependent load was considered a harmonic variation of the wheel-rail normal contact force. The normal contact pressure was assumed to follow the Hertzian distribution and the tangential force followed the Carter distribution. A wavy profile is formed on the running surface of the rail subjected to the harmonic variation of the normal (vertical) contact force. The developed wavelength of the profile corresponds to the frequency of the normal contact force for the actual train speed. The creepage or rolling-sliding condition plays an important role in the residual strains and deformations, but its influence on the residual stresses is insignificant. The residual stresses at the surface decrease with increasing rolling passes and gradually tend to stabilize. The residual strains and surface displacements increase with increasing rolling cycle, but the increases in residual strain and surface displacement per rolling pass (ratchetting rate) decay. The residual stresses, strains, and deformations near the wave trough of the residual wavy deformation are larger than those near the wave crest. For any given creepage including zero value, when the number of rolling passes increases, the surface depth of the wavy-deformed surface increases but the ratchetting rate decays. The results are useful in investigating the influence of plastic deformation on rail corrugation.

scholarly journals Closed-Form Equations for Contact Force and Moment in Elastic Contact of Rough Surfaces

2011 ◽  
Vol 2011 ◽  
pp. 1-14 ◽  
Author(s):  
Ali Sepehri ◽  
Kambiz Farhang
Keyword(s):  
Closed Form ◽  
Half Plane ◽  
Contact Force ◽  
Normal Force ◽  
Rough Surfaces ◽  
Tangential Force ◽  
Compressive Load ◽  
Angular Misalignment ◽  
Tangential Contact ◽  
Applied Forces

It is reasonable to expect that, when two nominally flat rough surfaces are brought into contact by an applied resultant force, they must support, in addition to the compressive load, an induced moment. The existence of a net applied moment would imply noneven distribution of contact force so that there are more asperities in contact over one region of the nominal area. In this paper, we consider the contact between two rectangular rough surfaces that provide normal and tangential contact force as well as contact moment to counteract the net moment imposed by the applied forces. The surfaces are permitted to develop slight angular misalignment, and thereby contact moment is derived. Through this scheme, it is possible to also define elastic contribution to friction since the half-plane tangential contact force on one side of an asperity is no longer balanced by the half-plane tangential force component on the opposite side. The elastic friction force, however, is shown to be of a much smaller order than the contact normal force. Approximate closed-form equations are found for contact force and moment for the contact of rough surfaces.

Research on Normal Motion of Specimen of Ultrasonic Feeding

2012 ◽  
Vol 433-440 ◽  
pp. 3826-3830
Author(s):  
Liang Li ◽  
Mian Zheng
Keyword(s):  
Contact Force ◽  
Structural Model ◽  
Contact Process ◽  
Low Frequency ◽  
Normal Velocity ◽  
Normal Contact ◽  
Nonlinear Dynamical ◽  
Normal Contact Force ◽  
Theoretical Results ◽  
Good Agreement

In this paper, a micro structural model is applied to study the normal contact process of the specimen of the ultrasonic feeding. Firstly, the normal velocity of the specimen with the actuation of the oscillator is calculated by solving the nonlinear dynamical equation of the specimen. The theoretical results of the normal velocity are in good agreement with the experimental results under the same conditions. The theoretical results indicate that for the low frequency of the oscillator, at most time, the normal contact force is zero, whereas for the high frequency the normal contact force is periodical. In addition, the theoretical results also indicate the contact time between specimen and the oscillator in a period decreases with the increasing amplitude of the oscillator.

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