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.

Contact Moment and Friction Force in Elastic Contact of Two Rough Surfaces

2007 ◽  
Author(s):  
A. Sepehri ◽  
K. Farhang
Keyword(s):  
Friction Force ◽  
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 non-even 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 through this 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.

Moment and Friction Force in Three Dimensional Elastic Contact of Two Rectangular Rough Surfaces

2007 ◽  
Author(s):  
A. Sepehri ◽  
K. Farhang
Keyword(s):  
Friction Force ◽  
Half Plane ◽  
Contact Force ◽  
Rough Surfaces ◽  
Tangential Force ◽  
Three Dimensional ◽  
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 non-even 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 through this 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.

Elastic Contact of Rough Surfaces Subject to Combined Force and Moment

2009 ◽  
Vol 131 (3) ◽  
Author(s):  
Ali Sepehri ◽  
Kambiz Farhang
Keyword(s):  
Half Plane ◽  
Normal Force ◽  
Rough Surfaces ◽  
Tangential Force ◽  
Contact Forces ◽  
Elastic Contact ◽  
Force Component ◽  
Angular Misalignment ◽  
Tangential Contact ◽  
Applied Forces

In this paper we consider the contact between two rectangular rough surfaces that provide normal and tangential contact forces, as well as contact moment, to counteract the net moment imposed by the applied forces. The surfaces are permitted to develop a 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.

Combined Force and Moment in a Three Dimensional Model of Elastic Contact of Nominally Flat Rough Surfaces

2008 ◽  
Author(s):  
A. Sepehri ◽  
K. Farhang
Keyword(s):  
Half Plane ◽  
Contact Force ◽  
Rough Surfaces ◽  
Tangential Force ◽  
Three Dimensional ◽  
Radius Of Curvature ◽  
Three Dimensional Model ◽  
Tangential Contact ◽  
Applied Forces ◽  
Approximate Equations

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 as functions of separation, asperity radius of curvature sum, mean plane slope and nominal contact dimension. The approximate equations are shown to give error within seven percent.

Contact of Rough Surfaces: Combined Elastic and Rate-Dependent Effects

2008 ◽  
Author(s):  
Ali Sepehri ◽  
Kambiz Farhang
Keyword(s):  
Half Plane ◽  
Contact Force ◽  
Rough Surfaces ◽  
Tangential Force ◽  
Approximation Error ◽  
Tangential Velocity ◽  
Contact Forces ◽  
Tangential Contact ◽  
Force Components ◽  
Approximate Equations

Approximate closed form equations are found for normal and tangential contact forces of rough surfaces in dry friction. Using a viscoelastic asperity behavior, mathematical formulae are derived for normal and tangential components of the contact force that depend not only on the separation of the two surfaces but also the rate of approach and relative sliding. The tangential force over a half-plane, corresponding to the moving direction, is found accounting for the directionality of the tangential component of asperity forces. A statistical approach is forwarded in which dependence of the asperity normal and tangential contact force on relative tangential velocity of two asperities can presented as corrective factors in the mathematical description of normal and tangential force components. These are force directionality corrective coefficient and force-velocity directionality corrective coefficient. Two sets of approximate equations are found for each of the normal and half-plane tangential force components. The simplest forms of the approximate equations achieve accuracy to within five (5) percent error, while other forms yield approximation error within 0.2 percent.

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%.

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

2007 ◽  
Author(s):  
A. Sepehri ◽  
K. Farhang
Keyword(s):  
Closed Form ◽  
Contact Force ◽  
Rough Surfaces ◽  
Tangential Force ◽  
Three Dimensional ◽  
Tangential Direction ◽  
Asperity Contact ◽  
Force Component ◽  
Elastic Plastic ◽  
Form Closure

Approximate closed-form (closure) equations governing the shoulder-shoulder contact of asperities are derived based on a generalization of Chang, Etsion and Bogy (CEB). The work entails the consideration of asperity shoulder-shoulder contact in which 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 elastic-plastic terms, which upon statistical summation yields the force component for the elastic and elastic-plastic force 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 closure equations are found. In the first set of equations the functional forms are simpler and provide approximation of contact force to within nine percent (9%). The second set of closure equations are closed form equations of more complicated form but with accuracy to within 0.2 percent (0.2%).

Viscoelastic Contact of Nominally Flat Rough Surfaces

2005 ◽  
Author(s):  
K. Farhang ◽  
A. Lim
Keyword(s):  
Contact Force ◽  
Rough Surfaces ◽  
Tangential Force ◽  
Tangential Velocity ◽  
Surface Profile ◽  
Contact Forces ◽  
Profile Measurement ◽  
Tangential Contact ◽  
Corrective Factor ◽  
Percent Accuracy

Approximate closed-form equations are derived for normal and tangential contact forces of rough surfaces in dry friction. Using an extension of the Greenwood and Tripp model, in which the derivations permit asperity shoulder-to-shoulder contact and viscoelastic asperity behavior. Mathematical formulae are derived for normal and tangential components of the contact force that depend not only on the proximity of the two surfaces but also the rate of approach and relative sliding. A statistical approach is forwarded in which dependence of the asperity tangential contact force on relative tangential velocity of two asperities can be cast as a corrective factor in the mathematical description of tangential force. In this regard two corrective coefficients are derived: force directionality corrective coefficient and force-velocity directionality corrective coefficient. The results show that for a moderate to high load ranges the contact force can be analytically described to within 20 percent accuracy, well below the uncertainties due to surface profile measurement.

A Kinetic Friction Model for Viscoelastic Contact of Nominally Flat Rough Surfaces

2007 ◽  
Vol 129 (3) ◽  
pp. 684-688 ◽  
Author(s):  
K. Farhang ◽  
A. Lim
Keyword(s):  
Contact Force ◽  
Rough Surfaces ◽  
Tangential Force ◽  
Tangential Velocity ◽  
Surface Profile ◽  
Friction Model ◽  
Contact Forces ◽  
Profile Measurement ◽  
Tangential Contact ◽  
Force Velocity

Approximate closed-form equations are derived for normal and tangential contact forces of rough surfaces in dry friction. Using an extension of the Greenwood and Tripp (1970, Proc, Inst. Mech. Eng., 185, pp. 625–633) model, in which the derivations permit asperity shoulder-to-shoulder contact and viscoelastic asperity behavior, mathematical formulae are derived for normal and tangential components of the contact force that depend not only on the proximity of the two surfaces but also the rate of approach and relative sliding. A statistical approach is forwarded in which dependence of the asperity tangential contact force on relative tangential velocity of two asperities can be cast as corrective factors in the mathematical description of tangential force. In this regard two corrective coefficients are derived: force directionality corrective coefficient and force–velocity directionality corrective coefficient. The results show that for a moderate to high load ranges the contact force can be analytically described to within 20% accuracy of that from a numerical integration of the contact equations, well below the uncertainties due to surface profile measurement.

Tangential Force Model for the Combined Finite-Discrete Element Method

2019 ◽  
Vol 17 (09) ◽  
pp. 1950068
Author(s):  
Xunnan Liu ◽  
Lanhao Zhao ◽  
Jia Mao ◽  
Tongchun Li
Keyword(s):  
Discrete Element Method ◽  
Contact Interaction ◽  
Contact Force ◽  
Tangential Force ◽  
Numerical Test ◽  
Discrete Element ◽  
Force Model ◽  
Normal Contact ◽  
Tangential Contact ◽  
Element Method

In the past, contact model in the combined finite-discrete element method (FDEM) does not include the influence of the tangential contact interaction, and the deficient model associated with the contact force can seriously degrade the computing accuracy. In order to overcome this defect, an improved FDEM is developed in this work. The potential contact mechanism is implemented to calculate the normal contact force; meanwhile, the force-displacement law by coupling the classical Mohr–Coulomb type frictional algorithm and the rotation transformation algorithm is applied for the accurate computation of the tangential contact force. Consequently, a holonomic system of the calculation algorithm for the contact interaction is proposed, accounting for the influence of the tangential contact force. The performance of the approach is validated with well-known benchmarks including a frictional numerical test, the dynamic response of the block under the seismic excitation, a sliding/toppling test of a joint rock slope, a numerical simulation for joints structure affecting a sliding rock mass and the 2008 Donghekou Landslide trigged by the Wenchuan Earthquake. The results are compared against the experimental data and analytical solutions. Excellent agreements between the computational result and existing measurements show that the proposed approach has an outstanding ability to describe the complex mechanical properties among the separate entities.

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