Finite element analysis is used to investigate an elastic-plastic coated spherical contact in full stick contact condition under combined normal and tangential loading. Sliding inception is associated with a loss of t...Finite element analysis is used to investigate an elastic-plastic coated spherical contact in full stick contact condition under combined normal and tangential loading. Sliding inception is associated with a loss of tangential stiffness. The effect of coating thickness on the static friction coefficient is intensively investigated for the case of hard coatings. For this case, with the increase in coating thickness, the static friction coefficient first increases to its maximum value at a certain coating thickness, thereafter decreases, and eventually levels off. The effect of the normal load and material properties on this behavior is discussed. Finally, a model for the static friction coefficient as a function of the coating thickness is provided for a wide range of material properties and normal loading.展开更多
The static friction behavior of an elastic–plastic spherical adhesive microcontact between a rigid flat and a deformable sphere under combined normal and tangential loading is studied by the finite element method(FEM...The static friction behavior of an elastic–plastic spherical adhesive microcontact between a rigid flat and a deformable sphere under combined normal and tangential loading is studied by the finite element method(FEM).The contact between the sphere and the rigid flat is assumed to be full-stick,and the sliding inception is related to a loss of tangential stiffness.The intermolecular force between the rigid flat and the sphere is assessed by the Lennard–Jones(LJ)potential,which is applied to the sphere and the rigid flat by a user subroutine.The evolution of the adhesive force with tangential displacement in the full-stick condition is revealed.The results indicate that the increasing effect of adhesive energy on the static friction coefficient gradually diminishes with an increase in the adhesive energy and the external normal load.Finally,based on an extensive parametric study,an empirical dimensionless expression is obtained to predict the static friction coefficient of the spherical adhesive microcontact considering the intermolecular force.展开更多
Relationship between contact size(A)and static friction(f)has been studied for rigid crystalline systems.We built a series of systems with two identical surfaces but different orientations and investigated the effects...Relationship between contact size(A)and static friction(f)has been studied for rigid crystalline systems.We built a series of systems with two identical surfaces but different orientations and investigated the effects of the size and shape of the contact area on static friction.In these systems,there are numerous nontrivial commensurate contacts.Our results confirmed that the relationship between A and f was determined by both commensurability and shape of the contact.For commensurate contacts,f∝A independent of the shape.For incommensurate contacts,generally f∝A^(0) for regular shapes or f∝A^(1/4) for irregular shapes;however,in very few cases of regular shapes,f∝A^(1/2).Moreover,in above systems,commensurability of a contact can be easily changed by a perturbation of the misfit angle.Therefore,if the perturbation caused by the lateral force and the deformation of the surface are considered(as is the case in real systems),further research is necessary.展开更多
In a recent publication the author derived and experimentally tested several theoretical models, distinguished by different boundary conditions at the contacts with horizontal and vertical supports, that predicted the...In a recent publication the author derived and experimentally tested several theoretical models, distinguished by different boundary conditions at the contacts with horizontal and vertical supports, that predicted the forces of reaction on a fixed (i.e. inextensible) ladder. This problem is statically indeterminate since there are 4 forces of reaction and only 3 equations of static equilibrium. The model that predicted the empirical reactions correctly used a law of static friction to complement the equations of static equilibrium. The present paper examines in greater theoretical and experimental detail the role of friction in accounting for the forces of reaction on a fixed ladder. The reported measurements confirm that forces parallel and normal to the support at the top of the ladder are linearly proportional with a constant coefficient of friction irrespective of the magnitude or location of the load, as assumed in the theoretical model. However, measurements of forces parallel and normal to the support at the base of the ladder are linearly proportional with coefficients that depend sensitively on the location (although not the magnitude) of the load. This paper accounts quantitatively for the different effects of friction at the top and base of the ladder under conditions of usual use whereby friction at the vertical support alone is insufficient to keep the ladder from sliding. A theoretical model is also proposed for the unusual circumstance in which friction at the vertical support can keep the ladder from sliding.展开更多
This work studies a mathematical model describing the static process of contact between a piezoelectric body and a thermally-electrically conductive foundation. The behavior of the material is modeled with a thermo-el...This work studies a mathematical model describing the static process of contact between a piezoelectric body and a thermally-electrically conductive foundation. The behavior of the material is modeled with a thermo-electro-elastic constitutive law. The contact is described by Signorini＇s conditions and Tresca＇s friction law including the electrical and thermal conductivity conditions. A variational formulation of the model in the form of a coupled system for displacements, electric potential, and temperature is de- rived. Existence and uniqueness of the solution are proved using the results of variational inequalities and a fixed point theorem.展开更多
By using the molecular dynamic simulation method with a fourth-order Runge--Kutta algorithm, a two-dimensional dc- and ac-driven Frenkel--Kontorova （FK） model with a square symmetry substrate potential for a square ...By using the molecular dynamic simulation method with a fourth-order Runge--Kutta algorithm, a two-dimensional dc- and ac-driven Frenkel--Kontorova （FK） model with a square symmetry substrate potential for a square lattice layer has been investigated in this paper. For this system, the effects of many different parameters on the average velocity and the static friction force have been studied. It is found that not only the amplitude and frequency of ac-driven force, but also the direction of the external driving force and the misfit angle between two layers have some strong influences on the static friction force. It can be concluded that the superlubricity phenomenon appears easily with a larger ac amplitude and lower ac frequency for some special direction of the external force and misfit angle.展开更多
In this paper, a method to posture maintenance control of 2-link object by nonprehensile two-cooperative-arm robot without compensating friction is proposed. In details, a mathematical model of the 2-link object is fi...In this paper, a method to posture maintenance control of 2-link object by nonprehensile two-cooperative-arm robot without compensating friction is proposed. In details, a mathematical model of the 2-link object is firstly built. Based on the model, stable regions for holding motion of nonprehensile two-cooperative-arm robot are obtained while the 2-link object is kept stable on the robot arms with static friction. Among the obtained stable regions, the robust pairs of orientation angles of the 2-link object are found. Under the robust orientation angles, a feedback control system is designed to control the arms to maintain the 2-link object's posture while it is being held or lifted up. Finally, experimental results are shown to verify the effectiveness of the proposed method.展开更多
The paper presents the formulation and approximation of a static thermoelasticity problem that describes bilateral frictional contact between a deformable body and a rigid foundation. The friction is in the form of a ...The paper presents the formulation and approximation of a static thermoelasticity problem that describes bilateral frictional contact between a deformable body and a rigid foundation. The friction is in the form of a nonmonotone and multivalued law. The coupling effect of the problem is neglected. Therefore, the thermic part of the problem is considered independently on the elasticity problem. For the displacement vector, we formulate one substationary problem for a non-convex, locally Lipschitz continuous functional representing the total potential energy of the body. All problems formulated in the paper are approximated with the finite element method.展开更多
文摘Finite element analysis is used to investigate an elastic-plastic coated spherical contact in full stick contact condition under combined normal and tangential loading. Sliding inception is associated with a loss of tangential stiffness. The effect of coating thickness on the static friction coefficient is intensively investigated for the case of hard coatings. For this case, with the increase in coating thickness, the static friction coefficient first increases to its maximum value at a certain coating thickness, thereafter decreases, and eventually levels off. The effect of the normal load and material properties on this behavior is discussed. Finally, a model for the static friction coefficient as a function of the coating thickness is provided for a wide range of material properties and normal loading.
基金supported by the Israel Academy of Sciences and Humanities and the Council for Higher Education Excellence Fellowship Program for International Postdoctoral Researcher,the National Natural Science Foundation of China(52105052)the China Scholarship Council(202308500207).
文摘The static friction behavior of an elastic–plastic spherical adhesive microcontact between a rigid flat and a deformable sphere under combined normal and tangential loading is studied by the finite element method(FEM).The contact between the sphere and the rigid flat is assumed to be full-stick,and the sliding inception is related to a loss of tangential stiffness.The intermolecular force between the rigid flat and the sphere is assessed by the Lennard–Jones(LJ)potential,which is applied to the sphere and the rigid flat by a user subroutine.The evolution of the adhesive force with tangential displacement in the full-stick condition is revealed.The results indicate that the increasing effect of adhesive energy on the static friction coefficient gradually diminishes with an increase in the adhesive energy and the external normal load.Finally,based on an extensive parametric study,an empirical dimensionless expression is obtained to predict the static friction coefficient of the spherical adhesive microcontact considering the intermolecular force.
基金supported by National Natural Science Foundation of China(No.51675395)Special Fund for Outstanding Young and Middle-aged Scientific and Technological Innovation Team in the University from Hubei Province(No.T201709)Doctoral Startup Fund for Scientific Research at Wuhan Polytechnic University(2014RZ31).
文摘Relationship between contact size(A)and static friction(f)has been studied for rigid crystalline systems.We built a series of systems with two identical surfaces but different orientations and investigated the effects of the size and shape of the contact area on static friction.In these systems,there are numerous nontrivial commensurate contacts.Our results confirmed that the relationship between A and f was determined by both commensurability and shape of the contact.For commensurate contacts,f∝A independent of the shape.For incommensurate contacts,generally f∝A^(0) for regular shapes or f∝A^(1/4) for irregular shapes;however,in very few cases of regular shapes,f∝A^(1/2).Moreover,in above systems,commensurability of a contact can be easily changed by a perturbation of the misfit angle.Therefore,if the perturbation caused by the lateral force and the deformation of the surface are considered(as is the case in real systems),further research is necessary.
文摘In a recent publication the author derived and experimentally tested several theoretical models, distinguished by different boundary conditions at the contacts with horizontal and vertical supports, that predicted the forces of reaction on a fixed (i.e. inextensible) ladder. This problem is statically indeterminate since there are 4 forces of reaction and only 3 equations of static equilibrium. The model that predicted the empirical reactions correctly used a law of static friction to complement the equations of static equilibrium. The present paper examines in greater theoretical and experimental detail the role of friction in accounting for the forces of reaction on a fixed ladder. The reported measurements confirm that forces parallel and normal to the support at the top of the ladder are linearly proportional with a constant coefficient of friction irrespective of the magnitude or location of the load, as assumed in the theoretical model. However, measurements of forces parallel and normal to the support at the base of the ladder are linearly proportional with coefficients that depend sensitively on the location (although not the magnitude) of the load. This paper accounts quantitatively for the different effects of friction at the top and base of the ladder under conditions of usual use whereby friction at the vertical support alone is insufficient to keep the ladder from sliding. A theoretical model is also proposed for the unusual circumstance in which friction at the vertical support can keep the ladder from sliding.
文摘This work studies a mathematical model describing the static process of contact between a piezoelectric body and a thermally-electrically conductive foundation. The behavior of the material is modeled with a thermo-electro-elastic constitutive law. The contact is described by Signorini＇s conditions and Tresca＇s friction law including the electrical and thermal conductivity conditions. A variational formulation of the model in the form of a coupled system for displacements, electric potential, and temperature is de- rived. Existence and uniqueness of the solution are proved using the results of variational inequalities and a fixed point theorem.
基金supported by the National Natural Science Foundation of China (Grand Nos. 50575217, 10875098 and 50421502)the Natural Science Foundation of Northwest Normal University (Grant Nos. NWNU-KJCXGC-03-17 and NWNU-KJCXGC-03-48)
文摘By using the molecular dynamic simulation method with a fourth-order Runge--Kutta algorithm, a two-dimensional dc- and ac-driven Frenkel--Kontorova （FK） model with a square symmetry substrate potential for a square lattice layer has been investigated in this paper. For this system, the effects of many different parameters on the average velocity and the static friction force have been studied. It is found that not only the amplitude and frequency of ac-driven force, but also the direction of the external driving force and the misfit angle between two layers have some strong influences on the static friction force. It can be concluded that the superlubricity phenomenon appears easily with a larger ac amplitude and lower ac frequency for some special direction of the external force and misfit angle.
文摘In this paper, a method to posture maintenance control of 2-link object by nonprehensile two-cooperative-arm robot without compensating friction is proposed. In details, a mathematical model of the 2-link object is firstly built. Based on the model, stable regions for holding motion of nonprehensile two-cooperative-arm robot are obtained while the 2-link object is kept stable on the robot arms with static friction. Among the obtained stable regions, the robust pairs of orientation angles of the 2-link object are found. Under the robust orientation angles, a feedback control system is designed to control the arms to maintain the 2-link object's posture while it is being held or lifted up. Finally, experimental results are shown to verify the effectiveness of the proposed method.
基金supported by the Minisitry of Science of the Republic of Serbia (No. 144005)
文摘The paper presents the formulation and approximation of a static thermoelasticity problem that describes bilateral frictional contact between a deformable body and a rigid foundation. The friction is in the form of a nonmonotone and multivalued law. The coupling effect of the problem is neglected. Therefore, the thermic part of the problem is considered independently on the elasticity problem. For the displacement vector, we formulate one substationary problem for a non-convex, locally Lipschitz continuous functional representing the total potential energy of the body. All problems formulated in the paper are approximated with the finite element method.
