Presence Of Coulomb Friction Research Articles

Static frictional indentation of an elastic half-plane by a rigid unsymmetrical punch

Static rigid 2-D indentation of a linearly elastic half-plane in the presence of Coulomb friction which reverses its sign along the contact length is studied. The solution approach lies within the context of the mathematical theory of elastic contact mechanics. A rigid punch, having an unsymmetrical profile with respect to its apex and no concave regions, both slides over and indents slowly the surface of the deformable body. Both a normal and a tangential force may, therefore, be exerted on the punch. In such a situation, depending upon the punch profile and the relative magnitudes of the two external forces, a point in the contact zone may exist at which the surface friction changes direction. Moreover, this point of sign reversal may not coincide, in general, with the indentor's apex. This position and the positions of the contact zone edges can be determined only by first constructing a solution form containing the three problem's unspecified lengths, and then solving numerically a system of non-linear equations containing integrals not available in closed form.

Upper-bound limit analysis of a rigid-plastic body with frictional interfaces

A finite element formulation of the upper-bound theorem for rigid-plastic solids, generalized to include interfaces with finite friction, is described. As proved by Collins [ J. Mech. Phys. Solids 17, 323 (1969)], the usual definition of a kinematically admissible velocity field is unnecessarily restrictive when the upper-bound theorem is applied to many practical problems. This paper shows that a relaxed inequality can be used successfully to derive upper bounds in the presence of Coulomb friction on interfaces, provided one considers a wide enough class of “admissible” velocity fields. One of the major advantages of using a numerical formulation of the upper-bound theorem is that both complex loading geometry and inhomogeneous material behaviour can be easily dealt with. Using a suitable linear approximation of the yield surface, the application of the necessary boundary conditions, the plastic flow rule and the yield criterion lead to a large linear programming problem. The numerical procedure uses constant-strain triangular elements with the unknown velocities as the nodal variables. An additional set of unknowns, the plastic multiplier rates, is associated with each element. Kinematically admissible velocity discontinuities are permitted along specified planes within the finite element mesh. During the solution phase, an active set algorithm is used to solve the linear programming problem.

Computing the frictional contact loads of horizontal steel pipes, loosely resting on saddles

The present paper concerns the computation of the local contact loads acting on a horizontal pipe, loosely resting on saddles in the presence of Coulomb friction. Within the framework of the Flügge shell theory, a discretization in patches and a force-method formulation is accepted, where the local contact loads are acting as redundants. The flexibility coefficients are obtained using a well-known Fourier series representation of local pipe loads. The boundary nonlinearity, introduced by the complicated nature of the unilateral contact-Coulomb friction boundary conditions at the saddle, is treated through an algorithm, consisting of two stages, consecutively executed until convergence is reached. The first stage considers the tangential loads as given and determines the regions of contact and noncontact. In the second stage the normal loads are considered as constant and the sticking/slipping regions are computed. Results are given and discussed for a two-span example.

Dynamic frictional indentation of an elastic half-plane by a rigid punch

Dynamic rigid indentation of a linearly elastic half-plane in the presence of Coulomb friction is studied in this paper. A rigid punch, which is either wedge- or parabolic-shaped, is rapidly driven into the deformable body so that stress waves are generated. The contact region is assumed to extend at a constant sub-Rayleigh speed (this situation can be achieved by conveniently specifying the kinetic and geometric characteristics of indentor), whereas, due to symmetry, friction acts in opposing directions on opposite sides of the indentor. As the present exact analysis shows, this sign reversal of the tangential traction along the half-plane surface creates an extra stress-singularity at the changeover point of the boundary conditions (due to symmetry, this point here coincides with the point where the indentor apex makes contact with the half-plane surface). The study exploits the problem's self-similarity by utilizing homogeneous-function techniques previously used by L.M. Brock, along with the Riemann-Hilbert problem analysis. Representative numerical results are given for the wedge indentation case.

Coulomb Friction and Optimal Rocker Arm Ratio for High-Speed Cam Systems

The operating speed of a high-speed cam system can be maximized by the proper choice of both kinematic and dynamic parameters of a lumped model. Considering rocker arm ratio as an unconstrained kinematic parameter and Coulomb friction as an unconstrained dynamic parameter, it was found that the camshaft speed at which toss occurred was characterized by several local extrema, all of which were sensitive to the presence of Coulomb friction. For a particular cam system and two separate cam lift curves, design charts have been developed to aid in the choice of optimal rocker arm ratio for maximum operating speed in the presence of Coulomb friction.

Toggle mechanisms: Dynamics and energy dissipation

The dynamic performance of a toggle mechanism is investigated. Particular attention is given to (i) the collapse of the toggle in the presence of Coulomb friction, and (ii) the effect of a varying periodic force on the mechanism with damped elastic coupling. For case (i), a method utilizing both equations of motion and the kinetostatic analysis is outlined to solve for frictional torque and it is concluded that the performance of the mechanism under the influence of Coulomb friction depends highly upon the input energy to the system. It is shown that there is an optimum impulse speed almost equal to a defined version of the quasi-natural frequency of the system which can minimize the energy loss. For case (ii), a dimensionless grouping in terms of the forcing amplitude and the parameters of the system is found for determining the stability of the system. An approximate analytical solution for the time history of motion under the assumed condition is obtained.

The end problem of a finite elastic cylinder pressed against a rough, rigid, sliding surface

The non-axisymmetric problem of a finite, circular, elastic cylinder, one end of which contacts a moving, rigid surface in the presence of Coulomb friction while the opposite end is constrained against in-plane displacements but subjected to a uniform normal displacement, is considered. The governing differential equations are converted to an infinite system of singular integral equations with the aid of the Papkovich-Neuber potentials and the subsequent application of multiple Fourier transformations. These are solved numerically and the components of stress and displacement at the ends of the cylinder are determined.For the frictionless case, the solution is shown to agree closely with known results.For the frictional case, stresses at the ends of the cylinder are given for two aspect ratios and several friction coefficients.

Sliding and indentation by a rigid half-wedge with friction and displacement coupling effects

Dynamic rigid indentation induced by sliding contact in the presence of Coulomb friction is studied by considering a rigid half-wedge which simultaneously translates tangentially and normally at constant speeds with respect to the surface of an elastic half-plane. The tangential displacements of half-plane points in the contact zone are not a priori assumed to be negligible, and are thus coupled with the normal displacements in imposing the contact zone boundary conditions. The contact zone itself, as defined on the undeformed half-plane, extends at a constant rate. A complete solution to the problem shows that the coupling effects may be small for low indentation speeds and relatively flat half-wedges. The coupling effect decreases the singularity order at the half-wedge apex, while the friction increases it. Indeed, the two effects may cancel out in this and other aspects of the solution. It is also found that apex particle velocity singularities occur only due to the tangential motion of the half-wedge.

Vibration isolation in the presence of Coulomb friction

Transmissibility curves for a Coulomb-damped flexible mounting are presented for both rigidly and elastically coupled damping. The closed solutions easily obtainable for the slipping and sticking phases of the motion are used in the method, and no conceptual approximation is involved. The transmissibility curves are compared with previously published approximations based on linearization of the damping. It is shown that the approximate method seriously underestimates the heights of significant resonant peaks and gives optimum friction values somewhat in error, but gives reasonable approximations to the transmissibilities at the high frequencies corresponding to effective isolation.

Impact dampers with coulomb friction

The modes and transitions of the auxiliary masses are identified for impact dampers with Coulomb friction. Analogue and digital simulation strategies are presented. A parametric study is conducted for containers with lengths shorter than the critical. It is known that the presence of Coulomb friction has adverse effects on the performance of impact dampers with containers of the critical length. It is shown here that for shorter containers, Coulomb friction may introduce stability to the motion, of the primary mass, improves the response for harmonic excitation, and accelerates the attenuation of the amplitude, of oscillations for step inputs.

The upper bound theorem for rigid/plastic solids generalized to include Coulomb friction

The usual definition of a kinematically admissible velocity field is unnecessarily restrictive for the validity of the upper bound inequality of limit analysis. In consequence, it is shown that this inequality can be used to derive overestimates of quantities of interest in metal-forming processes which have not been considered hitherto. In particular, upper bounds can be obtained for the total load in the presence of Coulomb friction on the tool/workpiece interface. In illustration, the technique is applied to problems of compression and extrusion.

Further Study of a Low-Pressure on-off Pneumatic Servomechanism

This paper compares experimental and theoretical transient and frequency response results for a low-pressure on-off pneumatic servomechanism comprising a polarized relay with dead zone and hysteresis operating a four-way flapper-nozzle valve via a torque-motor. The valve operates a linear pneumatic motor which drives a load in the presence of Coulomb friction and stiction. Position, velocity, and quasi-transient pressure feedback are provided. The effect of dynamic conditions on the valve characteristics is discussed.

Coulomb friction in feedback control systems

The presence of coulomb friction in servomechanisms often results in undesirable effects, such as an operating dead-zone, low-frequency wander, and poor dynamic performance for low level signals. Methods of compensation for these adverse effects are discussed and a specific example is presented. Also, a general procedure, using frequency-response techniques, is outlined for the synthesis of compensation in systems affected by coulomb friction. The methods employed are based on the recognition that coulomb friction in a control device has a describing function which reduces gain and introduces phase lag. The describing function is determined by both the amplitude and the frequency of the input signal to the device.

Coulomb friction in feedback control systems

The presence of coulomb friction in servomechanisms often results in undesirable effects, such as an operating dead-zone, low-frequency wander, and poor dynamic performance for low level signals. Methods of compensation for these adverse effects are discussed and a specific example is presented. Also, a general procedure, using frequency-response techniques, is outlined for the synthesis of compensation in systems affected by coulomb friction. The methods employed are based on the recognition that coulomb friction in a control device has a describing function which reduces gain and introduces phase lag. The describing function is determined by both the amplitude and the frequency of the input signal to the device.