Involving Coulomb Friction Research Articles

An Upper Bound Energy Formulation of Free-Chip Machining with Flat Chips and an Alternative Method of Determination of Cutting Forces without Using the Merchant’s Circle Diagram

An upper bound analysis of free-chip machining has been carried out, where the tool cutting and friction forces were determined from the deformation energy dissipated during the chip separation process. The method employed was based on the classical upper bound theorem, as formulated by Prager and Hodge, and Drucker, Prager, and Greenberg, and its modification by Collins, to deal with the metal forming processes involving coulomb friction. A straight shear plane and coulomb friction at the chip/tool interface were assumed and the energy required for cutting was calculated from a strain rate/velocity field that was constructed using the method proposed by Collins. Cutting forces, thrust forces, tool/chip contact lengths, and chip thickness ratios were determined for different tool rake angles and friction conditions. The theoretical results were also compared with some experimental results that are available in the published literature. The comparison between the two was not found to be satisfactory. This may be due to the non-unique nature of the machining process, as stated by Hill and demonstrated by other authors. The results calculated from the present method of ”energy balance” were also found to be in agreement with those obtained by Merchant using the principle of ”force balance”.

Small-scale effect on the vibration of thin nanoplates subjected to a moving nanoparticle via nonlocal continuum theory

The vibration of elastic thin nanoplates traversed by a moving nanoparticle involving Coulomb friction is investigated using the nonlocal continuum theory of Eringen. The eigen function technique and the Laplace transform method are employed to solve the governing equations of the nanoplate. The explicit expressions of the in-plane and transverse displacements are obtained when the moving nanoparticle traverses the nanoplate on an arbitrary straight line. In a special case, the obtained results are also compared with those of other researchers and a reasonably good agreement is achieved. The effects of small-scale parameters and velocity of the moving nanoparticle on the dynamic response as well as the dynamic amplitude factors (DAFs) of the in-plane and transverse displacements are then explored in some detail. The results indicate that the magnitude of DAF of the transverse displacement of the nanoplate (i.e., DAF w ) increases with the first small-scale effect parameter, irrespective of the values of the second small-scale effect parameter and the velocity of the moving nanoparticle. As the first small-scale effect parameter grows, the maximum values of DAFw as a function of the moving nanoparticle velocity increase and generally occur in the lower levels of the moving nanoparticle velocity.

Efficient Simulation of Motions Involving Coulomb Friction

A realistic treatment for numerical solution of equations of motion for systems involving coulomb friction requires three sets of dynamic equations: one for sticking, one for slipping, and one for transition from sticking to slipping. An alternative treatment of stick–slip motion is described, which involves only two sets of equations, one for sticking and the other for transition and slipping. The new approach uses a single equation that continuously relates frictional forces with normal forces for both the slipping and transition phases of motion. It turns out that this equation is also capable of approximating sticking as slipping at inŽ nitesimally small speeds, but it is computationallymore efŽ cient to use two sets of equations. The new approach is computationally efŽ cient and is uniŽ ed in the sense that when the equations of motion are cast into matrix form, the set of unknown variables is preserved during the various phases of motion (sticking, slipping, and transition), with only the last few rows of the aforementioned matrix having elements that change depending on the phase of motion. The equivalence of this new approach to the classical treatment of coulomb friction is established by comparisons of numerical results from several simulations, namely, the spin reversal of the rattleback, the effects of disturbances on a sleeping top, and the motion of a uniform sphere on a rough horizontal surface. It is shown that the same equations of motion describe the three systems for different choices of parameters.

Some test examples of 2D and 3D contact problems involving coulomb friction and large slip

In this paper, we propose three test examples of two- and three-dimensional contact problems with Coulomb friction and large slip. These examples are: (1) the contact between a 2D elastic slab and a rigid plate, (2) the contact between two semicircular rings, and (3) the contact between a 3D elastic block and a rigid surface.

On the frictional behaviour of thermally loaded beams resting on a plane

The problem of an elastic beam resting on a frictional surface and loaded by a uniform temperature moment is treated analytically and numerically. The introduction of proper non-dimensional parameters identifies the deformation pattern which varies with monotonically increasing temperature load in a self-similar manner. This fact reduces the complexity of the mathematical system considerably and offers the derivation of the solution on an analytical basis. Several approaches are described, discussed and compared against each other. This problem is typical for a broader class of problems involving Coulomb friction in beam deformation. In addition to the fact that it is interesting from the structural as well as from the mathematical points of view, it is of practical importance, for example in the simulation of the cooling processes of hot rolled railway rails.

ROBUST EXPLICIT COMPUTATIONAL DEVELOPMENTS AND SOLUTION STRATEGIES FOR IMPACT PROBLEMS INVOLVING FRICTION

New explicit dynamic computational developments in conjunction with finite element formulations for impact problems are described in this paper. The proposed methodology is based on employing a variational inequality for dynamic problems involving Coulomb friction with the so-called forward incremental displacement–central difference method specially formulated in this paper for this class of problems. To enforce the constraints on the contact boundary, a linear complementary equation is established by means of a minimization problem subjected to constraints, which is equivalent to discretization of the variational inequality of the dynamic problem. In conjunction with these developments, a new conjugate gradient based explicit solution strategy is described for effectively solving the linear complementary equations. With the motivation for providing effective computational procedures suitable for vectorization and parallel computations, the proposed developments not only provide a fundamentally sound and robust theoretical basis but also serve to be ideally suited for impact problems involving frictional contact on high speed computing environments.

Conjugate gradient based projection: A new explicit computational methodology for frictional contact problems

AbstractWith special attention towards the applicability to parallel computation or vectorization, a new and effective explicit computational approach for linear complementary formulations involving a conjugate gradient based projection methodology is proposed in this study for contact problems with Coulomb friction. The overall objectives are focused towards providing an explicit methodology of computation for the complete contact problem with friction. In this regard, the primary idea for solving the linear complementary formulations stems from an established search direction which is projected to a feasible region determined by the non‐negative constraint condition; this direction is then applied to the Fletcher‐Reeves conjugate gradient method resulting in a powerful explicit methodology which possesses high accuracy, excellent convergence characteristics, fast computational speed and is relatively simple to implement for contact problems involving Coulomb friction. Numerical test cases are also included to demonstrate the proposed methodology for contact problems with friction.

Design, Construction and Testing of a Single-axis Servomechanism for Control Experiments involving Coulomb Friction, Backlash and Joint Compliance

SUMMARY An investigation of the effects of system non-linearities, such as Coulomb friction and backlash, and undesirable structural dynamics, such as joint compliance, on the dynamic modeling and control of mechanical positioning systems is presented. These effects are often neglected in dynamic system analysis and control studies. An innovative, computer-controlled, mechanical positioning test bed was designed and constructed to facilitate investigations of these effects. The test bed allows fully adjustable, quantified and well-defined measurements of Coulomb friction, backlash, joint compliance and inertia. System identification and parameter estimation techniques are used to estimate and verify linear system parameters. Open-loop and closed-loop simulations of the system, incorporating the undesirable effects which can be exhibited by the test bed, are presented and compared with experimental results. The positioning performance of the servomechanism is shown to degrade with increases in Coulomb fric...

An Application of the Theory of Coulomb Friction to Nutation and Precession in a Gyroscope

The phenomenon considered is the transitory motion which takes place immediately following the removal of a support from the spinning rotor of a gyroscope. There, the damped nutation which is observed quickly gives way to a steady-state precession. A model involving Coulomb friction is put forward to fully explain the character of the gyroscopic motions and to properly account for the loss in energy of the system.

Convex superposition in piecewise-linear systems

Piecewise-linear systems of the type that arise in relay servomechanisms or problems involving Coulomb friction, which are usually regarded as nonlinear, are shown here to exhibit linear behavior in some circumstances. Specifically, for certain sets of input signals (or forcing functions) and associated responses, the responses are linear in the inputs with respect to convex linear combinations; equivalently, the average of a set of inputs has, as its response, the average of the associated responses. The result is illustrated by means of an explicit formula for periodic responses in a second-order on-off control system.