Fads and friction

The motion of an oscillator instantaneously loaded with a constant force under conditions of nonlinear external resistance, the components of which are quadratic viscous resistance, dry and positional friction, are considered. Using the first integral of the equation of motion and the Lambert function, compact formulas for calculating the ranges of oscillations are derived. In order to simplify the search for the values of the Lambert function, asymptotic formulas are given that, with an error of less than one percent, express this special function in terms of elementary functions. It is shown that as a result of the action of the resistance force, including dry friction, the oscillation process has a finite number of cycles and is limited in time, since the oscillator enters the stagnation region, which is located in the vicinity of the static deviation of the oscillator caused by the applied external force. The system dynamic factor is less than two. Examples of calculations that illustrate the possibilities of the stated theory are considered. In addition to analytical research, numerical computer integration of the differential equation of motion was carried out. The complete convergence of the results obtained using the derived formulas and numerical integration is established, which confirms that using analytical solutions it is possible to determine the extreme displacements of the oscillator without numerical integration of the nonlinear differential equation. To simplify the calculations, the literature is also recommended, where tables of the Lambert function are printed, allowing you to find its value for interpolating tabular data. Under conditions of nonlinear external resistance, the components of which are quadratic viscous resistance, dry and positional friction, the process of oscillations of an instantly loaded oscillator has a limited number of cycles. The dependences obtained in this work using the Lambert function make it possible to determine the range of oscillations without numerical integration of the nonlinear differential equation of motion both for an oscillator with quadratic viscous resistance and dry friction, and for an oscillator with quadratic resistance and positional and dry friction. Keywords: nonlinear oscillator, instantaneous loading, quadratic viscous resistance, Lambert function, oscillation amplitude.

Mechanical and magnetic requirements for Magneto-Resistive (MR) recording heads have caused media data zones to become increasingly smoother. Tribology conditions of the landing zone still require some roughness, however. Because of this, dual zone textured media has become a common solution for MR applications. Although some disks have been dual zone textured mechanically, laser textured landing zones have become an industry standard. Laser textured media has unique static and dynamic friction properties, and if careful attention is not paid to measurement set-up, measured static friction values could be extremely inaccurate (up to 100%). This is likely due to system inertia differences and a difference in /spl zeta//sub k/ (The ratio of Dynamic to True Static Friction). While mechanically textured media has typical /spl zeta//sub k/ values ranging from 0.4 to 0.6, laser textured media has typical values close to 1.0. A theoretical model of breakaway friction measurements by Li et al. predicts the above mentioned trend. The model shows that /spl zeta//sub p/ (The sensed to true static friction ratio) varies as a function of /spl zeta//sub i/ (The inertia force to true static friction ratio). This function is different for different values of /spl zeta//sub k/. The model predicts that laser textured media will be much more dependent on inertia force than mechanically textured media. The trend predicted by this model is now demonstrated experimentally. By using a small DC motor to drive a spindle, it is possible to reduce the instantaneous acceleration to an extremely low value. When measuring stiction at these extremely low acceleration rates, it is demonstrated that the measured values are much lower than they are when measured at higher acceleration rates. Even though laser textured media with a carbon coated MR head exhibits this phenomenon, a mechanically textured disk with a non-carbon coated inductive head does not (in the range of accelerations tested).

Mechanical and magnetic requirements for Magneto-Resistive (MR) recording heads have caused media data zones to become increasingly smoother. Tribology conditions of the landing zone still require some roughness, however. Because of this, dual zone textured media has become a common solution for MR applications. Although some disks have been dual zone textured mechanically, laser textured landing zones have become an industry standard. Laser textured media has unique static and dynamic friction properties, and if careful attention is not paid to measurement set-up, measured static friction values could be extremely inaccurate (up to 100%). This is likely due to system inertia differences and a difference in <k (The ratio of Dynamic to True Static Friction). (l) While mechanically textured media has typical <k values ranging from 0.4 to 0.6, laser textured media has typical values close to 1.0. A theoretical model of breakaway friction measurements by Li et al. (l) predicts the above mentioned trend. The model shows that rp (The sensed to true static friction ratio) varies as a function of C;i (The inertia force to true static friction ratio). This function is different for different values of &. The model predicts that laser textured media will be much more dependent on inertia force than mechanically textured media. The trend predicted by this model is now demonstrated experimentally. By using a small DC motor to drive a spindle, it is possible to reduce the instantaneous acceleration to an extremely low value. When measuring stiction at these extremely low acceleration rates, it is demonstrated that the measured values are much lower than they are when measured at higher acceleration rates. Even though laser textured media with a carbon coated MR head exhibits this phenomenon, a mechanically textured disk with a non-carbon coated inductive head does not (in the range of accelerations tested).

Internal friction in complex ferroelastic twin patterns

Recent experiments have revealed an unexpected deviation from a first power dependence of protein relaxation times on solvent viscosity, an effect that has been attributed to "internal friction". One clear source of internal friction in protein dynamics is the isomerization of dihedral angles. A key outstanding question is whether the global folding barrier height influences the measured internal friction, based on the observation that the folding rates of fast-folding proteins, with smaller folding free energy barriers, tend to exhibit larger internal friction. Here, by studying two alanine-based peptides, we find that systematic variation of global folding barrier heights has little effect on the internal friction for folding rates. On the other hand, increasing local torsion angle barriers leads to increased internal friction, which is consistent with solvent memory effects being the origin of the viscosity dependence. Thus, it appears that local torsion transitions determine the viscosity dependence of the diffusion coefficient on the global coordinate and, in turn, internal friction effects on the folding rate.

Rubber friction properties include adhesion friction characteristics of the interface, hysteresis friction characteristics originating from repeated rubber deformations, and cohesion friction characteristics due to wear and tear. Cohesion friction is generally sufficiently small (˂ 3%) that it can be ignored, whereas adhesion friction has a relatively large contribution of 15%, but has not been investigated thoroughly. Therefore, through an adhesion friction study, the adhesion mechanism was examined and the relationship between friction characteristics and adhesion friction on dry surfaces was derived. The wet grip characteristics of tread rubber are fully described by the hysteresis characteristics of tires, but friction characteristics on dry roads are difficult to determine without adhesion factors. The results presented herein demonstrate that the combination of hysteresis and adhesion properties in the tread rubber sufficiently explained the characteristics of the dry grip. Based on the results of this study, technologies will be developed to determine the key factors governing adhesion friction characteristics and improve dry tire braking performance.

Internal friction of an Fe–28Mn–6Si–5Cr–0.5NbC shape memory alloy

Internal friction characteristics of Ti 51.5Ni 26.0Pd 22.5 thin films formed by sputter deposition

Solids show the feature of internal friction and the feature of fatigue. As a cause for the both features we assume the migration of atomic items. The driving forces for the migration of the atomic items can be mechanical stress gradients and temperature gradients. In an earlier publication formulas have been derived for the internal friction and for the fatigue. From these formulas follows a relation between internal friction and fatigue. The mechanical stress gradients are the cause of the background of internal friction which shows a monotonous rise with temperature. Temperature gradients in the solid can be produced by total internal friction. In contrast to the background of internal friction the temperature dependence of the total internal friction shows maxima and minima. Because of the relations between internal friction and fatigue the temperature dependence of fatigue shows that the fatigue is caused by temperature gradients. The relation between internal friction and fatigue also shows the influence of the internal friction on the fatigue curve.

The measurement of friction and wear on hand–shifted transmission synchronizers (highly loaded cone clutches) is carried out by two different test machines: 1. a steady state synchronization test stand: friction surface diameter: 40–80 mm; wear and the coefficient of friction are measured under steady state test conditions (i.e. axial force and speed are constant); 2. a non–steady state synchronization test stand: friction surface diameter: 90–170 mm; the synchronization process is simulated under the same non–steady state conditions as there are in a vehicle transmission; all parameters (for example axial force, speed, work and power loss due to friction) coincide on the test machine with those of a transmission in practical use; the synchronization process is measured and evaluated by plots. The friction surfaces are inspected by a stylus instrument (Perth–0–Meter) and by a scanning electron microscope. The influence of various parameters (for example friction materials, work and power loss due to friction, roughness and geometry of friction surface, lubricant, additive, etc.) on the friction and wear of the synchronizers can be determined. The methods of testing and the results obtained from the investigations will be presented in examples.

It is known that problems arise over existence and uniqueness of solution in quasi–static contact problems involving large coefficients of Coulomb friction. This paper considers the behaviour of an elastically supported mass with three translational degrees of freedom that can make contact with a rigid Coulomb friction support. A critical coefficient of friction is identified, above which the quasi–static solution can be non–unique. A numerical solution of the corresponding dynamic problem shows that the state realized then depends on the initial conditions. Even below the critical coefficient of friction, the dynamic solution can deviate from the quasi–static even for arbitrarily small loading rates. Typical dynamic responses include limit–cycle oscillations in velocity, oscillations involving a brief period of zero velocity (stick) and ‘stick–slip’ motion in which the mass spends significant periods in a state of stick, interspersed with short rapid–slip periods. All these non–steady motions involve non–rectilinear motion, even in cases where the time derivative of the applied load is constant in direction. A perturbation analysis is performed on the quasi–static frictional slip solution and predicts instability for certain slip directions, depending on functions of the off–diagonal stiffness components and the coefficient of friction. These results are presented in dimensionless form in stability diagrams. It is also shown that quasi–static slip that is stable when there is no damping can be destabilized if the damping matrix has sufficiently large off–diagonal components.

ABSTRACTInternal friction (or damping) is a measure of energy dissipation during mechanical vibration. The internal friction peak induced by grain boundary (GB) relaxation was discovered by Kê in polycrystals in 1947. The GB internal friction and related anelastic effects have been successfully interpreted by Zener's anelastic theory and viscous sliding model. Since then, the GB internal friction peak has been widely used to study the dynamic process of GBs, impurity segregation at GBs and relevant processes in materials science.Previously, the GB internal friction was mostly studied with polycrystalline materials, in which mixed contributions of different types of GBs are involved. Since the microstructures and behaviors for different types of GBs are different, the detailed mechanism of the GB peak in polycryatals has not been clearly clarified.From the beginning of the 21th century, the internal friction in bicrystals (each has a single boundary) with different misorientations and rotation axes has been systematically investigated. The results indicate that the internal friction can be used to distinguish the individual behavior of different types of GBs and applied to the practice of “GB engineering.”Moreover, the coupling effect and compensation effect involved in GB relaxation has been recently observed and explained. The coupling effect means a correlated atomic motion occurred in GB relaxation. The compensation effect indicates that the apparent activation enthalpy is linearly related to the activation entropy in GB relaxation. These findings improve the understanding of the mechanism of GB internal friction.This article attempts to give a comprehensive review to the investigations of GB internal friction in polycrystals, bamboo-crystals, and bicrystals. The microscopic mechanisms and the further applications of GB internal friction are discussed and prospected.

The structural-energy interpretation of the diagram of the evolution of the friction contact is shown.The diagram of the evolution of the friction contact reveals two principal stages of the adaptation of the friction contact.These two stages characterize the occurrence of two fundamental states of frictionmaximum and minimum.The first stage of adaptation is due to the formation of the smallest deformable volume of friction, which has accumulated the maximum potential energy density of elementary defects and damage to the crystal structure.The second stage of adaptation is due to the formation of a unique nanostructural arrangement in this volume of friction, which is based on a mechanical quantum.The energy parameters of these two limiting states of friction contact are estimated.The universal energy constants of the limiting (adapted) states of the rubbing surfaces -friction contacts -are indicated.

Over the past few decades, oscillating flexible foils have been used to study the physics of organismal propulsion in different fluid environments. Here, we extend this work to a study of flexible foils in a frictional environment. When the foil is oscillated by heaving at one end but is not free to locomote, the dynamics change from periodic to non-periodic and chaotic as the heaving amplitude increases or the bending rigidity decreases. For friction coefficients lying in a certain range, the transition passes through a sequence of N-periodic and asymmetric states before reaching chaotic dynamics. Resonant peaks are damped and shifted by friction and large heaving amplitudes, leading to bistable states. When the foil is free to locomote, the horizontal motion smoothes the resonant behaviours. For moderate frictional coefficients, steady but slow locomotion is obtained. For large transverse friction and small tangential friction corresponding to wheeled snake robots, faster locomotion is obtained. Travelling wave motions arise spontaneously, and move with horizontal speeds that scale as transverse friction coefficient to the coefficient to and input power that scales as the transverse friction coefficient to the power 5/12. These scalings are consistent with a boundary layer form of the solutions near the foil's leading edge.

Frictions of Lock-loose brackets with ligated main wings or all six wings were measured as they slid along archwires in dry and artificial saliva environments. The Lock-loose brackets were then compared with traditional brackets and self-ligating brackets. The surface states of the stainless steel archwires were observed with atomic force microscopy before and after mechanical traction. The Lock-loose brackets, traditional brackets, and self-ligating brackets used in this study were composed of 0.406 4 and 0.457 2 mm stainless steel round archwires and 0.457 2 mm x 0.634 9 mm and 0.482 6 mm x 0.634 9 mm stainless steel rectangular archwires. Two different ligating methods were applied to the Lock-loose brackets, i.e., main wings ligated and all six wings ligated. Frictions were measured by using an electronic universal testing machine. No significant differences were found between the roughness of different archwires before and after mechanical traction in different brackets (P > 0.05). When the main wings of the Lock-loose brackets were ligated, the frictions of the four different stainless steel archwires were close to zero, and the difference with frictions of traditional brackets was significant (P < 0.05). When using 0.457 2 mm x 0.634 9 mm rectangular archwires, maximum friction (P < 0.05; significantly different from those of other brackets) was reached when all six wings of the Lock-loose brackets were ligated. Frictions in the dry state were higher than those in the wet state (P < 0.05). The Lock-loose brackets can adjust the friction efficiently with different ligating methods, thus solving the problem of low friction and strengthening anchorage.