Improved damping capacity and machinability of graphite particle-aluminum alloy composites

The damping capacity of cast graphitic aluminum alloy composites has been measured using a torsion pendulum at a constant strain amplitude. It was found that flake-graphite particles dispersed in the matrix of aluminum alloys increased the damping capacity; the improvement was greater, the higher the amount of graphite dispersed in the matrix. At sufficiently high graphite contents the damping capacity of graphitic aluminum composites approaches that of cast iron. The ratio between the damping capacity and the density of graphitic aluminum alloys is higher than cast iron, making them very attractive as light-weight, high-damping materials for possible aircraft applications. Machinability tests on graphite particle-aluminum composites, conducted at speeds of 315 sfm and 525 sfm, showed that the chip length decreased with the amount of graphite of a given size. When the size of graphite was decreased, at a given machining speed, the chip length decreased. Metallographic examination shows that graphite particles act as chip breakers, and are frequently sheared parallel to the plane of the

Harmonic response of a shock mount employing dual-phase damping

In this note, the application of dual-phase damping to a simple shock mount experiencing a harmonic input is described. The damping ratio is a function of the relative displacement between the foundation and the mounted mass. The purpose of employing such a damping is to reduce the absolute transmissibility over the whole frequency range.

Non-linear systems with quadratic and cubic damping - an analytical approach

The possible equivalence of second-order non-linear systems having quadratic and cubic damping with third-order linear systems is studied in this paper. It is shown that this equivalence can be established through transformation techniques under certain constraints on the form of the non-linearity of the given system.

Fractional damping: Stochastic origin and finite approximations

Fractional-order derivatives appear in various engineering applications including models for viscoelastic damping. Damping behavior of materials, if modeled using linear, constant coefficient differential equations, cannot include the long memory that fractional-order derivatives require. However, sufficiently great rnicrostructural disorder can lead, statistically, to macroscopic behavior well approximated by fractional order derivatives. The idea has appeared in the physics literature, but may interest an engineering audience. This idea in turn leads to an infinite-dimensional system without memory; a routine Galerkin projection on that infinite-dimensional system leads to a finite dimensional system of ordinary differential equations (ODEs) (integer order) that matches the fractional-order behavior over user-specifiable, but finite, frequency ranges. For extreme frequencies (small or large), the approximation is poor. This is unavoidable, and users interested in such extremes or in the fundamental aspects of true fractional derivatives must take note of it. However, mismatch in extreme frequencies outside the range of interest for a particular model of a real material may have little engineering impact.

Microscopic Frictional Response of Sodium Oleate Self-Assembled on Steel

The article peruses the frictional response of an important metal working lubricant additive, sodium oleate. Frictional force microscopy is used to track the response of molecules self-assembled on a steel substrate of 3–4 nm roughness at 0% relative humidity. The friction-normal load characteristic emerges as bell-shaped, where the peak friction and normal load at peak friction are both sensitive to substrate roughness. The frictional response at loads lower than that associated with the peak friction is path reversible while at higher loads the loading and unloading paths are different. We suggest that a new low-friction interface material is created when the normal loads are high.

Step function response of non-linear spring mass systems in the presence of Coulomb damping

The transient response of non-linear spring mass systems with Coulomb damping, when subjected to a step function is investigated. For a restricted class of non-linear spring characteristics, exact expressions are developed for (i) the first peak of the response curves, and (ii) the time taken to reach it. A simple, yet accurate linearization procedure is developed for obtaining the approximate time required to reach the first peak, when the spring characteristic is a general function of the displacement. The results are presented graphically in non-dimensional form.

Free vibrations of non-linear cubic spring mass systems in the presence of coulomb damping

An exact solution for the free vibration problem of non-linear cubic spring mass system with Coulomb damping is obtained during each half cycle, in terms of elliptic functions. An expression for the half cycle duration as a function of the mean amplitude during the half cycle is derived in terms of complete elliptic integrals of the first kind. An approximate solution based on a direct linearization method is developed alongside this method, and excellent agreement is obtained between the results gained by this method and the exact results. © 1970 Academic Press Inc. (London) Limited.

Prediction of inplane damping from deterministic and stochastic models

This paper reviews computational reliability, computer algebra, stochastic stability and rotating frame turbulence (RFT) in the context of predicting the blade inplane mode stability, a mode which is at best weakly damped. Computational reliability can be built into routine Floquet analysis involving trim analysis and eigenanalysis, and a highly portable special purpose processor restricted to rotorcraft dynamics analysis is found to be more economical than a multipurpose processor. While the RFT effects are dominant in turbulence modeling, the finding that turbulence stabilizes the inplane mode is based on the assumption that turbulence is white noise.

Correlation between stick-slip frictional sliding and charge transfer

A decade ago, Budakian and Putterman [Phys. Rev. Lett. 85, 1000 (2000)] ascribed friction to the formation of bonds arising from contact charging when a gold tip of a surface force apparatus was dragged on polymethylmethacrylate surface. We propose a stick-slip model that captures the observed correlation between stick-slip events and charge transfer, and the lack of dependence of the scale factor connecting the force jumps and charge transfer on normal load. Here, stick-slip dynamics arises as a competition between the viscoelastic and plastic deformation time scales and that due to the pull speed with contact charging playing a minor role. Our model provides an alternate basis for explaining most experimental results without ascribing friction to contact charging.

Effect of primary system damping on the optimum design of an untuned viscous dynamic vibration absorber

Explicit criteria for the optimum design of an untuned viscous dynamic vibration absorber are developed for the case of a viscously damped single degree of freedom springmass system. It is shown that for the particular case of an undamped main system, the results reduce to the classical ones obtained by using the concept of a fixed point on the response curve.

Steady incompressible flow of cohesionless granular materials through a wedge-shaped hopper: Frictional 14kinetic solution to the smooth wall, radial gravity problem

Hybrid frictional-kinetic equations are used to predict the velocity, grain temperature, and stress fields in hoppers. A suitable choice of dimensionless variables permits the pseudo-thermal energy balance to be decoupled from the momentum balance. These balances contain a small parameter, which is analogous to a reciprocal Reynolds number. Hence an approximate semi-analytical solution is constructed using perturbation methods. The energy balance is solved using the method of matched asymptotic expansions. The effect of heat conduction is confined to a very thin boundary layer near the exit, where it causes a marginal change in the temperature. Outside this layer, the temperature T increases rapidly as the radial coordinate r decreases. In particular, the conduction-free energy balance yields an asymptotic solution, valid for small values of r, of the form T proportional r-4. There is a corresponding increase in the kinetic stresses, which attain their maximum values at the hopper exit. The momentum balance is solved by a regular perturbation method. The contribution of the kinetic stresses is important only in a small region near the exit, where the frictional stresses tend to zero. Therefore, the discharge rate is only about 2.3% lower than the frictional value, for typical parameter values. As in the frictional case, the discharge rate for deep hoppers is found to be independent of the head of material.

Evaluation of interfacial frictional resistance

Three distinct mechanisms — sliding, bonding and bearing — for the mobilisation of interfacial friction have been identified. In the light of these mechanisms, the effect of variation in reinforcement parameters, such as extensibility, flexibility and hardness on mobilisation of interfacial friction, and the mechanisms themselves has been examined. The influence of boundary effects of apparatus on the interfacial friction has been discussed and a method of estimating the same in a pull-out box has been proposed.

Flap‐Lag Damping in Hover and Forward Flight with a Three‐Dimensional Wake

Prediction of lag damping is difficult owing to the delicate balance of drag, induced drag and Coriolis forces in the in‐plane direction. Moreover, induced drag” is sensitive to dynamic wake, bath shed and trailing components, and thus its prediction requires adequate unsteady‐wake representation. Accordingly, rigid‐blade flap‐lag equations are coupled with a three‐dimensional finite‐state wake model; three isolatcd rotor canfigurations with three, four and five blades are treated over a range of thrust levels, tack numbers, lag frequencies and advance ratios. The investigation includes convergence characteristics of damping with respect to the number of radial shape functions and harmonics of the wake model for multiblade modes of low frequency (< 1/ rev.) to high frequency (> 1/rev.). Predicted flap and lag damping levels are then compared with similar predictions with 1) rigid wake (no unsteady induced now), 2) Loewy lift deficiency and 3) dynamic inflow. The coverage also includes correlations with the measured lag regressive‐mode damping in hover and forward flight and comparisons with similar correlations with dynamic inflow. Lag‐damping predictions with the dynamic wake model are consistently higher than the predictions with the dynamic inflow model; even for the low frequency lag regressive mode, the number of wake harmonics should at least be equal to twice the number of blades.