L. C. Davis

Model of magnetorheological elastomers

Magnetorheological elastomers consist of natural or synthetic rubber filled with micron-sized magnetizable particles. During curing of the elastomer, an applied magnetic field aligns the particles into chains. The shear modulus of the resulting cured material is sensitive to magnetic fields of several kOe magnitude. Such sensitivity to magnetic field makes these materials attractive for applications in automotive mounting components. At large fields (magnetic induction B>1 T), the Fe particles are completely magnetized or saturated. Calculations using finite element analysis show that for typical elastomers the increase in shear modulus due to interparticle magnetic forces at saturation is about 50% of the zero-field modulus. The optimum particle volume fraction for the largest fractional change in modulus at saturation is predicted to be 27%. Calculations of the zero-field shear modulus perpendicular to the chain axis indicate that it does not exceed the modulus of a filled elastomer with randomly disper...

Polarization forces and conductivity effects in electrorheological fluids

Forces between particles aligned into chains by an applied electric field in an electrorheological (ER) fluid are calculated using finite‐element techniques and, approximately, using a dipole approximation with local‐field effects. Evaluation of the effective dielectric constant is emphasized and the shear modulus is derived from the shear dependence. For high‐frequency (f≳0.1–1 kHz) applied electric fields, the forces and the modulus depend upon the dielectric constants of the suspending fluid and the dispersed particles. For low‐frequency or dc electric fields, the conductivities of the components are dominant. These effects are treated within a Maxwell–Wagner approach. If the ratio of particle‐to‐fluid conductivities substantially exceeds the ratio of dielectric constants, a large enhancement of the modulus is found. Implications for the design of ER fluids are discussed briefly.

Thermal conductivity of metal‐matrix composites

The thermal conductivity of metal‐matrix composites, which are potential electronic packaging materials, is calculated using effective medium theory and finite‐element techniques. The thermal boundary resistance, which occurs at the interface between the metal and the included phase (typically ceramic particles), has a large effect for small particle sizes. It is found that SiC particles in Al must have radii in excess of 10 μm to obtain the full benefit of the ceramic phase on the thermal conductivity. Bimodal distributions of particle size are considered, since these are often used to fabricate high‐volume fraction composites. It is found that if the small particles (in a bimodal distribution) have a radius less than 2.5 μm in SiC/Al their addition reduces the thermal conductivity of the composite. Diamond‐containing composites, which have large thermal boundary resistance effects, are analyzed. Comparison of the effective medium theory results to finite‐element calculations for axisymmetric unit‐cell m...

Force on a Rectangular Coil Moving above a Conducting Slab

The force on a rectangular current‐carrying coil moving above and parallel to a conducting plate of arbitrary thickness is investigated. Expressions are developed for the lift and drag forces on the coil as a function of speed. Numerical calculations are made for a very thick plate and for plates with thickness of the order of the skin depth. Thick‐plate results are compared with experimental measurements of lift and drag on a superconducting coil suspended above a rotating aluminum wheel.

Time-dependent and nonlinear effects in electrorheological fluids

An integral equation method is used to calculate particle–particle forces in electrorheological fluids. The method focuses on the gap region between particles where large electric-field concentrations occur. Effects due to time-dependent excitation and nonlinear (field-dependent) fluid conductivity are analyzed. It is found that the response to step-function changes in applied field closely follows a simple form that can be derived from the dipole approximation. Qualitatively different stress-vs-time curves are obtained for large dielectric mismatch (e.g., barium titanate/dodecane) relative to large conductivity mismatch (zeolite/silicone oil). In fluids where the conductivity is strongly field dependent, it is found that particle–particle forces scale linearly with applied field E0 at large fields. Likewise, the shear yield stress scales as E03/2.

Lateral restoring force on a magnet levitated above a superconductor

The lateral restoring force on a magnet levitated above a superconductor is calculated as a function of displacement from its original position at rest using Bean’s critical‐state model to describe flux pinning. The force is linear for small displacements and saturates at large displacements. In the absence of edge effects the force always attracts the magnet to its original position. Thus it is a restoring force that contributes to the stability of the levitated magnet. In the case of a thick superconductor slab, the origin of the force is a magnetic dipole layer consisting of positive and negative supercurrents induced on the trailing side of the magnet. The qualitative behavior is consistent with experiments reported to date. Effects due to the finite thickness of the superconductor slab and the granular nature of high‐Tc materials are also considered.

The metal-particle/insulating oil system : an ideal electrorheological fluid

The electrorheological (ER) properties of a model system consisting of oxidized metal particles in an insulating oil are analyzed. It is suggested that previous dc experiments on such systems have failed to reveal strong ER activity because of conductivity effects. Recent experiments by Inoue at 50 Hz excitation appear to have nearly obtained the ultimate strength of the metal‐particle system studied.

Stability of magnets levitated above superconductors

The stability of a permanent magnet levitated above a slab of hard superconductor is considered. The force on a dipole magnet over a perfectly diamagnetic disk is calculated. It is found that the radial component of the force is directed outward and is 10%–20% of the image (vertical) force near the edge. Estimates of the magnetic friction force due to flux motion in a hard superconductor are made using Bean’s model. The magnitude of the magnetic friction is large enough to stabilize the magnet over most of the disk for typical values of the critical current in ceramic superconductors (∼103 A/cm2), but too small for the highest values reported (>106 A/cm2). It is conjectured that flux trapping due to inhomogeneities gives rise to transient restoring forces.

Force on a Coil Moving over a Conducting Surface Including Edge and Channel Effects

The lift force FL and the drag force FD on small conducting coils placed near a large rotating conducting cylinder have been measured as functions of velocity, height, and coil geometry. These data are compared with exact calculations based upon Fourier transforms for coils moving over infinitely wide flat plates. By placing the coil near the edge of the cylinder, the effect of the edge on FL and FD and the transverse force FT were studied. A channel was then cut in the cylinder, and the properties of a U‐shaped guideway were examined. Both the edge effects and channel effects were compared with approximate calculations. Agreement was generally good, substantiating a variety of predictions for the large magnets proposed for the suspension of high‐speed ground vehicles.

Analysis of Motion of Magnetic Levitation Systems: Implications for High‐Speed Vehicles

To study the motion of a magnetically suspended high‐speed vehicle, a simple example (the long wire above a thin conducting plate) is considered in detail. The lift and drag forces on the magnet (long wire) are derived for arbitrary motion above the plate. The stability of the system is analyzed for typical parameters (velocity = 300 mph, height = 0.1 m). By using a Laplace‐transform technique, it is shown that two types of modes occur (in the linearized equations of motion). One mode is a vertical oscillation with an amplitude that grows slowly in time. The other mode is an unbounded increase in the horizontal velocity error. This latter instability results from the fact that the drag force decreases with increasing velocity at high speeds. In this connection, an error is pointed out in a recent publication in which it was claimed that the system is stable. Detailed consideration of the effects of horizontal acceleration and vertical velocity on the magnetic forces is given. The effects of aerodynamic dr...