3,438 research outputs found
Digital control of magnetic bearings supporting a multimass flexible rotor
The characteristics of magnetic bearings used to support a three mass flexible rotor operated at speeds up to 14,000 RPM are discussed. The magnetic components of the bearing are of a type reported in the literature previously, but the earlier analog controls were replaced by digital ones. Analog-to-digital and digital-to-analog converters and digital control software were installed in an AT&T PC. This PC-based digital controller was used to operate one of the magnetic bearings on the test rig. Basic proportional-derivative control was applied to the bearings, and the bearing stiffness and damping characteristics were evaluated. Particular attention is paid to the frequency dependent behavior of the stiffness and damping properties, and comparisons are made between the actual controllers and ideal proportional-derivative control
A magnetic damper for first mode vibration reduction in multimass flexible rotors
Many rotating machines such as compressors, turbines and pumps have long thin shafts with resulting vibration problems, and would benefit from additional damping near the center of the shaft. Magnetic dampers have the potential to be employed in these machines because they can operate in the working fluid environment unlike conventional bearings. An experimental test rig is described which was set up with a long thin shaft and several masses to represent a flexible shaft machine. An active magnetic damper was placed in three locations: near the midspan, near one end disk, and close to the bearing. With typical control parameter settings, the midspan location reduced the first mode vibration 82 percent, the disk location reduced it 75 percent and the bearing location attained a 74 percent reduction. Magnetic damper stiffness and damping values used to obtain these reductions were only a few percent of the bearing stiffness and damping values. A theoretical model of both the rotor and the damper was developed and compared to the measured results. The agreement was good
Homogenization of the one-dimensional wave equation
We present a method for two-scale model derivation of the periodic
homogenization of the one-dimensional wave equation in a bounded domain. It
allows for analyzing the oscillations occurring on both microscopic and
macroscopic scales. The novelty reported here is on the asymptotic behavior of
high frequency waves and especially on the boundary conditions of the
homogenized equation. Numerical simulations are reported
Correctors for some nonlinear monotone operators
In this paper we study homogenization of quasi-linear partial differential
equations of the form -\mbox{div}\left( a\left( x,x/\varepsilon _h,Du_h\right)
\right) =f_h on with Dirichlet boundary conditions. Here the
sequence tends to as
and the map is periodic in monotone in
and satisfies suitable continuity conditions. We prove that
weakly in as where
is the solution of a homogenized problem of the form -\mbox{div}\left(
b\left( x,Du\right) \right) =f on We also derive an explicit
expression for the homogenized operator and prove some corrector results,
i.e. we find such that in
Locally periodic unfolding method and two-scale convergence on surfaces of locally periodic microstructures
In this paper we generalize the periodic unfolding method and the notion of
two-scale convergence on surfaces of periodic microstructures to locally
periodic situations. The methods that we introduce allow us to consider a wide
range of non-periodic microstructures, especially to derive macroscopic
equations for problems posed in domains with perforations distributed
non-periodically. Using the methods of locally periodic two-scale convergence
(l-t-s) on oscillating surfaces and the locally periodic (l-p) boundary
unfolding operator, we are able to analyze differential equations defined on
boundaries of non-periodic microstructures and consider non-homogeneous Neumann
conditions on the boundaries of perforations, distributed non-periodically
Numerical Computations with H(div)-Finite Elements for the Brinkman Problem
The H(div)-conforming approach for the Brinkman equation is studied
numerically, verifying the theoretical a priori and a posteriori analysis in
previous work of the authors. Furthermore, the results are extended to cover a
non-constant permeability. A hybridization technique for the problem is
presented, complete with a convergence analysis and numerical verification.
Finally, the numerical convergence studies are complemented with numerical
examples of applications to domain decomposition and adaptive mesh refinement.Comment: Minor clarifications, added references. Reordering of some figures.
To appear in Computational Geosciences, final article available at
http://www.springerlink.co
The Mean-Field Limit for Solid Particles in a Navier-Stokes Flow
We propose a mathematical derivation of Brinkman's force for a cloud of
particles immersed in an incompressible fluid. Our starting point is the Stokes
or steady Navier-Stokes equations set in a bounded domain with the disjoint
union of N balls of radius 1/N removed, and with a no-slip boundary condition
for the fluid at the surface of each ball. The large N limit of the fluid
velocity field is governed by the same (Navier-)Stokes equations in the whole
domain, with an additional term (Brinkman's force) that is (minus) the total
drag force exerted by the fluid on the particle system. This can be seen as a
generalization of Allaire's result in [Arch. Rational Mech. Analysis 113
(1991), 209-259] who treated the case of motionless, periodically distributed
balls. Our proof is based on slightly simpler, though similar homogenization
techniques, except that we avoid the periodicity assumption and use instead the
phase-space empirical measure for the particle system. Similar equations are
used for describing the fluid phase in various models for sprays
Experimental measurement and calculation of losses in planar radial magnetic bearings
The loss mechanisms associated with magnetic bearings have yet to be adequately characterized or modeled analytically and thus pose a problem for the designer of magnetic bearings. This problem is particularly important for aerospace applications where low power consumption of components is critical. Also, losses are expected to be large for high speed operation. The iron losses in magnetic bearings can be divided into eddy current losses and hysteresis losses. While theoretical models for these losses exist for transformer and electric motor applications, they have not been verified for magnetic bearings. This paper presents the results from a low speed experimental test rig and compares them to calculated values from existing theory. Experimental data was taken over a range of 90 to 2,800 rpm for several bias currents and two different pole configurations. With certain assumptions agreement between measured and calculated power losses was within 16 percent for a number of test configurations
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