24,214 research outputs found
Analytical prediction of chatter stability for variable pitch and variable helix milling tools
Regenerative chatter is a self-excited vibration that can occur during milling and other machining processes. It leads to a poor surface finish, premature tool wear, and potential damage to the machine or tool. Variable pitch and variable helix milling tools have been previously proposed to avoid the onset of regenerative chatter. Although variable pitch tools have been considered in some detail in previous research, this has generally focussed on behaviour at high radial immersions. In contrast there has been very little work focussed on predicting the stability of variable helix tools. In the present study, three solution processes are proposed for predicting the stability of variable pitch or helix milling tools. The first is a semi-discretisation formulation that performs spatial and temporal discretisation of the tool. Unlike previously published methods this can predict the stability of variable pitch or variable helix tools, at low or high radial immersions. The second is a time-averaged semi-discretisation formulation that assumes time-averaged cutting force coefficients. Unlike previous work, this can predict stability of variable helix tools at high radial immersion. The third is a temporal-finite element formulation that can predict the stability of variable pitch tools with a constant uniform helix angle, at low radial immersion. The model predictions are compared to previously published work on variable pitch tools, along with time-domain model simulations. Good agreement is found with both previously published results and the time-domain model. Furthermore, cyclic-fold bifurcations were found to exist for both variable pitch and variable helix tools at lower radial immersions
Traversable Wormholes in (2+1) and (3+1) Dimensions with a Cosmological Constant
Macroscopic traversable wormhole solutions to Einstein's field equations in
and dimensions with a cosmological constant are investigated.
Ensuring traversability severely constrains the material used to generate the
wormhole's spacetime curvature. Although the presence of a cosmological
constant modifies to some extent the type of matter permitted (for example it
is possible to have a positive energy density for the material threading the
throat of the wormhole in dimensions), the material must still be
``exotic'', that is matter with a larger radial tension than total mass-energy
density multiplied by . Two specific solutions are applied to the general
cases and a partial stability analysis of a dimensional solution is
explored.Comment: 19 pgs. WATPHYS TH-93/0
Quasilocal energy and naked black holes
We extend the Brown and York notion of quasilocal energy to include coupled
electromagnetic and dilaton fields and also allow for spatial boundaries that
are not orthogonal to the foliation of the spacetime. We investigate how the
quasilocal quantities measured by sets of observers transform with respect to
boosts. As a natural application of this work we investigate the naked black
holes of Horowitz and Ross calculating the quasilocal energies measured by
static versus infalling observers.Comment: 5 pages, 1 figure; submitted to the 8th Canadian Conference on
General Relativity and Relativistic Astrophysics. This paper is a condensed
version of gr-qc/990707
Exact Solution for the Metric and the Motion of Two Bodies in (1+1) Dimensional Gravity
We present the exact solution of two-body motion in (1+1) dimensional dilaton
gravity by solving the constraint equations in the canonical formalism. The
determining equation of the Hamiltonian is derived in a transcendental form and
the Hamiltonian is expressed for the system of two identical particles in terms
of the Lambert function. The function has two real branches which join
smoothly onto each other and the Hamiltonian on the principal branch reduces to
the Newtonian limit for small coupling constant. On the other branch the
Hamiltonian yields a new set of motions which can not be understood as
relativistically correcting the Newtonian motion. The explicit trajectory in
the phase space is illustrated for various values of the energy. The
analysis is extended to the case of unequal masses. The full expression of
metric tensor is given and the consistency between the solution of the metric
and the equations of motion is rigorously proved.Comment: 34 pages, LaTeX, 16 figure
N-body Gravity and the Schroedinger Equation
We consider the problem of the motion of bodies in a self-gravitating
system in two spacetime dimensions. We point out that this system can be mapped
onto the quantum-mechanical problem of an N-body generalization of the problem
of the H molecular ion in one dimension. The canonical gravitational
N-body formalism can be extended to include electromagnetic charges. We derive
a general algorithm for solving this problem, and show how it reduces to known
results for the 2-body and 3-body systems.Comment: 15 pages, Latex, references added, typos corrected, final version
that appears in CQ
Effects of an extra U(1) axial condensate on the strong decays of pseudoscalar mesons
We consider a scenario (supported by some lattice results) in which a
U(1)-breaking condensate survives across the chiral transition in QCD. This
scenario has important consequences for the pseudoscalar-meson sector, which
can be studied using an effective Lagrangian model. In particular, generalizing
the results obtained in two previous papers, where the effects on the radiative
decays eta,eta' --> gamma gamma were studied, in this paper we study the
effects of the U(1) chiral condensate on the strong decays of the "light"
pseudoscalar mesons, i.e., eta,eta' --> 3pi^0; eta,eta' --> pi^+ pi^- pi^0;
eta' --> eta pi^0 pi^0; eta' --> eta pi^+ pi^-; and also on the strong decays
of an exotic ("heavy") SU(3)-singlet pseudoscalar state eta_X, predicted by the
model.Comment: One misprint in Eq. (2.10) has been eliminated; Eqs. (B.8) and (B.9)
in Appendix B have been corrected; 46 pages, 1 tabl
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