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 $(2+1)$ and $(3+1)$ 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 $(2+1)$ dimensions), the material must still be ``exotic'', that is matter with a larger radial tension than total mass-energy density multiplied by $c^2$. Two specific solutions are applied to the general cases and a partial stability analysis of a $(2+1)$ 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 $W$ function. The $W$ 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 $(r, p)$ 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 $N$ 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$_{2}^{+}$ 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