50 research outputs found
In-Process Monitoring of Changing Dynamics of a Thin-Walled Component During Milling Operation by Ball Shooter Excitation
On the stability of periodic orbits in delay equations with large delay
We prove a necessary and sufficient criterion for the exponential stability
of periodic solutions of delay differential equations with large delay. We show
that for sufficiently large delay the Floquet spectrum near criticality is
characterized by a set of curves, which we call asymptotic continuous spectrum,
that is independent on the delay.Comment: postprint versio
A generic map has no absolutely continuous invariant probability measure
Let be a smooth compact manifold (maybe with boundary, maybe
disconnected) of any dimension . We consider the set of maps
which have no absolutely continuous (with respect to Lebesgue)
invariant probability measure. We show that this is a residual (dense
C^1$ topology.
In the course of the proof, we need a generalization of the usual Rokhlin
tower lemma to non-invariant measures. That result may be of independent
interest.Comment: 12 page
State-dependent distributed-delay model of orthogonal cutting
In this paper we present a model of turning
operations with state-dependent distributed time delay.
We apply the theory of regenerative machine tool chat-
ter and describe the dynamics of the tool-workpiece sys-
tem during cutting by delay-diferential equations. We
model the cutting-force as the resultant of a force sys-
tem distributed along the rake face of the tool, which
results in a short distributed delay in the governing
equation superimposed on the large regenerative de-
lay. According to the literature on stress distribution
along the rake face, the length of the chip-tool inter-
face, where the distributed cutting-force system is act-
ing, is function of the chip thickness, which depends on
the vibrations of the tool-workpiece system due to the
regenerative efect. Therefore, the additional short de-
lay is state-dependent. It is shown that involving state-
dependent delay in the model does not afect linear sta-
bility properties, but does afect the nonlinear dynamics
of the cutting process. Namely, the sense of the Hopf bi-
furcation along the stability boundaries may turn from
sub- to supercritical at certain spindle speed regions
Finding periodic orbits in state-dependent delay differential equations as roots of algebraic equations
In this paper we prove that periodic boundary-value problems (BVPs) for delay
differential equations are locally equivalent to finite-dimensional algebraic
systems of equations. We rely only on regularity assumptions that follow those
of the review by Hartung et al. (2006). Thus, the equivalence result can be
applied to differential equations with state-dependent delays (SD-DDEs),
transferring many results of bifurcation theory for periodic orbits to this
class of systems. We demonstrate this by using the equivalence to give an
elementary proof of the Hopf bifurcation theorem for differential equations
with state-dependent delays. This is an alternative and extension to the
original Hopf bifurcation theorem for SD-DDEs by Eichmann (2006).Comment: minor revision, correcting mistakes in formulation of Lemma 2.3 and
A.5 (which are also present in the Journal paper): center of neighborhood
must be in , which is the case for the main theore
Balancing with Vibration: A Prelude for âDrift and Actâ Balance Control
Stick balancing at the fingertip is a powerful paradigm for the study of the control of human balance. Here we show that the mean stick balancing time is increased by about two-fold when a subject stands on a vibrating platform that produces vertical vibrations at the fingertip (0.001 m, 15â50 Hz). High speed motion capture measurements in three dimensions demonstrate that vibration does not shorten the neural latency for stick balancing or change the distribution of the changes in speed made by the fingertip during stick balancing, but does decrease the amplitude of the fluctuations in the relative positions of the fingertip and the tip of the stick in the horizontal plane, A(x,y). The findings are interpreted in terms of a time-delayed âdrift and actâ control mechanism in which controlling movements are made only when controlled variables exceed a threshold, i.e. the stick survival time measures the time to cross a threshold. The amplitude of the oscillations produced by this mechanism can be decreased by parametric excitation. It is shown that a plot of the logarithm of the vibration-induced increase in stick balancing skill, a measure of the mean first passage time, versus the standard deviation of the A(x,y) fluctuations, a measure of the distance to the threshold, is linear as expected for the times to cross a threshold in a stochastic dynamical system. These observations suggest that the balanced state represents a complex timeâdependent state which is situated in a basin of attraction that is of the same order of size. The fact that vibration amplitude can benefit balance control raises the possibility of minimizing risk of falling through appropriate changes in the design of footwear and roughness of the walking surfaces