Modelling and Simulation of Nonlinear Jump Phenomena of a Non-ideal Rotor Involving Fractional Order PD Controller

Rotating machinery with high speed powered by industrial motors frequently suffers from instability by exhibiting non-linear jump phenomena, formally known as Sommerfeld effect. The drives whose excitation is a function of the system responses, referred to as non-ideal. The system dynamics of such systems exhibit a couple of complex and interesting features when the input power exceeds a critical value. The present research suggests a novel approach to study the efficacy of active magnetic bearing with fractional PD controller to suppress the instability caused by the Sommerfeld effect. The steady-state results obtained by solving the system characteristic equation numerically is compared with the transient analysis. Finally, root locus method is introduced to obtain the bifurcation points at which this kind of instability completely disappears.

Determining the energy efficiency of a resonance single-mass vibratory machine whose operation is based on the Sommerfeld effect

This paper reports determining the energy efficiency of a vibratory machine consisting of a viscoelastically fixed platform that can move vertically, and a vibration exciter whose operation is based on the Sommerfeld effect. The body of the vibration exciter rotates at a steady angular speed while there are the same loads in the form of a ball, a roller, or a pendulum inside it. The load, being moved relative to the body, is exposed to the forces of viscous resistance, which are internal within the system. It was established that under the steady oscillatory modes of a vibratory machine's movement, the loads are tightly pressed to each other, thereby forming a combined load. Energy is productively spent on platform oscillations and unproductively dissipated due to the movement of the combined load relative to the body. With an increase in the speed of the body rotation, the increasing internal forces of viscous resistance bring the speed of rotation of the combined load closer to the resonance speed, and the amplitude of platform oscillations increases. However, the combined load, in this case, increasingly lags behind the body, which increases unproductive energy loss and decreases the efficiency of the vibratory machine. A purely resonant motion mode of the vibratory machine produces the maximum amplitude of platform oscillations, the dynamic factor, the total power of viscous resistance forces. In this case, the efficiency reaches its minimum value. To obtain vigorous oscillations of the platform with a simultaneous increase in the efficiency of the vibratory machine, it is necessary to reduce the forces of viscous resistance in supports with a simultaneous increase in the internal forces of viscous resistance. An algorithm for calculating the basic dynamic characteristics of the vibratory machine's oscillatory motion has been built, based on solving the problem parametrically. The accepted parameter is the angular speed at which a combined load gets stuck. The effectiveness of the algorithm has been illustrated using a specific example

Thermal real scalar triplet dark matter

Real scalar triplet dark matter, which is known to be an attractive candidate for a thermal WIMP, is comprehensively studied paying particular attention to the Sommerfeld effect on the dark matter annihilation caused by the weak interaction and the other interaction between the dark matter and the Higgs boson. We find a parameter region that includes the so-called ‘WIMP-Miracle’ one is still surviving, i.e. it respects all constraints imposed by dark matter searches at collider experiments, underground experiments (direct detection) and astrophysical observations (indirect detection). The region is also found to be efficiently searched for by various near future experiments. In particular, the XENONnT experiment will cover almost the entire parameter region.

Sommerfeld-corrected relic abundance of wino dark matter with NLO electroweak potentials

Extending previous work, we calculate the electroweak potentials for all co-annihilation channels of wino dark matter at the one-loop order and obtain the wino relic abundance including the Sommerfeld effect at the next-to-leading order (NLO).

Final state Sommerfeld effect on dark matter relic abundance

If the annihilation products of dark matter (DM) are non-relativistic and if there is some long-range force between them, there can be Sommerfeld effect for the final state particles. We study this effect on DM relic abundance in the thermal freeze-out scenario. As a proof of concept, we consider the case of a DM pair annihilation into a final state pair, assuming that the mutual interactions between the two final state particles give rise to a Coulomb-like potential, and that the masses of the initial and final state particles are similar, so that both the initial and final state particles are non-relativistic. The size of the final state Sommerfeld (FSS) effect depends on the strength of the potential, as well as on the mass ratio of the final and initial state particles. We find that the impact of the FSS effect on DM relic abundance can be significant, and an electroweak sized long-range interaction is large enough to make a correction well beyond the observational accuracy. Another feature of the FSS effect is that it could be suppressed when its time scale is longer than the lifetime of the final state particles. As a corollary, we also study in the DM coannihilation scenario where the initial state Sommerfeld effect between two coannihilators could be reduced due to their instability, which may need to be taken into account for an accurate calculation of the DM relic abundance.