Damping Of Rotation Research Articles

Dynamic error fields derivation by inverting a validated interpretative perturbations model

The need for a model able to provide the dynamic evolution of the intrinsic magnetic error fields amplitude in tokamaks is of a significant importance in order to develop strategies to correct its destabilizing effect. The present paper specifically aims to deliver this kind of model and adjacent code. A previously built direct perturbations interpretative model (Miron (JET Contributors) 2021 Nucl. Fusion 61 106016) is used to calculate the plasma instabilities amplitude and frequency aiming to match the same quantities provided by the device diagnostics data analysis specific code for various discharges at JET. The mentioned good match ensures our model validity against the experimental results. Based on its proven structural validity, our model considering the error field quantities is inverted. This time the initial direct model output results, namely the plasma perturbations amplitude and frequency, become input data for our inverse model aiming to solve the corresponding error field modes system of equations searched as unknowns. The error fields basically satisfy the same outer plasma perturbed equations as the plasma perturbations do (vacuum/wall/plasma column external structures). Obviously they do not satisfy the perturbed plasma equations. A clear and explicit dynamic error field solution is finally provided. It has been demonstrated that whenever the error fields are responsible for the mode locking effect and plasma rotation damping, the calculated error fields shows its expected disruptive resonant behavior during various discharges at JET.

TEBEM for springing responses of a container ship with forward speed and nonlinear effects in time domain

In this paper, springing responses of a container ship with forward speed in regular waves are studied by a time-domain TEBEM which is generalized to elastic modes. TEBEM is used principally to solve the steady and unsteady flow and the infinity radiation condition is achieved by the Damping Zone Method. In the structure part, the Transfer Matrix Method is used to get the generalized structural mass, damping, stiffness and principal mode of displacement and rotation of vertical oscillation modes which will participate in the subsequent hydrodynamic calculation. In the hydrodynamic part, the fourth-order Runge–Kutta method is used to solve the hydroelasticity equations. The effects of forward speed and 2nd order wave forces generated by 1st order velocity potential in head sea are analyzed. Meanwhile, the variation of different load components against wave direction for corresponding different stations and contribution of different part of ship for different load components in head sea are studied. Compared with the experimental results, the motions and loads of a 6750-TEU container ship with different forward speeds predicted by TEBEM show an acceptable agreement.

Anti-sway method for reducing vibrations on a tower crane structure

Abstract We develop a solution to the problem of the behavior of a tower crane considered as a deformable system, and therefore subject to vibrations, whereas the controlled movement of a payload is implemented. The motion of the payload is calculated taking into account the normal vibration modes of the tower crane and the swaying of the payload. A “command smoothing” method relative to an open-loop system is used for reducing the sway of the payload, through smoothing the original command by the crane operator. This leads, as a consequence, to a reduction in the vibrations of the crane structure. An iterative calculation of the sway angle and the corresponding applied velocity profiles as input to the crane motors is applied. The tower crane is considered as a high nonlinear underactuated system; it is modeled considering the possible deformation of the structure. The results relating to the normal deformations of the crane are obtained, highlighting how these vibrations are strongly attenuated when an anti-sway system for the payload is implemented. Therefore, it is shown how this control leads to the best results in terms of performance for both the payload movement (shortest possible profile for the rotation movement and damping of the load oscillation) and the structure of the tower crane. Applying the method described in this paper, the structure of the tower crane does not undergo the strong horizontal and vertical oscillations that occur when the elastic structure is not considered in the crane model.

An Overview of the Effectiveness of Bicycle Helmet Designs in Impact Testing.

Cycling accidents are the leading cause of sports-related head injuries in the US. Conventional bicycle helmets typically consist of polycarbonate shell over Expanded Polystyrene (EPS) foam and are tested with drop tests to evaluate a helmet’s ability to reduce head kinematics. Within the last decade, novel helmet technologies have been proposed to mitigate brain injuries during bicycle accidents, which necessitates the evaluation of their effectiveness in impact testing as compared to conventional helmets. In this paper, we reviewed the literature to collect and analyze the kinematic data of drop test experiments carried out on helmets with different technologies. In order to provide a fair comparison across different types of tests, we clustered the datasets with respect to their normal impact velocities, impact angular momentum, and the type of neck apparatus. When we analyzed the data based on impact velocity and angular momentum clusters, we found that the bicycle helmets that used rotation damping based technology, namely MIPS, had significantly lower peak rotational acceleration (PRA) and Generalized Acceleration Model for Brain Injury Threshold (GAMBIT) as compared to the conventional EPS liner helmets (p < 0.01). SPIN helmets had a superior performance in PRA compared to conventional helmets (p < 0.05) in the impact angular momentum clustered group, but not in the impact-velocity clustered comparisons. We also analyzed other recently developed helmets that primarily use collapsible structures in their liners, such as WaveCel and Koroyd. In both of the impact velocity and angular momentum groups, helmets based on the WaveCel technology had significantly lower peak linear acceleration (PLA), PRA, and GAMBIT at low impact velocities as compared to the conventional helmets, respectively (p < 0.05). The protective gear with the airbag technology, namely Hövding, also performed significantly better compared to the conventional helmets in the analyzed kinematic-based injury metrics (p < 0.001), possibly due to its advantage in helmet size and stiffness. We also observed that the differences in the kinematic datasets strongly depend on the type of neck apparatus. Our findings highlight the importance and benefits of developing new technologies and impact testing standards for bicycle helmet designs for better prevention of traumatic brain injury (TBI).

Stability analysis and control of a flywheel energy storage rotor with rotational damping and nonsynchronous damping

Based on the principle of Lagrange mechanics, especially considering the effects of rotation damping and nonsynchronous damping, a radial 4-dimensional dynamic model of the flywheel bearing rotor system is proposed. Applying the Laplace eigenvalue method, the stability effects of rotational damping, nonsynchronous damping, and their coupling effects are investigated by means of root locus method. Under the control of the linear quadratic regulator, dynamical characteristics of the flywheel bearing rotor system with varied rotational damping and nonsynchronous damping are also studied. The results show that the rotation damping, nonsynchronous damping, and their coupling effects have vast and complex instability effects on high-speed flywheel bearing rotor system. However, there are three exceptions. The tiny proportional rotational damping, remaining below 12%, and the minuscule proportional co-nonsynchronous damping; the product of the nonsynchronous damping and the speed ratio below 5% both can enhance the stability of the system. Furthermore, in the situation that the counter-nonsynchronous damping is coupled with the large proportion of rotational damping, the stability of the system can also be boosted distinctly. On the other hand, the numerical experimental results show that the rotational damping and nonsynchronous damping have a beneficial effect on the flywheel system controlled by linear quadratic regulator. In addition, under the control of linear quadratic regulator, the transient dynamical behavior of the flywheel rotor system with rotational damping or co-nonsynchronous damping performed better than the flywheel rotor system with the coupled damping. The numerical simulations of the transient response of the flywheel rotor system under active control are consistent with some of the derived stability analysis results. The results about the stability analysis and the performance in vibration control give the suggestions for the instability control and fault detection of the system.

Bio-inspired toe-like structure for low-frequency vibration isolation

Inspired by the cushioning effect of the felid paws in contact with the ground, a novel bio-inspired toe-like structure (TLS) is developed and systematically studied for low-frequency vibration isolation. The TLS consists of two rods with different length (as phalanxes) and a linear spring (as muscle). Based on Hamiltonian principle, the dynamic model is established considering spring deformation and joint rotation damping. The derived equivalent stiffness reveals that the proposed TLS possesses favorable high static and low dynamic stiffness (HSLDS) characteristics in a wide displacement range. Besides, displacement transmissibility suggests that the proposed TLS isolator has low resonance frequency and can effectively isolate base excitation at low frequencies. Comprehensive parameter analysis shows that the inherent nonlinearities in stiffness and damping is conductive to vibration isolation and can be designed/adjusted on demand by selecting suitable structural parameters. This flexibility gives TLS advantages and great potential in extensive engineering applications when subjected to variable vibration loads. A prototype is fabricated and tested for a comprehensive recognize of its advantageous vibration isolation performance in low frequency band. The vibration with excitation frequency higher than 3 Hz can be effectively isolated. This novel bio-inspired TLS provides a feasible approach to passive vibration control and isolation in low frequency band.

Excitation of fishbone-like mode in tokamaks due to bounce resonances of trapped thermal ions

When the drift kinetic effect of thermal ions is taken into account, a high-frequency fishbone-like mode (FLM) is found to be driven unstable by trapped thermal ions (TTIs) in tokamak plasmas, according to self-consistent magneto-hydrodynamic (MHD)-kinetic hybrid modeling utilizing the MARS-K code [Liu et al., Phys. Plasmas 15, 112503 (2008)] as well as an analytic theory. It is found that, similar to energetic particles, TTIs can also stabilize the internal kink mode, whereas the FLM is excited when the effective beta of TTIs exceeds a threshold value. The real frequency of the FLM is comparable to the bounce frequency of TTIs. The mode structure of the FLM can be significantly different from the conventional step-like function for the associated plasma radial displacement. This drift kinetic induced modification of the mode structure near the q = 1 surface is captured by non-perturbative MHD-kinetic hybrid computations with MARS-K. Furthermore, the FLM can only be triggered by TTIs at sufficiently high thermal temperatures. Both the FLM and the internal kink can be stabilized by sufficiently fast plasma toroidal rotation and parallel sound wave damping. These two conditions of high thermal temperature and (fast) flow stabilization, though making it challenging to observe the TTI-driven FLM in present day experiments, are favorable for the mode excitation in future reactor scale devices.

Toroidal modelling of core plasma flow damping by RMP fields in hybrid discharge on ASDEX upgrade

In ASDEX Upgrade hybrid discharges, it is found that an externally applied n = 1 field preferentially distorts the plasma in the core, leading to significant flow damping there and elsewhere across the plasma radius. MARS-F/Q modeling of a neoclassical toroidal viscous NTV) torque that results from an amplified internal kink-type displacement in the plasma core is qualitatively consistent with the measured internal displacements, beta dependence, and rotation damping. Sensitivity studies indicate that the internal kink response and the resulting core flow damping critically depend on the plasma equilibrium pressure, the initial flow speed, the coil phasing and the proximity of q0 to 1. No appreciable flow damping is found for a βN plasma. A relatively slower initial toroidal flow results in a stronger core flow damping, due to the enhanced NTV torque. Weaker flow damping is achieved as q0 is assumed to be farther away from 1. Finally, a systematic coil phasing scan finds the strongest (weakest) flow damping occurring at the coil phasing of approximately 20 (200) degrees, quantitatively agreeing with experiments. This study points to the important role played by the internal kink response in plasma core flow damping in high-beta hybrid scenario plasmas such as that foreseen for ITER.

Investigation of chatter stability of cutting process with a rotating tapered cutter bar considering internal and external damping

The damping of cutting system is an important factor influencing stability in boring and milling process. However, systematical and thorough studies of the influencing mechanism of damping, especially on the chatter stability of rotating cutter bar, are still absent. The damping of a cutting system mainly consists of external damping and internal damping. This study focuses on these damping effects on chatter stability of the cutting system with a rotating tapered cutter bar. The partial differential equation of motion of the cutter bar is derived based on the Hamilton principle combined with the Euler-Bernoulli beam theory. It is assumed that the cutter bar is tapered, and its free ends acts on a two-dimensional regenerative cutting force with time-delay effect. The damping mechanisms of external and internal are described by the viscous damping model and the strain-rate-dependent Kelvin-Voigt model, respectively. The partial differential equation of motion is discretized as an ordinary differential equation using the Galerkin method. The Campbell diagram and the decay rate plots including critical rotating speed and instability threshold of the cutter bar are obtained by free vibration analysis. Also, the chatter stability lobes in the cutting process are plotted and the predicted results of stability in frequency domain are compared with those in time domain. The results indicate that the structural parameters of a cutter bar, including the rotation, the ratio of internal and total damping, damping ratio, and taper and aspect ratios have significant effects on cutter bar dynamics and chatter stability of cutting process. In particular, a new chatter instability is observed for the cutting system in higher rotating speed ranges due to the effects of rotation and internal damping. The onset rotating speed of the new chatter instability equals to the instability threshold of rotor system of cutter bar. Finally, the present model is validated by comparing both stability prediction given by previous study and natural frequencies and decay rates by ANSYS FE code.

Expanded capabilities of the CarMa code in modeling resistive wall mode dynamics with 3-D conductors

In this work, an improved version of the CarMa code is presented, called CarMa-D, for the analysis of resistive wall modes (RWMs) in fusion devices, simultaneously considering the effects of volumetric three-dimensional conducting structures, plasma dynamics, toroidal rotation or drift-kinetic damping. Unlike static CarMa, CarMa-D does not rely on the simplifying assumptions such as neglecting the plasma mass, toroidal rotation and kinetic damping. The new coupling strategy is based on matrix-based Padé rational functions approximation of plasma a response. The arising mathematical model is formally equivalent to the original CarMa model, but with a higher number of degrees of freedom to model the dynamics of the plasma. CarMa-D overcomes the main limitations of the original CarMa, in particular: (i) the massless assumption for the plasma is removed, allowing modeling of global modes growing both on ideal kink time scales and in the typical RWM growth rate regime, with a suitable treatment of the model; (ii) the effects of toroidal plasma flow and drift kinetic damping can be included into the new model, providing a powerful tool to study macroscopic phenomena where both plasma dynamics and 3-D conducting structures play important roles.

Saturated helical mode in EAST high β hybrid plasmas

A hybrid scenario with the minimum safety factor above unity and a safety factor profile with a wide range of low magnetic shear in the core is one of the candidates for ITER operations. Theory predicts that such equilibria are prone to quasi-interchange mode, which was confirmed by observations from several devices. The presence of those 3D quasi-interchange helical modes has both positive and negative effects on plasma performance. On the one hand, they can avoid low mode number instabilities such as sawteeth. On the other hand, they would lead to confinement degradation, significant fast ion losses and toroidal rotation damping. Such modes are observed for the first time in EAST high βp hybrid plasmas achieved with off-axis neutral beam injection (NBI) heating. The mode manifested itself as long-lived saturated helical instability. Notably, when the mode was destabilized, the toroidal rotation profile in the core was completely flattened. The extent of the flattened rotation profile reaches up to half of the minor radius. As the minimum safety factor qmin approaches unity, strong n = 2 and n = 3 harmonics are successively driven unstable as nonlinear consequences of the n = 1 mode. A 3D resistive nonlinear simulation with a realistic tokamak configuration has been applied to reproduce the evolution of long-lived helical instability with the M3D code. The simulated magnetic perturbation shows a strong n = 2 component. As the mode grows, the amplitude of the n = 2 harmonic grows immensely with respect to that of the n = 1 harmonic. The n = 2 harmonic gradually becomes dominant as the mode saturates. In saturation, the initial weak shear safety factor profile in the core becomes completely flat. This change of safety factor profile in the core corroborates a self-regulating magnetic flux pumping mechanism which is considered responsible for maintaining stationary non-sawtoothing hybrid discharges.

Experimental modal analysis of disk-like rotor–stator system coupled by viscous liquid

The vibrational behavior of a rotor–stator system coupled by a viscous liquid is investigated experimentally using a test bench with rotor and stator simplified as disks. The understanding of this vibration problem is of particular importance in the design of hydraulic machines such as Francis turbines, pump–turbines or hydraulic pumps, where the elastic rotor is coupled to the adjacent elastic stator by the intermediate water. The especially developed test bench enables high-resolution scan measurements of the rotor and stator disk vibrations by applying the modal analysis method in combination with the laser interferometer technique. We present the mode shapes, eigenfrequencies and damping factors measured over a large number of parameter combinations of the stator thickness, the rotor thickness, the clearance between rotor and stator as well as the rotation speed of the rotor. We identify and discuss fundamental vibration mechanisms of the system (for example, the characterization of varicose and sinuous modes, or the frequency split between co- and counter-rotating modes). The derived experimental results may serve as a benchmark for the validation of simulation models studying the linear vibration including effects of rotation, bias flow and viscous damping.

Magnetic braking and damping of differential rotation in massive stars

Fragmentation of highly differentially rotating massive stars that undergo collapse has been suggested as a possible channel for binary black hole formation. Such a scenario could explain the formation of the new population of massive black holes detected by the LIGO/VIRGO gravitational wave laser interferometers. We probe that scenario by performing general relativistic magnetohydrodynamic simulations of differentially rotating massive stars supported by thermal radiation pressure plus a gas pressure perturbation. The stars are initially threaded by a dynamically weak, poloidal magnetic field confined to the stellar interior. We find that magnetic braking and turbulent viscous damping via magnetic winding and the magnetorotational instability in the bulk of the star redistribute angular momentum, damp differential rotation and induce the formation of a massive and nearly uniformly rotating inner core surrounded by a Keplerian envelope. The core + disk configuration evolves on a secular timescale and remains in quasi-stationary equilibrium until the termination of our simulations. Our results suggest that the high degree of differential rotation required for $m=2$ seed density perturbations to trigger gas fragmentation and binary black hole formation is likely to be suppressed during the normal lifetime of the star prior to evolving to the point of dynamical instability to collapse. Other cataclysmic events, such as stellar mergers leading to collapse, may therefore be necessary to reestablish sufficient differential rotation and density perturbations to drive nonaxisymmetric modes leading to binary black hole formation.

Dependence of magnetic and microwave loss on evolving microstructure in yttrium iron garnet

The parallel magnetic and microwave loss dependence on microstructural evolutions in several polycrystalline yttrium iron garnet samples were studied in detail, focusing on the attendant occurrence of their relationships. In this study, polycrystalline YIG samples were synthesized by employing the mechanical alloying technique and sintering toroidal compacts at temperatures from 600 to 1400 °C. The samples were characterized for their evolution in crystalline phases, structure, microstructure, magnetic hysteresis parameters, microwave losses and electrical resistivity. The results showed an increasing tendency of the saturation magnetization with grain size, which is attributed to crystallinity increase in the grains. The M–H hysteresis loop results showed a transition from disordered-to-ordered magnetism which belongs to different magnetically dominant stages of formation. The starting appearance of room temperature ferromagnetic order suggested by the sigmoid-shaped loops seems to be dependent on crystallinity, phase purity and a sufficient number of large enough magnetic domain-containing grains having been formed in the microstructure. An increasing trend of transmission loss with grain size may be attributed to increment of loss contribution from hysteresis and domain wall resonance of the samples. The changes in crystallinity and microstructure, and the associated processes of microwave resonance and relaxation due to domain wall movements and damping of spin rotation contributes to the variations in transmission loss and ferromagnetic linewidth of the samples. The increased electrical resistivity while the microstructure was evolving is believed to strongly indicates improved phase purity and compositional stoichiometry.

Candidate magnetic dust structures for star light polarization

Rotation damping and alignment are discussed as prerequisites for polarization power. An expression is derived from first principles, for the damping time of the rotation of a particle in a magnetic field, under the Faraday braking torque, provided its electrical properties are known. This makes it possible to describe mathematically, in great detail, the motion of the particle and determine its ultimate state of motion, if a steady state is possible at all. This work defines, first, the necessary condition for the Faraday braking to be effective: a) the net electronic charge distribution should not be uniform throughout; b) the number of vibration modes should exceed a few tens. Resonance of rotation frequency with any of these modes is not a requirement. For alignment to be possible, the ratio of gyroscopic and conservative magnetic to non-conservative (retarding) magnetic torques must be low. Either dia-, para- or ferro-magnetism can do, and a small susceptibility is enough and even preferable. This opens up a wide spectrum of possible candidates. A few examples are given.

Variation of magnetic braking by non-axisymmetric magnetic fields depending on the perturbed field structure in the KSTAR tokamak

The variation of a magnetic braking profile by non-axisymmetric magnetic fields has been experimentally demonstrated and numerically validated in the KSTAR tokamak. Two types of n = 2 non-resonant magnetic fields were applied by changing the relative phase of non-axisymmetric field coils. One is even parity, of which non-resonant fields deeply penetrate into the plasma core, and the other is odd parity localized at the plasma edge. The even and odd parity produced significantly different perturbed magnetic field structures, and thereby drove global and edge-dominant toroidal rotation damping, respectively. These distinct braking profiles are consistently reproduced by drift-kinetic particle simulations, indicating the possibility of the predictive utilization of non-resonant magnetic fields for rotation profile control.

Design and analysis of a multi-stage torsional stiffness dual mass flywheel based on vibration control

This paper is aimed to investigate the kinetic parameters matching and designing method for a multi-stage torsional stiffness dual mass flywheel (DMF) based on torsional vibration control. Using the numerical analysis methods, three critical technological problems are resolved subsequently. The first one is that the kinetics simulation model of vehicle drivetrain is established, and the actual torsional vibration excitation of crankshaft and different gear pairs engaged multi-operating conditions for drivetrain are taken into account during modeling. The second one is that the kinetic parameters sensitivity of DMF with respect to torsional vibration control are obtained and the range of each kinetic parameter (i.e. rotation inertia ratio, torsional stiffness and damping) is derived further. The last one is that the parameters matching and designing methods for a multi-stage torsional stiffness DMF, considering the constraint conditions that transmission torque, relative angle and distribution of natural frequencies of DMF-drivetrain, are carried out. The results show that the torsional vibration of drivetrain is controlled effectively after matching a three-stage torsional stiffness DMF and the amplitude of angular velocity at input end of gearbox decreases significantly, which verifies that the designing and matching methods are effective and the result can thus be used in vibration control for vehicle drivetrain.

Modelling toroidal rotation damping in ITER due to external 3D fields

The linear and quasi-linear plasma response to the n = 3 and n = 4 (n is the toroidal mode number) resonant magnetic perturbation (RMP) fields, produced by the in-vessel edge localized mode control coils, is numerically studied for an ITER 15 MA H-mode baseline scenario. Both single fluid and fluid-kinetic hybrid models are used. The inclusion of drift kinetic effects does not strongly alter the plasma response compared to the fluid approximation for this ITER plasma. The full toroidal drift kinetic model is also used to compute the neoclassical toroidal viscous (NTV) torque, yielding results close to that of an analytic model based on geometric simplifications. The computed NTV torque from low-n RMP fields is generally smaller than the resonant electromagnetic torque for this ITER plasma. The linear response computations show a weak core kink response, contrary to a strong kink response often computed for plasmas from present day tokamak devices. Initial value quasi-linear simulations, including various torque models, show a localized damping of the plasma toroidal flow near the edge, as a result of the applied RMP fields. This localized rotation damping can be weak or strong depending on whether a weakly unstable edge localized peeling mode is present. No qualitative difference is found between the n = 3 and n = 4 RMP field configurations, in both the linear and non-linear response results.

Viscous damping of toroidal angular momentum in tokamaks

The Braginskii viscous stress tensor formalism was generalized to accommodate non-axisymmetric 3D magnetic fields in general toroidal flux surface geometry in order to provide a representation for the viscous damping of toroidal rotation in tokamaks arising from various “neoclassical toroidal viscosity” mechanisms. In the process, it was verified that the parallel viscosity contribution to damping toroidal angular momentum still vanishes even in the presence of toroidal asymmetries, unless there are 3D radial magnetic fields.

Modal Analysis of High-Speed Face Milling System Based on Composite Structure System Analysis Method

This paper adopts composite structure system analysis method to perform modal analysis of high-speed face milling cutter which is mounted on the machine tool through FEM modal analysis. The key problem of this method is to obtain joint surface parameters between the machine tool spindle and face milling cutter through experimental modal analysis and MATLAB software. The joint surface parameters consist of linear stiffness, linear damping, rotation stiffness and rotation damping. After getting the frequency response function (FRF) at the tool tip of the face milling system through experimental modal analysis, the contact surface parameters can be used to eliminate the influence of the machine tool to get modal parameters of the face-milling cutter itself. Based on the finite element model of face milling cutter, composite structure system analysis method can be used easily to acquire the dynamic performance of the face milling system through FEM modal analysis, greatly to improve the reliability of modal analysis, and is helpful to the dynamic design and the structure improvement of high speed face milling cutter.