Expression For Torque Research Articles

Spin-orbit coupling for close-in planets

We study the spin evolution of close-in planets in multi-body systems and present a very general formulation of the spin-orbit problem. This includes a simple way to probe the spin dynamics from the orbital perturbations, a new method for computing forced librations and tidal deformation, and general expressions for the tidal torque and capture probabilities in resonance. We show that planet–planet perturbations can drive the spin of Earth-size planets into asynchronous or chaotic states, even for nearly circular orbits. We apply our results to Mercury and to the KOI-1599 system of two super-Earths in a 3/2 mean motion resonance.

Effect of Rashba interaction at normal metal/insulator interface on spin-orbit torque of ferromagnet/normal metal/insulator trilayers

Based on a spin drift-diffusion model, we theoretically investigate the spin-orbit torque in ferromagnet/normal metal/insulator trilayers with considering the Rashba interfacial spin-orbit coupling at the normal metal/insulator interface. We find that the spin-orbit torque shows the opposite normal-metal-thickness dependences for the bulk spin-orbit coupling effect in the normal metal layer and for the interfacial spin-orbit coupling effect at the normal metal/insulator interface, offering a way to disentangle these two spin-orbit coupling effects. Moreover, we show that the conventional interpretation based on the bulk spin-orbit coupling effect overestimates the spin Hall angle and underestimates the spin diffusion length of the normal metal layer, when the interfacial contribution is non-negligible. Our result, a concise analytic expression of the spin-orbit torque considering both bulk and interface spin-orbit coupling effects, will be useful to design and interpret experiments on spin-orbit torque experiments in ferromagnet/normal metal/insulator trilayers.

Quasi-Static Torque Profile Expressions for Magnetic Resonance-Based Remote Actuation

Resonant wireless power transfer has been employed to transfer electrical power from a transmitter to a receiver coil over an air gap and to remotely charge consumer devices. In this paper, the receiver coil is replaced by a stator–rotor topology, enabling magnetic resonance based motoring over substantial air gaps. The principles of resonant wireless power transfer are used to induce currents in a strongly coupled magnetic resonance system. This results in its turn-in torque, which is applied on the rotor body, allowing for remote actuation. We propose a voltage or current controlled magnetic resonance motoring topology, for which we derive expressions for the generated torque depending on the rotor angle. Furthermore, torque profile expressions are derived for motoring systems with multiple stator and/or rotor coils. Finally, an experimental setup is built to validate the obtained torque expressions. Using the validated expressions, we present a sensitivity analysis of the key system parameters with respect to the torque profile. The presented torque profile expressions enable further topology exploration and optimization of magnetic resonance based motoring systems.

Hydrodynamics of three-dimensional skyrmions in frustrated magnets

We study the nucleation and collective dynamics of Shankar skyrmions [Shankar, J. Phys. 38, 1405 (1977)] in the class of frustrated magnetic systems described by a SO(3) order parameter, including multilattice antiferromagnets and amorphous magnets. We infer the expression for the spin-transfer torque that injects skyrmion charge into the system and the Onsager-reciprocal pumping force that enables its detection by electrical means. The thermally assisted flow of topological charge gives rise to an algebraically decaying drag signal in nonlocal transport measurements. We contrast our findings to analogous effects mediated by spin supercurrents.

Relative Motion Dynamics Modeling and Control of DFP Vibration Isolation Spacecraft

In order to better meet the future high precision task requirements, the DFP(Disturbance-Free Payload) spacecraft composed of non-contact PM(Payload Module)and SM(Support Module)is taken as the object to study the relative motion dynamics modeling and control between the two modules and verify the system vibration isolation performance. Firstly, the force and torque expressions of the two modules are derived by simplifying the configuration and analyzing the stress. In view of that couple effect, the relative motion dynamics equations between two modules of DFP spacecraft with high model accuracy, and simple and uniform format are established with the dual quaternions. Based on this, the PD control law is designed, and the relative motion of PM and SM could meet DFP spacecraft working requirements when the measurability of control quantity and the measurement error of sensors were taken into account. Simulation results verify the advantage of vibration isolation and attitude maneuverability of DFP spacecraft.

Comparisons of Torque Performance in Surface-Mounted PM Vernier Machines With Different Stator Tooth Topologies

Permanent magnet vernier (PMV) machines, as one of the flux modulation machines, have gained considerable attention due to inherent high torque density and low torque ripple. This paper mainly investigates the torque performance of PMV machines with different stator tooth topologies. First, it begins with the theoretical analysis of surface-mounted PMV machines, which has a generic number of flux modulation poles (FMPs), PM poles, and armature poles. Then, the expression of flux linkage, back-electromotive force (EMF) and electromagnetic torque are derived successively, where the equivalent winding factor is proposed and defined to evaluate the flux modulation of stator auxiliary teeth and multi-harmonics coupling effect. Next, the back EMF, torque, power factor, flux-weakening capability, and PM demagnetization of PMV machines with different number of stator teeth are analyzed and compared. The final results of theoretical analysis and finite-element analysis can match well. Meanwhile, the non-uniform distribution of FMPs for increasing the average torque is first proposed and analyzed. A parameter K titled as FMP ratio is defined to evaluate the relationship among the angles among FMPs, the influence of the variation of K on the back EMF and torque is deeply explored and analyzed. Besides, the optimal range of K is carefully validated, which will help to optimize the design parameters more conveniently in the future.

Performance Prediction and Analysis of Adjustable-speed Permanent Magnet Eddy-current Couplings

This paper presents an accurate yet simple analytical model to predict the torque characteristics of an adjustable-speed permanent magnet eddy-current coupling in the low slip working area. Based on an improved magnetic equivalent circuit method, the flux density is quantitatively calculated, and then the general explicit expression of electromagnetic torque is developed. Moreover, the saturation effect of ferromagnetic materials and the restricted slip have been reasonably taken into account. Compared with the 3-D finite element analysis and measurement results, the validity of this model is confirmed. In addition, several important parameters of such devices are analyzed and discussed.

Theory for spin torque in Weyl semimetal with magnetic texture

The spin-transfer torque is a fundamental physical quantity to operate the spintronics devices such as racetrack memory. We theoretically study the spin-transfer torque and analyze the dynamics of the magnetic domain walls in magnetic Weyl semimetals. Owing to the strong spin-orbit coupling in Weyl semimetals, the spin-transfer torque can be significantly enhanced, because of which they can provide a more efficient means of controlling magnetic textures. We derive the analytical expression of the spin-transfer torque and find that the velocity of the domain wall is one order of magnitude greater than that of conventional ferromagnetic metals. Furthermore, due to the suppression of longitudinal conductivity in the thin domain-wall configuration, the dissipation due to Joule heating for the spin-transfer torque becomes much smaller than that in bulk metallic ferromagnets. Consequently, the fast-control of the domain wall can be achieved with smaller dissipation from Joule heating in the Weyl semimetals as required for application to low-energy-consumption spintronics devices.

Characteristics Analysis of the Motions of the Two-Degree-of-Freedom Direct Drive Induction Motor

The 2-degree-of-freedom direct drive induction motor (2DoFDDIM) is capable of implementing rotary linear or helical motion, which has the definite advantages of integrated structure, high material utilization, and so on. In this paper, the characteristics analysis of the three kinds of motions is presented. The air-gap magnetic field distributions and mechanical characteristics of the 2DoFDDIM with three motions are derived respectively. The results show that there is super synchronous speed or velocity phenomenon for rotary or linear motion. Moreover, the coupling effects between the rotating and travelling wave magnetic fields and that between the two mechanical motions will deteriorate the performance of the three-dimensional (3-D) helical motion compared with the two-dimensional (2-D) motion (rotary or linear). The expressions of the resistant torque and force caused by the coupling effect are derived, which are verified by 3-D finite-element models (FEMs). The results regarding the weakening of the output torque of helical motion and interacting magnetic field obtained from FEMs are then verified by experimental tests. Finally, the skewed slot method is applied to 2DoFDDIM, which successfully improves the performance of helical motion aiming to compensate the coupling resistant torque and force.

Atmospheric tides and their consequences on the rotational dynamics of terrestrial planets

Atmospheric tides can have a strong impact on the rotational dynamics of planets. They are of most importance for terrestrial planets located in the habitable zone of their host star, where their competition with solid tides is likely to drive the body towards non-synchronized rotation states of equilibrium, as observed in the case of Venus. Contrary to other planetary layers, the atmosphere is sensitive to both gravitational and thermal forcings, through a complex dynamical coupling involving the effects of Coriolis acceleration and characteristics of the atmospheric structure. These key physics are usually not taken into account in modelings used to compute the evolution of planetary systems, where tides are described with parametrised prescriptions. In this work, we present a new ab initio modeling of atmospheric tides adapting the theory of the Earth’s atmospheric tides (Chapman & Lindzen 1970) to other terrestrial planets. We derive analytic expressions of the tidal torque, as a function of the tidal frequency and parameters characterizing the internal structure (e.g. the Brunt-Väisälä frequency, the radiative frequency, the pressure heigh scale). We show that stratification plays a key role, the tidal torque being strong in the case of convective atmospheres (i.e. with a neutral stratification) and weak in case of atmosphere convectively stable. In a second step, the model is used to determine the non-synchronized rotation states of equilibrium of Venus-like planets as functions of the physical parameters of the system. These results are detailed in Auclair-Desrotour et al. (2016a) and Auclair-Desrotour et al. (2016b).

Fast Analytical Modeling and Analysis of Flux Focusing Disk-Type Permanent Magnet Eddy Current Couplings

This paper presents an improved 2-D analytical model to predict the magnetic field distributions and torque characteristics for a flux focusing disk-type permanent magnet eddy current coupling. Due to the inhomogeneous physical properties in the permanent magnet regions, based on the equivalent magnetic circuit method, a fictitious magnetization for the iron cores is introduced to simplify the complexity of modeling. The magnetic flux density distributions are derived when the eddy current generated in the copper plate and its back iron is reasonably concerned in 2-D Cartesian coordinates. Then, the explicit expression of torque is given and the torque-speed characteristics are analyzed. In the end, the calculated results of the proposed model are compared with those obtained from the magnetic equivalent circuit model and 3-D finite-element simulations.

Modeling and Emulation of a Rotating Paddle Type Wave Energy Converter

Torque-speed characteristics of an oscillating wave energy converter (WEC) is necessary to determine its optimal power point and to extract the corresponding design parameters for the generator and power converters used to generate power from the WEC. In this paper, analytical expressions for the mechanical torque on the WEC due to the oscillating surge of seawater are derived, and the dynamic model of the WEC is developed. A method for hardware emulation of the WEC is proposed by controlling the torque of an electric motor. The reference torque of the motor is derived by solving the mechanical dynamics of the WEC system in a real-time computing device considering a typical sea wave input. The emulated WEC dynamics is validated through variable loading on a generator coupled with the emulator. Experimental results support the existence of an optimal power point of the derived WEC model.

Equivalent Circuit Model of Eddy Current Device

A new analytical model of axial-flux eddy current device is proposed in this paper, which is based on the equivalent circuit model. In order to simplify analysis, linearization at the mean radius is assumed in the 3-D model of eddy current device. In the equivalent circuit model, copper plate can be seen as a sum of coils in different volume elements. The equivalent circuit of coil is characterized by induced voltage, resistance, and inductance, which are calculated with the electromotive force, reaction flux, and linkage current in the copper plate frame of reference. To obtain these field solutions, the 3-D analytical computation method is employed to solve the Maxwell equations in Cartesian coordinate. The flux linkage equation, voltage equation, and torque equation are set up to depict the reaction field produced by eddy current and the function between the torque and slip speed in steady-state condition. With the equivalent resistance and inductance, the expression of torque becomes much simpler, and the inverse of which can also be obtained. Then, magnetic flux density, torque, and slip speed calculated by the proposed analytical model are compared with the 3-D analytical model and 3-D finite-element method.

One-dimensional reduction of viscous jets. I. Theory.

We build a general formalism to describe thin viscous jets as one-dimensional objects with an internal structure. We present in full generality the steps needed to describe the viscous jets around their central line, and we argue that the Taylor expansion of all fields around that line is conveniently expressed in terms of symmetric trace-free tensors living in the two dimensions of the fiber sections. We recover the standard results of axisymmetric jets and we report the first and second corrections to the lowest order description, also allowing for a rotational component around the axis of symmetry. When applied to generally curved fibers, the lowest order description corresponds to a viscous string model whose sections are circular. However, when including the first corrections, we find that curved jets generically develop elliptic sections. Several subtle effects imply that the first corrections cannot be described by a rod model since it amounts to selectively discard some corrections. However, in a fast rotating frame, we find that the dominant effects induced by inertial and Coriolis forces should be correctly described by rod models. For completeness, we also recover the constitutive relations for forces and torques in rod models and exhibit a missing term in the lowest order expression of viscous torque. Given that our method is based on tensors, the complexity of all computations has been beaten down by using an appropriate tensor algebra package such as xAct, allowing us to obtain a one-dimensional description of curved viscous jets with all the first order corrections consistently included. Finally, we find a description for straight fibers with elliptic sections as a special case of these results, and recover that ellipticity is dynamically damped by surface tension. An application to toroidal viscous fibers is presented in the companion paper [Pitrou, Phys. Rev. E 97, 043116 (2018)10.1103/PhysRevE.97.043116].

ОЦІНКА ВПЛИВУ КІЛЬКОСТІ ЛОПАТЕЙ НА ЕНЕРГЕТИЧНІ ПОКАЗНИКИ ВІТРОАГРЕГАТУ З ВЕРТИКАЛЬНОЮ ВІССЮ ОБЕРТУ

Within the framework of the classical impulse theory, the influence of the number of wind turbine blades on the general energy parameters of a wind turbine with the vertical-axis of rotation was investigated. The integral approach allowed using a two-disk impulse model to determine the main specific characteristics of the system. The power factor was calculated on the basis of the found value of the torque coefficient on the shaft, which, in turn, was determined by numerical integration of the expression for the total torque developed by the wind turbine. The NACA 0020 classic profile was used to calculate the test problem. The aerodynamic coefficients of this profile were determined by processing an array of experimental data obtained by studying its characteristics within a full range of attack angles in aerodynamic laboratories of different countries. The analysis of the aerodynamic coefficients was carried out at a fixed Reynolds number for the chosen profile. Based on the numerical algorithm, a software module has been developed that allows to vary the basic geometric and dynamic parameters of the wind turbine. When developing the software product, a single-disk model was used, wich this formulation of the problem, gives satisfactory results. Carried out computer simulation showed that when the number of blades is reducies, the maximum value of the power factor shifts in the direction of reducing the number of speed. The effective range of operation of the model wind turbine corresponding to the selected number of blades is determined. The developed software module can be used in the design of vertical-axis wind turbines of different power and purpose.

Reduction of torque ripple in a wound‐rotor brushless doubly‐fed machine by using the tooth notching

The torque ripple is a main source of the noise and vibration which has a considerable effect on the performance of the machine. A design technique, tooth notching, which was extensively used in permanent magnet machines, has been innovatively applied to a wound-rotor brushless doubly-fed machine (BDFM) to reduce the torque ripple. First of all, the winding structure, the winding space harmonics and magnetic fields of the stator and the rotor were studied. Then, general analytical expressions of the electromagnetic torque (EMT) for the BDFM were deduced. Finally, prediction of the results was verified by several models which were calculated by the finite-element analysis method, meanwhile, the influences of different tooth-notching structures and the notch depth on the EMT were investigated. It is shown that the torque ripple can be reduced by the suggested design with small increment of the magnetic field saturation and the currents of the control winding and the rotor winding.

Residents' journal review

Residents' journal review

Accurate Prediction and Analysis of Electromagnetic Fields and Forces in Flux-Focusing Eddy Current Coupling With Double Slotted Conductor Rotors

Permanent magnet eddy current couplings are promising devices for torque and speed transmission without any mechanical contact. In this paper, flux-focusing permanent magnet eddy current couplings with double slotted conductor rotors are proposed and investigated. Given the drawback of the accurate 3-D finite element method, the purpose of this paper lies to establish an accurate and fast analytical model to evaluate the electromagnetic field and torque of such devices with non-homogeneous boundary conditions. Thus, based on the 2-D sub-domain method, the magnetic vector potential in each sub-domain is formulated and solved by the separation of variables method. Taking into account the eddy current effects and slotting effects, the closed-form expressions of magnetic field, induced current, electromagnetic force, and torque for such devices are obtained. Finally, the 3-D finite element method is employed to validate the analytical results.

Investigation of the effects of the equivalent circuit parameters on induction motor torque using three different equivalent circuit models

In this study, the most vital characteristic properties of induction motor, motor starting, maximum and nominal torque are analyzed for what are affected. For the analysis of torque, L type, T type and IEEE 112 equivalent circuit model is employed. Torque change is investigated with the help of codes developed in MATLAB to be used in electrical machines course. First, the slip-moment characteristic curve of the induction motor is divided into three working zones and it was determined which equivalent circuit model gave the best results in these study zones. Later, such parameters as stator and rotor resistance, stator and rotor reactance, magnetization reactance, core resistance and slip are researched for how torque values are affected from. The obtained values for each of the three equivalent circuit models are given and compared with experimental results. 50 HP squirrel cage induction motor parameters are used in analysis. In the analysis, the most influential parameters on the starting torque are found as rotor resistance and stator and rotor reactance. Change of other parameters’ impact ratio depending upon right proportion and inverse proportion is observed. When nominal torque variations are investigated, again rotor resistance is the most influential parameter and by selecting proper factor effecting rotor resistance during design, the result of acquiring desired rotor resistance is obtained. When the maximum torque variations are examined, it appears that the stator and rotor reactance values are effective. Starting, maximum and nominal torque expressions change with square of voltage alters the effect on them a lot. Therefore, triangle or star connection importance arises during machine design.

Optical torque on small chiral particles in generic optical fields

We derive an analytical expression of the optical torque (OT) on chiral particles in generic monochromatic optical fields within the dipole approximation. Besides the extinction terms owing to the interaction between the dipoles excited on the particle and the incident field, our expression includes also some long missing terms that are understood as recoil due to the radiation of the dipoles excited on the particle. The recoil terms are shown to have a significant contribution to the OT in many situations. Inspired by our expression, we further proved that the net OT vanishes for a lossless isotropic chiral spherical particle of any size illuminated by arbitrary monochromatic optical fields. Finally, we trace the origin of OT on a small chiral sphere immersed in a zeroth-order vector Bessel beam, taking advantage of our analytical expression. It is found that the azimuthal OT perpendicular to the beam’s propagation direction comes from the transfer of the spin angular momentum of the incident field to the particle, while the longitudinal OT along the illumination direction originates from the particle chirality, which generates longitudinal angular momentum on the optical beam and thus makes the particle subject to a longitudinal OT by recoil. Thus the longitudinal OT tends to rotate the chiral particle with opposite helicities in opposite directions, while the transverse OT shows little dependence on the handedness of particle chirality. Our results may help in understanding OT as an extra handle for particle manipulations in optical tweezers.