Expression For Torque Research Articles

Analytical Modeling and Calculation of Electromagnetic Torque of Interior Permanent Magnet Synchronous Motor Considering Ripple Characteristics

<div class="section abstract"><div class="htmlview paragraph">Based on the classical <i>dq</i> theory, this paper proposes a new electromagnetic torque analytical model (AM) for interior permanent magnet synchronous motor (IPMSM) considering ripple characteristics, including permanent magnet (PM) torque ripple and reluctance torque ripple. The analytical expression of PM torque considering the effect of PM flux linkage harmonics is first derived according to <i>dq</i> transformation and energy method. Then, an improved inductance calculation method considering the non-sinusoidal magnetic field distribution and cross-coupling effect is proposed, and the reluctance torque model is established by taking the influence of inductance harmonics into consideration. Subsequently, the total electromagnetic torque can be obtained by the superposition of PM torque and reluctance torque. Finally, the proposed AM was verified by finite-element method (FEM). The results show that the proposed AM is accurate enough to predict the instantaneous electromagnetic torque waveforms and the average electromagnetic torque. In addition, according to the proposed AM, the sources and order features of torque ripples can be directly determined, and the intrinsic relationship between key electromagnetic parameters and torque harmonics can be revealed.</div></div>

Effects of inertia on the slow rotation of a slip spherical particle

The steady rotational motion of a spherical particle with frictionally slip surface about a diameter in a quiescent unbounded fluid is studied analytically for a small but finite Reynolds number Re. The Navier–Stokes equation governing the axisymmetric fluid flow around the particle is solved by using a regular perturbation method. The expansion expression for the retarding torque exerted by the fluid on the particle good to O(Re3) is obtained as a function of the scaled slip coefficient of the particle in closed form. This perturbation analysis shows that the perturbed fluid velocity field is of O(Re), the same as that for the translation of the particle, but the first correction to the hydrodynamic torque occurs at O(Re2), much weaker than that to the hydrodynamic drag force acting on a translating particle which is still of O(Re). The hydrodynamic torque is found to be a monotonic increasing function of the Reynolds number and a monotonic decreasing function of the scaled slip coefficient, similar to the effect of fluid inertia on the hydrodynamic force on a slip particle undergoing translation. The inertial effect on the hydrodynamic torque, which can be a sensitive function of the slip coefficient and vanishes as the particle surface is fully slip, is generally negligible for the case of Re<3 but significant as Re is greater than about 10.

Torsional static and vibration analysis of functionally graded nanotube with bi-Helmholtz kernel based stress-driven nonlocal integral model

A torsional static and free vibration analysis of the functionally graded nanotube (FGNT) composed of two materials varying continuously according to the power-law along the radial direction is performed using the bi-Helmholtz kernel based stress-driven nonlocal integral model. The differential governing equation and boundary conditions are deduced on the basis of Hamilton’s principle, and the constitutive relationship is expressed as an integral equation with the bi-Helmholtz kernel. Several nominal variables are introduced to simplify the differential governing equation, integral constitutive equation, and boundary conditions. Rather than transforming the constitutive equation from integral to differential forms, the Laplace transformation is used directly to solve the integro-differential equations. The explicit expression for nominal torsional rotation and torque contains four unknown constants, which can be determined with the help of two boundary conditions and two extra constraints from the integral constitutive relation. A few benchmarked examples are solved to illustrate the nonlocal influence on the static torsion of a clamped-clamped (CC) FGNT under torsional constraints and a clamped-free (CF) FGNT under concentrated and uniformly distributed torques as well as the torsional free vibration of an FGNT under different boundary conditions.

Analytical Model for the Design of Axial Flux Induction Motors with Maximum Torque Density

This article proposes a mathematical model of an axial flux induction motor (AFIM) with one stator and one rotor. The model is based on the expression for the electromagnetic torque, which presents a function of two independent variables: the axial length of the stator core and the flux density in the air gap. This allows calculating the main dimensions of the motor with the highest possible torque density. Thus, developed model is suitable for designing the motor of specified volume with maximum torque, and solving the inverse problem of minimizing the machine volume with the specified torque. The detailed output of the model and the results of the calculations for the low-power engine powered by voltage of 7.35 V (RMS) are given. The results are validated using FEM in ANSYS software: with the outer motor diameter of 0.11 m, the flux density in it reaches 1.2 T.

Бесконтактные двигатели постоянного тока с дискретным управлением и модуляцией тока по положению ротора

The article considers contactless DC motors with discrete control of the current in the three- and two-section armature winding using the rotor position feedback signal by means of a converter containing six and four power transistors, respectively. The motors are additionally equipped with a pulse width modulator (PWM) and a rectifier of the rotor position sensor signals. In the PWM, the periodic line-to-line voltage is compared with the rectified sensor signals to produce periodic rectangular pulses with the duration depending on the rotor position, which close the power transistors. Since the motor torque without PWM and the rectified sensor signals vary in a sine wave manner with turning the rotor (i.e., in the same way), a lower motor torque pulsation is obtained. The sensor and PWM designs and operation are described, and the requirements for their output voltages are formulated. Expressions for the contactless DC motor electromagnetic torque and its limit values are obtained. It is established that the electromagnetic torque pulsation levels in the contactless DC motors with three- and two-section armature windings do not exceed 1 and 1.5%, respectively, which is significantly lower than the pulsation level in the well-known contactless motors (4%).

Estimation of gas turbine shaft torque and fuel flow of a CODLAG propulsion system using genetic programming algorithm

In this paper, the publicly available dataset of condition based maintenance of combined diesel-electric and gas (CODLAG) propulsion system for ships has been utilized to obtain symbolic expressions which could estimate gas turbine shaft torque and fuel flow using genetic programming (GP) algorithm. The entire dataset consists of 11934 samples that was divided into training and testing portions of dataset in an 80:20 ratio. The training dataset used to train the GP algorithm to obtain symbolic expressions for gas turbine shaft torque and fuel flow estimation consisted of 9548 samples. The best symbolic expressions obtained for gas turbine shaft torque and fuel flow estimation were obtained based on their R2 score generated as a result of the application of the testing portion of the dataset on the aforementioned symbolic expressions. The testing portion of the dataset consisted of 2386 samples. The three best symbolic expressions obtained for gas turbine shaft torque estimation generated R2 scores of 0.999201, 0.999296, and 0.999374, respectively. The three best symbolic expressions obtained for fuel flow estimation generated R2 scores of 0.995495, 0.996465, and 0.996487, respectively.

Acoustic radiation torque on an off-axis elliptical cylinder in Gauss beams

As one of the nonlinear effects of acoustic waves, the time-averaged acoustic radiation torque expression is derived from the transfer of angular momentum from the incident beam to the object. In recent years, the acoustic radiation torque has received substantial attention since it is the underlying principle of well-controlled particle rotations and spins, which provides a new degree of freedom in particle manipulation and acousto-fluidic applications in addition to the translational displacement caused by the acoustic radiation force. Cylindrical particles, such as fibers, carbon nanotubes and other surface acoustic wave devices, are commonly encountered in various applications. The acoustic scattering coefficients for an elliptical cylinder arbitrarily located at the field of Gauss beam in two-dimensions are computed based on the partial-wave series expansion method and the Graf’s additional theorem for cylindrical functions to obtain the off-axis beam shape coefficients. It is worth mentioning that both the rigid and non-rigid cylinders are considered in this work, which requires different boundary conditions at the cylinder surface. Moreover, the closed-form expression of the acoustic radiation torque in this case is derived. On this basis, several numerical simulations are performed with particular emphasis on the off-axis distance, the incident angle and the beam waist. The simulated results show that both the positive and negative acoustic radiation torque can exist under certain conditions, which means that 1) the elliptical cylinder can be rotated in either the clockwise or the counterclockwise direction, 2) rigid elliptical cylinders are more likely to experience a strong acoustic radiation torque than non-rigid elliptical cylinders at low frequencies, 3) the incident wave field with a specific frequency can excite a different resonance scattering mode for a non-rigid elliptical cylinder, therefore the acoustic radiation torque peak is more related to the beam frequency than to the elliptical cylinder’s location in the field, and 4) increasing the beam width can enlarge the scattering cross section area, and thus enhancing the acoustic radiation torque on the elliptical cylinder. The results in this study are expected to provide a theoretical guide for the controllable rotation of a particle and the viscosity inversion of fluid by using the acoustic radiation torque. The exact formalism presented here by using the multipole expansion method, which is valid for any frequency range, can be used to validate other approaches by using purely numerical methods.

Casimir-Polder force and torque for anisotropic molecules close to conducting planes and their effect on CO2

We derive the Casimir-Polder force and Casimir torque expressions for an anisotropic molecule close to a conducting plane with a tensorial conductivity. We apply our general expressions to the case of a carbon dioxide CO$_2$ molecule close to a plane with pure Hall conductivity and to graphene. We show that the equilibrium position of this linear molecule is with its main axis perpendicular to the surface. We hence conjecture a possible way to exploit the Casimir torque to mechanically improve the performance of CO$_2$ separation membranes useful for an efficient atmospheric CO$_2$ reduction.

Analysis and Control of an In-Pipe Wheeled Robot With Spiral Moving Capability

Abstract This article presents analysis and control of a wheeled robot that can move spirally inside the pipeline. The wheeled robot considered is composed of two mechanical bodies, a pair of differential-drive wheels, a lifting motor, and a steering wheel. The mechatronic design allows the robot to easily press against the inner wall and spiral along pipelines of arbitrary inclination angles. Kinematic analysis shows how the lead angle of the differential-drive wheels and the steering angle should be coordinated so as to achieve stable spiraling. The steady-state force analysis further gives an analytic expression for the threshold torque needed for supporting the robot at different inclination angles. To ensure successful operation of the robot, four control systems that respectively regulate the spiraling speed, the lifting torque, the steering angle, and the lead angle are devised. Particularly for the lead angle control, it is theoretically proved that the feedback measurement can be obtained by performing algebraic operation on signals from a multi-axis gyro. A prototype robot is constructed and is controlled based on the analysis results. Experiments are conducted to verify the robot’s performance on moving spirally in pipelines of different inclination angles.

Torque Improvement in Dual M-Phase Permanent-Magnet Machines by Phase Shift for Electric Ship Applications

This paper proposes a design technique for electric ship traction machines to achieve high torque density and low torque ripple by adopting dual <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</i> -phase windings with an appropriate phase shift. Firstly, the general relationship between the slot number and the phase number for dual <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</i> -phase windings is investigated. Secondly, the uniform analytical expressions of torque with different phase shifts are derived. Also, the optimal phase shift angle is summarized from the perspective of improving torque performance. Then, the 48-slot and 22-pole permanent-magnet machines for electric ship with different windings configurations are designed. The finite-element method is used to calculate their electromagnetic performances, such as back electromotive force, torque capability, stator magnetic motive force and radial force. Finally, some experiments on the prototype machine for electric ship are carried out for validation.

Analytical Prediction and Minimization of Deadtime-Related Harmonics in Permanent Magnet Synchronous Motor

The current, torque, and speed harmonics caused by deadtime effect in voltage source inverter (VSI)-fed permanent magnet synchronous motor (PMSM) usually lead to undesired torque ripple and extra electrical loss, etc. In this article, a mathematical model is proposed to predict the deadtime-related harmonics in VSI-fed field-oriented control PMSM, and a deadtime-related harmonic minimization method is proposed based on proportional-integral (PI) controllers tuning and under the premise of keeping the same control strategy. The expressions of current, torque, and speed harmonics caused by deadtime effects are obtained based on the complex amplitude expression of the voltage error harmonic and the derivation of the closed-loop transfer function from the deadtime-related voltage error to the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d–q</i> axis current. Based on the derived expressions, optimization objective functions are built to search the optimal PI parameters for minimizing deadtime-related harmonics and reducing the torque ripple. The optimization constraint functions can be adjusted for transient performance requirements, so the transient performance can keep good even if the deadtime-related harmonics are minimized with the optimal PI parameters. Both simulation analysis and experimental data verify the correctness of the analytical prediction and the validity of the deadtime-related harmonic minimization method.

Radiation force and torque of light-sheets illuminating a cylindrical particle of arbitrary geometrical cross-section exhibiting circular dichroism

Unlike standard dielectric materials, the interaction of light-sheets of arbitrary wavefronts with a particle exhibiting circular dichroism, such as chiral, topological insulator, liquid crystal, or metamaterials to name a few examples, requires additional fundamental developments from the standpoint of scattering, radiation force and torque theories.The purpose of this work is therefore directed toward developing an exact analytical formalism applicable to a 2D object exhibiting TM ⇄ TE mode conversion and possessing an arbitrary geometrical cross-section. Exact mathematical expressions for the longitudinal and transverse optical radiation force and axial torque components are derived stemming from series expansions for the incident and scattered electromagnetic fields using the mode matching method in cylindrical coordinates. The generalized radiation force and torque expressions depend on the beam-shape coefficients (BSCs) of the incident light-sheet, and the scattering coefficients of the object. Extra new terms describing the generation of the scattered cross-polarized waves induced due to TM ⇄ TE mode conversion contribute to the radiation force and torque series. Numerical illustrative examples for a circular lossy electromagnetic conductor (LEMC) cylinder are provided assuming illumination by various wavefronts, ranging from plane progressive, standing and quasi-standing waves to other non-paraxial Airy light-sheets with linear and circular polarization. In essence, the present theoretical formalism provides a complete analysis in the framework of the generalized Lorenz–Mie theory in 2D for any particle exhibiting circular dichroism in any structured light-sheet. Potential applications are in the design, optimization and the numerical predictions and computation of the optical radiation force and torque for particle transport and rotation in the realm of optical tweezers, particle manipulation and stabilization. Some perspectives are discussed and replies to misleading comments made in the literature on the publication [F.G. Mitri, J Quant Spectro Rad Transf 2020;250:106994] given by Ref. [33] are provided.

Torque Characteristics Analysis of Slotted-Type Eddy-Current Couplings Using a New Magnetic Equivalent Circuit Model

In this article, a new magnetic equivalent circuit (MEC) model was presented to predict torque characteristics and reaction flux in slotted-type eddy-current couplings (SECs). The magnetomotive force and reaction field caused by eddy current in the conductor were innovatively introduced into the model; particularly, the modulations of the magnetic field and eddy current by iron teeth in conductor disk were taken into account by dividing magnetic flux paths in air gap into several branches. The expressions of magnetic flux and torque were obtained by combining Kirchhoff’s law and Ampere’s loop law. The torque was calculated using the method proposed and was compared with those obtained by the 3-D finite element method (FEM) and experiment, respectively. The results indicated that the method proposed is accurate and effective under conditions of low slip speeds and short air gap lengths.

Second-Time Fault-Tolerant Topology and Control Strategy for the Open-Winding PMSM System Based on Shared Bridge Arm

To further improve the fault-tolerant operation capacity of the open-winding permanent magnet synchronize motor system after second-time fault occurring, a novel fault-tolerant topology and a fault-tolerant control strategy for single phase open-circuit is proposed in this article. The fault-tolerant topology proposed in this article can operate stably in case of second-time fault that occurs after one-phase open-circuit fault by the way of sharing a bridge arm. Thus, the fault-tolerant ability of the driving system is further improved. In the terms of control strategy, the amplitude and the phase of the remaining two-phase current are redesigned to keep the system operating steadily according to the conventional expression of motor torque. Moreover, considering that the electromagnetic torque of the system will contain the third harmonic component when the three-phase current is unbalanced, the torque fluctuation will affect the stability of the system. A torque optimization strategy for suppressing the third harmonic component of the torque by injecting corresponding harmonics into the current is proposed. Finally, the experimental results validate the effectiveness of the proposed topology and strategy.

STUDY OF TORQUE NONUNIFORMITY IN DOUBLE-ACTION HYDRAULIC ROTARY VANE MO-TORS

Abstract. Aim. Hydraulic rotary vane motors rely on the principle of torque maintained at a nominal pressure. In this case, the most important parameter of the torque is its nonuniformity. The problem of determining nonuniform torque in hydraulic motors having ten and twelve vanes is investigated with the aim of ensuring the maximum stability of this parameter.Method. Braking torque occurs on the vanes of hydraulic rotary vane motors due to the pressure of the working fluid on the stator; the theoretical expression for torque does not take the braking effect of the vanes into account. Therefore, an expression is compiled for the braking torque of the vanes with a type of stator curve that provides constant acceleration of the vane relative to the rotor.Results. Plots of changes in braking torques were constructed for 10- and 12-vane motors. Ratios of the minimum and maximum braking torques equal to 0.33 and 0.5 for motors with ten and twelve vanes, respectively, were obtained.Conclusion. The torque nonuniformity coefficients for hydraulic motors for the given parameters of d =11,6% and d = 8,8% for motors having ten and twelve vanes, respectively, were obtained. The results of the analysis of the obtained parameters indicate a slight increase in the nonuniformity of torque in a ten-vane motor. In this case, a decrease in the number of vanes leads to an increase in the mechanical efficiency of the hydraulic machine.

Acoustic spin transfer to a subwavelength spheroidal particle.

We demonstrate that the acoustic spin of a first-order Bessel beam can be transferred to a subwavelength (prolate) spheroidal particle at the beam axis in a viscous fluid. The induced radiation torque is proportional to the acoustic spin, which scales with the beam energy density. The analysis of the particle rotational dynamics in a Stokes flow regime reveals that its angular velocity varies linearly with the acoustic spin. Asymptotic expressions of the radiation torque and angular velocity are obtained for a quasispherical and infinitely thin particle. Excellent agreement is found between the theoretical results of radiation torque and finite-element simulations. The induced particle spin is predicted and analyzed using the typical parameter values of the acoustical vortex tweezer and levitation devices. We discuss how the beam energy density and fluid viscosity can be assessed by measuring the induced spin of the particle.

Experimental investigation of drivetrain resistance applied to small wind turbines

Drivetrain resistance of wind turbines is still challenging, since determining static and dynamic frictional torque is rather complex. Hence, the main motivation of this work is to experimentally investigate resisting torques of a drivetrain typically found in small wind turbines. Measurements are carried out using a bench setup comprising torque sensor, rpm encoder, generator and electrical motor. For further evaluation, an approach combining Newton’s second law and blade element theory to assess the turbine behavior is employed, which is able to estimate the minimal wind velocity to start electrical generation, as well as the rated velocity of a small wind turbine. A theoretical expression for the friction torque is also demonstrated. An extension of SKF and Palmgren models are used to verify the friction torque on the bearings, which are often the main contributors to resistance in the turbine drivetrain. Assessments using a small wind turbine with 4 blades and 1.3 m diameter is performed to show the effect of the drivetrain resistance, in which its rotational speed changes according to the friction torque, yielding a more realistic response when the generator is loaded and unloaded.

Parametric analysis of magnetic field-dependent viscosity and advection–diffusion between rotating discs

The constitutive expressions of unsteady Newtonian fluid are employed in the mathematical formulation to model the flow between the circular space of porous and contracting discs. The flow behavior is investigated for magnetic field-dependent (MFD) viscosity and heat/mass transfers under the influence of a variable magnetic field. The equation for conservation of mass, modified Navier–Stokes, Maxwell, advection diffusion and transport equations are coupled as a system of ordinary differential equations. The expressions for torques and magnetohydrodynamic pressure gradient equation are derived. The MFD viscosity [Formula: see text], magnetic Reynolds number [Formula: see text], squeezing Reynolds number [Formula: see text], rotational Reynolds number [Formula: see text], magnetic field components [Formula: see text], [Formula: see text], pressure [Formula: see text] and the torques [Formula: see text], [Formula: see text] which the fluid exerts on discs are discussed through numerical results and graphical aids. It is concluded that magnetic Reynolds number causes an increase in magnetic field distributions and decrease in tangential velocity of flow field, also the fluid temperature is decreasing with increase in magnetic Reynolds number. The azimuthal and axial components of magnetic field have opposite behavior with increase in MFD viscosity.

Study of a magnetorheological brake under compression-shear mode

A magnetorheological (MR) brake under compression-shear mode is designed, simulated and experimentally investigated in this paper. A MR brake under compression-shear mode was first designed considering compression enhanced shear yield stress of MR fluid. Then, the operating principle of the MR brake was illustrated and mathematical torque expressions, operating under compression-shear mode assuming Herschel–Bulkley model, was further established. Moreover, simulation analysis of the designed magnetic circuit was performed as well. An experimental prototype was fabricated and tested to evaluate the transmission performance of MR brake. The results showed that the large torque could be produced at high applied currents, high compressive stress, large compressive strain and small initial gap distances. The rotational speed and compressive speed had little effect on the torque. The characteristic rising time of the torque was greatly affected by the rotational speed, the compressive strain, and compressive speed. However, the current had little effect on the rising time. The time constant would became shorter when both the rotational speed and the compressive speed were faster. Through analyzing the compression of particle chains in MR fluids directly, it was found that the diameter and the length of the particles chains brought a strong influence on the essential property of MR fluids under compression. Thus, the compressive stress or compressive strain and the initial gap distance also played an important role in enhancing the torque. The results also showed that the proposed MR brake could generate a maximum torque of 241 Nm, about 17.9 times the magnitude of braking torque without compression, and achieve a high torque density of 125.6 kN m–2 and a time constant of 58 ms. This study provides a better understanding of MR brake under compression-shear mode and the implications for many high-power applications.

Quantification of attitude effects on orbital dynamics near asteroids

This paper presents an analytical approach for quantifying the effects of spacecraft attitudes on the translational dynamics via the orbit-attitude coupling effect. First, an accurate model of the gravitational field that uses the polyhedron model for the main gravitational term, and the point-mass model for the coupling terms is presented. This allows to capture higher order coupling terms in the force and torque expressions with high resolution, accounting for the orbit-attitude coupling in the rigid body spacecraft dynamics. Next, the achievable set of values for the second order gravitational force due to coupling is analytically obtained for a single point-mass located at the asteroid center of mass. Following this, spacecraft attitudes that produce a coupled second order force in a specific direction are obtained. The equations of motion for a rigid body orbiter are then presented, and numerical propagations of the spacecraft dynamics are performed in close proximity to four different asteroids (216 Kleopatra, 433 Eros, 4769 Castalia, and 101955 Bennu), showing how different spacecraft attitudes impact the orbital dynamics for different scenarios. A numerical generalization is performed for a multiple point-mass case. It is concluded that the coupled force can be effectively controlled via the spacecraft attitude, and that this force can be used to control the orbital motion via attitude actuation on certain scenarios. Guidelines on how to minimize the impact of the orbit-attitude coupling effect are also provided.