Обзор и классификация пространственно-временных векторов дискретных состояний семифазного преобразователя

The subject of the research is the control algorithms for a seven-phase converter that implement space-vector voltage modulation of a seven-phase motor as an alternative to a three-phase engine in modern electric traction. The study used elements of set theory, combinatorics, Fourier series expansion and vector analysis. Checking research results was implemented on a special stand for experimental studies of spatial vector voltage modulation of a seven-phase motor.

Integral Representation and Explicit Formula at Rational Arguments for Apostol–Tangent Polynomials

The Fourier series expansion of Apostol–tangent polynomials is derived using the Cauchy residue theorem and a complex integral over a contour. This Fourier series and the Hurwitz–Lerch zeta function are utilized to obtain the explicit formula at rational arguments of these polynomials. Using the Lipschitz summation formula, an integral representation of Apostol–tangent polynomials is also obtained.

Transient Response of a Hollow Functionally Graded Piezoelectric Cylinder Subjected to Coupled Hygrothermal Loading

In this paper, transient response of a simply supported finite length hollow cylinder made of functionally graded piezoelectric material (FGPM) subjected to coupled hygrothermal loading was investigated. The coupled equations of heat conduction and moisture diffusion as well as motion equations and the electrostatic equation of FGPM were solved employing the Fourier series expansion method through the longitudinal direction, the differential quadrature method (DQM) along the radius and Newmark method for time domain. Finally, the distribution of temperature, humidity, electric potential, stresses and displacements was achieved. The effect of coupled and uncoupled hygrothermal loading, grading index and hygrothermal loading was illustrated in the numerical examples. The results show that using the coupled model is vital for analysis of transient response of the cylinder subjected to hygrothermal loading.

Combined optimization of a linear PM actuator with trapezoidal PMs and coils considering fringing effect for precision engineering

For precision engineering, a linear PM-moving actuator with trapezoidal PMs and trapezoidal coils considering the fringing effect is proposed. To take into account the effect of the finite-long trapezoidal PM array, an improved Fourier series expansion is developed to calculate the fringing-included magnetic field. Then the full-stroke thrust excited by the trapezoidal coils is accurately predicted and validated by the finite element method. Sensitivity of the trapezoidal parameters of PMs and coils is analyzed, and combined optimization is implemented by the genetic algorithm. Through the Pareto optimal solutions of thrust, the relation of the PM-coil parameter combination is described and formulated by curve fitting. Compared with the traditional rectangular PM actuators or other trapezoidal-typed actuators, the proposed actuator with trapezoidal PMs and coils further decreases the thrust ripple and largely increases the thrust magnitude simultaneously, and reaches an utmost-close effective stroke as well.

Cyclostationary Approach to the Analysis of the Power in Electric Circuits under Periodic Excitations

This paper proposes a cyclostationary based approach to power analysis carried out for electric circuits under arbitrary periodic excitation. Instantaneous power is considered to be a particular case of the two-dimensional cross correlation function (CCF) of the voltage across, and current through, an element in the electric circuit. The cyclostationary notation is used for deriving the frequency domain counterpart of CCF—voltage–current cross spectrum correlation function (CSCF). Not only does the latter exhibit the complete representation of voltage–current interaction in the element, but it can be systematically exploited for evaluating all commonly used power measures, including instantaneous power, in the form of Fourier series expansion. Simulation examples, which are given for the parallel resonant circuit excited by the periodic currents expressed as a finite sum of sinusoids and periodic train of pulses with distorted edges, numerically illustrate the components of voltage–current CSCF and the characteristics derived from it. In addition, the generalization of Tellegen’s theorem, suggested in the paper, leads to the immediate formulation of the power conservation law for each CSCF component separately.

Statistics of Sliding on Periodic and Atomically Flat Surfaces

Among the so-called analytical models of friction, the most popular and widely used one, the Prandtl-Tomlinson model in one and two dimensions is considered here to numerically describe the sliding of the tip within an atomic force microscope over a periodic and atomically flat surface. Because in these PT-models, the Newtonian equations of motion for the AFM-tip are Langevin-type coupled stochastic differential equations the resulting friction and reaction forces must be statistically correctly determined and interpreted. For this, it is firstly shown that the friction and reaction forces as averages of the time-resolved ones over the sliding part, are normally (Gaussian) distributed. Then based on this, an efficient numerical scheme is developed and implemented to accurately estimate the means and standard deviations of friction and reaction forces without performing too many repetitions for the same sliding experiments. The used corrugation potential is the simplest one obtained from the Fourier series expansion of the two-dimensional (2D) periodic potential, e.g., for an fcc(111) surface, which permits sliding on both commensurate and incommensurate paths. In this manner, it is proven that the PT-models predict both frictional regimes, namely the structural superlubricity and stick-slip along (in)commensurate sliding paths, if the ratio of mean corrugation and elastic energies is properly set.

Analytical Solutions for the Radial Consolidation of Unsaturated Foundation with Prefabricated Vertical Drain Based on Fourier Series Expansion Theory

This paper presents the analytical solution of the radial consolidation of a prefabricated vertical drain (PVD) foundation under the unsaturated condition. In the proposed modeling, air and water phases in the foundation are thought to dissipate horizontally toward to the drain, and the smear effect, drain resistance and external time-dependent loading are fully considered. The analytical mathematical tools, namely the general integration method, Fourier series expansion method, decoupling method and the constant variation method, are utilized to solve the partial differential equations. Moreover, the current solutions are verified with existing solutions in the literature. Finally, a case study considering the ramp loading and exponential loading is conducted to investigate the consolidation patterns under various loading parameters. The results show that smear effect and drain resistance can significantly hinder the dissipation process of excess pore pressures, and different external loading types will lead to various dissipation characteristics (i.e., peak values).

FAT-based robust adaptive control of cooperative multiple manipulators without velocity measurement

This article addresses the problem of pose and force control in a cooperative system comprised of multiple n-degree-of-freedom (n-DOF) electrically driven robotic arms that move a payload. The proposed controller should be capable of maintaining the position and orientation of the payload in the desired path. In addition, the force exerted by robot end effectors on the object must remain limited. The system has unmodeled dynamics, and measuring the robot joint velocities is impossible. Therefore, a FAT-based observer–controller is designed to estimate the uncertainty and velocities based on universal approximation property of Fourier series expansion. The stability of the system is confirmed based on Lyapunov’s stability theorem. Finally, the proposed adaptive controller–observer is applied on two 3-DOF cooperative robotic arms carrying a payload, and the results are precisely analyzed. The results of the proposed approach are also compared with two state-of-art powerful approximation method.

Effect of unbalanced magnetic pull on the thermal characteristics of traction motor bearing

Purpose The purpose of this paper is to analyze the unbalanced magnetic pull (UMP) of the rotor of traction motor and the influence of the UMP on thermal characteristics of traction motor bearing. Design/methodology/approach The unbalanced magnetic pull on the rotor with different eccentricity was calculated by Fourier series expansion method. A bearing thermal analysis finite element model considering both the vibration of high-speed train caused by track irregularity and the UMP of traction motor rotor was established. The validity of the model is verified by experimental data obtained from a service high-speed train. Findings The results show that thermal failure of bearing subassemblies most likely occurs at contact area between the inner ring and rollers. The UMP of rotor of traction motor has a significant effect on the temperature of the inner ring and roller of the bearing. When the eccentricity is 10%, the temperature can even be increased by about 12°C. Therefore, the UMP of rotor of traction motor must be considered in thermal analysis of traction motor bearing. Originality/value In the thermal analysis of the bearing of the traction motor of high-speed train, the UMP of the rotor of the traction motor is considered for the first time