Equations of Electrical Machines with a Rotating Permanent Magnet Playing the Role of the Stator and Their Nonlocal Analysis

A complete mathematical model is developed for the motion of a current loop powered from a constant voltage source and placed in the field of a permanent magnet rotating with a constant angular velocity. Local analysis of this model shows that it is unstable in the absence of external load, which contradicts the practice of motor operation. Therefore, the motor rotor model considered is incorrect although it is frequently used. The detected contradiction is eliminated by introducing an additional loop, which is orthogonal to the initial one and has the same parameters but is shortcircuited. The complete mathematical model of such a system is unstable in the absence of external load. For the case of an induction motor, the conditions of dichotomy, global asymptotic stability, and instability are formulated.     

控制力矩陀螺框架伺服系统的超低速测速方法

在超低转速下,有限的转速测量分辨率是影响控制力矩陀螺框架伺服系统控制性能的一个重要因素.在分析转速分辨率对超低速控制性能影响的基础上,提出了一种基于多周期后向差分的转速计算方法,可提高测速分辨率并保证测速带宽.针对后向差分带来的相位延迟会限制测速分辨率进一步提高的问题,在选取合适的差分周期基础上,采用Kalman预估器对框架转速进行预估,进一步提高了框架转速的测速分辨率及测速带宽.通过仿真表明,所提出的测速方法将转速分辨率提高了两个数量级,解决了框架伺服系统在超低转速下由于有限的转速测量分辨率造成的爬行现象.     

A novel framework to design and compare limit cycle minimizing controllers: demonstration with integer and fractional-order controllers

In this paper, a constrained optimization problem is formulated to tune the limit cycle minimizing controllers meeting additional loop-shaping performances such as phase margin and gain crossover frequency. A graphical approach is proposed so as to determine the superior controller in terms of better limit-cycle suppression. The framework is illustrated with a suitable case of elementary servo plant which has separable static backlash nonlinearity in its model. For this plant, integer-order controllers and their fractional counterparts (PI and \( PI ^\alpha , [ PI ]^\alpha \) ; PID and \( PI ^\alpha D^\beta \) ) are designed and compared. Interestingly, it is found that the fractional controllers produce better limit-cycle responses than their integer counterparts while both meeting the rest of the specifications. Correspondingly, the better sustained oscillations in the plant output response are obtained with fractional controllers. Such a ‘fractional superiority’ is further verified with the closed-loop nonlinear simulation.     

The development of acoustic generators and their application as a boundary layer transition control device

An experimental investigation of a controllable artificial boundary layer transition by means of electro-acoustic generators was carried out in flat-plate boundary layers. The acoustic generators were flush mounted with the model surface in order to minimize local surface roughnesses which may cause flow instabilities in the laminar boundary layer. The dependence of the input power, pulse ratio, and input frequency of the acoustic generators on the transition threshold values of the input power were determined with surface hot films. In addition, the functional application of the acoustic generators for a controllable artificial boundary layer transition was examined qualitatively by flow visualizations applying the liquid crystal technique.List of symbols A fluctuating component of the hot film anemometer output voltage - time mean hot film anemometer output voltage - ₀ time mean hot film anemometer output voltage at zero velocity - B spectral component of any measured quantity (the used dB-scale is referred to 1 Volt) - time mean hot wire anemometer output voltage - ₀ time mean hot wire anemometer output voltage at zero velocity - f frequency - I _av average input current of the acoustic generator - P mean input power of the acoustic generator - p pressure - Re Reynolds number, Re=U x t/ - t time - t _i period of pulse signal - t _p pulse width of input power - t _s time after switching off heating lamp - U freestream velocity - blowing or sucking velocity produced by the acoustic generator - x longitudinal coordinate from the leading edge (Fig. 2) - x _t distance from the flat plate to the transition location - y coordinate normal to the wall (Fig. 2) - z spanwise coordinate (Fig. 2) - angle of incidence - pulse ratio t _p /t _I - kinematic viscosity - density - ₀ wall shear stress     

Subharmonic Response of a Quasi-Isochronous Vibroimpact System to a Randomly Disordered Periodic Excitation

A quasi-isochronous vibroimpact system is considered, i.e. a linear system with a rigid one-sided barrier, which is slightly offset from the system's static equilibrium position. The system is excited by a sinusoidal force with disorder, or random phase modulation. The mean excitation frequency corresponds to a simple or subharmonic resonance, i.e. the value of its ratio to the natural frequency of the system without a barrier is close to some even integer. Influence of white-noise fluctuations of the instantaneous excitation frequency around its mean on the response is studied in this paper. The analysis is based on a special Zhuravlev transformation, which reduces the system to one without impacts, or velocity jumps, thereby permitting the application of asymptotic averaging over the period for slowly varying inphase and quadrature responses. The averaged stochastic equations are solved exactly by the method of moments for the mean square response amplitude for the case of zero offset. A perturbation-based moment closure scheme is proposed for the case of nonzero offset and small random variations of amplitude. Therefore, the analytical results may be expected to be adequate for small values of excitation/system bandwidth ratio or for small intensities of the excitation frequency variations. However, at very large values of the parameter the results are approaching those predicted by a stochastic averaging method. Moreover, Monte-Carlo simulation has shown the moment closure results to be sufficiently accurate in general for any arbitrary bandwidth ratio. The basic conclusion, both of analytical and numerical simulation studies, is a sort of smearing of the amplitude frequency response curves owing to disorder, or random phase modulation: peak amplitudes may be strongly reduced, whereas somewhat increased response may be expected at large detunings, where response amplitudes to perfectly periodic excitation are relatively small.     

On the optimal form of a signal in Fourier Transform Mechanical Spectroscopy

The analysis of the Fourier Transform Mechanical Spectroscopy (FTMS) method in application to measuring viscoelastic properties of a material in a linear viscoelastic domain shows that sensitivity of the method at higher harmonics strongly depends on the form of the input signal. Then the problem of the choice of the optimal signal is discussed. It is shown that the function f(t)=(sint)/t provides the best form of the input signal basing on the requirement to hold equal amplitudes of all higher harmonics. The comparison of data obtained by the FTMS method and viscoelastic properties measured in harmonic oscillations demonstrates that both methods give adequate results.The application of the FTMS method with the input signal of the optimal form for measuring linear viscoelastic properties of a material saves time of an experiment (up to 3–4 times) and might be specially interesting for analysis of unstable (rheokinetic) materials, in particular, curing oligomers, because the time evolution of different relaxation modes can proceed in different manner.     

Reduction of gas breakdown voltage with pulsed ionizing radiation

An algorithm is described for computer calculation of the dynamic breakdown voltage of a gas gap affected by a spatially uniform pulse of ionizing radiation. The algorithm is based on numerical integration of a system of nonlinear equations with integral boundary conditions. The program is used to calculate the breakdown voltage of an air gap affected by a bell-shaped ionizing pulse. It is shown that the relative reduction in breakdown voltage can amount to tens of percent for a radiation exposure dose rate P₀ 10⁸ R/sec.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 6, pp. 52–60, November–December, 1973.     

Deconvolution as a technique to improve measurement-system data integrity

Measurement is defined as the determination of a system input based on a knowledge of the system output and a characterization of the sytem. The frequency-response function of a measurement system can be defined as the rati of the Fourier transform of the system output to the Fourier transform of the system input which causes that output. This paper deals with the application of time-domain deconvoltuuion techniques to reduce signal distortion attributable to liminations in the measurement-system frequency-response function. The generality of time-domain deconvolution is increased by extending its application to ban-pass, band-reject and low-pass systems in addition to high-pass system. A procedure is described to verity the adequacy of the system characterization used in time-doman deconvolutuion, and application examples are provided.     

Investigation of nonlinear characteristics of the motor-gear transmission system by trajectory-based stability preserving dimension reduction methodology

Gear-motor system is a typically nonlinear system because of many nonlinear factors, such as time-varying meshing stiffness, backlash, and the nonlinear relationship between the electric motor torque and speed. At present, the nonlinear analytical methods can only be used for simplified gear dynamic model. Though the numerical methods can be used for the complicated dynamic model, the quantitative analysis of stability is difficult and rarely conducted. Therefore, a kind of trajectory-based stability preserving dimension reduction (TSPDR) methodology is proposed to investigate nonlinear dynamic characteristics of the gear-motor system. In the TSPDR methodology herein, the complementary cluster center of inertia-relative motion (CCCOI-RM) transformation is chosen and the stability margins are specially defined for distinguishing the stable motion modes of the motor-gear system, to make the TSPDR methodology used in the nonlinear analysis of the gear-motor system. Furthermore, the critical values are obtained for alteration of different motion modes and the nonlinear characteristics of each motion modes are analyzed. At last, combined with modal analysis, the relationship between the stability and resonance of the gear-motor system is revealed.     

Crack detection in a rotating shaft using artificial neural networks and PSD characterisation

The diagnosis of cracks in rotating shafts using non-destructive techniques provides a route for avoiding catastrophic failure of these common components. This study measured the dynamic response of a full-scale rotating shaft with three different crack depths. A novel non-destructive system is developed and described. The system uses vertical vibration of the system measured over time and characterises its behaviour using elements of the power spectral density (PSD) gained from a fast Fourier transform of the time-history. The PSDs were used as an input into an artificial neural network (ANN) to detect the presence of cracks using changes in the spectral content of the vibration of the system. A novel method for reducing the amount of data input into the ANN is described. The Peak Position Component Method (PPCM) reduces data transfer by using statistical characterisation of the position of the peaks in the PSD. The peak positions represent a small fraction of the information contained in the total frequency range. The number of the PSD peaks used as input to the neural net is a small fraction of the total frequency range. The ANN was a supervised feed-forward network with Levenberg-Marquardt back-propagation algorithm acting on the PPCM results. The frequency spectrum for the three different crack lengths examined show clear shifts in the peak positions of the PSD and the results clearly demonstrate the feasibility of using the new system to detect cracks in-service.     

Theory of plane flows of a readily conducting plasma in a pipe

Simplified equations are obtained describing slowly changing plane flows of a readily conducting quasineutral inviscid plasma in a pipe. The practically interesting case of flow in a channel with solid metal ideally conducting walls (electrodes) is analyzed. When the gas pressure is large by comparison with the magnetic pressure ( 1), the field and current distribution is determined by gas dynamic factors, and the solid electrodes perturb the longitudinal electric field in a skin of the flow, symmetrically on the two sides of the flow, leading to attenuation of the longitudinal electric field near the input to the pipe; we also consider problems in the motion of the plasma under ideal and under poor conductivity. In the converse limiting case ( 1), it is shown that as the motion of the plasma in the pipe accelerates near the anode, there is observed an increase in the intensity of the electric field which is sharply inhomogeneous in the transverse direction. The possibility of the plasma breaking away from the anode (the limiting regime) is indicated, this being accompanied by a divergence between the electron velocity and the velocity of the ions. A criterion is obtained for the breakaway of the plasma, and its possible connection with the occurrence of pre-anode explosions is noted. It is shown that for 1, Joule losses are small by comparison with the power in the charge and the magnitude of the losses is independent of the conductivity of the plasma.Translated from Zhurnal Prikladnoi Mekhaniki i Teknicheskoi Fiziki, No. 4, pp. 9–19, July–August, 1970.     

The micropolar fluid model for blood flow through a tapered artery with a stenosis

A micropolar model for axisymmetric blood flow through an axially nonsymmetreic but radially symmetric mild stenosis tapered artery is presented. To estimate the effect of the stenosis shape, a suitable geometry has been considered such that the axial shape of the stenosis can be changed easily just by varying a parameter （referred to as the shape parameter）. The model is also used to study the effect of the taper angle Ф. Flow parameters such as the velocity, the resistance to flow （the resistance impedance）, the wall shear stress distribution in the stenotic region and its magnitude at the maximum height of the stenosis （stenosis throat） have been computed for different values of the shape parameter n, the taper angle Ф, the coupling number N and the micropolar parameter m. It is shown that the resistance to flow decreases with increasing the shape parameter n and the micropolar parameter m while it increases with increasing the coupling number N. So, the magnitude of the resistance impedance is higher for a micropolar fluid than that for a Newtonian fluid model. Finally, the velocity profile, the wall shear stress distribution in the stenotic region and its magnitude at the maximum height of the stenosis are discussed for different values of the parameters involved on the problem.     

自由端受磁力吸引悬臂梁的非线性振动

研究了含分式函数的非线性磁力系统的受迫振动。磁铁吸引力横向作用在悬臂梁自由端处。根据含有非线性边界的连续体模型,给出了非平凡静平衡位形。以稳定位形作坐标变换后,计算了相应的固有频率,并求得微幅受迫振动稳态响应的近似解析解。研究了不同磁铁间距与频响曲线的关系,结果表明磁力方向和大小对它们均有较大影响。数值结果与解析结果吻合得很好。     

Investigation of a model of the Soyuz spacecraft washed by the control jets of the Apollo spacecraft

During mission design for the joint flight of the Soyuz and Apollo spacecraft in the ÉPAS program, a preliminary analysis was made of the thermal and force interactions of the motor jets of the Apollo control system on the Soyuz spacecraft. It was shown that the flow over the service, command, and docking modules of Apollo formed shock waves which intersected the communication antennas, the solar cells, and other structural elements of Soyuz during the docking. The flight program provided for possible simultaneous operation of four motors of the control system. In that case the jets interact, forming a complex three-dimensional flow. In the regions where shock waves interact with the Soyuz structural elements, the local convective heat fluxes, which are significant in magnitude, increase, since the temperatures and pressures in the Apollo engine combustion chambers are 3000 °K and 7·10⁵ Pa, respectively. The need for reliable operation of all devices of Soyuz located in the jet interaction zone required experimental investigations to be performed to determine the heat flux to the structure and the surface pressures on the spacecraft, with particular attention being paid to modeling of the phenomena. It should be noted that the results of analogous investigations carried out earlier by the USA with reference to the manned lunar flight program could not be used because of the difference of the Soyuz geometry and the newly developed docking module in the ÉPAS mission from the Apollo lunar module geometry.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 124–133, May–June, 1977.     

Hybrid Electromagnetic System for Acceleration of Solids

The electroexplosive and electrothermal mechanisms and the principles of conduction and induction electrodynamics are used simultaneously to convert electromagnetic energy to the kinetic energy of projectiles. This approach is implemented on the basis of the well–known configuration of a coaxial pinch accelerator. It is established that there is an active lengths of the barrel on which the system ensures launching with nearly constant acceleration. For a barrel length of 340 mm and a barrel diameter of 17 mm, bodies with a mass of 1—12 g are accelerated to velocities of 3.4—1.45 km/sec with an energy conversion efficiency of 25—29% at a capacitive storage voltage of 1.75 kV and a discharge current of up to 150 kA. Bodies with a mass of 40—80 g (barrel diameter 25 mm are accelerated to velocities of 1.3—1.0 km/sec with an efficiency of 28—20% at a voltage of 3.5 kV and a current of up to 220 kA.     

A Wollaston prism interferometer implemented with a digitizer

Objective of this work was to implement a Wollaston prism interferometer with a digitizer so as to perform the evaluation procedure of interferograms automatically by means of a microcomputer. The adopted opto-electronic sensing device is a linear array of 1,024 bar-shaped (15 m × 26 m) silicon photodiodes with center-to-center spacing 25 m. A stepping motor can move the array board in order to investigate the whole interferometric image. Scanning time is about 10 ms/line. Application of the system to measurements of concentration profiles in some mass diffusion processes of a binary gas mixture proves the ability of the digitizer to accurately measure gas densities. The performance and the potentiality of the sensor are analyzed and discussed.     

Nonlinear dynamic buckling of a viscoelastic model under impact loading

A simple nonlinear buckling analysis is applied to a one-degree-of-freedom arch under impact loading in which viscous damping may also be included. Such a loading consists of a falling body striking centrally the joint mass of the arch in such a way that a completely plastic impact can be postulated. When there is no damping the exact dynamic buckling load for such a kind of loading-associated with an unbounded motion can be established by using a static criterion (approach). More specifically, it was shown that the dynamic buckling load corresponds to that unstable equilibrium state where the total potential energy of the system is zero. Furthermore, it was proved that the second variation of the total potential energy at the foregoing unstable equilibrium state is negative definite. This implies that the curve loading versus displacement resulting by the vanishing of the total potential energy has always a maximum on the afore mentioned unstable state. It was also found that the system may become sensitive to initial conditions. If damping is included the foregoing static criterion yields lower bound buckling estimates. These findings were verified by employing a highly efficient approximate technique as well as the numerical scheme of Runge-Kutta for solving any nonlinear initial-value problem.     

Electrical charging of bodies as a consequence of charged-particle extraction by a hydrodynamic flow

We investigate the problem of electrical charging of bodies as a result of charged-particle extraction by a hydrodynamic flow. The analysis is performed in view of the application to the problem of motion electrification of aircraft caused by a stream of charged particles into the surrounding space. We formulate the appropriate system of nonstationary electrohydrodynamic equations. It is shown that in many applications the charging of electrically insulated bodies consists of two successive intermediate processes. The first process is the formation of charge Q on the body in time T₁ The second process consists of a change of the body potential (with a constant charge Q) as a consequence of the stream of charged particles into the outside space noted above. At the end of the second process (with duration T₂) the body potential is at . We also investigate the problem of charging a spherical source of neutral and charged particles. Using the analytical solution we find the quantities Q and and the characteristic times T₁ and T₂. It is shown that the time T₂ can exceed T₁ by several orders of magnitude. We formulate the problems of nonstationary electric fields during the extraction of several types of particles.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 94–103, September–October, 1977.     

A novel simulation model for ring type ultrasonic motor

In this paper, a novel mathematical model for a traveling wave ultrasonic motor, developed by Alenia Spazio, now Alcatel Alenia Space Italia S.p.A. (Roma, Italy), within an Italian Space Agency (ASI) program, is described. The dynamic equations for the stator and the rotors of the ultrasonic motor are assembled into a differential system, whose equations are coupled by terms which represent interface generalized forces. Neglecting transient conditions, the complete mathematic model of the system is solved and an iterative process is developed, in order to obtain the motor’s running curves for different operation parameters, geometric dimensions and physical features of the system. The algorithm is implemented in Matlab environment and a graphical user interface is constructed for user-friendly managing. The model, also validated by means of experimental tests, can be used for parametric analyses with respect to different parameters, in order to optimize motor’s configuration. It represents a simple but powerful aid to determine final motor design that can satisfy specifications or to predict motor’s behavior under different working conditions.