Harmonics in the Squirrel Cage Induction Motor,Analytic Calculation Part Ⅱ:Synchronous Parasitic Torques,Radial Magnetic Forces

The magnetic field generated in the air gap of the cage asynchronous machine and the harmonics of the magnetomotive forces creating that magnetic field,as well as the synchronous parasitic torques,radial magnetic forces have been discussed in great detail in the literature,but always separately,for a long time.However,systematization of the phenomenon still awaits.Therefore,it is worth summarizing the completeness of the phenomena in a single study–with a new approach at the same time-in order to reveal the relationships between them.The role of rotor slot number is emphasized much more than before.New formulas derived for both synchronous torques and radial magnetic forces are used for further investigation.It will be shown that both phenomena in subject must be treated together.Formulas will be provided to take into account attenuation.Design guide will be provided to avoid dangerous rotor slot numbers.It will be shown that the generation of synchronous torques and radial magnetic forces do not depend–in this new approach-on the slot combination,but on the rotor slot number itself.

Tooth Position and Deformation of Flexspline Assembled with Cam in Harmonic Drive Based on Force Analysis

Deformation of the flexspline is the basis of analyzing tooth trajectory and designing tooth profile.Considering the tooth influence on the position of equivalent neutral layer,a piecewise method for calculating the deformation of flexspline assembled with a cam wave generator is presented in this paper.Firstly,a mechanic model of a ring of uniform thickness in contact with a rigid cam is established.The displacements of the ring inside and outside an unknown wrapping angle are determined by the geometric constraints of the cam profile and the equilibrium rela-tionship,respectively.Meanwhile,the wrapping angle is solved according to the boundary conditions.The assembly forces are derived to investigate the circumferential elongation and strain.Then,considering the tooth effects on the neutral layer of flexspline,the tooth is positioned on the equivalent neutral layer,which is the non-elongation layer within one gear pitch but offset from the geometric mid-layer.The equivalent neutral layer is positioned by the empirical formula of the offset ratio,which is summarized by the orthogonal simulation on finite element models of racks.Finally,finite element models of a ring-shaped and a cup-shaped flexspline assembled with elliptical cam are established to verify the effectiveness and accuracy of the piecewise method.The results show that,compared with the geometric method,the tooth positioning deviation calculated by the piecewise method can be reduced by about 70%with a more accurate deformation description from the geometric condition and mechanic condition inside and outside the wrapping angle.

Theory of higher harmonics imaging in tapping-mode atomic force microscopy

The periodic impact force induced by tip-sample contact in a tapping mode atomic force microscope （AFM） gives rise to the non-harmonic response of a micro-cantilever. These non-harmonic signals contain the full characteristics of tip-sample interaction. A complete theoretical model describing the dynamical behaviour of tip-sample system was developed in this paper. An analytic formula was introduced to describe the relationship between time-varying tip-sample impact force and tip motion. The theoretical analysis and numerical results both show that the timevarying tip-sample impact force can be reconstructed by recording tip motion. This allows for the reconstruction of the characteristics of the tip-sample force, like contact time and maximum contact force. It can also explain the ability of AFM higher harmonics imaging in mapping stiffness and surface energy variations.

Ab Initio Calculations on Nitramide and Its Methyl Derivatives( Ⅱ )——The Harmonic Force Fields and Vibrational Spectra of Nitramide and Its Isotopic Derivatives

The harmonic force field and the vibrational spectrum of nitramide were calculated by using the ab initio gradient program TEXAS at the Hartree-Fock level with a 4-21G basis set. The directly computed theoretical harmonic force field was scaled by using empirical scale factors which are transferred from other molecules and provided an a priori prediction of fundamental frequencies and intensities. The average deviations between predicted vibrational frequencies of nitramide and experimental IR spectrum in an argon matrix are 63 cm-1 for symmetric vibrations and 41 cm-1 for antisymmetric modes. A new set of scale factors was optimized in this paper. These scale factors reduced the average deviations to 2. 3 cm-1 for symmetric modes and 0. 8 cm-1 for antisymmetric ones. The vibrational spectra of three isotopic derivatives of nitramide were predicted by using the force field resulted from the optimized set of scale factors, which are in good agreement with their experimental data in an argon matrix.

Propagator for a Time-Dependent Damped Harmonic Oscillator with a Force Quadratic in Velocity

The propagator for a time-dependent damped harmonic oscillator with a force quadratic in velocity is obtained by making a specific coordinate transformation and by using the method of time-dependent invariant.

Quantization of the 1-D Forced Harmonic Oscillator in the Space (<i>x</i>, <i>v</i>)

The quantization of the forced harmonic oscillator is studied with the quantum variable (x, v∧), with the commutation relation , and using a Schrödinger’s like equation on these variable, and associating a linear operator to a constant of motion K (x, v, t) of the classical system, The comparison with the quantization in the space (x, p) is done with the usual Schrödinger’s equation for the Hamiltonian H(x, p, t), and with the commutation relation . It is found that for the non-resonant case, both forms of quantization bring about the same result. However, for the resonant case, both forms of quantization are different, and the probability for the system to be in the exited state for the (x, v∧) quantization has fewer oscillations than the (x, p∧) quantization, the average energy of the system is higher in (x, p∧) quantization than on the (x, v∧) quantization, and the Boltzmann-Shannon entropy on the (x, p∧) quantization is higher than on the (x, v∧) quantization.

Second harmonic magnetoacoustic responses of magnetic nanoparticles in magnetoacoustic tomography with magnetic induction

Due to the unique magnetic, mechanical and thermal properties, magnetic nanoparticles(MNPs) have comprehensive applications as the contrast and therapeutic agents in biomedical imaging and magnetic hyperthermia. The linear and nonlinear magnetoacoustic responses determined by the magnetic properties of MNPs have attracted more and more attention in biomedical engineering. By considering the relaxation time of MNPs, we derive the formulae of second harmonic magnetoacoustic responses(2H-MARs) for a cylindrical MNP solution model based on the mechanical oscillations of MNPs in magnetoacoustic tomography with magnetic induction(MAT-MI). It is proved that only the second harmonic magnetoacoustic oscillations can be generated by MNPs under an alternating magnetic excitation. The acoustic pressure of the 2H-MAR is proportional to the square of the magnetic field intensity and exhibits a linear increase with the concentration of MNPs. Numerical simulations of the 2H-MAR are confirmed by the experimental measurements for various magnetic field intensities and solution concentrations using a laser vibrometer. The favorable results demonstrate the feasibility of the harmonic measurements without the fundamental interference of the electromagnetic excitation, and suggest a new harmonic imaging strategy of MAT-MI for MNPs with enhanced spatial resolution and improved signal-to-noise ratio in biomedical applications.

Analysis of Magnetic Field and Torque for All-Harmonic-Torque Motor with Surface-Mounted Permanent Magnets

With the development of the advanced industrial products and technologies,the requirements for permanent magnet synchronous motors(PMSM)with high torque density are increasing.This paper proposed a new type of PMSM,named All-Harmonic-Torque PMSM(AHT-PMSM),which could use all harmonics of the magneto motive force(MMF)generated by permanent magnets and armature currents to enhance the electromagnetic torque.The stator windings structure,drive converter configurations and control model of the AHT-PMSM are illustrated firstly.And then the harmonic characteristics of the MMF generated by permanent magnets and armature currents are analyzed.It is found that the MMFs of permanent magnets and armature currents include the same order harmonics and each order harmonic is orthonormal for each other.Finally the calculation process of the average electromagnetic torque for AHT-PMSM based on harmonic MMFs is deduced.It is demonstrated that the theoretical average electromagnetic torque of AHT-PMSM is improved by 23%comparing to that of the normal sinusoidal PMSM when they are with the same structure sizes and armature MMFs.A 24-slot/4-pole AHT-PMSM and sinusoidal PMSM prototypes with the same sizes are modeled and manufactured,the comparison conclusion is validated by the finite element analyses(FEA)and experimental results.

Forced response of quadratic nonlinear oscillator: comparison of various approaches

The primary resonances of a quadratic nonlinear system under weak and strong external excitations are investigated with the emphasis on the comparison of dif- ferent analytical approximate approaches. The forced vibration of snap-through mecha- nism is treated as a quadratic nonlinear oscillator. The Lindstedt-Poincar method, the multiple-scale method, the averaging method, and the harmonic balance method are used to determine the amplitude-frequency response relationships of the steady-state responses. It is demonstrated that the zeroth-order harmonic components should be accounted in the application of the harmonic balance method. The analytical approximations are com- pared with the numerical integrations in terms of the frequency response curves and the phase portraits. Supported by the numerical results, the harmonic balance method pre- dicts that the quadratic nonlinearity bends the frequency response curves to the left. If the excitation amplitude is a second-order small quantity of the bookkeeping parameter, the steady-state responses predicted by the second-order approximation of the Lindstedt- Poincar method and the multiple-scale method agree qualitatively with the numerical results. It is demonstrated that the quadratic nonlinear system implies softening type nonlinearity for any quadratic nonlinear coefficients.

A Multi-harmonic Method for Studying Effects of Mistuning on Resonant Features of Bladed Disks with Dry Friction Damping

An efficient multi-harmonic method is proposed for studying the effects of mistuning on resonant features of bladed disks with blade-to-blade dry friction damping. This method is able to predict accurately the forced response of bladed disks in frequency domain, which is validated by numerical integration method in time domain. The resonant features of both tuned and mistuned systems are investigated by using this method under various system coupling strengths, viscous dampings, and dry friction darnpings, etc. The results demonstrate that the proposed multi-harmonic method is very efficient for studying the mistuning effects on the resonant response of bladed disks with blade-to-blade dry friction damping, especially considering the combined effects of various system parameters.

A Fully Differential Interface Circuit of Closed-loop Accelerometer with Force Feedback Linearization

In this paper,a fifth-order fully differential interface circuit( IC) is presented to improve the noise performance for micromechanical sigma-delta( Σ-Δ) accelerometer. A lead compensator is adopted to ensure the stability of the closed-loop high-order system. A low noise capacitance detection circuit is described with a correlated-double-sampling( CDS) technique to decrease 1 /f noise and offset of the operational amplifier. This paper also proposes a self-test technique for the interface circuit to test the harmonic distortion. An electrostatic force feedback linearization circuit is presented to reduce the harmonic distortion resulting in larger dynamic range( DR). The layout of the IC is implemented in a standard 0. 6 μm CMOS technology and operates at a sampling frequency of 250 kHz. The interface consumes 20 mW from a 5 V supply. The post-simulation results indicate that the noise floor of the digital accelerometer is about- 140 dBV /Hz1 /2at low frequency. The sensitivity is 2. 5 V /g and the nonlinearity is 0. 11%. The self-test function is achieved with 98. 2 dB thirdorder harmonic distortion detection based on the electrostatic force feedback linearization.

SOUND RADIATION FROM PLATES ON ELASTIC FOUNDATION UNDER ACTION OF MOVING LINE FORCES

An analysis is made of the problem of sound radiation from infinite one-dimensional plateson elastic foundation, when the plates are subjected to the action of harmonic line forces movingat subsonic speeds (M 【 1). The expressions of nondimensional sound power are formulated andthe asymptotic forms of sound power in the low frequency regions are derived. The radiatedsound power is shown as a function of the stiffness of elastic foundation, in terms of stiffness fac-torψ, the moving speed of line force, in terms of Math number M, and the frequency, in termsof wavenumber ratio γ . The effects of the parameter ψ in conjunction with the parameters Mand γ on the radiated sound power level and the phenomenon of coincidence radiation are alsoinvestigated in detail.

Forced Resonance of a Slightly-Curved Hydraulic Pipe Fixed at Two Ends

The ideally straight hydraulic pipe is inexistent in reality. The initial curve caused by the manufacturing or the creep deformation during the service life will change the dynamic character of the system. The current work discusses the effect of the initial curve on the hydraulic pipe fixed at two ends for the first time. Based on the governing equation obtained via the generalized Hamilton’s principle,the potential energy changing with the height of the initial curve is discussed. The initial curve makes the potential energy curve asymmetric,but the system is always monostable. The initial curve also has very important influence on natural frequencies. It hardens the stiffness of the first natural mode at first and then has no effect on this mode after a critical value. On the contrast,the second natural frequency is constant before the critical value but increases while the height of the initial curve exceeds the critical value. On account of the initial value,the quadratic nonlinearity appears in the system. Forced resonance is very different from that of the ideally straight pipe under the same condition. Although the 2∶1 internal resonance is established by adjusting the height of the initial curve and the fluid speed,the typical double-jumping phenomenon does not occur under the initial curve given in the current work. This is very different from the straight pipe in the supercritical region. The work here claims that the initial curve of the hydraulic pipe should be taken into consideration. Besides,more arduous work is needed to reveal the dynamic characters of it.

Improvement of Harmonic Balance Using Jacobian Elliptic Functions

We propose a method for finding approximate analytic solutions to autonomous single degree-of-freedom nonlinear oscillator equations. It consists of the harmonic balance with linearization in which Jacobian elliptic functions are used instead of circular trigonometric functions. We show that a simple change of independent variable followed by a careful choice of the form of anharmonic solution enable to obtain highly accurate approximate solutions. In particular our examples show that the proposed method is as easy to use as existing harmonic balance based methods and yet provides substantially greater accuracy.

Multi-harmonic forced vibration and resonance of simple beams to moving vehicles

This study modeled the moving-vehicle-induced forcing excitation on a single-span prismatic bridge as a multiple frequency-multiplication harmonic load on the modal coordinates of a linear elastic simple Euler–Bernoulli beam,and investigated the forced modal oscillation and resonance behavior of this type of dynamic system.The forced modal responses consist of multiple frequency-multiplication steady-state harmonics and one damped mono-frequency complementary harmonic.The analysis revealed that a moving load induces high-harmonic forced resonance amplification when the moving speed is low.To verify the occurrence of high-harmonic forced resonance,numerical tests were conducted on single-span simple beams based on structural modeling using the finite element method(FEM)and a moving sprung-mass oscillator vehicle model.The forced resonance amplification characteristics of the fundamental mode for beam response estimation are presented with consideration to different end restraint conditions.The results reveal that the high-harmonic forced resonance may be significant for the investigated beams subjected to vehicle loads moving at specific low speeds.For the investigated single-span simple beams,the moving vehicle carriage heaving oscillation modulates the beam modal frequency,but does not induce notable variation of the modal oscillation harmonic structure for the cases that vehicle of small mass moves in low speed.

机械设备用感应电机电磁力动态特性计算与研究

机械设备用感应电机的动态性能是不可忽略的设计要求。为抑制电机动态电磁振动和噪声水平,展开了对电机电磁力动态特性分析及相应削弱措施的研究。首先利用经典气隙谐波磁场理论,确定磁场中的谐波磁势和谐波磁导来源,由此再通过张量法计算电机径向电磁力,并对比主要谐波分量的幅值、极对数和频率特征。然后采用有限元仿真和傅里叶分解法,确定电磁力时空行波的基本特征,推断主要力波的谐波磁场产生来源。结果表明谐波径向力绝对幅值的变化很难影响其占基波的相对比值。最后建立磁性槽楔理想模型对比仿真,谐波电磁力的削弱程度与槽楔磁导率正相关,样机振动测试试验间接验证了磁性槽楔的优越性,为电机动态特性研究及优化设计提供理论依据。

变频供电对异步电机电磁噪声的影响

针对某三相异步电机变频供电时,电机噪声明显增大且出现刺耳高频声的情况,利用数值仿真软件建立了电机磁场、振动和噪声模型,计算和分析了变频供电对电机定子电流、径向电磁力、电机振动和噪声的影响。研究发现,变频器供电时,电机定子电流在基波之外增加了基波的谐波分量和载波与谐波相互作用的频率分量,载波引起的电流分量增加了电磁力波的高阶分量,在研究频率范围内(个别频率除外),相比于正弦供电,电机振动速度增大至1.08~131.4倍,声压级增大了2.6~42.6dB。

大展弦比板弯扭耦合受迫振动分析

对于工程广泛存在的大展弦比结构,首次研究了大展弦比板弯扭耦合受迫振动响应.考虑弦向相对弯曲刚度远大于展向弯曲刚度,将弦向截面等效为刚体,考虑其绕展向轴线的扭转,应用Hamilton原理分别计算大展弦比板的势能与动能,建立两端简支的大展弦比板弯扭耦合受迫振动的动力学控制方程.将动力学控制方程进行Galerkin截断后,通过谐波平衡法和微分求积法/微分求积单元法,计算得到了大展弦比模型弯扭耦合受迫振动稳态响应的解析解及数值解,同时验证了解的截断收敛性及谐波收敛性.最后研究了外激励幅值对结构受迫振动响应的影响.结果将为工程中广泛存在的大展弦比结构设计提供指导.

轻微弯曲输流管道的非线性强迫振动特性

为了掌握轻微弯曲输流管道在外激励下的非线性振动特性,基于哈密顿原理建立了轻微弯曲输流管道的非线性振动方程,并使用伽辽金截断法将振动方程离散为非线性常微分方程组。利用增量谐波平衡法求解系统的非线性动力学响应,并使用Floquet理论研究系统响应的稳定性和分岔行为。研究结果表明,轻微弯曲输流管道在一些参数下同时具有软弹簧特性和硬弹簧特性。分析系统参数对响应的影响表明,随着管道弯曲程度增加,系统的响应特性由硬弹簧特性转变为软弹簧特性。可见,管道的初始弯曲是影响输流管道系统振动特性的重要因素,因此在输流管道的设计中必须考虑管道弯曲构型的影响。

复杂电网环境下并网逆变器强迫振荡机理分析与抑制

随着现代工业的迅速发展,非线性电力负荷不断增加,电网电压中出现了大量谐波和间谐波,电网环境日益复杂,这对并网逆变器的安全稳定运行提出了新的挑战。文章详细分析了复杂电网环境下由间谐波电压诱发并网逆变器产生振荡的机理,并提出了相应的振荡抑制措施。文中介绍了电网电压中间谐波的特点及其对并网逆变器输出功率的影响,发现间谐波电压会导致逆变器输出有功功率中存在持续性的周期性波动。通过一个保留主导特征值的逆变器降阶模型,从强迫振荡的角度揭示了周期性的功率波动诱发并网逆变器振荡的机理与特点。在此基础上发现强迫振荡的幅值和主导特征值的阻尼强相关,并提出了直流电压控制环时间尺度的有源阻尼来抑制强迫振荡。最后通过仿真验证了文中振荡机理分析的正确性和振荡抑制策略的有效性。