Diagnosis and performance analysis of threephase permanent magnet synchronous motors with static, dynamic and mixed eccentricity

Albeit permanent magnet synchronous motors (PMSMs) under static and dynamic eccentricity have been studied in few papers, so far mixed eccentricity has not been investigated. In this study, a novel index is introduced for dynamic and mixed eccentricity fault diagnosis in PMSM. This index is the amplitude of sideband components with a particular frequency pattern that is extracted from spectrum analysis of the motor torque. The index provides precise detection of the eccentricity occurrence, recognition of its type and determination of its degree. To evaluate the ability of the proposed index for the eccentricity diagnosis and estimation of its severity, first the correlation between indices, static and dynamic eccentricity degrees are calculated. The type of eccentricity is determined using k-nearest neighbour (KNN) classifier. At the next step, a three-layer artificial neural network is employed to estimate the eccentricity degree of torque profiles based on their type of eccentricity. After all, a white Gaussian noise is added to the simulated torque and robustness of the proposed index is analysed with respect to the noise variance. Meanwhile, the spectrum analysis of the stator current in faulty PMSM under static, dynamic and mixed eccentricities is studied and the influence of these eccentricities on ohmic, hysteresis and eddy current losses of PMSM are presented. In this examination, the time-domain elemental flux density waveforms and various time-domain waveforms of motor winding currents are computed using time stepping finite element method (TSFEM) for core loss and ohmic loss calculations punctually. The accuracy of obtained simulation results is verified using experimental results.     

Finite element analysis of non-linear static and dynamic response

The paper presents the theoretical and computational procedures which have been applied in the design of a general purpose computer code for static and dynamic response analysis of non-linear structures. A general formulation of the incremental equations of motion for structures undergoing large displacement finite strain deformation is first presented. These equations are based on the Lagrangian frame of reference, in which constitutive models of a variety of types may be introduced. The incremental equations are linearized for computational purposes, and the linearized equations are discretized using isoparametric finite element formulation. Computational techniques, including step-by-step and iterative procedures, for the solution of non-linear equations are discussed, and an acceleration scheme for improving convergence in constant stiffness iteration is reviewed. The equations of motion are integrated using Newmark's generalized operator, and an algorithm with optional iteration is described. A solution strategy defined in terms of a number of solution parameters is implemented in the computer program so that several solution schemes can be obtained by assigning appropriate values to the parameters. The results of analysis of a few non-linear structures are briefly discussed.     

Thermal analysis of induction motors using 3D finite element method

Abstract

To design a reliable and economical induction motor, it is necessary to be able to predict accurately the temperature distribution within the motor. In this paper, a 3D thermal model of an induction motor is presented. Except for providing a more accurate representation of the problem, the proposed model can also reduce computer memory and time. The finite element method (FEM) is used to analyze the three dimensional (3D) heat flow equation which describes the thermal model. Galerkin's procedure is used to derive the element equations and first order tetrahedral elements are used to discretize the field region. Galerkin's time‐stepping scheme is employed to treat time differential terms. Values of surface heat transfer coefficients are obtained from the empirical formula and heat losses are revised by the factory test. Application of the proposed method to the analysis of a 9,000 HP induction motor yields temperature distribution very close to the experimental data.     

动静轴结构旋翼轴载荷分离仿真分析与试验研究

动静轴结构旋翼轴是一种具有抗弹击能力的新型直升机旋翼轴构型,拟对自主设计的鼓形花键动静轴结构旋翼轴和柔性联轴节动静轴结构旋翼轴进行载荷分离特性研究。利用有限元软件对这2种动静轴结构旋翼轴的载荷分离系数进行仿真分析,并开展多通道加载试验加以验证。结果表明采用7 mm壁厚静轴时动静轴结构旋翼轴的载荷分离系数相比采用4 mm壁厚静轴时明显提高;柔性联轴节动静轴结构旋翼轴的综合载荷分离系数为77.37%,略高于鼓形花键动静轴结构旋翼轴的76.33%。研究结果可为直升机动静轴结构旋翼轴的设计提供指导。     

Finite element analysis of rotating flow in a skewed shrouded rotor geometry

The effect of slight shroud skewness on rotating flow in an enclosed rotor geometry is modelled as a perturbation about axisymmetric flow. Solutions are obtained by the finite element method. Mixed and penalty finite element formulation are employed.     

液体黏性软启动装置输出轴的有限元分析

针对液体黏性软启动装置的工作特点,要求输出轴传动力矩和输出转速变化范围较大,轴变形应该保持在较小范围内,输出轴的性能对液体黏性软启动装置正常工作有重要影响,需要对输出轴的结构作进一步分析.通过建立液体黏性软启动装置输出轴的Pro/E三维模型,采用有限元软件ANSYS Workbench对启动装置的输出轴进行有限元分析,确定输出轴的变形和应力状况,计算输出轴的模态和疲劳损伤.仿真结果表明：输出轴损伤最大部位位于较粗轴端键槽一侧.提出了一些改进措施,为液体黏性软启动装置输出轴的结构设计和疲劳寿命估算提供参考依据.     

Dynamic analysis of mixed eccentricity signatures at various operating points and scrutiny of related indices for induction motors

Load variation along with static and dynamic eccentricities degrees is one of the major factors affecting the dynamic behaviours of eccentricity signatures which is utilised for precise mixed eccentricity fault diagnosis. Without taking the effect of load variation into account properly and just by considering the change in the static and dynamic eccentricity degrees, inaccurate fault detection is acquired. This is of noticeable effects that load variations have on side-band components that are used as fault detection indices. These indices are extracted from the current spectrum of healthy and faulty motor. In this paper, all these factors are dealt in a unified framework by analysing various combinations both theoretically and experimentally. An incisive approach is developed to recognise mixed eccentricity and determine the static and dynamic eccentricities degrees individually at different load levels literally. In order to evaluate the impact of load-dependent indices on eccentricity detection and fault-severity estimation, a systematic relation between each other and eccentricity degree is proposed. Correlation coefficient and mutual information are applied to assess abilities of the obtained indices for eccentricity detection in terms of their relation to static and dynamic eccentricities, their degrees and dependency on the load of motor. The classification results indicate that the elicited indices estimate the eccentricity type and degree exactly. Since, the accuracy of calculated stator current, computed from simulated motor, has considerable effects on precise fault diagnosis, time-stepping finite element method (TSFEM) is employed to model the healthy and faulty induction motor.     

A comprehensive approach to the solution of direct-coupledmultislice model of skewed rotor induction motors using time-steppingeddy-current finite element method

Normally a complicated three-dimensional (3-D) approach is needed to study the field pattern of induction machines with skewed rotor bars. In this paper, a time-stepping two-dimensional (2-D) eddy-current finite element method, based on multislice technique, is described to study the steady-state operation and the starting process of skewed rotor induction machines. The fields of the multislices are being solved en bloc simultaneously, and thus, the effects of the eddy current and saturation can be taken into account directly. New forms of the governing equations for the multislice model are derived, which allow the meshes of multislices to be taken as one 2-D mesh so that the algorithm is very similar to that of general 2-D problems. Special techniques required for the mesh generation in the multislice model and the salient structures of the software are also described. The results obtained by using the program being developed have very good correlation with test data     

Finite element analysis of leakage magnetic flux from an induction heating system

The finite element method is applied to calculate the leakage magnetic field from an induction heating system consisting of an exciting coil and a conducting circular plate. The basic technique of the method is to draw a mathematical sphere to enclose the system. The total energy functional is assumed to be given by the interior and exterior functionals. The former is represented by using the usual axisymmetric triangular elements. On the other hand, the latter is given in a simple form by expanding exterior fields in terms of the solutions of a differential equation governing exterior empty spaces. The interior and exterior potentials are then matched on the spherical interface. After the validity of the method is verified by comparing results with analytic solutions for a single coil, the leakage magnetic flux from an induction heating system is computed at large distances.     

Finite element method for non-linear forced vibrations of circular plates

Geometric non-linearities for large amplitude free and forced vibrations of circular plates are investigated. In-plane displacement and in-plane inertia are included in the formulation. The finite element method is used. An harmonic force matrix for non-linear forced vibration analysis is introduced and derived. Various out-of-plane and in-plane boundary conditions are considered. The relations of amplitude and frequency ratio for different boundary conditions and various load conditions are presented.     

Finite element model of efficient zig-zag theory for static analysis of hybrid piezoelectric beams

Finite element model is presented for the analysis of hybrid piezoelectric beams under static electromechanical load, using the one-dimensional (1D) coupled zig-zag theory developed recently by the authors. Two noded elements are used with cubic Hermite interpolation for deflection and electric potentials at the sub-layers and with linear interpolation for axial displacement and shear rotation. The expressions for the variationally consistent stiffness matrix and load vector are derived and evaluated in closed form using exact integration. The formulation is validated by comparison with the analytical solution for simply-supported beam. The finite element model is free of shear locking. The present zig-zag finite element results for cantilever beams are compared with the 2D finite element results using ABAQUS to establish the accuracy of the zig-zag theory for these boundary conditions.S. Kapuria is grateful to Department of Science and Technology, Government of India, for providing financial assistance for this work.     

Finite element implementation of non-unified visco-plasticity model considering static recovery

Mechanics of Time-Dependent Materials - In order to examine relaxation behaviors of materials, static recovery term is always conducted in the backstress components for kinematic hardening in...     

Finite element analysis of plates with curved edges

The application of the high precision triangular plate bending element to problems with curved boundaries is considered. Appropriate edge conditions for nodal points on these boundaries are derived. The error inherent in representing the shape of a curved boundary by a series of straight segments is found to be the limiting factor on accuracy, while the effect of approximations in the actual boundary conditions is minor. To overcome the first type of error, the high precision element is modified to include one curved edge. Substantial improvements in accuracy are obtained, as demonstrated in example calculations for circular and elliptical plates.     

Finite element analysis of engines

The basic principles are outlined by means of a simple example, some applications given and the way is explained in which finite element analysis is carried out.     

考虑杨氏模量随轴向温度分布变化的转子有限元建模方法研究

根据转子材料杨氏模量随温度的二次多项式变化函数,推导了考虑温度分布的单元刚度矩阵,给出了考虑转子轴向温度分布的有限元模型,分析了在轴向温度均匀分布、线性分布和二次多项式分布情况下转子临界转速的变化趋势。结果表明,模型可以体现转子轴向温度分布对刚度矩阵的影响,能够有效提高高温下转子临界转速的计算精度。     

A static discrete element method with discontinuous deformation analysis

For discrete element methods (DEMs), integrating the equation of motion based on Newton's second law is an integral part of the computation. Accelerations and velocities are involved even for modeling static mechanics problems. As a consequence, the accuracy can be ruined and numerous calculation steps are required to converge. In this study, we propose a static DEM based on discontinuous deformation analysis (DDA). The force of inertia is removed to develop a set of static equilibrium equations for distinct blocks. It inherits the advantages of DDA in dealing with distinct block system such as jointed rock structures. Furthermore, the critical numerical artifact in DDA, ie, artificial springs between contact blocks, is avoided. Accurate numerical solution can be achieved in mere one calculation step. Last but not the least, since the method is formulated in the framework of mathematical programming, the implementation can be easily conducted with standard and readily available solvers. Its accuracy and efficiency are verified against a series of benchmarks found in the literature.     

Substructure variational analysis of the vibrations of coupled fluid–structure systems. Finite element results

The finite element method is used for the computation of the variational modes of the system composed of an elastic tank partially filled with a compressible liquied. We propose, on the one hand, a direct approcach based on a three field mixed variational formulation, and, on the other hand, a variational modal interaction scheme allowing the use of the acoustic eigenmodes of the liquid in a rigid motionless enclosure and the hydroelastic modes of the enclosure. Numerical results show the advantage of the second procedure.     

裂纹转子弯扭耦合振动非线性特性分析

以非线性涡动影响下的水平Jeffcott裂纹转子为研究对象,分别建立了刚性支承的纯弯曲振动、弯扭耦合振动和轴承支承的弯扭耦合振动三种运动微分方程,针对三种模型,分析了裂纹转子系统响应的分叉与混沌特性。数值计算结果表明： 较大时,三种模型下的弯振分叉图均呈现出复杂的非线性特性,尤其在 附近,各种周期、拟周期和混沌响应交替出现,阵发性特点非常明显,系统由拟周期路径通向混沌。模型1、2的弯振分叉图特性基本相似,模型3则具有更为复杂的非线性特性。模型2、3的扭振分叉图与各自的弯振分叉图极为相似,且非线性特性也基本相同。分析结果有助于更充分了解裂纹转子的动力学特性。     

Finite element analysis of sinusoidal small-amplitude vibrations in deformed viscoelastic solids. Part I: Theoretical development

A general method is presented for the isothermal mechanical analysis of incompressible material solids in which a small-amplitude time harmonic oscillation is superposed on a static finite deformation field. Material behaviour is assumed to be of the ‘fading memory’ type describable by the finite linear viscoelasticity theory of Coleman and Noll.⁴ Existing finite element codes, that treat finite elasticity material behaviour, can be extended with minor modifications to treat the subject problem. A specialized form of the finite linear viscoelasticity constitutive equations proposed by Morman⁸ has been implemented in the MARC nonlinear finite element program for predicting the response of statically deformed elastomeric components to small amplitude vibrations. Numerical results obtained with MARC for the static force-deflection behaviour and dynamic (complex) stiffness for a viscoelastic cylinder subject to combined axial and twisting pre-loads, are in excellent agreement with corresponding analytical results.