Diagnosis of the Thermal Bow of a Shaft in a Three Stage Centrifugal Compressor

In practice many turbo-machines driven by motors are started up to perational speed within a very short time,i.e.in less than 20 seconds .For this type of machines the compatibility of thermal deformaiton of the rotor stucture must be taken into account in the machine desing ,or the thermal defromation will be constrained and a huge resultant force can cause the shaft bending and consequently resulting in violent vibrations.In this paper,detection of thermal bow of a shaft in a three stage centrifugal compressor in a petrochemical plant is presented .The diagnostic results show that the thermal bow was induced by the incompatibility of axial thermal deformation of the rotor stucure.A remedial action allowing free axial thermal expansion of the outer parts of the rotor is suggested.     

Analytical Computation of the Full Load Magnetic Losses in the Soft Magnetic Composite Stator of High-Speed Slotless Permanent Magnet Machines

This paper presents an analytical model for predicting the stator full load magnetic losses in high-speed slotless permanent-magnet machines with surface-mounted magnets on the rotor and a stator core made of isotropic and conductive soft magnetic composite material (SMC). The losses are derived from the computation of the two-dimensional magnetic field distribution created by the rotor magnets, the currents in the stator windings and the eddy currents that circulate in the SMC stator core, according to the time and space harmonics. Both eddy currents and hysteresis losses are computed. The model is cross-validated by 2-D FE analysis in terms of magnetic field distribution and eddy currents losses. 3-D FE simulations are also carried out to quantify the end-effect on the stator no-load eddy current losses. The developed model is an efficient machine design tool, used here to quantify the variations of both the eddy currents and hysteresis losses under full load operation when the control angle is modified.      

Finite element analysis of relative shaft vibrations of two-pole induction motors with static rotor eccentricity

The paper shows a computational methodology for calculating the relative shaft vibrations in the sleeve bearings of two-pole induction machines regarding excitation due to an electromagnetic force, which is caused by static rotor eccentricity. For a worst case calculation concerning the height of exciting magnetic force electromagnetic field damping effects and magnetic resistance concerning the homopolar flux are neglected. The calculated magnetic force, acting on the rotor core with double supply frequency in direction of the smallest air gap, is implemented into a finite element rotor dynamic model. With this model the influence of the rotor speed as well as influence of the direction of the magnetic force on the relative shaft displacements can be analyzed. Therefore the paper shows a computational methodology to check, whether the rotor-bearing design is sensitive for electromagnetic excitations due to static rotor eccentricity and prepares therefore the possibility to introduce improvements during the design phase of the induction motor.     

A novel approach for temperature estimation in squirrel-cageinduction motor without sensors

In this paper, the authors present a coupled thermal and electromechanical model for squirrel-cage induction motor simulation and analyses. The effect of iron saturation, rotor parameter variation due to current displacement (skin-effect) and temperature variations of both stator and rotor resistances are taking into account simultaneously. A new device for the temperature measurement in the stationary as well as rotating parts of electric machines is built. The unique construction of the device for continuous rotor temperature monitoring is briefly described. This device is a part of a complete acquisition system, which is used for precise testing and investigating of a coupled thermal and electromechanical phenomena. An original thermal observer based on the direct stator temperature measurement under normal running condition with no additional sensors is proposed     

Analysis of Open-Ended Coaxial Probes by Using a Two-Dimensional Finite-Difference Frequency-Domain Method

A 2-D finite-difference frequency-domain (FDFD) method is presented to analyze open-ended coaxial probe problems. With the axial symmetry of geometry taken into account, the method reduces the original structure into an equivalent 2-D problem. Due to its ability to handle complex geometries, the presented method can tackle many practical situations when the analytical/semianalytical full-wave analysis is unfeasible. Numerical examples involving the infinite-flanged probes and the finite-flanged probes are included. In the examples of the infinite-flanged probes, the accuracy of the 2-D FDFD method and of the 2-D finite-difference time-domain (FDTD) method are checked with the results of the semianalytical full-wave analysis method. It is found that the accuracy of the 2-D FDFD method and of the 2-D FDTD method are the same, as long as their mesh structures are the same. In the examples of the finite-flanged probes, whose analytical/semianalytical full-wave analysis solutions are unfeasible, the results of the 2-D FDFD and 2-D FDTD methods are found to be in very good agreement. All the numerical examples show that the computational efficiency of the 2-D FDFD method is much higher than that of the 2-D FDTD method.     

Influence on the stability of generator rotors due to radial and tangential magnetic pull force

Forces due to nonuniform airgaps in rotating electrical machines have been a research topic for over 100 years. However, most research in the area of rotating electrical machines has been performed on motors. Large forces in hydropower generators can lead to expensive damage and failures. Therefore, it is of interest to calculate the forces that arise in a large synchronous generator with an eccentric rotor and study the influence these forces have on the stability of the generator rotor. A 74 MVA synchronous hydropower generator was simulated with an eccentric rotor, using a time-stepping finite-element technique. The forces were calculated using Coulomb's virtual-work method and simulations were performed for no-load and load cases. The resulting force was found to be reduced significantly when a damper winding was taken into account. An interesting effect of the rotor damper winding was that it reduced the eccentricity force and introduced a force component perpendicular to the direction of eccentricity. The results from the finite-element simulations were used to determine how the forces affect the stability of the generator rotor. Damped natural eigenfrequencies and damping ratio for load and no-load conditions are presented. When applying the forces computed in the time-dependent model, the damped natural eigenfrequencies were found to increase and the stability of the generator rotor was found to be reduced compared with when the forces were computed in a stationary model.     

Space and time harmonics related problems and their mitigation for position and speed sensorless slip-ring induction motor drives applications

There have been renewed interests in slip-ring induction machines due to their increasing use in both grid connected and stand-alone wind power generation schemes. Despite the squirrel cage induction generators’ advantages of being brushless, low-cost, needing less maintenance and having inherent overload protection, the biggest advantage of variable-speed wound rotor induction machines is in its doubled energy capture. Also in high power induction motor drives such as static Kramer drives or static Scherbius drives use of wound rotor induction motors is a must. Thus it becomes necessary to measure the speed of the machine for closed loop control for such high performance drives. Recently, a sensorless position and speed estimation scheme was proposed for wound rotor wind power generator. In this paper, the limitation of the scheme caused by space and time harmonics have been investigated. Simulation results have been presented to explain the mechanism of the space and time harmonics caused distortion of current. Experimental results showing the deterioration of speed detection scheme at light load for a slip-ring induction motor have been presented. Finally, improvements have been applied experimentally to obtain better speed estimation.     

基于声信号三维谱分析的转子复合碰摩故障特征提取

转子在运行过程中的声音包含了大量的转子运行状态信号,变速过程中故障声信号特征的提取及其识别对于旋转机械故障诊断是极其必要的,目前基于声信号三维谱分析的转子故障特征提取还不多,在对转子旋转机械中的一些典型产生的碰摩故障及复合碰摩故障进行了试验模拟,对故障发生过程中的声信号进行采集的基础上,对转子故障声信号的三维谱特性进行了分析。提取和总结出由故障造成的声信号突变和对应的声谱特征。分析结果表明:采用声信号对转子的碰摩故障进行诊断是有效的。声信号三维谱图丰富旋转机械碰摩故障诊断系统知识库中的特征信息,可以用于更准确地诊断转子中的碰摩故障。     

Optimal design of flux observer in induction machines

Abstract

Flux estimation is essential in most advanced control schemes of induction machines like indirect field‐orientation control and feedback linearizing approach. In this paper, optimal control theory and Lyapunov stability analysis are applied to design the full‐order flux observer of induction machines. The observer refers only to measurable quantities which are composed of terminal voltages, currents and rotor speed. The time‐invariant and time‐varying portions of the error dynamics of the observer are minimized separately. The degree of relative stability of the observer can be prescribed at the beginning of the design and is independent of speed variations. In the presence of uncertainty in rotor resistance, a sufficient condition for the design with bounded estimation errors is derived and the resultant residual can be formulated explicitly. Results from computer simulations show that the method exhibits excellent convergent characteristics and robustness to rotor resistance uncertainty.     

Fast Calculation of Field Currents and Reactances for Doubly Fed Generators With Rotor Duct Pieces

Doubly fed generators have been used as adjustable-speed pumped-storage generator motors and wind turbine generators. Accurate determination of field currents and reactances is important for the design of these machines. We propose a calculation method to obtain the field currents and reactances of machines with rotor duct pieces under any steady-state balanced load condition. The method links two-dimensional static finite-element analysis (FEA) with an approximate calculation to consider three-dimensional (3-D) skin effect in the duct pieces. Its advantage is that the computational time is much smaller than 3-D transient FEA when the slip frequency is not zero. The method will contribute to improvement of the design of doubly fed generators with rotor duct pieces. It was applied to a 395 MVA machine, and the calculated field currents agreed well with the measurements. Variation in the reactances due to saturation is also discussed     

Parametric variance consideration in speed control of single-phase flux reversal machine

The new flux reversal machine (FRM) has a simple robust rotor with a permanent magnet installed stator. However, the parameters of the FRM are dependant on the position of the rotor, operating temperature and magnetic saturation of the motor core. To obtain a robust performance in the speed control of the single-phase FRM, a control method that introduces an internal model of the motor is suggested for robustness against parameter variance and disturbance. The suggested control method is verified by both computer simulation and experiments and it is applied for popular AC induction/synchronous machines for their robust performance.     

A 2-D model that accounts for 3-D fringing in MEMS devices

MEMS devices such as comb drives and rotary drives are geometrically simple in that each of the components may be represented as a ‘sweep’ of a 2-D cross-section through a given height. This simplicity leads to simpler CAD requirements, geometric robustness, faster visualization, etc. Further, 3-D electrostatic simulation may be simplified to a 2-D problem over the cross-section if one neglects 3-D fringing. Such 2-D simulations provide a quick feedback to the designer on various parameters such as capacitance and electrostatic forces.However, as is well known, 3-D simulations cannot be avoided if fringing is significant, or when these devices need to be fully optimized. Such 3-D simulations unfortunately involve constructing the full 3-D geometry, volume/surface mesh, etc.In this paper, we demonstrate that one can pose and solve a 2-D problem that accounts for 3-D fringing. The proposed technique does not require the construction of the 3-D CAD model or surface/volume mesh. Instead, the 3-D electrostatics problem is collapsed to 2-D via a novel dimensional reduction method. Once the 2-D problem is solved, the full 3-D field and associated charges/forces can be recovered, as a post-processing step. The simplicity and computational efficiency of the technique lends itself well to parametric study and design optimization.     

小角度空间交错轴变厚齿轮传动的啮合动态特性研究

为揭示小角度空间交错轴变厚齿轮副的时变啮合特性与非线性动态特性,在精确几何建模的基础上,建立了空间小角度交错轴变厚齿轮传动时变啮合模型,获取其时变啮合刚度与时变传动误差;考虑外部载荷与侧隙变化的影响,采用集中参数法建立了齿轮传动非线性动力学模型,对其系统非线性特征进行了仿真。结果表明外部载荷的增加直接导致了齿轮副啮合刚度、传动误差、动态传动误差和动态啮合力的增加,同时啮合刚度的增加使得系统共振频率增加;侧隙的增加使得系统在轻载下出现与单边、双边冲击耦合的突跳现象,在重载下双边冲击区域变大,动态啮合力增加。     

Attenuation of Harmonic Rotor Vibration in a Cage Rotor Induction Machine by a Self-Bearing Force Actuator

In this paper, attenuation of flexural rotor vibration in electrical machines is considered. In order to generate force on the machine rotor, an electromagnetic actuator based on self-bearing machine working principle is examined. A control method for attenuating harmonic rotor vibration components is applied in a 30 kW two-pole cage induction machine. The machine is equipped with a four-pole supplementary winding for generation of lateral force on the rotor. Experimental results for the two-pole induction motor are presented. The main contribution of this paper is to apply a control method, specially designed for compensating harmonic excitations, by using a built-in electromagnetic actuator in an induction machine.      

Three-dimensional resistance calculation in end ring of inductionmotor by finite-element method

Among the components of induction motors, the end ring is needed to connect rotor bars electrically. Some approaches to calculating its resistance employ equivalent circuit methods, but they are not accurate because they assume ideal sinusoidal current distribution. This paper presents a method to calculate the current distribution in the end ring by the finite-element method (FEM). This paper uses both two-dimensional (2-D) A-Φ FEM analysis and three-dimensional (3-D) T-Ω FEM analysis. The magnetic flux density is obtained from 2-D analysis, and the electric vector potential is obtained from 3-D analysis. With these results, the current distribution in the end ring is calculated and the proper size of the end ring is selected by solving some case problems     

Second order air-gap element for the dynamic finite-element analysis of the electromagnetic field in electric machines

To obtain a dynamic analysis for the electromagnetic field in electric rotating machines working under unbalanced conditions or supplied by non sinusoidal current we previously conceived a first order Air-Gap-Element (AGE-1). Such an element allows to keep a constant topology while the rotor is moved ; in fact the relative position of the rotor is automatically taken into account by the method [1], [2]. In the present paper a second order Air-Gap-Element (AGE-2) is developed to be consistent with second order isoparametric finite elements, using the FLUX field computing program [3] which gives more accurate calculations. Moreover the use of AGE-2 permits us to consider a solution domain corresponding to either two pole-pitches or one pole-pitch To optimize the computing time spent on solving the equation system, we used the SICCG method [4]. The paper contains the development details of the AGE-2 and examples showing the merits of the proposed model.     

A study of finite size effects on cracked 2-D piezoelectric media using extended finite element method

The extended finite element method is applied on the two-dimensional (2-D) finite piezoelectric media weakened by a crack. The fourfold standard enrichment functions are taken in conjugation with the interaction integral to evaluate the intensity factors. Four sequence of analysis, namely crack–mesh alignment, aspect ratio, mesh with local refinement and domain independency is done on the center and edge crack problems. These four analyses when combined together give an optimum result to study the finite specimen. It is observed that for smaller values of strip width to crack length ratio the finiteness of the specimen size affects the intensity factors.     

Index of rotor losses in three-phase fractional-slot permanent magnet machines

The aim of here is to define an index of the rotor losses induced by the magnetomotive force (MMF) space harmonics in fractional-slot permanent magnet (PM) machines. Such an index facilitates a rapid discrimination of the various fractional-slot PM machines, based on the numbers of slots and poles. For the sake of generality, a simple model of the rotor losses is adopted to compute such an index of rotor losses. However, the index behaviour follows that of rotor losses computed by means of more complex models.     

Flux level selection in vector-controlled dual stator winding induction machines

The dual stator winding induction machine has two three-phase stator windings with dissimilar number of poles. This machine can be regarded from the point of view of control as two different induction machines coupled by a rotor. To improve the machine's performance, the total flux generation must be correctly distributed between the two windings. This study focuses on the flux distribution necessary to achieve a nearly maximum torque per stator ampere operation, which is indicated in applications requiring high dynamics. In addition, efficiency and voltage utilisation will be also considered.     

Dynamic electromagnetic torque model and parameter estimation for a deep-bar induction machine

A dynamic analytical electromagnetic torque model for a deep-bar induction machine is presented. The model is based on the space-vector theory of electrical machines. The parameters are estimated using the data provided by the numerical impulse response test performed within the two-dimensional time-stepping finite element analysis. Two different impulse tests are studied. The impulse excitation is applied to the stator voltage and rotor position angle, and the parameter estimates are compared. The applicability of the impulse test is based on the assumption of linear behaviour in the neighbourhood of an operation point. Hence, one of the main objectives is to study the validity of the impulse test. From the results of the angle impulse test, a frequency range of negative damping is detected. The phenomenon is also studied by measurements.