FE研发培训,设计培训

1、Synchronous MachinesElectromagnetic Finite Element AnalysisHaran KarmakerJune 1, 2006 Introduction Boundary Value Problem Fundamental Concept Pre-processing Processing Post-processing Parametric Modeling Topics FEA (Finite Element Analysis) is a well-established numerical method of solving field pro

2、blems. Commercial software packages are available to solve field problems in electrical machines, such as those of synchronous machines.Introduction Solution of a boundary value problem comprises the calculation of the distribution of a function over a specified domain. Boundary Value Problem The bo

3、undary value problem is described by a governing equation and boundary equation. Boundary Value Problem Dirichlet boundary equation Neumann boundary equationBoundary Value Problem Fundamental concept of FEA is that any continuous function defined over a domain can be approximated by a discrete model

4、 composed of a set of piecewise continuous functions defined over a finite number of subdomains. Fundamental Concept Consider an example of temperature distribution in a bar. Fundamental Concept The continuous function is T(x) and the domain is OL along x-axis. Six points along x-axis are identified

5、. We shall call these points as nodes. The domain is divided into five elements. Function T(x) is approximated by five piecewise continuous linear functions defined over a single element. Fundamental Concept The pre-processing includes the steps of identifying the domain of analysis, derivation of t

6、he governing and boundary equations and the division of the domain into sub-domains called finite elements. Pre-processing Consider one-dimensional bar element. The value of a function over the element i is defined Pre-processing Similarly, for element j Pre-processing The most common two-dimensiona

7、l element is a triangle. Pre-processing Pre-processing The governing equation for 2D magnetic field problem can be derived from Maxwells equations by defining a potential function A. A residual is defined for an approximate solution. Pre-processing Minimizing the weighted residual with respect to ea

8、ch nodal potential, we obtain Substituting from above, we obtain. Pre-processing Using Greens identity, we obtain. Substituting, we obtain the following equations. Pre-processing In the processing step, we solve the system of equations derived in the pre-processing step. Processing The coefficient m

9、atrix for the system of equations is sparse and is usually symmetrical along the diagonal. For non-linear magnetic field problems, the entries in the coefficient matrix are functions of permeability. An iterative method, such as, Newton-Raphson is used for solution of the nonlinear system of equatio

10、ns. Processing The principle of the Newton-Raphson method is to iteratively reduce this residual until it is sufficiently small (ideally zero). Processing The commercial software packages MagNet by Infolytica of Canada and MagSoft by Cedret of France are used by R&D for electromagnetic FEA. A pa

11、rametric modeling technique has been recently developed to automatically model synchronous machines by using MagNet. An example of the application for 4 poles 8500 HP motor 2511DA is used for illustration. Software There are four modules for creation of a FE model parametrically. - Stator (model sta

12、tor core, air )- Rotor (model rotor pole, spider and field coil)- Model (create model including all components)- Phase SET (create stator winding connection) Parametric Modeling The stator model has four buttons. After the parameters are entered, each button can be activated to complete the model. T

13、he scale is the number of poles to be modeled. The four buttons are - Build Stator Core- Build Stator Winding- Build Air- Build Stator Stator Model Stator Model The rotor model has six buttons. After the parameters are entered, each button can be activated to complete the model. The buttons are - Bu

14、ild Field Pole- Build Air Gap- Build Shaft- Build Damper Bars- Build Coil Rotor Model Phase Set Model Mesh Air Gap Mesh (Close-up) 2D FE models solve for field distribution over a machine cross-section by neglecting all fringing and end effects, called 3D effects. Since 3D modeling requires consider

15、able computer programming and CPU time, it is not yet practical to solve rotating machine transient problems in 3D. To improve correlation with test results, it is essential to include the 3D effects. 3D Effects Modeling 3D effects include stacking of core laminations, ventilation air ducts fringing

16、 flux and pole and stator end leakage flux. Some methods to include 3D effects in FE models have been developed. 3D Effects Modeling 3D Effects ModelingLdwFEsolutionregionF Figure shows a magnetic circuit in which flux F, width w and depth d are in the plane of the FE solution region, and the axial

17、length L is perpendicular to the plane of the FE solution domain. The permeance P of this magnetic circuitP = m w L / d 3D Effects Modeling The permeance Pmod of a circuit component in the FE model has to be identical with the actual permeance Pact of this componentPact = mact wact Lact / dact Pmod

18、= mmod wmod Lmod / dmod Width and depth of the FE model agree with the actual dimensions, which gives the scaling equation for the permeability mmod mmod = mact Lact / Lmod= mact fstack 3D Effects Modeling The scaled permeability is used in the FE model by scaling the actual B(H) characteristic of t

19、he steel material in each region by the stacking factor Hmod = Hact, Bmod = Bact fstack The field solutions obtained using this “equivalent” FE model are scaled back to the actual flux densities Bact = Bmod / fstack 3D Effects Modeling The duct fringing flux and end leakage flux effects can be model

20、ed in a static model to obtain the leakage correction factors 3D Effects Modeling Field SolutionOC Solution at 120% Rated Voltage Engineering parameters of interest can be derived by post-processing of the field solution. The software post-processing has many options to calculate the desired quantit

21、ies. The calculated quantities can be exported to excel spreadsheet for additional data analysis. Post-processing Graphical PlottingOC Saturation 00.81.823080130180230280330Field Current (Amps)Field Current (Amps)Stator Voltage (PU Rated)Stator Voltage (PU Rated)TestFEACALCFEA, 2D

22、 In integral slot machines the geometry and the magnetic field distributions repeat every pole pitch, and it is, therefore, sufficient to perform the field analysis using just one pole pitch. In fractional slot machines the stator coils do not repeat every pole pitch, but only after multiple pole pi

23、tches depending on the coil pattern. Fractional Slot Machines In a winding characterized by A+B/C slots per pole per phase, the winding pattern and magnetic fields repeat only after C pole pitches. Therefore, C pole pitches have to be modeled, which results in large FE models and long simulation tim

24、es. Fractional Slot Machines The periodicity of the magnetic fields is utilized to reduce the FE model with periodic boundary conditions for the magnetic vector potential A. The vector potential of the nodes on the left radial boundary has the same magnitude as the potential of the corresponding nodes on the right boundary, and the sign depends on t