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1. lt A D f 1 T ee fie lt 4 Nes nid lt TT f S Y FEARI M TS Ed RasultsCelonlater Wea Of P PEN says ee UA e i A MagneticVectorPotential FullVector tl nL Ny meamata seat jl g o i Frequency 30 Figure 4 7 Arrow Plot of Magnetic Flux Density along a Center Cross Section of the 360 Degree BDFM Model 6T 30 saturating The flux density values for this BDFM model 0 35925 tesla maximum show that the machine is not saturating for the previously specified excitation level of 100 amp turns peak per slot An arrow plot of magnetic flux density can also be used to observe the field symmetry pattern of the machine The arrow plot of Figure 4 7 also shows that the field pattern exhibits 180 degree symmetry giving credibility to this approach 4 4 2 5 3 Currents in the Rotor Bars The currents flowing in every rotor bar of the BDFM rotor were determined using MSC XL s solution calculator The currents were calculated by specifying a plane perpendicular to the rotor bar direction the xy plane and intersecting this plane with one rotor bar at a time The program then calculates the total current flowing in the rotor bar in the positive z direction from the conduction current density by the following formula I JJ ds Equation 4 4 where J is the conduction current density and ds is the integration surface The currents were calculated at several axial z posit
2. Quantity Symbol MKS Units Tike L i seo j v I weber c farad kg se mh Qa Table A 1 MKS Units A 4 1 2 Drawing a symmetry Wedge 76 A hand sketch of a radial cross section of the BDFM model should be drawn to prepare for geometry creation Figure A 4 shows an example sketch of the BDFM lab machine 77 22 5 45 Rotor radial 13 5 cross section 5 Stator radial cross section I 0 000 10 76 766 130 All measurements are in millimeters mm Figure A 4 Radial Cross Section of the BDFM Model The hand sketch should show the location of each point and curve that will be used to construct the geometry The intersection of each curve with the x axis should be labeled with a location as each of these points will be the start of the geometry A three dimensional finite element mesh is constructed in MSC XL by extruding or sweeping selected elements of a two dimensional mesh over a specified distance Therefore the two dimensional mesh which will be created first must include an element pattern that can be extruded to create a three dimensional mesh In other words for the BDFM problem the outline of the endring and nested loops must appear in the two dimensional mesh pattern Observe the radial symmetry of the machine cross section In other words notice what smallest radial section of the machine cross section geometry can be rotated 78 and or reflected to
3. A 8 Typical Mesh Errors c5scsc csscesipostkseesedoaysesaprasaceies veinioriateaies unsiee iv and on eeneeeee 102 A 9 Fixed Boundary Conditions sccscccaseissvaisoiuucestosonenes whesgesnenceassopscoetesaues wen eemevieien 123 A 10 Alternating Periodic Boundary Conditions ccececsesssessesseesessseseseesseeseeseens 125 A 11 Disk Space Requirements for MSC EMAS based on the cellular cube and flat plate for MSC NASTRAN solution 101 run 17 o on 133 A l A 2 A 3 A 4 A 5 A 6 A 7 List of Appendix Tables MKS UMIS arts eaa EE E EE a EAA cave trices ae R OR 76 Assignment of PIDs to Two Dimensional Elements ccccccsssesesseeseeseesees 95 Assignment of PIDs to Three Dimensional Elements cccccccscesseeseesseeees 95 Supplied Materials in MSC XL 0 0 ceeecccsccscsseesecseeeseeseesecseeecessecsussscssesseeseeseeeaes 116 Materials Used in the Setup of the BDFM Model ccceccescsseessessceeeeeeneeneees 118 Six Pole Stator Winding Layout ccccssccssscssecsssecesecescceesseceseeesseecsseeesseeeses 119 Two Pole Stator Winding Layout cccccccscescesscessccsseessecseessecseecsssessecnesenseeas 120 Three Dimensional Finite Element Design Procedure for the Brushless Doubly Fed Machine 1 Introduction Due to recent improvements in power electronics adjustable speed drives ASDs are being installed in increasing numbers in industrial applications However the majori
4. Choose the type of item to be deleted The items can then be deleted by picking them directly from the graphics tile A 4 2 2 Defining a New Coordinate System One coordinate system is defined automatically in MSC XL This is the basic Cartesian coordinate system which has identifier 0 and is centered at the origin 0 0 0 The direction of the basic coordinate system axes are shown in the MSC XL graphics tile The basic coordinate system provides the frame of reference for all entities including other coordinate systems It is possible for the user to define new coordinate systems relative to the basic coordinate system or some other previously defined coordinate system Use of alternate coordinate systems can make geometry creation easier MSC XL allows the user to define three types of coordinate systems rectangular cylindrical and spherical A cylindrical coordinate system is useful in geometry creation and problem setup A basic cylindrical coordinate system with center at the origin can be created as follows 1 Pick Geometry Coord System Define Coord System gt By Origin Angles from the cascading menus 2 Inthe pop up menu enter the following parameters e Origin X Y Z 0 0 0 Defines the origin of the new coordinate system 81 e Angle 1 2 3 0 0 0 Defines the rotation of the new coordinate system from an existing coordinate system about Axis 1 2 3 e Axis 1 2 3 X Y Z Defines how the coordinate axes are spe
5. More often engineers require accurate solutions involving complicated materials geometries and loading conditions For this reason engineers are turning to numerical methods for answers to real life problems FEA is one numerical method of solving Maxwell s differential equations There are several steps that make up the finite element method 3 2 Finite Element Model The first step in FEA is to specify a finite element model The model geometry describes the size and shape of the device to be analyzed The geometry is divided into subregions called finite elements Elements may be irregular so that the modeling of complicated geometries is both easier and more accurate Points where elements join are referred to as grid points Material properties excitations and boundary conditions are applied to the finite element model Material properties associated with elements represent the permittivity conductivity and permeability properties of the various materials in different regions of the model Excitations such as currents are applied to the model Boundary conditions are used to simulate physical behavior outside the model boundaries 3 3 Solution of Maxwell s Equations Maxwell s equations are the basis for electromagnetic field calculations These four partial differential equations relate the space and time variation of electric and magnetic fields to material properties and to excitations They describe a broad range of
6. This lack of customer support made it difficult for the user to effectively use the program 5 2 2 5 No results due to Problem Encountered Due to lack of program diagnostics and customer support no useful results where obtained by the Maxwell 3D Field Simulator for the BDFM problem Attempts were made to obtain a solution by reducing the size of the BDFM model by reducing the number of rotor bars and nested loops reducing the number of stator windings and reducing the length of the machine The program was finally able to generate a solution using a much simplified model However the program indicated that the solution had 120 percent error due to having a finite element mesh that was too coarse When the finite element mesh was refined the program was again unable to obtain a solution to the problem 5 3 MSC XL and MSC EMAS by MacNeal Schwendler Corporation 5 3 1 Advantages 5 3 1 1 Many Modeling Modules Available for a Variety of Problems MSC EMAS includes a large number of analysis modules solution methods so a large variety of electromagnetic problems can be modeled These solution methods 57 include electrostatic current flow magnetostatic magnetostatic with current flow nonlinear magnetostatic nonlinear magnetostatic with current flow AC modal AC transient modal transient nonlinear transient real eigenvalue complex eigenvalue and modal complex eigenvalue The MSC EMAS documentation includes a selection tr
7. discussed A 2 An Overview of MSC XL MSC XL is a graphical pre and post processor application designed for use in conjunction with MacNeal Schwendler s finite element analysis software 15 The two products that MSC XL currently supports are MSC NASTRAN mechanical engineering problems and MSC EMAS electromagnetic field analysis With MSC XL users can build complete ready to run finite element models then analyze them with MSC EMAS or MSC NASTRAN without leaving the MSC XL environment Analysis results can also be displayed by MSC XL This combination of 68 software tools provides users with a complete finite element modeling analysis and results processing package A 2 1 Screen Layout The screen layout for MSC XL is shown in Figure A 1 In MSC XL there are two methods of entering commands Commands can be entered by typing them in the blue bar command line or they can be entered by picking from the cascading pop up menus When a command is entered from picks on the cascading or pop up menus the equivalent typed command version is displayed in the history tile The two methods of entering commands in MSC XL can be used interchangeably MSC XL provides the user with control over all visual contents including labels visibility colors titles multiple views with different orientations multiple data displays etc A 2 2 Using the Mouse In MSC XL each of the three mouse buttons has a distinct function e Pick
8. the results are then summed over the elements to represent the energy of the entire problem volume When the energy function is set to zero a single equation is obtained 11 This equation is entirely equivalent to Maxwell s equations in their complete and general form This equation is 10 le J u o Ac Equation 3 9 u where the vector u represents the four DOFs per grid point the matrix represents permittivity the matrix c represents conductivity the matrix represents u permeability and J is an excitation vector which represents the contributions of all model excitations The associated initial condition is fe u 7 Equation 3 10 These matrix equations which are equivalent to Maxwell s equations in their complete and general form are solved using a formal series of matrix operations for the unknown potentials u 3 Equation 3 11 The numerical methods used to solve Equations 3 7 and 3 8 are specified by solution sequences 10 Each sequence represents a particular mathematical technique Thus a particular application may be analyzed using several techniques such as magnetostatic analysis frequency response analysis transient analysis or eigenvalue analysis 3 4 Data Recovery Once a solution for the potential DOFs at each grid point have been obtained the fields E and B are recovered within each element Other quantities such as electromagnetic ener
9. 4 1 Connect Points Points along the x axis are connected together to form straight line curves with the Connect Points option as follows 1 Pick Geometry gt Curves gt Connect Points from the cascading menus 2 Two points can easily be connected by picking them directly from the graphics tile Alternately enter the two point identification numbers in the pop up menu 83 A 4 2 4 2 Sweep Point Circular curves can be created by sweeping points through an angle around an axis of rotation The sweep point option is useful for creating the circular curves forming the outline of the rotor bars The curves outlining one half of one rotor bar should be formed by sweeping the points defining the edges of the rotor bar around the rotor bar center Curves are created with the Sweep Point option as follows 1 Pick Geometry gt Curves gt Sweep Point from the cascading menus 2 Inthe pop up menu enter the following parameters Iterate The number of times the point s will be swept Point The identification number of the point s to be swept From X Y Z Defines the center of rotation around which the point s will be swept To X Y Z Together with From X Y Z defines the axis around which the point s will be swept Angle Angle in degrees through which the point s will be swept Maximum value is 180 degrees Offset The initial angle offset before the sweeping begins CID The coordinate system in which the F
10. 5 1 Invoking MSC EMAG cccccsssseseseesesseesecssesseeneeneeeseens 129 A 4 5 2 System Requirement cccsscssccsscseccseccsssesneesereessenss 131 A 4 5 3 S l tion Tine sho encarna e 132 Results and Validation 2 0 cvcctecccacuccidvasiedeaceahinn sins ve cats en sedties 134 A 4 6 1 Accessing MSC EMAS Results ccccccscesessseseeseeeees 134 A 4 6 2 Producing Contour Plots cccecccessessecesscessesseeeseeseeesees 135 A 4 6 3 Producing Arrow Plots cccccscesseessesseeesecsteeseseescenseesaes 136 A 4 6 4 Results Plots on Cut Surfaces cccceesccessesesseeeeeeeeers 138 A 4 6 5 XY Plotting along Cut Paths 0 ccc cceseeeeeeeseeseeeeeeeeeeees 139 A 4 6 6 CalCulati otis 5 os cos dcsctasiscsntgnuvecvacteticaienn cetera healers 141 2 1 2 2 2 3 4 1 4 2 4 3 4 4 4 5 4 6 4 7 4 8 4 9 4 10 4 11 4 12 4 13 4 14 4 15 4 16 List of Figures BDEM Stator Struct re issu iaren NARAR E A EE aS BDEM Rotot Structure seee a E ia Velocities of Interacting Fields ss c vi 52 c0 21055 caceetsneeizcciel cseenisste aodinratioonemeate Stator Laminati n ires erter peet Ea E RAA a as eeneaa aaa Rotor Lamination seser enaa a n aada Coarse Three Dimensional 360 Degree BDFM Finite Element Model Stator Excitations for the 360 Degree BDFM Model cccccccccsssesecseeseeeeeees Boundary Conditions for the 360 degree BDFM Model ccccccccessess
11. 5 Mesh Checking Procedures Any mesh produced by MSC XL will initially contain errors Some errors are present by default because of the way MSC XL is designed other errors are user errors It is a good idea to use the mesh checking procedures included in MSC XL often to check the two dimensional mesh as it is being created The sooner errors are identified the easier they are to correct The mesh should always be checked before it is reflected or rotated Also after the two dimensional mesh is complete and before the three dimensional mesh is created it is necessary to check for common errors associated with meshing Mesh errors can be much more easily identified and corrected in two dimensions than in three dimensions Unidentified mesh errors will produce fatal errors 102 or warning messages during the solution process Typical mesh errors are duplicate grid points unconnected grid points duplicate elements free edges or free faces and element voids Several examples of these are illustrated in Figure A 8 Duplicate Grid Point Unconnected Grid Point Figure A 8 Typical Mesh Errors A 4 3 5 1 Duplicate Grid Points Duplicate grid points occur along the shared edges between surfaces and along the shared faces of solids when a finite element mesh is created Duplicate grid points will almost always be present in the model since they are generated by the meshing process MSC XL has an automatic check for duplicate grid po
12. Choose Field Results Contours from the cascading menus 2 Select a Style of contouring from one of the three choices LineContour was chosen for the contour plots presented in Chapter 4 3 Choose the AverageMethod that MSC XL will use to average results Default is acceptable 136 4 Use the QuickEditRT option to select the following e Select the Results quantity for the contour plot To obtain a contour plot of magnetic vector potential for Grid Results choose Magnetic Vector Potential and for Element Results choose GridResults Only element results are used for contour plots so if grid results are to be plotted the Element Results must be set to GridResults e Select the desired components VectorResult of the result Full Vector was chosen for the contour plots presented in Chapter 4 e Select the TypeOfData Magnitude was selected for the contour plots presented in Chapter 4 5 Display the contours in the chosen view by picking Plot in View A 4 6 3 Producing Arrow Plots Arrow plots are displays of vector fields An arrow plot displays arrows at the grid points or at the element centers The ColorRangeTable values show the magnitude of the field quantity and the arrows show the field direction For the BDFM analysis problem arrow plots of magnetic flux density B show the magnitude and direction of the B field in tesla This allows the user to examine if the flux density values are in appropriate ranges and if not w
13. Degree BDFM Model a oe aay a 7 ine ae ae es 10 rl 4 10331 3 86986 5 6403 43 3229 r12 lt _ 1 19341 28 932 28 9566 92 362 Pe sd pS 1 2 3 4 5 7 10 11 12 E 14 15 17 18 19 20 8 56011 39 4474 40 3655 102 243 1 19354 28 9307 28 9553 87 6376 4 10281 3 87263 5 64184 136 653 Information of this type on slot span vs rotor bar current magnitude for the range of operating frequencies should be used to design a more effective rotor for the 43 BDFM A grading of bar size within the loops of each nest with the outer loops having the largest conductor size should be investigated as a possible means of equalizing or improving current distribution within the loops or equalizing loss distribution to minimize thermal problems 4 4 4 1 2 Distribution of Conduction Current Density Within the Rotor Bars Distribution of conduction current density within each rotor bars was also examined for the detailed 180 degree model Plots of conduction current density across each rotor bar from bottom to top and also from right to left were made in order to observe how the current is distributed within the rotor bars Slot Span vs Rotor Bar Current Magnitude 160 140 Current Magnitude A Slot Span Degrees Figure 4 16 Slot Span vs Rotor Bar Current Magnitude 44 Figure 4 17 shows the path along which the conduction current density was plotted
14. Geometry gt Curves gt Define Curves gt Center 2 Points from the cascading menus 2 The center rotation point followed by the two points to be connected can be picked directly from the graphics tile Alternately the point identification numbers can be entered in the pop up menu Curves defining an outline of the model are created using a combination of the connect point sweep point reflect curve rotate curve and define curve options or other options available in MSC XL When creating curves it is important to realize that surfaces which will be defined next are created by connecting a maximum of four curves Therefore the curves must be laid out such that a surface can be created everywhere in the model by connecting at most four curves 87 A 4 2 5 Creating Surfaces After curves have been created the next step in creating geometry is to specify surfaces If the curves have been properly defined throughout the radial wedge such that surfaces can be defined by connecting at most four curves the creation of surfaces is an easy step Surfaces can be created using the Define Surfaces option as follows 1 Pick Geometry Surfaces Define Surface gt By Edges from the cascading menus Specify whether the surface will be created by connecting 3 or 4 edges curves 2 Curves defining the edges of the surface can be picked directly from the graphics tile Alternately the identification numbers of the curves can be e
15. as other types of electric machines have shown that machines have an identical magnetic field distribution on a pole by pole basis 11 The magnetic field patterns show that only one pole pitch needs to be modeled in a machine with identical poles Thus the number of elements and grid points in a finite element model can greatly be reduced if symmetry can be used and only one pole of the machine modeled This is advantageous because a model with fewer elements and grid points will have a faster solution time and require less resources such as disk space to solve In an induction machine having identical poles each pole boundary has periodic boundary conditions For a two dimensional model the periodic boundary conditions are expressed in polar 7 0 coordinates as 12 A r 8 p A r 8 Equation 4 1 where A is vector potential is the angle of one radial boundary and p the pole pitch angle This boundary condition is called an alternating periodic boundary condition If the geometry requires modeling two poles then the vector potentials on the boundary are set equal with no negative sign This is referred to as a repeating periodic boundary condition Generally an odd number of poles requires alternating and an even number repeating boundary conditions 15 4 2 FE Modeling of Doubly Fed Characteristics Applying the techniques of induction machine analysis described above to the BDFM is difficult due to the following consider
16. by entering off diagonal as well as diagonal terms for the relative permeability tensor p Most materials have a relative permeability very close to 1 Ferromagnetic material such as iron steel nickel and cobalt have relative permeability much higher than 1 Iron or steel is commonly used in magnetic devices because it has a relative permeability of several thousand and is inexpensive Ferromagnetic materials however have a highly nonlinear B H curve MSC XL allows the user to specify a B H curve for a material in its nonlinear analysis modules A 4 4 1 4 Setting Material Properties in MSC XL MSC XL provides default material properties for fifteen materials via the supplied Materials EMAS file located in the XL_PATH directory These default material properties all assume linear isotropic materials Table A 4 shows the default values for the relative permeability absolute electrical conductivity and relative permittivity of the supplied materials 116 Material Absolute Relative Conductivity Permittivity Aluminum 3 54E 07 Relative Permeability Bakelite 1 0E 09 1 0 1 0 4 74 1 0 0 0 0 AirorVacuum 10 oo Copper 10 53m0 Freshwater 81 0 Gol Laminated Seal 20000 09 10 Plexiglas a E Polyethylene D 70 0005 Payen E LOE 10 A 00 275 1002 Seawater 81 0 Silicon 98 Steel 2000 0 5 0E 06 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 Rubber 1 0 1 0 1
17. creates a hiddenline model hardcopy plot linecontour creates a linecontour hardcopy plot creates an arrow hardcopy plot To generate a hardcopy of the entire MSC XL screen type replay on create the desired picture then type replay off All refreshes after the replay on command is issued 143 are written to the plot file Refer to Chapter 5 of the MSC XL User s Manual 15 for more information about generating hardcopy files
18. finite elements that make up the geometry Therefore the user must keep track of which element identification numbers belong to what part of the geometry If the model is large this can be quite a task Also ina wireframe modeler once the finite element model is completed it is not possible to change or refine the mesh without creating the whole model over again which requires a substantial investment of time 51 With Maxwell 3D Field Simulator s solid modeling procedure analysis results can be calculated and displayed for a particular object by selecting its name The solid modeling procedure makes creation viewing refinement of the mesh and results analysis easy for the user 5 2 1 2 Step by Step Design Procedure Maxwell 3D Field Simulator uses a step by step design procedure which makes the program easy for users unfamiliar with finite element analysis to learn and use When the program is started the Maxwell 3D Field Simulator main menu appears listing the general procedure steps for the user to follow These general procedure steps are 14 Select Solver Type Draw Geometric Model Setup Materials Setup Boundary Conditions Setup Executive Parameters Setup Solution Parameters Solve View Fields The program displays a check mark next to each step after it has been successfully completed In general the steps must be chosen in the sequence listed above For example the Setup Materials step is operable on
19. for AC Finite Element Models The MacNeal Schwendler Corporation 1994 12 J R Brauer What Every Engineer Should Know About Finite Element Analysis The MacNeal Schwendler Corporation 1990 65 13 B E MacNeal MSC EMAS Modeling Guide The MacNeal Schwendler Corporation 1991 14 Maxwell 3D Field Simulator User s Reference Ansoft Corporation 1993 15 Ken Peterson MSC XL User s Manual The MacNeal Schwendler Corporation April 1993 16 MSC EMAS AC Analysis User Interface Guide The MacNeal Schwendler Corporation April 1993 17 MSC EMAS Installation Procedures for HP 9000 700 HP UX The MacNeal Schwendler Corporation August 1993 APPENDIX 66 67 A Tutorial for Setting up and Solving a 3D BDFM Model using MSC XL and MSC EMAS A 1 Introduction The goal of this tutorial is to guide a new user of MSC XL and MSC EMAS through the creation setup simulation and analysis of a BDFM model The 5 horsepower BDFM lab machine discussed in Chapter 4 is used as an example The step by step creation of the detailed 180 degree model presented in Chapter 4 is described in this chapter This tutorial will not attempt to give a full description of all the commands and options available in MSC XL and MSC EMAS An overview of basic commands used in MSC XL and one approach to creating a BDFM model is presented Topics important to creating an effective finite element model will be
20. from bottom to top Figure 4 18 is a plot of conduction current density in bar 6 along the path indicated in Figure 4 17 Figure 4 19 is a plot of conduction current density in bar 7 along the path indicated in Figure 4 17 These figures show that the conduction current density varies across the rotor bars from bottom to top but this variation is not great Figure 4 20 shows the path along which the conduction current density was plotted from right to left Figure 4 21 is a plot of conduction current density in bar 6 along the path indicated in Figure 4 20 Figure 4 22 is a plot of conduction current density in bar 7 along the path indicated in Figure 4 20 These figures show the conduction current density varies across the rotor bars from right to left This variation is greater than the variation observed from bottom to top This variation is due probably to the magnetic field distribution surrounding the rotor bars but is not of a sufficient magnitude to cause concern Figure 4 17 Path along which Conduction Current Density was Plotted from Bottom to Top Sr Current Density A sq m 46 Conduction Current Density E 06 4 22 4 21 4 2 4 19 4 18 4 17 4 16 4 15 4 14 4 13 0 1 2 3 4 5 6 7 Distance across Rotor Bar 6 mm Figure 4 18 Conduction Current Density in Bar 6 in reference to Figure 4 17 Conduction Current Density A sq m Conduction Current Density E 06 2 24 2 23 2 22 2 21 2 2 2
21. model cracks With the model option the only free edges or free faces that are displayed for a model without errors are the model 105 boundary The PID option is a useful technique for checking that the correct PID was assigned to each element When the PID option is used all of the boundaries between objects or PIDs should be observed If free edges or free faces exist in the interior of the model those areas must be investigated for missing elements improperly connected elements or other discontinuities Deleting the free edges or free faces by picking FEM gt Check FEM Free Edges Delete from the cascading menus does not fix the cracks it only removes the free edges or free faces from the display screen A 4 3 5 5 Element Voids Element voids or missing elements occasionally occur if an element is deleted and are sometimes difficult to detect Element voids will show up as a local grouping of free edges or faces in the model interior If a void is suspected it is easily confirmed by displaying a shrink plot of the model A shrink factor other than zero default will shrink the display of an element toward its center by the fraction amount For example a shrink factor of 0 2 will cause finite elements to be drawn 80 percent of their actual size The shrink factor can be changed by selecting Tables gt Display FE Visual gt Shrink from the cascading menus Voids are most easily repaired by editing in the mi
22. of the edge cause gross errors 94 e High aspect ratios may not be a problem in rectangular elements unless field gradients are too large e Keep the taper angles on trapezoidal QUAD elements less than fifteen degrees Figure A 7 illustrates these concepts Maybe OK Taper Figure A 7 Distortion of Midedge Nodes Aspect Ratios and Taper Angles A 4 3 3 Preparation for Meshing Assigning PIDs In preparation for meshing the geometry in MSC XL it should be determined how property identification numbers or PIDs will be assigned to elements PIDs are assigned to elements as they are created and later used to assign material properties to elements and to collect sets of elements together in groups In creation of the two dimensional mesh the important consideration is how objects can be assigned PIDs so they can be collected as groups since 2 D elements will not be assigned material properties in the final model this consideration is not important now These groups of 95 elements will later be selectively extruded to form three dimensional elements representing objects Tables A 2 and A 3 help to explain this concept Table A 2 shows how PIDs can be assigned to groups of two dimensional elements that form a Two Dimensional groups of PIDs assigned to two elements representing objects dimensional elements Peet ay Oe Coo o See CE aera Table A 2 Assignment of PIDs to Two Dimensional Ele
23. that Jre Sre Equation 2 4 with the result that f htl Equation 2 5 P P The control frequency f can either be positive same sequence as f or negative opposite sequence to f The electrical frequency of rotor currents in synchronous operation can be related to the system frequencies as 9 Sra fo PS PL FS Equation 2 6 2 3 Applications of the BDFM The BDFM can be used in place of commercial and industrial squirrel cage AC induction machines It is particularly suited for potential niche applications in ASD or VSG systems including but not limited to pump drives wind power generation and automotive alternators 3 Finite Element Analysis Method 3 1 Definition and Concept Finite Element Analysis FEA is a numerical method that is widely used to solve many engineering problems One application of FEA is to solve for the electromagnetic fields in electrical devices Electromagnetic fields represent the foundation of all electrical engineering Maxwell s equations a system of four coupled partial differential equations serve as the basis for electromagnetic field calculations The solution of these equations however is a very difficult task Often engineers approximate field behavior through abstract concepts Much insight can be gained from analytic techniques and approximations However such techniques are useful only in relatively simple devices and at some point approximations will fail
24. the Rotor Reference Frame vs the Stator Reference AAN Device Geometry naiinis etnies asi coetaeieeesndeai aine 20 4 4 2 A Coarse 360 Degree BDFM Model c ccccccecsscsesseeeseeeeseeeeseeees 22 44 21 Material Seyi oti ittash acs a aad e EE see anima eaten 23 4 A22 SEX CMAUIONS n nn n A O E S 24 4 4 2 3 Boundary Conditions sesseeeseoseessesssessresseersrssressressenssesne 24 4 4 2 4 Solution Frequency for an AC Analysis c cceseeees 26 4 425 PROSUNS cc ree AAE T a Ome 27 4 4 2 5 1 Contour Plot of Magnetic Vector Potential 27 4 4 2 5 2 Arrow Plot of Magnetic Flux Density 27 4 4 2 5 3 Currents in the Rotor Bars osessnosesssssessreseesee 30 4 4 3 A Coarse 180 Degree BDFM Model cc eeeeseeesseseeeeeeeeeeeteeeerens 32 4 4 3 1 Boundary Conditions sesseseeeseessssssessresseessrenenssnnsrenseesne 34 4 4 3 2 RESUS ecdecsizi casas acrechscasiassivtesnsasuncsssesatbanvetaeniiieeudeautsanioesads 34 4 4 3 2 1 Contour Plot of Magnetic Vector Potential 35 4 4 3 2 2 Arrow Plot of Magnetic Flux Density 36 4 4 3 2 3 Currents in the Rotor Bars cccccsecesseeseeeeees 36 4 4 4 A Detailed 180 Degree BDFM Model cesessesseesseesseeseeseees 39 FAAN RESUS onena e n dens saansa E A EAA 40 4 4 4 1 1 Currents in the Rotor Bars sseeseeseesesresreseese 40 4 4 4 1 2 Distribution of Conduction Current Density Within the Rotor Bars eseesess
25. to form a three dimensional mesh 97 A 4 3 4 1 Parametric Meshing The technique found to be the easiest for two dimensional mesh creation of the BDFM problem is parametric meshing of surfaces although other techniques are available In this procedure the number of elements to be created along the edges of a surfaces are specified Elements are created within the surfaces according to specifications and grid points are automatically created at element corners The parametric meshing procedure can be used as follows 1 Pick FEM Mesh Parametric Mesh Surfaces from the cascading menus 2 In the pop up menu enter the following parameters e NoMidNode Midnode Specifies whether the elements will contain midnodes quadratic elements e Surface The identification number of the surfaces to be meshed e Type The type of element to be created In created the two dimensional mesh QUAD should always be selected here as QUAD elements are more desirable than TRIA elements Ifthe shape of the surface dictates TRIA elements will automatically be created by the meshing routine even though QUAD was selected e U V Defines the number of elements to be created along the edges of the surface U and V directions depend on how the surface was created 98 e Pattern The element orientation corresponding to different element types The default 1 is acceptable e PID The property identification number to be assigned to the elemen
26. 0 Porcelain i a 1 0E 10 Table A 4 Supplied Materials in MSC XL The Materials EMAS file can be edited to include other materials Different materials can also be defined within MSC XL by choosing New from the materials pop up menu The Edit option provides a pop up for entering the desired relative permeability absolute electrical conductivity and relative permittivity Material properties are defined in MSC XL as follows 1 Choose FEM gt MaterialProperty from the cascading menus A material property identifier must be entered The material property identifier is a PID belonging to elements in the model A material property needs to be created for every PID in the model 117 2 After choosing a material property identifier corresponding to one of the model PIDs choose one of the materials from the FEM MaterialProperty Material pop up or pick New to specify the permittivity conductivity and permeability of a different material other than the defaults Toggling the FEM gt MaterialProperty Material Edit option allows values for the permittivity conductivity and permeability tensors to be edited by hand MSC XL allows isotropic anisotropic symmetric and unsymmetric materials to be specified This selection is made by toggling TypeOfMat The material tensors can also be either real or complex This type is selected by toggling TypeOfData The CID option under FEM MaterialProperty selects the coordina
27. 19 0 1 2 3 4 5 6 7 Distance across Rotor Bar 7 mm Figure 4 19 Conduction Current Density in Bar 7 in reference to Figure 4 17 Figure 4 20 Path along which Conduction Current Density was Plotted from Right to Left LY Conduction Current Density E 06 Current Density A sq m Distance across Rotor Bar 6 mm Figure 4 21 Conduction Current Density in Bar 6 in reference to Figure 4 20 Conduction Current Density E 06 Conduction Current Density A sq m 0 1 2 3 4 5 6 7 Distance across Rotor Bar 7 mm Figure 4 22 Conduction Current Density in Bar 7 in reference to Figure 4 20 48 49 5 Comparison of Two Three Dimensional Finite Element Analysis Software Packages 5 1 Introduction In the course of investigating three dimensional finite element analysis for the BDFM two different commercially available finite element analysis software packages were examined and tested The first was Maxwell 3D Field Simulator produced by Ansoft Corporation 14 and the second was MSC EMAS Electromagnetic Analysis System 10 and MSC XL 15 by MacNeal Schwendler Corporation MSC This chapter will compare these two software packages and discuss their advantages and disadvantages limitations 5 2 Maxwell 3D Field Simulator by Ansoft Corporation 5 2 1 Advantages The main advantages of Maxwell 3D Field Simulator by Ansoft Corporation are its solid modeling procedure step by step design proc
28. 3 Similarly to permittivity this tensor becomes isotropic if J and E are in the same direction in which case its only nonzero terms are diagonal entries of the same conductivity In anisotropic materials J and are not parallel so the full conductivity tensor is used The conductivity of air vacuum or other materials is zero because they conduct no current density J unless E is high enough to cause arcing The most common conductor copper has o 5 8E 07 siemens m Steel and iron have a conductivity in the range of about 1 0E 06 to 1 0E 07 siemens m If B changes with time then to reduce losses in machines the steel is often laminated The lamination lowers conductivity in the direction across the laminations and hence lowers the losses A 4 4 1 3 Permeability Permeability is defined by the equation B p vw A Equation A 5 where B is magnetic flux density webers m or teslas in MKS H is magnetic field strength amps m in MKS and u is the permeability of vacuum 12 7E 7 henries m in MKS The tensor relative permeability matrix dimensionless is 115 By By His oJ boo Hop Hz Equation A 6 H3 H32 B33 This tensor becomes isotropic if B and H are in the same direction in which case its only nonzero terms are diagonal entries of the same permeability Linear isotropic magnetic materials are characterized by a single scalar parameter the relative permeability u Linear anisotropic materials are characterized
29. 30 8915 186 883 189 419 99 386 132 463 33 4866 136 63 165 813 8 29609 25 0859 26 4221 71 7006 Table 4 3 Total Calculated Currents in the Rotor Bars for the Coarse 180 Degree BDFM Model 7 13555 87 3894 87 6802 85 332 28 0 06437 0 005 437 0 00547 0 00 2 4e 07 0 00109 0 009 1 0 00109 0 00219 0 9 213 0 003 6328 0 00 PELEKA ESE giaddi a CARE RT 1 ResultsCalculator FrequencyResponse Analysis MagneticVectorPotential FullVector GridResults FullVector TypeOfData Magnitude Subcase 1 Figure 4 11 Contour Plot of Magnetic Vector Potential along a Center Cross Section of the Coarse 180 Degree BDFM Model 1 Frequency 3000 Lt i UT UR N ENT AN ME hy WT NY ty Y ah EF ey s ie fA AU 2 ee a GEARY z h PAE A Mi E MagneticFluxDensity FullVector TypeOfData Real Subcase 1 Frequency 30 Figure 4 12 Arrow Plot of Magnetic Flux Density along a Center Cross Section of the Coarse 180 Degree BDFM Model 8E 39 Figure 4 13 Rotor Bars Labels for the Coarse 180 Degree BDFM Model These total currents calculated for the 180 degree model agree within about 2 with the total currents calculated for the 360 degree model The 2 error may be due in part to limitations within MSC XL for applying the boundary conditions that do not allow the boundary conditions to be applied such that the 360 degree model is exactly represented Since the cu
30. 4 Modeling Tasks Finite element modeling requires the following major analysis tasks e Produce the model e Create geometry e Generate the finite element mesh e Apply material properties excitations and boundary conditions e Solve the matrix problem e Validate the solution Each of these major analysis tasks will be discussed in relation to the BDFM motor model 75 A 4 1 Planning the MSC Session Several topics should be thought out before actually sitting down at the computer to create the model Planning beforehand can save lots of time correcting errors later A 4 1 1 Deciding on Units All the machine s geometric dimensions must be entered in the same units e g inches millimeters meters etc It is not necessary to specify the units being used until just before the model is run but one set of geometry units must be chosen at the beginning and used consistently when creating geometric entities The device dimensions may be in any set of length units as long as the same units are consistently used All other input quantities material properties and excitations must also be entered in a consistent set of units and all output quantities must be interpreted in these same units MSC EMAS uses the MKS system of units as its default system due to its wide acceptance The user can elect to use any other consistent set of units Table A 1 shows common input output quantities and the corresponding MKS units
31. AN ABSTRACT OF THE THESIS OF Brenda E Thompson for the degree of Master of Science in Electrical and Computer Engineering presented on January 17 1995 Title Three Dimensional Finite Element Design Procedure for the Brushless Doubly Fed Machine ZN 1 Redacted for Privacy n a Dr Alan K Wallace Abstract approved Brushless Doubly Fed Machines BDFM have potential advantages in variable speed generation and adjustable speed drive applications The most significant of these advantages is a reduction in the power electronic converter rating and therefore a reduction in overall system cost Presently efforts are being directed at optimizing the design of the BDFM and investigating areas of commercial feasibility One possible aid in the investigation of design alternatives is finite element analysis Finite element analysis is a numerical method for determining the field distribution in a dimensional model Finite element techniques have been successfully used for some time in the design of induction reluctance and permanent magnet machines However the characteristics of the BDFM require adjustment of the finite element design procedure used for conventional singly fed induction machines In this thesis a three dimensional finite element design procedure for modeling the BDFM has been developed This design procedure avoids the difficulties previously associated with finite element modeling of the BDFM The three dimensional
32. BDFM research and design group for their helpful suggestions about my work during BDFM meetings and other times Shibashis Bhowmik Michael Boger Bhanu Gorti Tim Lewis Sreekumar Natarajan Arif Salim Ernesto Weidenbrug and Donsheng Zhou I would like to thank Arif Salim for introducing me to finite element analysis and teaching me how to use Maxwell 2D Field Simulator by Ansoft Corporation I would like to thank James Neuner and Pat Lamers members of the Macneal Schwendler customer support staff for their willingness to answer questions about Macneal Schwendler s software in a timely manner Their help was very valuable in learning how to use this software I would like to thank Tom Lieuallan for his help in setting up the HP workstation installing the finite element software and for his willingness to provide help whenever I had a computer question or problem I would like to thank Ed Lake for helping me to proofread my thesis and for his help instructing me in the creation of the figures contained in this thesis with AutoCad Finally I would like to thank my parents and close friends for their love support and encouragement during my years at Oregon State University Table of Content T trod ctiO Eich cs ses gases wy ace cdnn ceadavs cet eo veeee eens en Io ee eae 1 Brushless Doubly Fed Machine wcccnccscisscscacdscessiceoresssaraciesseaveiassnvtacsoventseseataceeaenescases 3 2 1 BDFM Characteristics osciscs sishepestydeesseq
33. Button The left mouse button is used to pick items from the cascading menus the quick access menu QAM the graphics tile or the history tile e Change Button The middle mouse button is used to toggle items in the QAM activate pop up choices in the QAM activate blue bar input in pop up menus and act as a return key for blue bar input Calculate CurrentFrosH Field Results XY Plotting Interface with Curves Surfaces solids Coord Systems Delete Items Display Items Erase Items Graph Point Translate Point Rotate Point Scale Unifora Point Scale WonUniform Point Reflect Point Extract Point Intersect Curves Intersect Surfaces Project Point PointDistance Database reallabmach db Application MSC EMAS AC QAM Quick Access Menu Cascading menus Graphics tile History tile A replay on 1 Done gt Replay On Erase refresh Done gt Refresh View 1 NoFind Erase NoCenter Complete WireFrame Undeformed SoPlot MoArrow off vv Figure A 1 MSC XL Screen Layout 69 70 e Cancel Button The right mouse button is used to close a pop up menu or cancel blue bar input in a pop up menu A 2 3 Capabilities MSC XL supports all aspects of model building Model geometry is specified by defining various geometric entities including points curves surfaces solids and coordinate systems Meshing procedures are then used to subdivide geometric entities into meshes containing finite elements connected to grid po
34. ESIS submitted to Oregon State University in partial fulfillment of the requirements for the degree of Master of Science Completed January 17 1995 Commencement June 1995 Master of Science thesis of Brenda E Thompson presented on January 17 1995 APPROVED Redacted for Privacy Major Professor representing Electrical and Computer Engineering Redacted for Privacy Chair of Department of Electrical and Computer Engineering Redacted for Privacy Dean of Graduate ei a q i I understand that my thesis will become part of the permanent collection of Oregon State University libraries My signature below authorizes release of my thesis to any reader upon request Redacted for Privacy Brenda E Thompson Authbr ACKNOWLEDGMENTS I would like to thank my major professor Dr Alan Wallace for the amount of time and effort he has put into guiding me towards the completion of my thesis for first suggesting that I get involved in working with finite element analysis of the BDFM and for his willingness to help when I had questions about the BDFM or my finite element results I would also like to thank Dr Rene Spee and Dr G C Alexander for their helpful suggestions about my finite element work and other topics Special thanks to Dr Alan Wallace Dr Molly Shor Dr G C Alexander and Dr David Butler Graduate Council Representative for being on my defense committee I would like to thank all the student members of the
35. asily refine the mesh as with a solid modeler A solid modeler similar to that of Maxwell 3D Field Simulator would be beneficial for MacNeal Schwendler users MSC made available in September 1994 a new graphical pre and post processor called MSC ARIES meant to replace MSC XL which uses a solid modeling procedure MSC ARIES was not used for the work done in this thesis due to its late arrival 5 3 2 2 No Step by Step Procedure Menu MSC XL does not contain a main step by step procedure menu New users who are not familiar with the basic steps involved in finite element modeling would probably find MacNeal Schwendler s programs difficult to learn to use A step by step main menu similar to that of Maxwell 3D Field Simulator would make MSC XL easier and more intuitive to use 60 6 Conclusions and Recommendations The characteristics of the BDFM require adjustment of the finite element design procedure used for conventional singly fed induction machines In this thesis a three dimensional finite element design procedure for modeling the BDFM has been developed This thesis has shown how the difficulties previously associated with finite element modeling of the BDFM have been overcome Three dimensional finite element analysis of the BDFM was investigated which allows the nested loop structure of the BDFM rotor to be modeled It has been shown how an ac analysis of the BDFM using the rotor reference frame frequency as the solution fre
36. ation messages The only information provided to the user about the solution status was a shaded bar ranging from 0 to 100 percent that would appear on the screen supposedly to allow the user to monitor the progress of the system in completing the solution This presented the problem that sometimes the program would continue to solve sometimes for over one week with the shaded bar still at 0 percent and no other information available The program did not display any error or information messages such as disk full more swap space needed more memory needed etc to let the user know what was happening or what problems had been encountered The user was unaware whether to continue to let the program solve or to choose to terminate and make modifications Occasionally the solution process would cause the system to crash No error or information messages were available to the user about what caused such a crash 5 2 2 4 Poor Customer Support In addition to having no error messages available poor customer support was provided for Maxwell 3D Field Simulator Customer support was unable to identify exactly why the program was unable to solve the problem The only information provided by customer support was that the problem size was too large and more swap space was needed However they were unable to tell how much swap space was 56 needed Also customer support would often not even answer the questions e mailed to them
37. ations 4 2 1 Complications of the Nested Rotor Structure Because of the nested loop rotor structure the absence of a solid endring on one side the BDFM analysis problem is three dimensional in nature The nested loops impose electrical constraints on the model that cannot be properly represented with a two dimensional analysis 4 2 2 Inclusion of Two Excitation Frequencies The presence of two stator windings carrying currents of differing frequencies requires the consideration of two frequencies at any time This poses a problem because the ac solution method requires that a single solution frequency be specified 4 2 3 Boundary Conditions More Difficult to Determine The symmetry of the magnetic field distribution in the BDFM is not as simple to determine as that of an induction machine because of the presence of the two stator windings of different pole numbers Thus determining the section of the BDFM that should be modeled to properly represent the entire machine and the selection of the appropriate boundary conditions requires some consideration 16 This chapter discusses how these difficulties have been dealt with and a finite element procedure for modeling the BDFM has been developed 4 3 Three Dimensional Simulation of the BDFM Because the BDFM analysis problem is three dimensional in nature three dimensional finite element modeling of the BDFM has been investigated A three dimensional analysis avoids the a
38. behavior including electrostatics magnetostatics eddy currents waveguides antennas etc Thus Maxwell s equations form the basis for the analysis of virtually every electromagnetic device from computer microcircuitry to large power generators and transformers Maxwell s equations 10 are traditionally written as gt V D P ree Equation 3 1 V B 0 Equation 3 2 Vx E B Equation 3 3 VKH I 4D Equation 3 4 These four equations state the following Gauss s law the sources of D are free charge e B has no sources Faraday s law electric fields are induced by time varying magnetic fields Ampere s law the sources of H are conduction current plus the displacement current The fields electric field E and magnetic field B are the primary unknown quantities of interest in electromagnetic field analysis However there are three disadvantages to solving directly for the unknown vectors E and B First the six unknown components of these two fields in three dimensional space cannot be chosen arbitrarily because they are related through Maxwell s equations Thus the number of unknowns is larger than is actually needed The second disadvantage is related to discontinuities in material properties There are two well known boundary conditions that must be met at such interfaces 1 the normal component of D must be continuous across the interface 2 the tangent component of H must be continuous Any soluti
39. chine body be divided in three to four lengthwise sets of elements The nested loop end connections and the endring are sets of elements that extend beyond the machine body on opposite ends of the model It is recommended that the nested loop end connections and the endring be divided into two to three lengthwise sets of elements The two layers of air elements on each end of the machine are included to account for leakage effects on the end of the machine rather than causing the fields to be abruptly chopped off at the machine ends It is recommended that one set of lengthwise air elements be included on each machine end The detailed 180 degree model of the BDFM lab machine was constructed with two sets of lengthwise elements along the machine body one set of elements each for the nested loop end connections and the endring and without air elements on each end to reduce disk space requirements for solving the model Two dimensional elements can be extruded to form three dimensional elements in MSC XL by using the Extrude Element 2D option as follows 1 Select the part identification number for the part where the newly created three dimensional elements are to be placed 2 Choose FEM Mesh gt Extrude Element 2D from the cascading menus 110 3 Inthe pop up menu enter the following parameters NoMidNode Midnode Specifies whether the elements will contain midnodes quadratic elements Iterate The number of t
40. cified in relation to an existing coordinate system e Type Cylindrical The type of new coordinate system e CID 0 The identification number of the existing coordinate system on which the new coordinate system is based e Output 1 The identification number of the new coordinate system A 4 2 3 Creating Points Geometry is created by first defining points Points are created along the x axis of the basic coordinate system at the x coordinate positions labeled in Figure A 4 Points are created along the x axis by using the Define Point option A 4 2 3 1 Define Point Points can be created using the Define Point option as follows 1 Pick Geometry Points gt Define Point gt At XYZ from the cascading menus 2 Inthe pop up menu enter the following parameters e X Y Z Defines the coordinates of the point Enter the distance from the origin as the x coordinate 82 e CID The identification number of the coordinate system used to define the point e Output Each point is given an identification number as it is created Points are numbered in the order that they are created A 4 2 4 Creating Curves Once points have been specified along the x axis the next step is to create curves A curve will be created for every curve present in Figure A 4 Curves can be created by connecting points sweeping points reflecting curves rotating curves and defining curves Each of these operations is described here A 4 2
41. cnsesassedatacaiasaictansesdenchicstsanaseeaeves 79 A 4 2 1 Undo Command and Delete Item Option 0 79 A 4 2 2 Defining a New Coordinate System ccccccccseseeseeeesees 80 A425 Creatine Points ineco ninn ni aa a i aiara 81 AS 23 1 Deine Poi tninoicsenrninnireeni aihe 81 A AZ 4 Creatine Curves 5 sicctiut sistent ret alae ara a aiT 82 AAZA YL Connect Points se iesetireisinicsssecsariadstbecarweravieceeaees 82 A 4 2 4 2 Sweep Point vicsicsieletass Sicccesi acts sesvslnitaczatadenes 83 A 4 2 4 3 Reflect Curve oo cccccccccccccssecesesssssctccccccsccseeeeeese 84 A 4 2 4 4 Rotate Curve o oo eeccccccccccececeesessecstsncnccccccceceesees 84 Ai 4245 Define Carve x sasasedcon Seatectecsdesteeeyeeieaneietass 86 ALA 2 5 Creating Surfaces occisi tetris erence hen unease 87 A 4 3 Generating Finite Elements ccccccscesssesscessseseeeesceesccessesseeseees 87 A 4 3 1 Finite Element Terminology ccccccsccscsccscssseseeseeeeesees 88 A431 Grid Points scini nsoni ainen 88 PA Slice Elementsin innanti 89 A 4 3 2 Key Factors in Meshing cccccseseesseeseeeeceseeeeseeseeeaees 89 A 4 3 2 1 Element Choice seseeesensesesssesessssisnsrosessosesresesse 90 A 4 3 2 2 Element Connections c ccccccessesestsesseseeeseens 91 A 4 3 2 3 Mesh DENSItYy ieisirisinraserseriiiriiiiiriieate 92 A 4 3 2 4 Mesh Order scissile oesessessessssssesresssresoseororossesseseses 92 A 4 3 2 5 Elemen
42. d in the analysis simultaneously 4 3 2 Symmetry of the BDFM Model In induction machine analysis it has been shown that only one pole pitch of the machine needs to be modeled because of the symmetry of the magnetic field distribution by pole pitch The magnetic field symmetry of the BDFM model is not as simple to determine because of the presence of two stator windings of different pole numbers The finite element model of the BDFM presented in this thesis is based on the 5 horsepower BDFM laboratory machine The laboratory machine has a 6 pole power winding and 2 pole control winding configuration Theoretically the alternating periodic boundary conditions used to model induction machines should be appropriate for a 180 degree model of a 6 2 pole BDFM This is because one pole of the two pole winding and three poles of the six pole winding are present in a 180 degree model Therefore an odd number of poles is modeled for both windings Since alternating periodic boundary conditions are required for an odd number of poles theoretically alternating periodic boundary conditions should be the 19 appropriate boundary conditions for a 6 2 pole 180 degree BDFM model Results of the BDFM model simulations presented in this chapter verify this idea The MSC EMAS Modeling Guide 13 suggests that the best way to determine the correct boundary conditions is to make a coarse finite element model of the entire device and observe the relationship ob
43. degree model was calculated using the same method discussed previously The currents were again calculated at several axial z positions along each rotor bar and identical results were obtained The calculated total currents in each rotor bar are presented in Table 4 4 and the rotor bar labels are identified in Figure 4 15 LE qT i C J l Eg z z Sr e ee x a e a Wj My Mr 5 L9 Yj 5 My A AU N NNN Y S SS AV A 2 i Figure 4 15 Rotor Bars Labels for the Detailed 180 Degree BDFM Model 42 The rotor bar currents are equal in magnitude and 180 degrees out of phase for rotor bars connected by a loop The magnitude of the rotor bar currents becomes greater as the slot span of the loops becomes larger moving from the inner to outer loops Figure 4 16 is a graph of slot span vs rotor bar current magnitude which shows that the current magnitude increases from the inner to outer loops Bar Number Real Imaginary Magnitude Phase Amperes Amperes Degrees 2 3 10542 0 175448 3 11038 3 23362 _ s 11 1839 12 7192 16 9368 48 675 _ ae 30 2753 140 761 143 98 77 8615 8 09887 75 7353 76 1671 96 1038 20 010270078 0 372556 0 373534 85 8537 Table 4 4 Total Calculated Currents in the Rotor Bars for the Detailed 180
44. density can be calculated by dividing the total peak current flowing the slot 100 amperes by the total cross sectional area of the slot being excited CID The chosen coordinate system It is easy to use the default Cartesian coordinate system to define current density excitations Dirl1 2 3 Specify the direction of the excitation Dirl Dir2 Dir3 correspond to X Y Z in Cartesian coordinates If the length of the machine has been defined in the Z direction the current density will have a positive or negative Z direction only as in Tables A 6 and A 7 It is important to visually check each excitation as it is being applied Each current density excitation is represented visually by an arrow which indicates the direction of the excitation The current density excitation label includes the excitation 122 ID followed by a comma followed by the current density magnitude Displaying a 3 D view of only the stator windings while the excitations are being applied makes it easy to see where an excitation has been applied In an AC analysis a phase angle must be assigned for each excitation A multi phase analysis can be achieved by defining multiple excitations each with differing phase angles A phase angle is assigned to each excitation group as shown in Tables A 6 and A 7 for the BDFM To enter a phase angle for an AC excitation choose FEM gt Excitation Phase from the cascading menus and enter a phase angle degrees for the cho
45. dustry Conference 1990 pp 45 50 2 H K Lauw Characteristics and Analysis of the Brushless Doubly Fed Machine Final Report U S Department of Energy Contract No 79 85BP24332 June 1989 3 R Spee A K Wallace and H K Lauw Simulation of Brushless Doubly Fed Adjustable Speed Drives JEEE IAS Annual Meeting Conference Record 1989 pp 738 743 4 A K Wallace R Spee and H K Lauw Dynamic Modeling of Brushless Doubly Fed Machines JEEE IAS Annual Meeting Conference Record 1989 pp 329 334 5 R Li R Spee and A K Wallace Synchronous Drive Performance of Brushless Doubly Fed Motors IEEE IAS Annual Meeting Conference Record 1992 pp 631 638 6 L J Hunt A New Type of Induction Motor Journal IEE London 1907 vol 39 pp 648 677 7 F Creedy Some Developments in Multispeed Cascade Induction Motors Journal IEE London 1927 vol 59 pp 511 532 8 A R W Broadway and L Burbridge Self Cascaded Machine A Low Speed Motor or High Frequency Brushless Alternator Proceedings IEE London 1970 vol 117 pp 1277 1290 9 M A Salim and R Spee High Frequency Cage Rotor Designs JEEE IAS Annual Meeting Conference Record 1992 pp 18 24 10 J R Brauer B E MacNeal and J C Neuner MSC EMAS User s Manual The MacNeal Schwendler Corporation July 1994 11 J R Brauer A Frenkel and M A Gockel Complex Periodic Boundary Conditions
46. e The field results will be defined at the element centroid and at each of the corner grid points and midside grid points for any quadratic elements 131 The selection of either of the last two options will result in the creation of additional sets of ElementResults in the ResultsTable known as element nodal results or GPFields The MSC EMAS User s Manual describes the use of GPFields in post processing calculations as being more accurate However for the BDFM models the selection of CenterCorner and the use of GPFields caused problems in the calculation of total rotor bar currents and was found to produce inaccurate results Therefore the selection of Center as the output method for field quantities is recommended 4 Toggle Restart to On to do a restart of a previous analysis Select an existing MASTER file for the restart The above procedure will automatically invoke MSC EMAS and start the solution process A 4 5 2 System Requirements System requirements are important to keep in mind while constructing the finite element mesh and before the finite element model is run The work presented in this thesis was done on a Hewlett Packard 715 50 workstation with 48 MB of RAM and approximately 2 5 GB of hard disk space The system requirement of most concern for the models presented in this thesis was disk space since MSC EMAS creates very large output files and scratch files during the solution process The disk space requirem
47. e extrusion is the easiest method for creating a three dimensional BDFM model only PENTA and HEXA elements are used in the three dimensional BDFM finite element model Generally the most cost efficient results are obtained using QUAD and HEXA elements with nominal rectangular geometries These should be used throughout the mesh wherever the geometry allows A 4 3 2 2 Element Connections In connecting elements the following rules should be observed e Discontinuities in material properties or excitations should coincide with element boundaries In other words a transition between a steel rotor 92 and a copper rotor bar must occur at element boundaries not within an element If the geometry has been created properly this should not be a problem e Elements must share common grid points along boundaries In other words elements must match up along boundaries not be randomly connected to grid points A 4 3 2 3 Mesh Density Element density is a tradeoff between accuracy and solution cost Solution accuracy is determined by how fast field values change with position field gradients and the number of elements per unit length Mesh density may also be dictated by fine geometric detail Users must use engineering judgment and knowledge of field distributions to identify regions of high field gradients that require fine mesh density In the BDFM model high field gradients will usually be found in and surrounding the air gap and r
48. e of the 180 degree model Periodic boundary conditions are a type of dependent potential or multi point constraint MPC MPCs relate a potential of one grid point to a potential of another through a constant coefficient The easiest way to apply alternating periodic boundary conditions to the BDFM 180 degree model is to use the Periodic option as follows 1 Choose FEM gt BoundaryCondition and choose an arbitrary boundary condition identification number 2 Choose FEM gt BoundaryCondition Edit DependentPotential gt Periodic 3 Inthe pop up menu choose Alternating to force all of the grid point potentials on the two planes to be equal in value but opposite in sign Together the CID1 and Planel pop up entries define the dependent constant plane of grid points Similarly CID2 and Plane2 defines the independent 128 constant plane of grid points CID represents the coordinate system in which the plane is constant For the BDFM half model choose the defined cylindrical coordinate system for both CID1 and CID2 the choose 9 0 for Planel and 6 180 for Plane2 This will relate all potentials A Ag A y of the 6 0 plane to all potentials of the 6 180 plane It is important to note that a single grid point cannot simultaneously be constrained by a SPC and a MPC To do so causes a fatal error in MSC EMAS When SPCs are applied using the ByCSPlane option and MPCs are applied using the periodic option SPCs and MPCs will b
49. e resulting 90 degree section is rotated once about the 0 90 degree plane Elements can be reflected in MSC XL as follows 1 Pick FEM gt Element Reflect Element gt Coordinate System from the cascading menus 2 In the pop up menu enter the following parameters e Create Modify Specifies if existing elements are to be modified or new ones created e ExistID Identification numbers of elements to be reflected e CID The identification number of the coordinate system in which the reflection will occur e Plane The plane across which the elements will be reflected e Output The identification numbers of the new elements Similarly elements can be rotated in MSC XL as follows 1 Pick FEM gt Element Rotate Element from the cascading menus 2 In the pop up menu enter the following parameters 101 e Create Modify Specifies if existing elements are to be modified or new ones created e Iterate The number of times that the rotation is to be performed e ExistID Identification numbers of elements to be rotated e From X Y Z Define the center of rotation e To X Y Z Together with From X Y Z define the axis of rotation e Angle The angle through which the elements are to be rotated e Offset The initial offset angle before the rotation begins e CID The identification number of the coordinate system in which the reflection will occur e Output The identification numbers of the new elements A 4 3
50. e rotor laminations are shown in Figure 4 2 The rotor laminations were custom made to provide an air gap of 0 7 mm The rotor was designed with 40 slots For the 6 2 pole BDFM the required 4 nests have 5 loops each and no common cage 7 944 po 5 97 MN N79 dia 55 59 dia 6 76 5 30 All measurements are in millimeters mm dia 165 80 Figure 4 2 Rotor Lamination 10 16 6 86 36 identical slots 3 1 7 Slot Detail Stator Lamination 1 2 Size Figure 4 1 Stator Lamination 22 82 1 08 IZ 22 4 4 2 A Coarse 360 Degree BDFM Model A coarse 360 degree three dimensional finite element model of the BDFM was constructed The main goal in construction of this model was to determine if magnetic field symmetry exists within the BDFM and to verify what portion of the device can be modeled using appropriate boundary conditions to accurately represent the whole machine The 360 degree model had a rather coarse finite element mesh consisting of 7776 hexahedron and pentahedron elements and 8325 grid points The finite element model is shown in Figure 4 3 seg SS BUGA Y ea Ch oes Y N ON OE OES a a ae 25 2s lt gt lj pa aana Q AT V P NW an NA AA AENDA KZ QDYRQUBOA FA SSSR WSS ie DANAA NSE S S SIG Mj Ap Oa iN YZ KAAYA IRAN LIN Figure 4 3 Coarse Three Dimen
51. ection elements should be observed e Density Element and grid point density determines overall solution accuracy e Order The polynomial order or degree used for interpolation within each element affects solution accuracy e Distortion Elements may be somewhat distorted relative to their nominal geometries to accommodate geometry but such distortions affect accuracy The best mesh results from a tradeoff between model requirements accuracy and system requirements such as disk space available A 4 3 2 1 Element Choice Available elements in MSC XL are grouped into categories based on element dimensionality Different types within each category have different nominal geometries The basic element categories are three dimensional two dimensional axisymmetric one dimensional open boundary circuit elements and scalar elements Choice of elements depends on model requirements Since a three dimensional BDFM model is to be constructed three dimensional elements will be used These three dimensional elements will be created by extruding two dimensional elements Two and three dimensional elements available in MSC XL are shown in Figure A 6 91 fo 2 D Elements TETRA HEXA PENTA 3 D Elements Figure A 6 Available Two and Three Dimensional Elements Extruding a TRIA element results in a PENTA element extruding a QUAD element results ina HEXA element TETRA elements are formed by methods other than extrusion Sinc
52. ee and other suggestions to help users select the appropriate solution method for their particular problem 5 3 1 2 Well Documented Program Diagnostics MSC EMAS errors are well documented There are literally thousands of different fatal error warning and information messages that can be issued by the program These error messages each are assigned a number Errors found during the solution process are listed in the lt filename f06 gt file one of the output files of MSC EMAS Each message includes a brief explanation More detailed explanations are contained in Chapter 6 of the MSC EMAS User s Manual 10 If the program is unable to solve the problem for some reason the solution is automatically terminated within about one hour at maximum and an explanatory message is issued in the lt filename f06 gt file 5 3 1 3 Setup Parameters are Saved and only have to be Entered Once In MSC XL the setup parameters of the finite element model the material properties excitations and boundary conditions are each assigned an identifying 58 number and are saved as they are created so that they only have to be entered once During the analysis preparation step excitations and boundary conditions to be included in the analysis are selected by identification number All of the excitation and boundary conditions can be included or only selected ones If a modification needs to be made the appropriate material property or excitation ident
53. eeetseeees Contour Plot of Magnetic Vector Potential along a Center Cross Section of the 360 Degree BDFM Model vi o0csies siccde ties tea acevcndenscstaaceesbatiabeaecvectiadstnnndaled Arrow Plot of Magnetic Flux Density along a Center Cross Section of the 360 Degree BDFM Model xt ssivesccarssssosooxsssitavensctisdesaeotorniestienedtvensens wueetaeees Rotor Bar Labels for the 360 Degree BDFM Model 0 cccccscccssesseeseeeseeeseesees Coarse Three Dimensional 180 degree BDFM Finite Element Model Boundary Conditions for the Coarse 180 Degree BDFM Model 0 c000 Contour Plot of Magnetic Vector Potential along a Center Cross Section of the Coarse 180 Degree BDFM Model cccececsessssseceseesesssessessseseeneeseeeetenees Arrow Plot of Magnetic Flux Density along a Center Cross Section of the Coarse 180 Degree BDFM Model asiisccsicciscass casts lactucsaesaetidesncthncadeversosasdaedveviee Rotor Bar Labels for the Coarse 180 Degree BDFM Model ccccscesseesseeeees Detailed Three Dimensional 180 degree BDFM Finite Element Model Rotor Bar Labels for the Detailed 180 Degree BDFM Model cccesceee Slot Span vs Rotor Bar Current Magnitude 0 0 0 cccccscceseceesessesssseeseesesseesessens 4 17 Path along which Conduction Current Density was Plotted from Bottom to Top 45 4 18 Conduction Current Density in Bar 6 in reference to Figure 4 17 c e 46 4 19 Conduct
54. elements e ViewID 1 The identification number for the view from which the items are to be selected e PartIdList 0 The identification number for the parts from which the items are to be selected e Windowmode View The type of window to use in the grouping View is the entire screen view e CollectMode Inside Whether items to be grouped lie inside or outside the window e BoundaryMode Include Whether items intersecting the window boundary are to be included or excluded from consideration for group selection A 4 3 6 2 Using Parts A part is a method of grouping elements such that they can selectively be displayed or removed from the screen Use of parts allows sections of the model to be viewed separately on the screen and is a useful model checking tool One part with identifier 0 is automatically defined in MSC XL All entities are placed in part 0 by default unless new parts are created It is not really necessary to place elements of the two dimensional mesh into separate parts however it is useful for checking purposes to create additional parts before the three dimensional mesh is 108 created It is helpful to create a part for every object present in the three dimensional model such as the rotor stator air gap rotor bars etc Elements are then placed in selected parts as they are created This later allows each object making up the three dimensional model to be viewed separately from the r
55. ement corners are called corner nodes Grid points that lie along the element faces are called midedge nodes In the solution process potential values are directly calculated only at grid points Four potential degrees of freedom DOF three A components and are defined at each grid point Boundary conditions are applied to potential DOFs at grid points 89 A 4 3 1 2 Elements An element is the connection between grid points that embodies the spatial properties of the model Elements are assigned material properties of permeability permittivity and conductivity Excitations are also applied to elements The user must decide to construct either first order or second order elements In first order elements with only corner nodes potentials vary linearly along the element edges Interpolation of field values inside first order elements involves low order polynomials Second order elements contain midedge nodes between corner nodes and potentials vary quadratically along the element edges Figure A 5 illustrates the concept of grid points elements corner nodes and midedge nodes MODEL VOLUME CORNER NODE X GRID POINTS MIDEDGE NODE a Figure A 5 Finite Elements and Grid Points A 4 3 2 Key Factors in Meshing Key factors to consider in constructing the finite element mesh include e Element Choice the different types of elements available in MSC XL will be discussed 90 e Element Connections several rules for conn
56. en the permittivity is isotropic and its permittivity matrix e has zero off diagonal elements and the same values for the on diagonal elements Thus in the isotropic case only one number is needed to fully describe permittivity the scalar relative permittivity e Most materials have a constant isotropic permittivity because their relationship between D and is linear and the same in all directions 113 A 4 4 1 1 2 Anisotropic Symmetric Permittivity In anisotropic dielectrics permittivity changes with direction relative to the material and the polarization is no longer always parallel to the electric field This property is represented by specifying off diagonal as well as diagonal terms for the relative dielectric tensor The terms can be specified in Cartesian cylindrical or spherical coordinate systems A 4 4 1 1 3 Unsymmetric Permittivity There exist materials called ferroelectrics in which D is a nonlinear function of Although they are not very commonly used MSC XL allows unsymmetric permittivities to be specified A 4 4 1 2 Conductivity Conductivity o defines how currents are proportional to electric fields Ohm s law J o E Equation A 3 where J is the current density amps meter in MKS is electric field volts meter in MKS and o is the conductivity tensor Ohm meter in MKS The tensor conductivity matrix o is 114 On On O33 o 0 Cn O3 Equation A 4 G3 Gx O
57. ents of MSC EMAS vary depending on 132 the number of grid points in the model the number of degrees of freedom the chosen solution sequence output requests and other factors A graph estimating the amount of disk space required vs the number of grid points contained in a finite element model is included in the MSC EMAS Installation Procedures for HP 9000 7000 HP UX Guide 17 This graph is reproduced for convenience in Figure A 11 The data plotted in Figure A 11 represents two sets of problems The lower line represents typical two dimensional engineering problems the model is a flat plate The upper line represents a highly connected model the model is a cubical solid The data was generated for a static analysis using MSC NASTRAN solution Sequence 101 this would be similar to running a static analysis in MSC EMAS 17 The MSC EMAS AC BDFM model simulations presented in this thesis were found to approximately follow the cellular cube line of Figure A 11 The largest BDFM model that ran to completion with the existing system configuration was the detailed 180 degree BDFM model which contained 9510 grid points A 4 5 3 Solution Time The solution time for the BDFM models presented in this thesis was not a major consideration The time that MSC EMAS takes to generate a solution varies depending on the number of grid points in the model the number of degrees of freedom the chosen solution sequence output requests and o
58. ess and automated meshing technique 5 2 1 1 Solid Modeling Procedure In a solid modeler the finite element model is defined by the device structure or geometry which consists of a group of solid objects Throughout the modeling 50 process the solid objects that define the model are manipulated by referring to their names For example as the device structure or geometry is being created solid objects such as cylinders blocks spheres etc are each assigned a name Objects can then be rotated copied displayed or removed from the display and have material properties assigned to them by referring to their names This is a very convenient and easy way of manipulating the device geometry The main advantage of a solid modeling procedure is that the finite element model is defined by its geometry a set of solid objects and not by the finite element mesh itself This allows the mesh to be easily modified if necessary without having to redefine that entire model The mesh can be refined throughout the model or only ina particular object by specifying the object name The solid modeling procedure is one major advantage that Maxwell 3D Field Simulator has over MSC XL MSC XL uses a wireframe modeling procedure in which the finite element model is defined by the actual finite elements and grid points A wireframe modeler is more difficult to use than a solid modeler A wireframe model is manipulated by referring to collections of
59. est of the model New parts are created in MSC XL simply by picking Part selecting New and giving the new part an identification number Before a group of two dimensional elements is extruded to form three dimensional elements the appropriate part number should be selected by choosing its number All entities such as elements are placed in the currently selected part as they are created A 4 3 7 Extruding the Two Dimensional Mesh to Make a Three Dimensional Mesh Once a 180 degree two dimensional finite element mesh of the BDFM cross section has been completed a three dimensional mesh of the BDFM model can be created The three dimensional mesh will be created by extruding sections of the two dimensional mesh to create each of the three dimensional BDFM model objects as previously discussed in the section on assigning PIDs The two dimensional mesh lies in the Z 0 plane unless otherwise defined The origin 0 0 0 will be the center of the machine model and three dimensional elements will be formed by extrusion in both the positive and negative Z directions 109 The three dimensional BDFM finite element mesh should consist of several lengthwise sections These sections are the machine body the nested loop end connections the endring and two layers of air elements on each end of the machine The machine body includes the shaft rotor rotor bars air gap stator slots and stator It is recommended that the ma
60. eyed by the vector potential A at grid points one pole pitch or other distance apart Then these constraints are applied to a fine finite element model of that portion of the device 4 4 Results of BDFM Model Simulations Several three dimensional BDFM models were constructed and analyzed using MSC EMAS First results from a coarse 360 degree model of the BDFM are presented Next results from a 180 degree model with a finite element mesh identical to the 360 degree model and with alternating periodic boundary conditions applied along the symmetry plane are presented Comparison of the full model and half model results verifies that the alternating periodic boundary conditions are correct Finally results from a more detailed 180 degree BDFM model are presented For each analysis synchronous operation of the BDFM is assumed and the ac analysis module is used It should be noted that the ac analysis module is a linear analysis module that does not take into account the B H curve of magnetic materials 20 4 4 1 Device Geometry Each of the three dimensional finite element BDFM models was based on the 5 horsepower laboratory machine The dimensions of the laboratory machine stator laminations are shown in Figure 4 1 shown on the following page The stator windings consist of a 6 pole power winding and a 2 pole control winding The stator contains 36 slots and the stator stack length is 100 mm The dimensions of the laboratory machin
61. faster much easier for the 53 user and reduces the chance of user error An automated meshing technique is definitely a benefit for new users 5 2 2 Disadvantages Limitations 5 2 2 1 Only Two Analysis Modules Available At the time of this evaluation Maxwell 3D Field Simulator included only two analysis modules or solution methods that were available as full releases These were the Electrostat module and the Magnetostat module The Electrostat module is used to compute static electric fields due to voltage distributions and charges It has no use for the BDFM analysis problem The Magnetostat module is used to compute static magnetic fields due to DC currents static external magnetic fields and permanent magnets It has some use for the BDFM problem if the rotor bar currents are already known from lab data and the magnetic field distribution and magnitude needs to be calculated It cannot be used to calculate induced currents in the rotor conductors one of the main quantities of interest in the BDFM analysis problem The Maxwell 3D Field Simulator analysis module that was used predominately was the Eddy Current module This module can be used to calculate time varying magnetic fields due to AC currents and oscillating external magnetic fields It should be used for the BDFM problem to calculate currents induced in the rotor bars by the AC three phase stator windings However at the time of evaluation the Eddy Current 54 Modu
62. finite element design procedure developed in this thesis was used to model the 6 2 pole 5 horsepower BDFM laboratory machine From the simulation results the induced currents in the BDFM rotor bars were calculated In the course of investigating three dimensional finite element analysis for the BDFM two different commercially available finite element analysis software packages were examined and tested The first was Maxwell 3D Field Simulator produced by Ansoft Corporation and the second was MSC EMAS Electromagnetic Analysis System and MSC XL by MacNeal Schwendler Corporation These two software packages are compared and their advantages and disadvantages limitations are discussed A tutorial for setting up and solving a three dimensional BDFM model using MSC XL and MSC EMAS is presented This goal of this tutorial is to guide a new user of MSC XL and MSC EMAS through the creation setup simulation and analysis of a BDFM model This tutorial contains condensed information included in the MSC XL and MSC EMAS program documentation provided by MacNeal Schwendler In addition modeling techniques particular to the BDFM which are not included in the program documentation are described This tutorial is applicable only to those individuals interested in learning how to use MSC XL and MSC EMAS in order to simulate a BDFM model Three Dimensional Finite Element Design Procedure for the Brushless Doubly Fed Machine by Brenda E Thompson A TH
63. form the entire section of the machine being modeled The BDFM lab machine geometry shown in Figure A 4 exhibits 45 degree radial symmetry for the rotor and 5 degree symmetry for the stator Since the rotor and stator structure exhibit different degrees of radial symmetry two dimensional rotor and a stator radial wedges are created and meshed separately from each other First the 45 degree rotor wedge is created and meshed Then the 5 degree stator wedge is created meshed and reflected and rotated to create a 45 degree wedge The rotor and stator meshes are then connected by meshing the air gap Once a 45 degree model of the rotor stator and air gap is completed this section can be reflected and rotated to create a two dimensional 180 degree model Finally selected sections of the two dimensional mesh are extruded to form a three dimensional 180 degree model A 4 1 3 Entering MSC XL To begin an MSC XL session follow these steps 1 Type xl at the system prompt 2 In the Choose a Database File pop up menu pick an existing file or pick New and enter the new filename in the blue bar 3 Inthe Choose Application pop up menu pick MSC EMAS 4 Inthe Choose Subapplication pop up menu pick the subapplication to be used for this analysis The subapplication can easily be changed later by clicking on Application MSC EMAS Subapplication in the logo tile 79 A 4 2 Creating Geometry The first step in building a finite element mode
64. g a cross section of the BDFM located at the machine center is shown in Figure 4 11 This contour plot of magnetic vector potential is identical to Figure 4 6 the contour plot of magnetic vector potential for the 360 degree model This contour plot is one verification that the alternating periodic boundary conditions are correct 36 4 4 3 2 2 Arrow Plot of Magnetic Flux Density An arrow plot of magnetic flux density B along a cross section of the BDFM located at the machine center is shown in Figure 4 12 This arrow plot of magnetic flux density is almost exactly identical to Figure 4 7 the arrow plot of magnetic flux density for the 360 degree model This arrow plot is another verification that the selected alternating periodic boundary conditions are correct 4 4 3 2 3 Currents in the Rotor Bars The total current flowing in each rotor bar of the 180 degree model was calculated using the same method used for the 360 degree model The currents were again calculated at several axial z positions along each rotor bar and identical results were obtained The calculated total currents in each rotor bar are presented in Table 4 3 and the rotor bar labels are identified in Figure 4 13 Bar Number Real Imaginary Magnitude Phase Amperes Amperes Degrees 132 462 33 4865 136 629 165 813 8 29692 25 0857 26 4222 71 6987 30 8917 186 883 189 419 80 6139 7 13535 87 3859 87 6767 94 668
65. g in a crack or seam in the model Cracks usually represent a modeling error that must be corrected Duplicate grid points within the model will always produce free edges and free faces Duplicate grids should therefore be eliminated before trying to find free edges and faces Cracks in the interior of the mesh with causes other than duplicate grids can then be isolated and identified It is important to identify and correct all free edges in the two dimensional mesh before extruding to create a three dimensional mesh Free faces are usually the result of extruding a two dimensional mesh that has unidentified free edges The possibility of having a three dimensional model with free faces can almost be eliminated if free edges in the two dimensional model are corrected Also free edges are much easier to locate visually The easiest way to check for free edges or free faces that occur interior to the model boundaries is to have MSC XL plot free edges or free faces This can be done be picking FEM Check FEM gt Free Edges or Free Faces Find It is helpful to enter the command Refresh AxesOnly in the Blue Bar before finding the free edges or free faces because then only the free edges or faces are displayed not the entire finite element model when a subsequent Find is chosen Free edges or free faces can be found over the entire model or between Parts PIDs or MIDs The model option is the most helpful in location interior
66. gies induced conduction currents power losses etc can also be determined 12 13 4 Finite Element Design Procedure for the BDFM 4 1 Methods of Modeling Induction Motors Finite element analysis techniques have been used successfully for some time in the design of induction reluctance and permanent magnet machines Neglecting end effects these machines can easily be investigated using two dimensional finite element analysis In three phase ac squirrel cage induction motors the rotor current distribution is one of the main unknown quantities of interest One goal of finite element analysis for induction machines is to calculate the induced or eddy current distribution in the rotor conductors as well as the total resulting magnetic field This can be accomplished for an induction motor by doing an ac analysis of a two dimensional cross section of the machine 4 1 1 Solution Frequency In an ac induction machine analysis the frequency selected as the solution frequency is the slip frequency or frequency seen by the machine rotor 11 For example to model the machine at start up the solution frequency would be 60 Hz At high speed a low frequency as seen by the rotor is used The slip frequency is appropriate to use for an ac solution because currents are induced in the rotor conductors at the frequency seen by the rotor 14 4 1 2 Periodic Boundary Conditions Finite element simulations of ac induction machines as well
67. gree model of the BDFM with a finite element mesh identical to the 360 degree BDFM model was set up The material properties excitations and outer boundary conditions were identical to those used for the 360 degree model An ac solution was generated at a rotor reference frame frequency of 30 Hz as in the 360 degree model Alternating periodic boundary conditions were used Figure 4 8 Rotor Bars Labels for the 360 Degree BDFM Model along the symmetry plane of the 180 degree model The 180 degree finite element model is shown in Figure 4 9 This 180 degree model had a finite element mesh consisting of 3888 hexahedron and pentahedron elements and 4280 grid points basically half the number of elements and grid points utilized in the coarse 360 degree model BAS Az Comma o N Q gt AA xy a OS aE CNC KZA P XX GETTER Ky Ss EWS AAO A nea N EEZ ME SSS Za Figure 4 9 Coarse Three Dimensional 180 degree BDFM Finite Element Model The purpose of this coarse 180 degree model simulation was to verify that the use of alternating periodic boundary conditions on a 180 degree BDFM model produces results consistent with those obtained for a 360 degree model 34 4 4 3 1 Boundary Conditions Figure 4 10 shows the applied boundary conditions for the 180 degree BDFM model A cylindrical coordinate system is used to define the boundary directions The tangential components of the mag
68. here the problem areas exist 137 To make an arrow plot of magnetic flux density like the ones presented in Chapter 4 use the following procedure 1 2 Choose Field Results Arrows from the cascading menus Vary the arrow size with the vector magnitude by toggling AutoSize to on or produce plots with all arrows of the same size with AutoSize Off To make all arrows one color turn AutoColor Off Choose the AverageMethod for MSC XL to use to average the results Default is acceptable to use Since magnetic flux density is an element result toggle Grid Arrow to Invisible and Elt Arrows to Visible Use the QuickEditRT option to select the following e Select the Results quantity for which an arrow plot is to be obtained To obtain an arrow plot of magnetic flux density choose Magnetic Flux Density for Element Result e Select the desired components VectorResult of the result Full Vector was chosen for the arrow plots presented in Chapter 4 e Select the TypeOfData Do not select TypeofData Magnitude or Phase as these results do not have physical meaning while using arrow plots Pick Plot in View to graphically display the arrows 138 A 4 6 3 Results Plots on Cut Surfaces When examining field distributions it helpful to view plots of various field quantities along two dimensional surfaces within the three dimensional model Although it is possible in MSC XL to view three dimensional plots of field quant
69. his will remove all of the parts from the display screen so that only the outline of the Cutsurface will be displayed 3 Type refresh linecontour or refresh arrow in the command line to produce the results plot on the Cutsurface A 4 6 5 XY Plotting Along CutPaths XY plots of field quantities along a path through the finite element model can be created in MSC XL The plots of conduction current density across the BDFM rotor bars presented in Chapter 4 were examples of such plots To make an XY plot of a field quantity along a path through the finite element model first a path called a Cutpath must be defined A Cutpath can be defined in MSC XL as follows 1 Create a geometric curve within the finite element model defining the path over which the field quantity is to be plotted 2 Choose Tools CutPath Define CurvebyCurve from the cascading menus 140 In the pop up menu enter the identification number of the geometric curve to be specified as a Cutpath Choose Tools gt CutPath Intersect from the cascading menus In the pop up menu specify the element identification numbers or group names with which the Cutpath is to be intersected Once a Cutpath is defined and intersected with the finite element model MSC XL can create XY plots of field quantities along the Cutpath To obtain a XY plot of a field quantity along the Cutpath use the following procedure l 2 Pick XY Plotting gt Graph T
70. ied path through the model MSC XL can plot results calculated by MSC EMAS using the Results Database or can calculate new results based on database quantities using the Results Calculator 72 A 3 An Overview of MSC EMAS MSC EMAS Electromagnetic Analysis System is a general purpose finite element program for analyzing electromagnetic fields Analysis methods are based on a vector potential formulation of electromagnetism This formulation results in a single matrix equation which represents Maxwell s equations in their complete and general form as discussed in Chapter 3 Solutions to this equation are obtained using a formal series of matrix operations Though MSC EMAS has enough input and output capabilities to stand alone as a field analysis program it is generally used as the solver along with the graphics pre and post processor MSC XL The matrix equations representing Maxwell s equations are solved through a series of formal matrix operation e g multiplication decomposition eigenvalue extraction called solution sequences Each operation in the sequence is carried out by an independent group of subroutines called a module Matrix operations are specified in a unique internal programming language DMAP Direct Matrix Abstraction Programming MSC EMAS comes with a number of standard solution sequences which implement common forms of analysis e g static analysis frequency response AC analysis transient analysis a
71. ification number is selected and changed with no need to re enter all of the setup parameters In the setup procedure used by Maxwell 3D Field Simulator all of the setup parameters have to be re entered each time any modification is made Since the setup procedure is time consuming and painstaking the setup procedure used by MSC XL is much more convenient 5 3 2 Disadvantages Limitations 5 3 2 1 Wireframe Modeler MSC XL the graphical pre and post processor designed for use in conjunction with MSC EMAS is a wireframe modeler In a wireframe modeler a device geometry is created by specifying points curves and surfaces along the dimensions of the model The geometric surfaces serve as templates for creation of finite elements and grid points The geometric entities are no longer needed once the finite element mesh has been completed because the finite element mesh and grid points define the model Material properties excitations and boundary conditions are applied directly to elements by specifying their identification number 59 A wireframe modeler has two main disadvantages First a wireframe modeler is more difficult to use than a solid modeler In a model with several thousand elements keeping track of element identification numbers is more painstaking than simply manipulating objects by name Second in a wireframe modeler the model is defined by elements and grid points instead of by objects therefore it is not possible to e
72. imes that the two dimensional elements are to be extruded Element The identification numbers or the group names of the elements to be extruded Delta X Y Z The length in the geometry units of the new three dimensional elements Offset X Y Z The initial offset distance before the elements are extruded CID The identification number of the coordinate system in which the extrusion occurs PID The property identification number of the new extruded element GridOut The identification numbers of the newly created grid points Output The identification numbers of the newly created elements The machine body for the detailed 180 degree BDFM model was formed by extruding two dimensional element sets 50 mm in both the positive and negative Z directions using an iterate value of 1 The nested loop end connections and the endring were formed by extruding two dimensional element sets A 76 mm with an offset of 50 mm and A 76 mm with an offset of 50 mm respectively using an iterate value of 1 111 Once the entire three dimensional mesh has been completed it is important to check it using the mesh checking procedure previously discussed It is also helpful in checking the three dimensional mesh to display each object separately by part identification number This can easily be done if elements making up each object have been placed in separate parts Parts can be posted or unposted from the display screen by choosing Vie
73. ining the tangential components of A to be zero along the outer circumference of the machine and also on the two machine ends If the machine has been drawn with a cylindrical coordinate system and the z coordinate lies along the axis of the machine the tangential components of A along the radial boundary are Ao A and on the two machine ends the tangential components of A are A Ao In MSC XL setting the tangential components of A to zero or assigning any value to a DOF is called a fixed potential boundary condition also referred to as a single point constraint or SPC The easiest way to set the tangential components of A 0 in MSC XL is to use the By CSPlane option as follows 1 Choose FEM BoundaryCondition and choose an arbitrary boundary condition identification number 2 Choose FEM gt BoundaryCondition Edit Fixed Potential gt By CSPlane 127 3 In the pop up menu fix the desired potential in the chosen coordinate system CID and enter the value for the chosen potential Together the CID and Plane pop up entries define the constant plane to which the Fixed potential s will be applied CID represents the coordinate system in which the plane is constant The Plane options will be x y z for a Cartesian system r 0 z for a cylindrical system and r 0 b for a spherical system A 4 4 3 3 2 Periodic Boundaries for the 180 Degree Model Alternating periodic boundary conditions are set up along the symmetry plan
74. ints Excitations boundary constraints and material properties can then be added using forms unique to field analysis MSC XL also has a number of model checking features For standard types of analysis it is possible to set up the entire input file run an MSC EMAS analysis and look at results without leaving MSC XL For advanced applications a small amount of hand editing in the input file may be needed A 2 4 Data Files MSC XL has access to several data files as shown in Figure A 2 MSC XL has its own database lt filename db gt where it stores model data and data tables in binary form During each MSC XL session all the typed commands the appear in the history tile are stored in an ASCII file called lt filename hist gt MSC XL produces an ASCII input file lt filename dat gt which is read as input to the solver MSC EMAS Results from MSC EMAS are contained in a binary data base lt filename xdb gt MSC XL can 71 access multiple lt filename xdb gt files generated from a single model geometry same elements and grid points in order to compare results from different runs External ASCII data can also be brought in and plotted using MSC XL s XY plotting capabilities Figure A 2 Data Flow in MSC XL Output data can be represented in various forms Options include three dimensional arrow plots three dimensional contour plots arrow or contour plots through a cross section of the model or XY plots along a specif
75. ints The duplicate grid points must be deleted by selecting FEM Check FEM Duplicate Grids gt Find amp Equivalence from the cascading menus Duplicate grids should be eliminated first 103 before checking the mesh for other errors since duplicate grids can be the be the cause of other mesh errors free edges and free faces Duplicate grid points do not usually produce fatal errors A 4 3 5 2 Unconnected Grid Points An unconnected grid point usually produces a warning message when MSC EMAS tries to assemble system matrices They are sometimes quite difficult to identify visually Unconnected grid points are easily eliminated in MSC XL using the typed command Delete Grid All MSC XL will only delete grids that are not connected to elements A 4 3 5 3 Duplicate Elements Duplicate elements can occur when geometric entities are meshed more than once It s a good idea to check for duplicate elements by selecting FEM gt Check FEM Duplicate Elements Find amp Equivalence from the cascading menus A 4 3 5 4 Free Edges or Free Faces A free edge in a 2 D mesh is any element edge that is not shared by two elements Similarly a free face in a 3 D mesh is any element face that is not shared by two elements Free edges and free faces should only occur at the intended boundary 104 of the model When they occur in the interior it usually means that the elements have not been properly connected resultin
76. ion Current Density in Bar 7 in reference to Figure 4 17 eccess 46 4 20 Path along which Conduction Current Density was Plotted from Right to Left 47 4 21 Conduction Current Density in Bar 6 in reference to Figure 4 20 c c 000 48 4 22 Conduction Current Density in Bar 7 in reference to Figure 4 20 o 48 4 1 4 2 4 3 4 4 List of Tables Material Properties used in the 360 Degree BDFM Model cccccccceseeseeeees Total Calculated Currents in the Rotor Bars for the 360 Degree BDFM Total Calculated Currents in the Rotor Bars for the Coarse 180 Degree BDFEM Model ireann a a acelin at uaad decimate Total Calculated Currents in the Rotor Bars for the Detailed 180 Degree BRIDE Vera le E A A esas eee EAE List of Appendix Figures A 1 MSC XL Screen Layout 2 5 cians evant cossuncans vouieaian wseieneusesedeusatioluem anise Ui seeeeiees 69 A2 Data Flow in MSC X Doseer iei ce yiatues irni ined don eran ewes 71 A 3 Data Flow in MSC EMAS ssssiscscssvecvsonssiacvecovessennessaaeangneservavnadsnesdeaieugoavdarieesumnenetdas 73 A 4 Radial Cross Section of the BDFM Model c cccssssssssssesccsseccscesseseesteseeseseeeaens 77 A 5 Finite Elements and Grid Points x ss c2 scteesc se seiaseawaraeveaveaenctttadeeanintte hans tax 89 A 6 Available Two and Three Dimensional Elements cccccccscsssscesseseseseesesseseees 91 A 7 Distortion of Midedge Nodes Aspect Ratios and Taper Angles c c 00 94
77. ions along each rotor bar and identical results were obtained The calculated total currents in each rotor bar are presented in Table 4 2 and the rotor bar labels are identified in Figure 4 8 Table 4 2 shows that the rotor bars currents are equal in magnitude and 180 degree out of phase for rotor bars connected by a loop In other words the rotor currents 31 Real Imaginary Amperes Magnitude Phase PTF 8 26766 25 5532 26 8574 72 0712 C 2 133 208 33 6687 137392 165 815 3 30 8736 186 89 189423 80 6197 C s S 71383 8385 87616 8533 e 30 8734 186 89 189423 993803 C 7 S3272 33682 137463 165 816 e 828426 25 5654 26 8741 12 0455 LEEI a Ae 186 OO R l M i 203 33 668 137393 141851 16 8 6676 25 5533 26 8572 107 927 8 28503 25 565 26 874 107 956 133 271 33 6827 137 461 14 1839 1 2 3 4 5 7 10 11 12 13 14 15 16 Table 4 2 Total Calculated Currents in the Rotor Bars for the 360 Degree BDFM Model are equal in magnitude but flowing in opposite directions for connected bars as is expected Also the magnitude of the rotor bar currents in the first loop are greater than the currents in the third loop as is expected by consideration of the laboratory machine Thus the rotor bar currents indicate that the BDFM model has 180 degree symmetry 32 4 4 3 A Coarse 180 Degree BDFM Model A three dimensional 180 de
78. ities often two dimensional plots at different positions within the model are easier to view and to interpret For the BDFM model cross sectional contour plots of vector potential and arrow plots of magnetic flux density are helpful to view Several of these plots were presented in Chapter 4 To make a plot of a field quantity along a two dimensional surface first a plane called a Cutsurface must be defined A Cutsurface can be defined in MSC XL as follows l 2 Choose Tools gt CutSurface Edit from the cascading menus In the pop up menu specify values for the following parameters e CID The identification number of the coordinate system in which the cutsurface is to be defined e From X Y Z Defines the position of the cutsurface e To X Y Z Together with From X Y Z defines the positive direction of the cutsurface Choose Tools CutSurface Intersect from the cascading menus In the pop up menu specify the element identification numbers or group names with which the cutsurface is to be intersected 139 Once a Cutsurface is defined and intersected with the finite element model MSC XL will automatically extract the results defined in the results table from the elements the Cutsurface passes through To obtain a contour plot or an arrow plot on the Cutsurface only use the following procedure 1 Choose View 1 for displaying Cutsurface plots 2 Type unpost part all in the command line T
79. l for being an easier to use faster and more versatile user interface than MSC XL However since no actual experimentation with MSC ARIES was done it is unknown if it contains program flaws typical for first releases It is recommended that MSC ARIES be investigated however if program flaws are found to exist the modeling procedure presented in this thesis for MSC XL can be used Additional disk space is also needed for the HP 715 50 workstation Ideally a 4 GB hard disk should be purchased This 4 GB hard disk should be set up to contain both solution output files and the MSC EMAS scratch directory which contains scratch files created during the solution process Additional disk space is necessary because the HP 715 50 workstation contains only a 1 GB internal hard drive which is insufficient The work presented in this thesis was made possible by the loan of two additional external hard disks a 500 MB hard disk and a 1 GB hard disk Even this additional disk space was insufficient Several BDFM models that were created did not run because of lack of hard disk space MSC EMAS was created such that the solution output files and the scratch temporary files reside within the same directory on the same drive therefore requiring that a large hard disk be used 64 BIBLIOGRAPHY 1 A K Wallace R Spee and H K Lauw The Potential of Brushless Doubly Fed Machines for Adjustable Speed Drives Conference Record IEEE IAS Pulp and Paper In
80. l with MSC XL is to create the geometry that defines the model s shape Geometry is actually any number of points curves surfaces and solid figures that act as templates for the finite element mesh It is the geometry that normally fixes the exact size and position of object in the model The purpose of the geometry is only to serve as a template for the finite element mesh consequently it can be deleted once the mesh has been created The general procedure to be followed in creating BDFM model geometry is to use the hand sketch drawn earlier to create two radial cross sections 1 Create a geometric model of the 45 degree rotor radial cross section 2 Create a geometric model of the 5 degree stator radial cross section A 4 2 1 Undo Command and Delete Item Option The best way to learn how to create a model geometry and finite element mesh in MSC XL is to experiment and observe the results Two helpful options in this process are the Undo command and the Delete Item option The Undo command is located in the quick access menu Undesired results can quickly be reversed by using the Undo command which reverses the last command performed Only one command can be reversed If a mistake is several commands behind the Delete Item option removes unwanted points curves surfaces elements or grid points Items can be deleted with the Delete Item option as follows 80 1 Pick Geometry Delete Item from the cascading menus 2
81. le layer windings are assumed For both the 6 pole and 2 pole windings 100 amp turns peak per slot is assumed First the elements to be excited should be grouped together in logical sets This is done by using the Tools menu to define a group One procedure is to define each individual slot of the 6 pole winding as a group and each set of 2 pole slots with the same phase angle as a group This can be done by the following steps 1 Choose Default View 1 2 Display only the elements associated with the 6 pole or 2 pole winding one winding at a time the one being grouped 3 Pick Tools Group Define from the cascading menus 4 In the pop up menu define a name for the group and choose polygon window 5 Pick Do It and use the polygon window to select the elements to be part of that group 121 Once the elements that make up the three phase stator windings have been logically defined in groups the current density excitation can be applied A current density excitation will be created for every stator slot group that was defined as follows l Pick FEM gt Excitation from the cascading menus and give the excitation an identification number Choose FEM gt Excitation Edit and toggle to Current Density In the pop up menu enter the following parameters Elementlds The name of the group to which the excitation is to be applied Current Density The desired current density J in amperes m The current
82. le was still a beta test version which can explain the many glitches and problems that were encountered in working with it 5 2 2 2 Solution Parameters have to be Re entered each Time a Modification is Made In the setup procedure used by Maxwell 3D Field Simulator all of the material property and excitation setup parameters for the entire model have to be re entered each time any modification is made Likewise each time a modification is made to the model boundary conditions all of the boundary conditions must be re entered In finite element modeling it is often informative to observe the effect of changing one model property at a time For example the material property of one object in the model may be changed the magnitude of the excitations may be varied or a particular boundary condition may be changed Having to re enter all of the material properties and excitations or re enter every boundary condition each time a small modification is made is not very convenient 5 2 2 3 Very Poor Program Diagnostics The main problem with Maxwell 3D Field Simulator was its very poor program diagnostics No error messages are provided by the program to help the user identify problems during the solution process 55 5 2 2 3 1 Program Continues to Execute and Status is not Available to the User While Maxwell 3D Field Simulator was solving a finite element problem the program would continue to execute without issuing error or inform
83. ll occur e Define the Cutsurface by choosing Tools CutSurface Edit from the cascading menus Enter values in the pop up menu that define the Cutsurface location and direction e Intersect the Cutsurface with the elements over which the integration will occur by choosing Tools Cutsurface Intersect from the cascading menus Enter the identification numbers or group name of the elements to be intersected with the Cutsurface 2 Choose Calculate and choose CurrentFromJ from the list of options 142 3 Choose the AverageMethod for MSC XL to use to average the results Default is an acceptable choice 4 Choose Calculate gt Calculate from the cascading menus 5 In the pop up menu choose CutSurface as the Surface Type and choose the appropriate Cutsurface identification number 6 The calculation results will appear in MSC XL s history tile A 4 6 7 Generating Hardcopy Files To set up the specification for hardcopy plots it is necessary to edit the Hardcopy Table by choosing Table gt Hardcopy from the cascading menus and entering appropriate specifications Hardcopy files of the graphics tile only can be generated by typing the refresh plot command in the command line This command creates a hardcopy of the current display One of the following options can also be added on the refresh plot command to obtain various different hardcopy plots refresh plot creates a wireframe model hardcopy plot hiddenline
84. ly after a geometric model has been 52 created using the Draw Geometric Model step This step by step procedure is helpful for new users because it makes sure that each design step is completed and in the appropriate order 5 2 1 3 Automated Meshing Technique The Maxwell 3D Field Simulator uses an automated meshing technique The program automatically generates an initial finite element mesh when Setup Materials is chosen from the main menu If desired the user has the option of refining the mesh in selected areas once the initial mesh in complete by choosing the object to be refined The program then automatically adds a specified number of additional elements to the selected object The automated meshing procedure used by Maxwell 3D Field Simulator has the advantage of being faster and much easier to use than a manual meshing technique such as the one used by MSC XL Manual meshing is slow and requires a lot of attention from the user as it is prone to user errors An automatic meshing procedure is very helpful for users unfamiliar with finite element analysis who may not know how to design an effective finite element mesh The automated meshing procedure used by Maxwell 3D Field Simulator does not give the user control over the exact size shape and position of each individual element as the manual meshing technique used by MSC XL does However this type of user control is probably not necessary Automated meshing is
85. me The rotor reference frame frequency or frequency of the rotor currents during synchronous operation of the machine is determined from Equations 2 5 and 2 6 which are restated here Jos L Equation 4 2 P P Sra fo P f PSF fe Equation 4 3 Equation 4 3 determines the frequency seen by the BDFM rotor during synchronous operation Since during synchronous operation the fields induced in the rotor by the power and the control windings are locked together at the same frequency only this one rotor frequency needs to be specified in the ac analysis If it is desired to determine the induced rotor currents during synchronous operation of the machine Equation 4 3 can be used to determine the solution frequency to be used in an ac analysis Thus modeling the BDFM in the rotor reference frame eliminates the need for two frequencies to be included in the simulation at once 18 If it is desired to model the BDFM during startup or during other conditions when it is not operating in synchronous mode the fields induced in the rotor would not be locked together at one frequency Therefore it is not be possible to simulate the BDFM under dynamic conditions with the ac analysis module because the ac solution method requires that a single solution frequency be specified Possibilities exist to overcome this difficulty by using the transient analysis module which allows waveforms of different types and or frequencies to be include
86. ments _Three Dimensional groups Formed by extruding PIDs of three of elements representing two dimensional dimensional objects elements with PIDs elements E ee T Rotor as 3 E ae oo spe stator stot tr ha oal 2 pole stator slot Air surrounding nested loops 1 2 5 6 7 8 9 Air surrounding endring 1 2 7 8 9 Table A 3 Assignment of PIDs to Three Dimensional Elements 96 particular object in the two dimensional BDFM cross sectional model Table A 3 shows how these two dimensional groups of elements can be selectively extruded to form three dimensional elements that define objects by choosing certain PIDs of the two dimensional elements A 4 3 4 Meshing in MSC XL Once a plan for PID assignment has been made the finite element mesh is ready to be created A general procedure should be followed when creating the mesh for the BDFM model as follows Le Create a two dimensional mesh for the 45 degree rotor geometry radial cross section Create a two dimensional mesh for the 5 degree stator geometry radial cross section Reflect and rotate the 5 degree stator section to obtain a 45 degree stator section Connect the rotor and stator meshes together by connecting grid points in the air gap Reflect and rotate the complete 45 degree section to obtain a 180 degree two dimensional model Extrude selected elements of the two dimensional mesh
87. n the stator windings Shaft 5 8 Rotor 2000 2 pole Stator Slot Air 24 1 Rotor Bars Aar T Stator 2000 Relative Relative Electrical Permeability Permittivity Conductivity siemens meter ae o Air Gap Air 6 pole Stator Slot Air Nested Loops 5 8E 07 5 8E 07 End Ring Table 4 1 Material Properties used in the 360 Degree BDFM Model 4 4 2 2 Excitations For the 360 degree BDFM model an equivalent surface current density is used to establish a current flow of 100 amp turns peak in each of the 6 pole and 2 pole slots Figure 4 4 shows the 6 pole and 2 pole stator winding excitation locations and directions and specified for use in the ac analysis In Figure 4 4 for the 6 pole winding Phase 0 Phase 240 and Phase 120 For the 2 pole winding Phase 0 Phase 120 and Phase 240 4 4 2 3 Boundary Conditions Figure 4 5 shows the applied boundary conditions for the 360 degree BDFM model A cylindrical coordinate system is used to define boundary directions Along 25 6 pole Stator winding 2 pole Stator winding Figure 4 4 Stator Excitations for the 360 Degree BDFM Model the outer radius of the model the tangential components of the magnetic vector potential A are set to zero 4 A The tangential components of A are also set to zero along the motor ends A 4 Setting the tangential components of A to zero along the outer boundaries of the machine const
88. nd eigenvalue analysis Users can select any of the standard sequences or make up DMAP programs of their own MSC EMAS creates uses several data files as shown in Figure A 3 These include files are described briefly as follows 73 From MSC XL To MSC XL Figure A 3 Data Flow in MSC EMAS lt filename dat gt ASCII This is the input data file for MSC EMAS which can be written automatically by MSC XL for standard analysis methods lt filename f06 gt ASCII This file is the main user oriented program output file It contains echoes of the input data information from various numerical modules warning and error messages and tabulated output lt filename f04 gt ASCII This file contains information on the execution of modules including clock time CPU time and I O usage lt filename log gt ASCII This small file contains information on the configuration of the computer at execution time and final accounting statistics for the job 74 e lt filename dball gt Binary This large file contains the database for MSC EMAS It contains model information internal data tables and output information e lt filename xdb gt Binary This file contains model data and results to be used by MSC XL e Scratch Files Binary Temporary scratch space is needed during the solution process These output files from MSC EMAS contain much useful information especially when trying to correct model errors A
89. netic vector potential A are set to zero along the outer radius of the model and along the motor ends as in the 360 degree model Alternating periodic boundary conditions were applied along the two radial faces of the symmetry plane at 0 0 and 6 180 degrees This boundary condition forces every degree of freedom three A components and to be equal in magnitude but opposite in direction as follows A 7 8 p z A 7 8 9 2 Equation 4 5 A r 8 p Zz 4 7 9 5 2 Equation 4 6 A r 6 p z A 7r 8 2 Equation 4 7 V r 0 p z V r 8 9 2 Equation 4 8 where A is vector potential 69 is the angle of one radial boundary and p the pole pitch angle 4 4 3 2 Results Examination of the results obtained from the coarse 180 degree BDFM model are in close agreement with the results obtained from the 360 degree model verifying the symmetry of the BDFM model and the use of alternating periodic boundary conditions Ao Az 0 a Kd FL tS Al CZ gt N w QD j A AAT ie x RN K TSS KAS DEZ Z WAKA MK SAL ZK A87 4r 180 2 A r 0 2 Ail r 180 z r 0 z ond iA A A5 0 P r 180 z P 7 0 z Figure 4 10 Boundary Conditions for the Coarse 180 Degree BDFM Model 4 4 3 2 1 Contour Plot of Magnetic Vector Potential A contour plot of magnetic vector potential A alon
90. ngs of different pole numbers and 3 phase adj frequency Bidirectional Converter 25 rating Figure 2 1 BDFM Stator Structure different frequencies These two separate sets of windings are wound on the same stator frame and share the same slots One set of windings is the power winding which is connected directly to the power supply system and which supplies the bulk of the machine power The second set is the control winding which supplies a fraction of the machine power through a power electronic converter The advantage of the BDFM system Over more conventional motors and generators is that most of the power flows directly between the machine and the power system Therefore the rating of the required converter should be a fraction of that required to process all of the machine power thus reducing cost and induced harmonics of the power electronics The rotor design of the BDFM is based on work by Creedy and Broadway 7 8 As shown in Figure 2 2 the BDFM rotor is an unique cage type rotor with nested loops Unlike the squirrel cage rotor of an induction motor which has rings to short all the rotor bars on both ends the BDFM rotor has a ring to short all the rotor bars only on one end while at the other end the bars are selectively shorted together to form distinct loops The rotor design is mechanically simple enough to be die cast while at the same time having the capability of supporting two fields of different p
91. nlinearity of laminated steel stator and rotor is taken into account Other useful motor design parameters can be determined for the BDFM from finite element field solutions These parameters include but are not limited to power loss steady state torque and winding inductances MSC XL includes a built in calculation for determining power loss in any group of elements in the model Calculation of steady state torque and winding inductance would require more in depth consideration In the investigation of three dimensional finite element analysis of the BDFM two different finite element software packages were investigated Maxwell 3D Field Simulator by Ansoft Corporation and MSC EMAS and MSC XL by MacNeal Schwendler Corporation An evaluation and comparison of these two software packages was presented in this thesis MSC EMAS and MSC XL were found to be far superior to Maxwell 3D Field Simulator MSC EMAS and MSC XL shown good potential for being an effective design tool for the BDFM and it is recommended that this software continue to be used In September 1994 MacNeal Schwendler released a new user interface MSC ARIES which is meant to replace MSC XL the older user interface described in this thesis MSC ARIES uses a solid modeling procedure instead of the wireframe modeling procedure used by MSC XL MSC ARIES was not examined in depth 63 because of its late arrival A brief overview of the MSC ARIES manuals shows that it has potentia
92. ntered in the pop up menu When picking curves from the graphics tile curves should be picked consistently in either a clockwise or a counterclockwise direction around the surface boundary If curves are picked in a random order a deformed surface will result If a mistake is made delete the surface using Undo and try again When surfaces have been defined for all areas in the radial cross section the geometry creation is complete The finite element mesh can now be created A 4 3 Generating the Finite Elements After geometry creation the next step in producing the model is to generate a finite element mesh A finite element mesh is a collection of connected grid points and 88 elements that subdivide the geometry and represent the problem volume The ability of a model to represent the actual problem is determined in part by the quality of the finite element mesh Before discussing how the mesh is actually created in MSC XL several key factors to consider in meshing will be discussed A 4 3 1 Finite Element Terminology The two important components of the finite element mesh grid points and elements should first be defined A 4 3 1 1 Grid Points Grid points also called nodes play a central role in finite element modeling Grid points are the connection points between elements and are created along with elements as part of the meshing process Grid points are not the same as geometric points Grid points that exist at el
93. ole numbers and different frequencies from the stator Isolated Endring Common Endring Figure 2 2 BDFM Rotor Structure 2 2 Basic Performance Equations The number of loop groupings or rotor nests is determined by the sum of the pole pairs of the power and control windings Number of Nests P P Equation 2 1 where P is the number of pole pairs of the power winding and P is the number of pole pairs of the control winding The BDFM has all the robust maintenance free features of a squirrel cage induction machine In order to operate successfully the BDFM must switch from operation as two induction motors in the same magnetic circuit the double induction mode to a mode where the rotor field induced by one of the stator windings is locked together with the stator field of the other stator winding and vice versa the synchronous mode positive direction Figure 2 3 Velocities of Interacting Fields In the synchronous mode the field interaction and the mechanical speed of the rotor as shown in Figure 2 3 are related by 9 fr Fre sf P P P Equation 2 2 and A f fe Equation 2 3 where f and f are the frequencies applied to the power and control windings respectively frp and frc are the rotor frequencies induced by interaction with the fields of the power and control windings f is the mechanical rotational frequency For synchronous operation to be attained it is required
94. on of the machine shows the symmetry present in the machine s magnetic field distribution Figure 4 6 shows that the BDFM exhibits 180 degree symmetry 4 4 2 5 2 Arrow Plot of Magnetic Flux Density An arrow plot of magnetic flux density B along a cross section of the BDFM located at the machine center is shown in Figure 4 7 An arrow plot of magnetic flux density represents the direction and magnitude of the magnetic flux density with colored arrows The colors of the arrows indicate the magnitude of the magnetic flux density in tesla at every location along the machine cross section This allows the user to identify areas where the machine may be PEELE TD 327_ 0 00437 0 00546 0437 _ 0 09546 0 00655 aiiin T MM gitindaiild FELL ENN YI FFEN EIA U AN i 1777 NN AN Hi d T 0308 vagy AA Hiii PINEN WN A Figure 4 6 Contour Plot of Magnetic Vector Potential along a Center Cross Section of the 360 Degree BDFM Model Y 5 Mey s y be DE 9 EN Loe ai N N i X Uy y d AANS 1 ResultsCalculator FrequencyResponse Analysis MagneticVectorPotential FullVector GridResults FullVector Type0fData Magnitude Subcase 1 Frequency 30 87 0 03582 6 07158 0 10735 0 14311 14311 0 17887 p 0 29 6 07158 6 10735 0 14311 0 17887 AEI E 2h ie Wij ee AHi hs My CNG Cie H A IA ee cane 7 YAN NPL lt ee Bs X LO
95. on strategy that involves and B must enforce these conditions at every interface This requirement puts an unnecessary burden on numerical computations The third disadvantage is that E and B may be infinite at sharp corners of certain materials These infinite solutions cause numerical difficulties in computers 10 Therefore electromagnetic potential functions are introduced to eliminate the disadvantages of dealing with E and B directly These potential functions are the magnetic vector potential A anda time integrated electric scalar potential Y In terms of these potential functions the electric and magnetic fields are given by 10 gt VxA Equation 3 5 bys E VW A Equation 3 6 Maxwell s equations are rewritten in terms of these potential functions The values of A and at the model grid points are called degrees of freedom DOFs There are four DOFs at each grid point three components of the vector potential and one component of the scalar potential The principle of virtual work is now used to formulate the overall energy stored in the solution region according to the following energy relationships W H B Equation 3 7 E D Equation 3 8 The objective is to solve for the unknown potentials A and by minimization of the energy function 10 The problem volume is divided into finite elements The energy associated with each element is computed in terms of the potential degrees of freedom
96. opic Permittivity 00 112 A 4 4 1 1 2 Anisotropic Symmetric Permittivity wccccnmnbiasacaseeliicus 113 A 4 4 1 1 3 Unsymmetric Permittivity 113 A 4 4 1 2 Conductivity ccccecccscsscsssesscssssessesssensessees 113 A 4 4 1 3 Permeability c c scesessisacciesssasersesvanensssesscrsecedaves 114 A 4 4 1 4 Setting Material Properties in MSC XL 115 A 4 4 1 5 Material Properties for the BDFM Model 117 A442 EXOUAMONS aie enirere earls se E N a 118 A 4 4 2 1 Available Excitations 0 ccccccsscssessesseeseeeees 119 A 4 4 2 2 Applying Excitations to the BDFM Model 119 A 4 4 3 Boundary Conditions ccccccccccsscssesscessessessessesesessseeaeane 122 A 4 4 3 1 Fixed Boundary Conditions cccceeeeees 123 A 4 5 A 4 6 A 4 4 3 2 Periodic Boundary Conditions 0 0c008 125 A 4 4 3 3 Applying Boundary Conditions to the BDEM Modelo nru resia 126 A 4 4 3 3 1 Outer Boundaries eee 126 A 4 4 3 3 2 Periodic Boundaries for the 180 Degree Model c ccsseesseeseeees 127 A 4 4 4 AC Analysis Preparation ccccccesessceesscssseseeeseeereeaes 128 A 4 4 4 1 Control Section ccccssccsscssssessesseesreeseses 129 A 4 4 4 2 Unit Section ecccccccccscesssssseesseesessseeeseesseeees 129 A 4 4 4 3 Degrees of Freedom cccescecsseeseessesseeeeeees 129 Solving the Problemtyssccoecccstcernisc A cpsvadeseatsuaatstuanieiavcsehiont use 129 A 4
97. oth be present along all four edges of the symmetry plane The SPCs must be removed from these edges by choosing FEM gt BoundaryCondition ID of the SPC gt Delete and picking the SPCs along the edges from the graphics tile A 4 4 4 AC Analysis Preparation Once all material properties excitations and boundary conditions have been applied to the finite element model it can be prepared for analysis This is done by selecting Analysis gt Edit from the cascading menus and entering the appropriate values in the pop up menu 129 A 4 4 4 1 Control Section Select the excitations and boundary conditions to be included in the analysis by choosing their identification numbers A separate analysis is required to vary material properties excitations and or boundary conditions Enter the desired solution frequency for the AC analysis which is the rotor reference frame frequency A 4 4 4 2 Unit Section Choose the units for the geometry along with a factor to divide those units by if necessary For example Meters 10 is equivalent to decimeters Select the units for time A 4 4 4 3 Degrees of Freedom A degree of freedom can be removed for every grid point in the model by toggling the component to Inactive For the 3 D BDFM model all degrees of freedom are necessary and should be left active A 4 5 Solving the Problem A 4 5 1 Invoking MSC EMAS Once the Analysis gt Edit pop up has been completed the analysis to
98. otor bars These areas should be meshed more finely than the other areas such as the rotor and stator A 4 3 2 4 Mesh Order When a second order mesh is used with midedge nodes present potential functions are interpolated using second order polynomials instead of first order 93 polynomials This provides a larger set of functions and in general improves accuracy However the number of DOFs is also increased as well as the solution time and system requirements Although midedge nodes do provide more accurate answers the user must access the accuracy per unit cost For all the work done in this thesis first order meshes containing only corner nodes were used because of disk space limitations A 4 3 2 5 Element Distortion The finite elements in MSC XL are intended to be close to the following nominal geometries becvevcsvereveveseeeeserees prvcccssonccccvncenennenese boesssssssessssssasssesnenne Severe element distortion from these intended shapes can produce inaccurate results MSC XL will allow distorted elements to be created so it is up to the user to monitor this Severely distorted elements cause user warning messages to appear in the lt filename f06 gt output file The following guidelines are offered concerning element distortion e Itis recommended that midedge nodes be collinear with the associated corner nodes and be located at the middle of the edge Midedge nodes located outside of the center half
99. ould be investigated Since the inner rotor loop carries a very small current compared to the outer loops perhaps the inner loop could be eliminated entirely BDFM models should be set up with more realistic values for currents in the 6 and 2 pole stator windings The current magnitude of 100 amp turns peak per slot that was used in the excitation setup of the BDFM models as described in Chapter 4 was chosen for convenience The actual currents flowing in the 6 and 2 pole stator windings are larger in magnitude and not necessarily equal in magnitude A finite element field solution using more realistic values for the 6 2 pole stator winding currents should be generated The magnetic flux density values throughout the model should then be examined to determine areas where the stator or rotor cores may be saturating If the stator and or rotor cores are found to be saturating when more realistic values for the stator winding currents are applied then this saturation effect should be investigated further taking into account the nonlinearity of the laminated steel This could be accomplished by using the Nonlinear Magnetostatic module included with MSC EMAS which allows a B H curve for laminated steel to be included in the 62 analysis The induced rotor currents calculated from an AC analysis as well as the stator winding currents would be used as input excitations The field distribution and flux density values could then be examined when the no
100. pproximations involved in developing and or combining two dimensional models and allows accurate representation of the nested rotor structure For this three dimensional analysis a commercial software package produced by MacNeal Schwendler Corporation MSC called MSC XL and MSC EMAS Electromagnetic Analysis System was used The work was done on a Hewlett Packard workstation model 715 50 with 48 MB of RAM and approximately 2 5 GB of hard disk space Several three dimensional BDFM models will be presented along with the materials excitations and boundary conditions used in the setup of the models The results of these BDFM model simulations will also be presented Each of the BDFM models presented is based on the prototype 5 hp laboratory machine which has a 6 pole power winding and a 2 pole control winding configuration Analysis techniques used to model BDFM will also be discussed 17 4 3 1 Modeling in the Rotor Reference Frame vs the Stator Reference Frame In finite element simulation of ac induction machines the solution frequency used in an ac analysis is the frequency seen by the rotor or the slip frequency The frequency seen by the rotor is not as simple to imagine for the BDFM because of the presence of two sets of stator windings operating at different frequencies A way of obtaining the frequency observed by the BDFM rotor for use as the solution frequency for an ac analysis is to model the BDFM in the rotor reference fra
101. quency can be used to calculate the induced or eddy currents in the rotor conductors It has also been shown that the electromagnetic fields present in the 6 2 pole BDFM exhibit 180 degree symmetry Therefore the simulation of a 180 degree model of the BDFM with alternating periodic boundary conditions applied along the symmetry plane can be used in place of a full machine simulation for 6 2 pole machine For a BDFM with a different number of power and or control winding poles the symmetry of the electromagnetic fields would need to be reexamined in order to determine what portion of the machine to model The three dimensional finite element design procedure developed in this thesis was used to model the 6 2 pole 5 horsepower BDFM laboratory machine From the simulation results the induced currents flowing in the BDFM rotor bars were calculated These calculations indicated that an uneven current distribution exists within the nested 61 rotor loops The total current flowing in the rotor bars increases as one moves from the inner loop to the outer loop Potential exists to improve the rotor design of the BDFM using the three dimensional finite element design procedure A grading of bar size within the loops should be investigated as a possibility of improving current or loss distribution The outer loops should contain the largest conductor sizes since the largest currents are induced in the outer loops Variations of slot span for the loops sh
102. r bars is specified as the angle and the number of rotor bars to be created is specified for iterate Curves can be rotated using the Rotate Curve option as follows 1 Pick Geometry gt Curves gt Rotate Curve from the cascading menus 2 Inthe pop up menu enter the following parameters e Create Modify Specifies if new curves are to be created or existing ones modified e Iterate The number of times that the curve s are to be rotated e Exist ID The identification number of the curve s to be rotated e From X Y Z Defines the point around which the curve s is to be rotated e To X Y Z Together with From X Y Z defines the axis of rotation e Angle Defines the angle through which the curve s is to be rotated e Offset The initial offset angle before the rotation is started e CID The identification number of the coordinate system in which the rotation is defined e Output The identification number of the new curve The Rotate Curve option automatically creates new points at the ends of new curves 86 A 4 2 4 5 Define Curve The define curve option creates a curve by specifying the two endpoints and a center rotation point The define curve option is useful for creating curves defining the outlines of the nested loops The point along the x axis specifying one end of the loop and a point along the periphery of the rotor bar are connected together by a curve Curves can be created with the Define Curve option as follows 1 Pick
103. rains the magnetic fields to remain within the machine outer boundaries 26 Ao Az 0 l Zz iw P FS LZ le R os RWW ig ALLL Os X DA RLU I N W D gt Y x SAR oY KKH Zo A SRY RAS OOS GK AA SSA sss CtZ AA SSNS ce Ee ITN Vai eZ CRVI NPR SIZ ALN IK SANS LUA AAN WS A Ap 0 Figure 4 5 Boundary Conditions for the 360 degree BDFM Model 4 4 2 4 Solution Frequency for an AC Analysis An ac analysis was done for this 360 degree BDFM model utilizing the linear ac module The solution frequency used was determined from Equation 4 4 assuming synchronous machine operation A power winding frequency of 60 Hz and a control winding frequency of 20 Hz opposing sequence were assumed This results in a rotor 27 reference frame frequency of 30 Hz which was specified as the solution frequency in the ac analysis This corresponds to a machine speed of 600 rpm In the examination of the results that follow the reader should note that the stator solution is in the rotor reference frame 44 2 5 Results 4 4 2 5 1 Contour Plot of Magnetic Vector Potential A contour plot of magnetic vector potential A along a cross section of the BDFM located at the machine center is shown in Figure 4 6 A line of constant magnitude of vector potential A is called a magnetic flux line Observing the pattern of the magnetic flux lines along a planar cross secti
104. ready to be run Choosing Analysis Write from the cascading menus creates the lt filename dat gt 130 file the input file for MSC EMAS Choosing Analysis gt Run then starts the analysis The Write and Run steps are usually only done separately if the lt filename dat gt file needs to be edited by hand In most cases it is easier to combine the two steps by choosing Analysis gt Write amp Run and entering the following in the pop up menu 1 Enter a new file name for the output files or choose an existing file If chosen an existing file will be overwritten 2 Choose whether results should be printed to the f06 file Printed Results Printing results in the f06 file will increase the amount of disk space required for the output files Setting Printed Results to Off does not affect the ability to display results graphically the xdb file is not affected so if having enough disk space is a consideration Printed Results should be Off 3 Select the output method for the field results in the finite elements The field results B and will be recovered from the calculated vector potentials at a different number of locations depending on which output method is chosen The output methods are defined as follows e Center The field results will be defined at the element centroids only e CenterCorner The field results will be defined at the element centroid and at each of the corner grid points e CenterCornerMidsid
105. rom X Y Z and To X Y Z coordinates are specified and in which the sweeping occurs Output The identification number of the new curve s The identification numbers of curves is arbitrary 84 A 4 2 4 3 Reflect Curve New curves can be created by reflecting existing curves across a plane For example the entire rotor bar outline can be created by reflecting curves defining half of the rotor bar outline around the Y 0 plane Curves can be reflected around an axis using the Reflect Curve option as follows 1 Choose Geometry gt Curves Reflect Curve gt Coordinate System from the cascading menus 2 Enter the following parameters in the pop up menu e Create Modify Specifies if new curves are to be created or existing ones modified e Exist ID The identification number of the curve s to be reflected e CID The identification number of the coordinate system in which the reflection plane is specified e Plane Defines the plane across which the curve is to be reflected e Output The identification number of the new curve The Reflect Curve option also automatically creates new points at the ends of new curves A 4 2 4 4 Rotate Curve New curves can also be created by rotating existing curves For example curves outlining the other four rotor bars can be created by rotating the curves defining the first 85 rotor bar around the origin using the z axis as the axis of rotation The spacing angle between the roto
106. rrents are in close agreement the alternating periodic boundary conditions are verified 4 4 4 A Detailed 180 Degree BDFM Model A finer and more detailed 180 degree model of the BDFM was constructed The goal of constructing this model was to obtain a more accurate representation of the 5 horsepower BDFM laboratory machine 40 This detailed model included all 40 of the rotor bars present in the laboratory machine as well as all 5 of the loops per each of the 4 nests A finer finite element mesh was used especially in the rotor conductors and the air gap where field gradients change most rapidly The finite element mesh consisted of 8976 hexahedron and pentahedron elements and 9510 grid points The finite element model is shown in Figure 4 14 The body of the machine was modeled with two layers of three dimensional elements each 50 mm long as shown in Figure 4 14 The nested loops of the rotor as well as the common endring are modeled with one layer of three dimensional elements extending 6 76 mm beyond the machine body on opposite sides Identical excitations and boundary conditions and similar material properties to those used in the coarse 180 degree BDFM model were used in for the setup of this detailed 180 degree model An ac solution was generated again using a rotor reference frame frequency of 30 Hz 4 4 4 1 Results 4 4 4 1 1 Currents in the Rotor Bars The total current flowing in each rotor bar of the detailed 180
107. sadvantages Limitations cccccccssssseseessessesssessesseeseeseesseeseeseens 58 5 3 2 1 Wireframe Modeler s sn snsnsnseneseenosessoresnosesssesnesesssseseeses 58 5 3 2 2 No Step by Step Procedure Menu c cccscesseesseeseesseees 59 Conclusions and Recommendations csccsccsssssessecssesccseeeseeseeseeeseeeseseeseseaeenees 60 BIBLIOGRAPHY aonccivo naati shinee ins na a E A E A TS 64 APPENDIX ee one a E e aaa 66 Tutorial for Setting up and Solving a 3D BDFM Model using MSC XL and MSCE MEAS a a a a a E E Ea AEN 67 AE Introduction eeraa a OAN 67 A 2 An Overview of MSC XL e ssseseesesesesssssssssssesesesesesestararesisesesosrsresesesosesoro 67 A 2 1 Screen WAV OU cis 2ec bs biinasopatncetsacin utes scpadecdtacacustnsasien R 68 PD 2 Using the Mouse Aves dade cates ceed anengen ariei ieit 68 A2 3 Capabilities sianar a aa Ea TAER 70 A24 Data Files ariennir ripi ns Tap Ea ae T 70 A 3 An Overview of MSC EMAS esessseesereseesrssesssssesersesresresressesresroneeseesresese 72 A 4 Modeling Tasks iriserai eienenn er aira aaea 74 A 4 1 Planning the MSC Session sccssssssscsscsssssssssnssrsensssessesseseeseses 75 A 4 1 1 Deciding OnUnits gucci uineianuactwueaiacagsawen 75 A 4 1 2 Drawing a symmetry Wedge uo cceeccceseesssesseseeseeeeeeees 76 A 4 1 3 Entering MSC Xo ec cs cise tachoctseusleieug saissadsiusacavnsecdantaculaceetes 78 A 4 2 Creating Geometry siccscsstzccatsssadecadase
108. sen Excitation ID A 4 4 3 Boundary Conditions Electric and magnetic fields need to be constrained appropriately along the outer boundaries of the finite element model These boundary conditions or constraints on the electric and magnetic fields are on the three components of magnetic vector potential A and electric scalar potential also referred to as degrees of freedom or DOFs A constraint fixes a particular DOF to a specified value throughout all of the solution process Constrained DOFs are removed from the problem before it is solved and constrained values are substituted wherever they appear in the equations There are two main types of constraints in MSC EMAS Ina single point constraint or SPC a single DOF is assigned a fixed value In a multipoint constraint or 123 MPC a specified DOF is equal to some linear combination of any number of other DOFs Such constraints have a number of uses including periodic boundary conditions A 4 4 3 1 Fixed Boundary Conditions For the purposes of applying boundary conditions at surfaces DOFs are divided into three classes e A DOFs tangent to the boundary e A DOFs normal to the boundary e Y DOFs When one of the whole classes of DOFs listed above are constrained to zero along entire surfaces the following gross magnetic field boundary conditions are produced Gross Field Condition The effect of the fixed boundary conditions listed above is illu
109. sional 360 Degree BDFM Finite Element Model 23 In constructing the 360 degree model of the BDFM a simplifying assumption was made about the laboratory machine rotor The rotor was modeled with only 16 slots instead of the actual 40 slots and only the first and third loops of each nest were modeled or two loops for each of the 4 nests instead of the actual five loops for each of the 4 nests This simplification was made in order to reduce the complexity of the finite element mesh and hence reduce the amount of disk space required to generate a solution The body of the machine was modeled with two layers of three dimensional elements each 50 mm long as shown in Figure 4 3 The nested loops of the rotor as well as the common endring are modeled with one layer of three dimensional elements extending 6 76 mm beyond the machine body on opposite sides Ideally several more layers of elements should be used to obtain a more accurate representation of the machine The configuration described was used because of disk space limitations 4 4 2 1 Materials Table 4 1 lists the material properties that were assigned to the objects that make up the BDFM model Note that although the stator slot actually contain copper windings they are modeled as air since a current density excitation is used to specify the exact current flowing in the windings To model the stator windings as copper would cause the program to induce additional eddy currents i
110. ssesesessoresesesrssrenee 43 Comparison of Two Three Dimensional Finite Element Analysis Software Packages onean e a E A E E 49 5 1 Introductionis snie aae E E E E AA 49 5 2 Maxwell 3D Field Simulator by Ansoft Corporation cccccseeseeseeeeees 49 5 2 1 Adyantages icoana e ia aenaran isi 49 5 2 1 1 Solid Modeling Procedure ee seeseecesseeteceeeeeeeseeees 49 5 2 1 2 Step by Step Design Procedure cccccscsseeseeeseeseeeees 51 5 2 1 3 Automated Meshing Technique cccccscsseeseeeseesseeenes 52 5 2 2 Disadvantages Limitations ccccssecsscessesscesscessecsscestesseeeseeenseeaes 53 5 2 2 1 Only Two Analysis Modules Available cccceeeeee 53 5 2 2 2 Solution Parameters have to be Re entered each Time a Modification is Made sgssictsvstirdts bonita ina atenes 54 5 2 2 3 Very Poor Program Diagnostics cccccscssccessesesesseesseenes 54 5 2 2 3 1 Program Continues to Execute and Status is not Available to the User 0 0 ce eecseseseeseenees 55 5 2 2 4 Poor Customer Support fccies iinet edierienaccoielsceiseastasec teens 55 5 2 2 5 No results due to Problem Encountered ccccsseeseeeees 56 5 3 1 AAV ANAS ES eri E R A iat 56 5 3 1 1 Many Modeling Modules Available for a Variety of Problems ee a rE a E AEE E 56 5 3 1 2 Well Documented Program Diagnostics c ccsceseees 57 5 3 1 3 Setup Parameters are Saved and only have to be E tered Once aehos E e Ra E a ET 57 5 3 2 Di
111. ssing element by hand 106 A 4 3 6 Mesh Organization When the two dimensional mesh is completed it will contain many elements and will regenerate on the screen rather slowly Rather than having to always remember element identification numbers when manipulating groups of elements and always having to display all the elements on the screen at once it is helpful to use two mesh organization techniques groups and parts A 4 3 6 1 Using Groups A group collects several elements together by some common criterion The group is assigned a name so that the elements can be manipulated by name rather than having to always remember and enter their identification numbers A useful criterion for creating groups are property identification numbers PIDs A PID was assigned to every element as it was created It is helpful to collect elements in groups according to their PIDs One group is created for each PID with a name corresponding to the object that group of elements represents Groups can be created in MSC XL as follows some common settings used when grouping elements are included 1 Pick Tools gt Group Define from the cascading menus 2 Inthe pop up menu enter the following parameters e Name Assigns a name to the group e Type Element Select the type of entity to be grouped 107 e IDList All The elements to be considered in the grouping selection e Criterion PID PID The criterion to be used to group the
112. strated in Figure Constraint A 9 Arangi O Anoma O 0 iE Ba Ea E le S A 7 Figure A 9 Fixed Boundary Conditions 124 In two dimensional problems a line of constant normal magnetic vector potential A is called a magnetic flux line For most electric machines B flows in the plane of the steel laminations and the flux is assumed to be confined to the steel outer boundary Flux lines along such a boundary not crossing it are enforced by setting A 0 along the boundary The existence of three vector components of A in three dimensional electromagnetic problems makes boundary conditions more complicated than in two dimensional problems The three components of A may be A Ay and A or in cylindrical devices such as motors is conveniently expressed in the three cylindrical components A Ag A Although plots of contours of constant 4 in two dimensional problems are flux line plots in three dimensions flux line plots are not rigorously defined Contours of constant total magnitude of A are sometimes analogous to planar flux plots Boundary conditions of A in three dimensions are governed by the curl of A for example in cylindrical coordinates 5 2 A 24a 2 A Ala 2 za eae 4 Equation A 7 r 08 00 z z r Thus it can be seen that one way of enforcing B 0 is to set A Ag 0 In other words B can be prevented from crossing a boundary surface b
113. t Distortion ccccccscessesscseesseseeseeeneess 93 A 4 3 3 Preparation for Meshing Assigning PIDs 00066 94 A 4 3 4 Meshing in MSC XL uw ee cecceeceesesessessesseesesecseesseseeseseeneens 96 A 4 3 4 1 Parametric Meshing ccccccssecssesssesseesseeseees 97 A 4 3 4 2 Connect Grids cccssccsscsssessessseescessesseeeseeesssees 98 A 4 3 4 3 Reflecting and Rotating the Mesh 00 99 A 4 3 5 Mesh Checking Procedures 0 ccescssssseseseessesesseeseeeeees 101 A 4 3 5 1 Duplicate Grid Points ccscsssscsssssssssessens 102 A 4 3 5 2 Unconnected Grid Points 0 ceeeeceseeseeeeeens 103 A 4 3 5 3 Duplicate Elements ccsscsssssssssscsesscesceseess 103 A 4 3 5 4 Free Edges or Free Faces ccccescssssseeseeseseees 103 A 4 3 5 5 Element V Oids sicsanorvaccatitccdsaunevieannias 105 A 4 3 6 Mesh Organization scecsscsssssssssseecsnseceseeseeeseenescees 106 A 4 3 6 1 Using Groups cccccessescsessessessesesseseeeseeceeees 106 PB S0 2 Using PartSviscvser tasescaetiiegiatienuceetagnnk 107 A 4 3 7 Extruding the Two Dimensional Mesh to Make a Three Dimensional Mesh ccccsss cesssesesseeseeseeseeseeenees 108 A44 Problem SEU Dis cseasatanssevitiniuaeds land ariel cnddent ade teasedis pari eiyan eae 111 AAA Material Properties ssiitcnisdendamstenesmm ivan aan 111 A 4 4 1 1 Permittivity 00 csscseescsesseessscsssseesseeenees 112 A 4 4 1 1 1 Isotr
114. t Grids option as follows 1 Pick FEM gt Elements gt Connect Grids Create Type of Element from the cascading menus It is important to choose the correct type of element to be created MSC XL will create a TRIA element even if QUAD is chosen for the type of element and vice versa This error is not detectable with the mesh checking procedures but will result in an user fatal error during the solution process 2 In the pop up menu specify the PID for the elements being created The grid points to be connected can then be picked directly from the graphics tile A 4 3 4 3 Reflecting and Rotating the Mesh Portions of the mesh that are symmetrical to an already created portion can be created by reflecting and rotating the existing portion For example the full 45 degree section of the stator mesh can be created by reflecting and rotating the 5 degree stator radial wedge First the 5 degree section is reflected about the 6 5 degree plane then the resulting 10 degree section is rotated 4 times about the 0 10 degree plane This 100 will result in a 50 degree section The excess elements can easily be deleted to form the 45 degree section Also once the rotor stator and air gap have been entirely meshed to create a 45 degree radial machine section the full 180 degree model can be created by reflecting and rotating the existing 45 degree section First the 45 degree section is reflected about the 6 45 degree plane then th
115. te system to be used to enter anisotropic or unsymmetric material tensors The Thickness and Area fields are unnecessary for a 3 D model these fields should be left blank A thickness is entered for 2 D QUAD and TRIA elements while an area is entered for 1 D LINE elements but these elements are not present in a 3 D model Once a material has been selected for each PID in the model the material property setup is complete A 4 4 1 5 Materials for the BDFM Model Table A 5 shows typical material properties used in the material property setup of a BDFM model All materials used for the BDFM model are default materials included in MSC XL 118 3 D Objects Material Electrical Conductivity siemens meter ir Air surrounding Air end connections Table A 5 Materials Used in the Setup of the BDFM Model Note the stator windings are assigned the material property of air even though the windings actually consist of copper This is because a current density excitation will later be applied to the stator winding elements Since the exact current density will be specified in the windings a conductivity is not necessary for these elements To specify a conductivity for elements to which an excitation is applied will cause additional eddy currents to be induced in these elements Therefore the stator windings should be specified in the material setup as having material property air which has identical permittivity and permeabilit
116. ther factors 133 10 000 Cellular Cube upper bound 1000 0 Fiat Plate P BST120 typical Required Disk Space 100 0 Megabytes 10 0 100 1000 10 000 100 000 Number of Grid Points Figure A 11 Disk space requirements for MSC EMAS based on the cellular cube and flat plate fora MSC NASTRAN solution 101 run 17 The solution time for an AC analysis of the detailed 180 degree BDFM model which contained 9510 grid points was approximately 5 hours The solution time for an AC analysis of the coarse 360 degree BDFM model which contained 8325 grid points 134 was slightly faster at approximately 4 5 hours The coarse 180 degree BDFM model which contained 4280 grid points ran surprisingly quickly with a solution time of approximately 30 minutes The solution time required therefore seems to increase exponentially as the number of model grid points increases A 4 6 Results and Validation The first thing to do when the MSC EMAS run finishes is to read the lt filename f06 gt file to check for error messages If for some reason the lt filename f06 gt file contains error or warning messages these should be investigated Chapter 6 of the MSC EMAS User s Manual 10 contains error message numbers and explanations If no error messages are found in the lt filename f06 gt file the user can then proceed to the results processing functions in MSC XL to view the results graphically A 4 6 1 Accessing MSC EMAS Res
117. ts created e Uspace Vspace The spacing between the generated grid points for the surface s U and V parametric directions e GridIds The identification numbers of the new grid points e Output The identification numbers of the new elements Another useful parametric meshing procedure is parametric meshing of an already created element Parametric meshing of an element can be accomplished by 1 Picking FEM Mesh Parametric Mesh gt 4 grids from the cascading menus 2 The four grid points surrounding the element to be meshed can be picked directly from the graphics tile Alternately the grid point identification numbers can be entered in the pop up menu 3 The old element should be deleted after the new elements are created A 4 3 4 2 Connect Grids Connecting Grids is useful meshing procedure to use in areas of transition between fine and coarse elements The grid points that have been created by the parametric meshing procedure can be connected by picking them directly This technique is used to create the air gap in the BDFM model once the rotor and stator 45 99 degree radial section have been completed Grid points along the outer edge of the rotor are connected to grid points along the inner edge of the stator by using the Connect Grids option The air gap can contain QUAD or TRIA elements or usually both Elements are created within the air gap by connecting grids until the entire air gap is closed Use the Connec
118. ty of all industrial and commercial motors still operate at fixed speed Similarly fixed speed generators provide the bulk of the world s power supply although many power sources could be more efficiently converted if variable speed generation VSG were used The transition from fixed speed systems to ASD and VSG systems has been delayed by the fact that the speed of AC machines is linked to their frequency Although frequency control by power electronics has made significant advances in recent years it still has two major obstacles preventing its more widespread application First the cost of electronic power converters is many times higher than the cost of the machines they control Second the electronic power converters pollute the power supply system with harmonics of voltage and current Possible solutions to the harmonic problem serve to increase the cost of the system Therefore it is important to investigate possible methods for minimizing the ratings and hence costs of power electronic converters Ongoing studies at Oregon State University have shown the potential for many advantages by using a doubly fed connection of the self cascaded induction machine in ASD and VSG applications 1 5 The use of a self cascaded or brushless doubly fed machine BDFM in combination with a power electronic converter can offer a number of advantages over conventional induction machines in ASD and VSG systems These advantages include tolerance to po
119. ults The first step in results processing is to establish the connection between a Results Table and a file containing results data filename xdb The filename xdb file contains the model and the results from the MSC EMAS analysis The filename xdb file should be read into the filename db file from which the results were generated This can be done as follows 1 Make sure that the current filename db file loaded in MSC XL is the database file from which the results to be processed were generated 135 2 Choose Field Results ResultsTable from the cascading menus 3 Select the Type of results to be processed Analysis Results refers to results from an MSC EMAS analysis ImportResults refers to results quantities in an external file format 4 Choose the filename xdb File to be accessed The results contained in the filename xdb file are now available for processing in MSC XL A 4 6 2 Producing Contour Plots A contour plot is a plot in which MSC EMAS result quantities are displayed as colored lines or bands These contours are lines or colored regions representing constant values Contours can be displayed as colored lines or as colors which fill an element For the BDFM analysis problem line contour plots of magnetic vector potential 4 show the distribution of magnetic flux lines within the machine To make a contour plot of magnetic vector potential like the ones presented in Chapter 4 use the following procedure 1
120. unsd opsavaiseatnsea vivxsausidavs ncsanenstonceceszetesess 3 2 2 Basic Performance Equations vies ssesasssiratesavesnraccasurandeidovsyasdssasiaversGedlsvmeres 4 2 3 Applications of the BDEM cuuinsiamuniiacimutasciaamiaindaueiiman 6 Finite Element Analysis Method aiissescdecesassssincstadiscdactdarides dastasianciadiead isin unaneens 7 3 1 Definition and Concept recess cde eeitien deci angiacesncatsitiins tuning 7 3 2 Finite Element Mode 4 ss iieccet ch sccecs tect ancyetcian a R a 7 3 3 Solution of Maxwell s Equations sseeeseeeeeeseeeeseeeeresssesseseeneseseseerensesreresrees 8 3 4 Data RECOV ery cerala ees ee A EWA EE sees E a 12 Finite Element Design Procedure for the BDFM cccsscescesscesseceesseeeeeeeseenenes 13 4 1 Methods of Modeling Induction MOtors cceccesessesseeeseceseeeeeseeseneeaes 13 4 1 1 Solution Frequency scuinsaiwndiaddumrsunrinteeicinatauckn sn 13 4 1 2 Periodic Boundary Conditions essseseeseesesseseeseessessersrssesresreseesees 14 4 2 FE Modeling of Doubly Fed Characteristics 0 ccssecsseesceseeeseeeeeceaeenaes 15 4 2 1 Complications of the Nested Rotor Structure cesccseeseeeteeeeees 15 4 2 2 Inclusion of Two Excitation Frequencies c cccsscssestessseeseeeesees 15 4 2 3 Boundary Conditions More Difficult to Determine 0 15 4 3 Three Dimensional Simulation of the BDFM ce eceeeeseseeseeteeeseeseeees 16 4 3 1 Modeling in
121. w Contents and choosing the part identification numbers of the parts to be posted or unposted By selecting one part number at a time the user can check to see that the mesh was properly created Once the three dimensional finite element mesh has been completely created and checked material properties excitations and boundary conditions can be assigned to the model A 4 4 Problem Setup A 4 4 1 Material Properties Three properties are needed to describe materials in electromagnetic problems These three electromagnetic material properties are permittivity or dielectric constant electrical conductivity and permeability Material properties are assigned to groups of elements in MSC XL by specifying values for relative permittivity absolute electrical conductivity and relative permeability Before the process for setting material properties in MSC XL is discussed a brief background of these three properties is given 112 A 4 4 1 1 Permittivity Permittivity e is defined to satisfy the equation D le E Equation A 1 where D is a electric displacement coulombs meter in MKS is the electric field volts meter in MKS and is the permittivity of free space 8 854E 12 Farads meter in MKS The 3x3 relative dielectric tensor e relative to free space dimensionless is En En Eg e Ey Ez Equation A 2 E3 En 33 A 4 4 1 1 1 Isotropic Permittivity If D and fall in the same direction th
122. wer converter failure controllable power factor and reduced harmonic pollution Most importantly depending on the requirements of the application a reduction in the power electronic converter rating and therefore cost can be achieved Presently efforts are being directed at optimizing the design of the BDFM and investigating areas of commercial feasibility One possible aid in the investigation of design alternatives is finite element analysis Finite element analysis is a numerical method for determining the field distribution in a dimensional model This thesis will emphasize only the electromagnetic field distribution in a three dimensional model geometry Finite element techniques have been successfully used for some time in the design of induction reluctance and permanent magnet machines From a finite element solution important design quantities such as flux distribution flux density winding inductance eddy currents hysteresis losses force torque and losses can be calculated Applying the finite element technique to the BDFM however has posed a number of difficulties This thesis will present a design method for modeling the BDFM using finite element techniques 2 Brushless Doubly Fed Machine 2 1 BDFM Characteristics The stator winding connection of the BDFM is based on the work of L J Hunt 6 and later developments by Creedy 7 The BDFM stator as shown in Figure 2 1 consists of two sets of three phase stator windi
123. y setting the tangential components of A to zero 125 A 4 4 3 2 Periodic Boundary Conditions Many electric machines have identical poles The number of grid points contained in a finite element model can be greatly reduced if the mesh only needs to contain one pole In any electric machine having identical poles each pole boundary has periodic boundary conditions For three dimensional machine models periodic boundary conditions are expressed in cylindrical r 8 z coordinates by Equation 4 5 4 8 This periodic boundary condition is implemented with a multipoint constraint MPC and is called an alternating boundary condition If the geometry requires modeling two poles then the A s on the boundary are set equal instead of opposite which is referred to as a repeating boundary condition Generally an odd number of poles requires alternating periodic boundaries and an even number requires repeating periodic boundaries Figure A 10 illustrates the alternating periodic boundary conditions One Period Figure A 10 Alternating Periodic Boundary Conditions 126 Applying alternating periodic boundary conditions to a 180 degree model of a 6 2 pole BDFM provides results consistent will a 360 degree model simulation as discussed in Chapter 4 A 4 4 3 3 Applying Boundary conditions to the BDFM Model A 4 4 3 3 1 Outer Boundaries For the BDFM model we can constrain B to remain within the machine boundaries by constra
124. y to copper but zero conductivity A 4 4 2 Excitations Excitations are included in a finite element model to represent either applied electrical currents or permanent magnets For the BDFM model current excitations are 119 included to represent the three phase stator windings Methods for setting up current excitations in the AC module will be discussed A 4 4 2 1 Available Excitations The following excitations are available in the AC analysis module current density current region edge H field edge J field line current permanent magnetization point current point current axisymmetric point current scalar surface H field surface J field and volume current source A 4 4 2 2 Applying Excitations to the BDFM Model The appropriate excitation to use to model the three phase stator windings is the current density excitation The current density excitation can be applied to the elements representing the three phase stator windings by first grouping the elements to be excited and then applying the current density excitation where Phase 0 Phase 240 Phase 120 Table A 6 Six Pole Stator Winding Layout 120 Paya TAT B BB P1920 21 22 23 24 25 26 oe dees Ss ee where Phase 0 Phase 120 Phase 240 Table A 7 Two Pole Stator Winding Layout Tables A 6 and A 7 show how the stator source currents for the 6 pole and 2 pole windings were specified respectively Sing
125. ype Results from the cascading menus In the fourth cascading menu choose the following parameters e X Data Path e Y Data Instantaneous Results e CutPathID The identification number of the appropriate Cutpath e NumOfPoints The number of points to be selected by the program along the Cutpath for plotting purposes Use the QuickEditRT option in the fourth cascading menu to select the appropriate field quantity to be plotted along the Cutpath Select XY Plotting Load Data from the cascading menus MSC XL loads the appropriate field data along the Cutpath Pick XY Plotting Plot in View lt ID gt from the cascading menus to plot the graph 141 A 4 6 6 Calculations Several calculations are automatically defined in MSC XL for post processing of AC results The calculation that was used to calculate the total induced current in each of the BDFM rotor bars will be presented here For a complete list of calculations available in MSC XL refer to the MSC EMAS User Interface Guide for AC Analysis 16 The total current in the BDFM rotor bars was calculated using the Current from J calculation included in MSC XL This calculation is defined as follows I ja ds Equation A 8 where J is the conduction current density and ds is the integration surface Total currents are calculated using the Current from J calculation as follows 1 Define a Cutsurface and intersect it with the elements over which the integration wi

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