A Permanent Magnet DC Motor Problem

Ansoft RMxprt Application Note

A Permanent Magnet DC Motor Problem This application note describes how to set up, solve, and analyze the results of a two-pole 75-watt DC brush-type motor using RMxprt. You will then use the results from RMxprt as a basis for performing a more detailed analysis in the finite element time transient solver, EMpulse. RMxprt uses a combination of electric and magnetic circuit equations to predict the performance of this permanent magnet DC motor. EMpulse uses the time domain finite element method, coupled with the electrical equations of the drive circuit and the motion problem, to predict the dynamic and transient behavior of the switched reluctance motor. You can create the RMxprt project from scratch or open the pre-solved project stndj-1.pjt, which is located in the /ansoft/examples/rmxprt/ directory. You can create the finite element project from scratch or download stndj_fea.pjt from the Technical Support page for Maxwell 2D projects on the Ansoft web site, at www.ansoft.com. If you are creating the project from scratch, select Permanent-Magnet DC Motors as the motor type in RMxprt. These projects were created using version 3.0 of RMxprt and version 8.0 of Maxwell 2D.

Application Note

AP064-9911

General Data Use the General window to specify the motor characteristics. ➤

Define the general data: 1. Enter 0.075 kW in the Rated Output Power field for this two-pole motor. 2. Enter 12 V in the driving DC Rated Voltage field. 3. Enter 2 in the Number of Poles field. 4. Enter 2400 rpm in the Given Rated Speed field. 5. Optionally, you can enter the Friction Loss as a lumped parameter value, or allow it to be calculated according to the brush pressure. Allow RMxprt to calculate the friction loss due to the brush pressure; enter 0 in this field. 6. Enter 10 in the Brush Displacement field. This defines the displacement as 10 degrees from the axis of rotation in the counter-clockwise direction. 7. Enter 1.5 V in the Brush Drop field as the voltage drop for one pair of brushes. 8. Enter 75 degrees C in the Operating Temperature field.

Rotor Data Use the Rotor1 and Rotor2 windows to define the rotor data.

Define the General Rotor Data Use the Rotor1 window to define the number of slots and the diameter of the rotor. ➤

Define the general rotor data: 1. Select 2 as the Slot Type. This corresponds to a slot shape with a tapered neck that has a round bottom. 2. Enter 9 mm in the Inner Diameter field. 3. Enter 55 mm in the Outer Diameter field. 4. Enter 12 in the Number of Slots field. 5. Enter 0 in the Skew Width field. The stator lamination is a straight stack without any skew. 6. Deselect Auto Design. 7. Enter the following Slot Dimensions (in mm): • Enter 1.2 in the Hr0 field. • Enter 1.0 in the Hr1 field. • Enter 9.8 in the Hr2 field. • Enter 3.0 in the Br0 field. • Enter 8.6 in the Br1 field. • Enter 4.0 in the Br2 field.

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A Permanent Magnet DC Motor Problem

Define the Rotor Slots and Wires Use the Rotor2 window to define the rotor slots and wires. ➤

Define the rotor slots: 1. Select Lap as the Armature Winding Type. 2. Enter 40 mm in the Length of Rotor field. This value includes the length of the laminations. 3. Enter 0.92 in the Stacking Factor field. This gives an actual length of the steel to be 36.8 mm. 4. Select M36-29G (M36 Steel at 29 gauge) as the nonlinear Steel Type used in the manufacturing of the rotor lamination. 5. Choose Materials/BH from the RMxprt menu bar, and open M36-29G.h-b, which is the file that contains both the BH- and the loss curve used for this analysis. 6. Choose Save As. Select *.bh as the file extension. This is the format that EMpulse uses. Save this file as M36-29G.bh. Choose Save to save the file. Choose Exit to return to the Rotor2 window. 7. Enter 0.5 mm in the Slot Insulation field. The slot insulation is taken to be the thickness on one side of the rotor slot. 8. Enter 0 in the End Adjustment field. The end length adjustment is the length that the stator winding extends from the lamination in the vertical direction before bending across the stator into the return slot. For this motor, there is no vertical extension of the stator winding; therefore, the value is zero. 9. Enter 1 in the number of Virtual Slots per Slot field. The rotor is assumed to have two layers of conductors, an upper layer and a lower layer. Each layer of conductors can have a number of windings, which are referred to as virtual slots. For example, the upper and lower layer can have two windings each, which would yield a virtual slot number of two; for a 12 slot machine, this would be 24 commutation segments. For this motor, there is 1 winding in the upper layer and 1 winding in the lower layer, so the number of virtual slots in this case is 1. 10. Enter 20 in the number of Conductors per Slot field. If you want RMxprt to automatically calculate this value for you, then enter 0 in this field. 11. Enter 1 in the Multiplex Number field. For a lap winding, the multiplex number is the number of commutators between the start and end of one winding. The number of parallel branches is equal to the number of poles multiplied by the multiplex number. In this case, the multiplex number is 1, which yields 2 parallel branches. For a wave winding, the number of parallel


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branches equals the multiplex number multiplied by two.

12. Enter 5 in the Coil Pitch field. Even though RMxprt assumes there are two layers of conductors, a rotor that uses only one layer can still be modeled by making the coil pitch full instead of fractional. A full pitch for this motor would be 6 slots (12 slots/2 poles); instead of a full pitch, this motor is wound one slot short, or 5 slots, and is a lap-type winding. 13. Enter 2 in the number of Wires per Conductor field. 14. Enter 0.09 mm in the Wire Wrap field as the thickness of the insulations. This refers to the width of the insulation on both sides of the wire. 15. Enter 0.95 in the Wire Diameter field. This number is not a standard AWG value, so you must enter it in the field, rather than selecting an available value from the pull-down menu. When you enter this value, the Gauge field automatically changes to USER. If you do not have a wire standard defined, choose Tools/Options, select either American or Chinese as the Wire Setting, and choose OK. Once this is done, you can choose Materials/Wire to view the wire table. In this table, under Round Wire Data, there is a column for Wrap where all values are 0. Depending on your manufacturer, the value for the wire wrap can be entered here, and then, when you select the wire gauge, RMxprt looks up the value of wire wrap in this table. Any value greater than 0 entered in the Wire Wrap field in the Rotor2 window overrides the value in this wire table.

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Stator Data Use the Stator Pole window to define the stator data. ➤

Specify the stator: 1. Enter 0.5 mm as the Air Gap between the rotor and stator. 2. Enter 79 mm as the Outer Diameter of the stator. 3. Enter 100 mm in the Length of Stator field. 4. Enter 1 in the Stacking Factor field. The stator is not laminated. 5. Select M36-29G as the Steel Type. The rotor and stator are made from the same materials. 6. Enter 0 in the Pole Arc Offset field. The radius origin for the permanent magnet that creates the stator pole does not necessarily need to coincide with the radius origin for the stator inside diameter. In the case of a non-uniform air gap, these two origins will be offset from one another by a certain value; RMxprt refers to this value as the Pole Arc Offset. In this case, the air gap is uniform, so the offset is 0.

7. Enter 0.726 mm in the Pole Embrace field. The stator pole embrace represents a percentage of the maximum physical dimension of the permanent magnet stator pole. A pole embrace of 1 for a two-pole machine means that the physical rotor pole covers exactly 180 mechanical degrees; likewise, a pole arc radius of 0.667 (2/3) means that the stator pole covers 120 mechanical degrees. 8. Select TEM as the Magnet Type. TEM is a permanent magnet with a retentivity (or residual flux density (Br)) of 0.4 tesla, a coercivity of -318 kiloamps/meter, a maximum energy density of 31.82 kilojoules/meter3, and a relative recovery (or recoil permeability) of 1.0. 9. Enter 9.0 mm in the Magnet Thickness field. 10. Enter 40.0 mm in the Magnet Length field.


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Commutator and Brush Data Use the Commutator/Brush window to define the commutator and brush data. ➤

Specify the commutator and brush data: 1. Select Cylinder as the Commutator Type. 2. Enter 24 mm in the Commutator Diameter field. 3. Enter 10 mm in the Commutator Length field. 4. Enter 0.5 mm in the Commutator Insulation field. This value is the thickness of the insulation. 5. Enter 8 mm in the Brush Width field. 6. Enter 8 mm in the Brush Length field. 7. Enter 2 g/mm2 in the Brush Press field. This value represents the pressure of the brushes on the commutator. 8. Enter 0.25 in the Frictional Coefficient field.

Analyzing the Design Before analyzing the design, you need to set the lamination and wire setting options. ➤

Define the options, and generate the design: 1. Choose Tools/Options, make certain that the Stator, Rotor, and Slot boxes are selected in the Lamination section, and make certain that the Wire Setting is American. Choose OK. 2. Choose Analysis/Analytical Design. RMxprt calculates the motor performance parameters for this design. 3. Once the analysis is complete, choose Post Process/View Lamination to examine a cross-section of the motor. Choose File/Exit when finished viewing the laminations. 4. Choose Post Process/Design Output to view all of the motor performance characteristics.

Design Output The Design Output window is divided into nine sections: General Data, Rotor Data, Stator Data, Permanent Magnet Data, Commutator & Brush Data, No-Load Magnetic Data, Full-Load Data, Commutating Data, and Transient FEA Input Data. The second line of the Design Output file tells you where the results file is located; this file has the same name as the project, with the extension .res (stndj-1.res for this example).

GENERAL DATA This information is the same as the data you entered in the General window, except for the value of Frictional Loss. Since you entered 0 in this field, RMxprt calculated a value from the brush pressure value of approximately 2 watts.

ROTOR DATA This information is the same as the data you entered in the Rotor1 and Rotor2 windows, except that the width of the top and the width of the bottom of the rotor tooth are also calculated, along with the slot fill factor. The slot fill factor represents the percentage of the available slot area, which is the total slot area minus the slot insulation, that is filled with the wire (copper plus insulation). The area of the copper is calculated by A=d2, not A=πr2, where d is the diameter and r is the radius of the wire. For this example, the slot is completely filled to a value of 100%.

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STATOR DATA Most of this information is the same as the data you entered in the Stator Pole window. The polar arc radius is given instead of the pole arc offset value. Pole embrace is given in mechanical and electrical degrees. You defined the mechanical pole embrace in the Stator Pole window. The electrical pole embrace is based on the air gap flux density distribution and is the ratio of the average flux density to the maximum flux density over one pole. Please see the following figure:

PERMANENT MAGNET DATA This section displays the properties of the permanent magnet, as well as the demagnetization flux density. The recoil remanence and coercivity are given using a linear recoil permeability of 1.0.

COMMUTATOR & BRUSH DATA This information is the same as the data you entered in the Commutator/Brush window.

NO-LOAD MAGNETIC DATA This section displays the magnetic flux density in the stator teeth and yoke, and the flux density in the rotor yoke. All of the components of the magnetomotive force (mmf) are given for the entire reluctance path: rotor teeth, rotor yoke, stator yoke, air gap, and the permanent magnet. The mmf drop due to the permanent magnet opposes that of the windings, and, as expected, the sum of all of the mmf drops along this reluctance path is zero. The Armature Reactive Ampere Turns value refers to the magnetic force due to the armature current. The leakage flux factor takes into account any flux that does not link the stator and the rotor. The correction factors from the magnetic circuit length of the stator and rotor refer to the path used to calculate the mmf drop for the stator and rotor. The no-load speed in this case is 2716 rpm, and the current needed to achieve this speed is 0.36 amps DC. The no-load input power is 4.3 watts.


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FULL-LOAD DATA The following motor performance parameters are calculated at a rated output power of 75 watts: Input Current (A) 8.2 The DC line current value. Armature Current (A) 4.1 The input current divided by the number of parallel paths. Armature Thermal Load 16.3 Specific Electric Loading (A/mm) multiplied by Armature Cur2 3 (A /mm ) rent Density (A/mm2). Specific Electric Loading 5.7 The Specific Electric Loading value (A/mm). (A/mm) Armature Current Density 2.9 The current density of the armature winding. (A/mm2) Friction and Wind Loss (W) 2.0 The value calculated from the brush pressure. Iron-Core Loss (W) 1.4 The total core loss in the stator and rotor based on the loss curve. Armature Copper Loss (W) 7.2 The power loss due to the resistance of the armature winding. This is the total copper loss. Brush Loss (W) 12.2 The power loss due to the drop across the brushes. Total Loss (W) 22.8 Friction and Wind Loss + Iron-Core Loss + Armature Copper Loss + Brush Loss. Output Power (W) 75 The given Rated Output Power from the General window. If the motor cannot output this value of power, RMxprt calculates the maximum output power and displays that value here. Input Power (W) 98 The rated DC voltage multiplied by the Average Input Current. Efficiency (%) 76.6 The output power divided by the input power. Rated Speed (rpm) 2497 The running speed at the specified rated output power. . 0.3 The shaft torque available at the rated output power. Rated Torque (N m) Locked-Rotor Torque (N.m) Locked-Rotor Current (A)

3.6

The starting torque when the shaft speed is zero.

96.8 The total current that the stator will draw when starting this motor.

COMMUTATING DATA In this example, the total induced voltage of -0.3 volts is calculated from the inductance, the armature reaction, and the main fields.

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TRANSIENT FEA INPUT DATA This information is used when calculating the motor performance using the time transient finite element field solver, EMpulse. For Armature Winding: Number of Turns Parallel Branches Terminal Resistance (ohm) End Leakage Inductance (H) For 2D Equivalent Value: Equivalent Air-Gap Length (mm) Equivalent Stator Stacking Factor Equivalent Rotor Stacking Factor Equivalent Br (Tesla) Equivalent Hc (kA/m) Estimated Rotor Inertial Moment (kg-m2)

120 2 0.11 6.0e-5

The total number of turns. The total number of parallel branches. The total DC resistance. The end turn stator winding leakage inductance only.

40 2.5 0.92 0.4 318.3 0.00028 This value for inertia does not include any loading, bearings, and so forth.

Choose Exit to close the Design Output window.


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Performance Curves Examine the performance curves for the model. ➤

Examine the performance curves: 1. Choose Post Process/Performance Curves. The PlotData window appears, with an Open window visible. The following plot titles are available to open: n_curr.dat Input Current vs Speed n_effi.dat Efficiency vs Speed n_pow2.dat Output Power vs Speed n_torq.dat Output Torque vs Speed wv0_coil.dat Induced Coil Voltages at Rated Speed wv0_flux.dat Air-Gap Flux Density 2. Select the plot to view. 3. Choose OK. The plot appears in the PlotData window. After you’ve opened one plot, to open a different plot, choose Plot/Open. Note that the speed is measured per unit of the synchronous speed. The following figures show the performance plots for the sample problem:

• n_curr.dat: Input Current vs Speed

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• n_effi.dat, Efficiency vs. Speed

• n_pow2.dat: Output Power vs Speed


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• n_torq.dat: Output Torque vs Speed

• wv0_coil.dat: Induced Coil Voltages at Rated Speed

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• wv0_flux.dat: Air-Gap Flux Density

4. When you have finished viewing the performance curves, choose File/Exit to exit PlotData.


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Analyze the Geometry Now that the motor design is complete, examine the geometry, and define the options to be used for the time transient finite element analysis (FEA). ➤

Analyze the geometry: 1. Choose Tools/Options, and make certain the Maxwell Path is set to the directory where the Maxwell software is installed. There are three check boxes in the Field section of this window. The first box, Periodic, specifies how many periodic conditions you want to draw for the geometry: one for one pole, two for two poles, and so forth. If the number of rotor slots is a multiple of the number of poles, then a periodic condition exists. The second box, Difference, specifies how many degrees the rotor should turn. This is for viewing purposes only, When creating the final geometry, this should be deselected or assigned to 0. The third box, TeethTeeth, specifies whether the rotor geometry spans tooth-to-tooth or slot-to-slot; in most cases, you want this selected. Right now, though, leave all of these boxes deselected. 2. Make certain all three check boxes are deselected. 3. Choose OK to exit the Options window. 4. Choose Analysis/View Geometry. A full cut-away cross-section of the motor appears. Since this model has two poles and the windings are symmetrical, you can reduce the model from 360 to 180 degrees. 5. Choose File/Exit to exit the Maxwell 2D Modeler. 6. Choose Tools/Options again. Notice the check boxes for Difference and Teeth-Teeth. The Difference option allows you to specify the angular difference between the rotor and the stator (in electrical degrees) when creating the geometry. The Teeth-Teeth option specifies that none of the rotor teeth or permanent magnets will be cut in half; only entire teeth or permanent magnets will be modeled. You can modify some of these options to determine their effect on the geometry. 7. For this FEA analysis, use a geometry that includes a Periodic multiplier of 1 with the TeethTeeth box selected and the Difference box deselected. 8. Choose OK to accept the options and exit.

Create the Maxwell 2D Project Once you have analyzed the geometry, you can then create the Maxwell 2D project. ➤

Create the 2D project: 1. Choose Analysis/View Geometry again, and then choose File/Exit to exit the Maxwell 2D Modeler. Because Create Maxwell 2D Project may be disabled after you change the options, you need to view the geometry again before trying to create the project. 2. Choose Analysis/Create Maxwell 2D Project. The Create Maxwell 2D Project window appears. 3. Specify a Project Name and Path for this permanent magnet DC motor. The name of the presolved project is stndj_fea.pjt. 4. Choose Create. A Maxwell 2D project is created using the specified geometry options. 5. Return to the Project Manager to continue with the rest of this example. Leave RMxprt open to refer to later in the example.

This completes the RMxprt design of the 75-watt two-pole permanent magnet DC motor. You can continue the analysis of this design using the time transient FEA software program, EMpulse.

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Finite Element Analysis Define the finite element parameters for the 75-watt permanent magnet DC motor.

Set Up the Geometry ➤

Open the project, and set up the geometry: 1. From the Project Manager in the Maxwell Control Panel, open the Maxwell 2D project you created in the previous section. If you are using the pre-solved project, its name is stndj_fea.pjt. Upon opening the project, you will notice that the Transient Solver, the XY Drawing Plane, and Define Model are already set. 2. Choose Define Model/Draw Model. The model appears in the Maxwell 2D Modeler. 3. Choose Window/Change View/Zoom In, and zoom in on the air gap. There is an additional object in the air gap, called Band, which is used during the solution process to determine which objects are stationary and which rotate. This Band object is used later in the example and should not be deleted. 4. Choose File/Save to save the file, and then choose File/Exit to exit the Maxwell 2D Modeler.


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Assign Material Properties Assign the material properties for each object in the model. Because this example requires materials not included in the material database, you first need to create them in the Material Manager. Choose Setup Materials to access the Material Manager and assign material properties to all of the objects.

Add New Materials Create three new materials for the model: one for the rotor, one for the stator, and one for the permanent magnet. Because the rotor and stator have different stacking factors and lengths, their B-H curves are different; therefore, you need to create a separate nonlinear material for each the rotor and the stator.

Add a Material for the Rotor Add the first of two new nonlinear materials, called M36_29G_Rotor, to the local material database. ➤

Add a new material for the rotor: 1. Choose Material/Add. 2. Change the name to M36_29G_Rotor in the Material Properties area. 3. Select Nonlinear Material. 4. Choose B H Curve. The B-H Curve Entry window appears. 5. Choose Import. The Import Data window appears. There are two different bh curves you can select: rotor_eq.bh and statr_eq.bh, which RMxprt created and which are located in the current project directory. These bh curves take into account different values of the stacking factor and the different lengths. Because in this example, the rotor and stator have different stacking factors and lengths, the two curves are different. 6. For this material, select the rotor_eq.bh curve. Choose OK to import the file and return to the BH-Curve Entry window. Choose Exit to exit the BH-curve window and return to the Material Manager. 7. Enter 288 in the Conductivity field. The conductivity of the steel indicates how easily current will flow in the z direction. Since the steel is laminated, there is no current in the z direction. There are, however, currents that circulate in the xy plane. To account for this effect, calculate an effective conductivity, using the following equation:

σ orig ⋅ SF σ eff = ----------------------2 N where: • σeff is the effective conductivity. • σorig is the original conductivity. • SF is the stacking factor. • N is the number of laminations. For this example: • σorig is 2x106 siemens/meter. • The stacking factor, SF, is 0.92. • The object has 80 laminations. • The effective conductivity is calculated to be 288 siemens/meter. From the above formula, you can easily see that the effective conductivity decreases by a factor of the number of laminations squared; thus, the more laminations, the smaller this effect. 8. Choose Enter to enter this material into your local database. The new material M36_29G_Rotor is now available in the database for this project.

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Add a Material for the Stator Add the second of two new nonlinear materials, called M36_29G_Stator, to the local material database. ➤

Add a new material for the stator: 1. Choose Material/Add. 2. Change the name to M36_29G_Stator. 3. Select Nonlinear Material. 4. Choose B H Curve. The B-H Curve Entry window appears. 5. Choose Import. The Import Data window appears. 6. Select statr_eq.bh. 7. Choose OK to import the file and return to the BH-Curve Entry window. 8. Choose Exit to exit the BH-curve window and return to the Material Manager. 9. Enter 2e6 S/m in the Conductivity field. The stator is not laminated; therefore, its conductivity is 2x106 S/m. 10. Choose Enter to enter this material into the local database. The new material M36_29G_Stator is now available in the database for this project.

Add a Permanent Magnet Material The permanent magnet used for this analysis must also be created. ➤

Define the permanent magnet: 1. Choose Material/Add, and change the name to TEM. 2. Choose Material/Underive. You do not want to derive this magnet from any other material. 3. Choose Options. The Property Options window appears. 4. Deselect Mu and Mp, and select Hc and Br as the values to define this permanent magnet. Choose OK. The magnet will operate in the linear portion of its BH-curve, so it will be modeled as a linear permanent magnet. 5. Enter -318300 A/m in the Mag. Coercivity (Hc) field, and enter 0.4 T in the Mag. Retentivity (Br) field. 6. Choose Enter to enter this material into the local database. The new material TEM is now available in the database for this project.


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Assign the Materials ➤

Assign materials to the objects as follows: ■ Assign air to the AirGap, AirStator, and Band. ■ Assign copper to all windings (PhA0 through PhA5, PhReA0, and PhReA7 through PhReA11). ■ Assign M36_29G_Rotor to the Rotor. ■ Assign M36_29G_Stator to the Stator. ■ Assign steel_stainless to the Shaft. ■ Assign TEM to the magnet, Magnet0. • When you assign TEM to the magnet, the Assignment Coord. Sys. window appears. Select the Align relative to object’s orientation option. Select the Function check box, enter IN in the Angle field, and enter (0,0) as the function origin. Remember that function names used in Maxwell are case-sensitive. • Choose Functions to define the function IN. The Function Definitions window appears. Create a new variable, named IN, whose value equals PHI - 180. Choose Add to add the variable to the list, and then choose Done to close the Function Definitions window and return to the Assignment Coord. Sys. window. • Choose OK to return to the Material Manager. This creates a radially magnetized permanent magnet with its north pole pointing inward to the center of the motor. ■ Exclude the background from the model. The problem will have boundary conditions assigned to every outside edge; therefore, the background is excluded from the solution.

Choose Exit, and save the changes made in the Material Manager.

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Setting the Boundaries and Sources The first step in defining the boundary conditions is to define the Master/Slave boundary. You then need to define the value boundary, and define the armature winding. Choose Setup Boundaries/Sources to define the electric circuit and the boundaries.

Define the Master Boundary ➤

Define the master boundary: 1. Choose Window/New and then Window/Tile to open an additional window and arrange the windows in tile format. 2. Choose Window/Change View/Zoom In, and zoom in on the air gap so that you can easily the band, air stator, and rotor outer diameter. 3. Choose Edit/Select/Trace. Starting in the window with the full model shown, click on the center axis of the motor (u=0, v=0), and then click on the following intersection: • Rotor Inside Diameter (u=4.5, v=0) 4. Switch to the window where the air gap in enlarged, and click on the following intersections: • Rotor Outside Diameter (u=27.5, v=0) • Band (u=27.75, v=0) • AirStator (u=28.0, v=0) 5. Switch back to the window with the full model, and click on the following intersections: • Stator Inside Diameter (u=37, v=0) • Stator Outside Diameter (u=39.5, v=0). Double click here to end the definition. 6. Choose Assign/Boundary/Master. 7. Choose Assign.

Define the Slave Boundary Again, use the Edit/Select/Trace command to define the slave boundary. ➤

Define the slave boundary: 1. Choose Window/Change View/Zoom In, and zoom in on the air gap at the negative axis. 2. Choose Edit/Select/Trace. Starting in the window with the full model shown, click on the center axis of the motor (u=0, v=0), and then click on the following intersection: • Rotor Inside Diameter (u=-4.5, v=0) 3. Switch to the window where the air gap in enlarged, and click on the following intersections: • Rotor Outside Diameter (u=-27.5, v=0) • Band (u=-27.75, v=0) • AirStator (u=-28.0, v=0) 4. Switch back to the window with the full model, and click on the following intersections: • Stator Inside Diameter (u=-37, v=0) • Stator Outside Diameter (u=-39.5, v=0). Double click here to end the definition. 5. Choose Assign/Boundary/Slave, and select Slave = –Master. When solving for one or for an odd number poles of an electrical machine, use the Slave = –Master symmetry. When solving for an even number of poles, use the Slave = +Master symmetry. 6. Choose Assign.


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Define the Value Boundary Define the remaining boundaries. ➤

Define the value boundary: 1. To assign the outside diameter of the stator a zero value boundary, choose Edit/Select/Edge, and click on the outside diameter of the stator. 2. Choose Assign/Boundary/Value, and change the Name from Value1 to Zero_Flux. Keep the Value set to 0. A zero value boundary means that all of the flux will be contained in the motor; there will be no leakage flux. 3. Choose Assign.

Define the Armature Winding All of the rotor windings will go through commutation, and each coil needs to have a unique coil definition. The brushes are offset by 10 mechanical degrees. RMxprt automatically calculates the commutation period for each coil; this information is contained in the file called com_file.txt. ➤

Define the armature winding: 1. Choose Edit/Select/Object/By Name, and enter the name Ph* (be careful with capitalization; the names are case sensitive) to select all the armature windings. Choose OK. 2. Choose Assign/Source/Solid. Change the Name from source1 to Armature, and change its color. 3. Select Voltage, and then select Strand. Only stranded conductors can be used to create windings. 4. Choose Winding to define this group of armature coils. The Winding Setup window appears. 5. Enter 120 in the Total turns as seen from terminal field, and enter 2 in the Number of Parallel Branches field. These values were calculated by RMxprt. 6. Enter 0.11 ohms in the Resistance field, and enter 6e-5 henries in the Inductance field, for the DC resistance and end leakage inductance. These values were calculated by RMxprt. 7. Specify the polarity for each of the armature coils: • While still in the Winding Setup window, choose Functions, and then choose Dataset. The Dataset Editor appears. • Choose File/Import/Text File, select com_file.txt, and choose OK. This file is stored in this project directory stndj_fea.pjt. When you open this file, note PhA0 on the first line followed by a few numbers and then PhA1, and so forth. The values on the left are degrees, and the values on the right represent the polarity index. The polarity varies between +/-1 as a function of angle (0-360 degrees). The commutation values for PhA0 in this file correspond to object PhA0. • To import the data for PhA0: • Select the second line in the file, and then choose OK. This imports data until it reaches the next name, PhA1. You should now have a plot that ranges from –1 to +1 on the ordinate and 0 to 360 on the abscissa. • Choose File/Save As, and name the file PhA0_CD, which stands for Phase A coil 0 Commutation Data. Be careful about capitalization; all function names used by Maxwell are case-sensitive. Choose OK. • To import the data for PhA1: • Choose File/Import/Text File, and select com_file.txt again. • Select the line that immediately follows PhA1, which are the commutation values for Phase A coil 1. Choose OK. • Choose File/Save As, and name the file PhA1_CD. Choose OK. • Repeat this process to specify the polarity for each of the armature coils. • After the datasets for each of the coils have been defined, choose File/Exit to close the Edit

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Dataset window and return to the Boundary/Source Symbol Table window. 8. Create a function for each coil, which states that this dataset represents a piecewise linear function interpolated about the x-axis, that it is a function of position, and that any extrapolation beyond the range of data should be periodic. This can be accomplished by using the following function for coil PhA0: PhA0_PI = pwlx(P, periodic, PhA0_CD) where the variable PhA0_PI represents the polarity index for the Phase A 0 coil. The arguments for the piecewise linear function (pwlx) are P for position in degrees, periodic for extrapolating beyond the range of the data, and PhA0_CD, which is the dataset that represents this piecewise linear function. Choose Help for more information about piecewise linear functions. 9. Repeat this for each armature coil. For example, the next function will be: PhA1_PI = pwlx(P, periodic, PhA1_CD). As you type in these functions, you will see the value for each displayed in the window. You can select the variable P and change its value from 0 to 360 and the values for each of these expressions will change. 10. Once all of the functions have been defined, choose Done to exit the Boundary/Source Symbol Table.

11. In the Winding Setup window, select PhA0, and then select Function. Enter the function name


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PhA0_PI, and then choose Assign. Repeat this for each armature coil.

12. Once all the assignments have been completed, choose OK to close the Winding Setup window. 13. Enter 10.5 volts in the Value field. This value is the terminal voltage, which includes the brush drop. 14. Choose Assign to complete the definition. 15. Choose File/Save, and then choose File/Exit to save the changes and exit the 2D Boundary/ Source Manager.

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Setup Solution Options Since adaptive refinement is not available for the transient solver, the quality of the manual mesh is critical to the accuracy and the convergence of the field solution. The mesh must be fine in regions where a large magnetic field gradient occurs, such as the air gap and rotor teeth. However, for practical use, generating a mesh that is too fine can result in an excessive computational time.

Manual Mesh ➤

Manually create the mesh: 1. Choose Setup Solution/Options from the Executive Commands menu. The Solve Setup window appears. 2. Choose Manual Mesh. The 2D Meshmaker appears. 3. Choose Mesh/Seed/Object. Select all objects, enter 2 mm in the Seed Value field, and choose Seed. Choose OK. 4. Choose Mesh/Seed/Surface. Select all objects, enter 2 mm in the Seed Value field, and choose Seed. Choose OK. 5. Choose Mesh/Make. The basic mesh is generated for the model. This mesh is too coarse to provide an accurate solution and must be refined. 6. Choose Refine/Object, and select the AirGap. Enter 1000 in the Refine Number field, to increase the total number of triangles. Choose Accept, and then choose OK. 7. Choose Model/SnapTo Mode, turn off the snaps, and choose OK. 8. Choose Refine/Point, select Centroid, and click OK. Click to refine the mesh in the rotor teeth, and click the right mouse button when finished. 9. Choose File/Save, and choose File/Exit, to save the mesh and return to the Solve Setup window.


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Define the Solution Options ➤

Define the solution options: 1. Leave the Starting Mesh option set to Current. 2. Change the Solver Choice to Direct. For problems such as these, where all of the boundaries are well defined, the Direct Solver is the best choice. 3. Select Start from time zero. Since a solution does not already exist, starting from time zero is the only choice; if a solution already exists for this problem, then the problem setup can be changed in any manner (except for geometry changes), and the solution can continue from the previous one. 4. Because it is not known at what time the motor will reach rated speed, enter 0.15 seconds in the Stop time field. This value can always be increased, allowing the solution to continue from where it left off. 5. Enter 200 microseconds in the Time step field. In RMxprt, the rated speed was given to be 2400 rpm; from this we can determine a good value to use for the time step: 2400 rpm = 40 rev/sec or (1 rev)/(25 msec) Because there are 12 teeth in the rotor, and there is a ratio of 1 tooth pitch every 2.1 milliseconds, solve for the fields 10 times per one tooth pitch, or every 200 microseconds. This causes the software to solve for more steps at lower speeds, but then, once rated speed is achieved, this value for the time step prevents the software from taking too large of a step. 6. Enter 0.05 seconds in the Save fields time step field. It is a good idea to save the fields four or five times during the simulation intermittently. In this case, 0.05 seconds is a reasonable interval. 7. Enter 40 mm in the Model depth field, and enter 2 in the Symmetry multiplier field.The symmetry multiplier is a whole number which when multiplied by the fraction of the field domain (in this case one half) yields the entire model. The value of 40 mm is the equivalent air gap length calculated by RMxprt. The different lengths for the rotor and stator where taken into account by the rotor_eq.bh and statr_eq.bh BH-curves. 8. Choose OK to close the Solve Setup window.

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Motion Setup With the solution parameters defined, now define the motion parameters for the transient model. ➤

Define the motion setup: 1. Choose Setup Solution/Motion Setup from the Executive Commands menu. The Motion Setup window appears. 2. Select the Band object, and then choose Set Band, to define the band as a stationary object that contains all moving objects. 3. Select Rotation as the Type of Motion. 4. Choose Set Position, and select (0,0) as the center of rotation. 5. Choose Mechanical Setup. The Mechanical Setup window appears. 6. Select Consider Mechanical Transient because, in this example, the mechanical transient is considered. 7. Enter 0 in the Initial Angular Velocity field. Make certain the units list box beside the field is set to rpm. 8. Enter 280e-6 in the Moment of Inertia field. This value was calculated by RMxprt. 9. Enter 31.7e-6 N-m-sec/rad in the Damping constant field. The damping coefficient is calculated from the windage and friction loss in RMxprt. When RMxprt solved the permanent magnet DC motor problem, the value it calculated for windage and friction was 2.0 watts at a rated speed of 2400 rpm. This corresponds to a damping coefficient of:

2.0W D = ------------------------------2 251.3 rad ---------  s  or D = 31.7 x10-6 N-m-s/rad. 10. Enter -0.3 N-m in the Load Torque field. This value was calculated by RMxprt. Since the rotation of the motor is going to be counterclockwise, then the electromagnetic torque is positive; therefore, the load torque needs to be negative. 11. Choose OK to close the Mechanical Setup window. 12. Choose Exit to exit the Motion Setup window. Save the changes as you exit. 13. Choose Solve/Nominal Problem from the Executive Commands menu, to generate the solutions. The progress bar reports the solution status. To display the transient data, such as voltages, currents, torque, and power loss, choose Solutions/Transient Data. Choose Refresh during the solution process, and the plots will be redrawn after the software completes the current time step.


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Post Processing ➤

Access the transient data: 1. Choose Post Process/Transient Data. A file browser appears, listing the directories containing the plots. 2. Select one of the time step solutions (.dat files), and choose OK. The plot appears in the PlotData window. After you’ve opened one plot, choose Plot/Open to open a different plot.

The following figures show four of the transient plots for the sample problem:

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Comparison to RMxprt Compare the results between EMpulse and RMxprt. To post process the transient plots, choose Post Process/Transient Data; this launches PlotData and asks you to open a plot. Because RMxprt calculates all of its values based of the rated output power, in order to compare the two results, we need to calculate the output power from EMpulse and then use this value as an input to RMxprt. We can then compare other quantities such as torque, line current, and copper loss.

Calculate the Air Gap Power EMpulse calculates air gap power, not output power; the two are related by:

P out = P airgap – FW where FW is the Friction & Wind Loss. The average air gap power is calculated by taking the average torque in N-m multiplied by the speed in rad/sec. ➤

Calculate the air gap power: 1. Choose Plot/Open, select speed.dat, and choose OK, to open the torque plot. 2. Choose Tools/Show Coordinates, and click on the end of the plot. The final value for the speed is approximately 2627 rpms or 275 rad/sec. 3. Choose Tools/Calculator to access the Signal Calculator and perform the power calculation. 4. Select torque.dat from the Loaded Signals list, and then choose Copy to load the torque plot to the top of the calculator stack. 5. Choose Sample, and define the following parameters, to domain the torque plot between 0.1414 and 0.1488 seconds: • Sample in: Time • Specify by: Size • Enter 0.1414 in the Start field. • Enter 0.1488 in the Stop field. • Enter 500 in the Size field. 6. Choose OK. 7. Enter 275 in the Name/Constant field, and choose Enter to place the constant value on the stack. This value is the speed in rad/sec. 8. Choose *. 9. Choose the integrate key. 10. Enter 0.0074 in the Name/Constant field, and choose Enter. 11. Choose / to calculate the average. 12. Choose Preview. The last number in this plot is the average value. 13. Choose max. If the last number is the maximum value, this command displays that value, with the top value as the x-component and the bottom as the y-component.

This calculation gives a value of 88.2 watts for the air gap power. The friction and windage loss used in the RMxprt program at 2400 rpm is 2.0; thus, at a speed of 2627 rpm: F.W. loss = 2 * (2627/2400) = 2.2 watts Calculate the rated output power: Pout = 88.2 – 2.2 = 86 watts


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Complete the Design Output ➤

Open the Design Output window in RMxprt: 1. Return to RMxprt, and enter 0.086 kilowatts in the Rated Output Power field in the General window. 2. Choose Analysis/Analytical Design, and then choose Post Process/Design Output. Now you can compare other motor parameters.

Full Load Current RMxprt calculated the following value for the full load current (refer to the Post Process/Design Output window under the FULL-LOAD DATA section in RMxprt): Input Current = 9.4 amps In PlotData, open the current.dat file. Using the PlotData calculator, calculate the average value directly. ➤

Compute the RMS: 1. Choose Tools/Calculator to access the calculator. 2. Select current.dat from the Loaded Signals list, and choose Copy to load the plot to the top of the calculator stack. 3. Choose Sample, and define the following values: • Sample in: Time • Specify by: Size • Enter 0.1412 in the Start field. • Enter 0.1486 in the Stop field. • Enter 500 in the Size field. 4. Choose OK. 5. Choose the integrate key. 6. Enter 0.0074 in the Name/Constant field, and choose Enter. 7. Choose / to obtain the average value. 8. Choose Preview. The last number in this plot is the average value. 9. Choose max. If the last number is the maximum value, this command displays that value, with the top value as the x-component and the bottom as the y-component.

This calculation returns a value of 9.5 amps.

Copper Loss The copper loss consists of the I2R losses. Remain in the Signal Calculator, and perform the following calculation. ➤

Compute the copper loss: 1. Choose Pop to remove the top value from the calculator stack. 2. Choose Push, and then choose *, to obtain I2. 3. Enter 0.11 in the Name/Constant field, and choose Enter. 4. Choose * to multiply by the equivalent resistance.

This calculation returns a value of 10.0 watts. The value returned by RMxprt is 9.6 watts.

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Cogging Torque Calculating the cogging torque is straightforward: turn off all excitation, open the windings, and solve at a slow constant speed. Return to the 2D Boundary/Source window, change the voltage on the field winding from 10.5 volts to zero, and increase the resistance on the windings to simulate an open circuit. If you do not change the resistance, you will model a short circuit winding instead of an open circuit. ➤

Calculate the cogging torque: 1. Choose Setup Boundaries/Sources from the Executive Commands menu. 2. Select Armature from the list, and change its Value to 0. 3. Choose Winding, and change the Resistance to 1.0e9 ohms. Choose OK, and then choose Assign. 4. Chose File/Save, and then choose File/Exit, to close the 2D Boundary/Source Manager and return to the Executive Commands menu. 5. Choose Setup Solution/Options, and select Start from time zero. 6. Change the Stop time to 1.0 second. 7. Change the Time step to 0.005 msec. 8. Change the Save fields time step to 0.1 seconds. 9. Choose OK to save these changes and return to the Executive Commands menu. 10. Choose Setup Solution/Motion Setup, and then choose Mechanical Setup. The Mechanical Setup window appears. 11. Deselect Consider Mechanical Transient. Enter 90 in the Constant Angular Velocity field, and make sure the units list box reads degrees/sec. 12. Choose OK to close the Mechanical Setup window. 13. Choose Exit to close the Motion Setup window. Save the changes when exiting. 14. Choose Solve/Nominal Problem to re-solve the problem.


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The calculated torque value is the cogging torque:

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A Permanent Magnet DC Motor Problem

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