A Permanent Magnet Brushless DC Motor Problem

Ansoft RMxprt Application Note

A Permanent Magnet Brushless DC Motor Problem This application note describes how to set up, solve, and analyze the results of a four-pole 550-watt brushless DC motor using RMxprt. Once solved, the results from RMxprt will be used as a basis for performing more detailed analyses 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 brushless DC motor. You can create this project from scratch or open the RMxprt project called ws-1.pjt (located in the /ansoft/ examples/rmxprt/ directory) and the finite element project called ws1_fea.pjt (which can be downloaded from the technical support page for EM products at the Ansoft web site: www.ansoft.com, under the EMpulse Application Notes section). If you are creating a project from scratch, select Brushless Permanent-Magnet DC Motors as the motor type in RMxprt. These projects were created using version 3.00 of RMxprt and version 8.0 of Maxwell 2D.

Application Note

AP065-9911

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

Define the general data: 1. Enter 0.55 in the Rated Output Power field for this four-pole motor. Power is entered in kilowatts. When you place the mouse cursor over an entry field, the status bar on the bottom of the window displays a definition of that field. 2. Enter 220 in the driving DC Rated Voltage field. Voltage is entered in DC volts. 3. Enter 4 in the Number of Poles field. 4. Enter 1500 in the Rated Speed field. The speed of the motor is entered in rpm. 5. Enter 11 in the Friction Loss field. Friction and wind losses are typically assumed to be two to three percent of the rated output power. For this example, use 2% or 11 Watts. 6. Select C2 as the Circuit Type. The drive circuit for this two-phase motor consists of four pairs of transistors to switch the 220 VDC. Fly back diodes are used for the discharge loop when the transistors are turned off. This circuit is referred to as type C2, which stands for a Cross-Type 2-Phase circuit, as shown below:

The switching sequence is as follows: • For Maximum Positive A phase, T1A and T1B are ON while others are OFF; • For Maximum Positive B phase, T2A and T2B are ON while others are OFF; • For Maximum Negative A phase, T3A and T3B are ON while others are OFF; • For Maximum Negative B phase, T4A and T4B are ON while others are OFF. 7. The Lead Angle of Trigger is assumed to be zero degrees to yield the maximum average induced voltage in the triggered phase.

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A Permanent Magnet Brushless DC Motor Problem

8. Enter 90 in the Trigger Pulse Width field. Both the A phase and B phase are ON for 90 degrees. Similarly, both the A return and B return are ON for 90 degrees. 9. Enter 2 in the Transistor Drop field. The transistor drop is entered in volts. 10. Enter 2 in the Diode Drop field. The diodes across each transistor are used to create a return path for the phase current when the transistors are turned off. The voltage drop across one of these diodes is two volts. 11. Enter 75 in the Operating Temperature field. The operating temperature is measured in degrees Centigrade. 12. Select Inner in the Rotor Position field. 13. Leave Chopped Current Control deselected. This motor does not employ a chopped current control scheme.


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Stator Data Use the Stator1 and Stator2 windows to define the stator. ➤

Specify the stator: 1. Select the Stator1 tab. 2. Enter 120 mm in the Outer Diameter field. 3. Enter 75 mm in the Inner Diameter field. 4. Enter 24 in the Number of Slots field. 5. Enter 1 in the Skew Width field. The stator lamination stack is skewed by one stator slot. 6. Select 2 as the Slot Type. The slot shape has a tapered neck with a round bottom. 7. Deselect Auto Design. 8. Enter the following Slot Dimensions (in mm): • Enter 0.5 in the Hs0 field. • Enter 1.0 in the Hs1 field. • Enter 8.2 in the Hs2 field. • Enter 2.5 in the Bs0 field. • Enter 5.6 in the Bs1 field. • Enter 7.6 in the Bs2 field. 9. Select the Stator2 tab. 10. Enter 65 mm in the Length of Stator field. 11. Enter 0.95 in the Stacking Factor field. The length of the stator, including the laminations, is 65 mm, and the stacking factor is 95%, which gives a net length of steel of 61.75 mm. 12. Select M19-24G in the Steel Type field. This is a nonlinear steel used in the manufacturing of the stator lamination. 13. Enter 0.3 in the Slot Insulation thickness field. The slot insulation is the thickness on one side of the stator slot, in this case, 0.3 mm. 14. Enter 0 in the End Adjustment field. This value 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. 15. Select 21 as the Winding Type. This is a two-layer fractional pitch lap-type winding. 16. Enter 1 in the number of Parallel Branches field. For any one phase of the winding (A or B phase), all of the stator slots are wound in series, which means the number of parallel branches is one. 17. Enter 60 in the number of Conductors per Slot field. Each phase winding has 30 conductors per half slot, or 60 conductors per full slot. 18. Enter 5 in the Coil Pitch field. If the stator used a full pitch winding, the coil pitch would be 6 slots (24 slots/4 poles). Instead, this motor is wound one slot short, or 5 slots. A coil pitch of 5 means that a coil is wound down slot 1 and returns in slot 6. 19. Enter 1 in the number of Wires per Conductor field. This motor does not use multiwire conductors. 20. Select AUTO in the wire Gauge field to allow RMxprt to calculate the optimum wire diameter and corresponding gauge value for this motor. When AUTO is selected for the wire gauge, the field for the wire diameter automatically becomes zero.

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Rotor Pole Data Use the Rotor Pole window to define the rotor data. ➤

Specify the rotor: 1. Select 1 as the Rotor Type. The four permanent magnets used for this motor have tapered edges from the top of the magnet to the surface of the rotor; this is best modeled as rotor type number one. 2. Enter 0.5 mm in the Air Gap field to define the air gap between the rotor and stator. 3. Enter 26 mm in the Inner Diameter field.This is also the diameter of the shaft. 4. Enter 65 mm in the Length of Rotor field. This is the same as the length of the stator. 5. Enter 0.95 in the Stacking Factor field. 6. Select M19-24G in the Steel Type field. Because the rotor and stator are made from the same punching, the stacking factor and the nonlinear steel type are also the same, 95% and M19-24G, respectively. 7. Enter 0 in the Pole Arc Offset field. The radius origin for the permanent magnet that creates the rotor pole does not necessarily need to coincide with the radius origin for the rotor. 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 as the Pole Arc Offset. For this motor, the air gap is uniform.

8. Enter 0.7 in the Pole Embrace field. The rotor pole embrace represents a ratio of the maximum physical dimension of the permanent magnet rotor pole. A pole embrace of 1 for a four-pole machine means that the physical rotor pole covers exactly 90 mechanical degrees; likewise, a


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pole embrace of 0.667 means that the rotor pole covers 60 mechanical degrees.

9. Select XG196/96 as the Magnet Type. The rotor pole is comprised of a permanent magnet that has a retentivity (or residual flux density, Br) of 0.96 tesla, a coercivity of -690 KAmps/m, a maximum energy density of 183 KJ/m3, and a relative recovery (or recoil) permeability of 1.0. 10. Enter 3.5 in the Magnet Thickness field to define the thickness of the permanent magnet.

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Analyze the Design Before the design can be analyzed, you must specify a few options. ➤

Specify the options: 1. Choose Tools/Options. A window appears. 2. Under Lamination, select Stator, Rotor, and Slot, if they are not already selected. 3. Set the Wire Setting to American, if it is not already selected. 4. Set the Maxwell Path to the directory where the Maxwell software is installed. The default installation directory is c:\ansoft. 5. Choose OK. The window closes, and the options are set. 6. Now choose Analysis/Analytical Design. RMxprt automatically calculates the motor performance parameters for this design. 7. Once the analysis is complete, choose Post Process/View Lamination to examine a cross-section of the motor. Choose File/Exit when you are finished viewing the laminations. 8. Choose Post Process/View Winding Layout to examine how the two-phase winding is arranged. Choose File/Exit when you are finished viewing the winding arrangement. 9. Choose Post Process/Design Output. A Design Output window appears, listing the motor performance characteristics.

Design Output The Design Output window is divided into eight sections: General Data, Stator Data, Rotor Data, Permanent Magnet Data, Steady State Parameters, No-Load Magnetic Data, Full-Load Data, Winding Arrangement, and Transient FEA Input Data.

GENERAL DATA The information listed here is the same as the data you entered in the General window.

STATOR DATA The information is the same as the data you entered in the Stator1 and Stator2 windows, except for the wire information, which was computed during the design phase (because you selected AUTO for the gauge number). The values calculated by RMxprt are: Wire Diameter (mm): 0.8118 Wire Wrap Thickness (mm): 0 Stator Slot Fill Factor (%):61.4557 A wire diameter of 0.8118 mm corresponds to an AWG rating of 20. The slot fill factor represents the percentage of the available slot area, which is the total slot area minus the slot insulation, that contains the wire (copper plus insulation). Different manufacturers use an array of insulation materials, and RMxprt does not assume any particular type. Typically, wire wrap insulation is about 7% to 10% of the diameter of the wire.


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Resolve the Simulation Now that RMxprt has calculated wire diameter, you can go back to the program. Select a Wire Diameter of 0.8118 mm from the pull down menu, or select 20 Gauge wire. Set a Wire Wrap thickness of 0.08 mm. Run the program again by choosing Analysis/Analytical Design, and see the effect the wire wrap has on the total fill factor. Wire Diameter (mm): 0.8118 Wire Wrap Thickness (mm): 0.08 Stator Slot Fill Factor (%):74.165 A fill factor of 74% leaves enough space in the slot to assemble the stator windings.

ROTOR DATA Most of the information here is the same as the data you entered in the Rotor Pole window. The polar arc radius is given instead of the pole arc offset value, and the pole embrace is given in mechanical and electrical values. The mechanical pole embrace was defined in step 8 in the Rotor 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. Refer to 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.

STEADY STATE PARAMETERS The results in this section display information about the quadrature axis and direct axis inductance, leakage inductance, the resistance of one stator phase winding, and the stator winding factor.

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NO-LOAD MAGNETIC DATA This area displays the magnetic flux density in the stator teeth and yoke, and the flux density in the rotor yoke. A maximum value of 1.64 Tesla lies along the knee of the BH-curve but is below saturation. All components of the magnetomotive force (mmf) are given for half the reluctance path: stator teeth, stator yoke, air gap, rotor yoke, and the permanent magnet. Armature Reactive Ampere Turn 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 at the rotor. The correction factors from the magnetic circuit length of the stator and rotor yoke refer to the path used to calculate the mmf drop for the stator and rotor yoke. The free running, or no-load, speed of this machine is 1852 rpm.

FULL-LOAD DATA The following motor performance parameters are calculated at a rated output power of 550 watts: Parameter Value Description Average Input Current (A) 3.2 The average value of the current waveform over one period from the voltage source. RMS Armature Current (A) 2.7 The RMS value of the current waveform for one phase winding. 19.2 The current density multiplied by the specific electric loading, Armature Thermal Load not dependent on resistance. (A2/mm3) Specific Electric Loading (A/mm) Armature Current Density (A/mm2) Friction and Wind Loss (W)

3.7

The total current around the air gap.

5.2

The current density through the cross-section of one stator winding.

10.1

Iron-Core Loss (W)

21.3

Armature Copper Loss (W)

63.9

Transistor Loss (W)

10.2

Diode Loss (W) Total Loss (W)

0.71 106.1

Output Power (W) Input Power (W) Efficiency (%) Rated Speed (rpm)

601.5 707.7 85 1442 4.0

The friction and wind loss at the rated speed. This value is different from the input value if the rated speed is different. The total core loss in the stator and rotor, based on loss curve in the material definition. The power loss due to the resistance of the stator winding. This is the total copper loss. The power loss based on the operation of the switching transistor. The power loss based on the operation of the diode. The total power loss is equal to the combined losses of the friction and wind loss, the iron core loss, the copper loss, the transistor loss, and the diode loss. RMxprt calculates this quantity based on input parameters. The rated DC voltage multiplied by the Average Input Current. The output power divided by the input power. The running speed at the calculated rated output power. The shaft torque available at the rated output power.

34.4

The starting torque when the shaft speed is zero.

47.7

The total current the stator will draw when the shaft speed is 0.

Rated Torque (N.m) Locked-Rotor Torque (N.m) Locked-Rotor Current (A)


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WINDING ARRANGEMENT This is the winding arrangement for one full A-phase and one full B-phase winding. Taking a slot pitch of five into account, the total winding pattern can be seen by choosing Post Process/View Winding Layout. The following parameters are displayed in electrical degrees: Angle per slot 180 electrical degrees divided by the number of slots per pole (6). Phase-A axis The axis of the A-phase winding taken from the center of the first slot. The axis is 3.5 slots from the x-axis, which is 52.5 mechanical degrees, or 105 electrical degrees. First slot center The reference used to calculate phase A axes.

TRANSIENT FEA INPUT DATA This information is used when calculating the motor performance using the time transient finite element field solver. For the Armature Winding, this information is displayed for one phase of the stator winding: Number of Turns 360 The total number of turns as seen for the terminals. Parallel Branches 1 The total number of parallel branches, often called the number of circuits. Terminal Resistance (ohm) 4.5 The stator DC resistance at the given temperature (75 C here). End Leakage Inductance (H) 1.7 mH The end turn stator winding leakage inductance. For the 2D Equivalent Values, this information is displayed for the equivalent of 3D to 2D: Equivalent Air Gap Length 65 There are two entry fields for the rotor and stator. When per(mm) forming a 2D finite element analysis, only one value for the length is accepted. Equivalent Stator Stacking 0.95 If the rotor and stator have different lengths, this equivalent Factor stacking factor could be used in the finite element problem setup for an equivalent conductivity or BH-curve. Equivalent Rotor Stacking 0.95 If the rotor and stator have different lengths, this equivalent Factor stacking factor could be used in the finite element problem setup for an equivalent conductivity or BH-curve. Equivalent Br (T) 0.96 The residual flux density of the recoil line, taking the different length into account. Equivalent Hc (kA/m) 764 The coercivity for permanent magnets using recoil permeability. Estimated Moment of Inertia 0.0015 This is an estimated value of the moment of inertia. RMxprt 2 does not supply information about rotor bearing and similar (kg-m ) components. Choose Exit to exit the Design Output window.

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Performance Curves Now you can 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_flux.dat Air-Gap Flux Density at No-Load wv0_volt.dat Induced Winding Voltages at No-Load and Rated Speed wv0_coil.dat Induced Voltage at No-Load and Rated Speed wv1_curr.dat Load Currents at Rated Speed. wv1_volt.dat Load Voltages at Rated Speed. 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. 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. Notice the three check boxes in the Field section of this window. Make certain they are all deselected. Choose OK to exit this window. 2. Choose Analysis/View Geometry. A full cut-away cross-section of the motor appears in the Maxwell 2D Modeler. Since the model has four poles, and the windings are symmetrical, we can reduce this model from 360 degrees to 90 degrees. 3. Choose File/Exit to exit the Maxwell 2D Modeler. 4. Again, choose Tools/Options. Select Periodic in the Field section, and leave the value set to 1. Choose OK to exit this window. 5. Choose Analysis/View Geometry to view the model again. Notice that only a quarter (90 degrees) of the motor is modeled. If the Periodic field in the Options window was set to two, two poles of the motor geometry would be created. 6. Choose File/Exit to exit the Maxwell 2D Modeler again and examine some other options for creating the geometry. 7. Choose Tools/Options. 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 its effect on the geometry. 8. For the FEA analysis, select Periodic, with a multiplier value of one, and select Teeth-Teeth. Leave Difference deselected. 9. Choose OK to accept the options and exit.

Create the Maxwell 2D Project Once the geometry has been analyzed, 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 brushless DC motor. The name of the pre-solved project is ws1_fea. 4. Choose Create. A Maxwell 2D project is created using the specified geometry options. 5. Choose OK to close the message window. 6. 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 550-watt four-pole brushless 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 550-watt four-pole brushless 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 that was created in the previous section. The name of the pre-solved project is ws1_fea.pjt. Upon opening the project, notice that the Transient Solver, the XY Drawing Plane, and Define Model are already set. 2. Choose Define Model/Draw Model to open the Maxwell 2D Modeler. The model appears in the modeler window. 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 objects 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. 5. Choose Define Model/Group Objects, and group together the objects that belong to the same winding. RMxprt assigns names to all of the objects in the geometry. The name of the windings are abbreviated as follows: PhA0 Conductor set of coil zero belonging to Phase A PhA1 Conductor set of coil one belonging to Phase A PhB0 Conductor set of coil zero belonging to Phase B PhReB11 Return conductor of coil eleven belonging to Phase B If there were more windings, conductor groups for Phase A Return, Phase C, and Phase C Return would also be defined.

• In general, PhA and PhReA represent the main winding (go and return). However, Note:

• •

in this example, PhReA is not shown because we are only displaying a portion of the motor. PhB and PhReB represent the auxiliary winding (go and return). The stator windings of a brushless DC motor can be grouped into four different objects (PhA, PhReA, PhB, PhReB).

6. Select all of the Phase A Conductor Groups (PhA0, PhA1, PhA2, PhA9, PhA10, PhA11), and choose Group. Call this group Phase_A. 7. Select all of the Phase B Conductor Groups (PhB0, PhB1, PhB9, PhB10, PhB11), and choose Group. Call this group Phase_B. 8. Because there is only one conductor for Phase B Return, there is no need to group it with any other object. 9. Choose Exit and save the changes before closing the window.


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Assign Material Properties Assign material properties to the objects and groups. Because this example requires two materials not included in the material database, you 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.

Create M19_G24 Steel M19_G24 is not part of the global material database, so it must be added. Newly created materials are stored in the local material database and can be used in the active project. ➤

Define the material: 1. Choose Material/Add. 2. Under Material Properties, change the name to M19_G24. 3. Select Nonlinear Material, and choose BH Curve. The BH Curve Entry window appears, allowing you to define the BH-curve for the project. 4. Choose Import, select the directory where wsl_fea.pjt is installed. Once you have located the directory, select either rotor_eq.bh or statr_eq.bh, and choose OK. In the project directory, there are two files, rotor_eq.bh, and statr_eq.bh, which are the equivalent BH-curve, taking into account the stacking factor and length. For this example, the stator and rotor have the same length, so both curves are identical.

Note:

RMxprt automatically creates an equivalent BH-curve from both the rotor and the stator and stores a copy of each in the project directory when a Maxwell 2D project is created. Occasionally, the rotor length and the stator length are not equal. This difference can be realized by modifying the corresponding BH-curve.

5. Choose Exit to close the BH Curve window. 6. Choose Enter to add M19_G24 to the local material database for this project.

Create XG196_96 The permanent magnet used for this analysis also needs to be created. ➤

Define the permanent magnet: 1. Choose Material/Add. 2. Under Material Properties, change the name to XG196_96. 3. Choose Options. The Property Options window appears, allowing you to define the values used for the permanent magnet. 4. Deselect Hc, select Br, and choose OK. The magnet operates in the linear portion of its BHcurve, so it will be modeled as a linear permanent magnet. 5. Enter 1 in the Rel. Permeability field for the relative permeability of the magnet. 6. Enter 0.96 in the Mag. Retentivity field. RMxprt calculates the equivalent Hc and Mp values, as well as which values take into account the different rotor and stator lengths. It also computes any demagnetization effects. This data can be found in the Transient FEA Input Data section in the Design Output window. 7. Choose Enter to add XG196_96 to the local material database for this project.

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Assign the Materials ➤

Assign the materials to the objects: 1. Assign the following materials to the objects and groups: • Assign air to the AirGap, AirRotor, and Band. • Assign XG196_96 to the Magnet. Make certain the direction of magnetization is set to Align relative to object’s orientation, with an Angle value of 225 degrees. Choose OK to close the window. • Assign copper to PhReB11, [Phase_A], and [Phase_B]. • Assign M19_G24 to the Rotor and Stator. • Assign steel_stainless to the Shaft. 2. Exclude the Background from the model. Because this example will have boundary conditions assigned to every outside edge, the background is excluded from the solution. 3. Choose Exit and save the changes made in the Material Manager.


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Set the Boundaries and Sources The first step in defining the boundary conditions is to define the Master/Slave boundary. You then need to assign the zero-value boundary and set up the sources. Finally, you need to define the external circuit. First, choose Setup Boundaries/Sources. The 2D Boundary/Source Manager appears.

Define the Master Boundary ➤

Define the master boundary: 1. Choose Window/New and then Window/Tile, to open an additional window and to arrange the windows in tile format. 2. Choose Window/Change View/Zoom In, and zoom in on the air gap such that the area where the Band and the inside diameter of the stator cross the x-axis can be easily seen. 3. Choose Edit/Select/Trace, and, 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 intersections: • Rotor Inside Diameter (u=13, v=0) • Rotor Outside Diameter (u=33.5, v=0) 4. Switch to the window where the air gap is enlarged, and click on the following intersections: • Rotor Air (u=37, v=0) • Band (u=37.25, v=0) • Stator Inside Diameter (u=37.5, v=0) 5. Switch back to the window with the full model, and double-click on the Stator Outside Diameter (u=60, v=0) to end the master boundary definition. 6. Choose Assign/Boundary/Master. 7. Change its color to yellow. 8. Choose Assign.

The master boundary is now assigned.

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

Define the slave boundary: 1. 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 intersections: • Rotor Inside Diameter (u=0, v=13) • Rotor Outside Diameter (u=0, v=33.5) 2. Switch to the window where the air gap is enlarged, and click on the following intersections: • Rotor Air (u=0, v=37) • Band (u=0, v=37.25) • Stator Inside Diameter (u=0, v=37.5) 3. Switch back to the window with the full model, and double-click on the Stator Outside Diameter (u=0, v=60) to end the slave boundary definition. 4. Choose Assign/Boundary/Slave, and select Slave = –Master. When solving for one or 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. 5. Change the color to yellow. 6. Choose Assign.

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Assign the Zero-Value Boundary With the master and slave boundaries defined, you can now assign the zero-value boundary conditions to the outside diameter of the stator. ➤

Assign the zero-value boundary: 1. Choose Edit/Select/Edge. 2. Click on the outside diameter of the stator. Click the right mouse button to stop selecting. 3. Choose Assign/Boundary/Value, and change the name from Value1 to Zero_Flux. Make certain to keep the Value set to 0 weber/m. A zero value boundary means that all of the flux will be contained in the motor; there will be no leakage flux. 4. Change the color to blue. 5. Choose Assign.

Assign the Sources In this example, you will create a pulse width modulated drive circuit for this two-phase DC motor. First, you must define the A-phase and B-phase winding sources. ➤

Assign the A-phase and B-phase winding sources: 1. Choose Edit/Select/Object/By Clicking, and select the Phase_A group, to define the A-phase winding. Choose the right mouse button to stop selecting. 2. Choose Assign/Source/Solid, and select External Connection as the source for this winding. 3. Change the Name from source1 to A_Phase, and change the color to light green. 4. Choose Winding, and define the following parameters: • Set the Polarity of the [Phase_A] group to Positive. • Enter 0 in the Initial Current field. • Enter 360 in the Total turns as seen from terminal field. • Enter 1 in the Number of Parallel Branches field. The parameters defined in this window are calculated by RMxprt and are taken from the Transient FEA Input Data section of the Design Output window. 5. Choose OK to accept the values. 6. Choose Assign. 7. Choose Edit/Select/Object/By Clicking, and select both the Phase_B group and PhReB11, to define the B-phase winding. 8. Choose Assign/Source/Solid, and select External Connection as the source for this winding. 9. Change the Name from source2 to B_Phase, and change the color to light blue. 10. Choose Winding, and define the following parameters: • Set the Polarity of the [Phase_B] group to Positive. • Set the Polarity of the PhReB11 object to Negative. • Enter 0 in the Initial Current field. • Enter 360 in the Total turns as seen from terminal field. • Enter 1 in the Number of Parallel Branches field. 11. Choose OK to accept the values. 12. Choose Assign.


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Define the External Circuit Now you can define the external circuit. ➤

Define the external circuit: 1. Choose Edit/External Circuit. The Edit External Circuit window appears. The two windings you have defined, A_Phase and B_Phase, are shown in the second pane, under Winding. In Schematic Capture, each winding will be represented as an inductor, but, since the schematic as has not yet been created, the status under Has inductor in circuit is NO. 2. Select Create new circuit. 3. Choose Launch Schematic Capture. The two windings, named LA_PHASE and LB_PHASE, are automatically placed in the Schematic Capture window. Each has a value of 1 H; this value has no significance and is not used at any point in the calculation. It is important to know that the SPICE solver is not called during the solution process; we are using the schematic capture interface to create the drive circuit. 4. Choose Options/Sizing, select B(16X10), and choose OK. The initial default drawing size is too small to fit all of the components needed to complete the drive circuit.

Create the Drive Circuit The following figure shows how the drive circuit will look in Schematic Capture once created:

The LA_PHASE and LB_PHASE components represent only the winding. You must add the DC resistance and the end leakage inductance. Remember that in RMxprt in the Design Output file, there was a section called Transient FEA Input Data, which includes this information: Terminal Resistance (ohm): End Leakage Inductance (H):

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4.5 1.7 mH


➤

Create the drive circuit: 1. Choose Add/Resistor and Add/Inductor, and add a resistor and inductor in series with each of the windings. 2. Change the default names to something more descriptive. Refer to the following figure for names and values:

3. Add a current meter in series with the A phase winding and in series with the B phase winding. 4. Add the switches to the circuit. See the diagram on the previous page for precise placement. All of the switches are voltage controlled and have the same definition: VT [V] = 0.5 VH [V} = 0 RON [Ohms] = 0.001 ROFF [Ohms] = 1E+006 This definition indicates that: • when the controlling voltage is greater than 0.5 volts, the resistance of this switch is 1.0 milliohm. • when the controlling voltage is lower than 0.5 volts, the resistance of this switch is 1.0 megaohm. The controlling voltage for each switch is defined as follows: Switch

Positive Control Terminal

Negative Control Terminal

S1 & S6

V1:p

V1:m

S2 & S5

V3:p

V3:m

S3 & S8

V2:p

V2:m

S4 & S7

V4:p

V4:m

5. Add the diodes to the circuit. See the diagram on the previous page for precise placement. • Diodes D1-D8 have the same definition which is called D1 (this diode model is included


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with EMpulse). The switch in series with the diode act as a transistor to switch the voltage on and off to the phase winding. • Diodes D9-D16 are free wheeling diodes which gives the current a return path during a sharp transition state. The free wheeling diode definition is included with EMpulse. 6. Set up a subcircuit with position dependent sources, which will be used to control the switching sequence of the A_Phase and B_Phase winding. Assume the initial phase angle of the phase A fundamental induced voltage is zero, as shown in the following figure. This can be obtained by shifting the initial rotor position:

A zero load angle of trigger can be obtained by triggering A-phase, B-phase, A return, and B return at 45, 135, 225, and 315 electrical degrees, respectively. The switching sequence will implement the following waveform:

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This waveform can be formed using the following subcircuit:

For each voltage source, select Pulse as the Transient Waveshape, and enter the following values in the corresponding fields: V1

V2

V3

V4

V1, initial value [V]

0

0

0

0

V2, pulsed value [V]

1

1

1

1

TD, delay time [s]

22.45

67.45

112.45

157.45

TR, rise time [s]

0.1

0.1

0.1

0.1

TF, fall time [s]

0.1

0.1

0.1

0.1

PW, pulse width [s]

44.9

44.9

44.9

44.9

PER, period [s]

180

180

180

180

These values specify the definition for voltage sources V1-V4, which are position dependent. EMpulse treats these voltage sources as position dependent, and the values inserted as time are taken as angle in mechanical degrees. For example, voltage source V2 will transition from 0 to 1 after the rotor has turned 67.45 mechanical degrees. At this position, it will transition to a value of 1 volt over 0.1 degrees. It will maintain a value of one volt for 89.8 electrical degrees (44.9 mechanical degrees) and then transition


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back to a value of 0 over 0.1 degrees.

After the schematic is complete, and when you exit schematic capture, the software will prompt you to indicate which voltage sources are position dependent and which ones are time dependent. All four sources are position dependent.

Add the Voltage Source, and Complete the Model Finally, add the source DC voltage of 220 volts, along with some probes to measure line current and voltage. ➤

Complete the model: 1. Add a voltage source of 220 volts to the model. 2. Add a current probe to measure line current. 3. Add a voltage probe to measure line voltage. 4. Choose File/Save and then File/Exit. A window appears, asking you to specify which sources are time, speed, or position dependent. 5. Make certain that voltage sources V1-V4 are all listed under Position Dependent. 6. Choose OK to return to the Edit External Circuit window. 7. Choose OK finish the external circuit setup and return to the 2D Boundary/Source Manager. All boundaries and sources have now been defined. 8. Choose File/Save and then File/Exit to exit.

Now you must define the mesh.

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Define the Mesh The automatic adaptive meshing routine is unavailable for time transient problems, so a manual mesh must be created. Choose Setup Solution/Options, and then choose Manual Mesh to access the 2D Meshmaker and define a mesh for this problem. Many options are available for defining a mesh. For this example, use a surface and object seeding. ➤

Define the mesh: 1. From the 2D Meshmaker, choose Mesh/Seed/Surface. 2. Select all the object names, enter 2 mm in the Seed Value field, and choose Seed. 3. Choose OK. 4. Choose Mesh/Seed/Object. 5. Select all the objects names, enter 2 mm in the Seed Value field, and choose Seed. 6. Choose OK. 7. Choose Mesh/Make. The 2D Meshmaker generates a mesh for the model. 8. Choose Refine/Object. The Object Refinement window appears, allowing you to refine the mesh further. 9. Select the Band object, and increase the number of triangles by entering 1000 in the Refine Number field. 10. Choose Accept, and then choose OK. The mesh is refined in the area of the band object. 11. Choose Mesh/Line Match, and select the edges of both the master and slave boundaries, to ensure that the meshing points will match at your matching boundaries. If they do not, you will receive an error message about a missing transcript file during the nominal solution. 12. Choose File/Save and then File/Exit to return to the Solve Setup window.


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Setup Solution Options Use the Solve Setup window to define the solver type and solution parameters for the model. ➤

Define the solution options for the transient analysis: 1. Change the Solver Choice to Direct. For problems like this, where all of the boundaries are well defined, the direct solver is the best choice. 2. Leave Start from time zero set as the Solution type. Because a solution does not already exist, starting from time zero is the only choice. If a solution already exists for this problem, the problem setup can be changed in any manner (except for geometry changes), and the solution can continue from the previous one. 3. Enter 0.06 seconds in the Stop time field. Because it is unknown at what time the motor will reach rated speed, an arbitrary stop time will be used for now. You can always increase this value after a solution has been generated, allowing the solution to continue from where it left off. 4. Enter 100e-6 in the Time step field. In RMxprt, the rated speed was given to be 1500 rpm. From this you can determine what would be a good value to use for the time step. Because: 1500 rpm = 25 rev/sec = 1 rev/40 milliseconds and there are 24 teeth in the stator, where: 1 tooth pitch / 1.67 microseconds solve for the fields 15 times per one tooth pitch, or: Time Step = 111.3 microseconds Round this value down to 100 microseconds. This causes the software to solve for more steps at lower speeds, but once the rated speed is achieved, this value for Time step prevents the software from taking too large of a step. 5. Enter 0.02 seconds in the Save fields time step field. It is a good idea to save the files four or five times during the simulation. 6. Enter 65 mm in the Model depth field. 7. Enter 4 in the Symmetry multiplier field. The symmetry multiplier is a whole number that, when multiplied by the fraction of the field domain (in this case one-quarter), yields the entire model, or one. 8. Choose OK to accept the values and exit.

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Motion Setup The software needs to differentiate between which objects are moving and which ones are stationary. This is done by identifying the band object. ➤

Define the motion: 1. Choose Setup Solution/Motion Setup. 2. Select Band from the object list, and choose Set Band. Band now appears in the Attributes list. 3. Choose Mechanical Setup to identify and define the mechanical parameters. The Mechanical Setup window appears. 4. Deselect Consider Mechanical Transient. 5. Enter 1852 in the Constant Angular Velocity field. This is the no-load mechanical speed. 6. To obtain a zero initial angle of the induced A-phase voltage, you must change the initial position from 0 to 120 degrees. You must make certain that the permanent magnet axis is oppositely aligned with the A-phase axis. RMxprt indicates the location of this axis. For clarity, the following figure shows two poles. The A-phase axis is 105 degrees θe from the first slot center, or 150 degrees θe from the x-axis. The permanent magnet axis is 90 degrees θe from the x-axis. For the permanent magnet axis to oppositely align at the A-phase axis, the rotor must rotate 240 degrees θe in the counter-clockwise direction, or 120 mechanical degrees.

7. Exit the Mechanical Setup window. 8. Choose Exit, and save the changes to the motion setup.

Verify the Trigger Position Return to the 2D Boundary/Source Manager, and solve for the No-Load induced voltage to make certain that the mechanical setup is correct. ➤

Verify the trigger position: 1. Choose Setup Boundaries/Sources, and then choose Edit/External Circuit. 2. Choose Launch Schematic Capture. 3. Change the DC resistance for the A and B phase windings from 4.5 ohms to 4.5 gigaohms. 4. Change the DC value of the voltage source from 220 volts to 0. 5. Save the changes, and exit Schematic Capture. Click OK to close the Edit External Circuit window. 6. Save the changes, and exit the 2D Boundary/Source Manager.


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Generate the Solutions Now you are ready to run the program. ➤

Generate the solutions: ■ Choose Solve/Nominal Problem.

Once the solutions have been generated, you can view the No-Load induced voltage:

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Create the Multisignal Induced Voltage Plots Create a plot of the induced voltage against the position. ➤

Create the multisignal plot: 1. Choose Post Process/Performance Curves. The PlotData window appears, with an Open window visible. You can open a plot from this window, or choose Plot/Open within PlotData. 2. Open the plots named bkemf.dat and posi.dat. 3. Choose Tools/Show Coordinates, and determine the first period for the A-phase. The first period is approximately 0.0165 seconds if you followed the instructions in the guide without error. 4. Choose Tools/Calculator, and copy A-phase to the calculator stack. 5. Choose Sample, and define the domain of the A-phase back EMF to one period, using the following parameters: • Sample in: Time • Specify by: Size • Start: 0 • Stop: 0.0165 • Size: 500 6. Choose OK to accept the values and return to the Signal Calculator. 7. Enter EMF-APhase in the Name/Constant field, and choose Enter to place the name on the stack. 8. Choose Neg to take the inverse. 9. Enter EMF-AReturn in the Name/Constant field, and choose Enter to place the name on the stack. 10. Load position into the top register of the calculator stack. 11. Choose Sample to define the domain of the values for the position, and define the following parameters: • Sample in: Time • Specify by: Size • Start: 0 • Stop: 0.0165 • Size: 500 12. Choose OK to accept the values. 13. Enter 120 in the Name/Constant field, and choose - to subtract the value. The initial position was 120. You must subtract this so that the plot begins at zero. 14. Enter Theta-m in the Name/Constant field to define the value in mechanical degrees. 15. Choose Push to duplicate this value in the stack. 16. Choose RlUp and then Exch to exchange the top two plots on the stack. The top of the stack should be EMF-AReturn, and the value below it should be Theta-m. 17. Choose x(y) to display a plot of EMF-AReturn versus Theta-m. 18. Choose Load to load the EMF-AReturn plot into the Loaded Signals list. 19. Choose RlUp then x(y) to display a plot of EMF-APhase versus Theta-m. 20. Choose Load to load the EMF-APhase plot into the Loaded Signals list. 21. Repeat steps 4 through 20 for the B-phase. 22. Once you have completed the plots, exit the calculator.


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Plot the Results ➤

Plot the signals: 1. Choose Plot/New. 2. Select and plot each of the following: • EMF-APhase vs. Theta-m • EMF-AReturn vs. Theta-m • EMF-BPhase vs. Theta-m • EMF-BReturn vs. Theta-m

The induced voltage includes all harmonics, but it can be easily determined where waveforms cross. All of the initial conditions are correct.

Solve the Mechanical Transient Generate a solution for the mechanical transient. ➤

Solve the mechanical transient: 1. Choose Setup Solution/Motion Setup. 2. Choose Mechanical Setup. 3. Select Consider Mechanical Transient. 4. Enter 0.00145 kg/m2 in the Moment of Inertia field. RMxprt gives an estimated value of the moment of inertia in the FEA Transient Input Data section. 5. Enter 0.000452 in the Damping field. The windage and friction loss reported by RMxprt is 10.81 watts at a speed of 1474.55 rpm. This corresponds to a damping coefficient of:

10.81W D = ------------------------------2 154.4 rad ---------  s  6.

7. 8. 9.

or D = 452x10-6 N.m.sec/rad. Enter -3.6 N.m in the Load Torque field. This is the load torque calculated in RMxprt. Because the rotation of the motor is going to be counterclockwise, the electromagnetic torque is positive thus the load torque needs to be negative. Choose OK to exit the Mechanical Setup window. Choose Exit to exit the Motion Setup window, and save the changes as you exit. Choose Solve/Nominal Problem to run the program.

Once the solutions have been generated, you can view the solution plots.

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Back EMF The following plot displays the back EMF solution for the example:

Winding Current The following plot displays the winding current for the example:


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Flux Linkage The following plot displays the flux linkage for the example:

Phase Voltage The following plot displays the phase voltage solution for the example:

Page 30


Speed The following plot displays the speed solution for the example:

Torque The following plot displays the torque solution for the example:


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Compare Results Now compare the results between EMpulse and RMxprt. This will be done using the PlotData. ➤

Post process the transient plots: 1. Choose Post Process/Transient Data. 2. A window appears, asking you for a plot to open. 3. Select the speed.dat plot, and choose OK. PlotData appears.

RMxprt calculates all of its values based of the rated output power. In order to compare the two results, you must calculate the output power from EMpulse and then use this value as an input to RMxprt. Then you can compare other quantities such as current, copper loss, input power, speed, and efficiency.

Average Output Power EMpulse calculates air gap power, not output power; the two are related by the following: Pout = Pair_gap - FW where FW is the energy loss due to friction and wind forces. The average air gap power is calculated by taking the average torque in newton-meters multiplied by the speed in radians per second. From the speed.dat plot, you can see that the average rated speed is ~1575 rpm. ➤

Calculate the average power: 1. Choose Plot/Open, select torque.dat, and choose OK. 2. Choose Tools/Calculator to access the Signal Calculator. 3. Select torque.dat, and choose Copy to copy the torque plot into top of stack of calculator. 4. Choose Sample, and define the following parameters: • Sample in: Time • Specify by: Size • Start = 0.0487 • Stop = 0.0582 • Size = 500 5. Choose OK to accept the values and return to the Signal Calculator. 6. Enter 165 in the Name/Constant field. 7. Choose * to multiply by the speed in radians per second. 8. Choose the integrate button. 9. Enter 0.0095 in the Name/Constant field. 10. Choose / to calculate the average. 11. Choose Preview. The last number in this plot is the average value. 12. 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 613 watts for the air gap power. The friction and windage loss used in the RMxprt program at 1500 rpm is 11 watts; thus, at a speed of 1575 rpm: FW = 150 * (1575/1500) FW = 11.55 Watts

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Calculate the Rated Power Now calculate rated output power using: Pout = 613 - 11.55 Pout = 601.5 Watts ➤

Calculate the rated power: 1. Return to RMxprt, and input this value in the Rated Output Power field in the General window. 2. Change the Rated Speed to 1575 rpm. 3. In the Stator2 window, change the Wire Diameter to 0.8118 mm. 4. Choose Analysis/Analytical Design, and then choose Post Process/Design Output.

Now you can compare other motor parameters.

Full Load Current Return to PlotData to analyze the full load current. ➤

Analyze the full load current: 1. Open the extnl_i.dat plot. This plot represents the current measured in the external circuit you created in Schematic Capture. Using the Plot Data calculator, you can calculate the average line current value directly. 2. Choose Tools/Calculator to access the Signal Calculator: 3. Select I_Line, and choose to Copy the plot to top of stack of calculator. 4. Choose Sample, and define the following parameters: • Sample in: Time • Specify by: Size • Start = 0.0485 • Stop = 0.058 • Size = 500 5. Choose OK to accept the values and return to the Signal Calculator. 6. Choose the integrate button to integrate the results. 7. Enter 0.0095 in the Name/Constant field. 8. Choose / to divide the results and obtain the average or mean values. 9. Choose Preview. The last number in this plot is the average value. 10. 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 3.18 amps. RMxprt calculates a value of 3.22 amps.


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Copper Loss Use PlotData to calculate the copper loss, which will be the I2R losses. Do this by calculating the RMS phase current. ➤

From the Signal Calculator, compute the copper loss: 1. Select I_A, and choose Copy to copy the A-phase current to the top of the stack. 2. Choose Sample, and define the following parameters: • Sample in: Time • Specify by: Size • Start = 0.0388 • Stop = 0.0578 • Size = 500 3. Choose OK to accept the values and return to the Signal Calculator. 4. Choose Push to duplicate the entry. 5. Choose * to multiply the value in the top of the stack by itself, to obtain I2. 6. Choose the integrate button. 7. Enter 0.019 in the Name/Constant field. 8. Choose / to calculate the average. 9. Choose the square root button to take the square root of the quantity. 10. Choose Preview. The last number in this plot is the RMS value. 11. 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 2.4 amps RMS. The value given by RMxprt is 2.66 amps RMS. The total copper loss, including both A and B phase, is: Copper Loss = (2.4 amps)2 * 4.49 ohms * 2 phases Copper Loss = 51.7 watts RMxprt calculates a value of 63.9 watts.

Average Input Power This is the input voltage multiplied by the input current. From the calculation above, the average input current is 3.18 amps. Thus, the input power is: Pinput = 220 watts * 3.18 amps Pinput = 700 watts The value given by RMxprt is 708 watts.

Efficiency The efficiency is the ratio of the output power to the input power. Efficiency = 601.5/700 * 100% Efficiency = 86 % The value calculated by RMxprt is 85%. Now that you have computed a number of motor parameters, compare field quantities between RMxprt and EMpulse. Choose File/Exit to exit the plot data window.

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Post Process Field Quantities ➤

Post process the fields: 1. Choose Post Process/Fields, choose time step 0.04, out0.pjt, choose Post Process. The 2D Post Processor appears. 2. Choose Global/Display, turn the background off, and choose Execute and Return. 3. Create a number of lines on which to plot the field quantities. Choose Post/Line/Define, and define a line in each the following places: • the air gap • the stator tooth • the stator yoke • the rotor yoke • the magnet To do this, for each line, you need to draw the line segment, enter a name, and choose Execute. Refer to the following picture for line and arc placement:

Optionally, it may be helpful to turn off the snap to mode for the grid and vertices and to enable the keyboard entry when creating the lines and arcs. Do this by choosing Global/Defaults and toggling the Keyboard entry option to Yes and the Object snap and Grid snap options to No. You may also want to turn off the background by clicking on Global/Display and toggle background to No. 4. Once you have defined the lines in the air gap, stator tooth, stator yoke, rotor yoke, and magnet, then choose Execute and Return.


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Calculate the Flux Density Once the lines and arcs have been defined, we can calculate the flux density in these locations. The equation used for this calculation is:

∫ B dl B avg = ------------------∫ ( 1.0 ) dl ➤

Perform the calculation: 1. Choose Calc/Plane. 2. Choose B_Vector and then smooth. 3. Choose magnitude to define a magnitude of the flux density as B_mag. 4. Choose Line to access the line calculator. 5. Choose Enter. The Line Entry list appears. 6. Select the line in the stator tooth, and choose Execute. 7. Select the line in the stator pole, and choose Execute. 8. Enter 1000 in the value field to map B_mag onto this arc using 1000 points. 9. Choose value/integrate, and then choose Yes to enter the number calculator. You will integrate along this line. 10. Choose Plane to return to the plane calculator 11. Choose constant, enter a value of 1, and choose Execute to load a constant of 1.0 into the calculator stack. 12. Choose Line to enter the line calculator. 13. Choose Enter. The Line Entry list appears. 14. Select the line in the stator tooth, and choose Execute. 15. Select the line in the stator pole, and choose Execute. 16. Choose value/integrate, and then choose Yes to enter the number calculator. This gives the length of the line. 17. Choose Number to enter the number calculator. 18. Choose divide. This is the average flux density in the stator pole.

This calculation returns a value of 1.656 tesla. The value given by RMxprt is 1.641 tesla. Repeat this calculation for each of the line segments. The results of these calculations are as follows: EMpulse

RMxprt

Magnet Flux Density (tesla)

0.824

0.789

Rotor-Yoke Flux Density (tesla)

0.575

0.784

Stator-Yoke Flux Density (tesla)

1.813

1.564

Stator-Tooth Flux Density (tesla)

1.656

1.641

Air-Gap Flux Density (tesla)

0.818

0.729

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A Permanent Magnet Brushless DC Motor Problem

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