40223711 flux2d76 flux2d to simulink technology technical paper

Copyright September 2002

CAD Package for Electromagnetic and Thermal Analysis using Finite Elements

FLUX2D Version FLUX2D7.60

FLUX2D TO SIMULINK TECHNOLOGY TECHNICAL PAPER

FLUX2D and CAOBIBS are registered marks.

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This tutorial has been printed the 27 September 2002

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FLUX2D7.60 CONVENTIONS USED

CONVENTIONS USED

To make this tutorial easier to read, we use the following typeface conventions:

All comments are written in the same way as this sentence. All dialog text between the user and FLUX2D is written in courier font:

Name of the region to be created: magnet Colour of this region: AGENTA Select a surface or a menu item: uit [q]uit

Below are presented the conventions used for the dialog between the user and FLUX2D: Italic text Messages or questions displayed on the screen by FLUX2D.

Bold text magnet [q]uit

User input to FLUX2D, such as the coordinates of a point. The character symbolizes the Return/Enter key. You only have to enter enough of the response to remove any ambiguity between the response you want and other valid ones. In which case enter the character shown in square brackets [ ].

old text AGENTA

FLUX2D menu input. Make a selection by clicking on the menu item with the mouse or, if there is no ambiguity, by entering the first character of the word (shown in angled brackets < >).

FLUX2D graphical input, such as selecting a line or a point. The reply is by default. To enter a default response, simply press the

Return/Enter key.

- REMARK - The files corresponding to different cases studied in this tutorial are available in the folder:

..\doc_examples\examples\tutorial\2D\Simulink The correspondent applications are ready to be solved. This allows you to adapt this tutorial to your needs. If you do not know FLUX2D yet, we advise you to run through this entire

tutorial and to refer, if necessary to the given cases. If you already know FLUX2D, we advise you to redo only the

Parameterization, Solving and Analysis sections, in order to discover the new possibilities of FLUX2D.

FLUX2D7.60 TABLE OF CONTENTS

FLUX2D TO SIMULINK TECHNOLOGY TECHNICAL PAPER PAGE A

TABLE OF CONTENTS

PART A : Square wave motor - torque ripples 1

1. Materials ......................................................................................................................3

2. Definition of the electrical circuit ..................................................................................5

3. Physical properties ......................................................................................................7 3.1 General information .................................................................................................... 7 3.2 Materials ..................................................................................................................... 7 3.3 Boundary conditions ................................................................................................... 8 3.4 Electrical circuit........................................................................................................... 8

4. Definition of Simulink model ........................................................................................9 4.1 Description of the Simulink model............................................................................... 9

4.1.1 Whole model ..............................................................................................................9 4.1.2 Switching scheme ....................................................................................................10

4.2 Definition of the blocks.............................................................................................. 11 4.2.1 Coupling with Flux2d block ....................................................................................11 4.2.2 The command ..........................................................................................................12 4.2.3 Outputs.....................................................................................................................14

5. Solve ........................................................................................................................15

6. Results.......................................................................................................................17 6.1 With Simulink............................................................................................................ 17

6.1.1 Resistances values ..................................................................................................17 6.1.2 Mechanical quantities...............................................................................................19 6.1.3 Electrical quantities ..................................................................................................20

6.2 With Flux2d............................................................................................................... 21 6.2.1 Equiflux lines ............................................................................................................21 6.2.2 Flux density in the air gap ........................................................................................22 6.2.3 Currents....................................................................................................................24

TABLE OF CONTENTS FLUX2D7.60

PAGE B FLUX2D TO SIMULINK TECHNOLOGY TECHNICAL PAPER

PART B: Square wave motor - No load startup with electromechanical coulping 25

7. Physical properties.....................................................................................................27

8. Simulink model and solving .......................................................................................29

9. Results.......................................................................................................................31 9.1 With Simulink ............................................................................................................31

9.1.1 Mechanical quantities ...............................................................................................31 9.1.2 Electrical quantities...................................................................................................32

9.2 With Flux2d ...............................................................................................................33 9.2.1 Equiflux lines ............................................................................................................33 9.2.2 Mechanical quantities ...............................................................................................34 9.2.3 Electrical quantities...................................................................................................35

PART C: Square wave motor - Servo operation with electromechanical coupling 37

10. Physical properties.....................................................................................................39

11. Simulink model and solving .......................................................................................41

12. Results.......................................................................................................................43 12.1 With Simulink ............................................................................................................43

12.1.1 Mechanical quantities ...............................................................................................43 12.1.2 Electrical quantities...................................................................................................44

12.2 With Flux2d ...............................................................................................................45 12.2.1 Flux density distribution ............................................................................................45 12.2.2 Torque ......................................................................................................................45 12.2.3 Currents....................................................................................................................46

FLUX2D7.60 PART A: Square Wave Motor Torque Ripples

FLUX2D TO SIMULINK TECHNOLOGY TECHNICAL PAPER PAGE 1

PART A: Square Wave Motor Torque Ripples

PART A: Square Wave Motor Torque Ripples FLUX2D7.60

PAGE 2 FLUX2D TO SIMULINK TECHNOLOGY TECHNICAL PAPER

FLUX2D7.60 PART A: Square Wave Motor Torque Ripples Materials


1. Materials

The materials will be the same in all this technical paper. The magnet is modelled by a linear material, whereas the steel is modelled by a non-linear material.

Name of the material

Property Model Permeability Remanent flux density or saturation magnetisation

MAGNET_LIN 5_Magnet 1_scalar_cst 0.401 T MAGNET_LIN 1_iso_MU 1_scalar_cst 1.071

STEEL 1_iso_MU B_scalar_a_sat 1.99 T STEEL 1_iso_MU B_scalar_a_sat 7500

Table 1: Materials

PART A: Square Wave Motor Torque Ripples FLUX2D7.60 Materials


FLUX2D7.60 PART A: Square Wave Motor Torque Ripples Definition of the electrical circuit


2. Definition of the electrical circuit

The motor is supplied with a 3-phase bridge inverter where the free wheeling diodes have been neglected. The inverter switching scheme is dependent on the rotor position. The switches are modelled by resistances with a very low value to model on-state and very large value to model off-state. To model the drop voltage on the switches, a voltage source has been added to every resistance. Simulink will control the value of the resistances depending on the position of the rotor. In the electrical circuit will only be described the components: the values of the resistances will be set to 1 as a reference value.

Figure 1: Electrical circuit

PART A: Square Wave Motor Torque Ripples FLUX2D7.60 Definition of the electrical circuit


Name of the component

Comment Model Value

VSOURCE Voltage source Constant 6 V V1 Voltage source Constant 0.8 V V2 Voltage source Constant 0.8 V V3 Voltage source Constant 0.8 V V4 Voltage source Constant 0.8 V V5 Voltage source Constant 0.8 V V6 Voltage source Constant 0.8 V PA Coil Total value Number of turns: 10

Resistance: 0.017625 Ohm MA Coil Total value Number of turns: 10

Resistance: 0.017625 Ohm PB Coil Total value Number of turns: 20

Resistance: 0.03525 Ohm MC Coil Total value Number of turns: 20

Resistance: 0.03525 Ohm Resis34 Resistor Constant 1 Ohm Resis35 Resistor Constant 1 Ohm Resis36 Resistor Constant 1 Ohm Resis37 Resistor Constant 1 Ohm Resis38 Resistor Constant 1 Ohm Resis39 Resistor Constant 1 Ohm Induc15 Inductance Constant 7.75 H Induc16 Inductance Constant 7.75 H Induc17 Inductance Constant 7.75 H Resis18 Resistor Constant 100.000 Ohm

Table 2: Electrical components

FLUX2D7.60 PART A: Square Wave Motor Torque Ripples Physical properties


3. Physical properties

Complete this part in FLUX2D. Use the brushless machine geometry drawn in the first part.

3.1 General information In the following, the name of this file is TORQUE_RIPPLE. The problem has a constant cross section (plane problem) with a depth of 50.308 mm. It is solved with the Transient Magnetic application.

) Note : Flux2d Simulink coupling is available only for transient magnetic computations so far.

3.2 Materials There are only two materials that should be assigned to regions as follows:

Name of the region Material Property Model Value Nb of pair of poles PA VACUUM Source External circuit MA VACUUM Source External circuit PB VACUUM Source External circuit MC VACUUM Source External circuit

AIRGAP Rotational air gap Angular velocity Constant 2000 rpm 2 WEDGE VACUUM Source No source

AIR VACUUM Source No source SHAFT VACUUM Source No source ROTOR STEEL Source No source STATOR STEEL Source No source MAGNET MAGNET Direction of

magnetisation Radial + ( 0 , 0 )

MAGNET MAGNET Source No source

Table 3: Materials

PART A: Square Wave Motor Torque Ripples FLUX2D7.60 Physical properties


3.3 Boundary conditions FLUX2D automatically assigns the right boundary conditions taking into account the number of pole pairs of the motors and the number of displayed poles.

? 0 BREAK Quit Zoom Reset Move 1 Dirichlet 2 Float 3 Cyclic 4 Anticyclic 5 Translation 6 Periodic 7 Cancel

3.4 Electrical circuit The different electrical components are described in the second chapter. The Simulink model is described in the following chapter.

FLUX2D7.60 PART A: Square Wave Motor Torque Ripples Definition of Simulink model


4. Definition of Simulink model

4.1 Description of the Simulink model In the following is presented the Simulink model, with the definition of every block.

4.1.1 Whole model The whole model looks as follows:

Figure 2: Whole Simulink model

PART A: Square Wave Motor Torque Ripples FLUX2D7.60 Definition of Simulink model


The model includes: - a Coupling with Flux2d block: this block calls FLUX2D during the computation (see

paragraph 4.2.2) - the command (on the left part of the model): this part commands the value of the resistances

depending on the position of the rotor. (see paragraph 4.2.3) - the outputs to be displayed (see paragraph 4.2.4)

4.1.2 Switching scheme The switches states depend on the rotor position, expressed in electrical angle. The following table shows the moments where the switches are on, assuming one electrical period corresponds to 180 mechanical degrees.

) Note: According to the model we used, an on switch is equivalent to a resistance set to a low value. In the following, the on state will be represented by a resistance of 1e-4 Ohm, the off state by a resistance of 1e+6 Ohm.

Name of the resistance

On state minimum angle

On state maximum angle

R1 15 75 R2 105 165 R3 75 135 R4 164 45 R5 135 15 R6 45 105

Table 4: Switching scheme



4.2 Definition of the blocks

4.2.1 Coupling with Flux2d block This block enables a direct co-simulation with both Flux2D and Matlab Simulink.

After installing the files as explained in the users guide, this block is available in the Simulink Library Browser, in the folder flux_link.

It is defined by:

- the TRA file that will be solved: give the name of the TRA file without the extension .TRA TORQUE_RIPPLE

- Flux2D inputs: the resistances R1 to R6 representing the switches should be defined as inputs to Flux2D. The syntax to use is described in the users guide. [Resistance:resis37;Resistance:resis34;Resistance:resis38;Resistance:resis35;Resistance:resis39;Resistance:resis36]

) Note: The components names correspond to the name given to the components in page 4. Do not forget to check that it corresponds to your circuit.

- Flux2D outputs: the mechanical values are displayed (torque, angular velocity and position) as well as some electrical values (current in phase 1 and 2 and in the voltage source) [TORQUE;OMEGA;TETA;CURRENT:induc15;CURRENT:induc17;CURRENT:vsource]

- the time step: the computation has 48 time steps over an electrical period (180 degrees). Then each time step represent a rotation of 180 / 45 = 3.75 degrees. Assuming a constant speed of 2000 rpm, the time step is then 3.75 / ( 2000 * 6 ) = 0.3125 ms. 0.3125e-3

- the initial conditions: there is no initial conditions to set.

Figure 3: Coupling with Flux2D block



4.2.2 The command This part controls the electrical circuit of Flux2D. It will control the value of the resistances depending on the position of the rotor.

Figure 4: Command part of Simulink model

All six resistances are on in a certain range of values of the rotor position. The Min and Max values are the trigger on and trigger off times respectively. Assuming that there are 2 pole pairs, one mechanical period corresponds to 180 electrical degrees. That is why all the Min and Max values should be in the range [0; 180]. The Max values are then not necessary greater than the Min values. Two cases can be distinguished then: when the Max value is greater than the Min value (for R1, R2, R3 and R6), and when the Max value is lower than the Min value (for R4 and R5).



4.2.2.1 Resistance control subsystem for R1, R2, R3 and R6

Figure 5: Resistance control subsystem

4.2.2.2 Resistance control subsystem for R4 and R5

Figure 6: Resistance control subsystem



4.2.3 Outputs

Figure 6: Outputs

As six outputs have been defined in the Coupling with Flux2d block, 2 scopes with 3 graphs each can be used (one for the mechanical quantities, one for the electrical quantities). The output position of the rotor is expressed in mechanical degrees. As the resistances are controlled with electrical angles, a block should be added to convert mechanical angles to electrical angles : this is the block called modulo (block Math function to be find in Simulink - Math in the Simulink Library Browser).

Figure 7: Modulo block

FLUX2D7.60 PART A: Square Wave Motor Torque Ripples Solve


5. Solve

) Note: There is no need to open Flux2d to solve the problem. The simulation can be handled directly in Simulink.

The computation time step for Flux2d has been defined in the Coupling with Flux2d block. Before starting the solving, the computation range should be defined (start and stop times). In this case, as explained above, one electrical period will be simulated, representing 15 ms.

Figure 8: Simulation parameters

) Note: Do not forget to choose the same time step for Simulink computation as done for Flux2d.

PART A: Square Wave Motor Torque Ripples FLUX2D7.60 Solve


FLUX2D7.60 PART A: Square Wave Motor Torque Ripples Results


6. Results

Results can be displayed both with Simulink and with Flux2D. With Simulink, only the values defined as outputs will be displayed. With Flux2D, all the quantities usually reachable with Postpro_2D can be displayed and computed.

6.1 With Simulink

6.1.1 Resistances values The values of the resistances are displayed in Scope1 .

PART A: Square Wave Motor Torque Ripples FLUX2D7.60 Results


Figure 8: Resistance values



6.1.2 Mechanical quantities The torque, angular velocity and position is visualised with Scope

Figure 9: Mechanical quantities



6.1.3 Electrical quantities

Figure 10: Electrical quantities

The first computed time step is for 0.1 ns. This solution corresponds then to a static result. It explains why the first value of the electrical quantities is out of the range of the other ones. Let us go now in Flux2d postprocessor to deeper analyse this problem.



6.2 With Flux2d

6.2.1 Equiflux lines

Figure 11: Equiflux line for time step 2.19 ms



6.2.2 Flux density in the air gap The Flux density is computed on a path (arc of circle) located in the middle of the air gap.

Figure 12: Create a path



Figure 13: Flux density in the air gap

The harmonic spectrum of this curve can be computed.

Figure 14: Spectrum of the flux density



6.2.3 Currents The current in phase 1 is, between 0.3125 ms and 15 ms :

Figure 15: Current in phase 1

The current in the source is, between 0.3125 ms and 15 ms

Figure 16: Current in the source

FLUX2D7.60 PART B: Square wave motor No load startup with electromechanical coupling


PART B: Square wave motor No load startup with electromechanical coupling

PART B: Square wave motor No load startup with electromechanical coupling FLUX2D7.60


FLUX2D7.60 PART B: Square wave motor No load startup with electromechanical coupling Physical properties



The constant speed problem being already defined, the physical properties can be easily modified to simulate the no load startup of the motor. The only information that changes is the definition of the air gap properties. Instead of being defined as a rotational air gap with a constant angular velocity, it is defined as a rotational air gap with constant mechanical values, defined as below:

Property Value Unit Moment of inertia of the rotor 3.8675e-5 kg.m

Friction coefficient 0.005 N.m.s Drag torque 0 N.m

Initial angular velocity 0 rpm Spring constant 0 N.m

Initial streching / compression of the spring / position at rest 0 degrees All the other properties (materials, boundary conditions and electrical circuit) remain identical. Save this file as No_Load_Startup.

PART B: Square wave motor No load startup with electromechanical coupling FLUX2D7.60 Physical properties


FLUX2D7.60 PART B: Square wave motor No load startup with electromechanical coupling Simulink model and solving


8. Simulink model and solving

As the supply and the command remain identical, the Simulink model remains also the same. Then, it is just needed to Save as the Simulink model with another name, and give the new name of the TRA file to the Coupling with Flux2d block.

Figure 16: No load startup Coupling with Flux2d block.

This time, the problem will be solved on 3 mechanical periods, i.e. 1.5 electrical period (45 ms). The chosen time step is 0.5 ms.

PART B: Square wave motor No load startup with electromechanical coupling FLUX2D7.60 Simulink model and solving


Figure 17: No load startup simulation parameters.

FLUX2D7.60 PART B: Square wave motor No load startup with electromechanical coupling Results


9. Results

9.1 With Simulink

9.1.1 Mechanical quantities

Figure 18: Mechanical quantites

The represented torque is the magnetic torque.

PART B: Square wave motor No load startup with electromechanical coupling FLUX2D7.60 Results



Figure 19: Electrical quantities



9.2 With Flux2d

9.2.1 Equiflux lines

Figure 19: Equiflux lines for time step 3.5 ms




Figure 20: No load motor torque

As it could have been expected, the no load motor torque has a steady state mean value equal to zero. This torque is different from the magnetic torque, represented in Simulink. We have indeed :

&fTTT rm = where T is the motor torque mT is the magnetic torque rT is the drag torque (set here to zero) f is the friction coefficient & is the angular velocity



9.2.3 Electrical quantities The current in the source between 0.5 ms and 45 ms looks as follows:

Figure 21: Source current at no load

FLUX2D7.60 PART C: Square wave motor Servo operation with electromechanical coupling


PART C: Square wave motor Servo operation with electromechanical coupling

PART C: Square wave motor Servo operation with electromechanical coupling FLUX2D7.60


FLUX2D7.60 PART C: Square wave motor Servo operation with electromechanical coupling Physical properties



The no load startup problem being already defined, the physical properties can be easily modified to simulate the servo operation. The only information that changes is the definition of the air gap properties. It is still a rotational airgap with constant mechanical values, but you have to add a drag torque.

Property Value Unit Moment of inertia of the rotor 3.8675e-5 kg.m

Friction coefficient 0.005 N.m.s Drag torque 0.3 N.m

Initial angular velocity 0 rpm Spring constant 0 N.m

Initial streching / compression of the spring / position at rest 0 degrees All the other properties (materials, boundary conditions and electrical circuit) remain identical. Save this file as Servo_operation.

PART C: Square wave motor Servo operation with electromechanical coupling FLUX2D7.60 Physical properties


FLUX2D7.60 PART C: Square wave motor Servo operation with electromechanical coupling Simulink model and solving


11. Simulink model and solving

As the supply and the command remain identical, the Simulink model remains also the same. Then, it is just needed to Save as the Simulink model with another name, and give the new name of the TRA file to the Coupling with Flux2d block.

Figure 16: Servo operation Coupling with Flux2d block

This time, the problem will be solved on 3 mechanical periods, i.e. 1.5 electrical period (45 ms). The chosen time step is 0.5 ms.

PART C: Square wave motor Servo operation with electromechanical coupling FLUX2D7.60 Simulink model and solving


Figure 17: Servo operation simulation parameters

FLUX2D7.60 PART C: Square wave motor Servo operation with electromechanical coupling Results


12. Results

12.1 With Simulink


Figure 22: Mechanical quantities for servo operation

PART C: Square wave motor Servo operation with electromechanical coupling FLUX2D7.60 Results



Figure 23: Electrical quantities for servo operation

FLUX2D7.60 PART C: Square wave motor Servo operation with electromechanical coupling Results


12.2 With Flux2d

12.2.1 Flux density distribution

Figure 24: Flux density distribution at time step 28 ms

12.2.2 Torque

Figure 25: Motor torque for servo operation

PART C: Square wave motor Servo operation with electromechanical coupling FLUX2D7.60 Results


12.2.3 Currents Currents in the three phases look as below:

Figure 26: Current in the three phases between 1 ms and 65 ms

The current in the source is:

Figure 27: Source current for servo operation between 1 ms and 65 ms

40223711 flux2d76 flux2d to simulink technology technical paper

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