We have added a switch function to the NETWORK module of EMSolution. To verify this, we have analyzed the benchmark problem of DC brushless servo motors published by the Institute of Electrical Engineers of Japan (IEEJ) [Ref].
The analytical model is shown in Fig. 1. The model is a two-dimensional analysis with an axial length of 37.5 mm. The 1/4 region is analyzed using symmetry. The 90-degree antisymmetric periodic boundary condition is used. The gap between the stator and rotor is 0.8 mm and divided into 4 layers, equally divided by 1 degree in the circumferential direction. A sliding plane is set at the center of the gap to simulate rotational motion. The number of turns in each stator slot is set to 100 and the phase order is given as shown in the figure. The rotor position in Fig. 1 is set at an electrical angle of 0°, and the rotation is clockwise in the figure. The magnets are assumed to be uniformly magnetized to 0.9T, and the material properties such as B-H curves are as in the literature. The time step is defined as the time interval of 1 degree rotation.
Fig. 2 shows the electrical equivalent circuit used in the analysis. It is assumed that the voltage sources (Vu, Vv, Vw) are given
Fig. 4 shows the analysis results of the current waveform when the applied voltage is 30 V and the rotation speed is 600 rpm. Since the current reaches a steady state at the second cycle of the electric angle, the result of the second cycle is shown. It can be seen that the current between the windings is flowing as expected. Fig.5 shows the case where the rotation speed is 1304.4 rpm (with no load). Fig. 6 shows the torque waveform. These results are in close agreement with the results of the analysis in [Ref]. For example, the average torque value is 0.215492
The switches here are handled by the time variation of the resistance value. In the current case, the resistance at Off was analyzed as 100
For example, the induced EMF waveform in this benchmark problem is shown in Fig. 7. (The vertical axis of Fig. 7 is different from that of the induced EMF waveform reported in [Ref]. Here, the induced electromotive force for all turns of each phase is shown). The width and height of the voltage peaks are considered to depend on the calculation time step. The current transfer is considered to occur in a shorter time than the analysis time step, so a sufficiently small time step is required to see the details. Fig. 8 shows a comparison of the total power supplied to the coil obtained from the coil induced voltage and coil current, and the power supply output minus the resistance (including winding resistance) loss. In both cases, the output current and voltage were simply added at each step and averaged.
The two should be the same, but in this case, the former is about 4% smaller on average. This difference occurs during transients when spikes occur. Although the two values are in good agreement except during current transients, this is considered insufficient for the analysis of the spikes themselves. The mechanical work rate obtained by the torque agrees very well with that obtained by the coil induced voltage and coil current in the former case.
As described above, we hope that you understand that the above is fully applicable to the analysis of this brushless motor, although there are some problems during switching. We believe it can also be applied to circuits containing other switches.
The function of this switch will be released from EMSolution ver9.8.1. We hope you will make use of it. Please note that this function requires the NETWORK module.
Technical Report of the Institute of Electrical Engineers of Japan, No. 565, "Advanced Numerical Simulation Techniques for Electromagnetic Fields in Rotating Machines," October 1995.
The switch function works only in transient analysis. When using the switch function, set THETA_NETWORK=1 (backward difference) in the convergence conditions of Section 5 in the handbook. If set to 0.5 (central difference), the solution will oscillate. Enter the switch as an element of NETWORK. The input data is as follows.
NETWORK data for Fig.2 and 3 are as follows. The node number corresponds to the number in Fig. 2, and CYCLE is one cycle of the electric angle (0.05sec).
* NETWORK * REGION_FACTOR * NETWORK 4.0 * FEM * ID * NODE1 * NODE2 * SERIED_ID * FEM 11 1 11 1 * R * ID * NODE1 * NODE2 * RESISTANCE * R 12 11 12 7.9567 * SWITCH * ID * NODE1 * NODE2 * ON_RES * OFF_RES * SWITCH 13 12 13 0.0 100000 * NO_DATA * CYCLE * PHASE_OP * TIME_ID * 1 0.05 1 0 * ON_TIME * OFF_TIME * 210 330 * SWITCH * ID * NODE1 * NODE2 * ON_RES * OFF_RES * SWITCH 14 12 2 0.0 100000 * NO_DATA * CYCLE * PHASE_OP * TIME_ID * 1 0.05 1 0 * ON_TIME * OFF_TIME * 30 150 * VPS * ID * NODE1 * NODE2 * TIME_ID * VPS 15 13 2 3 * FEM * ID * NODE1 * NODE2 * SERIED_ID * FEM 21 1 21 2 * R * ID * NODE1 * NODE2 * RESISTANCE * R 22 21 22 7.9567 * SWITCH * ID * NODE1 * NODE2 * ON_RES * OFF_RES * SWITCH 23 22 23 0.0 100000 * NO_DATA * CYCLE * PHASE_OP * TIME_ID * 2 0.05 1 0 * ON_TIME * OFF_TIME * 0 90 330 360 * SWITCH * ID * NODE1 * NODE2 * ON_RES * OFF_RES * SWITCH 24 22 2 0.0 100000 * NO_DATA * CYCLE * PHASE_OP * TIME_ID * 1 0.05 1 0 * ON_TIME * OFF_TIME * 150 270 * VPS * ID * NODE1 * NODE2 * TIME_ID * VPS 25 23 2 3 * FEM * ID * NODE1 * NODE2 * SERIED_ID * FEM 31 1 31 3 * R * ID * NODE1 * NODE2 * RESISTANCE * R 32 31 32 7.9567 * SWITCH * ID * NODE1 * NODE2 * ON_RES * OFF_RES * SWITCH 33 32 33 0.0 100000 * NO_DATA * CYCLE * PHASE_OP * TIME_ID * 1 0.05 1 0 * ON_TIME * OFF_TIME * 90 210 * SWITCH * ID * NODE1 * NODE2 * ON_RES * OFF_RES * SWITCH 34 32 2 0.0 100000 * NO_DATA * CYCLE * PHASE_OP * TIME_ID * 2 0.05 1 0 * ON_TIME * OFF_TIME * 0 30 270 360 * VPS * ID * NODE1 * NODE2 * TIME_ID * VPS 35 33 2 3 * END NETWORK * END
In the above example, the On-Off time is given in phase (time zero is phase zero) for one cycle, but it can be given in real time as follows
* SWITCH * ID * NODE1 * NODE2 * ON_RES * OFF_RES * SWITCH 13 12 13 0 100000 * NO_DATA * CYCLE * PHASE_OP * TIME_ID * 2 0.05 0 0 * ON_TIME * OFF_TIME * 0.029166667 0.045833333 0.079166667 0.095833333
・ input_600rpm
To change the rotation speed, CYCLE in SWITCH must be changed.
・ input_cycle_600rpm
Input data (using CURCUIT) for step input by repeating the time table as shown in "Improvement of Power Supply Input Method” (improved in EMSolution r9.8.2)".
・ pre_geom2D.neu
・ rotor_mesh2D.neu
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