Florence Meier, KTH, 02/09/2008
Validation of Emetor: Example of the PMSM for a
forklift
In this report, the results from Emetor are compared to the results obtained from finite-element
(FE) simulations in the case of the PM motor for an electric forklift. The magnetic circuit
is linear in the FE simulations. The simulations are performed in Flux from Cedrat. The
calculations in Emetor are made with a “medium” computation time, which is the default value.
1
Calculations at open-circuit
The waveforms of the open-circuit airgap flux density and back-EMF obtained in Emetor and
Flux are shown in Figure 1. The FE waveforms contain dips due to the slotting. The effect of
the slotting is not considered in Emetor. Except for these dips, the waveforms match well. Other
results are given in Table 3. The differences in the fundamentals of the open-circuit airgap flux
density and phase back-EMF are mostly due to the slotting that is not considered. There is a
large discrepancy for the flux density in the rotor yoke. In Emetor, it is supposed that the flux
is uniformly distributed in the rotor yoke which is not the case when the rotor yoke is large.
40
FEM
Emetor
0.5
FEM
Emetor
30
20
Backemf [V]
Opencircuit airgap flux density [T]
1
0
10
0
-10
-20
-0.5
-30
-1
0
a)
0.5
1.5
1
2
2.5
Angular position [mech. rad]
3
-40
0
0.005
b)
0.01
0.015
0.02
Time [s]
Figure 1: a) Open-circuit airgap flux density. b) Phase back-EMF.
Table 1: Results at open-circuit conditions.
Fundamental open-circuit airgap flux density [T]
Max. no-load flux density in stator teeth [T]
Max. no-load flux density in stator yoke [T]
Max. no-load flux density in rotor yoke
Fundamental phase EMF (peak) [V]
2
Emetor
0.819
1.468
1.142
0.495
39.7
FEM
0.782
1.4
1.2
0.8
38.3
Relative error
4.7 %
4.8 %
-5 %
-40 %
3.6 %
Calculations with armature reaction
The FE-calculated phase armature reaction airgap flux density is obtained by subtracting the
airgap flux density when one phase of the winding is supplied with the rated current to the
open-circuit airgap flux density. This is not a problem since the magnetic circuit is linear. Both
airgap flux density from Emetor and Flux are shown in Figure 2.a. The main difference between
the waveform comes from the absence of slotting effect in Emetor. The values of the inductances
1
Florence Meier, KTH, 02/09/2008
are given in Table 2. The value of the self-inductance calculated in Emetor includes the endwinding leakage inductance which is not the case for the self-inductance calculated in Flux. As
can be seen, there is 12.7 % difference in the value of the slot leakage inductance, which suggest
that other models could be tested and eventually implemented in Emetor.
a)
66
0.3
64
FEM
Emetor
0.2
62
60
0.1
Torque [Nm]
Phase armature reaction airgap flux density [T]
0.4
0
-0.1
58
56
54
-0.2
52
-0.3
50
-0.4
0
48
0
b)
0.5
1
1.5
2
2.5
Angular position [mech. rad]
3
FEM
Emetor
0.005
0.01
Time [s]
0.015
0.02
Figure 2: a) Phase armature reaction airgap flux density. b) Torque at load conditions.
Table 2: Inductances.
Self inductance [mH]
Mutual inductance [mH]
Magnetizing inductance [mH]
Slot leakage inductance [mH]
3
Emetor
0.392
0.139
0.334
0.053
FEM
0.369
0.138
0.318
0.047
Relative error
6.2 %
0.7 %
5%
12.7 %
Calculations at load conditions
The FE simulation is performed as follows: A sinusoidal current is supplied to the coils. Its
amplitude is the one calculated in Emetor. The rotor is rotating at rated constant speed. From
this simulation, we can check if the phase current calculated in Emetor allows to obtained the
specified torque. The results are presented in Table 2.b and Figure 2.b. As can be seen, the
results are quite close. The discrepancy is again mostly due to the lack of slotting effect in
Emetor. The cogging torque in Emetor is not calculated and thus not included in the waveform
in Figure 2.b.
Table 3: Results at load conditions.
Mean torque
Torque ripple
Emetor
60
14.5 %
FEM
57.8
27.3 %
2
Relative error
3.9 %
47 %