ters
Some of the assumptions made when forming the thermal network are based on empir- ical reference data. It is not clear how representative these assumptions are for this type of motor. Contact air gaps between materials are for example highly dependent on the production process [102], which are not treated here. The thermal conductivity of the winding mix depends both on the fill factor and on the distribution pattern of the conduc- tors, as investigated between ideal hexagon and square patterns in [128]. Furthermore, various suggested approximations of the convection heat transfer coefficients to the in- ternal air showed to vary quite much.
Therefore, a sensitivity analysis with the original slot geometry is here presented, which gives the difference in temperature in the network nodes when varying selected uncertain parameters. The study is done with a coolant temperature at 65◦C and a flow rate at 6 L/min. The motor was operated at 50 Nm at 12000 rpm and the total losses are 3.5 kW.
Initially, two different values of the cooling convection coefficient hcool(1000 and
3000 W/m2K) and the correction factor kconv,korr(0.4 and 0.6) are implemented. Then
two contact air gaps are varied: between frame and stator yoke (5 µm and 15 µm), and between magnet and rotor yoke (10 µm and 200 µm). Also two values for the thermal conductivity of the winding mix is implemented, one that is λ × 0.5 and one that is λ × 1.5. Furthermore, two values of the thermal resistance of the bearing is studied (as Rth× 0.5 and Rth× 1.5). Finally, the internal air heat transfer coefficients are varied (as
h × 0.5 and h × 1.5). The resulting temperature difference compared to the non-modified network solution is presented in Table 8.5.
PMSM
Table 8.5 Change in steady state temperature in◦C between the modified network and the non- modified, for the Original slot geometry at 50 Nm and 12000 rpm.
Fr StYo StTe AcWi EnWi PM RoYo Be
Reference temperatures 78.1 95.5 126.4 138.0 164.3 123.7 120.2 91.1 hcool= 1000 12.7 12.7 12.1 12.5 13.9 12.3 12.5 12.7 hcool= 3000 -4.3 -4.2 -3.8 -3.9 -4.4 -3.9 -4.1 -4.3 kconv,korr= 0.4 -2.6 -2.5 -2.3 -2.3 -2.6 -2.3 -2.4 -2.5 kconv,korr= 0.6 2.6 2.5 2.3 2.3 2.6 2.3 2.4 2.5 lcontF r−Y o= 5µm 0.0 -5.2 -4.3 -4.2 -3.3 -3.2 -2.0 -0.3 lcontF r−Y o= 15µm 0.0 5.1 4.3 4.3 3.3 3.2 2.1 0.3 lM agGap= 10µm 0.0 0.0 -0.1 0.0 0.1 -1.3 1.5 0.2 lM agGap= 200µm 0.0 0.0 0.0 0.0 0.0 0.3 -0.4 -0.1 λW indM ix= 0.275m 0.1 0.0 -0.1 5.0 3.8 0.3 0.6 0.1 λW indM ix= 0.825m 0.0 0.0 0.0 -1.7 -1.3 -0.1 -0.2 -0.1 Rth,Be× 0.5 0.0 0.0 0.0 0.0 -0.1 -0.4 -0.7 -5.7 Rth,Be× 1.5 0.0 0.0 0.0 0.0 0.1 0.3 0.6 4.7 hF r,in× 0.5 (64 W/m2K) 0.0 0.7 2.1 2.9 9.4 6.7 11.3 1.8 hF r,in× 1.5 (192 W/m2K) 0.0 -0.3 -0.9 -1.3 -4.1 -2.9 -4.9 -0.8 hRo× 0.5 (138 W/m2K) 0.0 0.0 0.1 0.1 -0.3 3.2 6.3 1.0 hRo× 1.5 (414 W/m2K) 0.0 0.0 -0.1 0.0 0.2 -1.7 -3.2 -0.5 hEnW i× 0.5 (39 W/m2K) 0.2 1.3 3.4 5.2 18.9 0.5 -2.4 -0.2 hEnW i× 1.5 (115 W/m2K) -0.1 -0.7 -1.9 -2.8 -10.3 -0.3 1.3 0.1
Setting the coolant heat transfer coefficient hcoolto 1000 W/m2K gives a tempera-
ture increase in all network nodes of around 12-14◦C. When setting it to 3000 W/m2K,
the temperature decrease is 4◦C in all points. Hence, the temperature change when going from 1000 W/m2K to 2000 W/m2K is almost three times larger, compared to going
from 2000 W/m2K to 3000 W/m2K. Thus it seems that it is important to be able to
maintain a flow rate that can give a sufficient coolant heat transfer coefficient.
In the reference case, it is assumed that half (0.5) of the heat flux to the cooling channels pass through the lower duct surfaces. When instead setting the share to 0.1 more and less, the change in temperature in all network nodes is around 2-3◦C.
When the contact air gap between the magnet and rotor yoke is set to 10µm the magnet node temperature becomes about 1.3◦C colder, and the rotor yoke node 1.5◦C
warmer. The other nodes are very little affected from this change, and are even less affected in the case of a 200µm gap length.
The same weak dependence is also noted for changes in the thermal resistance of the bearing, except in the bearing node itself.
When varying the contact gap length between the frame and stator yoke, on the other hand, the stator yoke temperature changes about 1◦C per µm gap length. The other node temperatures also change, however, the values decrease in the motors inward radial direction. The end winding and active winding temperatures changes about 0.8-0.9◦C per µm gap length. In [102], gap lengths of up to 77µm are reported for some machines. Such a gap length in this operating point would lead to winding temperatures of around 200◦C.
The temperature changes are notable when varying the internal air heat coefficients to h × 0.5 and h × 1.5. The changes are the smallest for hRoand the largest for hEnW i.
rotor yoke, which is the closest node. The second closest node, the magnet, changes 1- 2%. The temperature differences in the windings are very small and about the same in both cases.
When varying hF r,in the largest temperature changes are noted in the rotor yoke
node, and the second largest in the end winding node. The end winding increases about 6% in the h × 0.5-case, and it decreases around 3% in the h × 1.5-case. The magnet temperature increase about 5% in the h × 0.5-case, and decreases around 2% in the h × 1.5-case.
The largest changes in the end wining temperatures are noted for changes of hEnW i.
In the h × 0.5-case the temperature increase is about 12%, and in the h × 1.5-case the decrease is around 6%. The effect on the active winding temperature is 2%-4%, on the stator teeth 1%-3%, and on the magnets it is less than half a percent.
When it comes to the studied contact gap lengths, winding mix thermal conductivity, and internal air heat transfer coefficients, it is difficult to analytically find assumptions that are more applicable than the empirical data presented in the references. However, if experimental results are available from a physical machine, it it highly recommended to calibrate such network parameters towards measurements in order for the lumped param- eter network to better fit the specific machine.