5.2.1 Time behaviour
Quasi-static test have been performed at ωref equal to 400 rpm: gure 5.6a shows the acquired behaviours of ωrot at dierent air gaps (experimental tests were conducted for 9 dierent air gaps shown in gure 5.6b).
The data acquisition consists of three phases:
the rst one is the acceleration phase during which the disk reaches the velocity set via Kollmorgen WorkBench;
the second one is the steady-state speed phase during which the disk have reached the set velocity, so the motor keeps it constant;
(a) SCADAS channel setup
(b) SCADAS acquisition setup
Figure 5.5: SCADAS setup
the third is the deceleration phase in which the power is disconnected so the velocity disk starts to decrease until it reaches zero: interest-ingly, the smaller the gap, the faster the disc decelerates, resulting in increasingly steep deceleration curves.
Even more interesting are the curves in gure 5.7a and gure 5.7b that show the time behaviours of lift and drag forces for the 9 experimental tests.
Regarding the magnitude, both for the drag and the lift force, it is inversely proportional to the air gap: so smaller air gaps produce higher values of forces.
Regarding the trend of the forces, when the power is disconnected, the lift force immediately decreases following a curve that is steeper the smaller the air gaps are; instead the drag curves show a slightly dierent trend: the force reaches its maximum value at the electromagnetic pole (3D FEM simulations in COMSOL Multiphysics®show an electromagnetic pole at 163 rpm) then decreases reaching the steady value; when the power is disconnected, there is a peak of the force that reaches almost the value before the electromagnetic pole and then decreases until zero as the lift force.
(a) Quasi-static time behaviour results
(b) Air gaps legend
Figure 5.6: Quasi-static time response
5.2.2 Speed behaviour
It is interesting to plot the speed behaviour of the drag and lift forces during the deceleration phase ( gure 5.8a and gure 5.8b): here too, it can be clearly seen that magnitude force increases with small gaps and the trend of the drag force before and after the electromagnetic pole.
5.2.3 Uncertainty zone
In section 4.4 was described the inclination and orientation of the pad with respect to the copper rim considering them as a possible source of non ideal-ities. Using COMSOL Multiphysics®is possible to draw an uncertanty zone due to this phenomenon on the lift and drag curve as shown in gure 5.9:
the upper bound represents the nominal pad set up, so the values of forces of the pad if it were not tilted, while the lower bound represents the tilted pad set up. It is important to notice that the experimental data lies within the numerical results' bounds.
(a) Lift forces time behaviour
(b) Drag Forces time behaviour
Figure 5.7: Lift and drag forces time response
5.2.4 Lift to drag ratio
The lift to drag ratio is an important parameter that indicates the e ciency of the system and it can be used to verify how accurate is the behaviour of the Halbach array. As we can see from gure 5.10 the lift to drag ratio increases with the speed but it has not a constant behaviour for all the airgaps: for higher values of the latter we get a higher ratio; this means that the system is more e cient.
5.2.5 Scaled results
As is understandable, for physical reasons, the entire test bench was designed to replicate and study the behaviour of a real system that will be mounted on an Hyperloop train in a smaller scale. After obtaining the lift and drag
(a) Lift forces speed behaviour
(b) Drag Forces speed behaviour
Figure 5.8: Lift and drag forces speeds response
curves for the scaled Halbach array, via 3D FEM simulations using COM-SOL Multiphysics®, it was possible to derive a scale factor that correlates the data obtained above with that which could be obtained with a full-size system: the value of the scale factor is equal to 4 and consequently, the scaled Fl and Fd are proportional to the scale factor2 while the velocity is proportional to the scale factor. Figure 5.11 shows the scaled lift and drag curves.
5.2.6 COMSOL simulation and experimental results com-parison
The behaviour of lift and drag forces are reported along with the related numerical results obtained via 3D FEM in COMSOL Multiphysics®. Sim-ulation results have been obtained considering to add an oset of 0.75 mm to each nominal air gaps: this oset takes into account all the non idealities discussed in section 4.4. Figure 5.12a shows the results for the scaled pad for 4 dierent airgaps: as we can see, the curve overlap quite well.
Figure 5.9: Uncertainty zone
5.2.7 Temperatures
During the experiment, the temperatures of the copper track and the pad before and after the test were monitored for each air gaps using a Fluke infrared thermometer (datasheet on Ref [38]). Table 5.1 shows the results:
as expected, the largest temperature dierence on the copper rim between the start and end of the test was recorded at the smallest gap (∆T = 4°).
Figure 5.13 shows an example of image taken by the infrared thermometer.
However, it is important to emphasise that the obtained values are only indicative as they were measured on re ective materials using an infrared camera and, therefore, subject to errors.
Figure 5.10: Lift to drag ratio
Figure 5.11: Scaled lift and drag curves
(a) Scaled lift and drag curves vs COMSOL simulations
(b) Air gaps legend
Figure 5.12: Scaled lift and drag curves behaviour
Figure 5.13: Example of Fluke temperature image
Gap [mm] Copper track [°] Pad [°]
Start End Start End
10 23 27 20.9 21.3
12 21.6 23 20.7 20.9
14 21.8 21.6 21.4 20.7
16 22.1 21.8 21.2 21.4
18 22 22.1 21.5 21.2
20 21.7 22 22.2 21.5
22 21.8 21.7 21.6 22.2
24 21.4 21.8 21.9 21.6
26 20.6 21.4 20.8 21.9
Table 5.1: Copper track and pad temperature during quasi-static experiment