Cogging Torque

99

Type of load Variation of the air gap, µm

Results of the simulation Results of the measurement

Axial load 70 62

Radial load 83 53

Torque load 58 51

Table 6.1 – Comparison of the simulated and measured values of the air gap variation

The results of the measurement of the air gap variation are 62 µm by axial load, 53 µm by radial load and 51 µm by torque load, which do not strongly align to the simulated results with a maximum error of 36.1% for the radial load case. The reason for this discrepancy can be caused by a higher level of the wheel hub bearing mounted in the prototype.

According to the presented loading cases, it can be seen that the motor is deformed in symmetric relation to the load. Furthermore, it is apparent that the air gap is more sensible in case of axial load. The reason for this is the lower stiffness of the hub bearing in axial direction.

The measured displacements between the stator and rotor under the applied loads are larger than the calculated values. It is caused by the calculation of the motor model with different simplified approaches (e.g. model of the bearing), which lead to the occurrence of this discrepancy.

100 The test stand has a portal design. In this design, a relative displacement of the rotor relative to the stator takes place by the piece of the back iron. An important condition for an accurate measurement of the cogging force is the deficiency of any effects from the possible slip of the moving parts of the motor and the guided stand parts. The relative motion between motor parts requires a smooth, stable, precise, and linear characteristic.

Therefore, the air bearing of the PI-glide RB series linear air bearings was adopted for the test stand implementation, because air bearings are inherently frictionless, they do not exhibit breakaway or running friction, even under their maximum load. A noncontact design between bearing parts means that they do not need maintenance and their accuracy will not degrade over time. For the supply of the compressed air in the air bearing, a standard air preparation module is used.

The relative movement of the parts is realized through an application of stepping motor with threaded spindle from Nanotec company. The stepper motor works by switching the power supply. Furthermore, it was ensured that no ferromagnetic materials were used in the area of the measurement in order to avoid measurement distortions. Due to the limited space of the air bearing for the test stand application, the usage of five poles according to the Halbach arrangement was chosen.

The measurement of cogging force occurs by the loading of the load cell, that is mounted between the spindle of the motor and an extension to the movable platform with the test sample. To evaluate the possible variations of the air gap between active motor parts, the laser sensors are mounted on both sides of the portal.

Figure 6.8 – Parts and units of test stand

For the measured value acquisition during an experiment, the software package LabVIEW and the associated NI-DAQmx data acquisition software was used, whereby all installed sensors were evaluated simultaneously.

The result of the measurement is the measurement protocol that was generated in LabVIEW.

6.2.2. Measurement Results

Within the first phase of the measurement, the verification of the test stand was realized with an idle condition.

During this test, all disturbances caused by the motor were detected. These values are important for further measurements, because the disturbances could be subtracted from measured values of the cogging force.

The measurement investigation was performed sequentially on the same test sample. Thus, the possibility of discrepancies in the results, which may be caused by geometric inaccuracy of the sample itself, was excluded.

The material that was used for the manufacturing of the test sample is NO20 electrical steel, which is equal to the simulated material. The test sample represents a flattened piece of the stator back iron with the same geometry parameters as it was used for the simulation of the cogging effect.

For the manufacturing of the test sample, the sheets were lasered with the same contours as by the back iron, stacked in a special press and pressed together. The test sample was then baked in an oven. The burrs were removed manually before the measurement was performed.

101 The measurement of the test sample without filling in the slots is shown in Figure 6.9. From the force distribution it can be seen that very high forces of up to 35 N occur at the beginning and at the end of the measurement. The reason for this high force level is obviously clear and can be explained as follows, since the area before and after the magnets is not sufficiently investigated. The simulation model is restricted by the master-slave boundaries, so the magnetic field dispersion is completely missing in the areas before and after the magnets. Therefore, the forces occurring during the entrance and leaving of a test sample in the magnetic field are of high importance. And this is why the simulation results in these areas have a very large difference compared to measured values. Thus, the range of interest by the measurement presents the area which is marked in Figure 6.9 with “A”.

For the correct positioning of the filling the copper wires were used, which were planned for the slot winding.

For the filling the sandwich (see Figure 5.13, (b) for details) from the in 4.1.2.3 presented material from Kemet was used.

Figure 6.9 – Force distribution during measurement of the test sample without filling

Figure 6.10 – Force distribution during measurement of the test sample with filling

The most intriguing areas of the measurement are presented in Figure 6.11. From the acquisition of the force distribution it is definite that the alternating force variation occurs at the same time as for the test sample with and without a filling of the slot. A further important implication from Figure 6.9, Figure 6.10 and Figure 6.11 is that the filling plays an important role in the reduction of cogging force, as the peak-to-peak values are lower than in a non-filled test sample.

102 Figure 6.11 – Comparison of the range of measurement of the cogging force associated by the slots The evaluation of the measurement results was performed by finding the minimum and maximum values over the apparent range of the cogging torque action. The values of interest represent the mean of the peak-to-peak values for both measurement cases – with and without slot filling. The average mean value of the cogging force can be calculated according to the following expression (6.1):

𝐹_{𝑐𝑚_1}=∑^𝑛_𝑖=0^𝑝𝑡𝑝𝐹_{𝑐𝑚,𝑖}

𝑛_𝑝𝑡𝑝 (6.1)

Where 𝑛𝑝𝑡𝑝 stands for the number of peak-to-peak amplitudes per measurement and 𝐹𝑐𝑚,𝑖 is the value of each peak-to-peak amplitude. For both variants of filling it a remarkable effect can be identified, because the mean value of the filled test sample amounts to 3.42 N in comparison with the non-filled test sample of 5.65 N. This demonstrates just how important the filling of the slots is and has a positive effect against cogging force. The mean value of the cogging force can now subsequently be used to calculate the cogging torque.

The cogging torque for the full motor is estimated by the empirical formula given in Equation (6.2):

𝑇𝑐𝑜𝑔= 𝐹𝑐𝑚∙ 𝑟𝑠𝑡= 𝐹𝑐𝑚_1∙^𝑝𝑝

𝑛_𝑠𝑡∙ 𝑟𝑠𝑡 (6.2)

The individual cogging torque value of the both test samples eventually resulted in 21.01 Nm for the non-filled test sample and 12.7 Nm for the filled sample. The motor with the filling of the stator has an almost 39.5%

lower cogging torque compared to the non-filled variant.

A clear trend in the results of the measurement bears a close resemblance to the simulation proposed in 4.1.2.3.

Therefore, the measured values of the cogging torque have certain differences to the simulated model. The reason for this is, firstly, the differences in the geometry and tolerances of the test sample, and secondly, the differences in material properties.

In addition, measurements on the test samples were used to track the position of the moving platform with the signals of the laser sensors. The high stability provided by the air bearing has prevented the keeping of the movable platform and the measured values of the relative displacements are in the range of less than 0.001.

These values are comparable or lower than the degree of roughness of the measured surfaces and therefore not considered in the analysis.