Force Results

4.4.2.1 Smoothing of Results

Figure 4.39: Example of experimental data, 6 Amps flowing in coils

During experimentation, the rotor was set to the necessary position by applying a force to it through the force transducer. For the position of zero magnetic force, it is clearly possible to apply a small force to the translator which, due to frictional effects of the testrig, will not result in movement. The value of force recorded by the load cell for this translator position could therefore vary, the range being from the minimum tensile force which causes displacement to its compressive counterpart. It follows that an important factor in determining the residual forces recorded in a situation such as this would be the direction in which the experiment was being performed, for example a more likely residual force being compressive when the rotor is being pushed by the load cell. Expressed another way, the frictional effect always acts to oppose the direction of motion and is actually present throughout the experiment and not just the positions of zero magnetic force. Figure 4.39 shows a typical set of force results for a 6 Amp current flowing in the phase coils. It shows a data set corresponding to the experiment being carried out in each direction. A separate bicubic spline interpolation is used to approximate each of the 2 data sets at regular intervals along the position axis. The average value of these two interpolations is shown as the solid line in the graph and demonstrates the method employed to eliminate directional dependent friction from the results. This method of averaging is used for all the force results. At any given point, the discrepancy between the two sets of data shown is in the region of 270 N and so becomes less significant as higher currents are used to excite the phase and electromagnetic forces dominate.

4.4.2.2 Current Direction

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Figure 4.40: Force results with 8 Amps flowing

For any given magnitude of current, its direction has been shown to play a significant role in the magnetic flux pattern and resultant force. Figure 4.40 shows the experimental force for 8 Amps flowing, plotted on the same axis as the force predicted by the co-energy method of Section 4.3.1.3 using a positive and negative 8 Amp current.

The two predicted force curves are 180° out of phase with each other, i.e. always in the opposite direction. The experimental force has a significant phase difference with either of those predicted, due to the arbitrary nature of the 'zero' position during the experiment. The aim here is to show that in analysing the force results, it is possible to ignore both the phase of the results and the direction of current in the FEA. The important feature of the curves is the shape, period and peak amplitude, the latter of which is within 5% for all the peaks shown.

There are two regions where the experimental data, despite being averaged, is not smooth, corresponding to the positions of 7 and 18 mm. It is likely that there was some debris on the bearing track at these positions, which would slightly affect the result in both directions.

4.4.2.3 High Current Co-energy Method Comparison

The comparison of experimental and co-energy method predicted force results for 16 Amps shown in Figure 4.41 shows a good correlation, with the peaks and troughs of the two curves lying within 10% of each other.

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Figure 4.41: Predicted and experimental force with 16 Amps flowing

Again there are two regions where the experimental data appears slightly erratic, approximately corresponding to the positions visible in the previous experiment.

4.4.2.4 Low Current Co-energy Method Comparison

Figure 4.42 shows the 2 Amp experimental results plotted on the same axis as the co-energy predicted force results for the positive and negative current directions. The experimental results have a different shape, period and peak value to either of the predicted curves. It must be deduced, then, that this force model is not valid at low currents, where cogging force is comparable to electromagnetic force.

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Figure 4.42: Predicted and experimental force with 2 Amps flowing

4.4.2.5 Cogging force

Figure 4.43 shows a comparison of the experimentally measured values for cogging force to that predicted using the magnet de-magnetisation curve method of Section 4.3.1.4. Comparing the turning points, starting from the left, gives percentage errors of 120, 18, 15 and 29%. It is likely, by inspection of the curve, that the largest discrepancy was caused by experimental error. Although the amplitude of the predicted results is only reasonable, the model clearly correctly predicts the shape of the force characteristic. In particular, the amplitude of the force-displacement curve can be seen to have two large peaks and two smaller ones, as discussed in 4.3.1.4, Figure 4.25.

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4.4.2.6 Maximum force

Figure 4.44: Experimental force results for 20 Amps

Figure 4.44 shows the force displacement experimental results for a phase current of 20 Amps. The average modulus of the peaks is 3.03 kN, equivalent to a shear stress

N. J. Baker Chapter 4: The Linear Vernier Hybrid Machine over the magnet area of 105 kNm-2. The current was limited by the test equipment available and not by the VHM itself.

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