Range of Frequencies
The frequency range of a person walking is 1.7Hz−2.3Hz, as was discussed in Chapter 2 [9, 17]. In order to ensure the simulation predicts the average power generation accurately for all frequencies in this range, data was taken from all four generators starting at a frequency of 1.5Hz and increasing by 0.1Hz to 2.5Hz. Simulations were performed on the four stators for the range frequencies to obtain a comparison between the simulated and experimental data. The RMS and Average generated power values were compared.
Figure 5.12 is a plot that displays the average power generated from the four stator coils over a frequency range of 1.5Hz−2.5Hz. The vertical axis displays the average power generated and the horizontal axis displays the frequency of motion. The experimental data is denoted with blue markers and the simulated data is denoted with red markers. The legend show the marker types of each data set. The legend is located on the right edge of the plot near the top. In the top-left corner of the plot area, the error of all of the averaged values is printed. The errors of Stator A ,B, C, and D were: 13.23%, 0.82%, 6.09%, and 11.27%, respectively. The error displayed is an average over the range of frequencies.
Figure 5.12: Plot of average power as a function of frequency of the four test generators
It can be seen in Figure 5.12 that simulations of Stator B produced the smallest error in the average generated power. The predicted power of Stator A has an error of 13.2%, which is the largest of the four stators. The curves all appear to have a linear trend with frequency over the given frequency range. The Stator A appears to have the steepest slope while Stator D has the smallest slope. The results of the average power indicates that the generator is accurate over the entire range of frequencies that the backpack will be expected to work in. The largest error is under the desired value of 15% error.
The plot shown in Figure 5.13 displays the RMS power of the generators as a function of frequency. Plots of the simulated and experimental RMS power generated by the four stators are plotted on a single graph. The experimental data is denoted with blue markers
and the simulated data is denoted with red markers. The generated power is shown on the vertical axis and the frequency on the horizontal axis. The legend is located near the top of the plot on the right side. Near the top of the plot on the left side, the error of the predicted power of the four stators is displayed. The errors in the predicted RMS power of Stator A, B, C, and D are as follows: 12.47%, 7.90%, 2.41%, and 26.76%. The smallest error is seen in the prediction of Stator C. The largest error is seen in the prediction of Stator D.
Figure 5.13: Plot of RMS power as a function of frequency for the four experimental generators
The curves appear to have an increasing slope as the frequency increases, indicating a polynomial or exponential relationship between the power and frequency. It is likely that the relationship is a power curve, but most of the generators appear to be linear because
of the small region of frequency that is shown.
The errors of Stators A, B, and C are acceptable but Stator D displayed a 26.76% error of the predicted RMS power. It can be seen in Figure 5.13 that the first two experimental data points of Stator D are significantly higher than the power generated at larger frequencies. The power should follow an increasing trend with increasing frequency. The data points at frequencies of 1.5Hz and 1.6Hz are likely due to some inconsistency in the experimental apparatus and are not indicative of a maximum power frequency at those points. The comparison of Stator D needs to be performed again before conclusions can be drawn.
5.6
Concluding Results
When looking at the error in the comparisons of the four experimental stators, it was shown the most error was indicated on the Stators A and D. These devices have larger coil widths than did the other two devices. When the coil width is large, at transitions between magnetic poles, coils at either side of the device will experience magnetic fields with opposing polarities. When the flux of the opposing fields changes, causing current to be induced in the generator, the induced current will flow in opposite directions. The opposing current will cancel out, causing zero net power generation through the device. This phenomena is likely the cause of the larger error experienced when modelling stators with larger coil widths because the simulation does not account for opposing current flow. When calculating the power, the absolute value is used, which forces the current to be positive. The width of the generators should be kept at approximately the width of the magnets in order to minimize the amount of error in the simulation.
The direction of the magnetic field would need to be accounted for as a first step to approximating the cancellation of current due to opposing magnetic fields. The position of the stator windings would then need to be indexed to determine what direction of field
each of the windings is experiencing. Currently, the stator position is based on a single point in the center of the width of the stator, which would not indicate if the windings at either edge of the stator experiencing opposing magnetic flux.
The average generated power of the experimental inductive generators was predicted with an error of less than 15%, indicating that the model was valid and should be used to determine an optimum stator size. In order to find the optimum size, a MATLAB script was written to vary coil width, coil height, and wire size of the stator, and run power simulations on the various configurations. The configuration to produce the largest average power generation was considered the optimum design for the backpack generator. The results of the optimization script are discussed in Chapter 6.
CHAPTER 6
CONCLUSIONS AND FUTURE WORK
The goal of this thesis was to experimentally validate the simulation developed by Bateman. The first step in this process consisted of designing and fabricating a test- ing apparatus and linear permanent magnet generators. With a working experimental apparatus, comparisons were made between the simulated power generation and the ex- perimental power generation. It was shown that the simulation was over predicting the power generation of the experimental data. To correct the simulation, adjustments were made to the magnetic field model to ensure that it was predicting a realistic magnetic flux through the stator coils. Power generation results from the modified simulation and the experimental apparatus were compared to determine the accuracy of the model. The comparisons displayed that the modified simulation was valid because it had an accuracy exceeding 80%. After the validation process was completed, the simulation was then used to predict an optimal generator design, which is presented in Section 6.1.