Hall Sensor Optimization and the Vibration Experiment
BE 309 Final Project
December, 2004
Group M8:
Vinod Anantharaman
Christa Baker
Charles Dunlap
Andy Gilmour
Abstract:
In this experiment it was found that a very strong magnet at a high vertical height (z) from the hall sensor (>15mm) will result in the best FFT for the vibrating bar experiment. Our project analyzed different types of magnets (bar vs. doughnut) at various orientations, angles and offsets. These preliminary tests suggested that the bronze magnet at a vertical height of 5mm would be best, due the noise minimization from the high slope of the linear range. After examining the FFT data from the vibrating bar under these conditions it was found that unwanted artifacts of the node frequency appeared. By shifting the height to 15mm, the high signal/noise ratio was maintained while limiting the artifact size. This unfortunately also attenuated the harmonic peaks higher than the first. It was found however that it takes the strong flux from the bronze magnet at z=1mm to show distinguishable signals at harmonic peaks greater than the first. The small vertical (z=1mm) distance of the magnet from the Hall sensor, however, limited the maximal horizontal distance the bar could be displaced. The many tradeoffs in this experiment led us to suggest that a strong magnet (stronger than available in the lab) at a high vertical height (15mm) would give a strong harmonic signal and limit noise and artifacts, while allowing a reasonable range of oscillation for the bar.
Background:
The goal of the Vibration Experiment is to determine the natural mode frequencies of a metal bar by measuring the displacement at the end of the bar and computing a Fast Fourier Transform (FFT). In order to compute the FFT a highly precise measure of the bar displacement is needed, which a Hall sensor can provide under the right conditions. The goal of this project is to determine those ideal conditions and examine the effect on the Vibration Experiment FFTs.
A Hall sensor works by measuring the strength of a magnetic field and converting that into an output voltage. These sensors use the Hall Effect where the application of a magnetic field perpendicular to the current flowing through the sensor generates a voltage potential orthogonal to the magnetic flux and incident current, see Figure 1. In the Hall Effect this orthogonal voltage is linearly correlated to the magnetic flux, and thus the sensors give in measurement the magnetic flux by detecting the voltage potential, see Castellan Ch. 31.3 “The Hall Effect” for the mathematical details. In this experiment the magnetic flux is generated by the permanent magnet attached to the end of the bar.
Figure 1: of Magnetic Flux, Incident Current, and Orthogonal Hall Voltage http://www.micronas.com/products/overview/sensors/index.php
However, the Hall sensors only give a liner voltage response for a limited range of magnetic flux. The sensor can be saturated with too much magnetic flux in cases where the magnet is too strong or too close, resulting in the flat peak cutoff seen in some Vibration Experiment data. The sensor output is also no longer liner when the magnet exceeds a certain distance from the sensor, see Figure 2. This distance is dependent on the strength of the magnet and the relative orientations of the sensor, and the goal of this project was to determine these linearity constraints using the materials provided and Vibration Experiment geometry, in order to find an ideal setup for precise position measurements.
Figure 2: Linearity Constraints on Hall Sensors
from Hall Sensor Data Sheet, BE 309 Files
Methods:
Three types of magnets were used in the horizontal displacement experiment; a white stir bar, a bronze cylindrical rare earth magnet, and a donut shaped alloy magnet. These magnets were mounted on the end of a micrometer and the micrometer clamped to a ring stand, see Figure 3. The vertical separation between the magnet and the Hall sensor was adjusted along the z axis between 5 and 20mm at increments of 5mm. The magnet was advanced from 0mm, directly on top of the sensor, to 8mm along the x axis at increments of .5mm by turning the micrometer. The output voltage from the Hall sensor was recorded and plotted against the x displacement in Excel to determine the range of linearity. Movement in the negative x axis was found to simple reflection of the curve across the y axis of the graph, and was not investigated further.
Figure 3: Experimental Setup
A crucial difference between the magnets lay in the orientation of the magnetic field generated. The bronze cylinder and stir bar were mounted vertically, so that the Hall sensor was exposed only to a north or south field. The donut magnet was mounted horizontally, such that the Hall sensor was exposed to the N/S boundary, see Figure 4
Figure 4: Magnet Orientations
The difference in the magnetic field orientations may have led to some of the differences seen between the bar and donut magnets.
The rotational experiment was carried out by changing the orientation between the advancement of the magnet along the x axis and the orientation of the Hall sensor. The bronze magnet was used and held at a constant z height of 15mm.
Figure 5: Overhead View of Rotational Experiment
The offset displacement experiment was carried out by advancing the bronze magnet along the x axis at a height of 15mm but offset from the Hall sensor by 5, 10 and 20mm, see Figure 6.
Figure 6: Overhead View of Offset Experiment
With the linear region and optimal placement experiments complete, the results were tested by setting up the vibrating bar according to the protocol of the Vibration Experiment. The control setup was with a minimized z height of approximately 3mm, use of the stir bar, and only general alignment of Hall axis and offset. These were the conditions under which the original Vibration Experiment was carried out. These results were recorded and compared to the FFT of what was determined to be near optimal setup; bronze rare earth magnet, 15mm z height, and careful alignment of the axis and offset.
Results:
The following figures show the Hall sensor voltage output for the horizontal displacement of the magnets at various z axis heights, see Figure 3 in Methods. For our investigation of linear range, only the positive x distance was recorded as the negative distance is a rotation of this around the origin.
For the doughnut magnet it can be seen that linear range of this output is truncated and that the 0mm displacement output voltages are highly variable, a possible result of the orientation of the magnetic field, see Figure 4 in Methods.
Figure 7: Hall Sensor Output vs. Horizontal Displacement of Doughnut Magnet
This figure shows the Hall sensor voltage output for the horizontal displacement of the white stir-bar magnet at various z axis heights. Note the tighter grouping of initial outputs and the much greater displacement distance before the voltage peak.
Figure 8: Hall Sensor Output vs. Horizontal Displacement of White Magnet
Figure 9 shows the Hall output for the horizontal displacement of the bronze cylinder magnet at various z axis heights. Note the high rate of change of the voltage in the linear regions and clear peak transition from linear to nonlinear segments.
Figure 9: Hall Sensor Output vs. Horizontal Displacement of Bronze Magnet
Table 1 summarizes the maximum linear range and slope of the Hall output data for the bronze and white magnets over a z axis height of 5 to 20mm. These linear ranges were found by applying the regression package in Excel over the range of data that was found to have R^2 > .95.
Z (mm) / Linear Range (+mm) / SlopeBronze / 5 / 2.5 / 0.5187
10 / 3 / 0.1526
15 / 4 / 0.0722
20 / 5 / 0.0233
White / 5 / 4 / 0.0499
10 / 5 / 0.0149
15 / 6.5 / 0.0076
20 / 7.5 / 0.0036
Table 1: Summary of Linear Range and Slope of Linear Section of Hall Sensor Outputs
The following figure shows the effect of a left or right offset of the magnet, see Figure 6 in Methods, on the Hall output. This data shows that the further away from the center line of the sensor the magnet is moved, the greater the deviance from the ideal curve, and a shift from linear to parabolic curvature.
Figure 10: Hall Sensor Output vs. y Axis Offset of Bronze Magnet
This figure shows the deviance from linearity when the magnet is advanced along a path at an angle of 45 or 90 degrees from the centerline of the Hall sensor, see Figure 5 in Methods.
Figure 11: Hall Sensor Output vs. Angular Rotation of Bronze Magnet
Figures 12a and 12b show the FFT of the bar with the white stir-bar magnet. The horizontal scales are again 0 to 15Hz while the vertical scales are 0 to .00017V and 0 to .00008V for the top and bottom respectively. These figures show the amplification of the artifacts and the low signal to noise ratio.
Figure 12: FFT of Bar Vibrations with White Stir-Bar Magnet at z=15mm
Figures 13A and 13B show the FFT of the vibrating bar with the bronze magnet at different magnifications. The top figure shows the y scale from 0 to .0009V and the bottom figure is 0 to .00020. Both figures are scaled from 0 to 15Hz. The top figure shows the clear attenuation of the 1st artifact, while the bottom shows that signal to noise ratio, see Table 2 for a summary.
Figures 13a and 13a: FFT of Hall Sensor of a Vibrating Bar with the Bronze Magnet at 15mm z Height
The “peak height” of the first natural mode vibration, artifact height, and average height of the noise was measured in volts and tabulated below to calculate the Signal to Noise and peak height to artifact height ratios. The bronze magnet at 15mm, shown in the Figures 13a and 13b, is superior with both a high signal to noise and high peak to artifact ratio. The signal to noise can be increased by decreasing the vertical height of the magnet from the sensor. This, at the same time reduces the peak to artifact ratio (Table 2). For the weaker white stir-bar magnet, both the signal to noise and peak to harmonic ratios were inferior.
Bonze z=30 / Bonze z=15 / Bronze z=5 / White z=15Peak Height (V) / 0.0019999 / 0.007419 / 0.072692 / 0.001411
1st Artifact Height (V) / 0.000059 / 0.000201 / 0.0047 / 0.000079
Noise Height (V) / 0.00001 / 0.000009 / 0.000016 / 0.000011
Signal/Noise Ratio / 199.99 / 824.33 / 4543.25 / 128.27
Peak/Artifact Ratio / 33.90 / 36.91 / 15.47 / 17.86
Table 2: Signal/Noise and Peak/Artifact Ratio for FFT’s of Vibrating Bars with Various Magnets and z Heights
The bar vibrations were then repeated at different vertical heights in order to maximize the value of the harmonic signal and minimize the artifacts. As seen in Figure 14, with a vertical height of the magnet at z=1mm, the harmonics at near 25, and 73Hz are distinguishable while the artifacts cannot be differentiated from the noise. The 60Hz frequency is also seen.
Figure 14: FFT Showing Harmonics of Frequency without Artifacts
Discussion:
This series of experiments was designed to optimize the methods of the Vibrating Rod Experiment by investigating the linear range and placement of the Hall sensor, magnet used, and resulting FFT. The goal was to find a setup that minimized the artifacts, and maximized the natural harmonics of the bar in the FFT.
Three magnets were investigated in this experiment, the white stir bar, the bronze rare earth, and the doughnut. While the stir bar and bronze magnets gave output voltages akin to the expected data from the Hall sensor manual, see Figure 2, the doughnut magnet experienced truncation of the linear region and a high variability of the voltage at 0cm displacement, see Figure 7. We believe that the orientation of the magnetic fields, as explained in Methods, is the cause of this variability between the bar magnet and the donut magnet. Because the field lies horizontal and in the plane of the Hall sensor, there is a very rapid transition from north to south (N/S), rather than the only south fields when a vertical bar type magnet was used. This rapid transition N/S requires that the hall sensor and magnet be perfectly aligned at 0cmdisplacement, otherwise a minute displacement will cause the truncation of the linear region. The doughnut setup, with a horizontal magnetic field and N/S transition, gives very precise position data if the perfect alignment could be achieved, however this is very difficult to do by eye in the lab, and we suggest that a bar type magnet be used.
The next property to be investigated with the bar type magnets was the linear range of the Hall sensor. By increasing the range that the bar and magnet could vibrate, data would not show the distortion or the truncation that would result if the bar was tapped too hard. It was found that there was an inverse correlation between the amount of magnetic flux and the linear range. Increasing the flux, by either moving the magnet closer to the Hall sensor (smaller z), or using a stronger magnet (bronze vs. white), shortened the linear range, but also increased the signal output. This can be seen best in Table 1, where the increased vertical distance and the use of a weaker magnet both tended to increase the linear range of the Hall sensor. This is a tradeoff however between signal strength and effective linear range of the Hall sensor.
The effects of angle on the Hall output data were also investigated. It was found that changing the relative axis between the hall sensor and the bar yielded a totally nonlinear response in the 90 degree case and distorted the signal at lesser angles, Figure 11. From this we concluded that further investigation of the effects of angular changes were unnecessary, and that any differences in angle between the vibrating bar and Hall sensor axis should be minimized.