A unique feature should be find to identify the contact distance from the rotating axis. Then that feature can be used to predict the distance in real world application (wheel robot).
By using collected data set for 5 different materials , try to optimize relationship between the contact distance and frequency of the maximum amplitude component. First average the 25 data sets and plot them. The resultant graph is shown in the figure 16.
Figure 16: Frequency of the maximum amplitude component Vs the contact distance (X axis Aluminium)
When comparing the figure 15 and 16 the figure 16 shows more linear relationship. But the acceleration is not only at the x axis. so it is needed to consider all the axis which affect the acceleration of the antenna. in that case the Y axis of the senor is along with the antenna so there can't be any acceleration in that direction. Therefore the X and Z data sets were combined and get the norm to represent the both axis. Obtained result was shown in figure 17.
Figure 17: Norm of the X and Z axis's maximum amplitude component's frequencies Vs the contact distance (Aluminium)
To get the more linear variation use the log scale axis for the frequency axis and resultant figure shown in the Figure 18.
Figure 18: Norm of the X and Z axis's maximum amplitude component's frequencies in log scale Vs the contact distance (Aluminium)
The distance to the contact point from the motor axis or the robot can clearly be identified by using the frequency of the maximum amplitude component of the vibration data set. The variation is closer to the linear variation and it is only depended on the contact distance not the material. The final results for the five different materials are plotted and shown in figure 19.
Figure 19: Variation of the contact distances Vs dominant frequency in the log scale for the five different materials
In the results observed in here were shown an unexpected variation on the graphs near to the tip of the antenna. Therefore the variation should be analyzed and given the reasonable proofs.
All the parameters except the antenna length were kept as in the previous experiment. The antenna length has increased from 400mm to 500mm.
When the antenna length is 400mm
By using the antenna length as 400mm, tested for 5 different materials in the previous experiment and finally came up with the following resultant graph in the figure 01. In the graph, although initially it shows a linear variation, there is an unexpected variations occurred when the contact distance is near to 300mm.
That variation can be occurred due to several reasons such that,
· The contact point is very close to the sensor.
· The contact point can be a resonance point.
Here the aim of the experiment was to check whether the contact point was at the resonance point. So the antenna length had increased to 500mm and experiment was repeated only using the object as Aluminum. The data have been collected only 25cm to 50cm contact distances.
The method used to obtained the results in previously was repeated for 500mm antenna length and following resultant graph was obtained and shown in figure 20.
Figure 20. Resultant Graph for the 500mm antenna length
When analyzing the graphs in figure 19 from and figure 20, both graphs are shown an unexpected variations at the 29.5cm and 39.5cm respectively. Although the contact distance from the rotating axis is different, the distance from the sensor to the contact point is very close. When considering the first case, when the antenna distance is 400mm the unexpected variation occurred at 80mm and in the 2nd case when the antenna distance is 500mm the unexpected variation occurred at 100mm away from the sensor.
So the assumption can be made such that at that point which shows the unexpected error it might me a resonant. For further clarification , Standard Deviation was calculated for both cases and plot them. Resultant figures were shown in figure 21 . The histograms were plotted for the each distances and 25 hits in both antenna distances 400mm and 500mm. They are shown under histogram reports.
Figure 21: Standard Deviation for the different antenna lengths (400mm and 500mm)
histograms with the 400mm antenna distance
histograms with the 500mm antenna distance
It was clear, the Standard deviation was increased at the point which shows the unexpected variations. Therefore the limitation has to be made for the antenna.