Vibrations induced by the Slip-Ring and the Spindle
+Table of Contents
+ +1 Experimental Setup
++Setup: +One geophone is located on the marble, the other one on the floor (see figure 1). +
+ + ++Two geophone are use: +
+-
+
- One on the floor (corresponding to the first column in the data) +
- One at the marble location (corresponding to the second column in the data) +
+Two voltage amplifiers are used, their setup is: +
+-
+
- gain of 60dB +
- AC/DC switch on AC +
- Low pass filter at 1kHz +
+A first order low pass filter is also added at the input of the voltage amplifiers. +
+ ++Goal: +
+-
+
- Identify the marble dynamics in all the directions +
+Measurements: +Three measurements are done: +
+| Measurement File | +Description | +
|---|---|
mat/data_037.mat |
+Z direction | +
mat/data_038.mat |
+N direction | +
mat/data_039.mat |
+E direction | +
+Each of the measurement mat file contains one data array with 3 columns:
+
| Column number | +Description | +
|---|---|
| 1 | +Geophone - Floor | +
| 2 | +Geophone - Marble | +
| 3 | +Time | +
+
Figure 1: Picture of the experimental setup
+
+
Figure 2: Picture of the experimental setup
+2 Data Analysis
++All the files (data and Matlab scripts) are accessible here. +
+ +2.1 Load data
+m_z = load('mat/data_037.mat', 'data'); m_z = m_z.data; +m_n = load('mat/data_038.mat', 'data'); m_n = m_n.data; +m_e = load('mat/data_039.mat', 'data'); m_e = m_e.data; ++
2.2 Time domain plots
+figure; +subplot(1, 3, 1); +hold on; +plot(m_z(:, 3), m_z(:, 2), 'DisplayName', 'Marble - Z'); +plot(m_z(:, 3), m_z(:, 1), 'DisplayName', 'Floor - Z'); +hold off; +xlabel('Time [s]'); ylabel('Voltage [V]'); +xlim([0, 100]); ylim([-2 2]); +legend('Location', 'northeast'); + +subplot(1, 3, 2); +hold on; +plot(m_n(:, 3), m_n(:, 2), 'DisplayName', 'Marble - N'); +plot(m_n(:, 3), m_n(:, 1), 'DisplayName', 'Floor - N'); +hold off; +xlabel('Time [s]'); ylabel('Voltage [V]'); +xlim([0, 100]); ylim([-2 2]); +legend('Location', 'northeast'); + +subplot(1, 3, 3); +hold on; +plot(m_e(:, 3), m_e(:, 2), 'DisplayName', 'Marble - E'); +plot(m_e(:, 3), m_e(:, 1), 'DisplayName', 'Floor - E'); +hold off; +xlabel('Time [s]'); ylabel('Voltage [V]'); +xlim([0, 100]); ylim([-2 2]); +legend('Location', 'northeast'); ++
+
Figure 3: Floor and ground motion
+2.3 Compute the power spectral densities
++We first compute some parameters that will be used for the PSD computation. +
+dt = m_z(2, 3)-m_z(1, 3); + +Fs = 1/dt; % [Hz] + +win = hanning(ceil(10*Fs)); ++
+Then we compute the Power Spectral Density using pwelch function.
+
[px_fz, f] = pwelch(m_z(:, 1), win, [], [], Fs); +[px_gz, ~] = pwelch(m_z(:, 2), win, [], [], Fs); + +[px_fn, ~] = pwelch(m_n(:, 1), win, [], [], Fs); +[px_gn, ~] = pwelch(m_n(:, 2), win, [], [], Fs); + +[px_fe, ~] = pwelch(m_e(:, 1), win, [], [], Fs); +[px_ge, ~] = pwelch(m_e(:, 2), win, [], [], Fs); ++
+The results are shown on figure 4 for the Z direction, figure 5 for the north direction, and figure 6 for the east direction. +
+ + +
+
Figure 4: Amplitude Spectral Density of the measured voltage corresponding to the geophone located on the floor and on the marble - Z direction
+
+
Figure 5: Amplitude Spectral Density of the measured voltage corresponding to the geophone located on the floor and on the marble - N direction
+
+
Figure 6: Amplitude Spectral Density of the measured voltage corresponding to the geophone located on the floor and on the marble - E direction
+2.4 Compute the transfer function from floor motion to ground motion
++We now compute the transfer function from the floor motion to the granite motion. +
+ ++The result is shown on figure 7. +
+[TZ, f] = tfestimate(m_z(:, 1), -m_z(:, 2), win, [], [], Fs); +[TN, ~] = tfestimate(m_n(:, 1), -m_n(:, 2), win, [], [], Fs); +[TE, ~] = tfestimate(m_e(:, 1), -m_e(:, 2), win, [], [], Fs); ++
+
Figure 7: Transfer function from floor motion to granite motion
+2.5 Conclusion
+-
+
- We see resonance of the granite at 33Hz in the horizontal directions +
- We see two resonances for the z direction: at 60Hz and 75Hz +