4.1. Tuning Platform and Actual Punching Effect
Finally, we build an online tuning platform based on femtosecond laser (as shown in
Figure 8). The platform is mainly composed of two parts: one is for tuning of the execution system based on femtosecond laser, which includes laser, light speed conversion system, galvanometer, miniature vacuum chamber and carrier platform; the other is a feedback system of frequency sweep, which includes a working computer (or a laptop), a lock-in amplifier and a DC power supply. The laser repetition rate is 200 kHz, single pulse energy is 20 W, jump speed is 150 mm/s and the processing speed is 120 mm/s.
The whole experimental process is: use lock-in amplifier to sweep the gyroscope’s modal frequencies, according to the size of the frequency split then operate the femtosecond laser to punch holes on the mass blocks. After the end of the punching, sweep the frequency again to observe how the frequency split changed. We determine the next punching position and hole size by frequency split and relative amplitude of two peaks of the curve. Punch holes without a break until the frequency split meets the requirement.
The gyro is separated from the test circuit board to avoid the influence of temperature, which will result in drifting in the angular frequency and lead to noise. As the laser parameters will have an impact on punching holes, such as diameter, depth and so on, we try punching holes on the dilapidated resonator for exploring which parameter is the best before the tuning experiment. The spot diameter of the laser is about 7–10 μm; we punch two holes of diameters 60 μm and 100 μm on the mass blocks, but we can see the hole’s diameters are about 70 μm and 110 μm under the electron microscope as shown in
Figure 9a, which is inevitable. Then, the second graph (
Figure 9b) below shows the sectional view of the punched holes, and we can see the diameters are gradually decreasing from top to bottom. In addition, the laser punching does not completely match the set value, and the actual punching shape is conical instead of cylindrical.
4.2. Tuning Experiment
After all the simulations above, it is so important to verify if these simulation or theories are consistent with the experiment. Firstly, we punch holes of diameter 100 μm and depth 150 μm on the mass blocks of a resonator with an initial frequency split which is 15.7 Hz under vacuum. The punching sequence of the mass blocks are numbers 13, 15, 11 and 9 which are at 90° intervals. However, in the actual punching, the holes’ centers do not completely coincide with the mass blocks. The results are shown in
Table 4.
From the results above, we can see the modal frequencies are all rising after punching, which is consistent with the simulation. Likewise, punching positions at 45° intervals cancels out the tuning effect mutually. Then, we continue punching holes on the mass blocks numbered 2, 6, 8 and 12 in order, whose diameters are 60 μm and depths are 150 μm. The results are shown in
Table 5.
As we can see in
Table 5, the frequency split is decreasing slowly; it reveals that the punching position is close to the low-frequency rigid axis and the removed mass is less, so that the frequency split is almost unchanged. These mass blocks are at 90° intervals, and every punch will result in about 1 Hz. We can deduce that the tuning positions at 90° intervals are equivalent to each other, in other words, the tuning effect will be multifold. These results show that the rigid axes are at 45° intervals for the
n = 2 mode of ring resonators.
Next, we begin to punch holes on another resonator under vacuum to achieve mode matching, of which the frequency sweep is shown as
Figure 10a. Its modal frequencies are 24,597.3 Hz and 24,620.6 Hz, respectively, so the initial frequency split is 23.3 Hz.
As shown in
Figure 10a, the frequency sweep curve has two peaks which indicates that the rigid axis position of the resonator is not fully aligned with the driving force direction. We need to punch holes on the resonator for sake of diminishing the frequency split. Now, we number the resonator’s mass blocks in the way shown in
Figure 5. The first set of experiments is punching holes on the mass blocks numbered 5, 1, 9 and 13 in sequence, of which the diameters are 60 μm and the depths are 500 μm. We record the frequency split after every time of punching so that we can decide which mass block is close or far to the low-frequency rigid axis. The first set of experiments ends up with the frequency split 31.2 Hz and the resonator’s modal frequencies are 24,609.9 Hz and 24,641.1 Hz, respectively, as shown in
Figure 10b. According to the above simulation, the tuning effect is equivalent for the mass blocks which are at 90° intervals. We can see the frequency split increase and the modal frequencies are also increasing gradually; therefore, we have punched the mass blocks far from low-frequency rigid axis.
On the basis of the first set of experiments, the second group of experiments goes on punching holes on the mass blocks numbered 12, 8, 16 and 4 sequentially. These holes’ diameters and depths are 60 μm and 500 μm respectively. As shown in
Figure 10c, the resonator’s modal frequencies are 24,614.0 Hz and 24,652.4 Hz, and its frequency split is 38.4 Hz. We can see the frequency split has a further increase, which means the high-frequency rigid axis is between the mass blocks numbered 1 and 16, so we can judge that the low-frequency rigid axis is between number 2 and number 3. Comparing the
Figure 10b,c, we can see the relative amplitude represent the defection angle of the rigid axis. The bigger the defection angle is, the smaller the relative amplitude among the frequency sweep’s two peaks.
On the basis of the second set of experiments, the third group of experiments continues to punch holes on the mass blocks numbered 2, 6, 10 and 14 in turn. From
Figure 10d, we can see the frequency split decreases. By means of the frequency sweep, we can acquire that the resonator’s modal frequencies are 24,635.8 Hz and 24,662.3 Hz, respectively, and the frequency split is 26.5 Hz.
On the basis of the third set of experiments, finally the fourth group of experiments is designed, in which we punch holes on the mass blocks numbered 15, 11 and 7 in order, of which the diameters are 100 μm and the depths are from 200 μm to 400 μm by the step of 100 μm. At the end of the final punching, the resonator’s modal frequencies are 24,662.3 Hz and 24,662.7 Hz. It is worth mentioning that the final frequency split is 0.4 Hz, as shown in
Figure 10e. We can see that the frequency sweep only has one peak which means the rigid axis is aligned with the driving force direction. Thus, if we want to find out what the frequency split is, we must change the electrode for frequency sweep.
The tuning parameters of the four sets of experiments are listed in
Table 6. In
Figure 11, we draw the curve of punching time and frequency split from the first set of experiments to the fourth. We also give the schematic diagram of the punching positions, the holes’ diameters and depths on the top of
Figure 11. It can be obtained that the removed mass is linear to frequency split, approximately, which is because during the punching of the holes, the rigid axis will deflect. Punching holes on the different mass blocks causes the frequency split to increase or decrease, depending on whether the mass block is close to the low-frequency rigid axis.