Research on measuring method of the angular displacement of muzzle vibration

2.1. Measuring method

To use the PSD serves as the sensitive element, the measuring method of the angular displacement of the muzzle was studied. Fig. 1 was sketch map of the measuring method about the angular displacement of the muzzle vibration (vertical view). Its measuring system included a laser, a two dimensional PSD, a controller, a reflector, a tripod, and so on. The laser and two dimensional PSD were fixed to same foundation support which was fixed to ground with a tripod. On the one hand, the controller provided power supply for the laser, on the other hand, the controller did the signal conditioning for the PSD. The angular displacements of the muzzle in elevation and azimuth were simultaneity measured by the two dimensional PSD. For the recording convenience, the output signal of the PSD was translated into the voltage signal.

To take the measuring method about the angular displacement of muzzle in azimuth as an example, the operational principle of the measuring system was given. The preparedness before measurement: a metal type reflector which was located lateral was fixed to a muzzle clamp, and the surface of the reflector faced on rear. The subassembly of the laser and two dimensional PSD was lain the tube lateral, the power supply of laser was turned on, and the incident light which was emitted by the laser illuminates to the reflector at muzzle position. After reflected, the reflected light illuminates to the sensitive surface of the PSD directly. The measurement while firing: reference Fig. 2, when firing, the angular displacement of muzzle was formed, and the reflector rotated with muzzle rotation. At the same time, the direction of the reflected light must change. The laser beam could move on the sensitive surface of the PSD, and the output voltage of the PSD was in proportional to the displacement of the laser beam. Taking the distance between the reflector and the sensitive surface of the PSD was $l$, when the reflector rotated the angle $\alpha$ from position $A$ to position $B$, the displacement of the laser beam on the sensitive surface of the PSD in the direction of azimuth was $z$. Thus, according to the triangle relation, had:

or

Note, according to the reflection law of light, when the reflector rotates the angle $\alpha$ from position $A$ to position $B$, the reflected light beam will rotate the angle $2\alpha$. In the measuring system, the distance $l$ was two orders of magnitude bigger than the displacement $z$. The angle $\alpha$ was very small, in general, the angle $\alpha$ was less than $\text{30}\text{'}$. Using the same method, the angular displacement of muzzle, or angle $\beta$ in elevation, could be obtained. Thus, the angular displacements of muzzle in elevation and azimuth where be obtained by the measuring method.

According to Eq. (2), as long as the distance $l$ and displacement $z$ were measured, the angular displacements of muzzle could be obtained. The PSD has higher frequency response, its response is (0.4-7.0) μs, the position resolution is 1 μm. By calibrating in laboratory, the angular displacement resolution of the measuring system was $\text{0.1}\text{'}$, and it could meet the need for measurement to the angular displacements of muzzle.

Fig. 1Sketch map of the measuring method about the angular displacement of muzzle vibration (vertical view)

Fig. 2Sketch map of the measurement principle of the angular displacement

2.2. Measures of removing environmental light

If the anti-environmental light measures in the measuring system was not taken, the more error could be formed. Therefore, as the optical filtering technique, and the laser modulation and demodulation technique were used, the precision in the measuring system could meet the need for measurement.

Using the optical filtering technique decreased the interference of the environmental light. The property parameters of the filter were 640 nm-660 nm in passband range. Thus, the filter could basically insulate the environmental light beyond the passband range into the sensitive surface of the PSD. Thereby, the capacity of resisting disturbance of the measuring system was enhanced.

2.3. Eliminating non-linear error of PSD

The software way was used by this paper. Using the experiment method, the mathematics relation between the laser point displacement and the PSD output signal was found, and then, experiment results were corrected. In the software way, the equation of the polynomial curve fitting was used for the error correction.

2.4. Property verification of measuring system

For verifying the property of anti-environmental light of the measuring system, the property experiments in different illumination conditions were done. The verification conditions were: 1) the indoor, nature light, in the daytime, 2) the indoor, strong light lamp, in the daytime, 3) the indoor, to turn off light, at night, 4) the indoor, strong light lamp, at night, 5) midday under the sun. Every experiment condition was repeated three times, and found average. The illumination intensity of the strong light lamp was more than 30 thousand lx. The results showed that the measuring relative errors were less than 2 %, the measuring system had the ability of anti-environmental light.

2.5. Simulation of measuring system

The known angle was given by an electronic theodolite, and the angle measured was obtained by the measuring system. Precision of the electronic theodolite was $\text{2}\mathrm{\text{'}}\mathrm{\text{'}}$. In order to simulate the known angle, a reflector on the running part of the electronic theodolite was fixed, the reflector was rotated with the running part of the electronic theodolite. The angles in elevation and azimuth were measured. The change ranges of the known angles were from –$\text{35}\text{'}$-+$\text{35}\text{'}$, its interval was $\text{5}\text{'}$. The results showed that the relative errors of the simulation results of angle in the measuring system were less than 2 %, and the angle resolution was $\text{0.1}\text{'}$.

2.6. Precision analysis

According to the data measured, the static characteristic analysis of the measuring system was done. The non-linearity of the measuring system was 0.56 %, the repeatability of the measuring system was 1.12 %, the overall precision of the measuring system was 1.25 %.