Hopkinson rod based high g shock sensor calibration

1 Introduction
Micro accelerometer is an important branch of MEMS (Micro Electromeclaanical System) and is widely used in aerospace, automobile, national defense and other fields. As a primary instrument, high-g acceleration sensor is widely used in high overload measurement during impact and high-speed movement. In the design of deep penetration weapons, it can be used to identify targets and can also be used to measure overload in aircraft crash resistance experiments and automobile collision tests. The accuracy of the sensitivity coefficient of high-g acceleration sensor directly affects the measurement accuracy. Since high-g acceleration sensor can be reused in many occasions, its sensitivity coefficient may change during use due to the high overload, and it needs to be calibrated frequently. Therefore, the measurement of the sensitivity of high-g acceleration sensor plays an important role not only in the development of high-g acceleration sensor, but also in the measurement of high overload resistance. This paper mainly introduces the micro Hopkinson bar technology, adopts the laser Doppler principle, uses diffraction grating as a cooperative target, and uses a digital demodulation method of frequency modulation signal to realize Doppler frequency shift data processing, with a time resolution of one sampling interval. This technology has the characteristics of good robustness, process convergence, and accurate results. The sliding least squares fitting straight line segment method is used to realize differential operations, obtain instantaneous measurement values ​​of impact velocity and acceleration, and give experimental results.

2 Acceleration sensor calibration device and working process
Figure 1 shows a high-g acceleration shock sensor calibration device, which consists of a Hopkinson rod, a differential laser Doppler interferometer, a digital oscilloscope and a computer system.

The Hopkinson laser interferometer shock test bench is a differential laser Doppler velocimeter and small air cannon loading system for acceleration sensor shock standards. It is mainly used for high g value measurement. It uses a Hopkinson rod to generate stress waves in the rod. At a distance of several times the rod diameter from the end face, the wave vibration surface of the stress wave actually becomes a plane wave. As long as the ratio of the length to the diameter of the rod is sufficiently large, the Hopkinson impact machine can be used to obtain a good waveform and a small lateral motion impact process at the calibration end face. The differential laser Doppler velocimeter measures the Doppler signal of the tracer particles through the laser probe, and then obtains the velocity based on the relationship between the velocity and the Doppler frequency. Because it is a laser measurement, there is no interference with the flow field. The velocity measurement range is wide, and because the Doppler frequency and velocity are linearly related. It has nothing to do with the temperature and pressure of the point. It is the instrument with the highest velocity measurement accuracy in the world. Its working process is shown in Figure 1. A Hopkinson impact machine is used to launch a projectile at the Hopkinson rod to generate impact acceleration, which acts on the grating and the acceleration sensor being measured at the same time. The signal measured by the acceleration sensor being measured is collected by the dynamic signal analyzer after passing through the signal conditioner. The grating displacement generates a frequency-modulated signal with a Doppler effect through a Doppler laser interferometer. The signal is collected by a digital oscilloscope. After frequency demodulation of the frequency-modulated signal, the acceleration value acting on the acceleration sensor can be obtained.

3 High-g shock accelerometer calibration principle
The laser Doppler single-shock calibration method uses the laser Doppler principle and uses a diffraction grating as a cooperative target to absolutely reproduce the shock acceleration value and calibrate the accelerometer. The Doppler frequency shift generated by the reflective diffraction grating is:

Where ψ is the incident angle, θ is the diffraction angle, v is the velocity of the grating plane, and λ is the laser wavelength.
The Doppler frequency shift generated by the double incident light grating is:

In the formula, ψ is the incident angle, v is the grating plane velocity, and λ is the laser wavelength.
According to formula (2), the impact velocity v(t) is obtained:

Differentiating equation (3) yields the impact acceleration a(t):

The peak value of the shock acceleration is obtained by taking the peak value of formula (4). The absolutely reproduced shock acceleration peak value ap is used as the reference value and compared with the peak value VP of the electrical quantity output by the calibrated accelerometer to obtain the shock calibration sensitivity of the calibrated accelerometer:

In addition, the sensitivity of the calibrated accelerometer can also be determined by the velocity change measured by the Doppler signal and the area enclosed by the accelerometer output waveform. The sensitivity is defined as:
Where Us is the output voltage of the accelerometer; a is the acceleration; g is the standard gravity. For the collision process, acceleration only exists during the time t1-t2, that is, the movement speed of the accelerometer increases from 0 to u during the time t1-t2, then equation (6) can be rewritten as:

Dividing both sides of formula (6) by A yields:

Where,
the average sensitivity of the accelerometer in the time interval t1-t2 is:

From equation (8), we can see that to determine Se, we need to measure From equation (6), we can know that can be obtained by integrating the output of the calibrated accelerometer, and is the velocity obtained by analyzing the laser Doppler signal.

4 Experimental data and result processing
Sensitivity tests were conducted on the 2225 and 2225M5A accelerometers produced by ENDEVCO and the 356820 accelerometers produced by PCB. The test results are shown in Table 1.

The curve waveforms of Figures 2 to 5 were obtained by using the 2225 impact sensor and the IM133 charge amplifier. The sensor under test was normalized by the charge generator, and the output scale was 1 mV/g. Figure 2 shows the laser Doppler interference signal obtained during the impact process in the actual experiment. The starting point of the Doppler signal was selected and the abnormal signal at the beginning was removed. In the impact calibration device, the filter cutoff frequency = 54 kHz, the laser wavelength K = 0.632 99 μm; the second-order diffraction fringes were used in the laser interference, p = 2; q = -2; the grating pitch d = 1/150 mm. The laser Doppler interference signal during the impact process is calculated to obtain the impact velocity curve. The impact velocity waveform curve shown in Figure 3 is obtained by formula (3), and the maximum velocity v = 5.33 m/s; the impact acceleration waveform curve shown in Figure 4 is obtained by formula (4), and its peak acceleration g = 4 497.533 7 m/s2, pulse width T = 185μs, Figure 5 is the output waveform of the acceleration sensor during the impact process, and the useful signal is intercepted. From this figure, its peak value VP = 5.13 V can be obtained. From formula (6), the impact calibration sensitivity of the calibrated acceleration sensor Sch = 1.14 mv/g can be obtained. From formula (8), the average sensitivity of the measured acceleration sensor can be obtained: Se = 0.766 pc/g.

The Hopkinson bar is a good experimental device for calibrating high-g acceleration sensors. Through the differential laser Doppler velocimeter, the sensitivity calibration experiment of the impact sensor in the high-g range can be carried out. The sensitivity of ENDEVCO's 2225 and 2225M5A impact sensors is well matched. Compared with the factory sensitivity of each impact sensor, the error is less than 0.1%. The 356820 sensor is a 3-axis impact sensor. The error of the X axis is small, while the sensitivity errors of the other two axes are large.

5 Conclusion
The shock acceleration calibration method used in this paper is the most complete and reliable laser Doppler shock calibration method at present. It realizes the absolute reproduction of shock acceleration value and uses grating differential laser interferometer to achieve accurate measurement of shock acceleration. It provides a relatively accurate reference standard for the repeated use of high g value acceleration sensors.