Experimental study on the generated pyroshock level under different amount of explosive

2.1. Test setup

A square aluminum alloy plate was suspended in the horizontal position using 4 elastic cords as shown in Fig. 1. The elastic cords simulate free boundary conditions. The plate made by aluminum alloy 2024 has a thickness of 10 mm and a surface of 600×600 mm. The closed bomb connected with an igniter and a pressure transducer was mounted onto the plate using a threaded hole. The volume of cavity inside closed bomb is 2.5 ml.

Fig. 1Test setup: a) schematic diagram of test setup, b) test facility

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b)

During the tests, the pyroshock signals were recorded by piezoelectric accelerometers of the range ±50,000 g, as shown in Fig. 1(a). Three measurement points were located on the upper surface of the plate, respectively 50 mm,100 mm and 150 mm away from the center. Piezoelectric accelerometers, the pressure transducer, and the sensor conditioner were used with a DAQ system. The sampling rate and the sampling time were set to 1 MHz and 20 ms respectively. The eight-pole Butterworth bandpass filter between 100 Hz to 30 kHz was applied for accelerometers results to resolve possible issues such as low frequency data drift and data aliasing during data processing [9].

Pyroshock measurement tests were performed 3 times under different amounts of explosive to improve the credibility of the test data. An abnormal data was obtained for 200 mg due to insufficient combustion of explosive and a test was performed again. The results of tests are discussed in next section.

3.1. Effect of amount of explosive on output pressure

After the detonation of the igniters, the pressure inside the closed bomb reaches peak value and then the pressure value gradually decreases. The peak pressure values under different amount of explosive are summarized in Table 1.

Fig. 5Effect of amount of explosive on output pressure

From the Fig. 5, it is clearly that the peak pressure values increase along with increased amount of explosive. Using the data, the Nobel-Abel equation of state [10] can be improved to estimate the explosive force of the main charge of the igniter:

where $f$ is the explosive force (J/g), $P_m$ is the peak pressure (MPa), $V_0$ is the volume of the closed bomb (2.5 ml); $M$ is the charge of the igniter (g); $\alpha$ is the co-volume of explosive (cm^-3/g). $P_0$ is the equivalent output pressure of the primers.

The relationship between the peak output pressure and the amount of explosive is in accordance with the Nobel-Abel equation of state. It is estimated that the explosive force $f$ and co-volume $\alpha$ of main explosive are respectively 402.1 J/g and 5.58 cm^-3/g. The equivalent output pressure of the primers $P_0$ is 12.37 MPa.

3.2. Effect of amount of explosive on pyroshock

The maximax shock response spectra (SRS) are calculated from 100 Hz to 10 kHz with a damping ratio 5 % ($Q=$10). The typical measured acceleration data is showed in Fig. 6(a), while Fig. 6(b) presents the corresponding calculated SRS.

Fig. 6Pyroshock results at point1 under 50 mg explosive: a) acceleration data, b) SRS calculated from acceleration data

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b)

Fig. 7 shows the variation of peak acceleration with different locations. For the same amount of explosive, the intensity of peak acceleration reduces as it is away from the pyroshock source. In particular, an igniter with larger amounts of explosive has higher pyroshock level at the same measured point.

From the experiment, it is found that the peak acceleration response will increase with the increased amount of explosive. Fig. 8 shows that acceleration trends of point 2 and point 3 are almost same, except for the point 1. The gradient of the curve is less for point 2 and point 3 while it is steep for point1. It shows that material stress wave propagation effects govern the response for point 1. However, pyroshock response is governed by the combination of material stress wave propagation and structural resonance response effects for point 2 and point 3 [5].

Fig. 7Effect of locations on peak acceleration

Fig. 8Effect of amount of explosive on peak acceleration

The SRS of different amounts of explosive are compared and analyzed for different locations as depicted in Fig. 9. Due to structural resonance response effects, the amount of explosive has smaller effects on SRS at low frequency (< 1000 Hz) compared with SRS at high frequency (> 1000 Hz), especially for point 2 and poin 3. To get a quantitative expression of the relation, dimensionless coefficients without regard to frequency are defined as:

where, the $A$ is the mean relative coefficient of SRS, the $M$ is the relative coefficient of max SRS. $SR{S}_1$ is the base SRS. In this study, the SRS of 50 mg is the base one.

Fig. 9SRS comparison: a) SRS at point1, b) SRS at point2, c) SRS at point3

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b)

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The $A$ and $M$ under different amount of explosive are shown in Fig. 10, as well as their linear fit. Increases of the $A$ and $M$ are observed when the amount of explosive increased. The linear correlation coefficients of the $A$ and $M$ are respectively 0.98 and 0.99. Both coefficients show an approximately linear relation between the explosive amount and the SRS coefficients.

Fig. 10A and M of different amount of explosive: a) A, b) M

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b)