Numerical simulation of separation shock characteristics of a piston type explosive bolt

4.1. Separation process

The pressure contours of the explosive bolt during separation processes are shown in Fig. 5. At 0 μs, the charge was detonated. Then, the propagation of detonation waves and the expansion of products started at 1us (Fig. 5(a)). The shock waves propagate reached the end face of the piston and the products fills the entire chamber around 3 us (Fig. 5(b). Then, the shock wave and expansion of products drove the piston to move forward, and a tensile stress is formed at the pre-groove. The pre-groove reached the failure criterion and began to fail around 70 us (Fig. 5(c)). At 83 us, the failure expands radially along the groove, eventually forming a fracture and starting separation (Fig. 5(d)). As the fracture is formed, the piston accelerated forward and released the screw free. At 155 μs, the piston hits the body shoulder, the velocity instantaneously decreased and eventually stopped moving (Fig. 5(e)). When the piston stopped moving, the screw is no longer subjected to the loading force and kept flying at a constant speed (Fig. 5(f)).

Fig. 5Pressure contour on separation process

a)$t=$ 1 μs

b)$t=$ 3 μs

c)$t=$ 70 μs

d)$t=$ 83 μs

e)$t=$ 155 μs

f)$t=$ 200 μs

4.2. Analysis of shock sources

When the charge amount is 442 mg, the shock acceleration history and SRS in the $X$ and $Y$ directions at 2 cm were shown in Fig. 6. It can be clearly seen from the acceleration history that there are two distinct peaks. Combined with the simulation of the separation process in Section 4.1, it can be seen that the two peaks are caused by the pyrotechnic explosion and the piston impact. In addition, the shock response in the $Y$ direction is significantly larger than in the $X$ direction. This is because $Y$ is the main direction of the explosion shock wave propagation and piston impact.

Fig. 6Output shock of explosive bolt in test

a) Acceleration history

b) SRS

4.3. Comparison of simulation and experiment

The SRS obtained by simulation and experiment at 5, 10 and 15 cm are compared in Fig. 7. The experimental SRS is enveloped by the ±6 dB of simulated SRS except for the individual frequencies, which indicates that the simulation model can predict the separation shock.

Fig. 7Comparison of SRS between simulation and experiment

a) 5 cm

b) 10 cm

c) 15 cm

4.4. Effect of charge amount on piston velocity

From the analysis of shock source in the section 4.2, it is known that the peak velocity of piston has a great influence on separation shock. The variation law of the piston velocity during the separation process under a 442 mg charge amount is analyzed, and the results shown in Fig. 8. The piston velocity first rised to about 20 m/s under the action of the detonation shock wave and the product expansion. Then, the front end of body was loaded to stretch the impair slot. At 70 us, the impair slot begins to fracture, the velocity of piston rised sharply, and finally the body was broken. The speed then drops sharply when the piston hit the body shoulder. However, due to the deformation of the body caused by the impact (Fig. 5(f)), the piston continued to move forward for a distance until it stopped.

The velocities of the piston for different charge amounts were calculated, and the results are shown in Fig. 9. As the charge increases, the piston velocity in the early stage increased, but the velocity of the piston collision does not continue to increase, reached at the maximum at 531 mg. When the design stroke is fixed, the overall velocity of the piston is larger as the charge amount is increased, but the collision time is advanced, so that the collision velocity does not necessarily increase.

Fig. 8Piston velocity and displacement in 442 mg

Fig. 9Piston velocity in different charge amount

4.5. Effect of charge amount on separation shock

The acceleration of $Y$ direction at four different distances from the source was extracted under different charge amounts, and the corresponding SRS calculated. To better study the influence of the charge amount on separation shock, two dimensionless coefficients of $M_r$ and $E_r$ that does not consider the frequency were defined. The expression is as follows:

where, $M_r$ is the maximum relative coefficient of the SRS and $E_r$ is the average relative coefficient of the SRS in the entire frequency domain. $SR{S}_b\left(f\right)$ is reference SRS. Here, the reference SRS is the SRS of the 442 mg charge amount in the $Y$ direction at 2 cm.

The $M_r$ and $E_r$ at four locations were calculated and are shown in Fig. 10.

It can be seen from Fig. 10 that the influence of the charge on the shock is not a simple linear relationship in terms of $M_r$ or $E_r$. The explosive bolt is not separated when the charge was 310 and 354 mg. Their separation shocks are basically consistent except for the near field 2 cm. Since the shock in the unseparated condition is only caused by the explosion shock wave, the shock wave dissipates quickly as the distance increases. The near-field shock response is directly affected by the shock wave, while the far-field shock response is mainly dominated by the stress wave and the structural resonance. When the charge was increased from 354 to 398 mg, the shock sharply increased because the explosion bolts achieved separation, and the shock caused by the impact of the piston was introduced. In the case of separation, the separation shock first increased with increasing charge amount and then tends to stabilize at 531 mg. Although the explosion shock increased as the charge amount increased, but the impact shock decreased as the impact speed of piston decreased. The combined result of the two causes resulted in an output shock that remained essentially unchanged.

Fig. 10Relationship curves between SRS and charge amount

a) Max coefficient

b) Mean coefficient