# High-Velocity Metal Fragment: Motion Characteristic and Optimization Design
## 2 Experimental System  
### Experimental Device and Process  
Experiments are carried out to analyze the movement characteristics of the fragment in the movement process, as shown in Figure 1. A 30 mm smoothbore gun drove by tubular powder with seven holes is designed to produce the fragment with high velocity in this experimental system. Figure 2 shows the detailed structure of the launching system, including gun breech, head tube, anti-recoil buffer device, displacement regulating device, transition base, connection case, back tube, and supporting base. The anti-recoil buffer device can absorb the recoil in the launching process. In this study, the buffer device is double buffer with recoil and advance and is installed on the back tube via adopting the apposition method of disc springs. The advance buffer is used to realize the brake and counter-recoil effect of the launching system, and the recoil buffer is mainly used to advance action when the counter-recoil is in place. This buffer device can satisfy the operating requirement of the maximum recoil of 183 KN that is enough for this experimental study. The combustion chamber in the head tube of the launching system is 35 mm caliber, and the length of the whole tube is 4.5 m.  
The launching tube made of gun-steel is always working under the effect of the high-pressure combustion-gas, and thus the strength of the tube is designed according to the linear deformation potential theory. The tangential stresses of the inner surface and outer surface of the tube are calculated as the following equations, respectively:  
\[\sigma_{i}=\frac{2}{3}P\frac{2R_{e}^{2}+R_{i}^{2}}{R_{e}^{2}-R_{i}^{2}} \tag{1}\]  
\[\sigma_{e}=P\frac{2R_{i}^{2}}{R_{e}^{2}-R_{i}^{2}} \tag{2}\]  
where, \(R_{i}\) and \(R_{e}\) are the inner radius and outer radius of the tube, respectively. \(P\) is the pressure of the corresponding position of the tube where the projectile is located, and the unit is MPa. \(\sigma_{i}\) and \(\sigma_{e}\) are the tangential stresses of the inner surface and outer surface of the tube. The safety factors of the inner and outer stresses \(n_{i}\) and \(n_{e}\) are calculated as the following equations:  
\[n_{i}=\frac{[\sigma]}{\sigma_{i}}\quad,\quad n_{e}=\frac{[\sigma]}{\sigma_{e}} \tag{3}\]  
where, the permissible stress of the tube is \([\sigma]\) = 1040 MPa and the maximum pressure of the tube is calculated as \(P_{\rm m}\) = 400 MPa and then the corresponding results are shown in Table 1.  
It can be seen in Table 1 that the safety factors of the inner and outer surface of the tube are all larger than 1.49 for the whole positions when the projectile is moving in the tube of the launching system. Consequently, the strength of the tube designed in the study satisfies the strength requirement. Figure 1: Schematic diagram of experimental system. Figure 2: Sub-caliber ultra-high speed fragment loading device. In addition, the dedicated experimental projectiles are also designed according to the STANAAG 4496, as shown in Figure 3. The projectile is composed of projectile sabot and fragment, and the fragment is surrounded by the projectile sabot to guarantee that the fragment cannot turn over in the tube. Meanwhile, the launching security in the tube and the flying stability in the air can be reached. The main function of the projectile sabot is to trap combustion-gases and transmit the thrust for the movement of the fragment. The projectile sabot is also preprocessed into four sections for the separation of the projectile sabot and fragment timely when the projectile is flying away from the muzzle of the launching system. In the experiment, the separation of the projectile sabot and fragment can be realized via adjusting the mass and shape of the fragment. The diameter of the fragment is 14.3 \(\pm\) 0.05 mm, and the length-diameter ratio is 1. The Brinell Hardness is HB \(\leq\) 270 with steel cylindrical body and the angle of the projectile is 160 \(\pm\) 0.5\({}^{\circ}\). Thus, the whole length of the experimental projectile is 15.56 \(\pm\) 0.05 mm.