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    • In the simulations the canards span

    2018-11-12

    In the simulations, the canards span freely until 5 s after launch. Fig. 9 shows the inherent vibration frequencies (include the fast and slow part) of 155 mm projectile during the entire flight domain. It can be seen from Fig. 5 when the rotation speed of the forward part is 0.5 revolutions per second (r/s), the amplitude of the angle of attack increases sharply in two periods: near 32 and 68s; when the rotation speed is 1.5 r/s, the resonance occurs at around 10 s; when the rotation speed is higher than 1.5 r/s, there is not a visible rise in the magnitude of the angle of attack. Compared to the red line in Fig. 9, the inherent slow part frequency of the projectile increases at about 40 s after a decrease. During the total flight, there are two points corresponding to 0.5 Hz, and only one to 1.5 Hz. When the rotation speed exactly equals to the value of the inherent frequency at this moment, a resonance occurs, and the number of points of intersection indicates the number of resonance. Similarly, Fig. 6 shows the angle of attack with the 13–25 Hz frequencies of cyclical force. Both the simulation result shown in Fig. 6 and the the theoratical result shown in Fig. 9 reveal that the inherent frequency (fast mode) keeps decreasing during the flight, and the magnitude of the angle of attack increases when the frequency of the cyclical force equals with that of the driving force. Based on the above analysis, the resonance region of the 155 mm projectile is 0–3 Hz and 13–25 Hz. Figs. 7 and 8 illustrate that the range decreases sharply and the drift changes slightly in the resonance region. Thus, to avoid an uncontrollable change of trajectory, the rotational speed of the forward part should be kept away from the resonance region. To evade the resonance region, the rolling speed of the forward part of the projectile should be chosen as 5–10 r/s to the 155 mm projetitle simulated above. When the parameters of the projectile is changed, the resonance region will chang accordingly, but it SCR7 can be calculated by the method described above. Specifically, as to most dual-spin projectiles, the control moment is unidirectional, so that it is impossible for the projectile to decrease the rolling speed of the forward section. Thus, if the uncontrolled rotation speed of the forward section is between 0 and 3 Hz, it is more proper to control it to 5–10 Hz. When the uncontrolled rotation speed is between 13 and 25 Hz, the propor rotational speed should exceed 25 Hz. In this section, the impact of the periodic force on the circular error probability (CEP) of the 155 mm projectile was verified using Monte Carlo simulations with the 7-DOF model established in section 2. Perturbations applied on the launch and flight conditions were included in muzzle velocity, gun azimuth, gun elevation and wind velocity, and they were varied randomly with normal distributions. The average and standard deviation of the launch and flight condition perturbations used in the analysis are summarized in Table 2. Each Monte Carlo simulation included 200 trajectories. The simulation result shows that the impact on CEP is not significant, when all perturbations are considered. According to Table 3, in which the CEPs are listed, the periodic force against the forward section can decrease the circular error probability caused by gun elevation and azimuth anomalies; and Isoaccepting tRNAs decreases the deviation on X axis caused by wind while simultaneously increasing it on Z axis.
    Conclusion
    Introduction Explosively-formed projectiles (EFPs) are used in numerous modern ammunition systems because of their advantages of effective stand-off and strong secondary effects after penetration. For the purpose of improving the penetration performance of warheads, one of the design goals of any designer is to obtain the most elongated and compact projectile with a high initial velocity [1]. Powerful explosives [2], detonation wave shaping [3], and the use of high-density and high-ductility liner materials are the main ways to achieve this goal [4]. The detonation wave shaping is considered to be the most efficient way of improving the penetration performance of warheads [5]. Embedding a wave shaper in charge is one of the ways to shape a detonation wave [6–8]. Weimann [1], Murphy et al. [6], and Men et al. [9] reported that the EFP length could be increased if a wave shaper is placed in charge. Zhang et al. [8,10] compared the performances of EFPs formed from warheads with and without wave shaper, and the results indicated that EFP formed from the warhead with a wave shaper has a higher velocity, larger length–diameter ratio, and higher penetration capability compared to that formed without a wave shaper. However, the researchers have not explored how to adjust the detonation wave contours shaped by the thickness of wave shaper on the formation of EFP.