Observer-based robust high-order fully actuated attitude autopilot design for spinning glide-guided projectiles

This paper investigates the design of an attitude autopilot for a dual-channel controlled spinning glideguided projectile(SGGP),addressing model uncertainties and external disturbances.Based on fixed-time stable theory,a disturbance observer with integral sliding mode and adaptive techniques is proposed to mitigate total disturbance effects,irrespective of initial conditions.By introducing an error integral signal,the dynamics of the SGGP are transformed into two separate second-order fully actuated systems.Subsequently,employing the high-order fully actuated approach and a parametric approach,the nonlinear dynamics of the SGGP are recast into a constant linear closed-loop system,ensuring that the projectile's attitude asymptotically tracks the given goal with the desired eigenstructure.Under the proposed composite control framework,the ultimately uniformly bounded stability of the closed-loop system is rigorously demonstrated via the Lyapunov method.Validation of the effectiveness of the proposed attitude autopilot design is provided through extensive numerical simulations.

High-speed penetration of ogive-nose projectiles into thick concrete targets:Tests and a projectile nose evolution model

The majority of the projectiles used in the hypersonic penetration study are solid flat-nosed cylindrical projectiles with a diameter of less than 20 mm.This study aims to fill the gap in the experimental and analytical study of the evolution of the nose shape of larger hollow projectiles under hypersonic penetration.In the hypersonic penetration test,eight ogive-nose AerMet100 steel projectiles with a diameter of 40 mm were launched to hit concrete targets with impact velocities that ranged from 1351 to 1877 m/s.Severe erosion of the projectiles was observed during high-speed penetration of heterogeneous targets,and apparent localized mushrooming occurred in the front nose of recovered projectiles.By examining the damage to projectiles,a linear relationship was found between the relative length reduction rate and the initial kinetic energy of projectiles in different penetration tests.Furthermore,microscopic analysis revealed the forming mechanism of the localized mushrooming phenomenon for eroding penetration,i.e.,material spall erosion abrasion mechanism,material flow and redistribution abrasion mechanism and localized radial upsetting deformation mechanism.Finally,a model of highspeed penetration that included erosion was established on the basis of a model of the evolution of the projectile nose that considers radial upsetting;the model was validated by test data from the literature and the present study.Depending upon the impact velocity,v0,the projectile nose may behave as undistorted,radially distorted or hemispherical.Due to the effects of abrasion of the projectile and enhancement of radial upsetting on the duration and amplitude of the secondary rising segment in the pulse shape of projectile deceleration,the predicted DOP had an upper limit.

Ballistic performance of additive manufacturing 316l stainless steel projectiles based on topology optimization method

Material and structure made by additive manufacturing(AM)have received much attention lately due to their flexibility and ability to customize complex structures.This study first implements multiple objective topology optimization simulations based on a projectile perforation model,and a new topologic projectile is obtained.Then two types of 316L stainless steel projectiles(the solid and the topology)are printed in a selective laser melt(SLM)machine to evaluate the penetration performance of the projectiles by the ballistic test.The experiment results show that the dimensionless specific kinetic energy value of topologic projectiles is higher than that of solid projectiles,indicating the better penetration ability of the topologic projectiles.Finally,microscopic studies(scanning electron microscope and X-ray micro-CT)are performed on the remaining projectiles to investigate the failure mechanism of the internal structure of the topologic projectiles.An explicit dynamics simulation was also performed,and the failure locations of the residual topologic projectiles were in good agreement with the experimental results,which can better guide the design of new projectiles combining AM and topology optimization in the future.

On the effect of pitch and yaw angles in oblique impacts of smallcaliber projectiles

A terminal ballistic analysis of the effects of 7.62 mm × 51 AP P80 rounds on inclined high-strength armor steel plates is the focus of the presented study.The findings of an instrumented ballistic testing combined with 3D advanced numerical simulations performed using the IMPETUS Afea? software yielded the conclusions.The experimental verification proved that slight differences in the pitch-andyaw angles of a projectile upon an impact caused different damage types to the projectile’s core.The residual velocities predicted numerically were close to the experimental values and the calculated core deviations were in satisfactory agreement with the experimental results.An extended matrix of the core deviation angles with combinations of pitch-and-yaw upon impact angles was subsequently built on the basis of the numerical study.The presented experimental and numerical investigation examined thoroughly the influence of the initial pitch and yaw angles on the after-perforation projectile’s performance.

Ballistic limit velocity of small caliber projectiles against SS400 steel plates:Live fire experiments and empirical models

This study presents the ballistic limit velocity of small caliber projectiles against SS400 steel plate derived from live-fire ballistic experiments. Four different small caliber projectiles were tested against SS400 steel plates of 9 mm, 10 mm, and 12 mm thicknesses. The ballistic limit velocity was calculated using two standard methods, MIL-STD-662F and NIJ-STD-0101.06, and additionally using a support vector machine algorithm. The results show a linear relationship between the plate thickness and ballistic limit velocity. Further, the relative penetration performance among five different small caliber projectiles was analyzed using the Penetration Performance Ratio(PPR) introduced in this study, which suggests the potential of PPR to predict the ballistic limit velocity of other untested materials and/or different projectiles.

Numerical simulation of projectiles with different structures penetrating multi-storey concrete target board

Because the difference between the acceleration curve of traditional projectile structure and the measured accelera- tion curve is large, refining projectile structure is proposed. After setting up multi-storey concrete target board penetrated by the projectiles with different structures, the simulations with traditional projectile structure and refining projectile structure are conducted using ANSYS/LS-DYNA, and two acceleration curves are obtained, respectively. And then the target experi- ment that the projectile penetrates eight-storey concrete board is conducted and the measured acceleration curves are ob- tained. By comparing the simulation acceleration curves with the measured acceleration curves, it can be concluded that the acceleration curve with refined projectile structure is closer to the measured curve. Therefore, the simulation curve with re- fined projectile structure is of higher reference value for simulation research.

A spherical cavity expansion model for penetration of ogival-nosed projectiles into concrete targets with shear-dilatancy

A dynamic spherical cavity-expansion penetration model is suggested herein to predict the penetration and perforation of concrete targets struck normally by ogivalnosed projectiles.Shear dilatancy as well as compressibility of the material in comminuted region are considered in the paper by introducing a dilatant-kinematic relation.A procedure is first presented to compute the radial stress at the cavity surface and then a numerical method is used to calculate the results of penetration and perforation with friction being taken into account.The influences of various target parameters such as shear strength,bulk modulus,density,Poisson＇s ratio and tensile strength on the depth of penetration are delineated.It is shown that the model predictions are in good agreement with available experimental data.It is also shown that the shear strength plays a dominant role in the target resistance to penetration.

Influence of control strategy on stability of dual-spin projectiles with fixed canards

Existing literature has shown that the control force at the nose could cause dynamic instability for controlled projectiles. To lower the adverse impact on the dual-spin projectile with fixed canards under the premise of meeting guidance system requirements, the influence of control moment provided by a motor on the flight stability is analyzed in this paper. Firstly, the effect of the rolling movement on stability is analyzed based on the stability criterion derived using the Hurwitz stability theory. Secondly, the evaluation parameters combining the features of different control periods that could assess the variation of stability features after the motor torque are obtained. These effective formulas are used to indicate that, to reduce the flight instability risks, the stabilized rolling speed of roll speed keeping period should be as small as possible; the variation trend of motor torque during the rolling speed controlling period and the roll angle of the forward body during roll angle switching period are recommended corresponding to the projectile and trajectory characteristics. Moreover,detailed numerical simulations of 155 mm dual-spin projectile are satisfactory agreement with the theoretical results.

Stability analyses of the mass abrasive projectile high-speed penetrating into concrete target. Part Ⅰ: Engineering model for the mass loss and nose-blunting of ogive-nosed projectiles

The mass loss and nose blunting of a projectile during high-speed deep penetration into concrete target may cause structural destruction and ballistic trajectory instability of the penetrator,obviously reducing the penetration efficiency of penetrator.Provided that the work of friction between projectile and target is totally transformed into the heat to melt penetrator material at its nose surface,an engineering model is established for the mass loss and nose-blunting of the ogive-nosed projectile.A dimensionless formula for the relative mass loss of projectile is obtained by introducing the dimensionless impact function I and geometry function N of the projectile.The critical value V c0of the initial striking velocity is formulated,and the mass loss of projectile tends to increase weakly nonlinearly with I/N when V0〉V c0,whilst the mass loss is proportional to the initial kinetic energy of projectile when V0

Oblique perforation of thick metallic plates by rigid projectiles

Oblique perforation of thick metallic plates by rigid projectiles with various nose shapes is studied in this paper. Two perforation mechanisms, i.e., the hole enlargement for a sharp projectile nose and the plugging formation for a blunt projectile nose, are considered in the proposed analytical model. It is shown that the perforation of a thick plate is dominated by several non-dimensional numbers, i.e., the impact function, the geometry function of projectile, the non-dimensional thickness of target and the impact obliquity. Explicit formulae are obtained to predict the ballistic limit, residual velocity and directional change for the oblique perforation of thick metallic plates. The proposed model is able to predict the critical condition for the occurrence of ricochet. The proposed model is validated by comparing the predictions with other existing models and independent experimental data.

A new analytical model for the low-velocity perforation of thin steel plates by hemispherical-nosed projectiles

Ballistic experiments were conducted on thin steel plates that are normally impacted by hemisphericalnosed projectiles at velocities higher than their ballistic limits. The deformation and failure modes of the thin steel plates were analyzed. A new method was proposed according to the experimental results and the perforation phenomenon of the thin steel plates to determine the radius of the bulging region. In establishing this new method, a dynamic method combined with the plastic wave propagation concept based on the rigid plastic assumption was adopted. The whole perforation process was divided into four consecutive stages, namely, bulging deformation, dishing deformation, ductile hole enlargement, and projectile exit. On the basis of the energy conservation principle, a new model was developed to predict the residual velocities of hemispherical-nosed projectiles that perforate thin steel plates at low velocities.The results obtained from the theoretical calculations by the present model were compared with the experimental results. Theoretical predictions were in good agreement with the experimental results in terms of both the radius of the bulging region and the residual velocity of the projectile when the strain rate effects of the target material during each stage were considered.

Rigid elliptical cross-section ogive-nose projectiles penetration into concrete targets

The elliptical cross-section ogive-nose projectile(ECOP) has recently attracted attention because it is well suited to the flattened shape of earth-penetrating weapons. However, the penetration performance of ECOPs has not been completely understood. The objective of this study was to investigate the penetration performance of ECOPs into concrete targets using a theoretical method. A general geometric model of ECOPs was introduced, and closed-form penetration equations were derived according to the dynamic cavity-expansion theory. The model was validated by comparing the predicted penetration depths with test data, and the maximum deviation was 15.8%. The increment in the penetration depth of the ECOP was evaluated using the proposed model, and the effect of the majoreminor axis ratio on the increment was examined. Additionally, the mechanism of the penetration-depth increment was investigated with respect to the caliber radius head, axial stress, and resistance.

Experimental investigation on enhanced damage to fuel tanks by reactive projectiles impact

Enhanced damage to the full-filled fuel tank,impacted by the cold pressed and sintered PTFE/Al/W reactive material projectile(RMP)with a density of 7.8 g/cm3,is investigated experimentally and theoretically.The fuel tank is a rectangular structure,welded by six pieces of 2024 aluminum plate with a thickness of 6 mm,and filled with RP-3 aviation kerosene.Experimental results show that the kerosene is ignited by the RMP impact at a velocity above 1062 m/s,and a novel interior ignition phenomenon which is closely related to the rupture effect of the fuel tank is observed.However,the traditional steel projectile with the same mass and dimension requires a velocity up to 1649 m/s to ignite the kerosene.Based on the experimental results,the radial pressure field is considered to be the main reason for the shear failure of weld.For mechanism considerations,the chemical energy released by the RMP enhances the hydrodynamic ram(HRAM)effect and provides additional ignition sources inside the fuel tank,thereby enhancing both rupture and ignition effects.Moreover,to further understand the enhanced ignition effect of RMP,the reactive debris temperature inside the kerosene is analyzed theoretically.The initiated reactive debris with high temperature provides effective interior ignition sources to ignite the kerosene,resulting in the enhanced ignition of the kerosene.

Vertical Water-Entry of Bullet-Shaped Projectiles

The vertical water-entry behavior of bullet-shaped projectiles was experimentally and theoretically studied. Particular attention was given to characterizing projectile dynamics, the resultant evolution of air cavity and particularly surface closure before deep closure in the moderate speed. We developed equations for the projectile motion with significant and negligible gravitational effects. Based on the solution to the Rayleigh-Besant problem, a theoretical model was developed to describe the evolution of the cavity shape, including the time evolution of the cavity on fixed locations and its location evolutions at fixed times. The gravitation effects during the initial stage of the impact of the projectile on the water can be ignored, but those during the later stage should be considered, many literatures do not have the report of this aspect. The theoretical predictions were consistent with the experimental observations. The evolution of air cavity had a significant effect on ballistic stability.

Vulnerability assessment to projectiles: Approach definition and application to helicopter platforms

Survivability is defined as the capability of a platform to avoid or withstand a man-made hostile environment. Military aircraft in particular, but also other kinds of platforms subjected to external, impacting threats, are commonly designed according to increasing survivability requirements. The concept of survivability was first formalized by R. Ball in 1985 in its seminal work on combat aircraft survivability.On the basis of the theory presented in his work, many computer programs have been developed which implement the modelling techniques and computations required by vulnerability assessments. However,a clear and general view of the operative computational procedures is still lacking. Moreover, to date only a limited number of applications to helicopter platforms have been investigated in the survivability field,even though these platforms experience numerous flight conditions exposing the system to different types of threats. In this context, this work aims at establishing a multi-purpose general framework for the vulnerability assessment of different types of platforms subjected to external threats, with a focus on helicopters. The in-house software specifically developed for this application is here described in detail and employed to present a case study on a representative military helicopter.

Key Techniques of Terminal Correction Mortar Projectiles

The operational principle, the impulse force and terminal guidance laws of terminal correction mortar projectiles（TCMP） are researched in this paper, by using the TCMP simulation program, key techniques such as the miss distance influenced by the acting point of impulse force, the impulse force value, the correction threshold, and the number of impulse rockets are researched in this paper. And the dual pulse control scheme is also studied. Simulation results indicate that the best acting point is near the center of gravity, sufficient correction resources are needed, the miss distance is insentive to the correction threshold, increasing the number of impulse rockets properly is beneficial to increase the hit precision, the velocity pursuit guidance law has less miss distance, the change of the attack angle is milder and the transient time becomes less in the dual impulse control scheme. These conclusions are important for choosing parameters and impulse correction schemes designed for TCMP.

Numerical Investigation of Penetration Performance of Non-Ideal Segmented-Rod Projectiles

The design of a segmented-rod projectile is often simplified into an ideal one in theoreti-cal analysis for the convenience of modeling of its performance.But the actual performance of non-ideal segmented-rod projectiles over the impact velocity range in practical applications was rarely explored.AUTODYN numerical code is used to investigate the influence of the component design upon the penetration performance of non-ideal segmented-rod projectiles over a wide range of impact velocities,which can be used to guide the optimal design of weaponry segmented-rod projectiles.

Firm embedding behavior of annular grooved projectiles impacting ductile metal targets

Annular grooved projectiles(AGPs)have drawn ongoing concerns as an advanced penetrator for their excellent anti-rebound capability in impacting metal plates.They could become embedded solidly in the target surface during low-velocity impact.In this investigation,the firm embedding behavior of AGP was observed by impact experiments.Corresponding numerical simulations provided a better understanding of this process.Experimental and numerical results indicated that the firm embedding behavior of AGP was mainly due to the filling-material in the groove rather than the friction between the projectile and target,unlike traditional shape such as conical projectile.According to observation,firm embedding process can generally be subdivided into four stages:initial-cratering stage,groove-filling stage,fillingmaterial failure stage and rebound vibration stage.Moreover,the damage mechanics of target material around crater was obtained through microscopic tests.A comparison of the cross-sectional figures between the experiment and simulation proved that the analysis and the proposed method were reasonable and feasible,which further demonstrated that the firm embedding behavior has application potential in new concept warheads.

Hydrodynamic Characteristics and Supercavity Shape of Supercavitating Projectiles Launched with Supersonic Speed

A supercavitating projectile is launched underwater with supersonic speed,and then,the speed decreases to transonic and subsonic conditions orderly because of the drag coming from surrounding water.The flow regime and hydrodynamic characteristics are significantly influenced by the flying speed,the influence laws in supersonic,transonic,and subsonic regions are totally different.These issues aren’t well studied.A numerical model consisting of VOF model,moving frame method and state equation of liquid is established to calculate the compressible supercavitation flow field,and validated by comparing with a published result.The influences of water compressibility and Mach number on supercavity shape and hydrodynamic characteristics are quantitatively summarized.The results show that the flying speed of supercavitating projectiles exerts significant influences on the flow regime,supercavity shape and hydrodynamic characteristics for the transonic and supersonic conditions.With the decrease of flying speed,the drag coefficient decreases gradually,and the dimensions of the supercavity near supercavitating projectiles significantly increases in the high-speed conditions.An underwater bow shock is numerically observed before the disk cavitator in supersonic condition.However,no obvious changes are found for the incompressible water cases with different speeds.For supersonic conditions,the supercavity near supercavitating projectiles of compressible water is smaller than that of incompressible water,the drag coefficient is larger,and the relative difference significantly increases with the flying speed.For the case of Ma 1.214,the relative difference of supercavity diameter at the tail section 3.98%,and the difference of the drag coefficient is 23.90%.

A novel method for determination of lethal radius for high-explosive artillery projectiles

A new model has been defined that enables the estimation of the lethal radius(radius of efficiency)of HE(High Explosive)artillery projectiles against human targets.The model is made of several modules:CAD(Computer Aided Design)modeling,fragment mass distribution estimation,fragment initial velocity prediction,fragment trajectory calculation,effective fragment density estimation,and high explosive projectile lethal radius estimation.The results were compared with the experimental results obtained based on tests in the arena used in our country,and the agreement of the results was good.This model can be used in any terminal-ballistics scenario for high explosive projectiles since it is general,parametric,fast and relatively easy to implement.