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.

A review of dual-spin projectile stability

This paper gives a succinct review of dual-spinprojectile stability and some technologies relating to them.It describes how the traditional stability factors from linear projectile theory are modified to better describe a controlled dual-spin projectile.Finally,it reviews works which have investigated how different aspects of a controlled dual-spin design can affect flight stability,primarily airframe structure and canard properties.A conclusion is given,highlighting important guidelines from the enclosed discussions.

Influence of yawing force frequency on angular motion and ballistic characteristics of a dual-spin projectile

A roll-decoupled course correction fuze with canards can improve the hit accuracy of conventional unguided ammunitions. The fuze increases accuracy by reducing the effect of angular and translational motion produced by the cyclical yawing forces applied on the projectile. In order to investigate the influence of yawing forces on angular motion, a theoretical solution of the total yaw angle function with the cyclical yawing forces is deduced utilizing the 7 degrees of freedom(7-DOF) model designed for this calculation. Furthermore, a detailed simulation is carried out to determine the influence rules of yawing force on angular motion. The calculated results illustrate that, when the rotational speed of the forward part is close to the initial turning rate, the total yaw angle increases and the flight range decreases sharply. Moreover, a yawing force at an appropriate frequency is able to correct the gun azimuth and elevation perturbation to some extent.

A guidance and control design with reduced information for a dual-spin stabilized projectile

In this paper,an integrated guidance and control method based on an adaptive path-following controller is proposed to control a spin-stabilized projectile with only translational motion information under the constraint of an actuator,uncertainties in aerodynamic parameters and measurements,and control system complexity.Owing to the fairly high rotation speed,the dynamic model of this missile is strongly nonlinear,uncertain and coupled in pitch,yaw and roll channels.A theoretical equivalent resultant force and uncertainty compensation method are comprehensively used to realize decoupling of pitch and yaw.In response to the strong nonlinear and time-varying characteristics of the dynamic system,the quasi-linear model whose parameters are obtained by interpolation of points selected as the segmentation points in the trajectory envelope,is used for calculation in each step.To cope with the system uncertainty caused by model approximation,parameter uncertainty and ballistic interference,an extended state estimator is used to compensate the output feedback according to the test ballistic angle.In order to improve the tracking efficiency and ensure the tracking error convergence with only translational motion information,the virtual guide point,whose derivative is deduced according to the Lyapunov principle,is calculated in real time according to the projection relationship between the real-time position and the reference trajectory,and a virtual line-of-sight angle and the backstepping method are used for the design of the guidance and control system.In order to avoid the influence of control input saturation on the guidance and control performance due to the actuator limitation and improve the robustness of the system,an anti-saturation compensator is designed according to the two-step method.The feasibility and effectiveness of the path-following controller is verified through closed-loop flight simulations with measurement,control,and condition uncertainties.The results indicate that the designed controller can converge to the reference path and evidently decrease the distance between the impact point and target under different uncertainties.

Enhanced structural damage behavior of liquid-filled tank by reactive material projectile impact

A series of ballistic experiments were performed to investigate the damage behavior of high velocity reactive material projectiles(RMPs) impacting liquid-filled tanks,and the corresponding hydrodynamic ram(HRAM) was studied in detail.PTFE/Al/W RMPs with steel-like and aluminum-like densities were prepared by a pressing/sintering process.The projectiles impacted a liquid-filled steel tank with front aluminum panel at approximately 1250 m/s.The corresponding cavity evolution characteristics and HRAM pressure were recorded by high-speed camera and pressure acquisition system,and further compared to those of steel and aluminum projectiles.Significantly different from the conical cavity formed by the inert metal projectile,the cavity formed by the RMP appeared as an ellipsoid with a conical front.The RMPs were demonstrated to enhance the radial growth velocity of cavity,the global HRAM pressure amplitude and the front panel damage,indicating the enhanced HRAM and structural damage behavior.Furthermore,combining the impact-induced fragmentation and deflagration characteristics,the cavity evolution of RMPs under the combined effect of kinetic energy impact and chemical energy release was analyzed.The mechanism of enhanced HRAM pressure induced by the RMPs was further revealed based on the theoretical model of the initial impact wave and the impulse analysis.Finally,the linear correlation between the deformation-thickness ratio and the non-dimensional impulse for the front panel was obtained and analyzed.It was determined that the enhanced near-field impulse induced by the RMPs was the dominant reason for the enhanced structural damage behavior.

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.

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.

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.

High-dimensional uncertainty quantification of projectile motion in the barrel of a truck-mounted howitzer based on probability density evolution method

This paper proposed an efficient research method for high-dimensional uncertainty quantification of projectile motion in the barrel of a truck-mounted howitzer.Firstly,the dynamic model of projectile motion is established considering the flexible deformation of the barrel and the interaction between the projectile and the barrel.Subsequently,the accuracy of the dynamic model is verified based on the external ballistic projectile attitude test platform.Furthermore,the probability density evolution method(PDEM)is developed to high-dimensional uncertainty quantification of projectile motion.The engineering example highlights the results of the proposed method are consistent with the results obtained by the Monte Carlo Simulation(MCS).Finally,the influence of parameter uncertainty on the projectile disturbance at muzzle under different working conditions is analyzed.The results show that the disturbance of the pitch angular,pitch angular velocity and pitch angular of velocity decreases with the increase of launching angle,and the random parameter ranges of both the projectile and coupling model have similar influence on the disturbance of projectile angular motion at muzzle.

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.

A possible probe to neutron-skin thickness by fragment parallel momentum distribution in projectile fragmentation reactions

Neutron-skin thickness is a key parameter for a neutron-rich nucleus;however,it is difficult to determine.In the framework of the Lanzhou Quantum Molecular Dynamics(LQMD)model,a possible probe for the neutron-skin thickness(δ_(np))of neutron-rich ^(48)Ca was studied in the 140A MeV ^(48)Ca+^(9)Be projectile fragmentation reaction based on the parallel momentum distribution(p∥)of the residual fragments.A Fermi-type density distribution was employed to initiate the neutron density distributions in the LQMD simulations.A combined Gaussian function with different width parameters for the left side(Γ_(L))and the right side(Γ_(R))in the distribution was used to describe the p∥of the residual fragments.Taking neutron-rich sulfur isotopes as examples,Γ_(L) shows a sensitive correlation withδ_(np) of ^(48)Ca,and is proposed as a probe for determining the neutron skin thickness of the projectile nucleus.

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.

Impact point prediction guidance based on iterative process for dual-spin projectile with fixed canards

The fixed canards configuration of a dual-spin projectile makes it difficult to apply the traditional guidance law. In this study, a modified impact point prediction guidance strategy based on an iterative process was developed for a class of dual-spin projectiles with fixed canards, to reduce the impact point dispersion. The guidance strategy is dependent on the modified projectile linear theory to rapidly predict the flight states and the impact point. For projectiles with control applied to the trajectory, the modified projectile linear theory method is known to achieve poor impact point prediction. To improve the prediction accuracy, improvements were made to the modified projectile linear theory by considering the products of the yaw rate and other small quantities.The guidance strategy is based on the iterative process for the continuous adjustment of the expected output of the roll angle of the course correction fuze, to minimize the direction error between the predicted impact point and target location. Studies were conducted on a model dual-spin projectile configuration to demonstrate the guidance details. The numerical simulations indicate that the proposed guidance strategy can effectively reduce the projectile impact point dispersion.

Time-sequenced damage behavior of reactive projectile impacting double-layer plates

The time-sequenced damage behavior of the reactive projectile impacting double-layer plates is discussed.The analytical model considering the combined effect of kinetic and chemical energy is developed to reveal the damage mechanism.The influences of impact velocity and reactive projectile chemical characteristics on the damage effect are decoupled analyzed based on this model.These analyses indicate that the high energy releasing efficiency and fast reaction propagation velocity of the reactive projectile are conducive to enhancing the damage effect.The experiments with various reactive projectiles impact velocity increasing from 702 to 1385 m/s were conducted to verify this model.The experimental results presented that,the damage hole radius of the rear-plate increases with the increase of impact velocity.At the impact velocity of 1350 m/s,the radius of damage hole formed by PTFE/Al/Bi_(2)O_(3),PTFE/Al/MoO_(3),PTFE/Al/Fe_(2)O_(3)projectile on the rear-plate become smaller in sequence.These results are consistent with the analytical model prediction,demonstrating that this model can predict the damage effect quantitatively.This work is of constructive significance to the application of reactive projectiles.

Perforation studies of concrete panel under high velocity projectile impact based on an improved dynamic constitutive model

The finite-depth concrete panels have been widely applied in the protective structures,and its impact resistance and dynamic fracture failures,especially the scabbing/perforation limits,under high velocity projectile impact,are mainly concerned by protective engineers,which are numerically studied based on an improved dynamic concrete model in this study.Firstly,based on the framework of the KCC(Karagozian&Case concrete)model,a dynamic concrete model is proposed which considers an independent tensile damage model and a continued transition between dynamic tensile and compressive properties.Secondly,the strength surface,equation of state and damage parameters of the proposed model are comprehensively calibrated by a triaxial compressive test with high confinement pressure,the rationality of which is further verified based on the single element tests,e.g.,uniaxial and triaxial compression as well as uniaxial,biaxial and triaxial tension.Thirdly,a series of projectile high velocity impact tests on thin and thick concrete panels are simulated,which indicates that the projectile residual velocity and dynamic fracture failures are reproduced satisfactorily,while the KCC model underestimates both the spalling and scabbing dimensions severely.Finally,based on the validated concrete model and finite element analyses approach,the validations of the existing five empirical formulae are evaluated,in terms of the depth of penetration(DOP)and scabbing/perforation limits of concrete panel.Both the Army corps of engineers(ACE)and modified National Defense Research Committee(NDRC)formulae are recommended in the design of the protective structure to avoid scabbing failure.

Damage of a large-scale reinforced concrete wall caused by an explosively formed projectile(EFP)

To quickly break through a reinforced concrete wall and meet the damage range requirements of rescuers entering the building,the combined damage characteristics of the reinforced concrete wall caused by EFP penetration and explosion shock wave were studied.Based on LS-DYNA finite element software and RHT model with modified parameters,a 3D large-scale numerical model was established for simulation analysis,and the rationality of the material model parameters and numerical simulation algorithm were verified.On this basis,the combined damage effect of EFP penetration and explosion shock wave on reinforced concrete wall was studied,the effect of steel bars on the penetration of EFP was highlighted,and the effect of impact positions on the damage of the reinforced concrete wall was also examined.The results reveal that the designed shaped charge can form a crater with a large diameter and high depth on the reinforced concrete wall.The average crater diameter is greater than 67 cm(5.58 times of charge diameter),and crater depth is greater than 22 cm(1.83 times of charge diameter).The failure of the reinforced concrete wall is mainly caused by EFP penetration.When only EFP penetration is considered,the average diameter and depth of the crater are 54.0 cm(4.50 times of charge diameter)and 23.7 cm(1.98 times of charge diameter),respectively.The effect of explosion shock wave on crater depth is not significant,resulting in a slight increase in crater depth.The average crater depth is 24.5 cm(2.04 times of charge diameter)when the explosion shock wave is considered.The effect of explosion shock wave on the crater diameter is obvious,which can aggravate the damage range of the crater,and the effect gradually decreases with the increase of standoff distance.Compared with the results for a plain concrete wall,the crater diameter and crater depth of the reinforced concrete wall are reduced by 5.94%and 9.96%,respectively.Compared to the case in which the steel bar is not hit,when the EFP hit one steel bar and the intersection of two steel bars,the crater diameter decreases by 1.36%and 5.45%respectively,the crater depth decreases by 4.92%and 14.02%respectively.The EFP will be split by steel bar during the penetration process,resulting in an irregular trajectory.

Computational Solution to the Problems of Projectile Motion under Significant Linear Drag Effect

This paper investigates the computational solution to the problem of projectile motion under a significant linear drag effect. The drag force acting on the particle within the medium of propagation is proportional to the cross-section area of the projectile, the velocity of the particle, and the medium’s density. From zero air resistance force (vacuum) the problems are well known with solutions, but with air resistance (drag force) the problems have no exact analytical solutions which lead to most of the significant scientific research works using numerical methods. Therefore, this study aims to present the analysis of the computational modelling of drag force exerted by the surrounding medium on the linear motion. However, the horizontal and vertical components of differential equations of motion were derived and characterized from the solutions governed by Newton’s 2nd law of motion. The baseball features were presented as the projectile (object) in this work. In addition, the numerical computational results were received from FreeMat. The results were discussed and compared with those from the vacuum. Moreover, the displacements, velocities, range, and trajectories of the projectile were all discussed and a conclusion was made.

Operational feasibility study of stagnation pressure reaction control for a mid-caliber non-spinning projectile

Controlled,guided munitions can reduce dispersion in the shot,while providing the capability of engaging both stationary and maneuvering targets.The Netherlands Organisation for Applied Scientific Research has developed a fin-less control technology called Stagnation Pressure Reaction Control(SPRC)that takes stagnation pressure air and directs it sideways to control non-spinning projectiles.In a previous study,this technology was demonstrated at Mach 2 wind-tunnel conditions to achieve up to 1.5°controllable angle of incidence for a non-spinning,aerodynamically unstable projectile-like test object.In an operational scenario,the decelerating projectile will experience a decline in control force while the simultaneous forward shift of the center of pressure increases the need for control force.Furthermore,angles of incidence exceeding 1.5°will be experienced under realistic flight conditions,especially against maneuvering targets.This work addresses these challenges and presents an operational feasibility study for a practical application of SPRC in a non-spinning mid-caliber gun-launched projectile,using experiment data on control latency and force of the earlier study.It illustrates the combined effect of the control-and stability dynamics and underlines the potential of an SPRC projectile as a precisionoperation ammunition.This research revealed that SPRC technology can stabilize and control the hypothesized projectile in a direct fire scenario against stationary and maneuvering targets.

Recognition model and algorithm of projectiles by combining particle swarm optimization support vector and spatial-temporal constrain

In order to improve the recognition rate and accuracy rate of projectiles in six sky-screens intersection test system,this work proposes a new recognition method of projectiles by combining particle swarm optimization support vector and spatial-temporal constrain of six sky-screens detection sensor.Based on the measurement principle of the six sky-screens intersection test system and the characteristics of the output signal of the sky-screen,we analyze the existing problems regarding the recognition of projectiles.In order to optimize the projectile recognition effect,we use the support vector machine and basic particle swarm algorithm to form a new recognition algorithm.We set up the particle swarm algorithm optimization support vector projectile information recognition model that conforms to the six sky-screens intersection test system.We also construct a spatial-temporal constrain matching model based on the spatial geometric relationship of six sky-screen intersection,and form a new projectile signal recognition algorithm with six sky-screens spatial-temporal information constraints under the signal classification mechanism of particle swarm optimization algorithm support vector machine.Based on experiments,we obtain the optimal penalty and kernel function radius parameters in the PSO-SVM algorithm;we adjust the parameters of the support vector machine model,train the test signal data of every sky-screen,and gain the projectile signal classification results.Afterwards,according to the signal classification results,we calculate the coordinate parameters of the real projectile by using the spatial-temporal constrain of six sky-screens detection sensor,which verifies the feasibility of the proposed algorithm.

Stability analysis of the projectile based on random center manifold reduction

The center manifold method has been widely used in the field of stochastic dynamics as a dimensionality reduction method.This paper studied the angular motion stability of a projectile system under random disturbances.The random bifurcation of the projectile is studied using the idea of the Routh-Hurwitz stability criterion,the center manifold reduction,and the polar coordinates transformation.Then,an approximate analytical presentation for the stationary probability density function is found from the related Fokker–Planck equation.From the results,the random dynamical system of projectile generates three different dynamical behaviors with the changes of the bifurcation parameter and the noise strength,which can be a reference for projectile design.