Dynamic analysis of a guided projectile during engraving process

Available online at www.sciencedirect.comDefenceTechnologyScienceDirectCrossMark中国兵工学会Defence Technology 10 (2014) 11-118www.elsevier.com/locate/dtDynamic analysis of a guided projectile during engraving processTao XUE a, Xiao-bing ZHANG a.*, Dong-hua cUIba School of Energy and Power Engineering, Nanjing University of Science and Technology Nanjing 210094, Chinab Navy Academy of Armament, Beijing 100061, ChinaReceived 10 December 2013; revised 14 March 2014; accepted 7 May 2014Available online 20 May 2014AbstractThe reliability of the electronic components inside a guided projectile is highly affected by the launch dynamics of guided projectile. Thengraving process plays a crucial role on determining the ballistic performance and projectile stability. This paper analyzes the dynamic responseof a guided projectile during the engraving process. By considering the projectile center of gravity moving during thengravingprocess, adynamics model is established with the coupling of interior bllistic equations. The results detail the stress situation of a guided projectile bandduring its engraving process. Meanwhile, the axial dynamic response of projectile in the several milliseconds following the engraving process isalso researched. To further explore how the different performance of the engraving band can affect the dynamics of guided projectile, this paperfocuses on these two aspects: (a) the effects caused by the different band geometry; and (b) the effects caused by different band materials. Thetime domain and frequency domain responses show that the dynamics of the projectile are quite sensitive to the engraving band width. Amaterial with a small modulus of elasticity is more stable than one with a high modulus of elasticity.Copyright◎2014, China Ordnance Society. Production and hosting by Elsevier B.V. All rights reserved.1. Introductionguided projectile. Jiang and Guo [3] dealt with the linear dy-namic response of a gun, including the effects of projectileGuided projectile is meant to be a precision location strikegravity and acceleration. Wang and Zhang [5] established thesystem and have the excellent accuracy of impact due to thedynamics model of projectile in consideration of the actualdelicate design of the inner electronic components. But if themovement of the projectile and inertial breech. Also, Chu andelectronic components do not work well in the projectile, itsZu [6] and Cordes et al. [7] analyzed various reasons whichaccuracy will be impaired. The dynamics of a guided projec-cause the unexpected projectile vibration, such as the masstile have been observed to cause a large number of electronicsbias, static unbalance and dynamic unbalance.failures in projectile, such as the impact and the separationFrom these researches, it can be known the vibration of theamong electronic components, which are described in Ref. [1].projectile frequently takes place in the barrel. However, theThere have been previous studies about the dynamics of thevibration which could cause the failure of inner electroniccomponents may take place at the moment when the projectileis experiencing loads, especially in a strong transient situation[3-7]. During the engraving process, the band is squeezedE-mail address: zhangxb680504@ 163.com (X B. ZHANG)into the gun bore by the high-pressure propellant gas. BecausePeer review under responsibility of China Ordnance Societyof the stringent requirement of preventing the propellant gasleakage, the diameter of the band around the projectile islarger than the inner diameter of barrel, which is called theLSEVIER Production and hosting by EIsevierradial exceeding中国煤化工has to overcomeMHCNMH Ghtp://dx. doi.org/10 1016/j.dt.2014.05.0032214-9147/Copyright◎2014, China Ordnance Society. Production and hosting by EIsevier B.V. All rights reserved.12T. XUE et al. / Defence Technology 10 (2014) 11-118the resistance R() when it is pushed into the gun bore by thepropellant gas, as shown in Fig. 1. The radial exceeding valueis shown in Fig. 2.pd(). RO.According to the experiments in Refs. [8] and [9], the timeof the engraving process is only about a few milliseconds, theresistance R(t) reaches 123 kN [9], but it drops to slidingfriction instantaneously at the end of the engraving process.The transient resistance is changed to be about 120 kN.However, Jin [8,9] focused on the deformation of the band andneglected the dynamic response of the projectile in theexperiment. Therefore, it is important to investigate the dy-namic response of the guided projectile during the engravingprocess. Meanwhile, since the resistance disappears abruptlyafter the band completely enters the gun bore, it is quiteFig. 2. Partially enlarged drawing of touch between band and barrel.necessary to explore the dynamic response of the guidedprojectile in the milliseconds following the engraving process.engraving dynamic model. Since the pressure on the base ofHence, the purpose of this paper is to study the axial dy-the projectile is generated by propellant gas, the engravingnamics characteristics of the guided projectile during thedynamic model must include the equation of propellantengraving process. The underlying idea for the guided pro-jectile is analogous to the analytic method in Refs. [2], inburning rate and the equation of propellant shape. And thewhich the projectile center of gravity (C.G.) moves backwardvelocity equation and the energy conservation equation shouldbe considered to form the interior ballistic equations.when the projectile is compressed by gas pressure. Jin's one-A lumped parameter model [8] is a simple but useful rep-dimensional engraving model which was established byresentation of the interior ballistic cycle, embodying such as-coupling with the interior ballistic equations was used to gainthe axial engraving resistance. The dynamic response of thesumptions as uniform and simultaneous ignition of the entireguided projectile in the several milliseconds after thepropellant charge. Combustion is assumed to take place in asmoothly-varying, well stirred mixture, and the burning rate isengraving process was researched. The infuences of banddetermined by the instantaneous, space-mean chamber pres-geometry and material on the dynamic response of guidedsure. In this paper, the interior ballistic equations are asprojectile were analyzed, too. This work proposed the theo-followsretical reference for the further research on the failures andreliability of electronics in guided projectiles.(xZ(1+2Z+μZz) Z<12. Dynamic model of the guided projectile duringx,Z(1 +λ,Z) 1≤Z≤Zengraving process1Z≥Zk2.1. Engraving processdZ(“Zmultiple- perforated propellant; e is the burned thickness; Zk isthe relative burned thickness rate at the end of propellantcombustion; dZ/dtis the burning speed of propellant and the. Barrelexperimental data u1 depends on the different kind of pro-pellants; l is the tube length; lvis the ratio of chamber freevolume to bore area; f is the propellant impetus, which is used-00to express the generated eneroy ner kiloram of propellant; W700000000is the mass of prope中国煤化工ressure behindPropellants ignition BandProjectilethe projectile; v is .YHCNMH G the sectionalarea of barrel; θ = KKIS auladauc 1nuex; and φ is a CO-Fig. 1. Schematic diagram of a typical gun and its initial stress.efficient accounting for secondary energy losses.T XUE et al. / Defence Teclmology 10 (2014) 11-11811The force on the projectile is analyzed with the interior250 -ballistic equations, as shown in Fig. 2. The dynamics equationt=5.64ms, R()=228kNis as follows [8- 10].00 t12xEnd of engraving process: Spa() - R(1)2)12where m is the mass of projectile; Spa()is the force on the baseof projectile; R()jis the resistance; x is the projectile0tdisplacement; and pd(t) is the pressure on the base of projectilewhich could be gained by p.3456In order to consider the dynamic loads, Jin's engravingt/msmodel [8] is used to gain the axial engraving resistance. R(t) isdivided into two parts while the band enters the gun bore. OneFig. 4. Resistance on band.is the internal friction of the material, FR, under the dynamicloads and the other is Fp caused by the deformation of band.According to [8,9], the resistance R() formula is as follows:The dynamic model shown in Fig. 3 is represented by thefollowing differential functionR(1)=Fr+ FD3)dx'dwhere FR = Ddx/dt, D = 2ξmwnis the damping coefficient+c+K'x =Spa(1)- R()(5caused by the internal friction of the material Wn =√K/m,Here c = 2ξ mon, is the damping coefficient, where ξ is thewhere K is the stiffness of the band. Fp= Kx, where x is the .projectile travel during the initial process. When the stress ondamping ratio; w'n= √K'/m, where w'n is the natural fre-the band reaches the material shearing yield limit stress Ts, thequency of projectile; K is the stiffness of projectile which isdeformation of the band is plastic deformation. Substitutingdifferent from K.Eq. (3) into Eq. (2), the equation of projectile motion can be3. Result and analysisgained as follows:In this section, the guided projectile during the engravingma+ D+ Kx= Spa(1)(4)process is researched. The infuences of band geometry andband materials on the dynamics of the guided projectile areanalyzed in detail. All the calculations performed are for a2.2. The dynamics of projectileguided projectile with 1 m in length and 130 mm in diameter.And the dynamics of projectile in this paper is relative to theThe model of projectile we shall begin with is very simple.projectile base.We assume that the projectile is a right circular cylinder andall the calculations of projectile dynamics is taken relative to3.1. The dynamics of guided projectile during engravingthe projectile base, which is different from that in Ref. [2]. Weprocessassume that the projectile wall is thick enough so that bulgingis negligible (This is just for ilustration purposes as bulgingTo understand the dynamic response of a guided projectilecan be significant in some projectile designs). This projectile isgenerally, the guided projectile with a typical engraved band isused as a demonstration case in which the material is copper.We could calculate R() via Eqs. (1)- -(4). The gap betweenprojectile and band is neglected so that they move together.0Mass centerof一x0Fn0|中国煤化工十一xYHCNMHG 6Fig. 3. Simple system model of projectile.Fig. 5. Pressure on projectile.114T: XUE e1 al. /Defence Technology 10 (01)11-1180.7外06-2:司0.5一20-E 0.403s 1.st|M量g 1.010.5ms4610/msFig. 6. C.G. velocity rlaive to poectile band during engraving.Fig. 8. C.G. velocity in the first 10 ms.The width of band is 0.025 m, and the exceeding radial valueFig. 10 shows the dynamic friction in 5 ms afer the bandis 0.001 times of the projectile diameter.completely enters the gun bore. Here the efects of tempera-As shown in Figs. 4 ancis about 5.64 ms when theture and relative velocity are igent is set as a constant.re ignored and the friction coeff-completely enters the gun bore, the resistance reachesig. 11 shows the gas pressure.228 kN, and the gas pessre reaches 56.4 MPa. At the end ofDuring the several milliseconds following the engravingthe band engraving process, the resistance drops to 23 kNprocess, as the gas pressure increases, the sliding friction isinstantaneously. According to Fig. 6, although both the gassmall relative to the gas pressure. The C.G velocity relative topressure and the resistance increase sharply, the resultant forceprojectile vibrates fiercely, as show in Fig. 12. The resultantforce on the projectile compresses it so that; location ofshowspwly s.C CC vleil iereaes soAC.G. acelerates to move backwards.G. acceleration increases as the band issqueezed in the gun bore. Yet, large osillations take place atcrease in pressure drives the compression ratio to be a con-the beginning of motion.stant. As shown in Fig. 13, C.G.acceleration decreasesThe resistance drops to sliding friction suddenly when thegradually towards - 300 m/s?.band completely enters the gun bore and the variation inresistance is about 205 kN. In sucha special stress situation,3.2. The efees of dfferent engraving bands onan analysis in the few milnlliseconds after the band enters gunprojectile dynamic responsebore is very important. It can be seen from Figs. 8 and 9 thatthere are huge variations in the proecile response at theIn this sectin, the numerical simulation program of themoment when the band is completely squeezed into the gunprojetile vibration function is modified to ilustrate how thebore. At the same moment, the resistance drops to slidingdifferent width and exceeding radial value affect the projectilefriction abruptly. In the millieconds afteror the resistance dropsdynamic response. The size of an engravingvaried forto sliding friction,maximum C.G. velocity relative totwo difet caes: dfferent widths with tha.ngs: dfferent widths with the same exceedingprojectile base is about 2.9 m/s and the maximum C.G. ac-radial value; :different exceeding radial values with theceleration relative to prijctile base is 10.576 m/s?. Undersame width. The infuence of different band materials on thesuch inertia force and shock, there is a very serious efct onprojectile dynamic response is also researched.the electronic components. The separation and even failure ofFive dfferent width assumptions within the accepted rangecomponents may easily occur in the guided projectile.are analyzed. The assumned widths are 0.021 mm, 0.0mm,0.025 mm, 0.027 mm and 0.029 mm. In this P23 mm,; part, we are50-10000召100500050- |-5 00-50f中国煤化工-10000YHCNMHGFig. 7. C.G. acleration rlaive to priectile band during engraving.Fig. 9. C.G. aceleration in the first 10 ms.T XUE et al. / Defence Technology 10 (2014) 111-11811180140 |2.5-心2.0100自1.5-Nh601.0个/mst/msFig. 10. Resistance after the band completely enters gun bore.Fig.12. Velocity after the band completely enters gun bore.completely enters the bore. As the description in Subsectionare chosen within this range to show its effect on the dynamic3.1, the vibrations during this period following engravingresponses of projectile C.G. The radial exceeding value δ isprocess are fiercer relative to the engraving process. The timeexpressed as a multiple of projectile diameter. As shown indomain response and frequency domain response of the pro-Table 1, the base frequency and its corresponding amplitude injectile C.G. acceleration to different band widths are shown inthe systems with different radical exceeding values are almostFig. 14. From the frequency domain responses, the frequencyunchanged.with high amplitude is mainly concentrated in the frequencyAccording to the two cases, we conclude that the width ofband from 0 Hz to 2 Hz. This frequency band contributes thethe band has a great infuence on the acceleration vibration ofmost energy to maintain the vibration of proectile C.G. Asguided projectile. However, the different exceeding valuesshown in Fig. 14(a)-(e), there are substantial changes in thehave little effects on the dynamic response of projectile C.G.acceleration amplitude. A large band width leads to moreDuring the engraving process, the band is designed to havesubstantial vibrations. This is because wider band has greaterthe functions of preventing the gas from leaking and stabi-engraving resistance than narrower band.lizing the axial position of projectile. So the band materialIn order to seal the gun bore, the diameter of the engravingmust have good flexibility and malleability to keep closeband is larger than the barrel inner diameter. The projectilecontact with the inner wall of the barrel. Lots of materialscould move only if the resultant force on the base of projectilecould be used for the band. In this part, the effects of differentis bigger than the shear force between the gun bore and theband material characteristics on the dynamic response of theband. Therefore, the radial exceeding value plays the crucialprojectile C.G. acceleration are calculated for three kinds ofrole of preventing the propellant gas from leaking. The effectmaterials, such as MC nylon, copper, and steel, which areof radial exceeding value on the dynamic response of guidedcommonly used in the design process. The properties of theprojectile is discussed as follows. During calculation, the bandthree materials are listed in Table 2.width is set as 0.025 m. According to Ref. [1] , theDuring numerical calculation, we assume that the band ismaximum radial exceeding value is less than 0.0025 times ofdeformed if the stress reaches 0.8 times of the material yieldthe projectile diameter to avoid excessively fierce collisionsstrength, which is an empirical value. In the calculation modelmeanwhile the minimum radial exceeding value has to be of the engraving process, the stiffness of band depends on thebigger than 0.001 times of the projectile diameter to preventelastic modulus of material. As shown in Fig. 15, the time10 000 t3005000t250参200导150-5 000中国煤化工81/ms9 10-10 00fYHCNMHG 1Fig. 11. Gas pressure after the band completely enters gun bore.Fig. 13. Acceleration after the band completely enters gun bore.16T. XUE et al. / Defence Technology 10 (2014) 11-118100007500 I2500 t| FreqQ.836Hz Amp2756.4500020002500-25001000t_7500Frequency(a)W = 0.021mm3500r10000 |00.Freq.0.852Hz Amp.3 135.2675002500t2500-营200其1500-2500--5000ooh-7500 |56/ms)10T(b)w = 0.023mm3500| Freqg0 869Hz Amp.3 470.8500-g 25002000t是1500Mws00(C)W = 0.025mm4 0oo| Feg.88SHz Amp.3 766.063 002 soo-1 000|Vv-7 500 |891011246810ms(d)w =0.027mm4000 | Freq0.9Hz Amp.4048.475000--000|\vv0000。中国煤化工(e)w = 0.029mmYHCNMH GFig. 14. Dynamic response of projectile C.G. acceleration to different band widths.T XUE et al. / Defence Teclmology 10 (2014) 11-118117Table 1domain response and frequency domain response of the pro-The base frequency and amplitude of the system with different radialjectile C.G. acceleration in the systems with different bandexceeding values.materials are presented. The characteristic frequencies ofBase frequencyAmplitudedifferent band materials are sucessfully extracted in the fre-0.86953470.84quency domain. The amplitude at 0 Hz shows the inherent0.0015347 1.03constant energy in the system, and the amplitude at 0.88 Hz0.86933470.21shows the energy which maintains the vibration of the pro-000250.8593jectile C.G. As shown in Fig. 15(a)-(C), the dynamic responseof the system with MC nylon contains more constant energyTable 2and less vibration energy in the frequency domain compared toThe material properties of MC nylon, copper, and steel.the systems with the other two kinds of materials. The reasonMaterial Density/Modulus ofPoisson Yield strength/GPafor this is that the modulus of elasticity of MC nylon is smaller(g.cm 3,elasticity/GPathan those of other two materials. Also, the proportion of theMC nylon 1.408.640.290.092energy, which could lead vibration, increases with the increaseCopper8.931180.350.184Steel7.852070.350in modulus of elasticity.n Freq.0Hz Amp.72.0630050H? 200-1(20-Freq0.88Hz Amp.19.043456msFrequency(a) MC nylon00厂| Freg.0Hz Amp.44150|40100当5o-\气20, Freq.0 8Hz Amp.20.6750-t/ms(b) Copper00-sh Freq0.17Hz Amp 25.82| Fre.0.88Hz Amp.22 04。50-o中国煤化工(c) SteelMHCNMH G .Fig. 15. The dynamic response of projectile C.G. in the system with different band materials during the engraving process.18T. XUE er al. / Defence Technology 10 (2014) 11-1184. ConclusionsAcknowledgmentsIn this paper, the dynamics of the guided projectile duringThe research was supported by the Research Fund for thethe engraving process were researched. The time domain andNatural ScienceFoundation .provincefrequency domain responses of the projectile C.G. evidently(BK20131348)，Key Laboratory Fund (Grant No.show the influences of the engraving band geometry size and9140C300103 140C30001), People's Republic of China.material on the dynamic response of the guided projectile.From the results, it can be concluded that the guided projectileReferencesdynamic response is strongly affected by the engraving forceand the band characteristics.[I] Oman J. National Missile Defense - an obligation. USAWC StrategyAfter the band completely enters the gun bore, the resis-Research Project NO.20000320095; 2000.[2] Carlucci D, Cordes J, Moris s, Gast R. Muzzle exit (set forward) efetstance drops sharply. This abrupt resistance leads to an extremeon projectile dynamics. Technical Report ARAET-TR-06003, AD- E403fierce vibration of the guided projectile, and this vibration may082. 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J Ballist 1994;4:24-8.dimensional dynamics of projectile C.G. could be considered[11] Wei H. Projectile design theory. Chapt. 1. Bejing: National DefenseIndustry Press; 1985.in the future work.中国煤化工MHCNMH G