Variable-mass Thermodynamics Calculation Model for Gas-operated Automatic Weapon

JOURNAL 0F CHINA ORDNANCEVariable-mass Thermodynamics Calculation Model forGas-operated Automatic WeaponCHEN Jian-bin(陈建彬), LV Xiao-qiang(吕小强)( Unit No. 77298, Qvjing 655000, Yunnan, China)Abstract: Aiming at the fact that the energy and mass exchange phenomena exist between barrel and gas-operated device ofthe automatic weapon, for describing its interior ballistics and dynamic characteristics of the gas-operated device accurately ,a new variable-mass thermodynamics model is built. It is used to calculate the automatic mechanism velocity of a certain au-tomatic weapon, the calculation results coincide with the experimental results better, and thus the model is validated. Theinfluences of structure parameters on gas-operated device' s dynamic characteristics are discussed. It shows that the modelis valuable for design and accurate performance prediction of gas-operated automatic weapon.Key Words: mechanics ; automatic weapon; variable-mass thermodynamics; gas-operated device; coupling; modeling andsimulationCLC Number: TJ2; 0313Document Code: AArticle ID: 1673-002X(2011 )04-0217-07The research improved the models in references [ 1 -Introduction3], and then applied it to the metal storm weapon sys-The gas-operated automatic weapon acts automati-tem' s ballistic consistency, optimal design of gas-cally by using the propellant gas of high pressure andoperated devices'°. But， obviously, in all refer-temperature from gas hole of the barrel to push the au-ences existing before, it can be found that, the estab-tomatic machine, and the proper use of gunpowder gaslishments of both numerical and empirical models dois greatly important to the dynamic performance of theot consider the variable-mass thermodynamic processautomatic weapons1. Therefore, the study on the dy- between interior ballistics and gas-operated device,namic characteristics of the gas-operated device is veryand the models have too many equations， parameterssignificant for using propellant gas and obtaining favor-and biggish error. In all applied researches, the cou-able dynamic characteristics. Most oversea studies onpling of the interior ballistics and the gas-operated dethe dynamic characteristics of automatic weapons arevice is not considered in the improved model. There-based on the experience methods, such as Bradleyfore, in order to overcome above deficiencies and ex-method，Mamun Rostov method, Brad Gongla W olfplore the methods of accurately predicting the perform-method, and so forth. Domestic research work primari-ance and determining the structural parameters of thely focuses on two aspects. One is introduction of for-gas- operated automatic weapon, by analyzing the ther-eign experience models 2] and establishment of numeri-modynamic process between the barrel and gas-opera-cal models based on the formers(2-3]. By using the nu-ted devices, the variable mass thermodynamic calcula-merical models, many parameters can be solved moretion model, which is more objective and accurately de-accurately ; compared with the empirical models. Thescribing the process of gas-operated automatic weaponother is improvement and application of the models.firing, should be established.中国煤化工YHCNMHGReceived 2011 08-13Biography CHEN Jian-bin(1976- ), male, master, E-mail: jian-bin@ 163. com一217一JOURNAL OF CHINA ORDNANCE, 2011, Vvol.7, No.41Variable-mass Thermodynamicsexceeds a certain value, the reverse gas flow near theModel of Gas-operated Automat-guiding. hole becomes. critical sonic flow. When theprojectile exits the muzze, its motion enters the after~ic Weaponeffect period, and the propellant gas sprays at extreme-1.1 Physical Process and Basic Assumptionsly high speed. For its flow velocity and pressure areThe typical structure of gas-operated automaticvery high, the projectile is still accelerated. With theweapon is shown in Fig. 1. After the hammer hits theincrease of projectile displacement, the velocity of pro-primer, the propellant starts bumning, and the borejectile decreases gradually, and the bore pressure de-pressure increases rapidly. When the pressure at thecreases also. At the end of the aftereffet period, thebottom of the projectile becomes greater than thevelocity of projectile reaches its maximum.squeeze pressure, the projectile begins to cut into theautomaticgas hole gAs chamber piston guides mechanism.ile and accelerates. With the gunpowder combustionand the space behind the projectile increase, the pre-barelssure at the projectile bottom gradually decreases.When the projectile goes over the gas-operated bhole,the propellant gas begins to flow from the gas chamberFig.1 Sketch ol gas-operated deviceinto the guiding hole. For the bore pressure is muchBasic assumptions:larger than the guiding hole pressure in the beginning,1) The classical model is employed to describethe gas flow near the hole appears in a positive criticalthe ballistic process;sonic flow.With the propellant gas flowing into the2) The flow in gas-operated device is a variable-guiding hole increases ，the pressure increases, and themass thermodynamic process with flow-in and flow-out;gas flow near gas hole becomes non-critical sonic flow.3) The heat exchange among the propellant gas,Then, the projectile moves forward continuously, andbarrel and gas chamber is ignored, for the transientthe piston moves backward. When the gas force actingcalculation;on the piston end and the resistant force of the recoil4) The gas-operated device and interior ballisticsspring are equal, the piston speed reaches the maxi-are coupled through the f1ux of propellant gas.mum，and then the bore pressure reduces further.1.2. Computational ModelWhen it becomes 8maller than the guiding hole pres-The variable-mass thermodynamics computationalsure and their ratio does not exeed a certain value,model of gas-operated automatic weapon includes inte-the propellant gas in guiding hole begins to flow intorior ballistic model, gas chamber model and coupled e-the barrel, and the gas flow near the guiding hole be-quations. They are listed as follows.comes reverse non-critical sonic flow. When the ratioEquation of bore pressure:S(I, +l(PL4(1 +2λZ +3u2*)- kSp,0-foc), ψ≤1, l≤L;dppdt={S(i +1)( - kSp,o-fG,),ψ>1, l≤L;(1)-knoL (A- c)端p，ψ>1, l>L .wherepp, s,l,l,f, w,么，z, k, v, Gq, μto, Pe,pressure中国煤化工thickness of thePk, L, n, ψ are gas chamber pressure , cros-sectionalpowderlet velocity, gasarea of barrel, chember length ，bullet displacement,flow, atTYHCNMHGflow cofficient,gunpowder force, charge amount of propellant， gasmuzzle gas pressure, muzzle gas density， berrel-218-CHEN Jian-bin, et al.1 Variable mass Thermnodynamics Calculation Model for Gas-operated Automaic Weapon .length, change index, percentage of gunpowder fired,specific heat ratio, chamber volume, initial volume ofrespectively. A and C are constants related to thechamber, piston ' s cross- sectional area, piston velocitychange index. x，λ and μ are shape coefficient of gun-and atmospheric pressure, respectively.powder.Flow equation in piston clearancel2Equation of proportional buming rate[7] :,0,Pq=Po;(2)Pq>Po,Equation of geometric combustion'7) :where G,，AS%, μq，γ and uq are gas flow in pistondψ[x(1 +2λz +3uZ2 )di，ψ≤1， (3)clearance, gap area of piston, flow coefficient of gasdl0ψ>1.chamber, specific heat ratio, gas internal energy per u-Motion equation of bullet'"] :nit mass , respectively, K。 is the constant related to y.=0.d_(4)Mass equation of gas in chamberl2] :dm。Velocity equation of bullet"):mg=G。-C,(11)dv_Spp.5)where m, is the mass of propellant gas in chamber.dt φmMotion equation of piston:where中is the secondary power coefficient, m is theF≤0;bullet mass.Mass equation of gas flowed out through guidingdi“一((p,-p.)S,-Kx.-B)， F>0,l m,'hole:(12)η= f G,dt,(6)where K, x，B, m are buffer spring sifness, pistonwhere η is the gas mass flowed from barrel.displacement，actuator friction resistance and pistonEquation of reduced diameter of chamber' s freemass, respectively, and F =(P、-p.)S, -Kxn -B isvolume' !the total force applied to the piston.Displacement equation of piston[2) :l∞g=-[w。-台(1-ψ) - awv]， (7)lx。where W。is the initial volume of chamber, δ is thed=(13)powder density, a is the residual volume.Mass conservation equation in gas chamber:Density equation of gunpowder gas inbarrel:dpp0l1,hole.Internal energy equation of unit gas mass in cham-where Pp is the gas density of gunpowder in barrel.Equation of gas pressure in gas chamber(2]:Pq =Pa;0，mq =0;Pa _u。S.(15){- -([6-6-)-2.s.]. p,>P.中国煤化工',≠0.((培)CouplingYHCNMHG(9)The interior ballistics and gas-operated device arewherepq，r, Vq, Vqρ，Sg, U, P. are bore pressure ,coupled with the flow equation.-219一JOURNAL oF CHINA ORDNANCE, 2011, Vvol.7, No.4l≤h; .usS,K。√PP,I>h, p、≤Pr;平，C,=uS。.0(影)一(台)“小1>. ,.p.en.(16)-uoS,告。(1)“一()小l>h,印.≤p,l,P,≤5p.where, Huo and s, are the hole' s flow coficient and 0- reliable.pening area, respectively, andξ= (y+1)内0-82 Model Verification and CalculationResults一- experimental、--- theoretical value2.1 Model VerificationFig.2 shows the experimental ut curve of auto-matie mechanism of an automatic weapon. In order to5t/msverify the crretness of the model, it is adopted to cal-Flg.3 1 v- in inital recol phaseculate the dynamic parameters of the weapon, by usingfourth-order Runge-Kutta method in MATLAB. And2.2 Calculation Results Analysisthe variation of the recoil speed of automatice mecha-2.2.1 Flow Flux at Gas-operated Holenism in the initial phase is obtained, then, it is com-The flow fAux at gas hole of a certain gas-operatedpared with the experimental result, as shown in Fig.3.automatie weapon is shown in Fig. 4. When the bulletIt can be seen that the theoretical speed is zero in thatreaches to the gas-operated hole, the bore pressure isphase, as the efect of recoil foree acting directy onrelative high, while the pressure in gas-operated devicehe bottom of projectile on the speed of automaticis only one atmosphere, so the positive critical flow a-mechanism is ignored. When the propellant gas pushespears at the hole, and the flow flux increases tthe piston and then causes the automatic mechanism to1. 16 kg/s instantly; then the flow fux begins to demove backward, the calculation result coincides withcline. When the bullet leaves the muzzle, the propel-the experiment result better, and the maximum recoillant gas sprays out quickly, and the bore pressurespeeds are accordant. It shows that the variable-massdrops rapidly, so the positive n-critical flow appearsthermodynamic calculation model of gas-operated auto-at the hole. When the bullet continues to move, thematic weapon established in this paper is accurate and1.5r1.0F司旨0.s-中国煤化工一-1050.050.100.15FHCNMH Gt1swmsFlg.4 Gas fnuxFig.2 v-4 curve of automatic mechanism-220 一.CHEN Jian-bin, et al. / Variable -mass Thermodynamics Calculation Model for Gas-operated Automatic Weaponbore pressure declines further, and then the pressure in1000gas-operated device becomes higher than the bore pres-800sure, so the reversed non-ritical flow appears at thehole and the maximum flow flux is about 0. 18 kg/s.一coupling factors not自With the propellant gas flows into the chamber, the: 400)taken into accout--- coupling factons takenpressure in gas -guiding device declines gradually, andinto accout200the flow flux decreases to zero finally.2.2.2 Influence of Coupling on Chamber Pressuret/msand Muzzle VelocityFig.5 compares the bore pressures consideringFig.6 Infuence of coupling energy on bullet speedand not considering the coupling effect. It can be seenon the pressure in gas-operated device and the maximumthat the difference of the bore pressures is less at therecoil velocity of automatic machines are shown inbeginning and end of the phase from the bullet movingFig.7 and Fig. 8, respectively. When the initial vol-to the gas hole and the ftereffect period, while theume of the gas chamber is 1.7 x10-° m' ，the theoreti-difference is relatively large in the middle of thecal maximum pressure is 23. 7 MPa, and the maximumprocess. When the bullet exits the muzzle, the pres-recoil velocity of automatic machine is 8.61 m/s. Ifsure difference reaches the maximum of 6.7 MPa.the initial volume is2.2x10- m' or2.7 x10 6 m',Fig. 6 shows the projectile velocity curve without thethe maximum pressure is 21.4 MPa or 19.7 MPa, andeffect of coupling. It can be seen that the influence ofthe maximum recoil speed is 8. 38 m/s or 8.24 m/s.coupling energy on the velocity is obvious, and the in-Thus, it can be seen that, with the initial volume' s in-fluence on the shell leaving speed is about 6 m/s. Atcrease, the pressure in gas chamber reduces and thethe end of afereffect period , the influence on the speedpressure peak delays and the maximum recoil speed re-reaches the maximum of 16 m/s. Thus, it can be seenduces also. In addition, the acceleration of pressurethat the propellant gas flowing into the gas-operated de-decreasing reduces. It shows that the initial volume ofvice has a certain influence on the bore pressure andgas chamber has impact on the bore pressure, the ap-projectile velocity, and the influence of coupling ener-pearance time of maximum pressure and the velocity ofgy on the bore pressure and projectile velocity shouldautomatic machines. In other words, in the gas-opera-be considered when solving the interior ballstics andted device design, the pressure, the emergence time ofthe dynamics of gas-operated device.maximum pressure and the recoil speed can be adjustedby changing the initial volume of gas chamber.- - coupling factors not3C--- coupling factors takenofinto acout---V=1.7x10* m'i =2.7x10- m'复0叶108.02.5Fig.5 Influence of coupling energy on bore pressuret/ms _2.2.3Infuence of Initial Volume of Gas-operatedFig.7 Infu中国煤化工hamber pressureCNMHGDevice2.2.4 Gap's Effect on Gas-operated DeviceThe influences of the initial volume of gas chamberThe influences of gas chamber' s gap on the auto--221一JOURNAL OF CHINA ORDNANCE, 2011, Vol.7, No.4----V =1.7x10+ m'. V=22x10+ m2V=2.7x10* m'一- AS-1.0 mm。V/msmFlg.8 Influence of inital volume on automatieFig.10. InMuence of clearance on automaticmechanism speedmechanlsm speedmatic machine recoil velocity and gas chamber pressureter on the gas chamber pressure and the recoil velocityare shown in Fig. 9 - 10，respectively. If the gapof automatic machine are shown in Fig. 11 - 12, re-measures 0.1 mm, the maximum pressure in the gasspectively. With the increase of hole' 8 diameter, thchamber is 23. 7 MPa, and the maximum recoil speedpressure in gas chamber and the recoil speed of auto-of automatic machine 8.61 m/s. If the gaps are 0.5matic machines increase. When the diameter of gasmm and 1 mm respectively, the maximum pressures arehole varies around a smaller value, the presure of gas23.2 MPa and 21.4 MPa，and the maximum recoilchamber and the maximum recoil velocity are morespeeds are 8.48 m/s and 8. 18 m/s, respectively. Isensitive.shows that the gap less than 0.5 mm influences on the30-gas chamber pressure and maximum recoil speed a lit---* d 3.0 mm" d=3.5 mmter. While the gap is increased to 1 mm, the pressure一do4.0mm一d=4.5 mmof gas chamber reduces by 1. 8 MPa compared with the曼|gap of0.5 mm, and the maximum recoil speed reducesofby0.3 m/s. It shows that the gap variance between0.5 mm and 1 mm has obvious effect on the pressure ofgas chamber and maximum recoil velocity. However ,the emergence time of peak pressure keeps no change ,t/mswhich indicates that the gap design as between 0.1 mmFig.11 Infuence of clearance on gas chamber pressureand 0.5 mm is appropriate.30p*--- d=3.0 mm--- 3.5 mm---- AS,=0.1 mm-de A4.0 mmAS.=0.5 mm一一d=4.5 mm20-一AS,-=1.0 mm10-2/msImsFig.12 Infuence of clearance on utomaticFig.9 Influence of clearance on gas chamber pressure2.2. 5 Influence of Hole' s Diameter on Gas-operated3C中国煤化工Device.MYHCNMHGThe influences of the gas-operated hole ' s diame-1) Analyzed the variable-mass thermodynamic一222一CHEN Jian-bin, et al. 1 Variable-mass Thermodynamics Calculation Model for Gas-operated Automatic Weaponprocesses of gas-operated automatic weapon, a varia-Beijing: Weapon Industry Press, 1988: 456 - 464. (inble-mass thermodynamics calculation model couplingChinese)the interior ballistics and gas-operated device is estab-[3] LIAO Zhen-qiang, WANG Tao, YUE Shi-hai. The calcu-lation method of gas dynamics of weapon[ M]. Beijing:lished and verified.Weapon Industry Press, 1988 : 221 - 228. ( in Chinese)2) The bore pressure and bullet velocity a[4] NI Zhi-jun, ZHOU Ke-dong, HE Lei. Consistency re-solved by using the model, and the trend of bore pres-search of interior ballistico performances of the metal stormsure is analyzed. It shows that the coupling factorweapon eystem with side powder chambers[J]. Acta Ar-should be considered in the calculation of the internalmamentani, 2005, 9(5): 595 -599. ( in Chinese)ballistics and dynamics of gas chamber accurately.[5] HAN Xiao-ming, BO Yu-cheng， WANG Hui-yuan, e3) The established model can be used to solve theal. Optimal design of gas-guiding device structure param-influences of the structural parameters on the gas cham-eter in interally-powered gatling weapon system [ J ] .ber pressure and the velocity of automatic mechanism.Journal of Gun Launch & Control, 2008, (2): 50-53.4) The model can also be used to quantitatively( in Chinese) .[6] WANG Wan-qing. Analysis on dynamics and optimizationanalyze the change of flow flux at the gas-guiding hole.of model M60 general purpose machine gun of the 7. 62mm caliber[D]. Nanjing: Nanjing University of ScienceReferencesand Technology, 2007. ( in Chinese)[1] GAN Gao-cai. Dynamics of automatic weapon[M]. Bei-[7] Compile Group of Infantry Automatic W eapon and Designjing: Weapon Industry Press, 1990: 26 - 33. ( in Chi-of Ammunition. Manual of infantry automatic weapon andnese) .design of ammunition[ M ]. Beijing: National Defense In-[2] LU Jia-peng. Gas dynamics of automatic weapon[ M].dustry Press, 1977: 39 -84. (in Chinese)中国煤化工YHCNMHG一223-