667. Design and research of a laser trainer with all the functions of the G-36

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1 667. Design and research of a laser trainer with all the functions of the G-36 A. Fedaravičius, L. Patašienė 2, M. Ragulskis 3, E. Sližys 4, A. Survila 5, 3, 5 Kaunas University of Technology, Institute of Defence Technologies Kęstučio str. 27, 4432 Kaunas, Lithuania 2, 4 Kaunas University of Technology, Kęstučio str. 27, 4432 Kaunas, Lithuania E-ail: algiantas.fedaravicius@ktu.lt, 2 laia.patasiene@ktu.lt, 3 invydas.ragulskis@ktu.lt, 4 egidijus.slizys@ktu.lt, 5 arvydas.survila@ktu.lt (Received 2 July 20; accepted 5 Septeber 20) Abstract. Rifleen trainers are effectively applied for the training of ared forces, police and shooting athletes. However, the training quality directly depends on the perfection of trainers as well as their functional features. Trainers should qualitatively develop the skills of correct leveling of the G-36 to the target, represent probable cobat situations and reproduce the process of single shots and shot series. This research work presents the theoretical and experiental investigation of the pneuatic drive for recoil iitation of the autoatic gun G-36 and its eployent in the laser rifleen trainers. Keywords: trainer, shot, recoil, iitation, pneuatic, echaniss, dynaics. Introduction Lately laser trainers have been effectively used in the training process of rifleen and sportsen. However, the ajority of trainers have neither real recoil nor sound iitation systes. The siulation trainers are used first for the foration of the new conscripts and then to train soldiers to the ore experienced one (Fig. ). 558 Fig.. Place of shooting laser trainer G-36 For this reason the objective of this work is to investigate the recoil of the autoatic rifle under single and serial shooting regies and their interaction with a shot so that training G-36 could be developed with a coplete recoil iitation. Recoil is a backward oveent of a rifle when it is fired up. It sees to as that there is quite a difference between recoil and kick. The gun recoiled, and we got a kick on the shoulder. The recoil is echanical, while the kick, or at least the effect of it, is ostly physical and psychological. The aount of kick resulting fro the recoil force applied by G-36 is largely dependent on the weight and conforation of the shooter, whether he holds the gun tightly or loosely. The location and shape of the shooter s bones and the texture of his flesh sees to have a big effect in soe cases. The recoil consists of three parts []. The first is the reaction, which

2 accopanies the acceleration of the bullet fro a state of rest to the velocity it possesses when it leaves G-36, that is, to its uzzle velocity. The second is the reaction, which accopanies the acceleration of the powder charge in the for of gas to a velocity in the order of half the uzzle velocity of the bullet. The third is reaction due to the uzzle blast, which occurs when the bullet leaves and releases the gas, which rushes out and gives the sae kind of reaction or push that propels a rocket or a jet plane. The effect of the secondary recoil is iniized by aking grooves at the end of the G-36 barrel. Outgoing gas dispersed and it has no great ipact on the gun otion when it is fired. Therefore, G-36 recoil will be further analyzed without taking into account the ipact of gas. Several pneuatic drives for recoil iitation developed by the authors we successfully applied in laser trainers [2,3]. In this paper the dynaics research of one way operation pneuatic drive for the training G-36 is presented. One way operation pneuatic drive for the G-36 recoil iitation Pneuatic drive of one way operation can be used very effectively for all shooting regies recoil iitation in laser training G-36 for rifleen (Fig. 2). In this case pneuatic drive of one way operation consists of a lock echanis, which operation is ensured by pressure pulses of copressed air supplied though the ain pipeline. As it is illustrated in Fig. 2, the copressed air fro the ain pipeline flows to the chaber of pneuatic cylinder 2. Under the action of copressed air on piston 3 the latter oves to the right thus copressing spring 4. After switching the valve the cylinder chaber is connected to the atosphere and pressure it starts dropping and the piston under the spring action is shifted to the other side position. Fig. 2. One way operation pneuatic drive schee: ) valve, 2) pneuatic cylinder, 3) piston, 4) spring The operation of one way drive is expressed by the following equation [6]: ( p p ) F c x c x P ɺx = ɺ a 2 () here c, c2 - coefficients of proportionality. The resultant of all acting forces with the exception of air pressure force is as follows: P = ± P ± (2) 0+ P P2 here P 0 - the force due to initial copression of the spring, P - friction force, P 2 - the force of resistance to otion. The ethodical calculation of one way operation pneuatic drive is presented in [5, 6]. In the case under investigation the dynaics of training G-36 when its lock is affected by the pulses of copressed air was analyzed. Dynaical odel of the investigation case is shown in Fig

3 The plane otion of the training weapon G-36 at the oent of a shot iitation is described by the atheatical odel where the influence of the oveent of the gunlock iitation echanis during firing is evaluated. The force F(t) (air pressure) initiating recoil in a training G-36 first of all akes the lock ove when the influence of recoil is transferred to the gun body. The gunlock iitation echanis oving inside the G-36 influences the oveent of the gun during firing. In order to adjust the atheatical odel in question the forces acting on the gunlock iitation echanis and the training weapon have to be deterined. Fig. 3. Dynaical odel of the training G-36 The plane otion of the training weapon G-36 at the oent of a shot iitation is described by the atheatical odel where the influence of the oveent of the gunlock iitation echanis during firing is evaluated. The force F(t) (air pressure) initiating recoil in a training G-36 first of all akes the lock ove when the influence of recoil is transferred to the gun body. The gunlock iitation echanis oving inside the G-36 influences the oveent of the gun during firing. In order to adjust the atheatical odel in question the forces acting on the gunlock iitation echanis and the training weapon have to be deterined. The piston of the gunlock iitation echanis oves along axis x. The equation describing piston oveent will depend on its position in this axis. The coordinates of the piston are (x,0). The following four cases will be considered: ) when x v< x < xd, then the equation describing oveent of the piston: 2) ɺ x c sign x x F t (3) ( ) () + ɺ = here sign( xɺ ), =, 0, kai xɺ kai xɺ kai xɺ > 0 < 0 = 0 At point B the gun will be ipacted by force sign( x ) c ɺ, and at point E the gun will be ipacted by force k x. When aking the equation describing the oveent of training weapon, the Coriolis and centrifugal forces are not evaluated because the training G-36 angular 560

4 velocity in the previously researched odel is < 2 rad/s (when 3 shots in a row are siulated). The equations describing the oveent of training weapon are as follows: sign( xɺ ) x = F() t + c sign( xɺ ) cosϕ x cosϕ + F + c sign( xɺ C ) sinϕ x sinϕ ( s sinϕ + z cosϕ) FDy ( s cosϕ z sinϕ) r( cosϕ w sinϕ) c sign( xɺ ) w k ɺɺ x + c x ɺɺ = FDx y ɺɺ = FDy (4) Iϕɺɺ = FDx + + FC x w 3) when x k< x < xv ɺ x c + c sign x x F t (5) ( ) ( ) ( ) () + ɺ 2 2 = At point B the gun will be ipacted by force( c c ) sign( xɺ ) +, and at point E the 2 weapon will be ipacted by force( k 2) x. Now it is possible to write the differential equations of weapon oveent: ɺɺ x x ɺɺ = y ɺɺ = Iϕɺɺ = + FC + ( c + c ) sign( xɺ 2 ) + ( k 2) x = F() t F + ( c + c ) sign( xɺ Dx 2 ) cosϕ + ( k 2) x cosϕ F + F + ( c + c ) sign( xɺ Dy C 2 ) sinϕ + ( k 2) x FDx ( s sinϕ + z cosϕ) FDy ( s cosϕ z sinϕ) + ( r cosϕ w sinϕ) ( c + c ) sign( xɺ ) w ( k ) 2 2 sinϕ x w (6) 4) when the piston hits the left edge at point E, the gunlock iitation echanis velocity before the ipact is xɺ, after the ipact Rs( xɺ ), here R s coefficient of restoration, 0<R s<. It is assued that the coefficient of restoration equals 0.56 (steel-to-steel ipact). The projections of change of the G-36 velocity will be as follows: ( + R ) xɺ a xɺ = cos( ϕ) ( + Ra) xɺ yɺ = sin( ϕ) Now, the forces ipacting the weapon at points C and D are evaluated: F = ( + ϕ + ϕ ) ( ɺ + ɺ + ϕϕɺ ϕϕɺ C - kc y r sin w cos L cc y y r cos - w sin ) F = ϕ + ϕ ɺ+ ɺ + ϕϕɺ + ϕϕɺ Dx - k Dx x s cos z sin L3 cdx x x s sin z cos F = - k y s sinϕ - z cosϕ L c yɺ + yɺ s cosϕϕɺ + z sinϕϕɺ Dy Dy 2 Dy ( ) ( ) ( ) ( ) (7) (8) In this case the differential equations of G-36 oveent will be the sae as in Eq. (6). When the piston hits the right edge at point B, the change in training G-36 velocity, the forces acting on the weapon at points C, D and the differential equations of training weapon oveent are represented by Equations (4), (7) and (8). Due to structural qualities of the weapon, it is assued that the restoration coefficient R s equals 0. Coparative analysis of theoretical and experiental research results of the developed training G-36 was perfored. As it is observed 56

5 fro dynaical characteristics of the G-36, the results of theoretical and experiental research are in good agreeent (Fig. 4). a) b) c) Fig. 4. Teporal characteristics of training G-36: a) - acceleration, b) - velocity, c) displaceent Laser trainer with all the functions of the G-36 The schee of the laser trainer with all the functions of the G-36 is presented in Fig. 5. The laser trainer consist fro: training rifle G-36, 2 IR laser, 3 recoil iitation echanis, 4 the shots sound iitation systes, 6 copressed air supply syste, 7 coputer projector, 8 video caera, 9 target screen, 0 laser bea tracking syste, coputer, 2 onitor, 3 printer. During the teaching process, the training rifle with a ounted IR laser 2 and recoil iitation echanis 3 iitates single shots and shot series. The control block 5 synchronically controls the shot sound iitation 4 and the copressed air supply systes and transits the inforation about the shooting regie to the personal coputer. The projector 7 projects the targets on the careen 9 and the inforation about the shooting process (the trajectory of weapon oveent, sight situation at the oent of shooting, target hits, etc.) is received by the video caera 8 and is transitted to the laser bea tracking syste 0, which is connected to the personal coputer. The shooting process, hitting results and the statistical data are visualized on the coputer onitor in real tie. With a riflean laser trainer designed in this way it is possible to conduct the whole training cycle of the riflean fro initial instruction to full preparation and to aintain already acquired shooting skills. It has been proven in practice that it is a very effective training tool which allows not only to econoize valuable recourses but also to iprove the quality of training as well as reduce its duration. Laser trainer G-36 in a practice roo is shown in Fig Fig. 5. Functional schee

6 Fig. 6. Training G-36 in a practice roo Conclusions The article presents a theoretical and experiental investigation of planar otion of recoil of the training G-36 when it is fired in single shots and shot series. The dynaical odel and differential equations of the training G-36 were constructed. Differential equations for planar otion of trainer G-36 were coposed and solved by using Runge Kutta algorith [5] in conjunction with MATLAB software. The dependencies were obtained that describe the otion of training G-36 in tie (acceleration, velocity, displaceent). The results of experiental investigation fully validated the data obtained during the solution of the atheatical odel. It was deterined that pneuatic pulse drives with forced control of operating conditions are the best choice for iitating recoil of sall ars. The structural synthesis of the training G-36 with full siulation of single shots and series of shots was accoplished and successfully used for the defense and sport institutions. References [] Hatcher J. S. Hatcher's Notebook: Standard Reference Book for Shooters, Gunsiths, Ballisticians, Historians, Hunters & Collectors. The Telegraph Press. Harrisburg, 957, p [2] Fedaravičius A., Ragulskis M., Sližys E., Survila A. The dynaics of the one-way pneuatic drive for training weapons // Journal of Vibroengineering / Vibroechanika, Lithuanian Acadey of Sciences, Kaunas University of Technology, Vilnius Gediinas Technical University. Vilnius: Vibroechanika. ISSN , Vol. 2, no. 3, p [3] Fedaravičius A., Ragulskis M., Sližys E. Theoretical Investigation of Recoil of Rifle under Gunlock Motion Influence. Transport Means 2004 : Proceedings of the International Conference, 2004, Kaunas: Technologija, ISBN , p [4] Ashavskij A. M., Volpert A. J., Scheinbau Power ipulse systes. Moscow: Maschinostroenije, 978, 200 p. [5] Papakostas S. N., Tsitouras Ch. Cheap Error Estiation for Runge - Kutta Methods. SIAM J. Sci. Coput., 999, V. 20, p