BENZKOFER DYNAMIC ANALYSTS OF A HAND-HELD WEAPON PHILIP D. BENZKOFER U.S. Army Armament Research, Development and Engineering Center Close Combat Armaments Center Picatinny Arsenal, NJ 07806-5000 INTRODUCTION Substantial internal pressures are developed by the propellant burning during firing of the M9 pistol. These pressures exert high force loads on the components of the weapon. In particular, the loads imposed upon the locking blocks and pistol slide are extrene. ‘These extreme loads have caused danage to componentry as evidenced by broken parts. Safety then becomes an issue. In light of these considerations a dynamic analysis of the pistol and its critical components has been deemed valuable, both in an immediate sense and also as a basis for any further analysis. THE WEAPON SYSTEM System Definition In order to address the analysis of the weapon a brief description of the weapon is relevant. The M9 pistol is a semiautomatic, magazine-fed, recoil operated, double action pistol, chambered for the M9 cartridge [1]. The weapon system is shown in Figure 1. The components of the weapon are shown in figure 2. A brief discussion of the major system components follows. Slide Assembly. Houses the firing pin, striker, extractor, and cocks the hammer during the recoil cycle. 2. Barrel Assembly. Houses the cartridge for firing and directs the projectile. Locking blocks lock the barrel in position during firing. 299BENZKOFER Figure 1. 49 pistolBENZKOFER 3. Recoil Springs and Recoil Spring Guide. Absorbs recoil and returns the slide assembly to its forward position. 4, Receiver. Serves as a support for all major components. Controls the action of the pistol through the four major components, 5. Magazine, Holds 15 cartridges in place for feeding and chambering. System Operation The M9 pistol has a short recoil system utilizing a falling locking block. Upon firing, the pressure developed by the propellant gases recoils the slide and barrel assembly rearward, After a short run, the locking block will stop the rearward motion of the barrel and release the slide which will continue in rearward motion, The slide will chen extract and eject the fired cartridge case, cock the hammer and compress the recoil spring. The slide moves forward under recoil spring pressure, feeding the next round from the magazine into the chamber. The slide stop holds the slide and barrel assembly open after the last round has been fired and ejected. The pistol is disassembled as follows: I, Clear/unload the pistol. 2. Allow slide to return fully forward. 3. Hold pistol in right hand with muzzle slightly elevated. With forefinger press disassembly lever release button and with thumb, rotate disassembly lever downward until it stops. 4, Pull the slide and barrel assembly forward and remove. 5. Slightly compress recoil spring and spring guide, while at the same time lifting and removing recoil spring and guide. Allow the recoil spring to expand slowly. 6. Separate recoil spring from spring guide. 7. Push in on locking block plunger while pushing barrel foward slightly. Lift and remove locking block and barrel assembly from slide. Weapon system data is shown in table 1 below (1]. 301BENZKOFER Table 1. M9 system data caliber... System of Operation. Locking system.... Length...» Width. Height. s..cseeeseeeee Weight (w/15 round magazine). Weight (w/enpty magazine. sie++960 gr (33.86 02.) Barrel length.+...++ peppogeu ae seee-125mm (4.92 in.) Rifling. :R.H., 6 groove [pitch 250mm (approx 1 turn in 10 in.)] Muzzle velocity. +375 meters/sec (1230.3 ft/sec) Muzzle energy.-...++- 569.5 newton meters (420 ft Lbs) Maximum effective range. 50 meters (54.7 yards) Front Sight..sssseeerees blade, integral with slide Rear Sight.seseseeeeeee tssssnotched bar, dovetailed to slide Sight radius. +++158mm (6.22 in.) Safety features...... anbidextrous safety - firing pin block ssssshelps prevent accidental discharge +++Staggered, 15 round capacity ‘sheild open upon firing of last round «plastic, checkered seeeeeee9 % 19mm (9mm NATO) short recoil, semiautomatic -falling locking block seeee217mm (8.54 in.) +38mm (1.50 in.) feeeee140mm (5.51 in.) ss 1145 gr (40.89 02.) Hammer (half cock). Magazine. Slide. Grips... 302BENZKOFER A schematic model of the pistol depicting the bodies or components of the system is shown in figure 3. The ground system, or body 1, is required by the computer code as an Inertial Refesence Frame (IRF) from which all other component measurements are made. This system then is an absolute one, In this particular model body 2 is defined to be the pistol Stock, or the receiver. The connectivity between bodies 1 and 2 is Fepresented by @ spring-damper element, which has a spring force and spring damping effect on connecting bodies. In actual application this spring rate is very rigid and represents the soldier's resistance to the pistol moving in his or her hand, with a large damping force existing. The spring-damper force between bodies 1 and 2 can be adjusted, then, to evaluate the damping effects for various coefficients. The third body is the locking block, which rotates at the connection to the barrel, and the barrel is defined to be body 4, Body 5 is defined as the pistol slide. At initial position, che lugs of the locking block are upright and essentially locked to body 5. .For the purpose of modeling, the weapon cycle is divided into phases, each phase representing a unique configuration/ condition of the weapon. The equations represnting a specific phase are unique to that phase. For the M9 pistol, 7 phases are identified. This is not to say that other phases could not be considered, but rather that based’ upon the assumptions and complexity of the model, a specific number of phases are required to adequately represent the system. Phase 1 represents the firing of the pistol, and the time for this phase is the in-bore time of the projectile. At this point phase 1 1s completed and phase 2 begins. At this point the projectile has left the barrel and the barrel and slide are still locked up. When the lugs of the locking block have moved a distance of approximately one fourth inch they align with slots in the slide and are free to move downward. Phase 2 ends at this point of initial lug movement and phase 3 begins. Phase 3 represents the recoil motion of the slide to the point of impact with the receiver. This motion is approximately 2 inches. Phase 4 represents the impact of the slide and receiver. This is modeled utilizing a spring-damper element with a high spring and damping rate. Phase 5 is the beginning of counterrecoil. This phase brings the slide back to the position where the locking lugs of the locking block are free to move upward and lock up the barrel and slide. Phase 6 represents the motion of the slide back to its battery position. At the tine it reaches battery position, the slide has velocity and impacts the receiver. Phase 7, then, Tepresents the damping out ‘of the slide motion and eventual static position of the weapon system. These 7 phases, then, represent one cycle of the pistol motion. ‘The dynamics are generated and solved by Lagrangian formulations. The driving force for the system is the pressure-time history for the round and the specific data is that for ammunition FNB83L-002-037, with a peak pressure of 35K psi. The results of the analyses are discussed in the following section, The data for the mathematical/computer model is shown in table 2 below, these being the weights of each body, or component, {ts Initial position as measured from the IRF, spring data and connectivity between bodies. 303yeaaeg - y KpoaBENZKOFER Table 2. Data for M9 computer model Component Weights: Body 1 - Ground Body 2 - 1,018 lbs Body 3 - 0,045 lbs Body 4 - 0.282 Ibs Body 5 - 0.730 lbs Body 6 ~ 0,018 Ibs Spring Identification: Recoil spring : Slide - Locking Block; k= 3.08 lbs/inch, c=0.0 Impact springs: Ground - Receiver; man - weapon interface k = 15000 Lbs/inch, ¢ = 10.06 Lb-sec/inch Barrel - Receiver: stop barrel motion k = 5000. Ibs/inch, c = 0.0 Lb-sec/inch Slide - Receiver: end of recoil k = 10000. Ibs/inch, ¢ » 8.218 lb-sec/inch Slide - Barrel: pickup of barrel in c recoil k = 5000. 1bs/inch, c = 0.0 1b-sec/inch Slide - Locking Block/Receiver: end of svcle k = 5000, Ibs/inch, c = 0.0 lb-sec/inch Connectivity Translational joints: between bodies 2 and 3 between bodies 2 and & Rotation joint : between bodies 4 and 5 305BENZKOFER WEAPON SYSTEM MODELING In order to simulate the motion of a weapon system, such as the 49 pistol, several steps are necessary. The first step is to develop a mathenatical model of the system which when computerized will reflect the actual motion of the system. The computer model details the mathematics for each defined component of the system. The motion will be quantified in terms of each component's displacement, velocity and acceleration. A dynamics computer code is utilized to generate and solve the equations of motion describing the pistol [2]. Essentially a set of rigid body dynamic equations are generated based upon the given generalized coordinates for each rigid body. In order to assemble 2 set of equations which account for all che defined components of the pistol, the connectivity between components is also defined. The external es acting upon the system ar defined in order to complete the model A pressure versus time history for the M9 round of ammunition is given as this extecnal force for the model. The equations of motion generated Beg thie te, q oo ot is the kinetic energy (translational and rotational) is the generalized coordinates to be defined is the set of external forces acting on the system the set of Lagrange Multipliers [4] associated with e constraints imposed on the system. The equations of constraint are of the form 4,0) = 0 These equations represent the mathematical description of constra: notion, such as imposing or allowing only translation between bodies of the systen. These equations cf constraint are then appended to the tions of motion. This model, then, can be exercised to obtain the dynamic motion for given parameter changes such as recoil spring race and pressure versus time history. The results of these analyses wil provide the input necessary for a dynamic stress analysis to determine Stress levels experienced by the pistol during a firing situacion. These analyses also provide the basis for any future redesign efforts directed toward improving pistol performance and extending its useful field life. The details of the model are provided below. 306BENZKOFER DYNAMIC SIMULATION The author has had significant experience not only in the formulation of dynamic equations of motion for rigid bodies and in particular weapon and armament systems, but has developed a systematic methodology for the automated generation of these equations for a special class of mechanisms (4]. This development has given the author an excellent background and basis for utilization of more recent general and powerful codes (2]. This code is utilized in [5] through [11]. The dynamics for the subject analysis utilizes this dynamics code. The motion of the weapon system is initiated when the pistol is fired. The external force on the system is the propellant burning, which drives the projectile down the rifled barrel and at the same tine exerting a rearward force on the barrel. Although the projectile is not denoted on Figure 3 as one of the defined rigid bodies, its displacement, velocity and acceleration ate shown in figures 4 through 6, with units as shown. The motion represents that for the in-bore cycle, with a time of approximately .5 millisecond. All referenced bodies from this point will be from figure 3. The motion depicted in the figures will represent that of the identified body for the entire weapon cycle from firing to return to initial position. The receiver motion, body 2, is shown in figures 7 through 12. The receiver displacement is shown in figure 7. The units of displacement are inches and time is shown in seconds. Key events are denoted on the figures. These events are specifically projectile exit, barrel and receiver impact, slide and receiver impact, end of recoil, pickup of barrel in counterrecoil, impact in counterrecoil and finally rest position. The actual recoil motion in figure 7 is slight. This is due to the fact that the spring-damper between the ground reference frame and the receiver as show in figure 3 is relatively rigid (see Table 2). The velocity of the receiver is shown in figure 8. The units of motion for velocity are as shown, inches per second. As would be expected from viewing the displacement curve, the velocity is relatively low. Acceleration of the receiver is shown in figure 9. Units of acceleration are inches per second per second, The angular motion of the receiver is given in figures 10 through 12, Angular displacement is given in radians, angular velocity in radians per second and acceleration in radians per second per second. Impacts are denoted on the figures and in addition to the above include the pickup of the slide by the barrel during counterrecoil. The values of the spring constants for the impact springs have significant effects on the time and the angular displacement (see Table 2). This will be discussed later in the paper. The displacement, velocity and acceleration, respectively, of the slide are shown in figures 13 through 15. The units are the same as for the receiver. The motion occuring during the full cycle of the pistol is predominantly of this component. Note that the slide motion shown in figure 13 is relatively smooth but is affected somewhat when it picks up the barrel during counterrecoil. This is of course based upon the spring damper values utilized, relatively rigid, to represent this collision (see Table 2). Key events are denoted on the figures. From figure 14 it can be seen that the velocity of the slide is relatively large, in excess of 200 inches per second. The end of recoil is abrupt due to the-high spring constant and damping coefficient utilized represent the slide receiver impact. The velocity of the slide is reduced Spon Biking up the barrel in counerrécoil. 307BENZKOFER Figure 4, Projectile displacement versus time aI — \ Figure 5. Projectile velocity versus tine Figure 6. Projectile acceleration versus time 308BENZKOFER Figure 9, Receiver acceleration versus tine 309BENZKOFER Figure 10. Receiver displacement versus time Figure Figure 11. Receiver velocity versus time | feat a fenefened ! tion versus timeBENZKOFER Figure 13. Slide displacement versus tine eos ryt Figure 15. Slide acceleration versus time 31BENZKOFER The sotion of the barrel is given in figures 16 through 18. Figure 16 gives barrel displacement in inches versus time in seconds. The significant events are denoted as the impact of the slide with the receiver and subsequently the stopping of the barrel due to impact with the receiver. During counterrecoil the slide picks up the barrel and brings it back to its battery position. Note that the displacement of the barrel is occuring only during the very early and the very late portions of the cycle, and that it is relatively small. In figure 17, the velocity in inches per second is shown. Since it is initially locked to the slide its velocity is high at this time. Note, however, that this is a very short period of time until it impacts the receiver and stops. This simulation is based upon the spring damper (see Table 2) utilized for this impact. In addition to the events noted on the displacement figure, the projectile exit is also given. As shown the tine to projectile exit from the barrel is extremely small in comparison to the total cycle time. Finally the acceleration is given in figure 18. Based upon analysis of the slide counterrecoil velocity, differences between simulated values and experimentally determined values do exist. This nas promoted a review of the simulation model, and this is discussed in the following section. PARAMETRIC ANALYSIS As discussed above, observed differences between model and actual values do exist. Additional simulation analysis suggests that one parameter which may .ccount for the disparities is the recoil spring stiffness. In order to further address this issue, then, the spring constant stiffness will be eval ated. Three values of the spring parameter have been arbitrarily sele-ted and subsequently utilized in the model. These results will be dis ussed below. Slide displacement for three unique values of spring stiffness, as noted in tie legend, is shown in figure 19. Similarly, the velocities and acceterations for these three values are shown in figures 20 and 21. The lowe=t spring constant value utilized, 1.08 Ibs/inch, results in the longest cycl time as shown on the figures. As expected, this value of spring cons:ant results in the lowest value of counterrecoil velocity. As shown on the chree figures, the value for the constant has little effect during the rece.l cycle. This is sensible in the physical sense due to the relatively high velocity attained by the slide. However, during counterrecoil the stored energy in the compressed recoil spring is more significant and the velc.ities of recoil have been significantly reduced due to the damping effect of tie impact with the receiver. There appears to be less variations when look ‘ng at the acceleration values in Figure 21, except to note that the spikes at or near tne enc of the cycle occur at different times, as would be expected. Review of actual experimertal data suggests that the actual velocity of the slide is best simulated when using a different value for spring stiffness than that given on the technical drawing of the spring. One possible explanation for this difference is that due to the repeated firing of the weapon, the recoil spring is subjected to extensive loading and consequently its stiffness is diminished. The technical drawing calls for a spring constant closer to the high end of the values utilized here. The idle and loyest value of spring constant vhen utilized in the model most accurately simulate actual firing test data. 312BENZKOFER Figure 17. Barrel velocity versus time Figure 18, Barrel acceleration versus time 313‘BENZKOFER Figure 19, Slide displacenent versus tine Figure 20, Slide velocity versus time Figure 21, Slide acceleration versus time 314BENZKOFER CONCLUSIONS Some inaccuracies in the model are apparent when observing motion results during the counterrecoil cycle, as simulation values do not fully coincide with test data. This appears to be dependent upon the recoil spring as discussed above. When the value of 2.08 ibs/inch is utilized for the recoil spring constant, reasonable values are obtained in the counter- recoil simulation. Good simulation values for recoil motion is evidenced, and total cycle time appears to be comparable with test data. Another area of critical concern is interaction between the man and the pistol. This can best be modeled by allowsxg spring and damper action where the soldier grips the pistol. This technique will provide a wide range of parameter variation. The spring and damping coefficients utilized (see Table 2) in this analysis for the man-weapon interaction represent a relatively rigid system as evidenced in the recoil notion of Body 2, the receiver. RECOMMENDATIONS The inaccuracies and changes discussed above will be further investigated and subsequently be incorporated into the model. The simulation values obtained to date, however, are preliminary in the sense that new test data for pressure-time may preclude that which is utilized in this model. Current efforts in modeling of a hand-held weapon include the evaluation of a full range of spring-damper variations for the impact springs as well as for the man-weapon connectivity. In essence, this model, with corrections and updates as discussed, will serve as a good reference in design and redesign efforts, as well as input to a dynamic stress analysis. 315,BENZKOFER REFERENCES 1, Unit and Intermediate Direct Support Maintenance Manual, PISTOL, SEMIAUTOMATIC, 9mm, M9, Technical Manual TM 9-1005-317-236P, U-S. Arny Armament, Munitions and Chemical Command, Rock Island, IL Jan 1986. 2. DADS 2D/3D Theoretical and User Manuals, University of Iowa, Iowa City, TA, 1982. T.R. Kane, Dynamics, Second Edition, Stanford University, CA, 1972. 4. Philip D. Benzkofer, Master of Science Dissertation, "An Equation- Generating Computer Code for the Dynamic Analysis of a Class of Mechanisms" University of Iowa, College of Engineering, Graduate College, Dec 1980. Philip D. Benzkofer, "Dynamics of High Cyclic Rate Weapon Systems", proceedings of the Fifth U.S. Army Gun Dynamics Symposium, Sep, 1987. 6. Philip D. Benzkofer, "Automated Dynamic Analysis of Weapon Systems", proceedings of the Fourth U.S. Army Gun Dynamics Symposium, May 1985. 7. Philip D. Benzkofer, “Dynamic Analysis of the 20mm General Purpose Heavy Machine Gun", proceedings of the Third U.S. Army Gun Dynamics Symposium, May 1982. 8. Philip D. Benzkofer, "Dynamic Analysis of the Caliber .45 “1911A1 Pistol", Technical Report, U.S. Army Armament Research, Development and Engineering Center, ARDEC, Dover, NJ, Dec 1989. 9. Philip D. Benzkofer, "An Evaluation of the Dynamics Inherent in an Advanced Primer Ignition Weapon System", Technical Report, U.S. Army Armament Research, Development and Engineering Center, ARDEC, Dover, NJ, Jan 1988. 10. Philip D. Benzkofer, "Precision Aircraft Armament Control Experiment Armament System Dynamics", Technical Report, U.S. Army Armament Research, Development and Engineering Center, ARDEC, Dover, NJ, Jan 1988. 11. Philip D. Benzkofer, "Automated Dynamic Analysis in Support of a Future Air Defense Test Bed", Technical Report, U.S. Army, Armament Research and Development Center, ARDC, Dover, NJ, May 1986. 316