Kinetic Energy Non-Lethal Weapons Testing Methodology

Transcription

1 Kinetic Energy Non-Lethal Weapons Testing Methodology BTTR Impact Force Model Development B. Anctil Biokinetics and Associates Ltd. Prepared By: Biokinetics and Associates Ltd. 247 Don Reid Drive Ottawa, Ontario K1H 1E1 Contractor's Document Number: R13-9 Contract Project Manager: Benoit Anctil, PWGSC Contract Number: W /1/QCL (AT69) CSA: Daniel Bourget, Defence Scientist, ext.4228 The scientific or technical validity of this Contract Report is entirely the responsibility of the Contractor and the contents do not necessarily have the approval or endorsement of Defence R&D Canada. Defence Research and Development Canada Contract Report DRDC-RDDC-216-C332 March 213

2 Principal Author Original signed by Benoit Anctil Benoit Anctil Senior Engineer Approved by Original signed by Daniel Bourget Daniel Bourget Defence Scientist Approved for release by Original signed by Dr. Dennis Nandlall Dr. Dennis Nandlall Head, Weapons Effects and Protection Section Her Majesty the Queen in Right of Canada, as represented by the Minister of National Defence, 213 Sa Majesté la Reine (en droit du Canada), telle que représentée par le ministre de la Défense nationale, 213

3 Abstract The Blunt Trauma Torso Rig (BTTR) consists of a flexible membrane tuned to match the human chest response. A sensor located behind the point of impact measures the dynamic deflection caused by the deformation of body armours or kinetic energy non-lethal weapon (KENLW) impacts. The deflection data is used to predict the associated risk of injury. A mathematical model, based on the undamped single degree of freedom system, was developed to complement the functionality of the BTTR by allowing calculation of the projectile impact force from the dynamic membrane deflection data. A series of experimental trials with instrumented and non-instrumented projectiles was conducted to estimate the model parameters. Despite good correlation between the measured excitation (projectile force impulse) and the system response (membrane deflection), the model predicted force impulse was always lower than the measured excitation and dependant of the projectile characteristics. The undamped single degree of freedom system was not found appropriate for the BTTR. System identification techniques should be considered in future attempts to build a more sophisticated dynamic system to represent the BTTR. i

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5 Executive summary Kinetic Energy Non-Lethal Weapons Testing Methodology: BTTR Impact Force Model Development Benoit Anctil; DRDC Valcartier CR [enter number only: ]; Defence R&D Canada Valcartier; March 213. Introduction: The Blunt Trauma Torso Rig (BTTR) consists of a flexible membrane tuned to match the human chest response. A sensor located behind the point of impact measures the dynamic deflection caused by the deformation of body armours or kinetic energy non-lethal weapon (KENLW) impacts. The deflection data is used to predict the associated risk of injury. To complement the functionality of the BTTR, a mathematical model, based on the undamped single degree of freedom system, would allow calculation of the projectile impact force from the dynamic membrane deflection data. This could provide relevant information on the severity of impact to better rank the performance of body armours and KENLWs. Results: A series of experimental trials with instrumented and non-instrumented projectiles simulating KENLW conditions was conducted to estimate the model parameters. However, the calculated force impulse was always lower than the measured force excitation. It was also found that the force prediction values were dependant on the projectile characteristics. As a result, the undamped single degree of freedom system was not found appropriate to model the response of the BTTR. Significance: A model able to predict the impact force from the dynamic membrane deflection will improve the BTTR capability to rank body armour and KENLW performance. Future plans: System identification techniques should be considered in future attempts to build a more sophisticated dynamic system to represent the BTTR. iii

6 Abstract i Executive summary... iii Table of contents...iv List of figures... v List of tables...vi 1 Introduction Materials and Methods Projectiles Setups... 5 Air Cannon... 5 Portable Gas Gun Results Instrumented Projectiles Non-instrumented Projectiles Single Degree of Freedom System Conclusions and Recommendations References Annex A.. Test Data Summary Annex B... Membrane Compression Annex C... Projectile Acceleration Distribution list iv

7 List of figures Figure 1. Single degree of freedom system representation of the BTTR Figure 2. Response of a single degree of freedom system (b) to an impulse (a)... 2 Figure 3. Instrumented projectile assembly... 3 Figure 4. Instrumented projectile components Figure 5. Accelerometer Kistler 8742A Figure 6. Cable setup Figure 7. Air cannon setup Figure 8. Portable gas gun setup Figure 9. Typical projectile and BTTR responses Figure 1. Peak deflection vs. velocity... 9 Figure 11. Peak deflection vs. measured FΔt Figure 12. Peak deflection vs. calculated FΔt Figure 13. Measured vs. calculated FΔt Figure 14. Peak deflection vs. velocity... 1 Figure 15. Peak deflection vs. calculated FΔt Figure 16. Calculated system s equivalent mass Figure 17. System s natural frequency Figure 18. Projectile mass vs. natural frequency v

8 List of tables Table 1. Test projectiles... 4 vi

9 1 The objective of this task is to develop a mathematical model of the Blunt Trauma Torso Rig (BTTR) to calculate the projectile impact force from the dynamic membrane deflection data. Assessment of the imparted force would complement the current BTTR measurement capability while enhancing its injury prediction functions. Testing with instrumented rigid (non-deformable) projectiles can be used to estimate the parameters of the BTTR model represented as a single degree of freedom system (Figure 1). By assuming the principles of energy conservation apply, i.e. there is no energy dissipation, the kinetic energy of the projectile (E p ) corresponds to the kinetic energy stored (T m ) in the effective mass m of the combine BTTR s membrane and projectile at maximum velocity and to the potential energy (U m ) stored in the spring (membrane s elastic deformation) at peak membrane s compression [1]: Figure 1. Single degree of freedom system representation of the BTTR. Thus, the system s equivalent mass m is given by: where m p and v p are the mass and velocity of the projectile and v max is the peak membrane velocity; and the system s spring constant is given by: where c max is the peak membrane compression. With the values for m and k, it will then be possible to calculate the system s natural angular frequency of vibration (w n ): 1

10 Measurement of the projectile s acceleration (a p ) will be used to calculate the impulsive force (Ft) to the system using Newton s second law: F a The impulsive force measured experimentally will be compared to the value calculated using the equation of an undamped (c=) single degree of freedom system subjected to an impulse excitation [2]: F tsin t F t sin t where t max corresponds to the time at peak compression (c max ). Testing with non-instrumented deformable projectiles having similar mass and diameter as the instrumented projectiles can be used afterwards to validate the model. The dynamic deflection data can be used to calculate the system s equivalent mass (m def ), stiffness (k def ), and natural angular frequency (w n ): Figure 2. Response of a single degree of freedom system (b) to an impulse (a). The impulsive force (Figure 2) for an impact with deformable projectile can then be estimated using the following equation: F t sin t 2

11 2 2.1 Test Projectiles The projectiles characteristics and the targeted impact velocities used in this study are presented in Table 1. Projectiles No. B4 to B7 were instrumented with a Kistler shock accelerometer Model 8742A5 (Figure 5) having a measurement range of ±5, G. Figure 3 shows an example of instrumented projectile assembly. A string was used to protect the cable in case of entanglement (Figure 4). The foam cylinder function was used to guide the projectile in the air cannon barrel and to provide protection to the accelerometer. Figure 6 shows the cable setup before inserting the projectile in the barrel. Figure 3. Instrumented projectile assembly. Figure 4. Instrumented projectile components. Figure 5. Accelerometer Kistler 8742A5. Figure 6. Cable setup. 3

12 Table 1. Test projectiles. ID No. Description Diameter (mm) Mass 1 (g) Test Velocity (m/s) B4 Cylinder (Al) B5 Cylinder (Al) B6 Cylinder (Al) B7 Cylinder (Al) + XM16 foam tip C12 12-gauge drag stabilized bean bag

13 ID No. Description Diameter (mm) Mass 1 (g) Test Velocity (m/s) C1 Cylinder (hard plastic) C9 Cylinder (hard plastic) C16 MK Ballistics 4mm Elastomeric Baton C19 Defense Technology Direct Impact Inert Note 1: The mass of the instrumented projectiles include the weight of the impactor, the accelerometer, and the foam cylinder. 2.2 Setups Air Cannon Projectiles No. B4 to B7 were launched using Biokinetics air cannon (Figure 7). A set of fiber optic light gates were used to measure the velocity of the projectile. Note that the instrumented projectiles were never in free flight. They were guided in a tube until impact with the BTTR membrane. A series of holes in the barrel toward the end of the muzzle was used to limit the acceleration of the projectile before impact. 5

14 The projectile accelerometer and the BTTR s laser transducer (Micro-Epsilon Model optoncdt 1627) signals were recorded at a sampling frequency of 1 khz using a National Instruments data acquisition system connected to a personal computer. The deflection signal was filtered using a similar filter but with a cut-off frequency of 1 khz at -3 db. The recorded acceleration signal used for the calculations was not filtered. Figure 7. Air cannon setup. Portable Gas Gun The non-instrumented projectiles were fired using a portable gas gun designed and manufactured by CADEX Inc. as per the requirements established by DRDC Valcartier under a previous contract. Light gates integrated into the gas gun were used to measure the velocity of the projectiles. The target (BTTR) was positioned at approximately.65 m from the muzzle. The output voltage signal of the BTTR s laser transducer was recorded at 1 khz using a National Instruments data acquisition system connected to a personal computer. The recorded deflection signal was filtered using a zero-phase forward and reverse digital lowpass filter (1 khz at -3 db). 6

15 Figure 8. Portable gas gun setup. 7

16 3 Results A summary table with the measured and calculated data is provided in Annex A. the membrane compression responses and the projectile acceleration traces are provided in Annex B and Annex C, respectively. 3.1 Instrumented Projectiles Figure 9 shows the measured acceleration signal for the B6 projectile at 41.8 m/s and the associated BTTR membrane deflection response. The shape of the measured excitation impulse is different from the theoretical square impulse (Figure 2). For the smaller projectile diameter (B4) and the foam tip projectile (B7) at low speed, the force impulse shape was triangular while for the other conditions the onset was very rapid, virtually instantaneous. Acceleration (G) Time (ms) t C (mm) Time (ms) Figure 9. Typical projectile and BTTR responses. There is a good correlation between projectile velocity and the peak membrane deflection (C max ), Figure 1. The relationship between the measured impulse (FΔt) and the peak deflection is similar for all the projectiles evaluated as shown in Figure 11. The force response corresponds to the product of projectile mass and the recorded acceleration (F=ma). The impulse was obtained by evaluating the area under the force curve for the time interval Δt (Figure 9). The impulse calculated with the equations provided in Section 1 is compared to the peak membrane deflection in Figure 12 and to the measured impulse in Figure 13. The calculated 8

17 impulse values were much lower than the measured responses. Better correlation between the calculated and measured values was observed for projectiles B5 and B5 in comparison with the lightest projectile (B4) and the projectile with a foam extremity (B7) Cmax(mm) 3 Cmax(mm) Projectile Velocity (m/s) FΔt - measured (N-s) B4 B5 B6 B7 B4 B5 B6 B7 Figure 1. Peak deflection vs. velocity. Figure 11. Peak deflection vs. measured FΔt Cmax (mm) FΔt - calculated (N-s) FΔt - calculated (N-s) B4 B5 B6 B FΔt - measured (N-s) B4 B5 B6 B7 Figure 12. Peak deflection vs. calculated FΔt. Figure 13. Measured vs. calculated FΔt. 9

18 3.2 Non-instrumented Projectiles Projectile impact velocities correlated well with the membrane s peak compression (C max ) as shown in Figure 14. Different trends were observed between projectile velocity and the calculated impulse (FΔt), Figure 15. The results for the rigid batons (C1 and C9) are comparable to the trends seen for the instrumented projectile (Figure 12) but the response is different for the lighter and deformable projectiles (C12, C16, and C19) Cmax (mm) 3 Cmax (mm) Velocity (m/s) C12 C1 C9 C16 C FΔt - calculated (N-s) C12 C1 C9 C16 C19 Figure 14. Peak deflection vs. velocity. Figure 15. Peak deflection vs. calculated FΔt. 3.3 Single Degree of Freedom System The parameters of the single degree of freedom system were calculated using the equations provided in Section 1. No trend was identified for the calculated system s equivalent mass (Figure 16) with the exception that the higher values corresponds to the most deformable projectiles, i.e. the elastomeric baton (C16) and the crushable direct impact projectile (C19) despite the fact that these projectiles are light (4 g) in comparison with rigid batons (e.g. 14 g for C9). The calculated system s natural frequency is variable ( /-1.5 rad/s) as shown in Figure 17. There is a good correlation between the projectile mass and the system s natural frequency but more variability is observed for the deformable projectiles with higher values for the lightest projectiles (Figure 18). Note that the calculated membrane s potential energy (Um) is identical to the kinetic energy of the projectile (Ep) as indicated in the data summary table (Annex A). 1

19 Figure 16. Calculated system s equivalent mass. Figure 17. System s natural frequency w n (rad/s) Projectile mass (g) B4 B5 B6 B7 C12 C1 C9 C16 C19 Figure 18. Projectile mass vs. natural frequency. 11

20 4 Conclusions and Recommendations Measurements from experimental BTTR trials provided the relevant data to estimate the single degree of freedom system s parameters. A good correlation was observed between the measured excitation (projectile force impulse) and the system response (membrane deflection) but using the single degree of freedom model to calculate the force impulse was not reliable. The predicted force impulse was significantly lower than the measured excitation. In addition, the predicted force impulse was found to be dependant of the projectile characteristics which can explain the limited success achieved with model. The findings of this study suggest that a single degree of freedom system cannot describe the input force response independently from the projectile s characteristics (e.g. impact area, mass, stiffness). This is obviously not ideal to predict the impulse force for body armour testing since the impact conditions are unknown and variable. The BTTR is too complex to be described simply with an undamped single degree of freedom system. Future work will benefit from the application of system identification techniques to build a BTTR mathematical model. This approach uses statistical methods and the measured data to define the parameters of complex dynamic systems. 12

21 References [1] Rao, S. S., Chapter 2: "Free Vibration of Single Degree of Freedom Systems," in Mechanical Vibrations: Addison-Wesley Publishing Company, 1986, pp [2] Rao, S. S., Chapter 4: "Vibration under General Forcing Conditions," in Mechanical Vibrations: Addison-Wesley Publishing Company, 1986, pp

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23 Annex A 15

24 Model No. C12 C1 C9 C16 C19 B4 16 Description Bean Bag 24mm/4g Plastic Cylinder 37mm/96g Plastic Cylinder 37mm/14g MK Ballistics 4mm/41g Direct Impact 4mm/35g Cylinder (AI) Diameter (mm) m p (g) v p (m/s) a p (G) at (m/s 2 - s) Ft (Ns) Ep (J) c max (mm) v max (m/s) VC max (m/s) Impulse (mm.s) m def (g) k def (kg/s 2 ) w n (rad/s) t max (ms) Ft (Ns) Um (J)

25 Model No. B5 B6 B7 Description Cylinder (AI) Cylinder (AI) Cylinder (AI) + XM16 foam Diameter (mm) m p (g) v p (m/s) a p (G) at (m/s 2 - s) Ft (Ns) Ep (J) c max (mm) v max (m/s) VC max (m/s) Impulse (mm.s) m def (g) k def (kg/s 2 ) w n (rad/s) t max (ms) Ft (Ns) Um (J) DRDC Valcartier CR [enter number only: ] 17

26 Annex B 6 B m/s 2.6 m/s 3.7 m/s 4.7 m/s C (mm) Time (ms) B m/s 2.5 m/s 29.9 m/s 4. m/s C(mm) Time (ms) 18 DRDC Valcartier CR [enter number only: ]

27 6 B m/s 21.3 m/s 31.2 m/s 41.8 m/s C (mm) Time (ms) 6 B m/s 18.3 m/s 3. m/s 4.9 m/s C (mm) Time (ms) DRDC Valcartier CR [enter number only: ] 19

28 6 C m/s 21.5 m/s 31.2 m/s 41.7 m/s C (mm) Time (ms) 6 C m/s 2.9 m/s 31.2 m/s 41. m/s C (mm) Time (ms) 2 DRDC Valcartier CR [enter number only: ]

29 6 C m/s 21.9 m/s 31.6 m/s 38.8 m/s C (mm) Time (ms) C m/s 15.3 m/s 21.4 m/s 32.6 m/s 38.2 m/s C (mm) Time (ms) DRDC Valcartier CR [enter number only: ] 21

30 6 C m/s 21. m/s 29.4 m/s 4.2 m/s C (mm) Time (ms) 22 DRDC Valcartier CR [enter number only: ]

31 Annex C 12 B m/s 2.6 m/s 3.7 m/s 4.7 m/s Acceleration (G) Time (ms) 12 B m/s 2.5 m/s 29.9 m/s 4. m/s Acceleration (G) Time (ms) DRDC Valcartier CR [enter number only: ] 23

32 12 B m/s 21.3 m/s 31.2 m/s 41.8 m/s Acceleration (G) Time (ms) 12 B m/s 18.3 m/s 3. m/s 4.9 m/s Acceleration (G) Time (ms) 24 DRDC Valcartier CR [enter number only: ]

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34 Distribution list Document No.: DRDC Valcartier CR [enter number only: ] LIST PART 1: Internal Distribution by Centre TOTAL LIST PART 1 LIST PART 2: External Distribution by DRDKIM 1 Library and Archives Canada 1 TOTAL LIST PART 2 1 TOTAL COPIES REQUIRED 26 DRDC Valcartier CR [enter number only: ]

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36 DOCUMENT CONTROL DATA (Security classification of title, body of abstract and indexing annotation must be entered when the overall document is classified) 1. ORIGINATOR (The name and address of the organization preparing the document. Organizations for whom the document was prepared, e.g. Centre sponsoring a contractor's report, or tasking agency, are entered in section 8.) 2. SECURITY CLASSIFICATION (Overall security classification of the document including special warning terms if applicable.) Biokinetics and Associates Ltd. 247 Don Reid Drive Ottawa, Ontario K1H 1E1 UNCLASSIFIED 3. TITLE (The complete document title as indicated on the title page. Its classification should be indicated by the appropriate abbreviation (S, C or U) in parentheses after the title.) Kinetic Energy Non-Lethal Weapons Testing Methodology: BTTR Impact Force Model Development 4. AUTHORS (last name, followed by initials ranks, titles, etc. not to be used) Anctil, B. 5. DATE OF PUBLICATION (Month and year of publication of document.) March 213 6a. NO. OF PAGES (Total containing information, including Annexes, Appendices, etc.) 4 6b. NO. OF REFS (Total cited in document.) 2 7. DESCRIPTIVE NOTES (The category of the document, e.g. technical report, technical note or memorandum. If appropriate, enter the type of report, e.g. interim, progress, summary, annual or final. Give the inclusive dates when a specific reporting period is covered.) Contract Report 8. SPONSORING ACTIVITY (The name of the department project office or laboratory sponsoring the research and development include address.) Defence R&D Canada Valcartier 2459 Pie-XI Blvd North Quebec (Quebec) G3J 1X5 Canada 9a. PROJECT OR GRANT NO. (If appropriate, the applicable research and development project or grant number under which the document was written. Please specify whether project or grant.) 9b. CONTRACT NO. (If appropriate, the applicable number under which the document was written.) 1a. ORIGINATOR'S DOCUMENT NUMBER (The official document number by which the document is identified by the originating activity. This number must be unique to this document.) 1b. OTHER DOCUMENT NO(s). (Any other numbers which may be assigned this document either by the originator or by the sponsor.) R DOCUMENT AVAILABILITY (Any limitations on further dissemination of the document, other than those imposed by security classification.) 12. DOCUMENT ANNOUNCEMENT (Any limitation to the bibliographic announcement of this document. This will normally correspond to the Document Availability (11). However, where further distribution (beyond the audience specified in (11) is possible, a wider announcement audience may be selected.))

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