Calhoun: The NPS Institutional Archive Theses and Dissertations Thesis Collection 2006-03 Design, fabrication, and testing of a scalable series augmented railgun research platform Black, Brian C. Monterey, California. Naval Postgraduate School http://hdl.handle.net/10945/2855 NAVAL POSTGRADUATE SCHOOL MONTEREY, CALIFORNIA THESIS DESIGN, FABRICATION AND TESTING OF A SCALABLE SERIES AUGMENTED RAILGUN RESEARCH PLATFORM by Brian C. Black March 2006 Thesis Advisor: Co-Advisor: William B. Maier II Terry R. McNelley Approved for public release; distribution unlimited THIS PAGE INTENTIONALLY LEFT BLANK REPORT DOCUMENTATION PAGE Form Approved OMB No. 07040188 Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instruction, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden, to Washington headquarters Services, Directorate for Information Operations and Reports, 1215 Jefferson Davis Highway, Suite 1204, Arlington, VA 22202-4302, and to the Office of Management and Budget, Paperwork Reduction Project (0704-0188) Washington DC 20503. 1. AGENCY USE ONLY (Leave blank) 4. of 6. 7. 9. 2. REPORT DATE 3. March 2006 TITLE AND SUBTITLE: Design, Fabrication, and Testing a Scalable Series Augmented Railgun Research Platform AUTHOR(S) Brian C. Black PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) Naval Postgraduate School Monterey, CA 93943-5000 SPONSORING /MONITORING AGENCY NAME(S) AND ADDRESS(ES) N/A REPORT TYPE AND DATES COVERED Master’s Thesis 5. FUNDING NUMBERS 8. PERFORMING ORGANIZATION REPORT NUMBER 10. SPONSORING/MONITORING AGENCY REPORT NUMBER 11. SUPPLEMENTARY NOTES The views expressed in this thesis are those of the author and do not reflect the official policy or position of the Department of Defense or the U.S. Government. 12a. DISTRIBUTION / AVAILABILITY STATEMENT Approved for public release; distribution is unlimited 13. ABSTRACT (maximum 200 words) 12b. DISTRIBUTION CODE The design and material properties of rails and projectiles are critical to the success of the Navy railgun. This thesis addresses the design, fabrication, and testing of a scalable square bore electromagnetic railgun. This railgun is designed to permit series augmented operation, and incorporates disposable rail liners to facilitate investigating the suitability of various rail materials. A series of shots has demonstrated performance consistent with theoretical modeling, including significant performance enhancement as a result of both slotted rail geometry and augmentation over solid rail and un-augmented configurations. A capacitor based stored energy supply input of 35 kJ resulted in a measured velocity of 294 m/s for an 11.4 gram projectile. Suggestions are provided for future power supply configurations, rail materials and surface treatments, and a variety of armature geometries. 14. SUBJECT TERMS Railgun, Rail-gun, Augmentation, Electromagnetic launch, Armature, Pulsed Power, Hypervelocity launch, Hypervelocity Projectile, Ion beam surface treatment, IBEST, Laser peening, Electromagnetic Weapon 17. SECURITY CLASSIFICATION OF REPORT Unclassified 18. SECURITY CLASSIFICATION OF THIS PAGE Unclassified NSN 7540-01-280-5500 15. NUMBER OF PAGES 135 16. PRICE CODE 20. LIMITATION 19. SECURITY OF ABSTRACT CLASSIFICATION OF ABSTRACT UL Unclassified Standard Form 298 (Rev. 2-89) Prescribed by ANSI Std. 239-18 i THIS PAGE INTENTIONALLY LEFT BLANK ii Approved for public release; distribution is unlimited DESIGN, FABRICATION AND TESTING OF A SCALABLE SERIES AUGMENTED RAILGUN RESEARCH PLATFORM Brian C. Black Lieutenant, United Stated Navy B.A., Political Science, Dickinson College, 1991 B.S., Mechanical Engineering, University of Pittsburgh, 1998 Submitted in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE IN MECHANICAL ENGINEERING from the NAVAL POSTGRADUATE SCHOOL March 2006 Author: Brian C. Black Approved by: William B. Maier II Thesis Advisor Department of Physics Terry R. McNelley Co-Advisor Department of Mechanical and Astronautical Engineering Anthony J. Healey Chairman, Department of Mechanical and Astronautical Engineering iii THIS PAGE INTENTIONALLY LEFT BLANK iv ABSTRACT The design projectiles railgun. and are material critical to properties the of success of rails and the Navy This thesis addresses the design, fabrication, testing railgun. of This augmented liners and to a scalable railgun operation, is and facilitate square designed electromagnetic to incorporates investigating various rail materials. bore permit series disposable the rail suitability of A series of shots has demonstrated performance consistent with theoretical modeling, including significant performance enhancement as a result of both the slotted rail geometry configurations. A and augmentation capacitor based over stored solid energy rail supply input of 35 kJ resulted in a measured velocity of 294 m/s for an 11.4 gram projectile. future power supply Suggestions are provided for configurations, rail materials surface treatments, and a variety of armature geometries. v and THIS PAGE INTENTIONALLY LEFT BLANK vi TABLE OF CONTENTS I. INTRODUCTION ............................................1 A. BACKGROUND .........................................1 B. OBJECTIVE ..........................................3 II. RAILGUN TEST PLATFORM DESIGN ............................5 A. GENERAL ............................................5 B. MATERIAL PROPERTIES ................................5 C. IMPROVED INDUCTANCE GRADIENT WITH SERIES AUGMENTATION .......................................7 D. IMPROVED INDUCTANCE GRADIENT WITH SLOTTED RAIL GEOMETRY ..........................................13 E. ADDITIONAL COMPONENTS .............................14 III. PULSED POWER SUPPLY ....................................19 A. PRESENT SYSTEM ....................................19 B. REDESIGNED POWER SUPPLY ...........................22 IV. DESIGN VERIFICATION ....................................25 A. PARAMETER MODEL ...................................25 B. CONSERVATION OF ENERGY CIRCUIT MODEL ..............26 C. STRUCTURAL DESIGN .................................28 V. RESULTS ................................................33 A. SHOT DIAGNOSTICS ..................................33 VI. CONCLUSION .............................................41 A. PERFORMANCE SUMMARY AND RECOMMENDATIONS ...........41 B. MATERIALS PROCESSING METHODS ......................43 APPENDIX A. MATERIAL PROPERTY DATA SHEETS ...................45 APPENDIX B. PRODUCTION DRAWINGS .............................55 APPENDIX C. MODELING .......................................71 A. KERRISK’S METHOD SPREADSHEETS [3] .................71 B. PARAMETER BASED MODELING [7] ......................72 C. CONSERVATION OF ENERGY INTEGRATION [4] ............79 D. STRUCTURAL DESIGN VERIFICATION ....................84 APPENDIX D. MAGNETIC FIELD AND CIRCUIT SIMULATIONS .........87 A. COMSOL MULTIPHYSICS MODELING ......................87 B. ORCAD 10.3 P-SPICE CIRCUIT MODELING ...............99 APPENDIX E. BREAK SCREEN AND CURRENT PROFILE SCREEN CAPTURES ..............................................103 APPENDIX F. TYPICAL POST-SHOT MATERIAL CONDITIONS .........111 LIST OF REFERENCES .........................................115 INITIAL DISTRIBUTION LIST ..................................117 vii THIS PAGE INTENTIONALLY LEFT BLANK viii LIST OF FIGURES Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. Figure 12. Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. Figure 33. Figure 34. Figure 35. Figure 36. Figure 37. Exploded Railgun Assembly .........................5 Series Augmented Current Path .....................8 Augmented Railgun Geometry where R = 3/16” .......10 Augmented Conductor Assembly .....................12 Slotted Rail Geometry ............................14 Railgun Loading Apparatus ........................15 3.0-µH Series Inductor and Components ............16 Target Chamber ...................................17 Power Supply Cabinet .............................20 Power Supply Cabinet Interfaces ..................21 Fixed End Distributed Load Beam Model [After Ref. 9] ...............................................30 Augmented Rail to Conductor Threaded and Braised Joint ............................................42 Armature Geometry Alternatives (Appendix B) ......43 Top Containment Half .............................55 Bottom Containment Half ..........................56 Solid Primary Conductor Rails ....................57 Slotted Primary Conductor Rails ..................58 Ceramic Insulators ...............................59 Augmented Rails, Rail liners, and Spacer .........60 Augmenting Conductor Components ..................61 External Conductor Connectors and Muzzle Shunt ...62 Full Conductor Assembly ..........................63 Full CAD Assembly with Loader and Muzzle Shunt ...64 Full Assembled Railgun with Loader ...............64 Basic U-Shape Armature ...........................65 Flared M-shape Armature ..........................66 Square M-shape Armature ..........................67 Altered U-shape Armature with Center Hollow ......68 Railgun Mounting Base ............................69 Kerrisk’s Method Rail Parameters [After Ref. 2] ..71 Simplified Beam Geometry (Not to scale) ..........84 Transformed Homogenous Beam Geometry (Not to Scale) .................................................84 Solid Non-Augmented Magnetic Flux Density ........87 Solid Non-Augmented Magnetic Field Across Bore ...88 Solid Non-Augmented Magnetic Field Across Rail Surface ..........................................89 Slotted Non-Augmented Magnetic Flux Density ......90 Slotted Non-Augmented Magnetic Field Across Bore .91 ix Figure 38. Slotted Non-Augmented Magnetic Field Across Rail Surface ..........................................92 Figure 39. Solid, Augmented Magnetic Flux Density ...........93 Figure 40. Solid Augmented Magnetic Field Across Bore .......94 Figure 41. Solid, Augmented Magnetic Field Across Rail Surface .................................................95 Figure 42. Slotted Augment Magnetic Flux Density ............96 Figure 43. Solid Augmented Magnetic Field Across Bore .......97 Figure 44. Solid Augmented Magnetic Field Across Rail Surface .................................................98 Figure 45. P-SPICE Single Module LRC Circuit Model ..........99 Figure 46. Single Power Module Current Profile .............100 Figure 47. P-SPICE Four-Module LRC Circuit Model ...........101 Figure 48. Four-Module Current Profile Output from Figure 46 Circuit Model ...................................102 Figure 49. Solid Non-Augmented Velocity Measurement ........103 Figure 50. Solid Non-Augmented Current Profiles ............104 Figure 51. Slotted Non-Augmented Velocity Measurement ......105 Figure 52. Slotted Non-Augmented Current Profiles ..........106 Figure 53. Solid Augmented Velocity Measurement ............107 Figure 54. Solid Augmented Current Profiles ................108 Figure 55. Slotted Augmented Velocity Measurement ..........109 Figure 56. Slotted Augmented Current Profiles ..............110 Figure 57. Typical Post-Shot Rail and Insulator Wear .......111 Figure 58. Typical Post-Shot Armature Wear .................112 Figure 59. Muzzle Block Indicating Muzzle Flash Arcing .....113 x LIST OF TABLES Table Table Table Table Table Table 1. 2. 3. 4. 5. 6. Table 7. Table 8. Table 9. Table 10. Table 11. Table 12. Table 13. Table 14. Table 15. Table Table Table Table Table Table Table 16. 17. 18. 19. 20. 21. 22. Table Table Table Table Table Table 23. 24. 25. 26. 27. 28. Nominal EM Gun Parameters, [From Ref. 1] ..........2 Summary of Rail Properties [After Ref. 2] .........6 Experimental Data Results ........................33 Predicted vs. Experimental Gain Factors ..........35 Total System Resistance and R/L’ Results .........38 Chromium Copper Rail Liner Material Properties [After Ref. 2] ...................................45 Oxygen Free Copper Rail Liner Material Properties [After Ref. 2] ...................................46 Phosphor Bronze Rail Liner Material Properties [After Ref. 2] ...................................47 Copper Tungsten Rail Liner Properties [After Ref. 2] ...............................................48 Aluminum 7075 T-651 Rail Liner Material Properties [After Ref. 2] ...................................49 Aluminum 6063 T-5 Armature Material Properties [After Ref. 2] ...................................50 G-11 FR-5 Containment Material Properties [After Ref 10] ..........................................51 Ceramic Insulator Material Properties [After Ref. 11] ..............................................52 Mylar Film Insulator Material Properties [After Ref. 12] .........................................53 Kerrisk’s Method and Augmentation Adjusted Inductance Gradient (L’) Calculations ............71 1500 m/s Solid Non-Augmented Parameter Model .....72 1500 m/s Slotted Non-Augmented Parameter Model ...73 1500 m/s Solid Augmented Parameter Model .........74 1500 m/s Slotted Augmented Parameter Model .......75 265 m/s Solid Augmented Parameter Model ..........76 290 m/s Slotted Augmented Parameter Model ........77 Parameter Estimate of Peak Current and Final Velocity for 3/8” diameter Grade 2 Bolts .........78 35 kJ Velocity Integral, Solid Non-Augmented. ....79 35 kJ Velocity Integral, Slotted Non-Augmented. ..80 35 kJ Velocity Integral, Solid Augmented. ........81 35 kJ Velocity Integral, Slotted Augmented. ......82 83 kJ Velocity Integral, Slotted Augmented. ......83 Transformed Geometry Moment of Inertia Calculation .................................................85 xi THIS PAGE INTENTIONALLY LEFT BLANK xii ACKNOWLEDGEMENTS Thank you Professor Bill Maier for your confidence and support throughout this project, and for facilitating exposure to resources beyond the Naval Postgraduate School. Thank you to Professor Terry McNelley and both the Physics and Mechanical Engineering Departments for facilitating a mixed curriculum tailored to this research. Snyder, George professional Jaksha, expertise and and Frank personal Thank you Don Franzen for commitments your which turned theory into practice in the fabrication and testing of this railgun prototype. Renk for your materials Thank you Tania Zaleski and Tim professional processing courtesy collaboration in between supporting the Laboratories and the Navy Postgraduate School. the National Thank you to all of the professional engineers at the Institute for Advanced Technology and the Center for Electromechanics at the University of Texas at Austin for direct contributions to the materials, throughout this design, thesis. and Thank modeling you Fred methods Beach, used Donald Gillich, Michael Lockwood, Michael Graham, and Juan Ubiera for building the NPS Railgun Laboratory infrastructure and establishing a standard of excellence. Finally, thank you Romina, Sophia, and Carmen for making success important. xiii THIS PAGE INTENTIONALLY LEFT BLANK xiv I. A. INTRODUCTION BACKGROUND The military electromagnetic missions is potential railgun well of for the U.S. Naval defined. The Navy’s notional surface-fire focused support investment and research of both Army and Navy sponsored programs through the Office identified of Naval the Research remaining and U.S. engineering Army ARDEC obstacles overcome prior to fielding a practical system. Postgraduate leverage School such (NPS) is investments uniquely in order has to be The Naval positioned to to investigate alternatives. The Center for Electromechanics (CEM) and the for Institute Advanced Technology (IAT) from the University of Texas at Austin have pushed the envelope in terms of materials, pulsed power, and systems engineering approaches to applied railgun technology. IAT engineers published an IEEE In January 2005, article entitled “Development of a Naval Railgun” summarizing the status of Naval railgun development and detailing areas where further research is warranted [1]. directly 10,000 related shots. identifying to extending Although the The railgun specific issues are bore progress destructive life has mechanisms to as been of high made as toward transitioning contacts and hyper-velocity gouging, no design parameters, material combination, or processing treatment have resolved their impact on bore life. Simultaneously parameters listed achieving the in 1 Table full while scale notional achieving shot frequencies of 6-12 rounds per minute is presently beyond the capacity of even large scale 1 laboratory facilities. Therefore, economy of simulation and scalable applied research is critical to the success of the railgun program. Table 1. Over produced Nominal EM Gun Parameters, [From Ref. 1] the past several decade, iterations NPS of railgun small research scale weapons to facilitate applied research. has demonstrator During the 2005 fiscal year, the NPS Railgun program has made a substantial investment in laboratory infrastructure including the purchase of ten 11 kV 830 µ−Farad capacitors from General Atomics and advanced high current switches, supplementing the existing pulsed power energy storage capacity by an order of magnitude. By leveraging the collaborative direct input of CEM, IAT, material modifications research support from Lawrence Livermore and Sandia National Laboratories, as well as multi-curriculum contributions from within the campus, NPS railgun research is now more than ever positioned to confront railgun technological deficiencies through applied engineering. 2 B. OBJECTIVE The objective fabrication, bore, and of this testing conventional of railgun thesis a is scalable, capable of square bore between single rail slotted rail performance configuration and series geometries. comparisons Shot are design, reconfigurable achieving package velocities in excess of 1500 m/s. (19mm) the The initial 3/4" supports comparisons augmentation, repetition accomplished launch solid and with and materials disposable rail liners at the rail to armature interface to protect the permanent main conductor rail structure. The railgun test platform incorporates a manual loading apparatus to facilitate consistent initial conditions including armature firing position and an interference armature fit which does not require Alternative full disassembly armature conditioning are geometries provided Unreliable performance spontaneous triggering practical capacitor between to of proposals inform the above charge and consecutive 7,000 limit 6500 power testing. switches volts, of for follow-on TVS-40 shots. caused requiring volts and a a corresponding total stored energy limit of 35 kJ. Chapter II examines weapon design including decisions regarding materials, geometry, and firing configurations. Chapter III discusses the design and limits of the existing pulsed power supply, as well as a proposed multi-module system. including static Chapter IV provides design verification analysis ideal railgun deflection conservation of parameter considerations, energy model. 3 modeling, and Chapter containment an V applied discusses experimental results. recommendations geometries, for and future Chapter VI testing, alternative processing materials. 4 methods concludes for with armature rail liner II. RAILGUN TEST PLATFORM DESIGN A. GENERAL The exploded assembly of Figure 1 below depicts the main structural elements of the railgun design without the loading apparatus. SolidWorks CAD software was used extensively for 3D modeling and for creating the technical drawings required for fabrication. comprehensive collection of Appendix B includes a individual parts and assemblies. Figure 1. B. Exploded Railgun Assembly MATERIAL PROPERTIES Materials selections were based on an analysis of the property tables included in Appendix A. These values were either obtained directly from the vendor or from the MATWEB online material database. None of the material selections are entirely new to railgun applications. The thickness and placement of the two insulating bars fixes the bore dimensions given the clamshell containment design. Due to superior compressive dimensional stability, 5 adequate over dielectric glass CoorsTek fired reinforced Alumina subsequent constant, to epoxy (Al203) fabrication and ceramic required specification of phenolics AD-96 was ease as including refurbishment such was as G-10, chosen. these +/-1% parts No were positional tolerances of through holes for the containment bolts and outer surface tolerance. dimensions finished to +/-0.005 inch Surface dimension tolerances were verified by micrometer measurements for both insulators. The main conductor and a range of rail liner materials were selected after a lengthy process that began with a much larger list extracted directly from materials handbooks based strictly on parameters of conductivity and hardness. This list was subsequently limited after a literature review of previously proven railgun materials, and by the final process of locating vendors with an inventory of 1/8” thick bar or plate stock suitable for the liner geometry. interest. Table 2 below summarizes the properties of The stainless alloy properties are included as a point of comparison. Untreated Material Properties Hardness Conductivity Rockwell B %IACS ** Material density (g/cm3) oxygen free copper 50 101 1.71E-06 8.94 chromium copper 79 80 2.16E-06 8.89 phosphor bronze 93 20 8.70E-06 8.86 copper tungsten 98 45 3.83E-06 14.84 aluminum 7075 87 33 5.15E-06 2.81 Stainless alloy 410 * 110 3 5.70E-05 7.8 * linear extrapolation from Rockwell C Table 2. Resisitivity (ohm-cm) @ 200C ** based on %IACS = (172.41e-6 / Resistivity) Summary of Rail Properties [After Ref. 2] 6 At the time of completion of this thesis, testing has been restricted to the chromium copper rail liners in order to preserve processed samples for higher velocity regimes. Several alternative armature geometries were fabricated by using three variants of aluminum including Al-6063, Al-6061, and Al-1100. All testing has been conducted using standard u-shaped Al-6063 armatures shown in Figure 25 of Appendix B. The main containment clamshell pieces were fabricated from 2” thick blocks of G-11 FR-5 glass reinforced epoxy laminate. This common small-bore railgun containment material has high resistance, high strength, and excellent machinability. 3/8” Grade 2 Containment stainless hardware steel hex includes cap nuts, twenty-two bolts, and washers. C. IMPROVED INDUCTANCE GRADIENT WITH SERIES AUGMENTATION One of the critical railgun design parameters is the inductance gradient, or inductance per unit length (L’). This parameter is a function of the rail and bore geometry. The most fundamental method for determining this parameter is based on modeling the rails as two infinite wires with a fixed radius, separated by a fixed distance representing the bore width between the rails. approximation, extensive more results accurate empirical applicable Although this is a fair research has to case the produced of the rectangular rail and square bore configuration, commonly referred to as Kerrisk’s Method [3]. Appendix C includes the spreadsheets used to evaluate the inductance gradient for the rail geometries selected for this design. 7 The energy efficiency of a small scale railgun driven through a pulse forming network is significantly limited even under ideal modeling conditions neglecting dissipative losses such as electrical resistance and friction. This ideal efficiency can be expressed by the following equation [4]. η= L'x ( L + L ' x) L’ is the inductance gradient, L is the total system inductance, and x is the rail length. values L= of 5.5 micro-Henries Applying the actual and L’ = 0.683 micro- Henries/meter for this specific design to a 10 meter gun length predicts an ideal energy efficiency approaching 50%. Using the actual effective railgun length of 50 cm, based on these same efficiency performance is values only L of 5.8%. emphasizes L’, and This the need the entering for maximum ideal argument maximizing L’ for while minimizing the total system inductance of the pulse forming network. There are several methods for enhancing the L’ parameter by enhancing the magnetic field in the bore above that created by a single rail pair. My design permits the use of series augmentation by incorporating a second pair of rails and connecting conductors to create the circuit path illustrated in Figure 2 below. Figure 2. Series Augmented Current Path 8 The result is an enhanced magnetic field in the bore region due to contributions from the same current pulse flowing through both rail pairs. Current through the outer rail pair establishes a field in the bore region ahead of the advancing armature as indicated in Figure 2. A review of literature regarding series augmentation indicates that for large fixed scale Lorentz high velocity force, the applications, benefits of based lower on a current requirements due to stronger magnetic fields in the bore region are offset by the resistive losses [5]. However, for my design, given the short rail length, no requirement to recover energy for high frequency repetitive shots, and considering supply, the constraint series of augmentation a is limited a stored practical energy method to improve projectile velocity. Whereas Kerrisk’s method for evaluating the inductance gradient is well defined for the simple railgun, a method for determining the new inductance gradient as a result of the augmenting rail contribution has not been empirically developed. The augmented L’ can be approximated by modeling each as rail integrating a the long magnetic thin current field carrying contribution region contributed by each wire. to wire and the bore Based on 1/4" outer rail width, and 3/8” width for the combined inner rail plus rail liner thickness, and making the assumption that current flows down the rail centerlines, the augmented geometry can be expressed in terms of the half-thickness of the inner rail, R as depicted in Figure 3. The factors used in Figure 3 are based on the actual augmented railgun geometry 9 with bore spacing of 3/4", a 1/32” insulation gap of mylar film and adhesive laminating sheets separating the rail surfaces, and R = 3/16”. Figure 3. The geometry Augmented Railgun Geometry where R = 3/16” magnitude depicted of in the Lorentz Figure following equation where µ0 3 is force (F) approximated for the by the is the permeability constant and I is current. ⎡ ⎛ ⎞ ⎛ ⎞⎤ ⎜ ⎟ ⎜ µ0 I 1 1 ⎟⎥ ⎛1⎞ ⎛ 1 ⎞ F= + + + ⎢ ⎜ ⎟ ⎜ ⎟ ⎥dx 4π R∫ ⎢⎜⎝ x ⎟⎠ ⎜⎝ 6 R − x ⎟⎠ ⎜ 11 + x ⎟ ⎜ 47 − x ⎟ ⎥ ⎜ ⎟ ⎜ ⎟ ⎝ 6 ⎠ ⎝ 6 ⎠ ⎥⎦ ⎣⎢ 2 5R ⎢ After integrating and reducing, ⎡ ⎛ 41 ⎞ ⎛ 41 ⎞ ⎤ ⎣⎢ ⎝ 6 ⎝ 6 ⎜ 6 R⎟ ⎜ 6 R ⎟ ⎥ µ 0 I2 ⎡ µ 0 I2 ⎢ ⎛ 5R ⎞ ⎛ 41 ⎞ ⎤ ⎛ 5R ⎞ F= ⎢ln ⎜ ⎢ 2ln ( 5 ) + 2ln ⎜ ⎟ ⎥ ⎟ + ln ⎜ ⎟ + ln ⎜ 17 ⎟ + ln ⎜ 17 ⎟ ⎥ = 4π ⎣ 4π ⎢ ⎝ R ⎠ ⎝ R ⎠ ⎝ 17 ⎠ ⎦ ⎜ R⎟ ⎜ R ⎟⎥ ⎠ ⎠ ⎦⎥ The equation can be written in terms of the components of the total L’. 10 F= µ 0 I2 1 ⎡ µ0 1 ⎤ 3.22 + 1.76 ) ⎥ I 2 = ⎡⎣ L ' pri + L ' aug ⎤⎦ I 2 ⎡⎣3.22 + 1.76 ⎤⎦ = ⎢ ( 4π 2 ⎣ 2π 2 ⎦ It is convenient to express the augmented inductance gradient as Kerrisk’s a gain method factor L’ that can calculated for be applied the to the non-augmented configuration. L ' pri + L ' aug 6.44i10 −7 + 3.52i10 −7 = = 1.55 L ' pri 6.44i10 −7 This gain factor of 1.55 is used for all subsequent discussions of the augmented inductance gradient for both slotted and solid rail configurations as demonstrated in the calculations of Appendix C. Appendix D applies COMSOL Multiphysics finite element software to model the relative improvement of the magnetic field and flux density across the center of the bore region and across the inner rail surface. liner COMSOL modeling neglects the geometry of the rail for all configurations. Electrical separation between inner and outer rail surfaces is accomplished by wrapping the outer rail in two full layers of 1.0 mil Mylar film. Although even a single layer of this film is rated to hold off the magnitude of breech voltage experienced across the rails, a slightly more robust physical interface was necessary to prevent defects in the rail surface finish from compromising the film integrity and short-circuiting the augmenting rails. Three layers of 3.0 mil adhesive laminating film supplementing the 2 layers of mylar film between the adjoining rail faces prevented the circuits seen in initial efforts to fire augmented. 11 short- Augmented Conductor Assembly -Initial configuration is 19mm (3/4”) square bore augmented / non-augmented firing options -Maximum non-augmented configuration: 38mm x 38mm (1-1/2” x 1-1/2”) -Ceramic insulator symmetry doubles working life Figure 4. Augmented Conductor Assembly Figure 4 demonstrates the augmented conductor assembly and bore geometry. By removing the external copper conducting rods the gun can be fired in the non-augmented configuration. external For initial non-augmented testing, both the conductor rods and the augmented rails were removed and a pair of G-11 FR-5 phenolic insulators was substituted to avoid eddy current losses in a disconnected rail pair. The inner rail pair is configured to support the use of a muzzle shunt. A copper conductor bar was used to short the muzzle shunt connection during initial testing prior to using actual armatures. The limited energy and short duration current pulse available for initial testing produced a minor muzzle flash. required to optimize muzzle Follow-on work will be shunt circuit elements for operating the gun at high power in order to prevent damage to the conductors as the armature breaks contact with the muzzle. At higher energies, an effective muzzle shunt may 12 become critical to preventing muzzle flash interference with the velocity measuring breaks-screens because of the confined operating range of the laboratory environment. D. IMPROVED GEOMETRY INDUCTANCE GRADIENT WITH SLOTTED RAIL Another technique to boost the L’ is to alter the rail geometry by a series of slots cut in to either side of the rails. The slotted geometry still provides the common rail height necessary for mechanical mounting of the rails within the containment structure, but confines current flow to a narrower center channel. This technique results in a more concentrated magnetic field within the bore region. To predict narrowed the rail gain provided height by dimension slotted of 1” geometry, was the the input parameter into the Kerrisk’s method calculation rather than the full exterior height, resulting in an expected gain factor of 1.45. Verifying an improvement in final armature velocity for a fixed input energy is significant because it has potential applications for both thermal management and rail containment designs for more advanced railgun systems. Figure 5 demonstrates the slotted rail geometry. detailed drawing is included in Appendix B, Figure A 17. Appendix D demonstrates COMSOL Multiphysics finite element software modeling of the relative magnitude of improvement of the magnetic field (H) and magnetic flux density (B=µoH) for slotted and non-slotted rail configurations. Figure 30 demonstrates how the altered slotted rail geometry affects the input parameters used to gradient. 13 calculate the inductive Figure 5. E. Slotted Rail Geometry ADDITIONAL COMPONENTS High tolerance structural design is required to limit rail deflection and maintain a consistent bore profile. Maintaining stiffness and straightness in a short, small bore railgun is significantly easier than for a large bore 10 m gun. In interference order fit when to achieve loading a the tight rail armature, to rail the gun incorporates a manual screw auger which advances a breech block and protruding 3” ram contoured to the back of the armature. The 3” ram provides a consistent longitudinal starting point for testing and places the armature in a region where magnetic fields are well established. effective railgun position is 50 cm. length beyond the loaded The armature The loading apparatus is mounted at four points to the containment shells via 3/8” stainless steel threaded rods and helicoil inserts. This apparatus is currently under-utilized because the lack of sufficient power to overcome static friction mandates a loose armature fit. Although a slight interference fit was used for the preliminary testing discussed 14 herein, the armatures fabricated to actual design bore geometry required some volume reduction via polishing in order to prevent binding. During testing, prior to installing the loading apparatus, a bore ram is used to force the polished armature through the entire length of the gun to identify excessive regions of binding. Figure 6 shows a side and overhead view of the assembled loading apparatus. Figure 6. The railgun Railgun Loading Apparatus design also includes a muzzle block mounted with four 1/4" stainless steel bolts into helicoil inserts set in the containment shells. The current muzzle block has a 1-1/4” diameter hole through which the armature exits. Although this design is adequate for testing at 35 kJ, must it supply. be improved prior to upgrading the power A square muzzle port properly sized to the bore dimension may assist in confining the deleterious effects of the muzzle flash to the rail liner rather than to the underlying main conductor rail. The photograph of the muzzle block in Appendix F Figure 59, was taken immediately following a shot, and hints at the potential for arcing damage at the muzzle exit at higher energies. 15 A series inductor was constructed by tie-wrapping 4/0 welding cable around a PVC shape. Although a much larger inductor was initially fabricated, optimized to maximize the pulse length, its effect of diminishing peak current resulted in the inability to overcome static friction when firing with a stored energy of 35 kJ. A final compromise between peak current and pulse length was accomplished by using the three turn inductor pictured among other components in Figure 7. 3-turn series inductor of welding cable wound around 13-1/2” diameter shape threaded through a protective hose Bore ram with G-10 endpiece G-11 rail substitute for non-augmented configuration Figure 7. In 3.0-µH Series Inductor and Components preparation for shooting at high velocities, a target chamber was custom designed and fabricated by MGM Targets. It consists of a three foot long, 10” diameter steel tube with a 6” entry portal. The tube is filled with ground rubber contained by solid rubber sheets at the entry point and along the top, where a bolted access panel allows projectile recovery. The target chamber is pictured in Figure 8. 16 Figure 8. Target Chamber 17 THIS PAGE INTENTIONALLY LEFT BLANK 18 III. PULSED POWER SUPPLY A. PRESENT SYSTEM The stored energy supply consists of two 830 µF, 11 kV rated Maxwell Model 32327 capacitors switched parallel Maxwell TVS-40 vacuum switches. by two These capacitors discharge through dedicated pairs of high power rectifier diodes connected crowbar the current waveform at peak value to prevent oscillation. The diodes by ABB pair is are to model Switzerland Ltd. a common 5SDD ground 50N5500, which manufactured Semiconductors. Each diode constrained by an ABB diode clamp model 5SAC 18V9001, rated at 90 kN. Downstream of the diode strings, current output from individual each capacitor is monitored Pearson Model 1330 wide band current monitors. with two The outputs from the parallel TVS-40 switches are connected by a single bus bar Pearson and currents model 1423 up to current 500 kA monitor. are monitored Output and by a return leads extend through the side of a steel framed, plexiglass covered enclosure, allowing connection to the railgun leads with 4/0 Flex-a-Prene heavy duty welding cable rated for 600 Volts. The input side welding cable is wound around a 13-1/2” PVC shape to serve as a series inductor as pictured in Figure 7. from extreme In order to protect the inductor cable run compressive forces experienced during discharges, the 3/4" cable is threaded through a 7/8” inner diameter rubber hose. Figure 9 shows an overhead view of the power supply cabinet. 19 Figure 9. The Pearson output, and attenuator Agilent Power Supply Cabinet 1330 is produces further before Infinium being S4852 an initial conditioned processed m-Volt/Amp through for oscilloscope. 5 display The a 10:1 using Pearson an 1423 produces a 1 m-Volt/Amp output, and is sent through both a 10:1 attenuator and 2:1 divider for display. screen captures for each included in Appendix E. shooting Oscilloscope configuration are Peak currents registered by the combined Pearson 1423 output ranged from 88-98 k-Amps for all four rail configurations when discharged from an initial capacitor voltage of 6500 volts. PSpice circuit modeling the is included in Appendix D for 6500 Volt initial charge and other experimentally determined values for the railgun test platform including, inductance, resistance and railgun resistance as specified in Figure 45. The railgun resistance 20 value of 0.3 m-Ohm was initially calculated based on the material properties and cross-sectional areas of the entire railgun conductor apparatus from input to output leads. The main capacitor pair is charged with a Bertan Associates Series 105 1kW High Voltage Power Supply through a separate capacitor circuit is of monitored diodes by a and resistor dedicated bars. voltmeter Each display panel. Simultaneous triggering of the TVS-40 switches is done with a Glassman High Voltage Inc. Series LX High Voltage Power Supply via catalog #315DM410. two 100 µF General Atomics capacitors On a single firing signal, each 100 µF capacitor discharge is stepped up to 5kV using homemade transformers. Figure 10 demonstrates the power supply cabinet interfaces for charging, triggering, and supply and return to the railgun test platform. Figure 10. Power Supply Cabinet Interfaces Throughout various stages of testing, elements within the pulsed power circuit delayed progress due to arcing, 21 failed diodes, non-triggering switches, and ruptured transmission cable leads. Although the initial goal was to operate the capacitors at 9 kV, which would have supplied a total stored energy of 67.2 kJ, erratic switch output and spontaneous triggering above 7 kV demanded that final data collection be conducted at 6.5 kV, which limited total stored energy to 35 kJ. As the TVS-40 switches are rated beyond documented these limits, a trigger rejuvenation procedure may restore them to improved functionality [6]. The oscilloscope current traces in Appendix E clearly identify both uneven current peaking and pulse decay rates from the two capacitors attributed to uneven coupling across the TVS-40 switches. B. REDESIGNED POWER SUPPLY The Naval Postgraduate School Physics Department has invested in ten new General Atomics capacitors with the same catalog number and ratings as the Maxwell Laboratories pair used for testing. limited to 35 kJ, Where testing for this research was incorporating the present and new capacitors into a multiple module system will provide a maximum stored energy capacity of 600 kJ. The older capacitors have been cycled at high voltages since at least June of 1999 and might be contributing to uneven power sharing through the TVS-40 switches. In addition to investigating switch refurbishment, a comparison of output current profiles using a pair of the new capacitors within the existing power supply would indicate whether the irregular discharge can be solely attributed to the TVS-40 switches. 22 In addition to the new capacitors, two new high current Titan ST-300A high action spark gap switches and associated triggering apparatus have been purchased. The Titan switches are rated for 600 kA peak current and 55 kV peak voltage and will permit a single switch to control the output of a module pair of capacitors. Figures practical 47 four and 48 module of Appendix ripple fired D demonstrate circuit designed a to maintain an average 280 kA current pulse for 0.67 ms, which should accelerate an 11.4 gram armature to 1500 m/s over the 50 cm configuration rail (See length Table for the 19). slotted, The model augmented circuit incorporates a 1 m-Ohm muzzle shunt resistor for a first look at the dynamics which occur as the armature breaks electrical contact with the muzzle. This model requires that each module be charged to near capacity at 10 kV, and incorporates optimized delay times and series inductors. Achieving the effective rise time and peak current required to overcome the static friction of a tight interference fit requires firing the first two modules simultaneously. Such a fit is critical to maintaining the solid armature to rail interface necessary to delay transition to arcing and to prevent rail damage from intermittent within the bore. 23 armature caroming THIS PAGE INTENTIONALLY LEFT BLANK 24 IV. DESIGN VERIFICATION A. PARAMETER MODEL On May 6, 2004, Dr. Mark Crawford, Pulsed Power and Electromagnetic Launch Team Leader from IAT, presented a colloquium lecture to the Naval Postgraduate School Physics Department [7]. The parameter-based system. dissertation approach The to outlined designing applicable a a top basic thumb-rules are level railgun based on simplifying assumptions such as a symmetric acceleration profile which accelerations performance, allows for conservative rail containment. identifying geometry, Appendix C both average modeling electrical applies and of velocity action, this peak and rail parameter-based approach to the four physical configurations, solid nonaugmented, slotted non-augmented, solid augmented, and slotted augmented, and to a range of energy inputs as a basis of comparison to other modeling techniques in order to validate containment bolt sizing, and to correlate average current to final velocity. P-Spice circuit model predictions in Appendix D for the average current required to reach 1500 m/s over the 50 cm effective railgun length are based on the average required current calculated from the parameter-based model. The experimental results from the solid augmented and slotted augmented experimental shots are also inputted into the parameter model (Tables 21 and 21) for comparison. The parameter model predicts that a final armature velocity of 1500 m/s requires a peak current of nearly 500 kA for the solid, non-augmented configuration as detailed in Table 16. Therefore, 500 kA is used to assess containment deflection, 25 and bolt diameter and spacing in Section C below. A final application of the parameter model uses bolt diameter and yield strength to predict the maximum current of 355 kA, and maximum achieved on final the velocity railgun of 1085 test m/s platform which with can be Grade 2 stainless 3/8” bolts, per Table 21. B. CONSERVATION OF ENERGY CIRCUIT MODEL In order to evaluate experimental results and estimate velocity performance for an effective rail length of 50 cm, a simplified circuit model was developed for module capacitive stored energy power supply. a single Appendix C details the process which applies conservation of energy principles to Kirchhoff’s Voltage law, coupling inductive energy transfer to projectile kinetic energy via Lorentz force parameters. In the following equation, F is the Lorentz force accelerating the armature, m is the armature mass, dv/dt is armature acceleration, L’ is the inductive gradient of the rails, and I is the time dependant value of current. F =m The model neglects dv 1 = L'I2 dt 2 frictional losses and relies on several simplifying assumptions including assuming that the total system inductance L is much larger than the product of L’ and rail length x. effective system The model also assumes that the total resistance R is much larger than the resistance R’x, where R’ is the rail resistance per unit length. In both cases, L and R are verified experimentally to be an order of magnitude larger then L’x and R’x for the 26 L is calculated based on the rise time 60 cm test platform. to peak current in a oscilloscope at 150 µs. discharge cycle, measured by The following equation for the period of oscillation T demonstrates how inductance can be solved based on the known capacitance C of 1.66 mF. T = 4∆trise = 2π LC In order to simplify the model to a purely inductive energy transfer between the total system inductance and the railgun, the capacitive stored energy is eliminated from the final expression by neglecting the initial 150 µs of current ramping up to its peak value. The increase in armature velocity during the rise time is small. The time dependent expression for current is an exponentially decaying waveform: I ( t ) = I o exp ⎛ − Rt ⎞ ⎜ ⎟ ⎜ L ⎟ ⎝ ⎠ , where the peak current Io is determined by: 1 2 ⎛C ⎞ ⎟ Vo L ⎝ ⎠ . I0 = ⎜ Vo is the initial state of capacitor voltage which for my experimental data runs was 6500 Volts. The resulting expression provides for a separable differential equation for rail length as a function of velocity [4]. dv 2 Rv L ' v 2 L ' I o2 v + + = dx L L 2m 27 An integral table gives the expression including the integration constant D. ( 1 2 ∫ dx = 2a ln av + bv + c ⎡ ⎛ 2av + b − b 2 − 4ac ⎞ ⎤ 1 ⎢ ⎟⎥ + D ln ⎜ 2 2 ⎜ ⎟ 2a ⎢ b − 4ac ⎝ 2av + b + b − 4ac ⎠ ⎦⎥ ⎣ )− b The circuit parameters which comprise factors a ,b , and c , are defined below. a= −L ' L b= −2R L c= ⎡ ⎛1 2 ⎞⎤ ⎢ L ' ⎜ CVo ⎟ ⎥ ⎠⎦ ⎣ ⎝2 ( mL ) The integration constant D scales the solution such that zero velocity corresponds to a zero length railgun. The actual values used for each variable are included in Tables 22-26 of Appendix C. Table 25 gives the integration for parameters associated with the slotted augmented rail configuration, and predicts a final velocity of 293 m/s corresponding to the 50 cm effective rail length, and total stored energy of 35 kJ. I have neglected the minimal projectile velocity which exists when I = Io, as well as losses due to friction between the rails and armature, the effects of which compensate for each other to some extent. C. STRUCTURAL DESIGN The 24” railgun containment halves are clamped by a total of 22 Grade 2 stainless hex-head steel bolts of 3/8” diameter, rated by the vendor at 57 ksi in accordance with the SAE J420 1985 abstract [8]. The bolts are longitudinally spaced at 2” intervals down the length of the containment beginning 1” from either end. 28 Conservative static modeling assumptions were applied to assess the overall containment design in terms of rail deflection, bolt spacing and diameter. augmented configuration and the From the solid non- 500 kA peak current predicted in Table 16 of Appendix C, rail repulsion force per unit length, p, is calculated by using the following equation. −7 lb f F µo I 2 ( 4π • 10 ) ( 500kA ) MN p= = = ≈ 1.75 ≈ 9983 x 2π d m in ( 2π • 0.0286 ) 2 In the previous equation, F is the rail repulsion force, x is the total rail length, µo is the permeability constant, I is peak current, and d is the length in meters between rail centerlines considering the rail liner and primary rail as a single solid conductor. Two specific structural design objectives are investigated. Maximum rail deflection must be limited to less than 0.0001 inches, Under worst case loading, the containment bolts must not exceed their static yield strength. A 2-D model of the distributed longitudinal rail repulsion force between any two consecutive bolt pairs is represented by the fixed-end beam model in Figure 11. 29 L ymax pL4 ⎛L⎞ = y⎜ ⎟ = ⎝ 2 ⎠ 384 EI p ymax Figure 11. Fixed End Distributed Load Beam Model [After Ref. 9] Maximum deflection, ymax, occurs at the midpoint between bolts spaced at a distance L, of 2”. E is the modulus of elasticity, and I is the moment of inertia based on the beam demonstrates materials cross-section. the and Appendix method used to geometry into a simplify single C, Section the C, composite representative, homogenous beam in order to determine maximum deflection. For 9983 lbf/in loading, the calculated deflection is less than 0.00002 inches, confirming adequate containment stiffness. The validity of the previous deflection calculation depends on achieving the fixed boundary conditions of no slope and no deflection based on bolt loading conditions. Here I consider the total rail length, x = 24”, and the total of 22 bolts of 3/8” diameter to determine the maximum load per unit length (pmax) achievable at the bolt Yield Strength (YS) threshold of 57 ksi. pmax lbf ⎞ ⎛ 22 *0.1104in 2 i57,000 2 ⎟ ⎜ # bolts i Abolt iYS ⎝ lbf lbf in ⎠ = = ≈ 5770 < 9983 x in in 24in 30 The maximum sustainable load of 5770 lbf/in is less than that which results from the 500 kA peak current condition corresponding to a 1500 m/s exist velocity for As such, pmax is the solid non-augmented configuration. used to determine the actual peak current capacity to Converting 5770 lbf/in to metric inform follow on testing. units yields approximately 1.01 MN/m. I max = The 2π d i pmax µo resulting ≈ 2π i0.0286mi1.01 4π i10−7 calculation N A2 MN m ≈ 380kA shows that the present containment design is capable of maintaining bolt loading below yield strength up to a maximum current of 380 kA. Based on parameter modeling in Table 22, this peak load capacity correlates with the alternative method of rail repulsion force and bore height to calculate the force per unit length. Table 22 indicates that the Grade 2 bolt yield strength threshold is achieved at 355 kA, correlating to a final velocity of about 1085 m/s. Therefore, in order to achieve the no-yield requirement at 500 kA, the grade 2 stainless bolts must be upgraded to grade 8. The ACF Components vendor quotes grade 8 hex head bolts at a yield strength of 130,000 ksi [8]. pmax kip ⎞ ⎛ 22*0.1104in 2 i130 2 ⎟ ⎜ # bolts i Abolt iYS ⎝ lbf lbf in ⎠ ≈ 13,156 = = > 9983 24in x in in The grade 2 hardware currently in use will suffice until considerable additional stored energy is integrated into the pulsed power supply. All containment modeling is based on conservative static loading rather than the actual 31 dynamic loading which occurs during firing. The previous design demonstrate an efforts improve verification containment such methods that future to adequate bore tolerance should concentrate on deficiencies in the rail liner surface finish rather than design. 32 the overall structural V. A. RESULTS SHOT DIAGNOSTICS Table 3 lists the experimental results. Shot 1 2 3 4 5 6 7 Configuration L' System Voltage (uH/m) L (µH) solid, non-aug 0.3037 5 solid, non-aug 0.3037 2.5 solid, non-aug 0.3037 5.5 slot, non-aug 0.4405 5.5 solid, aug 0.4707 5.5 slotted, aug 0.6828 5.5 slotted, aug 0.6828 5.5 Table 3. Shots 3-7 Initial Final Input Energy Ipeak Velocity KE Efficiency (KJ) 53 35 35 35 35 35 35 (k-Amps) N/A 110 97.8 88.0 95.0 91.4 88.9 (m/s) 246 168 105 117 265 294 286 (J) 332.8 160.9 62.8 78.0 393.3 492.7 466.2 0.63% 0.46% 0.18% 0.22% 1.12% 1.41% 1.33% (V) Mass(g) Mass(g) 8000 11 10.2 6500 11.4 10.6 6500 11.4 11 6500 11.4 10.9 6500 11.2 10.6 6500 11.4 11.2 6500 11.4 11.1 Experimental Data Results were all conducted with the same series inductor and initial capacitor charge of 6.5 kV in order to compare each configuration. Shot 1 was taken with a capacitor charge of 8 kV and a 5 µH total system inductance. This 8 kV shot produced two in a longer series of testing delays caused pulsed power by the supply. failure On of this components shot in within the particular, the series inductor solid copper cable lead separated from the cable run. coils Also, the forces squeezing the series inductor together axially ruptured the sheath and rendered the line unusable. rubber insulating The peak current value for the 8 kV shot was unreadable due to over-ranging the oscilloscope settings. After the 8 kV shot, the TVS-40 switches began to spontaneously trigger when charged up to 7 kV, ultimately demanding that the data runs be limited to 6.5 kV. Prior to re-introducing a new series inductor, a new sheathed cable run was threaded through a 7/8” inner diameter rubber hose to prevent a similar rupture, and new cable leads were fabricated. 33 The 2.5 µH inductance listed for shot 2 represents the total system inductance with no additional series inductor. Although the resultant velocity of 168 m/s surpassed all other subsequent non-augmented shots which did incorporate a series inductor, the higher current peaking resulted in one TVS-40 switch failing completely. Upon obtaining a replacement switch, a 3 µH series inductor was used for all further testing in order to avoid over-stressing the system while permitting consistent test parameters for all shooting configurations. The remaining experimental firings, shots 3-7 of Table 3, were conducted at 6.5 kV with a total system inductance of 5.5 µH. Although statistically insignificant for the single point sampling, the resultant velocities demonstrate a trend consistent with each improvement in the inductance gradient, ranging from 105 m/s for the solid non-augmented configuration to an average of 290 m/s for the two slotted augmented shots. The respective gain factors for slotted geometry, series augmentation, and their combined totals as predicted by the L’ and magnetic field models detailed in Appendix C are compared to the experimental gain in Table 4. The experimental gain factors are determined by the following ratios. 2 maug vaug 2 mslotted vslotted = Gaingeometry 2 msolid vsolid 2 mnon − aug vnon − aug = Gainaug For all cases other than solid augmented, the initial mass is 11.4 grams and cancels square of the final velocities. 34 leaving a ratio of the The augmented gain factor is an average of the gains calculated for both the slotted and solid rail geometries. The lower than expected velocities for the non-augmented configurations in shots 3 and 4, suggest that given only 35 kJ of stored energy and diminished magnetic accelerating static force fields is friction. configuration near Shot with no without 2 augmentation, the threshold for the series of solid inductor the overcoming non-augmented produced a final velocity closer to the value expected by the conservation of energy model in Table 23. non-augmented shot without Although data for a slotted a series inductor is not available at this time, the experimentally determined gain factors in Table 4 marked with an asterisk (*) use the 168 m/s velocity result of shot 2. L' Geometry Modeling 1.55 1.45 2.25 Gain Factors Series Augmentation Slotted Geometry Total Gain Table 4. Magnetic Field Modeling 1.66 1.5 2.49 Experimental Results (mv2) 6.26 ( * 2.49 ) 1.22 7.63 ( * 2.98 ) Predicted vs. Experimental Gain Factors There is close agreement between gain factors produced by the two respective modeling techniques. limited data runs, the experimental unreliable and deviate from the models. the augmentation and the slotted Due to the gain factors are In all cases, both geometry resulted in improvements in final velocity. Additional operational velocity shots velocity results from which were diagnostics shots 3 performed suggest and 4 may that have prior the to lower been the result of insufficient power to overcome static friction. During two early shots at the 35 kJ level, using a 22.5 µH series inductor intended to match the current pulse length 35 to the total rail length, the armature in one case did not break static friction at all, and in another traveled only 3 inches down the barrel. Significant enhancement of the stored energy supply is necessary to generate valid experimental results for comparison to the idealized models which neglect frictional losses. Furthermore, the moderately loose interference fit between the entirely armature inadequate and for bore used maintaining contact at higher velocity regimes. in these effective tests is electrical When the pulsed power supply is adequately hardened to permit extracting stored energy near the capacity of individual modules, and when multiple modules contribute to building an adequate current waveform, the loader mechanism can be used to provide an appropriately tight interference fit. The consistency of this fit along the bore length as indicated by the torque required to manually advance a test round, and the use of a torque wrench on the loading mechanism may be critical to establishing conditions necessary to validate gain factors experimentally. The parameter based modeling in Appendix C predicts no violations of generally accepted thresholds such as rail heating and linear current density for all configurations when the muzzle velocity is 1500 m/s. The peak current, parameter based calculations for the minimum adequate bolt diameter performed are in using close classic agreement beam with bending the calculations analysis. Both methods indicate that the Grade 2 bolt will reach their yield strength threshold between 335 and 380 kA, with the resulting exit velocity ranging from 1085-1150 m/s. 36 The conservation of energy model prediction of 293 m/s velocity for the slotted augmented configuration with 35 kJ of stored energy compares velocity of 290 m/s. with the average experimental The conservation of energy model was also evaluated to predict the maximum velocity which could be achieved by a single module of two capacitors charged to 10 kV, which corresponds to 83 kJ of stored energy. The resultant velocity for the 50 cm effective rail length is 495 m/s. The current traces in Appendix E from the experimental shots indicate that the magnitude of current (I) is small as the projectile exits the gun. A total system resistance of 3.3 m-Ohm has been used for all simulations. The power supply resistance was measured to be 3 m-Ohm and the rail resistance was calculated to be 0.3 m-Ohm from the resistivity and geometry of the copper conductors within the railgun assembly from input to output leads. calculated for each shot in Table 5. calculated by the following equation R/L’ is The R/L’ ratio is where each of the terms is defined in Table 5. R 1 = (Wo _ − KE ) L ' 2mv Shots 1-2, and 5-7 support the model parameter of 3.3 m-Ohms of total system resistance. The two low velocity non-augmented results for shots 3 and 4 are outliers at 4.44 and 5.78 m-Ohms respectively, suggesting additional frictional losses. 37 Shot Configuration L' Armature Input Energy Velocity Kinetic Energy (uH/m) Mass(g) 1 2 3 4 5 6 7 solid, non-aug solid, non-aug solid, non-aug slot, non-aug solid, aug slotted, aug slotted, aug 0.3037 0.3037 0.3037 0.4405 0.4707 0.6828 0.6828 Table 5. R/L' R Wo (KJ) (m/s) KE (J) (Ohm-m/H ) (m-Ohm) 53 35 35 35 35 35 35 246 168 105 117 265 294 286 332.8 160.9 62.8 78.0 393.3 492.7 466.2 9793 9137 14620 13120 5896 5221 5367 2.97 2.77 4.44 5.78 2.78 3.57 3.66 11 11.4 11.4 11.4 11.2 11.4 11.4 Total System Resistance and R/L’ Results Appendix F includes photographs insulator, and armature wear. of typical rail, Every shot resulted in a thin coating of melted aluminum deposited along the rail length. Gaps in the presence of the coating correlated to the localized damage in the chromium copper rail material suggesting specific locations where between the armature and rail. the as-fabricated measure at 0.748” 3/4" the developed Micrometer measurements of square where arcing Aluminum same 6063 measurements armatures for the ceramic insulator thickness hold the tighter tolerance of 0.750” +/- 0.0001 along the entire length. Although these dimensions suggest an ideal fit, the surface finish in the bore region of the rail liner is accomplished by 400 grit belt sanding followed by 600 grit hand sanding. Hand feeding of the armatures down the bore length indicates alternating regions of binding and slipping. As a result, the final loose sliding fit was accomplished by polishing the outer armature faces. The volume of material removed by this polishing was significant: all of the as-fabricated armatures had an initial mass of 11.6 grams but the typical final armature launch mass was 11.4 grams. In general, the more material removed from the armature during polishing to provide a working fit, the more rail damage observed postfiring due to caroming of the round back and forth between 38 the rails during launch. The extreme variation in electrical contact during launch which results from such a poor fit contributed to the rail damage as demonstrated by localized blackened aluminum and copper regions where arcing likely occurred. In one shot, the results of which are not included in Table 3 due to occurring prior to effective diagnostics, the as-fabricated armature provided a working fit without polishing. This particular shot produced an even aluminum coating down the entire rail length with no visible damage to the underlying rail liner. Inspections of the spent armatures reveal that the highest velocity shots experience the least loss of armature mass, and the least deformation of the trailing arms. Root radius wear for the augmented higher velocity shots was grainy but retained the aluminum metallic tone whereas the root radius of the non-augmented shots was obscured by blackened deposits. Although the current levels experienced in this testing are far less than the 900 kA threshold for root radius melting observed by Francis Stefani and Trevor Watt for a 40 mm square bore railgun, visual inspection of the spent armatures suggest that the onset may occur at significantly lower currents for this small bore test platform [13]. 39 THIS PAGE INTENTIONALLY LEFT BLANK 40 VI. CONCLUSION A. PERFORMANCE SUMMARY AND RECOMMENDATIONS The trend of improved velocity corresponding to engineered inductance gradients, and qualitative agreement between alternative modeling approaches indicates that there are no immediate impediments to scaling the stored energy supply in order to experiment with higher velocity regimes on this railgun test platform. However, incremental advances are recommended in order to allow the development of diagnostics. pulsed power supply components and Before moving to multi-module pulsed energy configurations, fully harnessing single must be module the stored demonstrated. energy As of a previously discussed, a 10 kV charge corresponding to a total stored energy of 83 kJ should produce nearly 500 m/s. Concurrent with fully utilizing a single module, the armatures can be loaded into a mid-bore position, reducing the effective rail length to an appropriate value such as 25 cm in order to investigate behavior when there is significant current as the armature exits the rails. This would provide the opportunity to experiment with a muzzle shunt present. The present method of connecting the series inductor welding cable directly to the railgun conductor leads must be improved decouple the railgun by the physical itself. directly addition coupled Such to stress a the of of fixed fixed the manifolds inductor manifold railgun from could supply which and then the be return conductors via a solid copper bus-bar. The basic mechanical containment is sound for scaling to at least 1085 m/s using 41 Grade 2 stainless bolts. Upgrading to Grade 8 stainless steel bolts permits scaling above 1500 m/s for all configurations. weak points threaded related and to braised augmenting rails conductor rods the mechanical conductor connect used to However, the likely connections the for design containment augmented are the where the penetrating operation, as demonstrated in Figure 12. Potential for thermal and mechanical failure at location of threaded / braised joint connecting conductor rod to augmented outer rail Figure 12. As Augmented Rail to Conductor Threaded and Braised Joint adequate addition to stored targeting energy becomes increases in available, the degree in of interference fit, incorporating a bore rider in front of the armature either attached or as an independent projectile load may help both seal the bore in front of the armature to prevent blowing by of the liquid interface layer, and stabilize the armature ride within the bore, preventing the damage due to caroming which currently exists. A variety of armature geometries, pictured in Figure 13, have been fabricated to provide options for improving 42 the elastic response in the trailing arms in order to maintain solid to solid electrical contact with the rails. Figure 13. B. Armature Geometry Alternatives (Appendix B) MATERIALS PROCESSING METHODS Anticipating the maturation of the power supply, preparations for the first application of the railgun test platform have been initiated. A collaboration between Lawrence Livermore (LLNL) and Sandia National Laboratories (SNL) is underway in order to conduct in-bore testing of laser peened untreated [13], rail ion-beam liner surface samples for treated the [14], chromium and copper, phosphor bronze, copper tungsten, and aluminum 7075 alloys discussed in Table 2. Timothy Applications Modification Renk, of Project Ion Beams Materials Sandia’s Materials surface treatments on pairs of each of these materials. Tania Project Leader has at for beam Zaleski, Laboratory, Leader for 43 performed Laser ion Peening at LLNL, has conducted preliminary micro-hardness testing on each material treated by a range of laser parameters in order to determine the optimal parameters to be used on the full rail liners. Following completion of the rail liner peening, and nano-hardness testing on the ion beam treated samples, LCDR Paul Clifford, USN, will conduct a series of shots at the Naval Postgraduate School in order to assess the suitability of these processes for enhancing rail life over untreated liner materials. 44 APPENDIX A. MATERIAL PROPERTY DATA SHEETS Rail liner: Chromium Copper UNS C18200, TH04 MatWeb Data Sheet Date: 7/12/2005 Chromium Copper, UNS C18200, TH04 Temper flat products, aged KeyWords: CDA 182, CC101, ISO CuCr1, CEN CW105C, A2/1 SubCat: Copper Alloy, Nonferrous Metal, Metal Material Notes: Good to excellent corrosion resistance. Excellent cold workability; good hot Applications: resistance welding electrodes, seam welding wheels, switch gear, electrode Available as flat products, wire, rod, tube, and shapes. Component Value Min Max Chromium, Cr 0.6 1.2 Copper, Cu 99.1 Iron, Fe 0.1 Lead, Pb 0.05 Silicon, Si 0.1 Properties Value Min Max Comment Physical 8.89 --at 20°C (68°F) Density, g/cc Mechanical Hardness, Rockwell B 79 --460 --Tensile Strength, Ultimate, MPa Tensile Strength, Yield, MPa 405 --Elongation at Break, % 14 --In 50 mm 130 --Modulus of Elasticity, GPa Poissons Ratio 0.3 --UNS C36000 (free-cutting Machinability, % 20 --brass) = 100% Shear Modulus, GPa 50 --Electrical Electrical Resistivity, ohm-cm 2.16E-06 --at 20°C (68°F) Thermal CTE, linear 20°C, µm/m-°C Heat Capacity, J/g-°C Thermal Conductivity, W/m-K Melting Point, °C Solidus, °C Liquidus, °C Processing 17.6 0.385 171 -1070 1075 ---1070 --- -from 20-100°C (68-212°F) --TB00 temper at 20°C (68°F) 1075 --- Solution Temperature, °C Aging Temperature, °C Hot-Working Temperature, °C ---- 980 425 800 For 10-30 minutes, water 1000 quench 500 For 2-4 hours 925 Table 6. Chromium Copper Rail Liner Material Properties [After Ref. 2] 45 Main conductor rails: OFE Copper C10100, H04 MatWeb Data Sheet Date: 7/12/2005 Oxygen-free Electronic Copper (OFE), UNS C10100, H04 Temper, flat products KeyWords: BS C110, C103 , ISO Cu-OFE, CEN CW009A, oxygen-free high conductivity copper (OFHC), CDA 101 SubCat: Copper Alloy, Nonferrous Metal, Wrought Copper, Metal Material Notes: Flat test specimens, 1mm and 6mm thick, H04 temper. Applications: busbars, bus conductors, waveguides, hollow conductors, lead-in wires and anodes for vacuum tubes, Processing: Excellent hot and cold workability; good forgeability. Fabricated by bending, coining, coppersmithing, Corrosion Resistance: Good to excellent. Susceptible to galvanic corrosion when coupled with iron, aluminum, Component Value Min Max Copper, Cu 99.99 Properties Value Min Max Comment Physical Density, g/cc 8.94 --at 20°C (68°F) Mechanical Hardness, Rockwell B 50 --Hardness, Rockwell F 90 --Hardness, HR30T 57 --1mm thick flat specimen Tensile Strength, Ultimate, MPa 345 --Tensile Strength, Yield, MPa 310 --0.5% extension Elongation at Break, % 6 --1mm thick flat specimen Elongation at Break, % 12 --6 mm specimen. Modulus of Elasticity, GPa 115 --Poissons Ratio 0.31 --Fatigue Strength, MPa 90 --1E+09 cycles, 1 mm thick flat test specimen. Machinability, % 20 --UNS C36000 (free-cutting brass) = 100% Shear Modulus, GPa 44 --Shear Strength, MPa 195 --Electrical Electrical Resistivity, ohm-cm 1.71E-06 --at 20° C (68°F) Thermal CTE, linear 20°C, µm/m-°C 17 --from 20-100°C (68-212°F) CTE, linear 100°C, µm/m-°C 17.3 --from 20-200°C (68-390°F) CTE, linear 250°C, µm/m-°C 17.7 --from 20-300°C (68-570°F) Heat Capacity, J/g-°C 0.385 --at 20°C (68°F) Thermal Conductivity, W/m-K 391 --at 20°C (68°F) Melting Point, °C 1083 --Processing Annealing Temperature, °C -375 650 Hot-Working Temperature, °C -750 875 Recrystallization Temperature, °C 18.3 --C37700 (forging brass) = 100% Table 7. Oxygen Free Copper Rail Liner Material Properties [After Ref. 2] 46 Rail liner: Phosphor bronze C51000, H06 MatWeb Data Sheet Date: 7/12/2005 Phosphor bronze 5% Sn, UNS C51000, H06 Temper flat products KeyWords: CDA 510, PB102, ISO CuSn5 SubCat: Copper Alloy, Nonferrous Metal, Bronze, Metal Material Notes: Good to excellent corrosion resistance. Excellent cold workability. Fabricated by blanking, Applications: bellows, bourdon tubing, clutch discs, cotter pins, diaphragms, fasteners, lock washers, wire brushes, chemical hardware, textile machinery, welding rod. Trace content of Phosphorus. Test specimen: flat products - 1mm Component Value Min Max Copper, Cu 93.6 95.6 Iron, Fe 0.1 Phosphorous, P 0.03 0.35 Lead, Pb 0.05 Tin, Sn 4.2 5.8 Zinc, Zn 0.3 Properties Physical Density, g/cc Mechanical Hardness, Rockwell B Tensile Strength, Ultimate, MPa Tensile Strength, Yield, MPa Elongation at Break, % Modulus of Elasticity, GPa Poissons Ratio Fatigue Strength, MPa Machinability, % Shear Modulus, GPa Electrical Electrical Resistivity, ohm-cm Thermal CTE, linear 250°C, µm/m-°C Heat Capacity, J/g-°C Thermal Conductivity, W/m-K Melting Point, °C Solidus, °C Liquidus, °C Processing Annealing Temperature, °C Table 8. Value Min Max 8.86 -- -- 93 535 550 6 110 0.341 205 20 41 ---------- ---------- 8.70E-06 -- -- 17.8 0.38 84 -975 1060 ---975 --- ---1060 --- -- 475 675 Comment at 20°C (68°F) 0.5% extension under load In 50 mm At 10^8 cycles, 1 mm strip UNS C36000 (free-cutting brass) = 100% at 20°C (68°F) from 20-300°C (68-570°F) at 20°C (68°F) Phosphor Bronze Rail Liner Material Properties [After Ref. 2] 47 Rail liner: CW 75 Class 11 25%Copper 75%Tungsten MatWeb Data Sheet Date: 7/12/2005 CMW ELKONITE® 10W3 (Copper Tungsten) RWMA Class 11 SubCat: Metal Matrix Composite, Copper Alloy, Tungsten Alloy, Nonferrous Metal, Metal Material Notes: Electrical contacts resistant to arcing, power transformer switches, resistance / projection welding electrodes, and EDM electrodes Information provided by CMW Inc. Component Value Min Max Copper, Cu 25 Tungsten, W 75 Value Min Max Comment Properties Physical Density, g/cc 14.84 --Mechanical Hardness, Rockwell B 98 --Flexural Modulus, GPa 1.03 --Electrical Electrical Resistivity, ohm-cm 3.83E-06 --(45% IACS) Thermal Thermal Conductivity, W/m-K 220 --Melting Point, °C -1085 3410 Solidus, °C 1085 --Liquidus, °C 3410 --- Table 9. Copper Tungsten Rail Liner Properties [After Ref. 2] 48 Rail liner: Aluminum 7075-T651 MatWeb Data Sheet Date: 7/12/2005 Aluminum 7075-T6; 7075-T651 Material Notes: General 7075 characteristics and uses (from Alcoa): Very high strength material used for highly stressed structural parts. The T7351 temper offers improved stress-corrosion cracking resistance. Applications: Aircraft fittings, gears and shafts, fuse parts, meter shafts and gears, missile parts, regulating valve parts, worm gears, keys, aircraft, aerospace and defense applications; bike frames, all terrain vehicle (ATV) sprockets. Data points with the AA note have been provided by the Aluminum Association, Inc. and are NOT FOR DESIGN. Component Value Min Max Aluminum, Al 87.1 91.4 Chromium, Cr 0.18 0.28 Copper, Cu 1.2 2 Iron, Fe 0.5 Magnesium, Mg 2.1 2.9 Manganese, Mn 0.3 Silicon, Si 0.4 Titanium, Ti 0.2 Zinc, Zn 5.1 6.1 Properties Value Min Max Comment Physical Density, g/cc 2.81 --AA; Typical Mechanical Hardness, Brinell 150 --AA; Typical; 500 g load; 10 mm ball Hardness, Knoop 191 --Converted from Brinell Hardness Value Hardness, Rockwell A 53.5 --Converted from Brinell Hardness Value Hardness, Rockwell B 87 --Converted from Brinell Hardness Value Hardness, Vickers 175 --Converted from Brinell Hardness Value Ultimate Tensile Strength, MPa 572 --AA; Typical Tensile Yield Strength, MPa 503 --AA; Typical Elongation at Break, % 11 --AA; Typical; 1/16 in. (1.6 mm) Thickness Elongation at Break, % 11 --AA; Typical; 1/2 in. (12.7 mm) Diameter AA; Typical; Average of tension and compression. Compression modulus is about 2% Modulus of Elasticity, GPa 71.7 --greater than tensile modulus. Poissons Ratio 0.33 --Fatigue Strength, MPa Fracture Toughness, MPa-m½ Fracture Toughness, MPa-m½ Fracture Toughness, MPa-m½ Machinability, % Shear Modulus, GPa Shear Strength, MPa Electrical Electrical Resistivity, ohm-cm Thermal CTE, linear 68°F, µm/m-°C CTE, linear 250°C, µm/m-°C Heat Capacity, J/g-°C Thermal Conductivity, W/m-K Melting Point, °C Solidus, °C Liquidus, °C Table 10. 159 29 20 25 70 26.9 331 -------- -------- 5.15E-06 -- -- 23.6 25.2 0.96 130 -477 635 ----477 --- ----635 --- AA; 500,000,000 cycles completely reversed stress; RR Moore machine/specimen K(IC) in L-T Direction K(IC) in S-L Direction K(IC) in T-L Direction 0-100 Scale of Aluminum Alloys AA; Typical AA; Typical at 68°F AA; Typical; Average over 68-212°F range. Average over the range 20-300ºC AA; Typical at 77°F AA; Typical AA; Typical AA; Typical Aluminum 7075 T-651 Rail Liner Material Properties [After Ref. 2] 49 Armature: Aluminum 6063-T5 Date: 7/12/2005 MatWeb Data Sheet Aluminum 6063-T5 UNS A96063; ISO AlMg0.5Si; Aluminium 6063-T5; AA6063-T5 KeyWords: UNS A96063; ISO AlMg0.5Si; Aluminium 6063-T5; AA6063-T5 SubCat: Aluminum Alloy, Nonferrous Metal, 6000 Series Aluminum Alloy, Metal Material Notes: Data points with the AA note have been provided by the Aluminum Association, Inc. and are Component Value Min Max Aluminum, Al 97.5 0.1 Chromium, Cr Copper, Cu 0.1 Iron, Fe 0.35 Magnesium, Mg 0.45 0.9 Manganese, Mn 0.1 Silicon, Si 0.2 0.6 Titanium, Ti 0.1 Zinc, Zn 0.1 Value Min Max Comment Properties Physical Density, g/cc 2.7 --AA; Typical Mechanical Hardness, Brinell 60 --AA; Typical; 500 g load; 10 mm ball Hardness, Knoop 83 --Converted from Brinell Hardness Value Hardness, Vickers 70 --Converted from Brinell Hardness Value Ultimate Tensile Strength, MPa 186 --AA; Typical Tensile Yield Strength, MPa 145 --AA; Typical Elongation at Break, % 12 --AA; Typical; 1/16 in. (1.6 mm) Thickness AA; Typical; Average of tension and compression. Compression modulus is about Modulus of Elasticity, GPa 68.9 --2% greater than tensile modulus. Poissons Ratio 0.33 --AA; 500,000,000 cycles completely reversed Fatigue Strength, MPa 68.9 --stress; RR Moore machine/specimen Shear Modulus, GPa 25.8 --Shear Strength, MPa 117 --AA; Typical Electrical Electrical Resistivity, ohm-cm 3.16E-06 --AA; Typical at 68°F Thermal CTE, linear 68°F, µm/m-°C 23.4 --AA; Typical; Average over 68-212°F range. CTE, linear 250°C, µm/m-°C 25.6 --Average over the range 20-300ºC Heat Capacity, J/g-°C 0.9 --Thermal Conductivity, W/m-K 209 --AA; Typical at 77°F AA; Typical range based on typical composition for wrought products 1/4 inch thickness or Melting Point, °C -616 654 greater Solidus, °C 616 --AA; Typical Liquidus, °C 654 --AA; Typical Processing Annealing Temperature, °C 413 --hold at temperature for 2 to 3 hr; cool at 50 °F Solution Temperature, °C 521 --Aging Temperature, °C 204 --hold at temperature for 1 hr Aging Temperature, °C 182 --hold at temperature for 1 hr Table 11. Aluminum 6063 T-5 Armature Material Properties [After Ref. 2] 50 Containment: G-11 FR-5 Glass-reinforced epoxy G-11 NEMA Grade FR5 Glass reinforced, high temperature epoxy, laminate Tensile Strength lengthwise, PSI crosswise, PSI 40,000 35,000 flatwise, PSI edgewise, PSI 60,000 35,000 lengthwise, PSI crosswise, PSI 55,000 45,000 6 2.7 2.2 19,000 Compressive Strength Flexural Strength Modulus of Elasticity in flex lengthwise, PSI x 10 6 crosswise, PSI x 10 Shear Strength, PSI IZOD Impact flatwise, ft lb per inch of notch edgewise, ft lb per inch of notch Rockwell Hardness M scale Specific Gravity Coefficient of Thermal Expansion cm/cm/ deg C x 10 -5 7 5.5 110 1.82 0.9 Water Absorption .062" thick, % per 24 hrs .125" thick, % per 24 hrs .500" thick, % per 24 hrs 0.25 0.15 0.1 .062" thick .125" thick 500 400 Dielectric Strength, volt/mil perpendicular to laminations; short Dissipation Factor condition A, 1 megacycle 0.025 condition A, 1 megacycle 5.2 Dielectric Constant Insulation Resistance Condition: 96 hours at 90% relative humidity (in mega ohms) 200,000 Flame Resistance 94V-0 Underwriter Labs, Classification 1,600 Bond Strength, in lbs Max Continuous Operating Temperature All Phenolics can withstand -100º F 300 Approximate degrees F sheet mil spec: Mil-I-24768 / _ _ 28 Table 12. G-11 FR-5 Containment Material Properties [After Ref 10] 51 Insulator: CoorsTek AD-96 alumina ceramic AD-96 Alumina Material Properties Trade Name: AD-96 Composition: Nominal 96% Al2O3 2/23/2006 Color: White Units gm/cc Microns % -- Value 3.72 6 0 0 358 (52) GPa (psi x 10 ) ASTM-F417 303 (44) -- ASTM-C848 0.21 ASTM-C773 2068 (300) Property Density Crystal Size Water Absorption Gas Permeability Flexural Strength (MOR), 20 degrees C Elastic Modulus, 20 degrees C Test ASTM-C20 Thin-Section ASTM-373 -6 Poisson's Ratio, 20 degrees C 3 Compressive Strenght MPa(psi x 10 ) Hardness GPa(kg/mm ) KNOOP 1000 gm Rockwell 45 N 11.5 (1175) 78 3 ACMA TEST #4 NOTCHED BEAM ASTM-C408 221 (32) 5-Apr 24.7 1 x 10 /degrees C J/kg*K ASTM-C372 ASTM-E1269 8.2 880 degrees C NOTE 3 250 degrees C ac-kV/mm (acV/mil) 25 degrees C 25 degrees C ohm-cm ohm-cm ohm-cm --- NO-LOAD COND. 1700 ASTM-D116 ASTM-D150 ASTM-D2520 ASTM-D1829 ASTM-D1829 ASTM-D1829 Note 4 Note 4 8.3 (210) 9 0.0002 14 >10 9 4 x 10 6 1 x 10 0.5 0.6 2 Tensile Strength, 25 degrees C Fracture Toughness K(Ic) Thermal Conductivity, 20 degrees C Coefficient of Thermal Expansion, 25-1000 degrees C Specific Heat, 100 degrees C MPa (psi x 10 ) 1/2 Mpa m Wm degrees K -6 Thermal Shock Resistance, (delta)Tc Maximum Use Temperature Dielectric Stength Dielectric Constant, 1MHz Dielectric Loss (tan delta) 1MHz Volume Resistivity 25 degrees C 500 degrees C 1000 degrees C Impingement Rubbing Table 13. Ceramic Insulator Material Properties [After Ref. 11] 52 Augmenting Rail Insulator: Mylar (polyester) Table 14. Mylar Film Insulator Material Properties [After Ref. 12] 53 THIS PAGE INTENTIONALLY LEFT BLANK 54 APPENDIX B. PRODUCTION DRAWINGS Top Containment Half Figure 14. Top Containment Half 55 Bottom Containment Half Figure 15. Bottom Containment Half 56 Solid Primary Conductor Rails Figure 16. Solid Primary Conductor Rails 57 Slotted Primary Conductor Rails Figure 17. Slotted Primary Conductor Rails 58 Ceramic Insulator Figure 18. Ceramic Insulators 59 Augmented Rails, Rail liners, and Spacer Figure 19. Augmented Rails, Rail liners, and Spacer 60 Augmenting Conductor Components Figure 20. Augmenting Conductor Components 61 External Conductor Connectors and Muzzle Shunt Figure 21. External Conductor Connectors and Muzzle Shunt 62 Full Conductor Assembly Figure 22. Full Conductor Assembly 63 Full Assembly CAD Model and Finished Result Figure 23. Figure 24. Full CAD Assembly with Loader and Muzzle Shunt Full Assembled Railgun with Loader 64 Basic U-shape Armature Figure 25. Basic U-Shape Armature 65 Flared M-shape Armature Figure 26. Flared M-shape Armature 66 Square M-shape Armature Figure 27. Square M-shape Armature 67 Altered U-shape Armature with Center Hollow Figure 28. Altered U-shape Armature with Center Hollow 68 Railgun Mounting Base Figure 29. Railgun Mounting Base The mounting base is fabricated from a 1.5” thick slab of insulating phenolic. bolts extend through the Three pairs of the containment base for mounting. The base itself is then bolted directly to the firing line table. 69 THIS PAGE INTENTIONALLY LEFT BLANK 70 APPENDIX C. A. MODELING KERRISK’S METHOD SPREADSHEETS [3] Inductance Gradient Calculations for Solid and Non- slotted Rail Geometries Kerrisk's Method for L' Determination - Los Alamos National Laboratory 1981 [Ref.2] L' = [A + B*ln(1 + a1*(w/h) + a2*(w/h)*(s/h))*ln(b1 + b2*(s/h) + b3*(w/h) + b4*(s/h)*(w/h)] s = bore spacing(mm) h = rail height (mm) w = rail width (mm) ( NOTE: Augmented configurations apply gain factor of 1.55 over their respective non-augmented L' ) Solid Rails Slotted Rails Solid Augmented Slotted Augmented A 0.440641 0.440641 0.440641 0.440641 B -0.07771 -0.07771 -0.07771 -0.07771 a1 3.397143 3.397143 3.397143 3.397143 a2 -0.06603 -0.06603 -0.06603 -0.06603 b1 1.07719 1.07719 1.07719 1.07719 b2 2.743651 2.743651 2.743651 2.743651 b3 0.022093 0.022093 0.022093 0.022093 b4 0.263739 0.263739 0.263739 0.263739 s 19 19 19 19 h 50.8 25.4 50.8 25.4 w 9.5 9.5 9.5 9.5 s/h 0.374015748 0.748031496 0.374015748 0.748031496 w/h 0.187007874 0.374015748 0.187007874 0.374015748 Solid Rail L' Solid augmented L' Slotted Augmented L' Slotted L' 0.30368 0.44051 0.47070 0.68279 Table 15. Kerrisk’s Method and Augmentation Adjusted Inductance Gradient (L’) Calculations Table 14 input parameters of bore spacing (s), rail height (h), and rail width (w) are demonstrated in Figure 28 below. h s w Figure 30. Kerrisk’s Method Rail Parameters [After Ref. 2] 71 B. PARAMETER BASED MODELING [7] 1500 m/s Solid Non-Augmented Parameter Modeling Solid Rail Non-Augmented Parameter Model µH/m L' 0.30368 Target velocity: Projectile mass: Effective length: Armature height: t = 2x/(delta v) 2 aavg =2x/(t ) Avg. Current: Iavg = (2ma/L' ) 0.5 Peak Current Ipeak = (Iavg2/0.7)0.5 Linear current density: Ipeak' = Ipeak / armature height Electrical Action: G=2mv/L' ∆T= (ρe/ρmCp)*(G/A2) 1500 11.4 50 19 t (ms) m/s grams cm mm 0.67 2.25E+06 aavg (m/s ) 225 aavg (kG's) 411.01 k-Amps 491.25 k-Amps 25.86 (kA/mm) 1.13E+08 Amp s Electrical Action is a measure of heating due to current flow 40.00 Kelvin (K) Based on thumbrule of a delta T of 40 K across the rail due to resistive heating, where A = conductor cross-sectional area 2 2 Conductor Area = 2 [(ρe/ρmCp)(G/∆Τ)]0.5 118.65 mm Required rail width (mm) Actual rail width (1/4" rail + 1/8" rail liner) Lorentz Force at peak current: 6.24 mm 9.53 mm 36642.86 N F = (1/2)L'Ipeak 2 2 2 m 0.000361 Bore Area (m ) Base Pressure = F/A 102 Mpa Repulsion force per unit length (Base Pressure x Bore height) 1.93 MN/m Grade 2 SAE J429 3/8" diameter stainless steel bolts Minimum Yield Strength Individual bolt area required to avoid exceeding Yield Strength for static longitudinal repulsion force along entire 24" rail length distributed between 22 bolts Minimum Bolt Diameter Required Actual Bolt Diameter Table 16. Assume: average acceleration is 70% of peak acceleration and this ratio is 2 proportional to (Iavg /Ipeak2) Note: linear current densities > 45 kA/mm are regarded as unstable for railgun design The expression (ρe/ρmCp) is a ratio of electrical resistivity to the product of mass density and specific heat capacity, a typical value for the ratio for copper is 0.005 2 4 (K/Amp s)/mm . 8238 lbf 0.56 14.73 square inches ksi 11.05 kip/in 57000 psi 0.21 square inches 0.519 0.375 inches inches 1500 m/s Solid Non-Augmented Parameter Model 72 1500 m/s Slotted Non-Augmented Parameter Modeling Slotted Rail Non-Augmented Parameter Model µH/m L' 0.44051 Target velocity: Projectile mass: Effective length: Armature height: t = 2x/(delta v) 1500 11.4 50 19 t (ms) m/s grams cm mm 0.67 2.25E+06 aavg (m/s ) 225 aavg (kG's) 341.26 k-Amps 407.88 k-Amps 21.47 (kA/mm) 7.76E+07 Amp s 40.00 Kelvin (K) [(ρe/ρmCp)(G/∆Τ)]0.5 98.51 mm Required rail width (mm) Actual rail width (1/4" rail + 1/8" rail liner) Lorentz Force at peak current: 5.18 mm 9.53 mm 36642.86 N 2 aavg =2x/(t ) Avg. Current: Iavg = (2ma/L' ) 0.5 Peak Current Ipeak = (Iavg2/0.7)0.5 Linear current density: Ipeak' = Ipeak / armature height Electrical Action: G=2mv/L' ∆T= (ρe/ρmCp)*(G/A2) 2 2 Conductor Area = F = (1/2)L'Ipeak 2 2 2 2 m Bore Area (m ) 0.000361 Base Pressure = F/A 102 Mpa Repulsion force per unit length 1.93 (Base Pressure x Bore height) MN/m Grade 2 SAE J429 3/8" diameter stainless steel bolts Minimum Yield Strength Individual bolt area required to avoid exceeding Yield Strength for static longitudinal repulsion force along entire 24" rail length distributed between 22 bolts Minimum Bolt Diameter Required Actual Bolt Diameter Table 17. Assume: average acceleration is 70% of peak acceleration and this ratio is 2 proportional to (Iavg /Ipeak2) Note: linear current densities > 45 kA/mm are regarded as unstable for railgun design Electrical Action is a measure of heating due to current flow Based on thumbrule of a delta T of 40 K across the rail due to resistive heating, where The expression (ρe/ρmCp) is a ratio of electrical resistivity to the product of mass density and specific heat capacity, a typical value for the ratio for copper is 0.005 2 4 (K/Amp s)/mm . 8238 lbf 0.56 14.73 square inches ksi 11.05 kip/in 57000 psi 0.21 square inches 0.519 0.375 inches inches 1500 m/s Slotted Non-Augmented Parameter Model 73 1500 m/s Solid Augmented Parameter Modeling L' 0.47070 Target velocity: Projectile mass: Effective length: Armature height: t = 2x/(delta v) Solid Rail Augmented Parameter Model µH/m 1500 11.4 50 19 t (ms) m/s grams cm mm 0.67 2.25E+06 aavg (m/s ) 225 aavg (kG's) 330.13 k-Amps 394.58 k-Amps 20.77 (kA/mm) 7.27E+07 Amp s 40.00 Kelvin (K) [(ρe/ρmCp)(G/∆Τ)]0.5 95.30 mm Required rail width (mm) Actual rail width (1/4" rail + 1/8" rail liner) Lorentz Force at peak current: 5.02 mm 9.53 mm 36642.86 N 2 aavg =2x/(t ) Avg. Current: Iavg = (2ma/L' ) 0.5 Peak Current Ipeak = (Iavg2/0.7)0.5 Linear current density: Ipeak' = Ipeak / armature height Electrical Action: G=2mv/L' ∆T= (ρe/ρmCp)*(G/A2) 2 2 Conductor Area = F = (1/2)L'Ipeak 2 2 2 2 m Bore Area (m ) 0.000361 Base Pressure = F/A 102 Mpa Repulsion force per unit length 1.93 (Base Pressure x Bore height) MN/m Grade 2 SAE J429 3/8" diameter stainless steel bolts Minimum Yield Strength Individual bolt area required to avoid exceeding Yield Strength for static longitudinal repulsion force along entire 24" rail length distributed between 22 bolts Grade 2 Minimum Bolt Diameter Required Grade 8 SAE J429 3/8" diameter stainless steel bolts Minimum Yield Strength Individual bolt area required to avoid exceeding Yield Strength for static longitudinal repulsion force along 2" rail length distributed between 4 bolts Grade 8 Minimum Bolt Diameter Required Actual Bolt Diameter Table 18. Assume: average acceleration is 70% of peak acceleration and this ratio is 2 proportional to (Iavg /Ipeak2) Note: linear current densities > 45 kA/mm are regarded as unstable for railgun design Electrical Action is a measure of heating due to current flow Based on thumbrule of a delta T of 40 K across the rail due to resistive heating, where The expression (ρe/ρmCp) is a ratio of electrical resistivity to the product of mass density and specific heat capacity, a typical value for the ratio for copper is 0.005 2 4 (K/Amp s)/mm . 8238 lbf 0.56 14.73 square inches ksi 11.05 kip/in 57000 psi 0.21 square inches 0.519 inches 130000 psi 0.09 square inches 0.344 0.375 inches inches 1500 m/s Solid Augmented Parameter Model 74 1500 m/s Slotted Augmented Parameter Modeling Slotted Rail Augmented Parameter Model µH/m 0.68279 L' Target velocity: Projectile mass: Effective length: Armature height: t = 2x/(delta v) 2 aavg =2x/(t ) Avg. Current: Iavg = (2ma/L' ) 0.5 Peak Current Ipeak = (Iavg2/0.7)0.5 Linear current density: Ipeak' = Ipeak / armature height Electrical Action: G=2mv/L' ∆T= (ρe/ρmCp)*(G/A2) 1500 11.4 50 19 t (ms) m/s grams cm mm 0.67 2.25E+06 aavg (m/s ) 225 aavg (kG's) 274.10 k-Amps 327.62 k-Amps 17.24 (kA/mm) 5.01E+07 Amp s 40.00 Kelvin (K) 2 2 Conductor Area = 2 [(ρe/ρmCp)(G/∆Τ)]0.5 79.13 Required rail width (mm) Actual rail width (1/4" rail + 1/8" rail liner) Lorentz Force at peak current: 4.16 mm 9.53 mm 36642.86 N F = (1/2)L'Ipeak 2 mm 2 2 m Bore Area (m ) 0.000361 Base Pressure = F/A 102 Mpa Repulsion force per unit length 1.93 (Base Pressure x Bore height) MN/m Grade 2 SAE J429 3/8" diameter stainless steel bolts Minimum Yield Strength Individual bolt area required to avoid exceeding Yield Strength for static longitudinal repulsion force along entire 24" rail length distributed between 22 bolts Grade 2 Minimum Bolt Diameter Required Grade 8 SAE J429 3/8" diameter stainless steel bolts Minimum Yield Strength Individual bolt area required to avoid exceeding Yield Strength for static longitudinal repulsion force along 2" rail length distributed between 4 bolts Grade 8 Minimum Bolt Diameter Required Actual Bolt Diameter Table 19. Assume: average acceleration is 70% of peak acceleration and this ratio is 2 proportional to (Iavg /Ipeak2) Note: linear current densities > 45 kA/mm are regarded as unstable for railgun design Electrical Action is a measure of heating due to current flow Based on thumbrule of a delta T of 40 K across the rail due to resistive heating, where The expression (ρe/ρmCp) is a ratio of electrical resistivity to the product of mass density and specific heat capacity, a typical value for the ratio for copper is 0.005 2 4 (K/Amp s)/mm . 8238 lbf 0.56 14.73 square inches ksi 11.05 kip/in 57000 psi 0.21 square inches 0.519 inches 130000 psi 0.09 square inches 0.344 0.375 inches inches 1500 m/s Slotted Augmented Parameter Model 75 265 m/s Solid Augmented Parameter Modeling Solid Rail Augmented Parameter Model for Experimental Velocity Result: 265 m/s µH/m L' 0.47070 Target velocity: Projectile mass: Effective length: Armature height: t = 2x/(delta v) 265 11.4 50 19 t (ms) m/s grams cm mm 3.77 7.02E+04 aavg (m/s ) 7.0225 aavg (kG's) 58.32 k-Amps 69.71 k-Amps 3.67 (kA/mm) 1.28E+07 Amp s 40.00 Kelvin (K) [(ρe/ρmCp)(G/∆Τ)]0.5 40.06 mm Required rail width (mm) Actual rail width (1/4" rail + 1/8" rail liner) Lorentz Force at peak current: 2.11 mm 9.53 mm 1143.66 N 2 aavg =2x/(t ) Avg. Current: Iavg = (2ma/L' ) 0.5 Peak Current Ipeak = (Iavg2/0.7)0.5 Linear current density: Ipeak' = Ipeak / armature height Electrical Action: G=2mv/L' ∆T= (ρe/ρmCp)*(G/A2) 2 2 Conductor Area = F = (1/2)L'Ipeak 2 2 2 2 m 0.000361 Bore Area (m ) Base Pressure = F/A 3 Mpa Repulsion force per unit length 0.06 (Base Pressure x Bore height) MN/m Grade 2 SAE J429 3/8" diameter stainless steel bolts Minimum Yield Strength Individual bolt area required to avoid exceeding Yield Strength for static longitudinal repulsion force along entire 24" rail length distributed between 22 bolts Grade 2 Minimum Bolt Diameter Required Grade 8 SAE J429 3/8" diameter stainless steel bolts Minimum Yield Strength Individual bolt area required to avoid exceeding Yield Strength for static longitudinal repulsion force along 2" rail length distributed between 4 bolts Grade 8 Minimum Bolt Diameter Required Actual Bolt Diameter Table 20. Assume: average acceleration is 70% of peak acceleration and this ratio is 2 proportional to (Iavg /Ipeak2) Note: linear current densities > 45 kA/mm are regarded as unstable for railgun design Electrical Action is a measure of heating due to current flow Based on thumbrule of a delta T of 40 K across the rail due to resistive heating, where The expression (ρe/ρmCp) is a ratio of electrical resistivity to the product of mass density and specific heat capacity, a typical value for the ratio for copper is 0.005 2 4 (K/Amp s)/mm . 257 lbf 0.56 0.46 square inches ksi 0.34 kip/in 57000 psi 0.01 square inches 0.092 inches 130000 psi 0.00 square inches 0.061 0.375 inches inches 265 m/s Solid Augmented Parameter Model 76 290 m/s Slotted Augmented Parameter Model Slotted Rail Augmented Parameter Model for Experimental Velocity Result: 290 m/s µH/m L' 0.68279 Target velocity: Projectile mass: Effective length: Armature height: t = 2x/(delta v) 2 aavg =2x/(t ) Avg. Current: Iavg = (2ma/L' ) 0.5 Peak Current Ipeak = (Iavg2/0.7)0.5 Linear current density: Ipeak' = Ipeak / armature height Electrical Action: G=2mv/L' ∆T= (ρe/ρmCp)*(G/A2) 290 11.4 50 19 t (ms) m/s grams cm mm 3.45 8.41E+04 aavg (m/s ) 8.41 aavg (kG's) 52.99 k-Amps 63.34 k-Amps 3.33 (kA/mm) 9.68E+06 Amp s 40.00 Kelvin (K) 2 2 Conductor Area = 2 [(ρe/ρmCp)(G/∆Τ)]0.5 34.79 Required rail width (mm) Actual rail width (1/4" rail + 1/8" rail liner) Lorentz Force at peak current: 1.83 mm 9.53 mm 1369.63 N F = (1/2)L'Ipeak 2 mm 2 2 m Bore Area (m ) 0.000361 Base Pressure = F/A 4 Mpa Repulsion force per unit length 0.07 (Base Pressure x Bore height) MN/m Grade 2 SAE J429 3/8" diameter stainless steel bolts Minimum Yield Strength Individual bolt area required to avoid exceeding Yield Strength for static longitudinal repulsion force along entire 24" rail length distributed between 22 bolts Grade 2 Minimum Bolt Diameter Required Grade 8 SAE J429 3/8" diameter stainless steel bolts Minimum Yield Strength Individual bolt area required to avoid exceeding Yield Strength for static longitudinal repulsion force along 2" rail length distributed between 4 bolts Grade 8 Minimum Bolt Diameter Required Actual Bolt Diameter Table 21. Assume: average acceleration is 70% of peak acceleration and this ratio is 2 proportional to (Iavg /Ipeak2) Note: linear current densities > 45 kA/mm are regarded as unstable for railgun design Electrical Action is a measure of heating due to current flow Based on thumbrule of a delta T of 40 K across the rail due to resistive heating, where The expression (ρe/ρmCp) is a ratio of electrical resistivity to the product of mass density and specific heat capacity, a typical value for the ratio for copper is 0.005 2 4 (K/Amp s)/mm . 308 lbf 0.56 0.55 square inches ksi 0.41 kip/in 57000 psi 0.01 square inches 0.100 inches 130000 psi 0.00 square inches 0.066 0.375 inches inches 290 m/s Slotted Augmented Parameter Model 77 Solid Non-Augmented Parameter Model for Peak Current, Maximum Velocity for Grade 2 Bolt Diameter Solid Rail Non-Augmented Parameter Model for Actual Grade 2 Bolt Design µH/m L' 0.30368 Target velocity: Projectile mass: Effective length: Armature height: t = 2x/(delta v) 2 aavg =2x/(t ) Avg. Current: Iavg = (2ma/L' ) 0.5 Peak Current Ipeak = (Iavg2/0.7)0.5 Linear current density: Ipeak' = Ipeak / armature height Electrical Action: G=2mv/L' ∆T= (ρe/ρmCp)*(G/A2) 1085 11.4 50 19 t (ms) m/s grams cm mm 0.92 1.18E+06 aavg (m/s ) 117.7225 aavg (kG's) 297.30 k-Amps 355.34 k-Amps 18.70 (kA/mm) 8.15E+07 Amp s Electrical Action is a measure of heating due to current flow 40.00 Kelvin (K) Based on thumbrule of a delta T of 40 K across the rail due to resistive heating, where A = conductor cross-sectional area 2 2 Conductor Area = 2 [(ρe/ρmCp)(G/∆Τ)]0.5 100.91 mm Required rail width (mm) Actual rail width (1/4" rail + 1/8" rail liner) Lorentz Force at peak current: 5.31 mm 9.53 mm 19171.95 N F = (1/2)L'Ipeak 2 2 2 m 0.000361 Bore Area (m ) Base Pressure = F/A 53 Mpa Repulsion force per unit length (Base Pressure x Bore height) 1.01 MN/m Grade 2 SAE J429 3/8" diameter stainless steel bolts Minimum Yield Strength Individual bolt area required to avoid exceeding Yield Strength for static longitudinal repulsion force along entire 24" rail length distributed between 22 bolts Grade 2 Minimum Bolt Diameter Required Grade 8 SAE J429 3/8" diameter stainless steel bolts Minimum Yield Strength Individual bolt area required to avoid exceeding Yield Strength for static longitudinal repulsion force along 2" rail length distributed between 4 bolts Grade 8 Minimum Bolt Diameter Required Actual Bolt Diameter Table 22. Assume: average acceleration is 70% of peak acceleration and this ratio is 2 proportional to (Iavg /Ipeak2) Note: linear current densities > 45 kA/mm are regarded as unstable for railgun design The expression (ρe/ρmCp) is a ratio of electrical resistivity to the product of mass density and specific heat capacity, a typical value for the ratio for copper is 0.005 2 4 (K/Amp s)/mm . 4310 lbf 0.56 7.71 square inches ksi 5.78 kip/in 57000 psi 0.11 square inches 0.375 inches 130000 psi 0.05 square inches 0.249 0.375 inches inches Parameter Estimate of Peak Current and Final Velocity for 3/8” diameter Grade 2 Bolts 78 C. CONSERVATION OF ENERGY INTEGRATION [4] 35 kJ Solid Non-Augmented Velocity Integration Rail length as an integral function of velocity for solid/non-augmented input parameters: ∫ dx = ( 1 ln av 2 + bv + c 2a ⎡ ⎛ 2av + b − b 2 − 4ac 1 ⎢ ln ⎜ 2a ⎢ b 2 − 4ac ⎜ 2av + b + b 2 − 4ac ⎝ ⎣ )− b ⎞⎤ ⎟⎥ + D ⎟⎥ ⎠⎦ 2 Table integral form: V = av + bv + c Input Parameters: Velocity (m/s) mass (g) 0.0114 120 C (farads) 1.66E-03 121 L (Henries) 5.50E-06 122 R (ohms) 3.30E-03 123 Volts 6.50E+03 124 W 0 (J) 3.51E+04 125 First Term: -9.17E+01 -9.13E+01 -9.08E+01 -9.03E+01 -8.98E+01 -8.92E+01 Second Term: -6.23E+01 -6.28E+01 -6.32E+01 -6.37E+01 -6.43E+01 -6.48E+01 Required Rail Length (m): 0.12 0.13 0.13 0.14 0.14 0.15 126 127 128 129 130 -8.86E+01 -8.80E+01 -8.73E+01 -8.65E+01 -8.57E+01 -6.54E+01 -6.60E+01 -6.67E+01 -6.75E+01 -6.83E+01 0.16 0.16 0.17 0.18 0.19 -3.75E+04 131 -8.48E+01 -6.91E+01 0.20 1.44E+06 1.09E+04 132 133 -8.38E+01 -8.27E+01 -7.01E+01 -7.12E+01 0.21 0.23 Square Root (b - 4ac) 134 -8.14E+01 -7.25E+01 0.24 1.22E+03 135 -8.00E+01 -7.39E+01 0.26 1/Square Root(b - 4ac) 136 -7.82E+01 -7.57E+01 0.28 8.23E-04 D = Integration Constant: 154.17 137 138 139 -7.60E+01 -7.31E+01 -6.87E+01 -7.79E+01 -8.08E+01 -8.50E+01 0.31 0.35 0.40 140 -6.01E+01 -9.36E+01 0.51 141 -5.54E+01 -9.82E+01 0.57 L' (H/m) 3.04E-07 Integral factors: a = -L'/L -5.52E-02 b= -2R/L -1.20E+03 c =(L' W o)/(mL) 1.70E+05 4ac 2 b b / 2a 2 2 Table 23. 35 kJ Velocity Integral, Solid NonAugmented. 79 35 kJ Slotted Non-Augmented Velocity Integration Rail length as an integral function of velocity for slotted/non-augmented input parameters: ∫ dx = ( 1 ln av 2 + bv + c 2a ⎡ ⎛ 2av + b − b 2 − 4ac 1 ⎢ ln ⎜ 2a ⎢ b 2 − 4ac ⎜ 2av + b + b 2 − 4ac ⎝ ⎣ )− b ⎞⎤ ⎟⎥ + D ⎟ ⎠ ⎦⎥ 2 Table integral form: V = av + bv + c Input Parameters: Velocity (m/s) mass (g) 0.0114 160 C (farads) 1.66E-03 162 L (Henries) 5.50E-06 164 R (ohms) 3.30E-03 166 Volts 6.50E+03 168 W 0 (J) 3.51E+04 170 L' (H/m) 4.41E-07 Integral factors: a = -L'/L -8.01E-02 b= -2R/L -1.20E+03 c =(L' W o)/(mL) 2.46E+05 4ac 172 174 176 178 180 First Term: -6.78E+01 -6.75E+01 -6.72E+01 -6.69E+01 -6.65E+01 -6.62E+01 Second Term: -3.58E+01 -3.61E+01 -3.64E+01 -3.67E+01 -3.71E+01 -3.74E+01 Required Rail Length (m): 0.13 0.13 0.14 0.15 0.15 0.16 -6.58E+01 -6.53E+01 -6.49E+01 -6.44E+01 -6.39E+01 -3.78E+01 -3.82E+01 -3.87E+01 -3.91E+01 -3.97E+01 0.17 0.18 0.19 0.20 0.21 -7.89E+04 182 -6.33E+01 -4.02E+01 0.23 1.44E+06 7.49E+03 184 186 -6.27E+01 -6.19E+01 -4.08E+01 -4.15E+01 0.24 0.26 Square Root (b - 4ac) 188 -6.11E+01 -4.23E+01 0.28 1.23E+03 190 -6.02E+01 -4.32E+01 0.30 1/Square Root(b - 4ac) 192 -5.91E+01 -4.43E+01 0.33 8.11E-04 D = Integration Constant: 103.74 194 196 -5.78E+01 -5.62E+01 -4.55E+01 -4.72E+01 0.36 0.40 198 200 -5.39E+01 -5.03E+01 -4.94E+01 -5.29E+01 0.46 0.55 202 -4.09E+01 -6.20E+01 0.80 2 b b / 2a 2 2 Table 24. 35 kJ Velocity Integral, Slotted NonAugmented. 80 35 kJ Solid Augmented Velocity Integration Rail length as an integral function of velocity for solid/augmented input parameters: ∫ dx = ( 1 ln av 2 + bv + c 2a ⎡ ⎛ 2av + b − b 2 − 4ac 1 ⎢ ln ⎜ 2a ⎢ b 2 − 4ac ⎜ 2av + b + b 2 − 4ac ⎝ ⎣ )− b ⎞⎤ ⎟⎥ + D ⎟⎥ ⎠⎦ 2 Table integral form: V = av + bv + c Input Parameters: Velocity (m/s) mass (g) 0.0114 150 C (farads) 1.66E-03 152 L (Henries) 5.50E-06 154 R (ohms) 3.30E-03 156 Volts 6.50E+03 158 W 0 (J) 3.51E+04 160 First Term: -6.61E+01 -6.59E+01 -6.57E+01 -6.55E+01 -6.53E+01 -6.51E+01 Second Term: -3.05E+01 -3.07E+01 -3.09E+01 -3.11E+01 -3.12E+01 -3.14E+01 Required Rail Length (m): 0.08 0.09 0.09 0.09 0.10 0.10 162 164 166 168 170 -6.49E+01 -6.47E+01 -6.44E+01 -6.42E+01 -6.40E+01 -3.17E+01 -3.19E+01 -3.21E+01 -3.23E+01 -3.26E+01 0.11 0.11 0.12 0.12 0.13 -9.01E+04 172 -6.37E+01 -3.28E+01 0.13 1.44E+06 7.01E+03 174 176 -6.34E+01 -6.31E+01 -3.31E+01 -3.34E+01 0.14 0.15 Square Root (b - 4ac) 178 -6.28E+01 -3.36E+01 0.16 1.24E+03 L' (H/m) 4.71E-07 Integral factors: a = -L'/L -8.56E-02 b= -2R/L -1.20E+03 c =(L' W o)/(mL) 2.63E+05 4ac 2 b b / 2a 2 180 -6.25E+01 -3.40E+01 0.16 1/Square Root(b - 4ac) 182 -6.22E+01 -3.43E+01 0.17 8.08E-04 D = Integration Constant: 96.65 184 186 188 190 192 194 196 198 200 202 204 206 208 -6.18E+01 -6.15E+01 -6.11E+01 -6.06E+01 -6.02E+01 -5.97E+01 -5.91E+01 -5.85E+01 -5.78E+01 -5.70E+01 -5.61E+01 -5.51E+01 -5.38E+01 -3.46E+01 -3.50E+01 -3.54E+01 -3.58E+01 -3.63E+01 -3.67E+01 -3.73E+01 -3.79E+01 -3.86E+01 -3.93E+01 -4.02E+01 -4.12E+01 -4.25E+01 0.18 0.19 0.20 0.21 0.22 0.24 0.25 0.27 0.29 0.31 0.34 0.37 0.40 210 212 -5.21E+01 -4.98E+01 -4.41E+01 -4.64E+01 0.45 0.52 214 -4.58E+01 -5.02E+01 0.64 2 Table 25. 35 kJ Velocity Integral, Solid Augmented. 81 35 kJ Slotted Augmented Velocity Integration Rail length as an integral function of velocity for slotted/augmented input parameters: ∫ dx = ( 1 ln av 2 + bv + c 2a ⎡ ⎛ 2av + b − b 2 − 4ac 1 ⎢ ln ⎜ 2a ⎢ b 2 − 4ac ⎜ 2av + b + b 2 − 4ac ⎝ ⎣ )− b ⎞⎤ ⎟⎥ + D ⎟⎥ ⎠⎦ 2 Table integral form: V = av + bv + c Input Parameters: Velocity (m/s) mass (g) 0.0114 150 C (farads) 1.66E-03 155 L (Henries) 5.50E-06 160 R (ohms) 3.30E-03 165 Volts 6.50E+03 170 W 0 (J) 3.51E+04 175 First Term: -4.91E+01 -4.90E+01 -4.89E+01 -4.87E+01 -4.86E+01 -4.85E+01 Second Term: -1.57E+01 -1.59E+01 -1.60E+01 -1.61E+01 -1.63E+01 -1.64E+01 Required Rail Length (m): 0.05 0.05 0.05 0.06 0.06 0.07 180 185 190 195 200 -4.83E+01 -4.82E+01 -4.80E+01 -4.78E+01 -4.76E+01 -1.65E+01 -1.67E+01 -1.69E+01 -1.70E+01 -1.72E+01 0.07 0.08 0.09 0.09 0.10 -1.90E+05 205 -4.74E+01 -1.74E+01 0.11 1.44E+06 4.83E+03 210 215 -4.72E+01 -4.70E+01 -1.76E+01 -1.78E+01 0.12 0.12 Square Root (b - 4ac) 220 -4.68E+01 -1.80E+01 0.13 1.28E+03 L' (H/m) 6.83E-07 Integral factors: a = -L'/L -1.24E-01 b= -2R/L -1.20E+03 c =(L' W o)/(mL) 3.82E+05 4ac 2 b b / 2a 2 225 -4.66E+01 -1.82E+01 0.14 1/Square Root(b - 4ac) 230 -4.63E+01 -1.84E+01 0.16 7.83E-04 D = Integration Constant: 64.93 235 240 245 250 255 260 265 270 275 280 285 -4.61E+01 -4.58E+01 -4.55E+01 -4.52E+01 -4.48E+01 -4.44E+01 -4.40E+01 -4.35E+01 -4.29E+01 -4.23E+01 -4.15E+01 -1.87E+01 -1.90E+01 -1.92E+01 -1.96E+01 -1.99E+01 -2.03E+01 -2.07E+01 -2.12E+01 -2.17E+01 -2.23E+01 -2.30E+01 0.17 0.18 0.20 0.21 0.23 0.25 0.27 0.30 0.33 0.36 0.41 290 295 -4.05E+01 -3.93E+01 -2.39E+01 -2.51E+01 0.46 0.53 300 305 310 -3.74E+01 -3.37E+01 -3.07E+01 -2.69E+01 -3.03E+01 -3.32E+01 0.64 0.86 1.03 2 Table 26. 35 kJ Velocity Integral, Slotted Augmented. 82 83 kJ Slotted Augmented Velocity Integration Rail length as an integral function of velocity for slotted/augmented input parameters: ∫ dx = ( 1 ln av 2 + bv + c 2a ⎡ ⎛ 2av + b − b 2 − 4ac ln ⎜ 2 2 ⎜ ⎣ b − 4ac ⎝ 2av + b + b − 4ac ) − 2ba ⎢⎢ 1 ⎞⎤ ⎟⎥ + D ⎟ ⎠ ⎦⎥ 2 Table integral form: V = av + bv + c Input Parameters: Velocity (m/s) mass (g) 0.0114 350 C (farads) 1.66E-03 355 L (Henries) 5.50E-06 360 R (ohms) 3.30E-03 365 Volts 1.00E+04 370 W 0 (J) 8.30E+04 375 First Term: -5.26E+01 -5.25E+01 -5.25E+01 -5.24E+01 -5.24E+01 -5.23E+01 Second Term: -1.20E+01 -1.21E+01 -1.21E+01 -1.22E+01 -1.22E+01 -1.23E+01 Required Rail Length (m): 0.10 0.33 0.34 0.34 0.34 0.35 380 385 390 395 400 -5.22E+01 -5.22E+01 -5.21E+01 -5.21E+01 -5.20E+01 -1.23E+01 -1.24E+01 -1.24E+01 -1.25E+01 -1.26E+01 0.35 0.36 0.36 0.37 0.37 -4.49E+05 405 -5.19E+01 -1.26E+01 0.38 1.44E+06 4.83E+03 410 415 -5.19E+01 -5.18E+01 -1.27E+01 -1.27E+01 0.38 0.39 Square Root (b - 4ac) 420 -5.17E+01 -1.28E+01 0.39 1.37E+03 L' (H/m) 6.83E-07 Integral factors: a = -L'/L -1.24E-01 b= -2R/L -1.20E+03 c =(L' W o)/(mL) 9.04E+05 4ac 2 b b / 2a 2 425 -5.17E+01 -1.29E+01 0.40 1/Square Root(b - 4ac) 430 -5.16E+01 -1.29E+01 0.40 7.28E-04 D = Integration Constant: 64.93 435 440 445 450 455 460 465 470 475 480 485 490 -5.15E+01 -5.14E+01 -5.14E+01 -5.13E+01 -5.12E+01 -5.11E+01 -5.10E+01 -5.10E+01 -5.09E+01 -5.08E+01 -5.07E+01 -5.06E+01 -1.30E+01 -1.31E+01 -1.31E+01 -1.32E+01 -1.33E+01 -1.34E+01 -1.34E+01 -1.35E+01 -1.36E+01 -1.37E+01 -1.38E+01 -1.38E+01 0.41 0.42 0.42 0.43 0.44 0.44 0.45 0.46 0.46 0.47 0.48 0.49 495 -5.05E+01 -1.39E+01 0.50 500 505 510 -5.04E+01 -5.03E+01 -5.02E+01 -1.40E+01 -1.41E+01 -1.42E+01 0.51 0.52 0.53 2 Table 27. 83 kJ Velocity Integral, Slotted Augmented. 83 D. STRUCTURAL DESIGN VERIFICATION Rail containment deflection is modeled based on static loading from 500 kA peak current conditions predicted for the solid non-augmented configuration in Table 15. railgun test simplified platform by considering The cross-sectional geometry is the primary, and rail liner, augmenting conducting rails as a single solid oxygen free copper conducting bar. The homogenous beam bending model considers only the 1-3/8” G-11 material from the outer face of the augmenting containment. geometry conductor rail to the top of the The resultant combined rail and containment contributing to the beam bending model are represented in Figure 30. G-11 4-3/4” 1-3/8” 5/8” Figure 31. OFE Copper 2” Simplified Beam Geometry (Not to scale) The transformed geometry after expressing the copper in terms of G-11 for purposes of calculated the rectangular moment of inertia is depicted by Figure 31. xG −11 = 4.75" yG-11=1.375” YG-11 yc=0.625” y Ycentroid Yc xc = ηc i2" = 12.4" Figure 32. Transformed Homogenous Beam Geometry (Not to Scale) 84 The centroid and moment of inertia for the transformed geometry of Figure 31 are based on the following equations. ⎛ y A + yG −11 AG −11 ⎞ Ycentroid = ⎜ c c ⎟ Ac + AG −11 ⎝ ⎠ 2⎤ ⎡1 I = ∑ ⎢ xi yi3 + Ai Ycentroid − Yi ⎥ ⎣12 ⎦ Table 27 lists the values used in the previous equations to calculate the rectangular moment of inertia for the transformed cross-section. Centroid and Moment of Inertia Calculations for Equivalent Homogenous Beam Section Elasticity Modulus (psi) Area ( in2 ) y (in) yA ( in3 ) Centroid ( in ) Moment of Inertia ( in4 ) Copper 1.67E+07 7.75 0.1875 1.453 0.6448 8.370 G-11 2.70E+06 6.5313 1.1875 7.756 Table 28. Transformed Geometry Moment of Inertia Calculation 85 THIS PAGE INTENTIONALLY LEFT BLANK 86 APPENDIX D. A. MAGNETIC FIELD AND CIRCUIT SIMULATIONS COMSOL MULTIPHYSICS MODELING 100 k-Amp DC, Solid Non-Augmented Figure 33. Solid Non-Augmented Magnetic Flux Density X and Y axes units are in meters. 87 Figure 34. Solid Non-Augmented Magnetic Field Across Bore X axis is in units of meters, Y axis is Magnetic field strength A/m. 88 Figure 35. Solid Non-Augmented Magnetic Field Across Rail Surface X axis is in units of meters, Y axis is Magnetic field strength A/m. 89 100 k-Amp DC, Slotted Rail, Non-Augmented Figure 36. Slotted Non-Augmented Magnetic Flux Density X and Y axes units are in meters. 90 Figure 37. Slotted Non-Augmented Magnetic Field Across Bore X axis is in units of meters, Y axis is Magnetic field strength A/m. 91 Figure 38. Slotted Non-Augmented Magnetic Field Across Rail Surface X axis is in units of meters, Y axis is Magnetic field strength A/m. 92 100 k-Amp DC, Solid Rail, Augmented Figure 39. Solid, Augmented Magnetic Flux Density X and Y axes are units are in meters. 93 Solid Augmented Magnetic Field Across Bore Figure 40. Solid Augmented Magnetic Field Across Bore X axis is in units of meters, Y axis is Magnetic field strength A/m. 94 Solid Augmented Magnetic Field Across Rail Surface Figure 41. Solid, Augmented Magnetic Field Across Rail Surface X axis is in units of meters, Y axis is Magnetic field strength A/m. 95 100 k-Amp DC, Slotted Rail, Augmented Figure 42. Slotted Augment Magnetic Flux Density X and Y axes units are in meters. 96 Solid Augmented Magnetic Field Across Bore Figure 43. Solid Augmented Magnetic Field Across Bore X axis is in units of meters, Y axis is Magnetic field strength A/m. 97 Solid Augmented Magnetic Field Across Rail Surface Figure 44. Solid Augmented Magnetic Field Across Rail Surface X axis is in units of meters, Y axis is Magnetic field strength A/m. 98 B. ORCAD 10.3 P-SPICE CIRCUIT MODELING LRC Model of the existing power supply, and resultant current profile at 35 kJ Rail Resistance System Inductance System Resistance Diode delay Capacitance 0.3 m-Ohms 5.5 µH 3 m-Ohms 100 µs 1.66 mF Figure 45. P-SPICE Single Module LRC Circuit Model 99 Figure 46. Single Power Module Current Profile 100 Four-Module Ripple Fired 332-kJ Circuit Model 1.0 mOhm 0.3 mOhm Circuit Parameters Rail Resistance 3.0 mOhm 0 µs Shunt Resistance 100 µs Resistance per Module Diode delay Switch delay 2.5 µH 3.0 mOhm 1.66 mFarad Inductance 0 µs Resistance 100 µs 5.0 µH Diode delay 200 µs Switch delay Inductance 300 µs 3.0 mOhm Switch delay 3.0 mOhm Resistance Resistance Diode delay 400 µs 12.0 µH Switch delay 500 µs Inductance Diode delay 14 µH 3.0 mOhm 101 Capacitance per Module Module 1 Module 2 Module 3 Module 4 Inductance Resistance P-SPICE Four-Module LRC Circuit Model Figure 47. Figure 48. Four-Module Current Profile Output from Figure 46 Circuit Model 102 APPENDIX E. BREAK SCREEN AND CURRENT PROFILE SCREEN CAPTURES 6500 Volts, Solid Rail, Non-augmented TVS-40 switches triggered Armature exits muzzle Figure 49. Solid Non-Augmented Velocity Measurement Green and yellow traces are from break screens located at 0.5 meter interval for velocity measurement. 103 Figure 50. Solid Non-Augmented Current Profiles Green and Purple Traces are the Pearson 1330 current monitor traces through the individual TVS-40 switches, the Yellow curve is the Pearson railgun. 104 1423 total current to the 6500 Volt, Slotted Rail, Non-Augmented 6500 volts / slotted / non-augmented Figure 51. Slotted Non-Augmented Velocity Measurement See caption for Figure 49. 105 Figure 52. Slotted Non-Augmented Current Profiles See caption for Figure 50. 106 6500 Volt, Solid Rail, Augmented Figure 53. Solid Augmented Velocity Measurement See caption for Figure 49. Fluctuation in green trace is due to loose electrical connection and vibration during shot at break-screen mount, corrected for subsequent shots. 107 Figure 54. Solid Augmented Current Profiles See caption for Figure 50. 108 6500 Volts, Slotted, Augmented Figure 55. Slotted Augmented Velocity Measurement See caption for Figure 49. 109 Figure 56. Slotted Augmented Current Profiles See caption for Figure 50. 110 APPENDIX F. TYPICAL POST-SHOT MATERIAL CONDITIONS Rails and Insulators Figure 57. Typical Post-Shot Rail and Insulator Wear 111 Armature Wear Figure 58. Typical Post-Shot Armature Wear 112 Muzzle Figure 59. Muzzle Block Indicating Muzzle Flash Arcing 113 THIS PAGE INTENTIONALLY LEFT BLANK 114 LIST OF REFERENCES 1. McNab,I.R., Stefani,F., Crawford,M., Erengil,M., Persad,C., Satapathy,S., Vanicek,H., Watt,T., and Dampier,C., Development of a Naval Railgun, IEEE Transactions on Magnetics, Vol.41, No.1, pp.206-213, January 2005. 2. Materials Web website, last accessed 23 February 2006, http://www.matweb.com/search/ 3. Kerrisk,J.F., Current Distribution and Inductance Calculations for Rail-Gun Conductors, LANL report LA-9092MS, Nov. 1981. 4. Maier, B., Selected Topics in Railgun Technology Course Notes, Naval Postgraduate School, July 2005. 5. Kotas,J.F., Guderjahn,C.A., Littman,F.D., A Parametric Evaluation of Railgun Augmentation, IEEE Transactions on Magnetics, Vol.22, No.6, November 1986. 6. Chen,Y.G., Dethlefsen,R., Crumley,R., HighCoulomb Vacuum Switch, IEEE International Digest of Technical Papers, Pulsed Power Conference 1993,Digest of Technical Papers, Vol.2, pp.938-941, June 1993. 7. Crawford, M., Railgun System Technology, Naval Postgraduate School Physics Department Colloquium Lecture, May 2004. 8. ACF Component & Fasteners, Inc. Specification Handbook, 2005 Edition, last accessed 05 March 2006, www.acfcom.com 9. Ugural, A.C. and Fenster, S.K., Advanced Strength and Applied Elasticity, Fourth Edition, Prentice Hall Publishers, Upper Saddle River, NJ, 2003, pp.527. 10. K-Mac Plastics website, last accessed 23 February 2006, www.k-mac-plastics.net/data%20sheets/Acculamtechnical-data.htm 115 11. CoorsTek Ceramics website, last accessed 23 February 2006, www.coorstek.com/materials/ceramics/ alumina/ad96.asp 12. American Micro-Industries website, last accessed 23 February 2006, www.electricalinsulationmaterial.com/ electrical-insulation-products/mylar_polyester_film/ mylarpolyester-film.html#mylar-properties 13. Stefani,F., Watt,T., Experimental and Computational Investigation of Root-Radius Melting in CShaped Solid Armatures, IEEE Transactions on Magnetics, Vol.41, No.1, pp.442-447, January 2005. 14. Hackel,L., Chen,H., Laser Peening – A Processing Tool to Strengthen Metals or Alloys to Improve Fatigue Lifetime and Retard Stress-Induced Corrosion Cracking, Lawrence Livermore National Laboratory Laser Science and Technology Program UCRL-ID-155327, September 2003. 15. Renk,T., Buchheit,R., Sorensen,N., Senft,D., Thompson,M., Grabowski,K., Improvement of Surface Properties by Modification and Alloying with High-Power Ion Beams, Physics of Plasmas, Vol.5, No.5, pp.2144-2150, May 1998. 116 INITIAL DISTRIBUTION LIST 1. Defense Technical Information Center Ft. Belvoir, VA 2. Dudley Knox Library Naval Postgraduate School Monterey, CA 3. Professor William B. Maier II, Code PH/MW Department of Physics Naval Postgraduate School Monterey, CA 4. Professor Terry McNelley, Code MAE/MC Department of Mechanical and Astronautical Engineering Naval Postgraduate School Monterey, CA 5. Engineering and Curriculum Office, Code 34 Naval Postgraduate School Monterey, CA 6. LT Brian C. Black Pittsburgh, PA 7. Tania Zaleski Laser Peening Project Leader Lawrence Livermore National Laboratory Livermore, CA 8. Tim Renk Beam Applications and Initiatives Project Leader Sandia National Laboratory Albuquerque, NM 9. Prof. Hans Mark Institute for Advanced Technology Austin, TX 10. Prof. Ian McNabb Institute for Advanced Technology Austin, TX 117 11. Dr. Mark Crawford Institute for Advanced Technology Austin, TX 12. Francis Stefani Institute for Advanced Technology Austin, TX 13. Dwayne Surls Institute for Advanced Technology Austin, TX 14. Chadee Persad Institute for Advanced Technology Austin, TX 15. Fred Beach Institute for Advanced Technology Austin, TX 16. Robert Hebner Center for Electromechanics Austin, TX 17. John Pappas Center for Electromechanics Austin, TX 18. Dr. Roger McGinnis Air Warfare and Naval Weapons Applications Division Office of Naval Research Arlington, VA 19. Roger Ellis EM Railgun INP Office of Naval Research Arlington, VA 20. John Kinser Office of Naval Research Arlington, VA 20. Elizabeth D’Andrea Office of Naval Research Arlington, VA 118 21. Dr. Irwin Singer Tribology Section, Naval Research Lab Washington, DC 22 Robin Keesee US Army Research and Development Command Aberdeen Proving Ground, MD 23. Mark McCormick, Northrop Grumman Corporation Ship Systems Pascagoula, MS 119

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