High velocity linear induction launchers

International Journal of Impact Engineering 35 (2008) 1405–1409 Contents lists available at ScienceDirect International Journal of Impact Engineering journal homepage: www.elsevier.com/locate/ijimpeng High velocity linear induction launchers A. Balikci* Gebze Institute of Technology, Istanbul Caddesi No. 101, 41400 Gebze, Kocaeli, Turkey a r t i c l e i n f o a b s t r a c t Article history: Received 7 May 2007 Accepted 6 June 2008 Available online 24 July 2008 Electromagnetic launchers (EMLs) have received great attention in the last decades because of their potential application to a variety of energy, transportation, space, and defense systems. Particularly, they can serve as kinetic weapons, such as ground-based and naval artillery, space-based anti-missile guns, Earth-to-Orbit launcher, and mass transportation. The main advantage is that EMLs can accelerate projectiles to hyper velocities, i.e. velocities greater than those achievable with conventional cannons. The Linear Induction Launcher (LIL) is an air-cored electromagnetic coil launcher operating on the principle of the induction motor. Polyphase excitation of the coils constituting the barrel is designed to create an electromagnetic wave packet, which travels with increasing velocity from the breech to the muzzle. The projectile is a hollow conducting cylinder (sleeve) carrying the payload within it. Relative motion (slip) of the wave packet with respect to the projectile induces azimuthal currents in the sleeve that interacts with the exciting magnetic field to produce both propulsive and centering forces. This paper deals with the design of a high velocity linear induction launcher with muzzle velocity up to 6000 m/s. It addresses the design specifications of the launcher and utilizing a projectile weighing 1 kg. In the paper, the design specifications with simulation results for the phase voltages, the currents, the velocity, and the temperature rise of the sleeve are presented. Ó 2008 Elsevier Ltd. All rights reserved. Keywords: Liner induction launcher Coilgun High velocity 1. Introduction Electromagnetic launchers (EMLs) are essentially a group of special linear electric motors, which convert electromagnetic energy stored in a stationary or rotational electric power supply into kinetic energy of moving projectile. Electromagnetic railgun, electromagnetic coilgun, electrostatic gun, and electro-thermochemical gun are the major types of EMLs. Among them, railguns are at more advanced stage of development. Even though they are relatively complicated when compared with the railguns electromagnetic coilguns are promising alternatives to the railguns. One of the major advantages that coilguns have over other EMLs is that can accelerate heavy projectiles [1]. Because of their potential application to a variety of energy, transportation, space, and defense systems, electromagnetic launchers have received great attention in the last decades. Particularly, they can serve as kinetic weapons, such as ground-based and naval artillery, space-based anti-missile guns, Earth-to-Orbit launcher, and mass transportation. The main advantage over the conventional cannons is that EMLs can accelerate projectiles to hyper velocities. EMLs use the electromagnetic field to produce propulsive force and these can overcome many of the disadvantages of chemical * Tel: þ90 262 605 2411; fax: þ90 262 653 8490. E-mail address: [email protected] 0734-743X/$ – see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijimpeng.2008.07.004 cannons such as velocity limitations. EMLs are relatively cheap when compared with conventional rockets since they are reusable, could project almost pure payloads, and relative low cost in using electricity. The Linear Induction Launcher (LIL) is an air-cored electromagnetic coil gun. The operating concept is based on the principle of the classical induction machine. Polyphase excitation of the coils constituting the barrel is designed to create an electromagnetic wave packet, which travels with increasing velocity from the breach to the muzzle. The projectile is a hollow conducting cylinder (sleeve) carrying the payload within it. Relative motion (slip) of the wave packet with respect to the projectile induces azimuthal currents in the sleeve that interacts with the exciting magnetic field to produce both propulsive and centering forces (Fig. 1) [2]. To reduce the ohmic loss and, therefore, the temperature in the sleeve, one must limit operation to a small slip and this forces division of the barrel of the linear induction coilgun into many sections. Every section of the barrel has a different frequency and a different voltage level. To obtain a constant average force on the sleeve in every section of the barrel, it is desirable to have a constant air-gap flux density in all section. This implies that the electric field must be proportional to the frequency [1]. Under ideal conditions, the exciting magnetic wave produced by the barrel and the current wave induced in the sleeve are sinusoidally distributed in space [3]. As in the induction motor, there should be a difference between the traveling wave and the actual speed of the projectile in order to induce azimuthal currents in the 1406 A. Balikci / International Journal of Impact Engineering 35 (2008) 1405–1409 Fig. 1. Cross-section of the linear induction coil launcher. sleeve. This induced current wave lags behind the exciting magnetic wave, so that in the some regions these two waves may have opposite signs, the resulting force is decelerating, instead of accelerating. Maximizing the coupling between the stationary barrel and the moving projectile will minimize this negative effect on the force. But a necessary mechanical clearance (an air-gap) between the barrel and the projectile sets a limit to the coupling. Even with this phase delay, the net force on the whole projectile is still, ideally, a constant. By energizing the launcher from a flywheel motor-generator set [4], the current in the barrel coils are sinusoidal pulses of near constant amplitude. However, fluctuations of the net accelerating force on the projectile would exist. Partition of the barrel into sections, finite length of the sleeve (end effects), dc components in the drive coils, and finite drive coil length (dimension along the barrel) can be the reasons for the fluctuations. To reduce these fluctuations, it has been suggested in the publications [5–7] that a practical approach would be to increase the number of phases in each barrel section. Using a 5-phase instead of a 3-phase system [8], fluctuations in the accelerating force reduces, leading to a smoother velocity curve and more efficient operation. Reference [9] considers two possible configurations for the flywheel motor/generator set arrangements. The first arrangement has one generator for each section; therefore the number of generator is equal to the number of section. If the launcher is designed to obtain the same gain in projectile speed for each section, the last generator (supplying the last section in the barrel) will have to be much larger than the first one. The second arrangement is such that each pole-pair along the barrel requires a set of two shaft-coupled generators; that is, one generator per pole (Fig. 2). In this case, for a 5-phase system, 10 drive coils are used to make one pole-pair. This configuration leads to a substantial reduction in input voltage levels, and to more efficient energy utilization. The electrical stresses on the drive coils and the heat generated in the sleeve of the projectile are the most critical issues on the design of the linear induction coil launchers [10]. The preliminary design procedure and the final simulation results for the phase voltages, the currents, the velocity, and the temperature rise of the sleeve along the barrel are discussed in the following sections. LILs are unlike classical electric machines in the following aspects [11]: – High velocities may be obtained as much as few kilometers per second. – To make it possible to have high magnetic loading, as much as 10 T, non-ferromagnetic materials are used. – The primary may be only partially energized. The traveling wave has finite length both in space and in time therefore forms a wave packet. – The secondary is relatively shorter than the primary and may not have any windings and connections, but may consist of a sleeve. – Energy is supplied by a special source, such as a capacitor bank, a pulsed-power flywheel motor/generator set, etc. – For a very short time of operation (few milliseconds), very high power is needed. 2. Design procedure LILs are essentially linear electric motors in which the polarity of the magnetic alternates. Due to their special applications, Fig. 2. Set of two shaft-coupled generators fed two-poles, 10 drive coils, for 5-phase system. 1407 A. Balikci / International Journal of Impact Engineering 35 (2008) 1405–1409 Therefore, the design formulas for classical machines are not directly applicable to LILs. The major consideration in designing an LIL is to minimize the size of the launcher needed to attain a specified velocity at the muzzle, within the limitations of permissible thermal and mechanical stresses of the materials [11]. As stated above, the most critical requirement is the maximum temperature increase in the sleeve material. As a result, the LIL design should be based on a quasi-steady-state preliminary procedure [12]. A transient analysis [1] is required to validate and modify that preliminary design. Reference [10] discuses how to carry out the quasi-steady-state preliminary design procedure. However, to use this procedure requires some advance level of design proficiency for LIL. The design algorithm with some additional steps is the following: 1. Breach velocity Vin, muzzle velocity Vout, acceleration am, and payload weight ML of the launcher are specified. 2. The projectile specifications such as sleeve material, the length LS, outer diameter D, and the thickness of the sleeve d should to be selected. The projectile length LS sets the pole pitch s. 3. The mass MS of the sleeve is: MS ¼ pdðD  dÞLS d (1) where d is the density of the sleeve material. 4. Condition for the total number of section n is: n ðVout  Vin Þ 4am s Vout ðnÞ 1  S0 VSðnÞ fn ¼ 2s SCðnÞ ¼ (8) 1 dgm0 VSðnÞ (9) where g is the electrical conductivity of the sleeve material and m0 is the permeability of air. The electrical conductivity assumed to be not temperature dependent and has the value when the temperature is at 25  C. 13. Check – The speed gain DVn must be modified at the step 8, if there is no match between the critical slips SC(n) at the steps 11 and 12. Consequently, the design begins at the last section and continues back down to the first section by repeating the series of steps 8–13. 14. Check – If the specified breech velocity Vin is not obtained, then the whole iteration procedure has to be re-started with a different exit slip S0 at the step 5. 15. The transit time tn in section n is: Vo ðnÞ  Vin ðnÞ am ln ¼ (10) Vin ðnÞ þ Vo ðnÞ tn 2 (11) 17. The gain in kinetic energy Wk(n) of the projectile during its transit of section n is: (3) WkðnÞ ¼ ðMS þ ML Þ 2 Vo2 ðnÞ  Vin ðnÞ 2 (12) 18. The average slip Savg(n) in section n is: Savg ðnÞ ¼ Sin ðnÞ þ So 2 (13) (4) 19. The energy Wn required for barrel section n to obtain the above kinetic energy is: Wn ¼ (5) (6) 10. The input slip Si(n) of the section n is: VSðnÞ  Vin ðnÞ VSðnÞ SiðnÞ S0 2 A 16. The length ln of section n is a function of the transit time tn: 9. The input velocity Vin(n) of section n (equal to the exit velocity Vo(n1) of the preceding section) is the subtraction of the speed gain DVn from output velocity of the previous section Vout: VinðnÞ ¼ Vout  DVn 2ln 11 (2) 8. The speed gain DVn in the final section of an n-section launcher is assumed to be: V  Vin DVn y out n S2iðnÞ  S20 12. The critical slip SC(n) [3] must also relate to the frequency of the section n (Eq. (4)): 2 7. Dividing the synchronous speed VS(n) by the two-pole-pitch 2s gives the power supply frequency fn needed for the each section: SiðnÞ ¼ SC ðnÞ ¼ @ tn ¼ 5. The desired exit slip S0 between excited wave in the barrel and the induced wave in the projectile must be specified. 6. The synchronous speeds VS(n) of every section are obtained related to the exit slip S0: VSðnÞ ¼ 0 11. The critical slip SC(n) of section n is a function of input slip Si(n) and exit slip S0: (14) 20. The ohmic loss DWn in the sleeve material during its transit of section n is: DWn ¼ Wn Savg ðnÞ (15) 21. The temperature rise qS developed in the sleeve is: qS ¼ (7) WkðnÞ 1  Savg ðnÞ n 1 X DWi cMS i ¼ 1 (16) where c is the specific heat of the sleeve material. The specific heat assumed to be not temperature dependent and has the value when the temperature is at 25  C. Also, the dissipated power in the sleeve assumed to be uniformly distributed in the sleeve mass. 1408 A. Balikci / International Journal of Impact Engineering 35 (2008) 1405–1409 22. Check – If temperature qS is excessively close to the melting point of the sleeve material, the number of sections n has to be increased and all iteration should be re-started again at step 4. 3. Design specifications of a 6000-m/s launcher The quasi-steady-state procedure shown above is used to design an LIL launcher whose breech velocity is Vin ¼ 0 m/s and muzzle velocity is Vout ¼ 6000 m/s. The acceleration, am, of the projectile is 784,800 m/s2. The payload inside the projectile, ML, is zero. Therefore, the projectile is only a hollow conducting sleeve. Aluminum as the sleeve material is preferable since it leads to a shorter barrel [11]. Aluminum has a melting point of 660.1  C and a mass density, d, of 2700 kg/m3 [13]. The followings are the dimensions of the sleeve: the length, Ls, is 0.2 m, outer diameter, D, is 0.07 m, the thickness, d, is 0.01 m. Then the mass of the sleeve, which can be calculated by using Eq. (1), MS, is 1.018 kg. The projectile length, LS, sets the pole-pitch at s ¼ 0.1 m. Assume a total number of sections n is 40. The desired exit slip S0 between excited wave in the barrel and the induced wave in the projectile is 0.005. The results of the procedure are shown at Table 1. The radial thickness of the drive coils should be minimum allowed by the mechanical and thermal stress limits, in order to have a good coupling with the sleeve [11]. Therefore, the number of turns per coil should be reduced. For a 5-phase system, each pole pitch, s, must have 5 drive coils. At a pole pitch of s ¼ 0.1 m, each coil has a width of 0.02 m with insulation. The dimensions of each drive coil and the projectile are given in Fig. 3. Each coil is assumed to have 6 turns. The air-gap between the barrel and the projectile is Table 1 Quasi-steady-state results for the design of the 6000 m/s LIL Table 2 Simulation results for 40-section LIL Section Section number frequency (Hz) Exit velocity (m/s) Transit time (s) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 189 376 561 744 925 1104 1281 1456 1629 1800 1969 2136 2301 2464 2625 2784 2941 3096 3249 3400 3549 3696 3841 3984 4125 4264 4401 4536 4669 4800 4929 5056 5181 5304 5425 5544 5661 5776 5889 6000 0.000241 0.000238 0.000236 0.000233 0.000231 0.000228 0.000226 0.000223 0.00022 0.000218 0.000215 0.000213 0.00021 0.000208 0.000205 0.000203 0.0002 0.000198 0.000195 0.000192 0.00019 0.000187 0.000185 0.000182 0.00018 0.000177 0.000175 0.000172 0.000169 0.000167 0.000164 0.000162 0.000159 0.000157 0.000154 0.000152 0.000149 0.000147 0.000144 0.000141 Total 0.007645 22.9 950 1889 2819 3739 4648 5548 6437 7317 8186 9045 9894 10,734 11,563 12,382 13,191 13,990 14,779 15,558 16,327 17,085 17,834 18,573 19,302 20,020 20,729 21,427 22,116 22,794 23,462 24,121 24,769 25,407 26,035 26,653 27,261 27,859 28,447 29,025 29,593 30,151 Section length (m) 0.02 0.07 0.11 0.15 0.19 0.23 0.27 0.31 0.34 0.37 0.41 0.44 0.47 0.49 0.52 0.55 0.57 0.60 0.62 0.64 0.66 0.68 0.70 0.71 0.73 0.74 0.76 0.77 0.78 0.79 0.80 0.81 0.82 0.82 0.83 0.83 0.84 0.84 0.84 0.84 Gain in kinetic energy (J) Temperature increase ( C) 18,179 53,770 88,219 121,538 153,740 184,836 214,839 243,761 271,615 298,412 324,164 348,885 372,585 395,278 416,975 437,690 457,433 476,217 494,055 510,958 526,939 542,011 556,184 569,472 581,887 593,440 604,145 614,013 623,057 631,288 638,719 645,363 651,231 656,335 660,688 664,303 667,190 669,364 670,834 671,615 19.0 18.8 18.6 18.4 18.2 17.9 17.7 17.5 17.3 17.1 16.8 16.6 16.4 16.1 15.9 15.7 15.4 15.2 15.0 14.7 14.5 14.3 14.0 13.8 13.6 13.3 13.1 12.9 12.6 12.4 12.1 11.9 11.7 11.4 11.2 11.0 10.7 10.5 10.3 10.0 18,321,228 583.7 Fig. 3. Dimensions of the drive coil and the projectile. Section Peak phase number voltage (kV) Average peak phase current (kA) Exit velocity (m/s) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 42.0 41.4 41.0 40.6 40.2 40.0 39.8 39.7 39.5 39.3 39.1 39.0 39.0 38.8 38.8 38.7 38.7 38.7 38.6 38.6 38.6 38.5 38.5 38.4 38.3 38.3 38.3 38.2 38.2 38.2 38.0 38.0 38.0 37.9 37.8 37.8 38.7 38.7 38.7 38.6 190 372 564 751 923 1101 1278 1461 1632 1805 1967 2131 2295 2461 2622 2787 2946 3102 3248 3405 3552 3699 3846 3988 4128 4269 4405 4540 4668 4806 4932 5061 5185 5309 5427 5549 5665 5780 5893 6011 20.1 19.2 18.7 18.5 18.3 18.1 17.9 17.4 17.4 17.2 17.1 16.3 16.5 16.1 16.1 15.5 15.6 15.4 15.2 14.6 14.4 14.4 14.2 13.9 13.6 13.2 13.2 13 12.7 12.4 12.3 12.1 11.5 11.6 11.3 11.1 10.6 10.5 10.4 10.2 Total 6011 587.8 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 10.5 11.0 11.5 12.0 12.5 13.0 13.5 14.0 14.5 15.0 15.5 16.0 16.5 17.0 17.5 18.0 18.5 19.0 19.5 20.0 20.5 21.0 Maximum temperature increase ( C) Section length (m) 0.2 0.2 0.2 0.2 0.2 0.2 0.3 0.3 0.3 0.4 0.4 0.4 0.5 0.5 0.5 0.5 0.6 0.6 0.6 0.6 0.6 0.7 0.7 0.7 0.7 0.7 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 23 A. Balikci / International Journal of Impact Engineering 35 (2008) 1405–1409 1409 0.001 m. The length of each section must be at least two-pole-pitch (2s) long and an integral number of the pole-pitch. Evidently, the calculated length of each section in Table 1 must be adjusted to satisfy the above requirement (see Table 2). the linear induction coil launchers can be used for high velocity applications. 4. Simulation results [1] He JL, Levi E, Zabar Z, Birenbaum L. Concerning the design of capacitively driven induction coil guns. IEEE Trans Plasma Sci 1989;17(3). [2] Liao M, Zabar Z, Czarkowski D, Levi E, Birenbaum L. On the design of a coilgun as a rapid-fire grenade launcher. IEEE Trans Magn 1999;35(1). [3] He JL, Levi E, Zabar Z, Birenbaum L, Naot Y. Analysis of inductive-type coil-gun performance based on cylindrical current sheet model. IEEE Trans Magn 1991;27:579–84. [4] Balikci A, Zabar Z, Czarkowski D, Levi E, Berenbaum L. Flywheel motor/generator set as an energy source for coil launchers. IEEE Trans Magn 2001;37:280–3. [5] Lu XN, Zabar Z, Levi E, Birenbaum L. Transition between two sections in a linear induction launcher (LIL). IEEE Trans Magn 1995;31:493–8. [6] Liao M, Zabar Z, Levi E, Birenbaum L. Analysis of generator-driven linear induction launchers. IEEE Trans Magn 1997;33:184–9. [7] Zabar Z, Lu XN, Levi E, Birenbaum L, Creedon J. Experimental results and performance analysis of a 500 m/s linear induction launcher (LIL). IEEE Trans Magn 1995;31:522–7. [8] Balikci A, Zabar Z, Czarkowski D, Birenbaum L. Reduction in fluctuation of the accelerating force in linear induction launchers. IEEE Trans Magn 2003;39(1):97–102. [9] Balikci A, Zabar Z, Birenbaum Z, Czarkowski D. Improved performance of linear induction launchers. IEEE Trans Magn 2005;41(1):171–7. [10] Balikci A, Zabar Z, Birenbaum Z, Czarkowski D. On the design of coilguns for super-velocity launchers. IEEE Trans Magn 2007;43(1):107–10. [11] He JL. Analysis and design of EM launchers. Ph.D. Dissertation, Polytechnic University; 1999. [12] Fitzgerald AE, Kingsley C, Umans SD. Electric machinery. 5th ed. NY: McGrawHill; 1990. [13] Christiansen D. Electronics engineers’ handbook. 4th ed. New York: McGraw Hill; 1996. The specifications shown in Table 1 are fed into the transient analysis program [8]. If the sleeve thickness is small as compared with the skin-depth, which is a function of the slip frequency Savgfn, a relatively uniform current distribution is achieved [11]. Therefore, in the simulation program, the power dissipated in the projectile may be assumed uniformly distributed in the sleeve mass. Table 2 shows the simulation results. 5. Conclusion An improved steady-state preliminary design of a linear induction coil launcher has been discussed in the paper. Also, the specifications of high velocity launcher, which accelerates 1 kg projectile from 0 m/s to 6000 m/s with 784,800 m/s2 are addressed. The simulation results show that the design procedure agrees with the simulation. The maximum temperature rise, the most critical specification, in the sleeve material is below the melting point of aluminum. If one wants to have lower than this maximum temperature rise, the number of section should be increased, not the length of the launcher. The results suggest that References