Experiments with brush projectiles in a parallel augmented railgun

Transcription

1 Experiments with brush projectiles in a parallel augmented Johan Gallant Department of Weapons Systems and Ballistics Royal Military Academy Brussels, Belgium Pascale Lehmann Division of Accelerators and Projectiles French-German Research Institute of Saint-Louis Saint-Louis, France 2005 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. Abstract One of the main issues of s is the ablation of the rails due to the existence of a plasma arc occurring at high currents. To avoid the heat load on the rails it is necessary to reduce the current intensities. The use of a parallel augmented is one method of lowering the current without reducing the electromagnetic force on the projectile. One- and two-brush projectiles have been fired in a parallel augmented with a 15 mm x 15 mm caliber and with a barrel length of 1.5 m. These experiments have shown that the maximum kinetic energy at the muzzle without the transition of the solid contact between the rails and the brush to a plasma contact can be significantly increased in an augmented. The maximum kinetic energy has increased by a factor of 5 for one-brush projectiles and by a factor of 9 for two-brush projectiles. A model for the electromagnetic force in the augmented and a friction model for the brush projectile are presented. The kinematics of the projectile in the gun are simulated with these models and are compared to the measured velocity. A good agreement is obtained. Keywords-s; mutual coupling; armature; friction Published in IEEE Transactions on Magnetics 41, pp , DOI : /TMAG I. INTRODUCTION Railguns have the potential to accelerate projectiles to velocities higher than 2000 m/s. The accelerations needed to attain these velocities, however, demand high currents (order of magnitude: mega-ampère). The heating of the sliding contacts between the rails and the brush armatures due to the Jouleeffect and to the friction can cause the melting of these contacts; the solid contact transits then to a plasma contact. The result of this contact transition is an increase of the armature resistance and thus a decrease of the efficiency, and the deterioration of the rails. In a parallel augmented, a circuit with its own energy supply is added to the conventional (nonaugmented) in order to establish an additional magnetic field. This field is added to the magnetic field produced by the current in the rails and increases in this way the electromagnetic force on the projectile without increasing the current in the armature. The current, and thus the magnetic field, is limited by the repulsion forces on the rails [1]. In this paper we present the parallel augmented that was constructed and tested at the French-German Research Institute of Saint-Louis (ISL) in France. The objective of the study is to compare the parallel augmented with the conventional and to determine by what factor the kinetic energy of the projectile at the muzzle can be increased without contact transition. The conventional is readily available by opening the exterior circuit of the parallel augmented. II. EXPERIMENTAL SETUP The gun is made up of two electric circuits (Fig. 1). The inner circuit is composed of two rails, the projectile and an energy source. The rails guide the projectile and provide current to the brush in the projectile. The outer circuit is composed of two rails, a bridge at the muzzle of the launcher and an energy source; it generates the augmenting field. The currents in the inner and the outer circuit are respectively I R and I A. A cross-section of the gun (A A ) is shown in Fig. 2. The copper rails are 15 mm x 15 mm wide and 1500 mm long; the thickness of the isolation between the rails of the inner and the outer circuit is 6 mm. The rails are fixed by a structure made of glass fiber reinforced plastics and steel bolts. The projectile, with a caliber of 15 mm x 15 mm (Fig. 3), is accelerated over a length of 1500 mm. It consists of one or two Cu-Cd fiber brush armatures incorporated in a sabot of glass fiber reinforced plastics. The diameter of a brush is 7 mm. The advantage of the small caliber is that the stresses on the rails are well below the maximum yield strength of the structure and that the preparation of a shot takes significantly less time than in the case of a medium or large caliber gun.

2 1 4 Figure 1. Side-view of the parallel augmented 3 2 The energy source is composed of five capacitor banks with a capacity of 3.08 mf per bank. Two banks are connected to the inner circuit, the three other banks to the outer circuit. The current profile is determined by the charge voltage of the capacitors (between 7 and 10 kv) and the time between the injection of the first bank and the injection of the following banks. The pulse forming network for the outer circuit has not been optimized. Future work will focus on specific energy sources for parallel augmented s. Fig. 4 shows the parallel augmented at the ISL. Visible are the capacitor banks (1), the coaxial cables connecting the banks to the gun (2), the gun (3) and the target in the safety drum (4). III. Figure 4. The parallel augmented at the ISL MODELING OF THE PARALLEL AUGMENTED RAILGUN A. The forces on the projectile The total force on the projectile F proj is given by F proj = F EM F f (1) where F EM is the electromagnetic force on the projectile and F f the friction force, on the assumption that all other forces are negligible. The friction force is a function of the normal force exerted by the brush on the rails F N and the friction coefficient µ: F f = µ F N (2) The normal force has two components, mechanical (F N,mech ) and electromagnetic (F N,EM ): F N = F N,mech + F N,EM (3) The electromagnetic normal force (F N,EM ) is proportional to the electromagnetic force (F EM ): F N,EM = α F EM (4) The axial and normal components of the electromagnetic force are depicted in Fig. 5 [2]. By combination of (1) to (4) we find an expression for the force on the projectile Figure 2. Cross-section of the parallel augmented gun. F proj = F EM F f = (1 α µ) F EM µ F N,mech (5) The electromagnetic force and the friction force will be discussed in detail in the following chapters. B. The electromagnetic force The expression of the electromagnetic force is Figure 3. Projectiles with one and two brushes before launch. F EM = ½ L I R ² + M I R I A (6) where I R is the current in the inner circuit, I A the current in the outer circuit, L the inductance gradient and M the mutual inductance gradient.

3 Figure 5. The axial and normal component of the electromagnetic force at the brush-rail interface Figure 6. Current injections in the inner and the outer circuit. In order to calculate the electromagnetic force on the projectile, we used the finite element code MEGA [3]. The injected currents of the shot with the augmented that will serve as an example are shown in Fig. 6. The current in both circuits is injected by capacitor banks charged at 10 kv; one bank is connected to the inner circuit, the two banks connected to the outer circuit are switched with an interval of 0.5 ms. A complete 3D-model (with simulation of the rails and the armature) was used to calculate the forces on the projectile, with the measured currents as input. The resulting electromagnetic force is represented by the dotted line on Fig. 7. In order to compare this numerical result with the analytical formula (6), the coefficients L and M have to be determined. Several methods exist. The easiest and fastest way is to calculate the magnetic energy in the by using a 2D or 3D finite element code to simulate the rails without the armature. The length of the rails is 1 m. For the calculation with MEGA we assume that the injected current has a constant amplitude and a high frequency (100 khz) in order to concentrate the current on the inner surface of the rails. The coefficients of the electromagnetic force L' and M' are calculated by varying the amplitude of the current in one circuit of the augmented while the amplitude of the current in the other circuit is fixed. The following values are used for the simulation : the amplitude of the current in the inner circuit is fixed (200 ka) and the amplitude of the current in the outer circuit is varied from 0 MA to 0.3 MA. The magnetic energy E M calculated with MEGA, is represented by the dots on Fig. 8. The equation of the parabolic regression line through these dots is E M = I A ² I A (7) The correlation coefficient of the regression line is 1. The general expression for the magnetic energy of the augmented is Figure 7. Comparison of different methods to calculate the force on the projectile with the simulated force in the case of the augmented. (The different curves are defined in Table I and Table II.) Figure 8. The magnetic energy in the, calculated with MEGA. E M = ½ L A I A ² + M I R I A + ½ L I R ² (8) where L A is the inductance of the outer circuit. Since I R equals 200 ka, the inductances can be determined by combination of (7) and (8) : L A = µh, L = µh and M = µh. Another method is to simulate the with the armature and to calculate the force on the projectile. The frequency of the current in this case is of the order of the frequency of the real current ( 1 khz). The coefficients can be derived from (6) by the same procedure as described above. The third method is in principle the same as the second method, but with a constant current instead of the 1 khz-current. The coefficients calculated with the three methods are presented in Table I. The coefficients for the conventional are nearly equal for the three methods, so all methods are equivalent as far as the result is concerned (Fig. 9). For the augmented, however, there is a large difference between the

4 methods due to the different values of M. As shown on Fig. 7, neither of the three methods coincides with the dotted line, which is considered as being the correct force. On the other hand, curve 3 gives a good result at the beginning of the current injection, and after 1.5 ms curve 4 fits well with the simulated force. Therefore, we propose time dependent coefficients of the force equation. The values are listed in Table II. (Fig. 9). This induced current has an influence on the current and the magnetic field distribution in the brush armature, resulting in a lower electromagnetic force than was predicted by the calculations with the 100 khz-coefficients (compare the dotted line of Fig. 7 with curve 2). It is principally the mutual inductance gradient M' which is decreased: µh/m instead of the theoretical value of µh/m (Table II). TABLE I. COEFFICIENTS OF THE ELECTROMAGNETIC FORCE Simulation method Conventional Railgun L (µh/m) M (µh/m) Curve Fig. 7 8 Rails, 100 khz Rails and armature, 1 khz Rails and armature, constant current Augmented Railgun Rails, 100 khz Rails and armature, 1 khz Rails and armature, constant current TABLE II. VARIATION OF THE COEFFICIENTS L AND M (CURVE 1, FIG. 7 AND 9) Time Coefficients L (µh/m) M (µh/m) t 0,2 ms ,2 ms < t < 1,5 ms linear decrease from to linear decrease from to t 1,5 ms Figure 10. Current distribution in the rails at 0.2 ms. The breech of the is on the right, the muzzle on the left. Figure 9. Comparison of different methods to calculate the force on the projectile with the simulated force in the case of the conventional. (The different curves are defined in Table I and Table II.) Curve 1 on Fig. 7 is calculated with these coefficients. It coincides nearly exactly with the dotted line. The same time dependence is applied to the coefficients of the conventional ; the result (curve 1) is shown on Fig. 9. The time variation of the coefficients is necessary to take an induction effect into account. Fig. 10 and 11 show a part of the MEGA model of the augmented, simulating a half of the inner rail and the outer rail, and a quarter of the armature. The current profiles used for the simulation are shown in Fig. 6. At 0.2 ms, when the current is just injected, the current in the inner rail is concentrated on the surface of the rail. Some current is induced by the outer rail in front of the armature Figure 11. Current distribution in the rails at 2.5 ms. The breech of the is on the right, the muzzle on the left. The ratio between the values is 0.80, what is consistent with the 0.85 ratio calculated by Keefer, Crawford and Taylor [4]. At 2.5 ms, the current has diffused in the rails and the influence of the induction on the electromagnetic force is much higher than at 0.2 ms (Fig. 11). Due to the induction, M' is decreased by 50 %, from µh/m to µh/m.

5 C. The friction force The equation of the friction force F f is formed in section III.A. (5). Two parameters (α and F N,mech ) and a function (µ) have to be determined. The contribution of the electromagnetic force F EM to the normal force F N is determined by α (4). This parameter is a function of the geometry of the brush. For the brushes used in our experiments the value of α is [5].

6 Figure 12. The dynamic friction coefficient as a function of the velocity The friction coefficient µ has not been determined yet for sliding brushes at the high velocities that are typical for s. Therefore, assumptions will have to be made. A typical value of the sliding friction coefficient µ is 0.3 for sliding Cu-brushes on flat Cu-surfaces, but only for low velocities, normal forces and current densities. As soon as a projectile gains velocity, the friction mechanism changes and µ decreases sharply [2]. Values of µ at high velocities are not available in the literature, but are certainly very low and are estimated at 0.1 [6]. Taking these observations into account, we propose an exponential function for µ (Fig. 12). This function provides a good agreement between the measured and the simulated kinematics of the projectiles, but experimental work will be necessary to obtain more information on the friction coefficient at high velocities. To estimate the friction force F f at rest, the electromagnetic force F EM is calculated at the start of the projectile movement, which is detected by a Doppler radar. The friction force at rest equals the electromagnetic force just before the start of the movement of the projectile. By combining this friction force at rest and the values for α and µ, the mechanical normal force F N,mech can be calculated. The mean value for F N,mech is 680 N. This value will be used in the model. IV. RESULTS A. Validation of the model The model for the simulation of projectile kinematics is based on (5) with the time dependent coefficients for the electromagnetic force shown in Table II, and the parameters for the friction force described in section III.C. To validate the model, the measured velocity (by breaking wires at the muzzle) is compared with the velocity calculated with the model. The experimental data of one- and two-brush projectiles launched with the conventional and the augmented are listed in Table III. For each test, the mass of the projectile (m proj ), the maximum current in the inner circuit (I R,max ) and the maximum current in the outer current (I A,max ) (if applicable) are shown. N m proj (g) I R,max (ka) I A,max (ka) Velocity test (m/s) Velocity model (m/s) Δ (%) Type Conv brush Augm brush Conv br Augm br. The difference between the measured and the calculated velocity (Δ) varies between 6 % and 4 % in the case of the one-brush projectiles (Table III, 1-10). The calculated velocity of the two-brush projectiles, however, is systematically too low (Table III, 11-14). This is due to the fact that the electromagnetic force distribution between the two brushes is not exactly known. Hence, the electromagnetic force on the projectile and the friction force, which is distributed over the two brushes, are not easy to model [2]. The muzzle velocity of the projectiles ranges from 291 to 1121 m/s. Taking this wide range of muzzle velocities into account, the model presented in this paper can be considered as a good simulation of the kinematics of one- and two-brush projectiles launched with the augmented at ISL. B. Transition of the contact between rails and armature During the acceleration of the projectile in the, the contact between the rails and the armature is heated by friction and by the Joule-effect. This heating can lead to the melting of the brush fibers at the contact and consequently to a shortening of the fibers. Wear is another mechanism that can cause the loss of brush material. If the fibers become too short, arcing will occur. The transition of a contact is characterized by a abrupt increase of the muzzle voltage [7]. For this kind of and projectile, the voltage change is about 25 V. The muzzle voltages of a transitioning and a nontransitioning contact are shown in Fig. 13 and 14. The projectiles are launched with an augmented. The muzzle voltage is considerably higher than the muzzle voltage in a conventional due to the current in the outer circuit, that induces a voltage in front of the projectile. The periods during which current is injected in the circuits are indicated on the time axis of the graphs. If transition should occur during these injections, it will be difficult to detect due to the high muzzle voltage during the current injections ( -500 V). TABLE III. COMPARAISON BETWEEN THE MEASURED AND THE CALCULATED VELOCITY OF ONE- AND TWO-BRUSH PROJECTILES

7 Figure 13. Muzzle voltage of a transitioning contact (Table III, shot 10) Figure 14. Muzzle voltage of a nontransitioning contact (Table III, shot 14) TABLE IV. MAXIMUM KINETIC ENERGY AT THE MUZZLE OF A ONE- BRUSH PROJECTILE Conventional Augmented Mass of the projectile 17.5 g 16.1 g Maximum muzzle velocity 350 m/s 850 m/s Electric energy 151 kj 459 kj Kinetic energy 1.1 kj 5.8 kj TABLE V. MAXIMUM KINETIC ENERGY AT THE MUZZLE OF A TWO-BRUSH PROJECTILE Conventional Augmented Mass of the projectile 20.7 g 20.9 g Maximum muzzle velocity 370 m/s 1120 m/s Electric energy 151 kj 505 kj Kinetic energy 1.4 kj 13.1 kj C. Comparison of maximum kinetic energy at the muzzle of a conventional and an augmented In order to compare the conventional and the augmented with respect to contact transition, a maximum kinetic energy at the muzzle is defined. It is the maximum kinetic energy of the projectile at the muzzle for which no contact transition has occurred. Four results are presented: one- and two-brush projectiles in the conventional and the augmented. The maximum kinetic energy of a one-brush projectile at the muzzle of the conventional is 1.1 kj, to be compared with a maximum kinetic energy of 5.8 kj 5 times higher for a projectile launched with the augmented (Table IV). In the case of two-brush projectiles, the current is distributed over the two brushes. The brushes are less loaded by heating, which leads to a higher maximum kinetic energy. In the case of the conventional the maximum is 1.4 kj and for the projectile launched with the augmented it is 13.1 kj, thus a factor 9 higher (Table V). It is obvious that the nonarcing acceleration of projectiles up to 1100 m/s is not extraordinary. In fact, projectiles have been accelerated without contact transition up to 2000 m/s in s with a medium caliber (40 mm) [7], [8]. However, the results presented in Table V show that the combination of augmentation and multibrush projectiles can lead to a higher velocity without transition in small caliber s ( 15 mm). The next step is to study an augmented with a larger caliber in order to attain velocities without transition higher than 1120 m/s. V. CONCLUSION One- and two-brush projectiles were launched with a nonaugmented and with an augmented. The maximum kinetic energy at the muzzle at which a projectile can be launched without contact transition is considerably higher in the augmented : a factor 5 for the one-brush projectiles and a factor 9 for the two-brush projectiles. The experiments with two-brush projectiles in the augmented have shown that muzzle velocities up to 1100 m/s can be attained in a small caliber without contact transition. A model for the conventional and the augmented is presented. The friction force and the electromagnetic force are discussed in detail. Due to current induction by the outer rails in front of the projectile, the electromagnetic force on the projectile is lower than the force predicted by the analytical model with the 100 khz-coefficients. Therefore, the coefficients of the force equation in the model (L and M ) must be corrected. There is good agreement between the model and the experiments. REFERENCES [1] J. Gallant, Parametric study of an augmented, IEEE Transactions on Magnetics., vol. 39, pp , January [2] M. Schneider, D. Eckenfels, and S. Nezirevic, Doppler-Radar: a possibility to monitor projectile dynamics in s, IEEE Transactions on Magnetics., vol. 39, pp , January [3] Code developed and commercialized by the Applied Electromagnetics Center of the University of Bath, U. K. [4] D. Keefer, R. Crawford, and J. Taylor, "Inductance gradient scaling experiments in an augmented," IEEE Transactions on Magnetics., vol. 31, pp , January [5] M. Schneider, D. Eckenfels, and F. Hatterer, Kontaktmechanismen multipler elektrischer Bürstenkontakte in Schienenbeschleunigern (in German), ISL, Saint Louis, France, Rep. ISL-R 120, [6] M. Schneider, private communication. [7] J. Barber, D. Bauer, K. Jamison, J. Parker, F. Stefani and A. Zielinski, A survey of armature transition mechanisms, IEEE Transactions on Magnetics., vol. 39, pp , January [8] A. Zielinski and J. Parker, Demonstration of a hypervelocity massefficient integrated launch package, IEEE Transactions on Magnetics., vol. 39, pp , January 2001.