Analysis of the performance of a combined coil-rail launcher

IEEE TRANSACTIONS ON MAGNETICS, VOL. 39, NO. 1, JANUARY 2003 103 Analysis of the Performance of a Combined Coil–Rail Launcher Sami Barmada, Member, IEEE, Antonino Musolino, Marco Raugi, and Rocco Rizzo Abstract—An electromagnetic system that operates both as a rail and as a coil launcher is proposed, and its performance is analyzed. The device has a composite stator that consists of two rails properly slotted in order to allow the presence of a system of coils. The armature consists of a conductive slab sliding between the rails. Another system of slots is present in the armature where a system of short-circuited coils is placed. A source of constant voltage is connected to the rails and the current flowing in the armature through the sliding contacts produces a thrust force on it. If a proper system of currents able to produce a traveling wave of flux density in the region between the rails is used to feed the barrels, the induced currents that flow in the armature’s short-circuited coils produce a further thrust force on the armature itself. The analysis of the behavior of this launcher is performed via a computer code based on an integral formulation and a tool that analyzes the phenomena related to the velocity skin effect; the interactions between the two systems of currents on the armature and the currents on the stator (rails and barrels) are investigated. The thermal behavior of the device has been taken into account by a simple adiabatic model since the short operating time allows one to neglect heat diffusion in the conductive parts of the system. A comparison between the velocities, respectively obtained by separately feeding rails and coils and the system with the combined feeding, has been performed. Preliminary results of the analysis show that this device, because of the presence of two systems of thrust forces acting on the armature, can be successfully used in the acceleration of heavy masses at relatively high velocities, the maximum achievable speed being limited by thermal and mechanical stresses. Index Terms—Coil launchers, induction launchers, rail launchers, sliding contacts. I. INTRODUCTION R AIL and coil launchers are alternative solutions in the electromagnetic acceleration of appreciable masses to velocity of several hundreds of meters per second. A rail launcher is basically composed of two parallel conductive rails and a conductive slab (armature) free to slide between them. The armature is initially located at one edge of the rails; a constant voltage generator is connected between the rails at the edge near the armature. The interaction between the current flowing in the armature and the magnetic flux density produced by the currents on the rails produces a thrust force that accelerates the armature. The main drawback that heavily affects the performances of rail launchers is the velocity skin effect (VSE) that consists of a strong current concentration at the rear of the armature. The consequent Manuscript received January 14, 2002. The authors are with the Dipartimento di Sistemi Elettrici e Automazione, University of Pisa, 56126 Pisa, Italy (e-mail: [email protected]; [email protected]; [email protected]; [email protected]). Digital Object Identifier 10.1109/TMAG.2002.805858 heating can cause melting and subsequent vaporization of part of the armature and can lead to the destruction of the armature itself. This effect becomes more and more important with increasing velocity and may prevent the use of these launchers at sufficient high velocity; nevertheless, rail launchers are characterized by a good efficiency in the velocity range where sliding contacts are effective [1]–[3]. Induction launchers essentially consist of a barrel formed by an array of coils and of a conductive tube moving inside the barrel. Two configurations of coil launchers are commonly used: the traveling wave induction launcher [4] and the pulsed induction launcher [5], [6]. In the traveling wave induction launcher, the driving coils are grouped in sections that are energized in a polyphase fashion in order to create a traveling wave of flux density in the region occupied by the sleeve. Traveling wave induction launchers, as all asynchronous machines, suffer from a reduced efficiency at low speed. In pulsed induction launchers, the coils of the barrel are fed in sequence by a set of capacitor–driven circuits. Pulsed induction launchers are characterized by an acceleration profile with a large amount of ripple which can cause strong vibrations and mechanical stress in both the armature and the barrel. The combined use of sliding contacts and a traveling wave to thrust an armature seems to be appealing because of the complementarity of the two systems. In the range of low speeds, where brush operation is effective because of a limited VSE, the thrust force on the armature is mainly provided by a railgun-like operation. At higher speeds, thrust force is produced by the currents induced on the armature coils by the traveling wave. In this way, the best characteristics of the two thrust mechanisms are exploited; furthermore, heavy masses can be accelerated because of the increased total thrust force on the armature. The coils used to produce the traveling wave of magnetic flux density are grouped in sections characterized by an increasing velocity of the wave. The latest stages of the launcher, where the velocity may be higher than that usually admissible in rail launchers, can operate as a pure induction launcher. The ultimate velocity is then limited only by ohmic heating in the armature coils. An analysis of the performances of the proposed device has been performed by means of a numerical model based on an integral formulation that has been modified to take into account the presence of sliding contacts between the rails and the armature. II. NUMERICAL MODEL The procedure in [7], briefly summarized here in the case of absence of ferromagnetic materials, has been used to build the 0018-9464/03$17.00 © 2003 IEEE 104 IEEE TRANSACTIONS ON MAGNETICS, VOL. 39, NO. 1, JANUARY 2003 Fig. 2. Fig. 1. Branch of the equivalent network. Elementary volumes and their interconnections. equivalent network of the device to be analyzed. Conductive reslabs. We connect the centers gions are subdivided into of nearby elements obtaining a three-dimensional (3-D) grid as shown in Fig. 1. Then, we associate with each segment of the grid a new slab having four edges parallel to the segment and the faces normal to the segment with their centers placed at the nodes of the grid. Inside each elementary volume, a uniform distribution of current density is assumed. We can write the following expressions for the magnetic vector potential and flux density distribution at a point (1a) (1b) where the subscripts and refer to the fields respectively produced by the source and the induced currents. Because of the assumed distribution of currents, fields in (1b) can be evaluated by using analytical expressions and written as and . We write Ohm’s law at the point inside the th conductive element (2) is the where is the velocity relative to the flux density , is the temperature, supposed uniformly current density, and distributed inside the th conductive slab. Equation (2) is projected along the direction of the segment used to build the new elementary conductive volume , averaging the result on the section . We obtain (3) and represent mutual inductance coefficients between the current in the th volume and the induced and source Fig. 3. Auxiliary branches to take into account contacts between two conductors in relative motion. The two discretised volumes slide one on the other. currents, respectively, flowing in the th and in the th volume. and take into account the motional effects on the th volume produced by induced and source currents respectively is the resisflowing in the th and in the th volume. and tance of the th volume evaluated at the temperature is the voltage between the two faces of the volume orthogonal to the direction used to project (2). Equation (3) represents the electric equilibrium equation of the network branch shown in generator is controlled by the currents in the Fig. 2. The branches of the network related to the elementary volumes in relative motion with respect to the th volume. The mesh analysis is used to determine the electrical equilibrium of the network (4) By (4), provided with the initial conditions, we obtain the time evolution of currents that are used to evaluate the thrust force acting on the th elementary volume of the armature by means of the Laplace formula The resultant of these forces is introduced in the motion equation. By this procedure, separate networks for the stator (rails and coils) and the armature have been obtained. If elementary volumes belonging to rails and armature share a face or a fraction of it, an electric contact exists between these volumes; further branches connecting such volumes have to be introduced. A new branch is set for each couple of volumes that can have a contact during the motion, as shown in Fig. 3. A proper algorithm is used to set the value of these branches as a function of the shared portion of the face (if any) between two volumes. This method retains the topological invariance of the equivalent BARMADA et al.: ANALYSIS OF THE PERFORMANCE OF A COMBINED COIL–RAIL LAUNCHER 105 Fig. 4. The combined coil-rail launcher. network but introduces additional branches, resulting in an increased dimension of the number of equation to be solved. and respectively be the inductance and resistance Let of a slab whose size is obtained by averaging the sizes of the elementary volumes obtained by the discretization of the armature. A branch formed by an inductor and a resistor whose values are and times the reciprocal of the shared portion one tenth of of the surfaces normalized to the smaller of them is inserted. If no contact is present, a branch with inductance and resisand is inserted. A time-stepping protance 1000 times cedure is used to integrate the governing equations of the two networks. The continuity of the currents and of the temperature distributions is used to obtain the initial value in the differential equations. As the armature moves and the temperature changes, the matrices involved are updated. A time step small enough has to be chosen in order to consider the elements of the matrices reasonably constant. The heat produced by ohmic losses in each elementary volume is used as a source to update the thermal distribution and the resistivity in the launcher. Melting and evaporation of metal in the regions with high temperature are taken into account [1], [2]. Heat produced by friction between rails and armature and in the auxiliary network described before is used to increase the temperatures of elementary volumes of rails and armature in contact. III. COMBINED RAIL–COIL LAUNCHER A. Description of the Launcher The proposed launcher is shown in Fig. 4. Both rails and armature are slotted in order to allow the presence of the driving and induced coils respectively. The 24 driving coils, properly fed in order to produce a traveling wave of flux density, are grouped in two stages: the first stage is composed by ten coils, the second by 14 coils. The axial length of the armature occupied by the induced coils is approximately a half of the pole pitch of the first stage of the traveling wave in the first inductive stage; the part of the armature involved in the sliding contact with the rails is about one quarter of the above pole pitch. Because of the presence of a sinusoidal magnetic flux density mainly directed along the direction of the motion ( axis), rails and armature should be laminated in order to keep as low as possible the power losses due to eddy currents (especially in the rails). Both rails and Fig. 5. Current density profile in the upper rail and in the sliding part of the armature at t = 1:06 ms and in the symmetry plane of the launcher. armature are constituted by laminae orthogonal to the axis. cm, cm, and The sizes of the rails are cm. Those of the conductive sliding part of the arcm, cm, and cm. A mature are constant electromotive force of 50 V is used to feed the rails at the edges near the armature. The stator coils are grouped in two sections; for both sections the cross section of each coil is 25 mm and the total magnetomotive force is 200 kAT. The frequency is 1.2 kHz. Stator coils have square cross section; cm and cm. Armatheir overall sizes are ture coils have a cross section 0.7 0.5 cm , and an overall size cm and cm. The first section of the stator coils is constituted by ten coils equally spaced in the direction whose currents are shifted in phase by 0.6283 rad with respect to each other. This arrangement of coils produces a traveling wave of flux density, whose approximate expression inside every section of the launcher could be written as , where is the pole pitch. In the cm and the velocity of the traveling first section is m/s. The wave of magnetic flux density is second section is constituted by 14 coils of the same size and spaced along the axis; the total magnetomotive force and frequency are unchanged. Currents are shifted in phase by 0.449 rad; the pole pitch is 13.95 cm and the velocity of the traveling wave is 167 m/s. The increase of the velocity of the traveling wave is obtained by an increase of the pole pitch and by keeping the frequency unchanged: this is made in order to avoid possible mismatching between the currents in the coils on the armature and the coils on the stator in correspondence of the transition between two adjacent sections [8]–[10]. The total mass of the moving part including the payload is 2.330 kg. B. Results and Discussion Figs. 5 and 6 show the current density distributions in the rails and in the sliding part of the armature at the times ms and ms, respectively, and in correspondence of the symmetry plane of the launcher. The arrows related to the rails are normalized with respect to the maximum values of 106 Fig. 6. Current density profile in the upper rail and in the sliding part of the armature at the end of the launch and at the symmetry plane. IEEE TRANSACTIONS ON MAGNETICS, VOL. 39, NO. 1, JANUARY 2003 Fig. 8. Velocity and force profiles during the whole launch. Fig. 9. Current density in the armature coils. Fig. 7. Velocity during the transition in the first section. 8.83 10 MA/m and of 5.33 10 MA/m , while those related to the armature to their maxima that are 5.14 10 MA/m and 5.49 10 MA/m . Fig. 7 shows the velocity profiles obtained during the op), as pure coil eration of the device as pure rail launcher ( launcher ( ), and in the combined mode ( ) during the motion of the armature inside the first section. In the same figure is also shown the velocity , where . The agreement between and shows the effectiveness of the combined feeding. In Fig. 8 are reported the profiles of thrust force, velocity, and lateral force during the whole launch, normalized to their m/s, maximum values that respectively are kN, and kN. The lateral force, due to the interaction between the axial component of the magnetic flux density produced by the stator coils and the current in the armature in the axis direction, may assume high values that require a proper containment of the armature in the axis direction. The waveforms of the current density in the induced coils are reported in Fig. 9. The corners located approximately at the time ms are due to the transition between the first and the second section. The frequency of these waveforms decreases during the launch as the speed of the armature approaches that of the traveling wave of flux density produced by the stator coils. Fig. 10(a) and (b) shows the temperature distribution at the end of the launch, respectively, in the armature and in the rail. The white squares refer to the slots occupied by stator and armature coils. The temperatures reached by the armature coils are (from left to right as represented in Fig. 4) 520 K, 626 K, 580 K, 499 K, and 713 K. IV. CONCLUSION An electromagnetic system that operates both as a rail and a coil launcher for the acceleration of heavy masses has been proposed. An integral formulation based on an equivalent electric network, able to take into account the phenomena involved in the VSE, has been used to analyze the performances of this launcher. 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