E. Levi

Mutual inductance of noncoaxial circular coils with constant current density

The purpose of this paper is to determine the mutual inductance between two noncoaxial circular coils. In many cases, such as coil guns or tubular linear motors, one of them is fixed while the other one is moving, and if not supported, its axis may not coincide with that of the fixed coil. This paper presents a method for the calculation of the mutual inductance in the case of noncoaxial coupled coils, the characteristics of this inductance, and experimental results. The computation is based on complete elliptic integrals and on the mesh-matrix technique. The method enables one to obtain accurate results from a relatively simple procedure and calculation program.

Analysis of induction-type coilgun performance based on cylindrical current sheet model

A method which is based on a cylindrical current sheet model for the analysis and design of induction-type coilguns is presented. The work starts with a derivation of closed-form formulae which relate the dimensions of the gun to the performance expressed in terms of propulsive and local maximum forces on the projectile, power factor and efficiency of the system, thermal stress of the projectile armature, distributions of the flux density around the launcher, and the system parameters in a multisection coilgun. A numerical example is given. >

Concerning the design of capacitively driven induction coil guns

The authors consider the design of capacitively driven, multisection, electromagnetic coil launchers, or coil guns, taking their transient behavior into account. A lumped-parameter computer simulation is developed to predict the performance of the launcher system. It is shown that a traveling electromagnetic wave can be generated on the barrel by the resonance of drive coils and their capacitors. More than half of the energy initially stored in the capacitor bank can be converted into kinetic energy of the projectile in one shot, and an additional quarter can be utilized in subsequent shots, if the launcher dimensions, resonant frequency, and firing sequence are properly selected. The projectile starts smoothly from zero initial velocity and with zero initial sleeve current. Section-to-section transitions which have significant effects on the launcher performance are also discussed. Experimental results were obtained with a small model and are in good agreement with theoretical predictions. >

Design and power conditioning for the coil-gun

The author describes the power conditioning scheme for a contactless coilgun called the linear induction launcher (LIL). The barrel of the LIL consists of a linear array of coils carrying polyphase currents. These create an electromagnetic wave pocket which moves with increasing velocity from breech to muzzle, smoothly accelerating a conductive sleeve which carries a set of azimuthal currents sinusoidally distributed along its length and which encloses the projectile payload. The power conditioner provides high energy utilization by transferring energy from capacitor to capacitor simultaneously with the projectile movement. The modular construction of the barrel is described together with laboratory results obtained with a breadboard model of the power conditioner circuit. >

Restoring force between two noncoaxial circular coils

Considered here are the forces between two current-carrying circular coils, one of which, the primary coil, has a larger diameter than the other, the secondary. In the case in which the secondary coils central axis does not coincide with that of the primary, there exists a transverse force which we call the restoring force. It is found that this force decreases with increasing distance between the coils and changes sign. This paper presents a calculation of this force and its characteristics. Finally, it introduces some experimental results.

Transient performance of linear induction launchers fed by generators and by capacitor banks

Computer simulation is used to investigate the transient performance of induction-type coilguns as a function of the dimensions, material properties, type of supply, firing sequence of switching elements, and connections of drive coils. The performance of both generator-driven and capacitor-driven coilguns is addressed. It is shown that the generator-driven coilgun performs satisfactorily in the starting section. However, at high velocity, the transit time is close to the electrical transient time constant, and therefore the DC components produce a retarding force. To avoid this problem, the three phase voltages should not be switched on simultaneously, but rather phase-by-phase according to their zero current crossing points. This can also alleviate the problem in the transient between the sections. The capacitor-driven coilguns, instead, derive the alternating current needed to create a traveling wave from resonance with the inductance of the coils. Therefore, the initiation of the sinusoidal current oscillation coincides with the switch-on time. They are ideally suited for short-time, high-acceleration operation, but they are likely to require higher operating voltages than the generator-driven coilguns, because of the constraint imposed on the capacitance by the resonance condition with attenuation. >

Analysis of generator-driven linear induction launchers

This paper deals with the analysis and design of high-speed, multi-section, generator-driven, polyphase, linear-induction-type electromagnetic launchers. During a launch, steady state is never reached. Hence, a transient simulation model, based on lumped-circuit parameters, was developed, for purposes of analysis, in earlier work with capacitor-driven launchers. This model, as well as its related computer code, is also applicable to generator-driven launchers. From earlier work, we found that simultaneous energizing of the three phases of generator-driven launchers gives rise to DC current components in the barrel-coils that can cause strong braking forces, especially at the transitions between sections. In this paper, an alternate energizing mode, in which the three phases of the barrel coils are switched on in sequence, phase by phase, with the appropriate phase shifts, is investigated. Numerical results of the transient simulation show that the initial position of the projectile at a section transition at switch-on time, and the switch-on phase angle, significantly influence the performance. With some poorly-chosen initial positions or phase angles, DC components of the currents in the armature can produce very large retarding forces, thus resulting in actual deceleration of the projectile. On the basis of the transient model, simulations were done to search for the optimal switch-on phase angles and initial positions of the projectile. The results show that smoother transitions between sections and higher muzzle velocities can be achieved with these optimal phase angles and initial positions.

In-bore projectile dynamics in the linear induction launcher (LIL). 1. Oscillations

The projectile in a linear induction launcher is subject to centering (levitation) forces, as well as propelling ones. Due to their uneven distribution, these forces give rise to rotation, as well as translation of the projectile axis. This paper assesses these motions. >

Experimental results and performance analysis of a 500 m/sec linear induction launcher (LIL)

A computer model, previously validated, was used to study the performance of an experimental three-phase launcher energized by a capacitor bank and designed to impart to a 137 gram projectile a muzzle velocity of 500 m/s: (1) the build-up of the traveling wave was examined; (2) the connection of the drive coils was changed; (3) the resistances of the drive circuits were calculated and measured; and (4) the effect of the conductivity of the cylindrical tube (sleeve) constituting the projectile was assessed. Experimentally, a doubling of the muzzle velocity was achieved, from an earlier-obtained 250 m/s, to its present 476 m/s. This was done by strengthening the thin-walled aluminum sleeve by heat treatment (aging) to prevent it from being crushed when the input energy was raised to its design value. >

Test results for three prototype models of a linear induction launcher

The work on the linear induction launcher (LIL) started with an analytical study that was followed by computer simulations and then was tested by laboratory models. Two mathematical representations have been developed to describe the launcher. The first, based on the field approach with sinusoidal excitation, has been validated by static tests on a small-scale prototype fed at constant current and variable frequency. The second, a transient representation using computer simulation, allows consideration of energization by means of a capacitor bank and a power conditioner. Tests performed on three small-scale prototypes up to 100-m/s muzzle velocities show good agreement with predicted performance. >