Computation and scaling of inductance gradients in electromagnetic launch systems

When a pulsed electric potential is applied to the terminals of a sliding electrical contact system, the armature translates under the influence of Lorentz forces caused by diffusing currents. The inductance gradient is conventionally used as a parameter to quantify the total Lorentz force acting on the armature and size the systems. The determination of the variation of the inductance gradient with system parameters such as the dimensions of the rails and armature, and the ramp rate of the applied potential is of interest in the design of sliding electrical contact systems with specified objectives. It is also useful in scaling results from laboratory to fieldable systems. The inductance gradient can be calculated with finite-element analyses using codes such as EMAP3D; this will be a time-consuming process. Semi-analytical formulations are possible for systems with simple and regular geometries such as rectangular sections. Solutions of the field diffusion equation can be expressed as a weighted sum of eigen functions characteristic of the geometry with imposed boundary conditions. A semi-analytical formulation based on eigen functions is presented here for computing and scaling inductance gradients of a sliding electrical contact system with rectangular rails and armatures. The effects of the dimensions of the rails and armatures, and the effect of the external ramp rate of the applied current on the inductance gradients are studied. The results are compared with available computational and experimental data.