Energy Transfer Efficiency Optimization in an Electromagnetic Railgun

Electromagnetic railguns (EMRs) launch projectiles by the systematic triggering of current pulse forming units (PFUs), which release stored capacitor energy. Past work has focused on maximizing projectile velocity at the muzzle for given PFU capacitor charge voltages, which maximizes efficiency. However, operators in naval applications need to be able to select the muzzle velocity for a projectile to achieve a desired ballistic path. Thus, there is a demand to maximize efficiency for a given muzzle velocity. As such, this paper investigates maximizing the efficiency of transferring the stored PFU capacitor electrical energy to projectile kinetic energy while minimizing the current value when the projectile exits the rails to reduce damage to them from arcing. This is accomplished by optimizing the choice of the initial capacitor voltage in each PFU and the trigger timing subject to an electrical-mechanical dynamic model of the EMR and projectile and any additional scenario constraints (described shortly). This optimization is solved using numerical programming in the context of a relaxation with the initial capacitor voltages and triggering times as the only explicit variables to the optimizer; additional needed values are obtained from a differential algebraic equation solver. The optimization is successfully demonstrated for three scenarios: operation for a projectile mass and muzzle velocity associated with published operating parameters, operation for several projectile mass-muzzle velocity pairs with both equal and distinct initial capacitor voltages, and operation for several projectile mass-muzzle velocity pairs with a load current bound and equal initial capacitor voltages. Results show improved efficiency in comparison to the use of the published parameters, the independence of efficiency from projectile mass when there is no current bound, virtually identical results for equal and distinct initial capacitor voltages, and decreased efficiency with a current bound.