Inductance Gradient Calculations of EMFY-3 Electromagnetic Launcher

—ASELSAN Inc. has been working on electromagnetic launch technologies since 2014. The ﬁrst prototype, EMFY-1, has a 25 mm × 25 mm square bore and 3-m-length rails. The second prototype, EMFY-2, has a 50 × 50 mm square bore and 3-m-length. In this paper, a recently developed prototype, EMFY-3, is presented, which has a 50 × 75 mm rectangular bore and 6-m-length. The input energy of the PPS is doubled to 8 MJ, and the 2.91 MJ muzzle energy is obtained up to now. Rail currents, breech, and muzzle voltages are measured to investigate electromagnetic calculations. Velocity curves are captured with Doppler radar, which enables us to establish propulsive inductance gradient L (cid:48) pr transients empirically. The results conﬁrm that L (cid:48) pr is constant throughout the launch, as no signiﬁcant breaking mechanism occurs with the non-magnetic containment. However, a slight variation ( %2 at maximum) happens from one launch to another with different rails’ current magnitudes. The transition phenomenon is a candidate for the drop in the L (cid:48) pr , as it occurs more likely at launches with higher linear current densities.


I. INTRODUCTION
E Lectromagnetic launchers (EMLs) are an accelerator concept that transforms the stored electrical energy to linear kinetic energy. It consists of two conducting rails, an armature, and a projectile. A significant amount of pulse-shaped current provided by a pulsed-power supply (PPS) flows through rails and armature in a short duration (a few milliseconds) of time. Lorentz force acts on the armature as the EML seeks to maximize its inductance.
ASELSAN Inc. has been conducting experimental and theoretical research on EML technologies since 2014 [1]- [4]. Firstgeneration 1-MJ and second-generation 3.25-MJ PPSs were developed and tested with 25 mm x 25 mm bore EMFY-1 at an open area test range. EMFY-2 is built in the laboratory, an 8-MJ PPS system, a flash X-ray system, a 6-m-long catch tank, and diagnostic tools [5]. These two EMLs are used to improve electromagnetic analysis in terms of transient EMF calculations [6], and velocity skin effect (VSE) analysis [7]. Propulsive inductance gradient, which is denoted as L pr , is an essential parameter to characterize EML. It is directly linked to efficiency since additive inductance on the armature creates Lorentz force. If the containment surrounding rails is not electrically conducting, L pr is regarded as constant throughout the launch as there is no eddy breaking mechanism. EMFY-3 has a non-conductive composite containment material. EMFY-3 launcher is presented in Fig. 1. The geometric parameters of the launcher are shared in Table I. Apart from previous EML experiments, the Doppler radar system is equipped to ASELSAN Laboratory to examine possible transients in L pr . As the armature acceleration and rail currents are measurable, L pr can be calculated empirically. An et. al [8] stated that VSE induces the temporal variation of inductance gradient. However, they neglected aerodynamics and friction effect, which can influence launch dynamics. In this study, not only temporal changes are investigated, but also the launch dynamics are regarded. Moreover, a sensitivity analysis is performed to study the importance of L pr calculation. A kine-mechanical model is constructed to model the armature acceleration. Three different tests are shared to demonstrate the reliability of the model, as well as to observe L pr . It is observed that L pr tends to decline when the magnitude of the rail current is increased. However, the result is surprising, as there is no expected brake mechanism with a non-conductive containment. The first suspect for the loss/brake phenomenon is transition. The transition phenomenon is termed the transition of solid contact into arcing contact. Multiple mechanisms can induce transition.
[9]- [12]. As the deficit at L pr is associated with maximum rail current density [13], the transition is the main candidate for such a loss mechanism. The deficit at the acceleration has occurred at the late stage of the launch, which is a shred of strong evidence for transition.

II. SENSITIVITY ANALYSIS
In this section, the central focus is to investigate the sensitivity of the kine-mechanical calculations to propulsive inductance gradient L pr estimation errors. As in Fig. 2, electromagnetic modeling of an EML can be approximated as a series-connected variable resistance and inductance. These variable circuit elements, the resistance and the inductance of EML denoted as R EML , and L EML , depends on the mechanical states. Therefore, the electromagnetic analysis depends profoundly on kine-mechanical calculations; any deviation from the actual value can cause a cumulative error in the system's total inductance and resistance calculations. As a doppler radar is used to obtain velocity measurements during the launch, the armature acceleration can be obtained, which can be linked with any possible L pr transients. The propulsive force at the armature, which is denoted as F pr , can be determined by (1), where I rail is the rail current.
However, F pr is not the only force that acts on the armature. Friction and drag forces denoted as F f ric and F drag action in a direction that opposes the movement as in (2). F f ric can be modelled as in (3) where µ d and µ s are dynamic and static friction coefficients respectively [14]. ζ is the friction damping factor, and F C is the contact force. F f ric calculation is simplified considering their net influence on the launch. µ d and µ s are not constant throughout the launch; they depend on the contact state. When the liquid film starts to occur in the electrical contact, µ s and µ d diminish significantly. Moreover, the determination of ζ is challenging. However, assuming the contact transformation occurs at t = 0.5 ms gives coherent results with experimental findings. Dynamic variations of the friction coefficients are demonstrated in Fig. 3 as a function of time. The model parameters are given in Table III. Two different drag mechanisms occur at the launch package. These are named electromagnetic drag and aerodynamic drag. Aerodynamic drag is more straightforward than electromagnetic drag in terms of the analytical model's complexity. Aerodynamic drag, which is denoted as F drag can be modeled as in (4). C d is the drag coefficient (it is a dimensionless quantity.), A lp is the area that frontier to the air, ρ air is the density of air.
Electromagnetic drag is the force associated with the eddycurrent brake mechanism at the conductive containment [15]. This force can have more drastic effects than the aerodynamic drag if the conductive containment is not laminated. Parker et. al [16] introduced the infeasibility of employing conductive containments. They assert that loss of F net due to eddy brake may be as large as 20% to 25%. Even if infinitely thin laminations are utilized, the magnetic field suppression at the armature can not be reduced, which eventually reduces L pr [17]. However, EMFY-3 has non-conductive containment; thus, electromagnetic drag can be neglected from (4). Mechanical state transformations are exhibited from (5) to (9), where m lp is the mass of the launch package. T exit is the exit moment of the armature, X pre is the pre-load position, and x rail is the rail length.
Considering (1-8), a kine-mechanical model is constructed. It should be noted that, the only design parameter is L pr if I rail measurements are used for (1). L pr is calculated 0.515 µH/m from 3-D FE model. Three different launch test are used for analysis. Test parameters are given with their label in Table II. Rail current measurements are illustrated in Fig. 4. C d is dependent on the launch package geometry. It can be reduced with well-designed geometry, which improves efficiency. C d of an armature with a dummy weight can be approximated as 1. An example of armature with a dummy weight is illustrated in Fig. 5.
Simulation results of the kine-mechanical model are illustrated with experimental velocity curves in Fig. 6. Red curves are used to demonstrate the simulation results where (2) is used. Blue curves, on the other hand, represent simulation results where F net is equal to F pr , meaning that the friction and drag forces are neglected. Gray dashed vertical lines indicate the armature's exit moment, obtained from the muzzle and breech voltages. The effect of the F f ric can be understood from Test A-C, where the velocity measurement span is  complete. Fig. 7 is used to better illustration of F f ric influence. There are negligible F drag influence on the velocity curves; thus, blue curves show the effect of F f ric more dominantly. Exit velocities are overestimated Just a few dozens m/s only, which has a slight influence. However, at the initial stage of the launch, the effect of F f ric is more dominant. Determination of L pr is critical for electromagnetic analysis. As the EML's inductance and resistance are increasing with armature motion. These variations are modelled as position gradients, i.e. R rail represent rail resistance per meter, and L EML is used to model inductance change of the EML for 1-m armature displacement. Armature movement is modeled with force equilibrium as in (2); thus, any variation from actual L pr will introduce an error to the analysis. These errors influence simulated I rail which affect (1) even more. To examine the sensitivity of L pr calculation on kine-mechanical calculation,   Table IV in terms of muzzle velocities. In Fig. 8

III. DISCUSSIONS
The main focus of this paper is to investigate the importance of accurate calculation L pr for EML analysis. Moreover, any deviations in L pr are tried to understand from experimental measurements such as muzzle voltages. The compatibility of electromagnetic simulations with experimental findings is not the scope of this work, but it will be shared with a subsequent paper. In that paper, findings related with electromagnetic impacts of the bus geometry will be shared, as the effect has a significant influence on the simulation results.
F f ric calculation is simplified considering its net influence on the launch. µ d , and µ s are not constant throughout the launch; they depend on the contact state. The contact state transition happened at t = 0.5 ms, which is obtained from an analysis not covered here. Thus, µ d and µ s are diminished using a time-dependent step function.

IV. CONCLUSIONS
In this study, the importance of the correct L pr calculation is demonstrated by a sensitivity analysis. For this regard, a simplified kine-mechanical model is shared, which uses empirical data to examine L pr transients. Results show that L pr is constant launch to launch, whereas its value diminished slightly at the late stage of the launch. This L pr reduction is correlated with linear current density; higher the rail current corresponds with higher reduction. However, reductions are limited to 2%, not as significant as eddy brakes due to the conductive environment. The transition phenomenon is the candidate for explaining the brake effect. The remarks which are obtained throughout the EMFY-3 experiments can be listed as: 1) Simulation models are susceptible to L pr accuracy. An %5 deviation from the actual value can cause muzzle velocity error up to %6.23.
(c) %1 L pr deviation. 2) Friction and aerodynamic forces are not dominant to determine muzzle velocities. Although friction forces influence the initial moments of the launch, aerodynamic forces do not affect kine-mechanical calculations. 3) L pr is constant throughout the launch as the containment is non-conductive. A slight decrease (up to %2) is observed in Test C, where I rail exceeds 2.12 MA. A severe transition effect can explain such a decrease.