287. The Transient behavior of rails used in electromagnetic railguns: numerical investigations at constant loading velocities

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1 287. The Transient behavior o rails used in electromagnetic railguns: numerical investigations at constant loading velocities L. Tumonis 1, a, R. Kačianauskas 1,b, A. Kačeniauskas 2,c, M. Schneider 3,d 1 Department o Strength o Materials, Vilnius Gediminas Technical University, Saulėtekio 11, 1223 Vilnius, Lithuania 2 Laboratory o Parallel Computing, Vilnius Gediminas Technical University, Saulėtekio 11, 1223 Vilnius, Lithuania 3 French-German Research Institute o Saint Louis (ISL), 5 rue G'al Cassagnou, 6831 Saint-Louis, France a liudas.tumonis@m.vgtu.lt, b rkac@m.vgtu.lt, c arnka@m.vgtu.lt, d schneider_m@isl.tm.r (Received 15 May 27, accepted 3 July 27) Abstract. Electromagnetic railguns are mechatronic systems working at very high power levels (in the range o GW). Here, one important issue, namely, the dynamical reaction o the rails and their supporting structure to the moving (due to the projectile) magnetic pressure loads is still not suiciently described. In this paper the above described problem is investigated using a purely mechanical 2D inite element model. The aim is to describe the displacement o the rail suraces because o its importance or the electrical perormance o the system. The boundary conditions correspond to the moving electromagnetic pressure repelling the rails one rom each other. The oscillation proiles under several loading histories with constant velocities ranging between.6 and 1.4 km/s are examined. Keywords: Electromagnetic railgun, transient dynamics. Introduction Electromagnetic railguns are mechatronic systems working at very high power levels (in the range o GW). While the unctional principle is relatively simple and muzzle velocities up to 2.5 km/s or masses o several hundred grams have been demonstrated experimentally the perormance limits o the technique are still under investigation worldwide [1-3]. Here, due to its inluence on electric contact conditions, one important point is the dynamical reaction o the rails and their supporting structure to the moving (due to the projectile) magnetic pressure [4, 5]. The unctional principle o the railgun is illustrated in Fig. 1. The projectile has a conducting part (armature). This armature is in sliding contact with two rails which are connected to a power source being able to deliver the current in the order o MA. The magnetic pressure (in the order o 1 MPa) generated by this coniguration not only propels the projectile via the armature but also repels the rails one rom the other. One o the most critical parts o the system is the contact interace between armatures and rails where enormous current densities (up to ka/mm 2 ) have to exist while simultaneously low riction orces have to be established. The dynamical interaction at this contact interace presents a great challenge to all scientists working in this interdisciplinary research area. The railgun EMA3 o the French German Research institute o Saint-Louis (ISL) is depicted in Fig. 2 [6]. EMA3 has rails with a length o 3 m and a caliber o 15x3 mm 2. The housing o the rails is not closed laterally which permits lash radiography during launch. Projectiles with masses o 5 g have been accelerated to velocities o up to 18 m/s with excellent sliding contact behavior [7]. In this paper the mechanical behavior o EMA3 is simulated numerically. The aim is to study an important aspect o the contact interace, namely the displacement o the inner rail suraces due to the magnetic pressure mentioned above. Finite element calculations concerning the mechanical behavior o EMA3 have been perormed with ANSYS 1 [8]. In order to simpliy the problem the railgun is represented by an axisymmetric 2D model o the rails and discrete elastic supports. The boundary conditions o loading correspond to the magnetic pressure that expands with very high velocities behind the projectile. It is interesting to mention that the velocity o the projectile can be in the range and even greater than those o elastic waves in the rails. At this stage a constant velocity o the movement o the magnetic pressure is assumed. Results are presented or dierent loading velocities (.6 km/s-1.4 km/s). 1 ANSYS is a trademark o Ansys Inc. 15

2 - Current Magnetic ield Rail Rail Fig. 1. Functional principle o the rail gun Armature experiment. Only the expansion o the magnetic pressure volume being caused by the moving projectile is considered and not local transversal orces due to the projectile itsel. It is assumed that the expansion takes place at a constant velocity and that the magnetic pressure is not time-dependent but has a constant value q = 31.2 MPa. This value corresponds to experiments presented in [6]. 34 Steel Railgun Power supply X-ray tube CRM 16N EPM Fig. 3. Cross-section o the railgun Fig. 2. The ISL-railgun EMA3 Problem description. Rail geometry, material data and loading A view o the railgun cross-section is shown in Fig. 3. The housing o the two rails consists o a combination o bars o EPM 23, a glass iber reinorced plastics (GRP) material, and discontinuous steel bolts in order to withstand the high orces between the rails. At both sides o the rails GRP-bars are used to guide the projectile. The rails are made rom a Cu alloy (CRM 16N). The material properties used or the numerical calculations o the railgun are given in Table 1. In this paper in a irst step the boundary conditions or the calculations (loading) are simpliied by comparison to the Thereore, the load proile at an arbitrary point x along the direction o movement is deined by the ollowing equation ( x, x ) q, =, i x x, i x > x, q (1) where x represents the position o the load ront (projectile) at time point t: x ( t) = vt, (2) and v is the constant velocity o the projectile. Table 1. Material properties Structural member Material Physical properties Housing EPM 23 Density: ρ =1.85 g/cm 3 Elast. modulus: E = 18. GPa Rail CuCr1Zr (CRM Density: ρ =8.9 g/cm 3 16N) Elast. modulus: E = 12 GPa Bolt Steel Density: ρ =7.85 g/cm 3 Elast. modulus: E =21 GPa 16

3 The load proile along entire rail length L is illustrated in Fig. 4. load presure q x L x In order to save computational time a 2D model has been developed and due to symmetry reasons only hal o the cross section is considered. The rails and the GRP bars are represented by a T-shaped bimaterial proile (see Fig. 3). The steel bolts are transormed into elastic rods. The mechanical characteristics o these rods are equivalent to the bolts. The rail is considered as 2D domain, while the supporting rods are modeled as elastic springs. The computational model o the rail gun is illustrated in Fig. 5. Fig. 4. Load proile Computational model y x L=3 Sliding surace EPM 23 Y (CRM 16 N) Z X a) b) Fig. 5. 2D model o the rail gun: a) total view, b) ragment o the mesh Numerical results and discussion The inite element mesh used consists o D plane elements. The supporting bolts are approximated by 86 elastic spring elements. The whole model has degrees o reedom. The loading is deined as normal pressure acting on the rail suraces. The dynamic loading proiles are computed with the pre-processing program MOVLOAD written by using C. The resulting values o the nodal loads are stored in a macro ile in native ANSYS [8] ormat. The ile includes inormation on all load steps or each time point. Macro iles are loaded by the speciic pre-processor MOVLOAD. This pre-processor automatically computes all values o the nodal loads and signiicantly reduces time or data preparation. The STRUCTURAL module o the FEpackage ANSYS 1. was used. The described FE model was used or dynamic analysis o the railgun under loading conditions speciied above. Four dierent velocities were simulated including the static case serving as reerence. The latter was realized using a ixed loading along the entire rail length. The dynamic behavior o the rail is characterized by considering the time-dependent displacements in y- direction (Fig. 5) u y o the nodes belonging to the sliding contact surace. Displacement proiles o the node being in the middle o the rail (x =1.5 m) are drawn in Fig. 6. Here, small circles indicate the time points when the load ront reaches the node. It can be seen that dynamic loading leads to oscillations with the static solution acting as oset. However, with regard to the contact conditions the absolute values are o interest and here it has to be stated that amplitudes due to dynamic loading are two times greater than the static ones..6 Static v=6 m/s v=12 m/s v=14 m/s.4 u y, mm t, ms Fig. 6. Displacement histories o point (x =1.5 m) on the sliding surace at dierent velocities 17

4 Note that even variations o some tenth o millimeters are important in this context [6], i they occur at the position o the sliding contact. A comparison o displacement histories o dierent nodes along the sliding contact surace at a sliding velocity o 12 m/s is presented in Fig. 7. Here, again circles indicate time points o the load-arrival or the dierent nodes. The static solution is also presented. Two details should be pointed out here. Firstly, despite the two nodes at.75 m and 2.25 m have a symmetric position along the rail with respect to the central node the corresponding displacement proiles are entirely dierent. Secondly, and o great importance or the railgun: one observes amplitudes o relevant magnitude beore the pressure ront arrives. These increase in orward direction and are at maximum or the node at 2.25 m. uy, mm Static.75 m 1.5 m 2.25m t, ms Fig. 7. Displacement histories o dierent points at velocity v = 12 m/s In order to illustrate the dynamic behavior o the rails the concept o the eective amplitude is used. It is illustrated in Fig. 8. The excitation period t o a particular node located in position x n is deined as dierence between entire loading period t sh and time interval t beore the point is loaded. It is expressed in terms o loading data as ollows uy t = ( L x ) n. (3) t v uy.s tsh t Fig. 8. The concept o eective amplitude ue.d t,a.u Finally, the eective amplitude u e.d is obtained using least square method by integrating the dierence between dynamic displacements u y (t) and static solution u y.s : u e.d = 1 t t t sh ( u () t u ) y y.s 2 dt. (4) It is obvious that or static behavior u e.d =. The dependence o eective amplitudes (Eq. 4) on the sliding velocity or dierent locations along the rail is presented in Fig. 9. It shows that the rail dynamics during shot is a rather position-dependent phenomenon. Due to symmetry reasons the behavior o the middle point (1.5 m) o the rail may be considered as the most characteristic o the entire system. I the velocity approaches 14 m/s a resonance behavior can be stated or this case. Resonance eects are to be expected i the velocity o the projectile reaches the velocity o elastic waves inside the rails [4, 5]. In this context it is interesting to note that or very similar rail geometry to the one considered here the lowest possible velocity or elastic waves inside the rails (Timoshenko beam on elastic oundation) was calculated to be about 147 m/s [5]. 18

5 ue.d v, m/s.376 m.75 m m 1.5 m m 2.25 m m Fig. 9. Dependence o eective amplitudes on sliding velocities at dierent locations Concluding remarks Reerences A 2D FE model was developed and an eective displacement amplitude method was suggested to investigate the dynamic behavior o the rails with regard to dierent sliding velocities. The observed resonance velocities dier in the range between 125 and 14 m/s depending on the position along the rail. The resonance velocity o the middle point is about 14 m/s. However, detailed explanation o the resonance phenomenon requires comprehensive uture investigations. [1] Fair H. IEEE Trans. on Magnetics Vol. 43(1) (27), p. 93. [2] Shvetsov G., Rutberg P. and Budin A. IEEE Trans. on Magnetics Vol. 43(1) (27), p. 99. [3] Lehmann P., Peter H. and Wey J. IEEE Trans. on Magnetics Vol. 37 (21), p [4] Tzeng J. T. IEEE Trans. on Magnetics Vol. 41(1) 25, p [5] Johnson A. J. and Moon F. C. IEEE Trans. on Magnetics Vol. 42(3) (26), p [6] Schneider M., Eckenels D. and Hatterer F. IEEE Trans. on Magnetics Vol. 39 (23), p [7] Schneider M. and Schneider R. IEEE Trans. on Magnetics Vol. 41 (25), p [8] ANSYS Theory Reerence, 8 th edition (SAS IP INC. 23). 19