Simulation of mechanical behaviour of the electromagnetic railgun by finite element method ; Elektromagnetinės šaudyklės mechaninės elgsenos modeliavimas baigtinių elementų metodu
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Simulation of mechanical behaviour of the electromagnetic railgun by finite element method ; Elektromagnetinės šaudyklės mechaninės elgsenos modeliavimas baigtinių elementų metodu

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Liudas TUMONIS SIMULATION OF MECHANICAL BEHAVIOUR OF THE ELECTROMAGNETIC RAILGUN BY FINITE ELEMENT METHOD Summary of Doctoral Dissertation Technological Sciences, Mechanical Engineering (09T) 1689-M Vilnius 2009 VILNIUS GEDIMINAS TECHNICAL UNIVERSITY Liudas TUMONIS SIMULATION OF MECHANICAL BEHAVIOUR OF THE ELECTROMAGNETIC RAILGUN BY FINITE ELEMENT METHOD Summary of Doctoral Dissertation Technological Sciences, Mechanical Engineering (09T) Vilnius 2009 Doctoral dissertation was prepared at Vilnius Gediminas Technical University in 2005–2009. Scientific Supervisor Assoc Prof Dr Arnas KAČENIAUSKAS (Vilnius Gediminas Technical University, Technological Sciences, Mechanical Engineering – 09T). The dissertation is being defended at the Council of Scientific Field of Mechanical Engineering at Vilnius Gediminas Technical University: Chairman Prof Dr Habil Rimantas BELEVIČIUS (Vilnius Gediminas Technical University, Technological Sciences, Mechanical Engineering – 09T).

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Published 01 January 2010
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    Liudas TUMONIS     SIMULATION OF MECHANICAL BEHAVIOUR OF THE ELECTROMAGNETIC RAILGUN BY FINITE ELEMENT METHOD     Summary of Doctoral Dissertation Technological Sciences, Mechanical Engineering (09T)       
 
Vilnius 2009
1689-M
 
VILNIUS GEDIMINAS TECHNICAL UNIVERSITY          Liudas TUMONIS     SIMULATION OF MECHANICAL BEHAVIOUR OF THE ELECTROMAGNETIC RAILGUN BY FINITE ELEMENT METHOD      Summary of Doctoral Dissertation Technological Sciences, Mechanical Engineering (09T)       
 
Vilnius   2009 
 
Doctoral dissertation was prepared at Vilnius Gediminas Technical University in 2005–2009. Scientific Supervisor Assoc Prof Dr Arnas KAČENIAUSKAS Gediminas Technical (Vilnius University, Technological Sciences, Mechanical Engineering – 09T). The dissertation is being defended at the Council of Scientific Field of Mechanical Engineering at Vilnius Gediminas Technical University: Chairman Prof Dr Habil Rimantas BELEVIČIUS Gediminas Technical (Vilnius University, Technological Sciences, Mechanical Engineering – 09T) . Members: Assoc Prof Dr Kęstutis ARLAUSKAS University, Physical (Vilnius Sciences, Physics – 02P), Prof Dr Habil Juozas ATKOČIŪNAS Gediminas Technical (Vilnius University, Technological Sciences, Mechanical Engineering – 09T), Prof Dr Habil Algimantas FEDARAVIČIUS(Kaunas University of Technology, Technological Sciences, Mechanical Engineering – 09T), Prof Dr Habil Mindaugas Kazimieras LEONAVIČIUS(Vilnius Gediminas Technical University, Technological Sciences, Mechanical Engineering – 09T). Opponents: Prof Dr Habil Saulius BALEVIČIUS Physics Institute, (Semiconductor Physical Sciences, Physics – 02P), Prof Dr Vytautas TURLA(Vilnius Gediminas Technical University, Technological Sciences, Mechanical Engineering – 09T).  The dissertation will be defended at the public meeting of the Council of Scientific Field of Mechanical Engineering in the Senate Hall of Vilnius Gediminas Technical University at 1 p. m. on 8 January 2010. Address: Saul÷tekio al. 11, LT-10223 Vilnius, Lithuania. Tel.: +370 5 274 4952, +370 5 274 4956; fax +370 5 270 0112; e-mail: doktor@adm.vgtu.lt The summary of the doctoral dissertation was distributed on 7 December 2009. A copy of the doctoral dissertation is available for review at the Library of Vilnius Gediminas Technical University (Saul÷tekio al. 14, LT-10223 Vilnius, Lithuania). © Liudas Tumonis, 2009
 
 
VILNIAUS GEDIMINO TECHNIKOS UNIVERSITETAS          Liudas TUMONIS    ELEKTROMAGNETINöS ŠAUDYKLöS MECHANINöS ELGSENOS MODELIAVIMAS BAIGTINIŲELEMENTŲMETODU      Daktaro disertacijos santrauka Technologijos mokslai, mechanikos ininerija (09T)       
 
Vilnius  2009   
 
Disertacija rengta 2005–2009 metais Vilniaus Gedimino technikos universitete. Mokslinis vadovas doc. dr. Arnas KAČENIAUSKAS (Vilniaus Gedimino technikos universitetas, technologijos mokslai, mechanikos ininerija – 09T). Disertacija ginama Vilniaus Gedimino technikos universiteto Mechanikos ininerijos mokslo krypties taryboje: Pirmininkas prof. habil. dr. Rimantas BELEVIČIUS Gedimino technikos (Vilniaus universitetas, technologijos mokslai, mechanikos ininerija – 09T). Nariai: doc. dr. Kęstutis ARLAUSKAS (Vilniaus universitetas, fiziniai mokslai, fizika – 02P), prof. habil. dr. Juozas ATKOČIŪNAS(Vilniaus Gedimino technikos universitetas, technologijos mokslai, mechanikos ininerija – 09T), prof. habil. dr. Algimantas FEDARAVIČIUS(Kauno technologijos universitetas, technologijos mokslai, mechanikos ininerija – 09T), prof. habil. dr. Mindaugas Kazimieras LEONAVIČIUS (Vilniaus Gedimino technikos universitetas, technologijos mokslai, mechanikos ininerija – 09T). Oponentai: prof. habil. dr. Saulius BALEVIČIUS(Puslaidininkiųfizikos institutas, fiziniai mokslai, fizika – 02P), prof. dr. Vytautas TURLA(Vilniaus Gedimino technikos universitetas, technologijos mokslai, mechanikos ininerija – 09T.)  Disertacija bus ginama viešame Mechanikos inineroijs mokslo krypties tarybos pos÷dyje 2010 m. sausio 8 d. 13 val. Vilniaus Gedimino technikos universiteto senato pos÷diųsal÷je. Adresas: Saul÷tekio al. 11, LT-10223 Vilnius, Lietuva. Tel.: (8 5) 274 4952, (8 5) 274 4956; faksas (8 5) 270 0112; el. paštas doktor@adm.vgtu.lt Disertacijos santrauka išsiuntin÷ta 2009 m. gruodio 7 d. Disertaciją peri galimaūr÷ti Vilniaus Gedimino technikos universiteto bibliotekoje (Saul÷tekio al. 14, LT-10223 Vilnius, Lietuva). VGTU leidyklos „Technika“ 1689-M mokslo literatūros knyga.  © Liudas Tumonis, 2009
 
 
Introduction  Topicality of the problem. is a Mechatronic system used to The railgun accelerate projectiles up to very high velocities (from 1 to 10 km/s). The accelerations needed to attain these velocities, however, demand high currents generating high magnetic fields and very large Lorentz forces acting on the projectile and rails. On the basis of existing practice one can conclude that fundamental theoretical issues have been solved and several electromagnetic rail gun systems have been designed. The question concerning characterization of the particular rail gun systems in terms of technical parameters is, however, still open and many details require careful examination. Dynamic deformation behavior is an important component of railgun physics. As in the case of classical guns, the mechanical response of the housing to the transient loading (magnetic pressure) may lead to disturbances of the projectile trajectory due to momentum transfer. Additionally, deflections of contacting surfaces causes damage of the rails due to armature interaction and to occurring of high stresses. Dynamic effects, especially at velocities near the critical, cause a drastic difference in the structure response. Therefore, evaluation of the mechanical behavior of the electromagnetic railgun is a mandatory task for future development.  The object of investigations.The object of investigation is electromagnetic accelerator EMA-3 at French-German institute of Saint-Louis (ISL).  Aim and tasks of the work. The aims of presented work to investigate numerically the mechanical behaviour of the EMA-3 railgun under action of the moving load, to investigate relationships between dynamic state variables and loading parameters, to compare various loading regimes. For this purpose the following tasks have to be performed: 1. Development and investigation of the numerical model of the EMA-3 railgun. 2. Finding of the most suitable parameters for characterisation of the dynamic behaviour of railgun under moving load. 3. Comparison of influence of various loading regimes to dynamic deformation of rails and evaluation of results. 4. Algorithmic and software development of suggested methodology and data processing.  
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Methodology of researchinvolves analysis of theoretical investigations by applying analytical and numerical methods, numerical experiments, data synthesis and comparative analysis.  Scientific novelty 1. The firstly obtained numerical characterisation of the dynamic behaviour of EMA-3 railgun. 2. Specification of two parameters – the effective amplitude and friction factor – for characterisation of railgun mechanicalbehaviour. 3. Characterisation of influence of discrete supports. 4. Characterisation of breech-feed and distributed energy system (DES) loading regimes and motivation of preference of the DES regime.  Practical value. obtained results of investigations were summarised The and could be used for development of new railguns or upgrading existing systems and finding better loading regimes.  Defended propositions 1. The developed 2D FE model of the EMA-3 railgun aimed for dynamic behaviour under moving load and justification of its quality. 2. The firstly obtained characteristics of the railgun under real loading regimes. 3. The originally developed software for characterisation of real loads during pre-processing and post-processing.  The scope of the scientific work. The scientific work consists of the general characteristic of the dissertation, introduction, 4 chapters, the summary of results and conclusions, the list of cited literature, list of publications of the author and appendix. The total volume of the dissertation – 93 pages, 30 equations, 41 pictures, 3 tables and 1 addenda.  1. Review of Electromagnetic Railguns and Analysis Methods  Various approaches and models have been recently employed for modelling purposes. The mechanical, or structural, analysis of the railgun system can be decoupled from electromagnetic phenomena in a first step. The next simplification concerns dynamic model. It is still obvious that the railgun housing dynamics can also be treated as being independent on the projectile behaviour. The magnetic pressure, repelling the rails one from the
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each other and expanding with the speed of the projectile, serves as force boundary condition for purely mechanical calculations. Another issue concerns the structural model. Probably, the simplest model used considers the rail as one-dimensional beam on an elastic foundation. This analytical model suffers from many simplifications with respect to structure model and loading, therefore, numerical methods offer many new possibilities. Thereby, the most powerful engineering tool – the Finite Element Method (FEM) is applied for mechanical behaviour of the railgun.  2. Numerical Model of the EMA-3  The mechanical behavior of the railgun EMA-3 (Fig. 1) of the French-German Research Institute of Saint-Louis (ISL) was investigated.  
Power supply
Railgun
X-Ray tube 
  Fig. 1.The ISL-railgun EMA-3 railgun facility  The EMA-3 has a length of 3 m and a calibre of 15x30 mm2. The pecularity of the investigated system is originally constructed railgun housing. A view of the railgun cross-section is presented in (Fig. 2a). In order to withstand the high forces repelling the rails from each other, the housing consists of a combination of bars with section size 160 80 mm of EPM 203 glass fibre reinforced plastic (GRP) material and discontinuous steel bolts. The rails of section with size 30 15 mm are made of Cu alloy (CRM 16N). Multiple brush armatures were used. Considering the axial symmetry of the rail, only half of its cross section can be investigated. A simplified model of the railgun structure is presented in Fig. 2b. Here, two section bolts fabricated from steel are modelled by a single rod located on the section center.
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A 2D finite element model resting upon discrete elastic supports has been developed in order to represent the complex housing. The model is able to capture bending and shear effects described conventionally by beam models as well as pinching deformation of a cross-section.
q y 30x yzq 160160   a c)) b)   Fig. 2. )b ;eruifilpmiselod med ; tcoian livwe :)a original structaR uglistn ctrue urse– c) 2D FE model of the rail gun with loading  The transient loading profile represents the magnetic pressureq(x,t) at an arbitrary pointxmoving in timetwith the velocityv(t). Independently on the particular type, loading variation along the direction of movement is defined in a form of the Heaviside step functionH(x) (Fig. 3a):  q x,t= H xp tftx, (1)  wherep(x,t) represents magnetic pressure, distributed between zero and moving local coordinatexf, whilexf(t) represents the position of the load front (projectile) at time instantt. Variation of pressurepdepends on the loading type. Three-dimensional view of the typical loading with moving constant pressure profile is depicted in Fig. 3b. Series of static and dynamic problems were solved and the quality and suitability of the FE model was investigated. The model was examinated by comparison with available solutions.  
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q
, m 0 1 2 3 30 20 10 0
0xfL x   a)         b)  Fig. 3.Load variation: a) fixed in time profile; b) distribution in time  The static analysis of the railgun housing was initially performed by applying a constant pressurepthe entire rail length. One of the goalsload along of the static analysis is to evaluate transversal deformation of the rails and bolts separately. Therefore, both discrete and continuous models of the elastic supports were considered. The transversal deformation behavior of the cross-section is characterized by transversal displacementsuyvariation of which through the section height of the rail is presented in Fig. 4. The solution obtained with continuous supports is represented by the curve Cont, while the solutions obtained with discrete supports are illustrated by the curves Discr1 and Discr2. In particular, the curve Discr1 denotes the section on the support, while the curve Discr2 represents the section between supports. The graph demonstrates the nature of difference between both support models. 0. 0.19 0.18 0.17 0.16 0.15 0.14 0 1 2 3 4 5 6 7 8 9 y,cm  Fig. 4.the middle of the rail through the heightTransversal displacement variation in
Discr1 Discr2 Cont
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Based on static calculations, it could be stated that the total transversal displacement of the sliding surfaceuy 0.195 mm comprises deformation of the section heightuy,sect  mm and model error 0.03uy,leodm  0.02 mm. The remaining displacement ofuy,bolt  0.145 mm is due to deformation of the bolts. As conclusion, it can be stated that the pinching of the section amounts to approximately 15 % of the total transversal displacement of the sliding surface, while the relative error of the discrete support model s is about 10 %. By applying the FE model the value of critical velocity equal to 1440 m/s was obtain. This value was employed to characterize real loading, which may be classified to category of pre-critical loadings.  3. Investigation of Velocity Dependent Mechanical Behavior  In order to illustrate mechanical behaviour, two problem-related parameters are suggested. For dynamic effects the concept of the effective amplitude is used. The excitation periodt a particular node located in of positionxn is defined as difference between entire loading periodtsh time and intervaltf before the point is loaded. It is expressed in terms of loading data as followst=tsh tf . Finally, the effective amplitudeuef,dis obtained using least square method by integrating the difference between dynamic displacementsuy,d(t) and static solutionuy,s:   uef ,d=1tttsfhuy ,d(t) −uy ,s2dt. (2)  It is obvious that for static behavioruef,d = 0. Mechanical behaviour also comprises deformation of gun structure. Deformation of the sliding surface play important role for energy transformations. Increase of deflections increases friction of sliding brushes and reduce supplied electric energy. Another important parameter in this work, the relative dynamic friction ratio factor is proposed in order to investigate deformation of the rail at the projectile-rail contact. Here deformation of the rail occurs due to moving loading related with the position of the projectile. This factor evaluates the ratio between dynamical friction force and statical friction forceη=Ffr,d/Ffr,s. It is indirectly assumed, that static friction phenomenon is related to undeformed state of the rail, while dynamic phenomenon is reflected by time dependent deformed behaviour of the rail.
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