Jtam-A4.dvi JOURNAL OF THEORETICAL AND APPLIED MECHANICS 54, 1, pp. 163-177, Warsaw 2016 DOI: 10.15632/jtam-pl.54.1.163 CONCEPT OF THE MAGNETIC LAUNCHER FOR MEDIUM CLASS UNMANNED AERIAL VEHICLES DESIGNED ON THE BASIS OF NUMERICAL CALCULATIONS Mirosław Kondratiuk, Leszek Ambroziak Faculty of Mechanical Engineering, Bialystok University of Technology (BUT), Białystok, Poland e-mail: m.kondratiuk@pb.edu.pl; l.ambroziak@pb.edu.pl The paper presents a concept of a magnetic coil launcher for unmanned aerial vehicles of mass up to 25kg.The idea is not new, nevertheless in the paper, an innovative application of magnetic launcher technology for selected class of unmanned aerial vehicles is presented. So far, atBialystokUniversityofTechnology,amagnetic coil launcher formicroaerialvehiclesof mass up to 2.5kg has been investigated. In the article, simulations of a conceptualmulti-coil launcherwithamagnetic core systemarepresented.Thefinite elementmethodhasbeenused in calculations.Moreover, in the paper, the concept of a magnetic support for transmission of mechanical power from the magnetic core to the launched payload is proposed. The applied methodology, computational results and potential technical difficulties of practical applications are also widely discussed. Keywords: electromagnetic launcher, EML, magnetic support, permanent magnet, FEM 1. Introduction Fast development and constantly increasing industrial applicability of unmanned aerial vehicles (UAVs) require new solutions as far as their operation systems are concerned. For instance, modern engineering associatedwithUAVs focuses especially ondeveloping innovative navigation systems (Gosiewski et al., 2011; Kownacki, 2013), robust control of flight (Mystkowski, 2014), reliable security solutions, efficient electrical engines and power cells, formation of flight control algorithms (Gosiewski and Ambroziak, 2012), adaptive aerodynamics structures (Mystkowski, 2013), applications of so-called intelligent materials, etc. Generally speaking, most works are being carried out in order to increase the level of UAVs autonomy. There is also a major need for applying systems of assisted take-off and landing. Starting launchers are used formany classes of UAVs frommicro planes of mass up to a few kilograms to large military drones. Systems assisting take-off procedures increase the level of operators’ safety, ensure recurrenceof starts, decrease periodsof timebetween consecutive starts, protect onboard equipment and UAV construction from undesired vibration and acceleration pulses. Employment of automatic launchers for UAV may also considerably increase the level of their autonomy and gives new possible applications, for example to autonomous systems for monitoring of countries boarders as well as unmanned systems of forest fire protection or unmanned aerial post services. Presently, many different constructions are used as launching devices. Main solutions invo- lve devices based on pneumatic (Perkowski, 2008) and hydraulic technology or are equipped with rubber or steam drive systems. Since the early 50’s, advanced research on electromagnetic launchers (EML) have been conducted in the world. In some publications, the knowledge of magnetic launchers was clearly systematised, e.g. Kolm et al. (1980). Electromagnetic launchers are a completely different group of starting devices basing on conversion of stored electrical 164 M. Kondratiuk, L. Ambroziak energy into kinetic energy of the launched object. Generally, there are twomain types of EMLs: rail launchers and coil launchers. Moreover, coil launchers can be divided into synchronous and asynchronous (inductive) devices. More specified nomenclature and theory were presented in the following publications byKondratiuk (2013), Tomczuk andWaindok (2009), Tomczuk et al. (2012). The idea of application ofmagnetic technology for aircraft launch is not new. Interesting papers concerning such topics havebeenalreadypublished (Patterson et al., 2002;McNab, 2007). Among others, very innovative research was carried out on electromagnetic launch systems for large airplanes. The investigations were conducted in the frame of big European project called GABRIEL (Sibilski et al., 2014). GABRIEL’s research teamproposed a systembased on pheno- mena of superconducting levitation. As a result, the system can be capable of launching airliners such as Airbus A320. In the frame of the project, a magnetic drive system has been developed. The investigations involved numerical models, vibration analysis, CAD and design optimiza- tion procedures.Moreover, successful laboratory tests of a small scale launch system have been carried out and the outcomes were published, see Ładyżyńska-Kozdraś etal (2014a,b). Conse- quently, systemGABRIEL has been designed for a large class of planes – commercial airliners. The concept of an electromagnetic linear drive for launching amedium class of UAVs significan- tly differs from solutions proposed by GABRIEL’s research team. Main differences involve the type of magnetic linear drives, scale of the device, target performance, field of applications and approach to design. In this paper, investigations on a synchronous coil launcher are described. Such a device consists of several serially located driving coils (usually made of a copper isolated wire) and a cylindrical coremoving inside those coils.The coremaybemadeof a ferromagneticmaterial, or a permanentmagnetmaybeused.Comparingtopneumaticandrubbercatapults, the synchronous coil launcher has many advantages, for instance, a quick recharging process and readiness for another shot, control of the launching force, modular construction and lack of complicated constructional parts exposed to damage. So far, at BialystokUniversity of Technology (BUT) the electromagnetic launcher formicro- -unmanned aerial vehicles (MAVs) has been developed and investigated (Kondratiuk, 2013). The construction of this device consists of ten serially located copper coils with a ferromagnetic core placed inside. The controlled magnetic field of the solenoids affects the core, and, in that way, the magnetic driving force is produced. The core is connected by means of a diamagnetic pusher to the carriage to which the launched plane is attached. The whole system is controlled by the open-source ArduinoMEGAplatform (ATMEGA2560) with the implemented algorithm of feedback control of MAV’s position and acceleration. The construction, conducted design works and control structure were widely described in the previous papers by Kondratiuk and Gosiewski (2013a,b, 2014). The main goal of the present work is to investigate and test some technical concepts of a multi-coil EML for middle class of UAVs. As tools for the testing, numerical simulations have been applied.Moreover, the article involves modifications, adaptation and scaling procedures of the previously constructed coil EML in order to launch objects of mass up to 25kg. 2. Main assumptions Among different types of UAVs, there are various requirements for start conditions. The most important one is connected with the initial speed which is necessary to generate a proper lift force. Because of differentUAVs geometries (shape,wing configuration,wingspan, etc.) different initial speed values are required. For instance, 25kg delta wing planes require much greater velocity (about 25m/s) than 25kg gliders (about 15m/s). In the paper, the design of an EML for 25kg UAVs which ensure starting speed on the level of at least 20m/s is described. That value has been chosen arbitrarily as the goal to achieve. Concept of the magnetic launcher for medium class... 165 Another aspect connected with UAVs catapults concerns the source of power. In pneumatic and hydraulic launchers, the working fluid is accumulated under pressure in special tanks or containers. On the other hand, rubber launchers require an external force to stretch the elastic material while steam catapults need a whole complex system for preparing vapour of proper parameters. In EMLs, electrical energy should be accumulated in a suitably large storage from which it can be rapidly released by the launcher driving system. Previous investigations clearly showed that the capacitor bank perfectly meets this requirement. In the proposed EML for 25kg UAVs there can appear the necessity of switching very high currents flowing through driving coils (even up to 200A). From the practical point of view, for current control, IGBT transistors can be used in electronic switching circuits. During FEM simulations, data sheets of such electronic devices as transistors and capacitors are strictly taken into account. Launchers for UAVs should also ensure sufficient stability, vibration and a safety level under take-off circumstances. These factors should be taken into account during design procedures. One of the main assumptions connected with the coil EML for 25kg UAVs is that initial investigations will be carried out on the already existing EML model for micro UAVs. Thus, this paper starts from possible modifications of the construction described in the PhD Thesis by Kondratiuk (2013). 3. Model of the coil-core system The first possible modification is connected with the application of a permanent magnet as a driving core instead of the ferromagnetic one. Force characteristics of the coil-core system with the ferromagnetic and with the magnetic cores were computed by means of the finite element method, (Tomczuk et al., 2007). COMSOLMultiphysics software is employed as the ready-made computer program for electromagnetic computations. In theFEMmodel of the coil-core system, the advantage of the axial symmetry is used. The partial differential equation (PDE) describing the distribution of static magnetic field in the coil-core system is called Ampère’s law, and in the ferromagnetic core domain it takes the following form ∇× ( ∇×A µ0µr(|B|) ) =Je (3.1) where∇denotes thenabla operator;A –magnetic vector potential, [Wb/m];µ0 =4π·10 −7H/m –permeability of vacuum; µr(|B|) – relative permeability of a nonlinear ferromagneticmaterial, [dimensionless]; |B| – magnetic flux density, [T]; Je – external current density, [A/m 2]. In the cylindrical coordinate system, the vector A can be written as A=Arr̂+Aϕϕ̂+Azẑ (3.2) whereAr,Aϕ,Az are components of the vector A, [Wb/m]; r̂, ϕ̂, ẑ – unit vectors. Thus, rotation of A is equal ∇×A= (1 r ∂Az ∂ϕ − ∂Aϕ ∂z ) r̂+ (∂Ar ∂z − ∂Az ∂r ) ϕ̂+ 1 r (∂(rAϕ) ∂r − ∂Ar ∂ϕ ) ẑ (3.3) Ampère’s law for the magnet domain has a different form than (3.1) ∇× (∇×A µ0µr −Br ) =Je (3.4) whereBr is the magnet remanent flux density vector, [T]. 166 M. Kondratiuk, L. Ambroziak Coil and ferromagnetic core parameters used in the simulation are taken from the real EML model previously described by Kondratiuk (2013), Kondratiuk and Gosiewski (2013a,b, 2014). Thecataloguevalueof remanentmagneticfluxdensity of the simulatedmagnet is equal to 1.24T. Relative permeability of the magnet material is equal to µr ≈ 1.05, but it can be modelled as close to 1 because, in order to generate a magnetic force, the magnet should be remagnetized so the external magnetic field produced by the coils increasesmagnetic induction in themagnet according to the following constitutive relation B=µ0µrH+Br (3.5) whereH is the magnetic field vector, [A/m]. Differences in the values of magnetic flux density for µr = 1 and µr = 1.05 obtained in a freely chosen point located inside the magnet are shown in Fig. 1. Fig. 1. Magnetic flux density in the magnet material during remagnetization In fact, relative permeability of a permanentmagnet decreases under influence of very strong external field and finally achieves the value of 1. Then, both lines in Fig. 1 line up parallelly. In the model, this effect is neglected. A permanent magnet has been proposed instead of a ferromagnetic one in order to increase themagnetic force. In theFEMmodel, theMaxwell surface stress tensormethod (MSST)andthe virtual work (VW) method have been tested. Generally, both methods give similar results and they are applied alternatively. In order to present the advantage of application of a permanent magnet, the computedmagnetic forces acting on both cores (magnetic and ferromagnetic) under influence of coil current ic =1A and ic =3A are compared in Fig. 2. Fig. 2. Comparison of magnetic forces acting on the ferromagnetic andmagnetic core The calculations clearly show that the magnetic core can provide much greater magnetic force than the ferromagnetic core. The computed results for the ferromagnetic core have been experimentally verified and high level data similarity has been revealed (Kondratiuk, 2013). Concept of the magnetic launcher for medium class... 167 In Fig. 3, 3D and 2D views of the modelled coil-magnet system are presented. Both repre- sentations are developed from the 2D axi-symmetric model by 2D revolution and 2D mirror functions respectively applied to the FEM solution. Fig. 3. Development of the FEM axi-symmetric solution for the coil-magnet system into 3D and 2D views: (a) magnetic flux density for the system under coil current i c =10A and with the magnet position z m =−12cm, (b) magnetic field distribution (z-coordinate) around the systemwithout current and with the magnet inside In order tomodelmotions of the core along the coil z-axis theEulermethodhas been applied (Kondratiuk, 2013). In the FEM model, a function of core length has been introduced. That function multiplied by remanent magnetic flux density, magnet permeability or conductivity describes properties of the core along the z-coordinate. In the model, isotropy of the above mentioned parameters has been assumed. In Fig. 3b, the evaluation line is drawn. Along this line, some crucialmodel parameters have been calculated and the results are presented inFig. 4. Fig. 4. Distribution of crucial parameters of the model along a selected line in the z-coordinate (coil current i c =20A, coil position p c =0, magnet position z m =−12cm) Positions of the core/magnet (zm) or the coil (pc) are defined as locations of their centres in the global coordinate system. Themagnetic flux density distribution presented in Fig. 4 comes from themagnet (higher pick) and from the coil (lower pick). This also explains fromwhere the magnetic force comes from. Themagnetic field tries to retain uniformity and always acts in the opposite way to any changes, for example in the coil current value or in the system geometry. When the coil generates an external field, the magnet and solenoid are attracted to each other because only in that way the total magnetic field can becomemore uniform. 4. Multi-coil EML model Themodel of a multi-coil EML can be divided into two strongly related parts: electromagnetic andmechanical. 168 M. Kondratiuk, L. Ambroziak 4.1. Electromagnetic part of the multi-coil EML The first model of EML with a permanent magnet as the core is based on the previously constructed andwidely investigated 10-coil EMLwith a ferromagnetic core. Parameters of that construction were presented in previous publications by Kondratiuk (2013), Kondratiuk and Gosiewski (2013a,b, 2014). It is worth noticing that the investigated coils weremade of a 0.8mm isolated copper wire in configuration 27 per 52 turns (1391 turns in total). In the paper, a code for coils description was proposed. For instance, the aforementioned solenoid can be coded as 0.8×27×52. Each coil in the model affects the magnetic core through magnetic field. Strength and di- stribution of the field depend on coils configuration and currents intensity flowing through the wires. However, the magnetic force is directly proportional to the current value, so in order to simplify the model, it is possible to compute the magnetic force distribution for different core positions in relation to the coil centre and only for one current value ic = 1A. It incorporates the function F(1A, [zm−pn]) in the multi-coil EML model as follows Fn(in,zm)= inF(1A, [zm−pn]) (4.1) where Fn(in,zm) is the magnetic force generated by the n-th coil, [N]; in – coil current flowing through the n-th coil, [A]; pn – n-th coil position, [m]. The total force acting on the magnet can be defined as Fm = N∑ n=1 Fn(in,zm) (4.2) whereN is the number of coils located serially. As thecore, anassemblyof 6 ring-shapedmagnets of remanenceBr =1.24Tmadeofmaterial N38 (Arnold, 2014) is proposed.Dimensions of selectedmagnets are the following: 27mm–outer diameter, 5mm – inner diameter, 10mm – magnet height. Each magnet is magnetized along 10mm dimension. The assembled core is 60mm long. The number and shape of magnets are selected arbitrarily. Similarly to the coils, in the paper, a code for core description is proposed. The above described core can be coded as 6×RSM-27×5×10-N38 where RSM means a ring- shapedmagnet. Visualization of the proposed core in front of two coils 0.8×27×52 is presented in Fig. 5. Fig. 5. Cross-sectional visualization of the core 6×RSM-27×5-10-N38 in front of the two coils 0.8×27×52 Stationary calculations for the coil 0.8×27×52 and the assembled magnetic core 6×RSM- -27×5×10-N38 have been carried out and the functionF(1A, [zm−pn]) calculated (Fig. 6). The function presented inFig. 6 has been used according to equation (4.1) in the 10-coil EMLmodel. Regarding the power source in the model, a single bank of capacitors connected parallelly has been applied. First calculations have been conducted for the systemvoltage of 340Vand the Concept of the magnetic launcher for medium class... 169 Fig. 6. Function F(1A, [z m −p n ]) calculated for p n =0 total capacity of 94mF. In the simulation, the capacitor discharging process has beenmodelled according to the following equations uc(t)=uc0− 1 C t∫ 0 ic(t) dt ic(t)= N∑ n=1 in(t) (4.3) where uc(t) is capacitor voltage, [V]; uc0 – initial capacitor voltage, [V]; C – capacity of the bank, [F]; ic(t) – total capacitor discharging current, [A]; in(t) – current flowing through n-th coil, [A]. 4.2. Mechanical part of the multi-coil EML In the mechanical part of the model, the damping force (Fd) is introduced Fd(vm)= bdvm︸ ︷︷ ︸ holds always or Fd(vp)= bdvp︸︷︷︸ holds during acceleration (vm=vp) (4.4) where bd denoted the damping coefficient, [N·s/m]; vm, vp –magnet and payload (UAV) veloci- ties, respectively, [m/s]. A simplifiedmechanical scheme of the system is presented in Fig. 7. Fig. 7. Mechanical scheme of the investigated system During simulations, the damping coefficient value has been arbitrarily chosen as constant bd =5N·s/m.Dynamic behaviour of themulti-coil EMLwithmagnetic core and a 25kg payload (launching UAV) is described by the following equations: — for zp