Abstract: An important problem that appears in the study of sloped rocket launch is to determine the launchers oscillations during firing and also the disturbances ...
NUMERICAL AND EXPERIMENTAL STUDY OF THE LAUNCHING DEVICE OSCILLATIONS DURING THE LAUNCH Pamfil SOMOIAG, Cristian-Emil MOLDOVEANU Abstract: An important problem that appears in the study of sloped rocket launch is to determine the launchers oscillations during firing and also the disturbances the rocket gets in the moment of the launch, phenomenon that influence the stability of the launcher and firing precision. The main preoccupation in the rocket launching system design, fabrication, experimentation and maintenance is the rigorous evaluation of the launching system oscillations influence upon the rocket’s performances and upon the rocket’s flight parameters as well as the study of the rocket compatibility with the launching system. The article presents the calculations by numerical and experimental methods of the launching device oscillations during the launch. Key-Words: launching device, oscillations, intrinsic frequency
1. INTRODUCTION The study of the launching device’s oscillation during firing is necessary for the design of precise and efficient rocket-launching system, especially in the case of unguided rocket. We consider that the launching device with the moving rocket form an oscillating system, described by an assemble of the rigid bodies (as depicted in fig.1). The system is bound together by elastic elements, consisting of the following main components: the vehicle chassis (supporting the launching device’s basis with the revolving support of the mechanisms), the tilting platform (with the rocket’s containers) and the rockets (including the moving rocket). When launching the rocket, the system acts as a complex oscillating system. This system is considered as a set of the rigid bodies bound together by elastic elements. It has a high number of degrees of freedom; hence a complex study of the oscillations is induced. To simplify the computation while still avoiding any limitation in generalization the study, we consider that the motion of the rocket-launching device system during launching can be completely described by 6 status-variables [1]. They are: the rocket linear translation in the container’s guiding tube, s , two angles that define the tilting platform’s position (pitch and gyration oscillations), ϕ y ,
ϕ z , other two angles that define the vehicle chassis pitch and rolling motion, γ x , γ y , and the chassis center of masse oscillating vertical displacement, z S . In this study, all the forces and moments acting on the rocket-launching device system during firing are taken into consideration. Since the differential equations system [1] that defines the system’s oscillating motion is quite complex, it can’t be solved in an analytical way; hence we need to use a numerical solving. So, it was necessary to create a programming algorithm and to develop a numerical application (named ILANPRN [2]), consisting of numerical solving rocket-launching device system’s movement equations by successive iterations. With each iteration the rocket-launching device system status variables are computed one by one by the means of the container, the guiding tube movement equation, the tilting platform and the chassis angular oscillation equations, as well as of the chassis vertical translation equation.
Vehicle chassis
Rocket s OR
Tilting platform OB
Revolving support pivotant
ϕy
ϕz
γx
z S
γy
Fig.1. The components of the rocket-launching device system We use the 122 mm unguided rocket-launching device with a container of 40 rockets. In order to validate the programming algorithm and the numerical application ILANPRN the experimental results were compared to the numerical results concerning the launching device oscillations.
2. THE NUMERICAL DETERMINATION OF THE LAUNCHING DEVICE OSCILLATIONS DURING FIRING 2.1 Computational diagrams In order to solve the differential equations system [1] that describes the launching device oscillations during firing, we use the numerical methods. In this respect the authors developed a programming algorithm and a numerical application named ILANPRN (fig.2). This programming algorithm allows the computation of the launching device oscillations as well as the computation of the rocket flight evolution on the trajectory. The numerical application is structured on 5 main modules: the „data management” module, the „launching device parameters” module, the „launching device calculus” module, the „results of the launching device calculus” module and the „rocket flight evolution on the trajectory” module. Solving the equations that describe the rocket-launching device system motion [1] assumes an iterative method. Any iteration separately solves the equations corresponding to each system component levels (the moving rocket, the tilting platform and the vehicle chassis) considering that the status variables of the other known components. To solve the rocket-launching system equations we need to know the initial firing parameters. Some of them are as follows: the rocket’s parameters, the presence of the rockets on the container as well as the initial firing position (the orientation of the tilting platform upon the firing direction). Because the rockets are in the guiding tube of the container, these will have the same movement like the tilting platform: the rotation γ and the translation z S from the vehicle chassis, and the rotation ϕ from the tilting platform (fig.3). In relation
with the tilting platform, the rocket has a translation motion with the velocity s& and a rotation motion with the angular velocity β& .
Fig. 2 The numerical application ILANPRN for the launching device calculus MRbx FRbx MRby FRby MRbz FRbz
zs , γ x , γ y
CHASSIS TILTING PLATFORM
ϕ y , ϕz
ROCKETS s
s
Fig. 3 Rocket’s computational diagram Solving the rocket equations allow getting the values of the link forces and moments between the rocket and the tilting platform, as well as the time history of the rocket’s velocity, acceleration and position during the rocket’s movement in the guiding tube. Subsequently we compute the tilting platform movement parameters ( ϕ y , ϕ z ) and the link forces and moments between the tilting platform and the vehicle chassis (fig. 4). zs , γ x , γ y
CHASSIS MRbx FRbx MRby FRby MRbz FRbz
ROCKET
TILTING PLATFORM
Mηx RΠx Mηy RΠy Mηz RΠz ϕy , ϕz
s
Fig. 4 The tilting platform’s computational diagram
ROCKET
TILTING PLATFORM
M ηx RΠx M ηy RΠy M ηz RΠz
CHASSIS
ϕ y , ϕz
Fig. 5 The vehicle’s chassis computational diagram
zs , γ x , γ y
Eventually, we calculate the chassis movement parameters (fig.5). We obtain the time history of the vehicle’s chassis center of masse vertical translation z S , as well as the rotation of the vehicle’s chassis around the center of the masse γ x , γ y during firing. So, in this application we determine the motion parameters of the launching system during firing (the rocket’s translation s , the tilting platform’s rotation ϕ as well as the chassis’ translation z S and rotation γ ). Using these status variables, the numerical application allows the calculations of the motion evolution for any point located on the launching device during firing. 2.2 Numerical results We further present some results obtained by numerical solving of the equation system in according to the previously presented programming, in order to study the rocket-launching device system. Many simulations are computed in a single rocket firing case with the rocket in central position in the container (position no. 15). The time history of the status variables that describe the rocket-launching device system ( z S , γ x , γ y ,ϕ y ,ϕ z , s ) is presented in fig. 6 - 11. We notice that the displacement z S of the chassis center of masse has an oscillatory evolution (fig. 6) having a 0.75 s oscillating period. The oscillating amplitude has the initial value of 1.6 mm, and after the first period it decreases to 1 mm (62.5% from the initial amplitude).
Fig. 6 Time history of the z S displacement
Fig. 7 The time history of the rotation angle γ x
Fig. 8 Time history of the rotation angle γ y The chassis angle rotations γ x and γ y have also a damped oscillatory evolution (fig. 7 and fig. 8). Moreover, the oscillating period for γ x (0.4 s) is smaller than the oscillating period for γ y (0.8 s). The γ x oscillating amplitude is 0.18 degrees while the γ y oscillating amplitude is only 0.028 degrees leading to the conclusion that the rolling oscillation is more important than the pitch oscillation.
Fig. 9 Time history rotation angle ϕ y
Fig. 10 Time history of the rotation angle ϕz
As the oscillations of the tilting platform are concerned, the rotation angle ϕ y (see fig. 9 and fig. 10) has a larger period (0.5 s) and larger amplitude (0.8 degrees) than ϕ z (0.2 s oscillating period and 0.04 degrees oscillating amplitude). So, we can say that, at the tilting platform level, the main oscillation is the pitch oscillation ( ϕ y ).
Fig. 11 Time history of the displacement s Fig. 11 depicts the trajectory of the rocket’s center of masse during the launching. The evolution range starts from zero (initial position) to 3 m (the position of the rocket’s center of masse when it leaves the launching device).
3. EXPERIMENTAL RESULTS OF THE LAUNCHING DEVICE OSCILLATIONS 3.1 Experimental configurations The aim of the experimental tests is to evaluate the measured parameters of the oscillations and to compare these values with the ones given by the numerical application ILANPRN, developed using the theoretical model [1]. Considering the hypothesis that was used to develop the theoretical model (concerning the type of the launching device), the experiments were developed upon an unguided rocket sloped launching device (122 mm unguided rocket launching device with 40 guiding tubes in 2 containers – APRA 122). The experimental configuration used to measure the parameters of the launching device oscillation as time histories is shown in fig. 12. The experimental development aimed at obtaining the intrinsic frequency, the dumping time response as well as other parameters that describe the free oscillating motion. We use many sets of records corresponding to the 4 configurations based upon the position of the displacement sensor (TD) and upon the two cases possible for the chassis suspension: fixed (as in the time of firing) or free. 3.2 Experimental results We present the experimental results for the particular cases when the displacement sensor has its body fixed at the horizontal platform, and the sliding rod attached on the left extremity of the second vehicle axle. Fig. 13 and 14 depict the time history of the displacement of the point placed on the left extremity of the second vehicle axle.
Sensor resistive for the forces
Sensor inductive for the displacements
Fig.12 Experimental configuration
Fig. 13 Time history of the displacement in vertical plan of the point placed on the left extremity of second vehicle axle (fixed suspension case assumed) We notice that a visible difference occurs between the two cases for the maximal value of the oscillating amplitude: in the case of the fixed suspension the maximal amplitude is 2.33 mm, and in the case of the free suspension the maximal amplitude is 2.69 mm. Analyzing the previously presented experimental results, we notice that the launching device has an oscillating motion (in fact the vehicle chassis’ oscillating motion is transmitted to all other components: the tilting platform and the rockets). The intrinsic frequency measured is about 8.01 rad/s corresponding at 0.78 s the oscillating period. These experimental values are close to the ones that have been obtained by numerical means (8.15 rad/s and 0.77 s). The determination of these parameters (intrinsic frequency and oscillating period) is very important in order to study the optimal time between two successive launches. This study is useful in avoiding the resonance phenomenon that may lead to the amplification of the launching device oscillations (in this case the rocketlaunching device system will be unstable).
Fig. 14 Time history of the displacement in vertical plan of the point placed on the left extremity of second vehicle axle (free suspension case assumed)
4. CONCLUSION The evolution calculus of the rocket-launching device system state variables during firing sequences allows the evaluation of dynamic forces that are present at all levels of the launching device system component, and therefore the analysis of the dynamic behavior of the whole assembly system. Evaluating the oscillation parameters of a rocket-launching device system, their influence upon the system’s stability during firing, such as the initial rocket flight condition, leads implicitly to the evaluation of the firing accuracy. This last issue is essential in the design of a precise rocket-launching device system. In conclusion, a rocket launching phase design needs to take into account the system’s oscillations. These oscillations can be computed by numerically solving a theoretical model [1] that has also confirmed by the experimental results, which, at their turn, validate and lead to the improvement of the numerical programming algorithm. BIBLIOGRAPHY [1] Şomoiag P., Cercetări privind determinarea oscilaţiilor la lansare şi influenţa acestora asupra zborului rachetei, PhD thesis, Military Technical Academy, Bucharest, 2007. [2] Şomoiag P., Moldoveanu C., Application numérique pour la détermination des oscillations du lanceur pendant le tirage, The 31th Internationally attended scientific conference of the Military Technical Academy – MODERN TECHNOLOGIES IN THE 21st CENTURY, Bucharest, 3–4 November, 2005.
