Analizira se efekt proizvodnih pogrešaka na povećanje disperzije padnih točaka nevođenog
projektila. Korištena metoda primjenjiva je na sve tipove nevođenih projektila, a prikazana je na
primjeru rakete poznatih karakteristika. Kao studija slučaja simulira se pojava četiri proizvodne
pogreške: izvedbe bojeve glave, spoja bojeve glave i komore motora, izvedbe mlaznice te
ugradnje bloka goriva u komoru motora. Navedene pogreške uzrokuju dinamičku
neuravnoteženost projektila i asimetriju potisne sile.
Predložena metoda povezuje CAD 3D model rakete (u koji su uvodi asimetrija mase i
potisne sile uslijed nabrojanih pogrešaka) sa 6DOF modelom leta koji je prilagođen praćenju leta
upravo ovakvih asimetričnih projektila. Ova dva modela spojena su u jedinstvenu sveobuhvatnu
Monte Carlo simulaciju. Na taj način se jednoznačno pokazuje kako nesavršenosti pojedinih
proizvodnih faza povećavaju disperziju padnih točaka. Identificiraju se kritične faze proizvodnje
kod koji je potrebno inzistirati na posebno strogim tolerancijama, dok se u drugim fazama (a
koje daju slabiji efekt na preciznost projektila) mogu dozvoliti blaže tolerancije i tako sniziti
cijenu proizvodnje. Pokazuje se koliko dominantni mogu biti neki poremećaji u smislu
povećanja nepreciznosti, npr. loša kvaliteta izvedbe mlaznice, nakon čega disperzija padnih
točaka prelazi dozvoljene granice čak i ako se za sve druge faze proizvodnje nametnu najstrože
Opisana metoda predstavlja analitički opravdani način postizanja kompromisa između
kriterija cijene i kriterija preciznosti, a što je ključni zahtjev kod izrade nevođenih projektila.
|Abstract (english)|| |
The doctoral dissertation has been divided into eight chapters, of which the first chapter is
introductory, and the eighth concludes the dissertation. The list of used literature, as well as the
lists of figures, tables, and variables used in the text, are especially singled out.
The first introductory chapter brings the motivation for research and an overview of
previous research. The goal and hypothesis of the work are set, and the methodology of problemsolving
is presented. In the end, an overview of the entire doctoral dissertation is given. The
research is based on the following hypotheses: by applying the non-deterministic model of the
unguided missile flight, it is possible to determine the functional dependence between mass
imbalance and thrust asymmetry with increasing area of impact points dispersion, and to give
recommendations for projectile production aiming to reduce dispersion area. The aim of this
dissertation is to improve a non-deterministic flight model with six degrees of freedom for
unguided projectiles, to show the sensitivity of the trajectory to various disturbances. The model
will incorporate the mass imbalance and thrust asymmetry for the selected rocket and will assess
the impact of these disturbances on the increase of impact points dispersion area.
The second chapter presents a parametric CAD model of a projectile manufactured with
certain errors. The whole dissertation tries to solve the problem of the influence of production
errors on the flight of the projectile and emphasizes the differences between the ideal and nonideal
projectile trajectory, where the latter is burdened with production errors. At the beginning
of the chapter, a CAD 3D model of the projectile is given, and it is shown why it is divided into
two main parts (components): the spacecraft and the propellant. After that, it is shown how the
parameterization of production errors in the CAD 3D model was performed. The newly
introduced geometric coordinate system (G-KS) is explained. After that, the production errors
are described: errors in the connection of the warhead and the engine chamber.
The third chapter describes the adjusted 6DOF flight model of the projectile. The basic
differential equations of the 6DOF model are given, where the aerodynamic force and torque are
especially elaborated. The reason is that it is necessary to adjust the aerodynamics due to the
noncollinearity of the warhead and the engine chamber symmetry axes (due to the faulty
produced joint between the warhead and the engine chamber). After that, the inertia
characteristics of the projectile are presented, separately for each component: the aircraft and the
propellant. For the first time, the reason for the introduction of the CAD 3D model is visible,
because its output variables (geometrical and inertial characteristics) become the input for the 6DOF model. Finally, the classic and modified 6DOF model (called G6DOF for the sake of
distinction, but also because of the coordinate system in which it was developed) are compared.
The fourth chapter presents the software solution of the 6DOF flight model. This is
important to explain the interrelationships of individual program parts, but also to explain the
capabilities of the program itself as it can incorporate not only manufacturing errors but also
many other disturbances (e.g., atmospheric conditions, weapons conditions, etc.). The main
program is presented, and it is shown how the production errors are introduced. The setting of
differential equations and connections with other parts of the program is further clarified. An
example of determining the trajectory of an (ideal) missile is also given, and the flight
parameters are compared with the data from the corresponding Firing tables. The 122 mm M-21
GRAD rocket is taken as an example.
In the fifth chapter, the impact of production errors is analyzed, and these errors are
treated as deterministic variables. The methods of classical analysis of the production errors
impact are described, followed by the separate analysis for each of the four previously described
production errors: erroneously manufactured joint of the warhead and engine chamber, warhead
(or its bore), nozzle, and propellant installation. The first three described errors change the
geometrical and inertial characteristics of the component "frame", while the last error relates to
the component "propellant". The chapter provides a comparison of the effects for all analyzed
errors, first at the maximum allowable angles of noncollinearity i
and then at the same angle
for all errors. Finally, the impact point deviation (i.e., the inaccuracy of the missile) is analyzed
due to the described errors and the rocket effectiveness on the target.
The sixth chapter describes the statistical processing of the simulation results. Errors are
treated as nondeterministic variables, and the simulation is performed by the Monte Carlo (MC)
method. The MC method is commented at the beginning, and the methods of determining the
MC simulation parameters are described: defining the sample size, selecting the probability
distribution function according to which the input variables will be dispersed (normal
probability, Weibull, or Rayleigh). The parameters included in this MC Monte Carlo simulation
are given, and the occurrence of just one and then all four production errors at the same time is
simulated separately. The chapter describes methods for estimating the normality of the impact
points distribution. Further, it compares the simulation results if the input parameters follow the
normal, or if they follow the Rayleigh distribution. All results are compared with the area of the
dispersion as stated in the corresponding Firing tables. It is analyzed which error explains most
of the dispersion listed in the Firing tables. Chapter 7 describes a statistical analysis of the relationship between production quality
levels and projectile precision. The terms "level of production quality" and the "index of
potential capacity of the process Cp" (which directly determine the limits of the specification, i.e.
the limits of the allowed parameter's value) are introduced. Nine combinations of production
quality levels are simulated (where each stage of production can be performed in high-, standardor
low- quality) and it is shown not only that one production error is dominant, but also how
dominant. This error effect cannot be compensated even by reducing other errors to a minimum.
A comparison of the trajectory of an ideal projectile and a projectile produced with the maximum
permissible errors is given.
Chapter eight gives the conclusion of the doctoral dissertation. Scientific contributions of
the dissertation are: 1) improvement of the flight model with six degrees of freedom for
unguided projectiles, in such a way as to enable the implementation of statistical simulations and
analysis of non-deterministic characteristics of projectiles having the unbalanced mass and
asymmetric thrust; 2) determining the functional relationships between mass imbalance and
thrust asymmetry and increased impact points dispersion area, by using statistical methods; 3)
improving the assessment of the allowable limits of non-deterministic projectile design errors,
according to the allowable limits of the projectile impact points dispersion area.
Finally, possible directions for further research are given.