Research of the mine imitator interaction with deformable soil and its practical realisation/Minosvaidzio minos imitatoriaus ir besideformuojancio pavirsiaus sa veikos tyrimas ir praktinis pritaikymas.
Fedaravicius, A. ; Kilikevicius, S. ; Survila, A. 等
1. Introduction
The mine imitator's facilities are designed for artillery
specialists training. The simulator consists of a housing the external
surface of which in fact reconstructs contour of the mine with a barrel
and charge installed inside. With the purpose to imitate blast of the
mine the simulator the charge of which is filled with smoke gunpowder is
fired at the necessary distance and then when falling and hitting the
soil it is initiated thus imitating the blast. The simulator has four
parts which consist of the mine imitator, the shell and the charges with
the corresponding amount of gunpowder, what ensures semi-natural field
firing at the distances scaled by the factor of 1/10 with respect to the
natural ones. When the mine imitator hits the soil surface the detonator
is initiated thus imitating the blast and "smoke cloud"
appearance [1].
The simulator should ensure reliable performance of the mine
imitator using it at different conditions of soil surfaces. This is
predefined by sufficient displacement of the detonator's stud with
respect to the capsule during interaction process of the
detonator's cap and the soil. Mathematical model of the interaction
of the simulator and the soil and the results obtained are presented in
the following sections [2].
In the problem analysed two aspects can be
distinguished--displacement of the free falling shell structure and its
deformation at the interaction with the mass (body), which has
characteristic elastic--dissipative properties as in analysed in
literature [3, 4]. But the analysed case is distinctive by the fact that
the process under analysis evolves at the same time and parameters and
characteristics of certain dynamical system are evaluated.
Strength characteristics of the soil due to dynamic effects
strongly depend on microstructure of the soil, the size and distribution
of its grains. Humidity level of the soil has a certain effect on
initiation of the imitator. Pores in between the grains can be filled
with air or water.
A mathematical model of the interaction of the mortar mine imitator
and the soil is presented in the paper. Simulation of the mine's
imitator penetration into the soil is performed using MATLAB software.
FEM simulation of the penetration is also performed by LS-DYNA FEM code.
The penetration characteristics obtained by the simulation both using
MATLAB and LS-DYNA has similar tendencies.
2. Dynamical model of the interaction of mortar mine's
imitator and the soil
Dynamical model of the interaction of the mortar mine's
imitator and the soil is constructed with the purpose to determine
penetration rate of the imitator, its penetration depth and displacement
of the stud of the detonator's cap towards capsule-detonator. These
three main parameters are described by two differential equations of
motion.
Dynamical model of the interaction of the mortar mine's
imitator and the soil is presented in Fig. 1.
[FIGURE 1 OMITTED]
Equations of motion
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]
where [m.sub.2] is mass of the body of the mine imitator; [m.sub.1]
is mass of the cap of the mine imitator; [c.sub.1], [b.sub.1] are
stiffness and damping coefficients of the soil for which elasticity and
damping properties are characteristic; [c.sub.2], [b.sub.2] are
stiffness and damping coefficients of the cap.
From the presented above model in the form of differential
equations of motion it can be concluded that depending on the parameter
values motion of the system can be of two types--nonperiodic or
oscillatory with decaying amplitude.
Stiffness and damping coefficients of the soil for which elasticity
and damping properties are characteristic and the cap in the lumped
parameter model presented above are selected as presented in Table.
Also the two main parameters are selected as follows: the mass of
mine imitator's cap [m.sub.1] = 0.005 kg and the mass of mine
imitator's body [m.sub.2] = 0.25 kg.
3. Results of the theoretical research
The dependences of penetration rate of the mine imitator,
displacement of the stud of the detonator's cap towards
capsule-detonator and penetration depth of the mine imitator into the
soil on time obtained by the simulation using MATLAB 6 [5] and LS-DYNA
[6] are shown in Figs. 2 and 3.
[FIGURE 2 OMITTED]
The dependences of penetration rate of the mine imitator and
displacement of the stud of the detonator's cap towards
capsule-detonator are shown in Fig. 3, a and b at different
imitator's initial speeds--v = 35, 45, 52 m/s.
The penetration rate after the imitator hits the soil starts to
decay. Simultaneously after hitting the soil by the imitator the
displacement of the stud of the detonator's cap A grows with time
until it reaches capsule-detonator. For initiation of the detonator the
displacement of the stud towards capsule-detonator should be not less
than 2.5 mm. The obtained results show that the detonator will be
initiated at the hitting speed of v = 52 m/s.
[FIGURE 3 OMITTED]
The most important indicators of the penetration of the mine
imitator into the soil are penetration rate of the mine imitator and
composition of the soil. The more porous is the soil the greater
penetration depth will be reached. Penetration depth of the mine
imitator into the soil (the soil--sand) in dependence on penetration
rate is shown in Figs. 4 and 5.
[FIGURE 4 OMITTED]
[FIGURE 5 OMITTED]
Comparison of the simulation results obtained using MATLAB 6
software and LS-DYNA FEM code indicate that the displacement of the stud
of the detonator's cap towards capsule-detonator and the
penetration rate of the mine imitator coincide with sufficient level.
The contact force acting the cap reaches the maximum value at the
beginning of the penetration into the soil material. The FE simulations
shows that in case of soft sand soil and impact velocity v = 35 m/s, the
reliability of mine imitator is on the limit to initiate explosion. It
is obtained, that the cap deforms just in first 20 mm of penetration.
This also seen from the cap deformations presented in Fig. 6, b
comparing to the initial form Fig. 6, a. Residual impact energy (about
99% at v = 35 m/s) is absorbed only by deformations of the soil
material.
[FIGURE 6 OMITTED]
Comparing the structural behaviours of mine imitator was estimated
that the deformations of the caps in all analyzed velocities were
similar. In all cases cap deforms similarly and differs just final
penetration depth of the soil.
4. Experimental field tests and practical realisation
The trainer is used at different soil surface conditions and should
ensure the reliable performance of the mine imitator. This is predefined
by sufficient displacement of the detonator's stud with respect to
the capsule during interaction process of the detonator's cap and
the soil. The methodics of experimental interaction research of
detonator's cap of the mine imitator and non deformable or
deformable surface, test rig structure and results of the performed
experiments are presented in this section.
Experimental field tests of the developed training facilities were
performed. For this purpose a batch of 100 test imitators was
manufactured. Imitators of the batch were tested simulating all firing
charges and all firing angles -45[degrees], 60[degrees], 80[degrees].
There were at all no non performance cases during the tests.
For test simulation cap views of the mine imitator after initiation
when firing with initial speed v = 45 m/s at
45[degrees], 60[degrees], 80 firing angles are shown in Fig. 7. The
60 mm and 120 mm mortar training equipment was created on the basis of
obtained theoretical and experimental research results (Fig. 8).
This equipment was successfully implemented in practice for
training of solders and combat units.
[FIGURE 7 OMITTED]
[FIGURE 8 OMITTED]
5. Conclusions
1. Dynamical and mathematical models of the interaction of the
mortar mine's imitator and the soil are developed, FEM model is
generated by LS-DYNA code, the characteristics of penetration rate and
depth of the imitator into the soil, the displacement of the stud of the
detonator's cap towards capsule-detonator are determined.
2. Comparison of the simulation results obtained using MATLAB 6
software and LS-DYNA FEM code indicate the sufficient level of their
agreement.
3. The created semi natural mortar shooting equipment in
successfully implement in practice.
Acknowledgements
This research was funded by a grant (No MIP89/2010) from the
Research Council of Lithuania.
Received March 10, 2011
Accepted December 05, 2011
References
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(online) Southampton, UK, 381-389.
[2.] Fedaravicius, A.; Griskevicius, P.; Saulys, P.; Klimavicius,
Z.; Patasiene, L. 2008. Experimental research of mine imitator
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of Armament and Safety Technology, Volume II,--ISBN 978-83-98399-94-6,
Warsaw, Poland, 537-542.
[3.] Kabelkaite, A.; Miliunas, L.; Kibirkstis, E.; Ragulskis, L.;
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[4.] Gonca, V.; Shvab, J. 2010. Design of elastomeric shock
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ISSN 1392-8716, 347-354.
[5.] A Guide to MATLAB, 2-nd edition. 2006. Cambridge University
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[6.] ANSYS CFX-Solver Theory Guide, ANSYS, Inc. Southpointe 275
Technology Drive Canonsburg, PA 15317, 53-96.
A. Fedaravicius *, S. Kilikevicius **, A. Survila ***, P. Saulys
****, V. Lendraitis *****
* Kaunas University of Technology, K?stucio 27, 44312 Kaunas,
Lithuania, E-mail:
[email protected]
** Kaunas University of Technology, K?stucio 27, 44312 Kaunas,
Lithuania, E-mail:
[email protected]
*** Kaunas University of Technology, K?stucio 27, 44312 Kaunas,
Lithuania, E-mail:
[email protected]
**** Kaunas Technical College, Tvirtoves al. 35, 50155 Kaunas,
Lithuania, E-mail:
[email protected]
***** Kaunas Technical College, Tvirtoves al. 35, 50155 Kaunas,
Lithuania, E-mail:
[email protected]
Table
Stiffness and damping coefficients
[c.sub.1] [c.sub.2]
Stiffness coefficient 10 N/m 57 N/m
[b.sub.1] [b.sub.2]
Damping coefficient 2.5 Ns/m 5 Ns/m