Experimental investigation of weapon system mounted on

Mathematical Methods in Science and Mechanics
Experimental investigation of weapon system mounted on track vehicle
JIRI BALLA, ZBYNEK KRIST, CONG ICH LE
Department of Weapons and Ammunition
University of Defence
Kounicova street 65, 662 10 Brno
CZECH REPUBLIC
[email protected], [email protected], [email protected], http://www.unob.cz)
Abstract: - The purpose of this article is to familiarize with an attitude of research of automatic weapons
mounted on vehicles. Procedures enabling to determine the exciting force from weapon to the mount, angular
movement of weapon turret, elevating parts, and recoil of automatic cannon barrel are discussed. The analyses
technique of measurements results using FFT and correlation functions have been applied on real system
having double 30mm automatic cannons mounted on the board cradle, and on the turret.
Key-Words: - Automatic weapon, Combat vehicle, Dynamic model, Exciting force, Weapon mounting, Turret,
Elevating parts, Cradle, Correlation function, Spectrum analysis
1 Introduction
 - angular displacement of hull,
Analyses of mounts and carriages vibration of
weapon systems when fire burst revealed that the
cardinal reason defending to successful research in
this area is not sufficient experimental base for
measuring on weapon system vibration in extreme
conditions, [1], [2]. Successful managing of whole
complex questions connecting with measuring in
these conditions exceeds possibilities of an
individual workplace as are the apparatus, and
know-how published in measuring methodologies.
Pursuit of achievement of the high hit probability of
the air targets in course of burst antiaircraft firing
lead to lowering of vibrations of the main parts of
the tube weapon systems. Ways how to determine
weapon system vibrations are three. One of them is
pure calculation method of the main parts
movements. The second is pure experimental
investigation of the oscillations of the hull, turret,
and elevation parts. The last technique is a
combination of both previous together with retrieval
of the forces acting onto the weapon. In [3], [4]
there were published the dynamic model having
eight DOF (degrees of freedom). Some
characteristics used there were set experimentally on
the real system. The considered system, see Fig. 1,
has the structure according to the Fig. 2 where the
coordinates are labeled as follows:
xV
yV
V
xE
yE
[q] = [yko, , xv, yv, v, xE, yE, E ],
Fig. 1: Dynamic model
All bodies are connected with reduced flexible
bindings indicated as ki. This article deals with an
experimental attitude in dynamic problem solution.
- longitudinal displacement of turret,
- vertical displacement of turret,
- angular displacement of turret,
- longitudinal displacement of elevating parts,
- vertical displacement of elevating parts,
E - angular displacement of elevating parts.
(1)
where
yko - vertical displacement of hull,
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Mathematical Methods in Science and Mechanics
analog tape recorders with limited number of
channels had to be used two for individual signals
after their amplifying, see Fig. 4, where the
measuring chain is introduced.
FL
aKP
yVP
yVZ
Hartmann Braun amplifier
xZ
KWS amplifier
1st recorder
2nd recorder
Fig. 4: Measuring chain
Fig. 2: Weapon structure
From experience the estimated maximal frequency
of the mechanical system had been set at 300 Hz,
and then the 615 Hz sampling frequency has been
sufficient for purposes of signals digitalization.
Before digitalization the signals had been filtered
with low-pass filters as follows: FL , aKP - 300 Hz,
yVP , yVZ - 200 Hz, xZ - 120 Hz.
Afterwards signals have been analyzed using of the
Next View® software, see [5], and then the results
have been exported in Microsoft Excel® format for
final drawing in MATLAB® software. The selected
sampling frequency gives the maximal frequency
307 Hz during determination of the spectrum
density estimations from the formula
2 Problem Formulation
Fig. 3 shows location of gauges used for
identification of main parameters of the cradle, and
turret. On the weapon system there were measured
the following characteristics:
- xZ linear displacement of recoiling barrel,
- FL forces acting onto carriage during burst fire,
- aKP vertical acceleration of board cradle,
- yVP , yVZ linear displacements of the front, and
rear of turret with respect to the hull.
GXX  f  
2
2
 X T  jf  ,
T
(2)
where
X T  jf  - Fourier transform of signal,
T – length of signal, f – frequency, j – imaginary
unit.
Fig. 3: Gauges location on weapon system
The minimal length of signal T and the minimal
frequency in signal spectrum fmin are connected with
equation
These parameters will be successively discussed in
the next parts. The xZ barrel recoil stroke was
determined with the W20 inductance gauge having
the ±20 mm measuring range.
The HBM
(Hottinger Baldwin Messtechnik), force transducers
(strain gauges) located on the weapon casing have
been electrically connected into the Wheatstone
bridge and after a laboratory calibration have been
found out forces acting from weapon casing onto a
board cradle. The vertical acceleration of the cradle
was measured using of the tensometric
accelerometer BWH 401 with 5000 m∙s-2 limited
acceleration value. The vertical displacements of the
turret were determined with two W5 inductance
gauge having the ± 5 mm measuring range. The
ISBN: 978-960-474-396-4
T
8
f min
.
(3)
This formula explains the fact that in course of the
spectral power density calculations the shift of the
lowest frequencies contained in the spectrum signal
to the higher frequencies can occur. The results of
the experiments without any corrections in Fig. 5
and Fig. 6 show that records are shifted in time, and
they have to be reconstructed to obtain right values,
mainly for the turret motion. Fig. 5 shows the xZ1
record of the barrel recoil during the same six-round
167
Mathematical Methods in Science and Mechanics
burst, and Fig. 6 the same motion recorded in the
xZ2 signal serving as
second recorder as
The first records will be move forward according to
the lag time between both records caused by the
different tape speed, and the different time of tapes
starting. In addition, the second record of the barrel
recoil xZ2 is distorted after the third shot during
synchronizing one. Every shot occurs when the
barrel recoil stroke has minimal (negative) value
since the weapon is operates as soft recoil system,
see [6], [7], [8], [9], [10], [11], and [12], where the
barrel is moving forward before shot. Externally
powered weapons are loaded by the different way,
theoretically easier, see [13].
 
its registering. But the beginning of this registration
is clear and it corresponds to the first record xZ1 .
 
The correlation theory enables to set the lag time,
and to give the all signals into the time alignment.
This solution will be used in the part of dealing with
the turret angular vibration, see [14], [15], and [16].
80
FL (kN)
60
40
20
0
0
0.1
0.2
0.3
0.4
0.5
0.6
time (s)
0.7
0.8
0.9
3 Problem Solution
1
3.1 Forces acting onto mount
For automatic weapons held in any type of mount it
is necessary to know the forces acting on the
different parts of the weapon mount during firing.
The firing force is represented by vector acting in
the center of gravity of recoiling parts in parallel
direction with a barrel axis. The variation of the
applied force with respect to time depends on the
firing force, its damping and the type of automatic
system used. Maximum force of shot is very high
(250 kN for 30 mm cannon for example), and
therefore the barrel (or the whole weapon with fixed
barrel) is designed as recoiling. It is explained on
the examples of Czech 30 mm AA gun M53/59
during burst firing, see [1] and 5.56 mm rifle FNC,
see [2]. The forces applied to the automatic weapon
mount are periodic in nature. Displacement
transducers (for a barrel recoil), and strain gauges
(for determining of the time when the projectile
leaves the barrel) was used, see Fig. 7, Fig. 8. The
variation in firing force over a six-shot burst was
shown in Fig. 5 before. It can be seen that the force
transmitted to the mount has a maximum value for
the first shot fired. For the second shot there is a
reduction in the firing force which is still further
reduced for the third shot. From the analysis follows
that the maximum force applied to the mount occurs
at the instant when the barrel is arrested and the
breech carrier begins to act on the buffer, see [1].
aKP (m.s )
100
-2
50
0
-50
-100
0
0.1
0.2
0.3
0.4
0.5
0.6
time (s)
0.7
0.8
0.9
1
1
yVP (mm)
0.5
0
-0.5
0
0.1
0.2
0.3
0.4
0.5
0.6
time (s)
0.7
0.8
0.9
1
0
0.1
0.2
0.3
0.4
0.5
0.6
time (s)
0.7
0.8
0.9
1
xZ1 (mm)
20
10
0
-10
-20
Fig. 5: First recorder.
yVZ (mm)
1
0.5
0
-0.5
0
0.1
0.2
0.3
0.4
0.5
0.6
time (s)
0.7
0.8
0.9
1
Detail
0.02
xZ2 (m)
0.01
T1
0
T2
gauge moving part
fixed part
-0.01
-0.02
Detail
0
0.1
0.2
0.3
0.4
0.5
0.6
time (s)
0.7
0.8
0.9
1
Fig. 6: Second recorder
Fig. 7: Position of recoil gauge on 30 mm cannon
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Mathematical Methods in Science and Mechanics
acceleration individual components contained in the
signal spectrum.
1
Detail
0.8
Detail
0.6
T3
T4
0.4
T4
T2
0.2
Right side of weapon
casing
0
Left side of weapon
casing
0
Fig. 8: Position of force gauges on 30 mm cannon
200
400
600
800
1000
1200
Fig. 10: Correlation function of cradle acceleration
The spectral density variation of the firing force
acting on the mount is shown in Fig. 9, where the
basic frequency of 7.5 Hz is given by the rate of fire.
Frequencies of 15 Hz, 23 Hz and 30 Hz are higher
harmonics, and they can belong to the other weapon
parts. For example 23 Hz is contained in the turret
vibration. The force magnitude belonging to the
basic frequency is much greater than other higher
harmonics components. It was used for calculation
of the firing stability which allows quick and simple
substitution of the force applied to the mount by
analytical formula, see [2], [3], [6], [10], and [12].
7
6
5
GXX
4
3
2
1
0
5000
0
50
100
150
200
250
300
350
f (Hz)
4500
X: 7.609
Y: 4563
Fig. 11: Spectrum density of cradle acceleration
4000
The other cradle kinematic parameters as are the
absolute velocity and the absolute displacement with
respect to the basic system can be calculated by way
of the double integration of the cradle acceleration.
It is necessary to note that they would be absolute
parameters with respect to the earth. Since there was
used only one sensor were not possible to get the
angular motion of the elevation parts. Then the
results can be used for the estimation of the linear
vibration of the system after the end of the fire. The
last 100 samples were inserted for the spectrum
density calculation of the cradle linear vibration.
The result is depicted in Fig. 12.
3500
X: 15.22
Y: 2933
GXX
3000
X: 22.83
Y: 2310
2500
2000
1500
1000
500
0
0
50
100
150
f (Hz)
200
250
300
Fig. 9: Spectral density of forces 30 mm AA cannon
3.2
6
Cradle vibration
5
From the time course of the linear cradle
acceleration in Fig. 4 is possible to estimate that it
has spread spectrum and the normalized correlation
function is very narrow. Fig. 10 and Fig. 11 confirm
these
prerequisites.
The
basic
statistical
characteristics of the aKP cradle acceleration are
mean value = 0.51m∙s-2, minimal value = -117 m∙s-2,
maximal value = 131 m∙s-2, standard deviation = 31
m∙s-2, and median = - 2.29 m∙s-2. High values of the
acceleration likely belong to the instant values of the
ISBN: 978-960-474-396-4
G
XX
4
3
2
X: 18.46
Y: 2.421
X: 43.08
Y: 2.341
1
0
0
50
100
150
f (Hz)
200
250
300
Fig. 12: Spectrum of disappearing cradle vibration
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Mathematical Methods in Science and Mechanics
The frequency about 18 Hz belongs to the linear
vibration f y of the turret and higher 43 Hz belongs
The individual stiffness in the dynamic model can
be set according to the given DOF. In Fig. 1 the
whole linear stiffness in the vertical direction is
(6)
ky  k3  k4 ,
V
to the elevating parts (cradle) vibration.
V
for example.
Fig. 4 and Fig. 5 show that both signals are time
postponed due to of time different records of the
barrel recoil xZ1 and xZ2 , yVP and yVZ . It is
3.3
Turret vibration
The turret motion was measured with respect to
the hull. Identically as at the cradle
disappearing vibration we can proceed
according to the previous case for linear turret
vibration. The significant frequencies are
nearby the frequencies belonging to the cradle.
necessary to give them into the same time relation.
The correlation theory is one of the best procedures
how to do it. The maximum value of the Rx Z , x Z
1
2
cross-correlation function between xZ1 , and xZ2
Although the courses of the turret linear
displacement are enough different in Fig. 5, Fig. 6,
the significant similarity is clear from their
spectrums. Fig 13 is the evidence, and the turret
spectrum yvp is very similar with the main
frequencies.
signals which are stored in both recorders indicates
time lags between them, see [13]

 delay  arg max Rx
Z1 , x Z2
.
(7)
After insertion into (7), the time delay is 0.112s and
it corresponds to 69 postponed samples, see Fig. 14.
1
1
0.8
0.8
X: 7.586
Y: 0.6271
0.6
GXX
RXZ1,XZ2
0.6
0.4
X: 22.76
Y: 0.3071
0.4
0.2
0
0.2
-0.2
0
0
50
100
150
200
f (Hz)
250
300
-0.4
-600
350
Fig. 13: Turret spectrum yvp
V
determine the angular stiffness of the turret elastic
bearing on the hull in model displayed in Fig. 1.
When we know turret mass moment of inertia with
respect to the transverse axis passing through the
gravity center IV, the turret angular stiffness k γ is
V

kγ  I V 2 f γ
V
.
2
V
(4)
The linear stiffness of the turret elastic bearing on
the hull k γ in the vertical direction is defined by the
y
similar way, where mV is turret mass

kγ  mV 2 f y
y
.
2
V
ISBN: 978-960-474-396-4
-200
0
200
sample
400
600
Fig. 14: Cross-correlation function
Then the angular displacement of the turret with
respect to the hull can be determined using simple
relation
y  yVZ
 V  VP
,
(8)
lS
where
lS is known distance between both turret sensors.
The time course of the angular turret vibration with
respect to the hull is shown in Fig. 15. The better
interpretation of the turret motion gives
autocorrelation function and the spectral density of
vibrations. Figures 16 and 17 prove it. In the
autocorrelation function, see Fig. 16, there are
distinct peaks belonging to individual shots, and it is
shown in Fig. 13 where the basic fire frequency is
7.5 Hz as it was explained in Fig. 9, and Fig. 12.
The frequency 22.7 Hz is natural frequency of the
turret angular vibration.
The frequency about 7.5 Hz is rate of fire, and 22.7
Hz is natural frequency of the turret angular
vibration f γ . The important result is that we can
given as
-400
(5)
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Mathematical Methods in Science and Mechanics
elevating parts, and weapons as well. All these
clearances are not possible to express because they
are not known their size, and they change in course
of the use.
0.8
0.6
 V (mrad)
0.4
4 Conclusion
0.2
The new experimental procedures for estimating of
the dynamic parameters of the burst firing automatic
weapons have been proposed. Using of the
correlation and spectral analysis have been revealed
substantial properties of the weapon system parts as
are natural frequencies, dependences of the
individual parts on the behavior of the whole
system, and each other. Finally, the procedures can
serve as methodology for an investigation of the
other similar systems. The problems, which were
shown in this paper, are the ground of the theory,
and the other investigation of automatic weapons
mount dynamics problems, see [4], [6], [10], [11],
[12] , and [13].
0
-0.2
-0.4
-0.6
0
0.1
0.2
0.3
0.4
0.5
0.6
time (s)
0.7
0.8
0.9
1
Fig. 15: Angular turret vibration
1
0.8
0.6
Acknowledgment:
The work presented in this paper has been supported
by the research projects of University of Defence,
Brno, Czech Republic: Research project of
Department of Weapons and Ammunition 2014.
0.4
0.2
0
-0.2
-0.4
0
200
400
600
800
1000
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Fig. 16: Turret autocorrelation function
0.2
0.18
X: 7.586
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0.12
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0.06
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0
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ISBN: 978-960-474-396-4
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172

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