Lalanne C. Mechanical Vibrations and Shocks: Mechanical Shock Volume II
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224
Mechanical
shock
variations observed
are not in a
range which includes
the
resonance frequencies
of
the
test
item.
This example
was
treated
for a
shock
on
shaker carried
out
with symmetrical
pre-
and
post-shocks.
Let us
consider
the
case
where only
one
pre-shock
or one
post-
shock
is
used. Figure 7.28 shows
the
response spectra
of:
- the
nominal signal (half-sine,
500
m/s
2
,
10
ms);
- a
shock
on a
shaker with only
one
post-shock (half-sine,
p =
0.1)
to
cancel
the
velocity
change;
- a
shock
on a
shaker with
a
pre-shock alone;
- a
shock
on a
shaker
with
identical pre-
and
post-shocks.
Figure 7.28.
Influence
of
the
distribution
of
pre-
and
post-shocks
on the SRS
of
a
half-sine
shock
It
is
noted that:
-the variation between
the
spectra decreases when pre-shock
or
post-shock
alone
is
used.
The
duration
of the
signal
of
compensation being then larger,
the
spectrum
is
deformed
at a
lower
frequency
than
in the
case
of
symmetrical pre-
and
post-shocks;
- the
pre-shock alone
can be
preferred with
the
post-shock,
but the
difference
is
weak.
On
the
other hand,
the use of
symmetrical pre-
and
post-shocks
has the
already
quoted well-known advantages.
Generation
of
shocks
using
shakers
225
NOTE:
In the
case
of
heavy
resonant test items,
or
those assembled
in
suspension,
there
can be a
coupling between
the
suspended mass
m and the
mass
M
of
the
coil-
table
-fixture
unit, with resulting modification
of
the
natural frequency according
to
the
rule:
Figure 7.29 shows
the
variations
of
0
/f
0
according
to the
ratio
m / M. For m
close
to M, the frequency f
0
can
increase
by a
factor
of
about 1.4.
The
stress
undergone
by the
system
is
therefore
not as
required.
Figure 7.29.
Evolution
of
the
natural
frequency
in the
event
of
coupling
This page intentionally left blank
Chapter
8
Simulation
of
pyroshocks
Many
works have been published
on the
characterization, measurement
and
simulation
of
shocks
of
pyrotechnic origin (generated
by
bolt cutters, explosive
valves, separation
nuts,
etc) [ZIM 93].
The
test
facilities
suggested
are
many,
ranging
from
traditional machines
to
very exotic means.
The
tendency today
is to
consider that
the
best simulation
of
shocks measured
in
near-field
(cf. Section 3.9)
can be
obtained only
by
subjecting
the
material
to the
shock produced
by the
real device (which
poses
the
problem
of the
application
of an
uncertainty factor
to
cover
the
variability
of
this shock).
For
shocks
in the
mid-field
,
simulation
can be
carried
out
either using real
the
pyrotechnic source
and a
particular mechanical assembly
or
using specific
equipment
using explosives,
or by
impacting metal
to
metal
if the
structural
response
is
more important.
In the
far-field,
when
the
real shock
is
practically made
up
only
of the
response
of the
structures,
a
simulation
on a
shaker
is
possible (when
use
of
this method allow).
8.1. Simulations using pyrotechnic facilities
If
one
seeks
to
carry
out
shocks close
to
those experienced
in the
real
environment,
the
best simulation should
be the
generation
of
shocks
of a
comparable
nature
on the
material concerned.
The
simplest solution consists
of
making
functional
real pyrotechnic devices
on
real structures. Simulation
is
perfect
but
[CON
76], [LUH 76]:
228
Mechanical
shock
- It
can
be
expensive
and
destructive.
-One cannot apply
an
uncertainty
factor
without being
likely
to
create
unrealistic local damage
(a
larger load,
which
requires
an
often
expensive
modification
of the
devices
can be
much more destructive).
To
avoid this problem,
an
expensive solution consists
of
carrying
out
several tests
in a
statistical matter.
One
often
prefers
to
carry
out a
simulation
on a
reusable assembly,
the
excitation
still being pyrotechnic
in
nature. Several devices have been designed. Some
examples
of
which
are
described
below:
1.
A
test
facility
made
up of a
cylindrical structure [IKO
64]
which
comprises
a
'consumable' sleeve
cut out for the
test
by an
explosive cord (Figure 8.1).
Preliminary tests
are
carried
out to
calibrate 'the facility' while acting
on the
linear
charge
of the
explosive cord and/or
the
distance between
the
equipment
to be
tested
(fixed
on the
structure
as in the
real
case
if
possible)
and the
explosive cord.
Figure 8.1.
Barrel
tester
for
pyroshock
simulation
2. For a
large-sized structure subjected
to
this type
of
shock,
one in
general
prefers
to
make
the
real pyrotechnical systems placed
on the
structure
as
they could
under
operating conditions.
The
problem
of the
absence
of the
uncertainty
factor
for
the
qualification tests remains.
3.
D.E. White, R.L. Shipman
and
W.L. Harlvey
proposed
placing
a
greater
number
of
small explosive charges near
the
equipment
to be
tested
on the
structure,
in
'flowers
pots'.
The
number
of
pots
to be
used axis depends
on the
amplitude
of
the
shock,
of the
size
of the
equipment
and of the
local geometry
of the
structure.
They
are
manufactured
in a
stainless
steel pipe which
is
10cm
in
height,
5 cm in
interior diameter,
15 cm in
diameter external
and
welded
to
approximately
13 mm
steel base plates [CAR 77],
[WHI65].
Simulation
of
pyroshocks
229
Figure
8.2.
'Flower
pot
'provided with
an
explosive charge
A
number
of
preliminary shots, reduced
as a
result
of
experience
one
acquires
from
experiment,
are
necessary
to
obtain
the
desired shock.
The
shape
of the
shock
can be
modified within certain limits
by use of
damping
devices, placing
the pot
more
or
less close
to the
equipment,
or by
putting suitable
padding
in the
pot.
If, for
example,
one
puts sand
on the
charge
in the
pot,
one
transmits
to the
structure more
low frequency
energy
and the
shape
of the
spectrum
is
more regular
and
smoother.
One can
also place
a
crushable material between
the
flower
pot and the
structure
in
order
to
absorb
the
high
frequencies.
When
the
explosive charge necessary
is
substantial,
this
process
can
lead
to
notable permanent deformations
of the
structure.
The
transmitted shock then
has an
amplitude lower than that sought and,
to
compensate,
one can be
tempted
to use a
larger charge
with
the
following shooting.
To
avoid entering this vicious circle,
it is
preferable,
with
the
next shooting, either
to
change
the
position
of the
pots,
or to
increase
the
number
by
using weaker charges.
The
advantages
of
this method
are the
following:
- the
equipment
can be
tested
in its
actual assembly configuration;
-
high intensity shocks
can be
obtained simultaneously along
the
three principal
axes
of the
equipment.
There
are
also some drawbacks:
-no
analytical method
of
determination
a
priori
of the
charge
necessary
to
obtain
a
given shock exists;
- the use of
explosive requires testing under specific conditions
to
ensure safety;
-the shocks obtained
are not
very reproducible,
with
many
influential
parameters;
- the
tests
can be
expensive
if,
each time,
the
structure
is
deformed [AER 66].
230
Mechanical shock
4. A
test
facility made
up of a
basic
rectangular
steel
plate (Figure 8.3)
suspended horizontally. This plate receives
on its
lower part, directly
or by the
intermediary
of an
'expendable' item,
an
explosive load (chalk line, explosive
in
plate
or
bread).
Figure
8.3.
Plate with resonant system subjected
to
detonation
A
second plate supporting
the
test
item rests
on the
base
plate
via
four
elastic
supports.
Tests
carried
out by
this means showed that
the
shock spectrum generated
at the
input
of the
test item depends
on:
-
the
explosive charge;
- the
nature
and
thickness
of
the
plate carrying
the
test item;
- the
nature
of
the
elastic supports
and
their prestressing;
- the
nature
of
material
of
the
base
plate
and its
dimensions; constituting
-the mass
of the
test
item [THO 73].
The
reproducibility
of the
shocks
is
better
if the
load
is not in
direct contact with
the
base plate.
8.2. Simulation using metal
to
metal impact
The
shock obtained
by a
metal
to
rnetal impact
has
similar
characteristics
to
those
of a
pyrotechnical shock
in an
intermediate
field:
great amplitude; short
duration; high
frequency
content; shock response spectrum comparable with
a low
frequency
slope
of 12 dB per
octave etc. Simulation
is in
general satisfactory
up to
approximately
10
kHz.
Simulation
of
pyroshocks
231
The
shock
can be
created
by the
impact
of a
hammer
on the
structure
itself,
a
Hopkinson
bar or a
resonant plate [BAI 79], [DAY 85], [DAV
92] and
[LUH 81].
Figure 8.5.
Simulation
by the
impact
of
a
ball
on a
steel beam
With
all
these
devices,
the
amplitude
of the
shock
is
controlled while acting
on
the
velocity
of
impact.
The frequency
components
are
adjusted
by
modifying
the
resonant geometry
of
system (length
of the bar
between
two
points
of
fixing,
the
addition
or
removal
of
runners, etc)
or by the
addition
of a
deformable material
between
the
hammer
and the
anvil.
To
generate shocks
of
great amplitude,
the
hammer
can be
replaced
by a
ball
or a
projectile with
a
plane
front
face
made
out of
steel
or
aluminium,
and
launched
by a
pneumatic
gun
(air
or
nitrogen) [DAV 92].
The
impact
can be
carried
out
directly
on the
resonant beam
or to a
surmounted plate
of
a
resonant mechanical system composed
of a
plate supporting
the
test
item
connecting
it to the
impact plate.
8.3. Simulation using electrodynamic shakers
The
possibilities
of
creating shocks using
an
electrodynamic shaker
are
limited
by
the
maximum stroke
of the
table
and
more especially
by the
acceptable maximum
force.
The
limitation relating
to the
stroke
is not
very constraining
for the
pyrotechnical shocks, since they
are at
high frequencies. There remains
a
limitation
on
the
maximum acceleration
of the
shock [CAR 77], [CON 76], [LUH
76] and
Figure
8.4.
Simulation
by
metal
to
metal impact (Hopkinson bar)
232
Mechanical
shock
[POW 76].
If,
with
the
reservations
of
Section
4.3.6,
one
agrees
to
cover only part
of
the
spectrum, then when
one
makes
a
possible simulation
on the
shaker; this gives
a
better
approach
to
matching
the
real spectrum.
Exciters have
the
advantage
of
allowing
the
realization
of any
signal
shape such
as
shocks
of
simple shapes [DIN 64], [GAL 66],
but
also random noise
or a
combination
of
simple elementary signals with
the
characteristics
to
reproduce
a
specified
response spectrum
(direct
control
from a
shock spectrum,
of.
Chapter
9).
The
problem
of the
over-testing
at low frequencies as
previously discussed
is
eliminated
and it is
possible,
in
certain
cases,
to
reproduce
the
real spectrum
up to
1000
Hz. If one is
sufficiently
far
away
from the
source
of the
shock,
the
transient
has a
lower level
of
acceleration
and the
only limitation
is the
bandwidth
of the
shaker,
which
is
about 2000
Hz.
Certain facilities
of
this type were
modified
in the
USA
to
make
it
possible
to
simulate
the
effects
of
pyrotechnical shocks
up to
4000
Hz.
One can
thus manage
to
simulate shocks whose spectrum
can
reach 7000
g
[MOE
86].
We
will see, however,
in
Chapter
9 the
limits
and
disadvantages
of
this
method.
8.4. Simulation
using
conventional shock machines
We
saw
that, generally,
the
method
of
development
of a
specification
of a
shock
consists
of
replacing
the
transient
of the
real environment, whose shape
is in
general
complex,
by a
simple shape shock, such
as
half-sine, triangle, trapezoid etc, starting
from
the
'shock
response spectrum' equivalence criterion (with
the
application
of a
given
or
calculated
uncertainty
factor^
to the
shock amplitude) [LUH 76].
With
the
examination
of the
shapes
of the
response
spectra
of
standard
simple
shocks,
it
seems that
the
signal
best
adapted
is the
terminal peak
saw
tooth pulse,
whose
spectra
are
also appreciably symmetrical.
The
research
of the
characteristics
of
such
a
triangular impulse (amplitude, duration) having
a
spectrum envelope
of
that
of a
pyrotechnical shock
led
often
to a
duration
of
about
1ms and to an
amplitude being able
to
reach several tens
of
thousands
of
ms"
1
.
Except
in the
case
of
very
small
test
items,
it is in
general
not
possible
to
carry
out
such shocks
on the
usual drop tables:
-
limitation
in
amplitude
(acceptable
maximum
force
on the
table);
-
duration limit:
the
pneumatic programmers
do not
allow
it to go
below
3 to
4 ms.
Even with
the
lead programmers,
it is
difficult
to
obtain
a
duration
of
less than
2 ms.
However spectra
of the
pyrotechnical shocks with,
in
general, averages close
cf.
Volume
5.
1
Simulation
of
pyroshocks
233
to
zero have
a
very weak slope
at low frequencies,
which leads
to a
very small
duration
of
simple shock,
of
about
one
millisecond
(or
less);
- the
spectra
of the
pyrotechnical
shocks
are
much more
sensitive
to the
choice
of
damping than simple
shocks
carried
out on
shock machines.
To
escape
the
first
limitation,
one
accepts,
in
certain cases, simulation
of the
effects
of the
shock only
at low frequencies, as
indicated
in
Figure 8.6.
The
'equivalent'
shock
has in
this
case
a
larger amplitude
since
f
a
, the
last
covered
frequency is
higher.
Figure 8.6.
Need
for
a
TPS
shock
pulse
of
very
short
duration
Figure 8.7.
Realizable
durations
lead
to an
over-test
With
this
approximation,
the
shape
of the
shock
has
little importance,
all the
shocks
of
simple shape having
in the
zone which
interests
us
(impulse
zone)
symmetrical
spectra.
One
however
often
chooses
the
terminal
peak
saw
tooth
to be
able
to
reach,
with lead programmers, levels
of
acceleration
difficult
to
obtain with
other types
of
programmers.
This procedure,
one of the
first
used,
is
open
to
criticism
for
several reasons:
-if the
tested item
has
only
one frequency f
a
,
simulation
can be
regarded
as
correct (insofar
as the
test facilities
are
able
to
carry
out the
specified shock
perfectly).
But
very
often,
in
addition
to a
fundamental
frequency f
f
of
rather
low
resonance such
as one can
realize easily
for f
a
> f
f
, the
specimen
has
other
resonances
at
higher
frequencies
with
substantial
Q
factors.
In
this
case,
all
resonances
are
excited
by
shock
and
because
of the frequency
content particular
to
this kind
of
shock,
the
responses
of the
modes
at
high