Lalanne C. Mechanical Vibrations and Shocks: Mechanical Shock Volume II
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(neglecting
the
kinetic energy
of the
elastic cords).
Figure
6.5.
Principle
of
operation
using elastic
cords
Figure
6.6.
Principle behindpendular shock test machine
If
machine
is of the
pendular type,
the
impact velocity
is
obtained
from
i.e.
where
L is the
length
of the arm of the
pendulum
and a is the
angle
of
drop.
154 Mechanical shock
During impact,
the
velocity
of the
table changes quickly
and
forces
of
great
amplitude
appear between
the
table
and
machine
bases.
To
generate
a
shock
of a
given
shape,
it is
necessary
to
control
the
amplitude
of the
force
throughout
the
stroke during
its
velocity change. This
is
carried
out
using
a
shock programmer.
Figure 6.7.
MRL
universal shock test
machine (impact mode)
Figure 6.8.
MRL
universal shock test
machine (impulse mode)
The
MRL
Company (Monterey Research Laboratory) markets
a
machine
allowing
the
carrying
out of
shocks according
to two
modes: impulse
and
impact
[BRE
66].
In the two
test
configurations,
the
test item
is
installed
on the
upper
face
of
the
table.
The
table
is
guided
by two
rods which
are
fixed
at a
vertical
frame.
Universal
shock test machine
Standard shock machines
155
156
Mechanical
shock
To
carry
out a
test
according
to the
impact mode (general
case),
one
raises
the
table
by the
height required
by
means
of a
hoist attached
to the top of the frame, by
the
intermediary assembly
for
raising
and
dropping (Figure 6.7).
By
opening
the
blocking system
in a
high position,
the
table
falls
under
the
effect
of
gravity
or
owing
to the
relaxation
of
elastic cords
if the
fall
is
accelerated.
After
rebound
on the
programmer,
the
table
is
again
blocked
to
avoid
a
second impact.
NOTE:
A
specific
device
has
been developed
in
order
to
make
it
possible
to
test
relatively
small specimens with
very
short duration high acceleration pulses
(up to
100,000
g,
0.05
ms) on
shock machines which would
not
otherwise
be
capable
of
generating these pulses.
This
shock
amplifier
("Dual mass shock
amplifier",
marketed
by
MRL)
consists
of
a
secondary shock table (receiving
the
specimen)
and
a
massive base which
is
bolted
to the top
of
the
carriage
of
the
shock machine.
When
the
main table impacts
and
rebounds
from
the
programmer
on the
base
of
the
machine
(shock
duration
of
about
6
ms),
the
secondary table,
initially
maintained
above
its
base
by
elastic shock
cords,
continues downward, stretching
the
shock cords.
The
secondary table
impacts
on an
high
density
felt programmer
placed
at the
base
of
the
shock
amplifier,
the
generating
the
high acceleration shock.
The
impulse mode shocks (Figure 6.8)
are
obtained while placing
the
table
on
the
piston
of the
programmer (used
for the
realization
of
initial peak
saw
tooth shock
pulses).
The
piston
of
this hydropneumatic programmer propels
the
table upward
according
to an
appropriate force profile
to
produce
the
specified acceleration signal.
The
table
is
stopped
in its
stroke
to
prevent
its
falling
down
a
second time
on the
programmer.
Pre-
and
post-shocks
The
realization
of
shocks
on free or
accelerated
fall
machines imposes
de
facto
pre- shocks and/or post-shocks,
the
existence
of
which
the
user
is not
always aware,
but
which
can
modify
the
shock severity
at low frequencies
(Section
7.6).
The
movement
of
shock starts with dropping
the
table
from the
necessary height
to
produce
the
specified shock
and finishes
with stopping
the
table after rebound
on the
programmer.
The
pre-shock takes place during
the
fall
of the
table,
the
post-shock
during
its
rebound.
Freefall
Let
us set a as the
rate
of
rebound (coefficient
of
restitution)
of the
programmer.
If
AV is the
velocity change
necessary
to
carry
out the
specified shock
(AV
= J
x(t) dt),
the
carriage rebound velocity
and the
carriage impact velocity
are
Standard
shock machines
AV
related
by
[5.15]
AV =
v
R
-v
i
and v, = . One
deduces
from
this
the
1 + ct
necessary drop height
where
g =
acceleration
due to
gravity.
Figure 6.9.
Movement
of
the
table
The
movement
of the
table
of the
machine since
the
moment
of its
realease
until
impact
is
given
by
yielding,
at
impact,
the
instant
of
time
where
tjis
the
duration
of the
pre-shock,
which
has as an
amplitude
-g.
Since
the
rebound
velocity
is
equal,
in
absolute
terms,
to V
R
= a v
i?
the
rebound
of the
carriage assembly occurs until
a
height
H
R
is
reached
so
that
es
157
158
Mechanical shock
The
whole
of the
movement thus
has the
characteristics summarized
in
Figure
6.10.
and it
lasts
Figure 6.10.
Shock
performed
A
cceleratedfall
Let
us set m as the
total impacting mass (table
+
fixture
+
test item),
and k as the
stiffness
of the
elastic
cords.
Figure
6.11. Movement
of
the
table during
accelerated
fall
and
the
duration
of the
pre-shock
is
Standard shock machines
159
The
differential equation
of the
movement
has as a
solution
where
yielding
At
impact,
z = 0 and t = t;
such that:
In
addition
The
impact velocity
is
equal
to
yielding
160
Mechanical shock
After
the
shock,
the
rebound
is
carried
out
with velocity
V
R
= a v, . We
have
in
the
same
way
and
6.3. High impact shock machines
6.3.1.
Lightweight
high
impact shock machine
This
machine
was
developed
in
1939
to
simulate
the
effects
of
underwater
explosions (mines)
on the
equipment onboard military ships. Such explosions, which
occur basically large distances
from the
ships, create shocks which
are
propagated
in
all the
structures.
The
high impact shock machine
was
reproduced
in the
United
States
in
1940
for use
with light equipment;
a
third machine
was
built
in
1942
for
heavier
equipment
of
masses ranging between
100 and
2500
kg
[VIG 6la] (Section
6.3.2).
Standard shock machines
161
Figure
6.12. High
impact
shock
machine
for
lightweight
equipment
The
procedure
consisted
not of
specifying
a
shock
response
spectrum
or a
simple
shape shock,
but
rather
of the
machine being used,
the
method
of
assembly,
the
adjustment
of the
machine etc.
The
machine consists
of a
welded
frame of
standard steel sections,
of two
hammers,
one
sliding vertically,
the
other describing
an arc of a
circle
in a
vertical
plane,
according
to a
pendular motion (Figure 6.12).
A
target plate carrying
the
test item
can be
placed
to
receive
one or the
other
of
the
hammers.
The
combination
of the two
movements
and the two
positions
of the
target makes
it
possible
to
deliver shocks according
to
three perpendicular directions
without
disassembling
the
test item.
Each
hammer weighs approximately
200 kg and can
fall
a
maximum height
of
1.50
m
[CON 52].
The
target
is a
plate
of
steel
of 86 cm x 122 cm x 1.6 cm,
reinforced
and
stiffened
on its
back
face
by
I-beams.
In
each
of the
three impact positions
of the
hammer,
the
target plate
is
assembled
on
springs
in
order
to
absorb
the
energy
of the
hammer with
a
limited displacement
(38 mm to the
maximum). Rebound
of the
hammer
is
prevented.
Several intermediate standardized plates simulate various conditions
of
assembly
of
the
equipment
on
board.
These
plates
are
inserted between
the
target
and the
equipment
tested
to
provide certain insulation
at the
time
of
impact
and to
restore
a
shock considered comparable with
the
real
shock.
162
Mechanical shock
The
mass
of the
equipment tested
on
this machine should
not
exceed
100 kg. For
fixed
test
conditions (direction
of
impact, equipment mass, intermediate plate),
the
shape
of the
shock obtained
is not
very sensitive
to the
drop height.
The
duration
of
the
produced shocks
is
about
1ms and the
amplitudes range between 5000
and
10000
m/s
5
.
6.3.2.
Medium
weight
high impact shock machine
This machine
was
designed
to
test equipment whose mass, including
the
fixure,
is
less than
2500
kg
(Figure 6.13).
It
consists
of a
hammer weighing 1360
kg
which
swings through
an arc of a
circle
at an
angle greater than 180°
and
coming
to
strike
an
anvil
at its
lower face. Under
the
impact, this anvil,
fixed
under
the
table carrying
the
test item, moves vertically upwards.
The
movement
of
this unit
is
limited
to
approximately
8 cm at the top and 4 cm at the
bottom ([CON 51], [LAZ67],
[VIG
47] and
[VIG 61b]
by
stops which stop
it and
reverse
its
movement.
The
equipment
being tested
is fixed on the
table
via a
group
of
steel channel beams (and
not
directly
to the rigid
anvil structure),
so
that
the
natural
frequency of the
test item
on
this
support metal structure
is
about
60 Hz.
The
shocks obtained
are
similar
to
those produced with
the
machine
for
light
equipment.
It is
difficult
to
accept
a
specification which would impose
a
maximum
acceleration.
It is
easier
'to
control' starting
from a
velocity change,
the
function
drop height
of the
hammer
and
total mass
of the
moving assembly (anvil, fixture
and
test
item) [LAZ 67].
Figure
6.13. High
impact
machine
for
medium weight equipment
Standard
shock
machineses
163
The
shocks
carried
out on all
these facilities
are not
very
reproducible,
sensitive
to the
ageing
of the
machine
and the
assembly (the results
can
differ
after
dismantling
and
reassembling
the
equipment
on the
machine under identical
conditions,
in
particular
at
high
frequencies)
[VIG 6la].
These machines
can
also
be
used
to
generate simple shape shocks such
as
half-
sine
or
T.P.S.
pulses [VIG 63], while inserting between
the
hammer
and the
anvil
carrying
the
test
item either
an
elastic
or
plastic material.
One
thus obtains durations
of
about
10 ms at 20 ms for the
half-sine
pulse
and 10 ms for the TPS
pulse.
6.4. Pneumatic machines
Pneumatic machines
in
general consist
of a
cylinder separated
in two
parts
by a
plate
bored
to let
pass
the rod of a
piston located lower down (Figure 6.14).
The rod
crosses
the
higher cylinder, comes
out of the
cylinder
and
supports
a
table receiving
the
test item.
Figure
6.14.
The
principle
of
pneumatic machines