Lalanne C. Mechanical Vibrations and Shocks: Mechanical Shock Volume II
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144
Mechanical
shock
Table
5.11. Summary
of
the
conditions
for the
realization
of
a TPS
shock
Impulse
Impact without
rebound
Impact with
perfect rebound
Impact with
rebound
to 50%
of
the
initial
velocity
5.6.
Initial
peak
saw
tooth pulse
5.6.1.
Definition
Figure 5.6.
IPS
shock
pulse
for
elsewhere
Generalized
form
for
elsewhere
Reduced
form
for
elsewhere
5.6.2.
Shock motion
study
General expressions
146
Mechanical shock
Impulse
Impact
Table
5.12.
)
Impact without
rebound
Impact
with
perfect
rebound
Impact
with
50%
rebound
Velocity
and
displacement needed
to
carry
out an IPS
shock pulse
Velocity
Displacement
Kinematics
of
simple shocks
147
Table
5.13. Summary
of
the
conditions
for the
realization
of
an IPS
shock
Impulse
Impact
without
rebound
Impact
with
perfect
rebound
Impact with
rebound
to 50%
of
the
initial
velocity
Whatever
the
shape
of the
shock, perfect rebound leads
to the
smallest
displacement (and
to the
lowest drop height). With traditional shock machines, this
148
Mechanical shock
cannot
be
really exploited, since
one is not
able
to
choose
the
kinematics
of the
shock.
Chapter
6
Standard shock machines
6.1. Main
types
The first
specific machines developed
at the
time
of
World
War II
belong
to two
categories:
-Pendular
type
machines, equipped with
a
hammer which,
after
falling
in a
circular motion, strike
a
steel plate which
is
fixed
to the
specimen (high-impact
machine)
[CON
51]
[CON
52]
[VIG 61a].
The first of
these machines
was
manufactured
in
England
in
1939
to
test
the
light equipment which
was
subjected,
on
naval ships,
to
shocks produced
by
underwater explosions (mines, torpedoes).
Several models were developed
in the
United
States
and in
Europe
to
produce
shocks
on
equipment
of
more substantial mass. These machines
are
still used (cf.
Figure
6.1).
-
Sand
drop
machines
are
made
up of a
table sliding
on two
vertical guide
columns
and free
falling into
a
sand box, characteristics
of the
shock obtained being
a
function
of the
shape
and the
number
of
wooden wedges fixed under
the
table,
as
well
as the
granularity
of
sand (cf. Figure 6.2) [BRO
61]
[LAZ
67]
[VIG 61b].
NOTES:
An
alternative
to
this machine which
was
used
simply
comprised
a
wooden
table
supporting
the
specimen, under which
a
series
of
wooden
wedges
was
fixed.
The
table
was
released
from
a
given height, without guidance,
and
impacted
the
sand
in the
box.
150
Mechanical shock
Figure
6.1. Sand-drop shock testing machine
Figure
6.2. Sand-drop impact simulator
Standard shock machines
151
The
test
facilities
now
used
are
classified
as
follows:
-Free
fall
machines, derived
from the
sand-drop machines,
the
impact being
made
on a
programmer adapted
to the
shape
of the
specified shock (elastomer discs,
conical
or
cylindrical lead pellets, pneumatic programmers etc).
To
increase
the
impact velocity, which
is
limited
by the
drop height, i.e.
by the
height
of the
guide
columns,
the
fall
can be
accelerated
by the use of
bungee cords.
-
Pneumatic machines,
the
velocity being derived
from a
pneumatic actuator.
-
Electrodynamic exciters,
the
shock being specified either
by the
shape
of a
temporal signal,
its
amplitude
and its
duration,
or by a
shock response spectrum.
-
Exotic machines, designed
to
carry
out
non-realizable shocks
by the
preceding
methods,
generally because their amplitude
and
duration characteristics
are not
compatible
with
the
performances
from
these means, because
the
desired shapes,
not
being normal,
are not
possible with
the
programmers delivered
by the
manufacturers.
A
shock machine, whatever
its
standard,
is
primarily
a
device allowing
modification
over
a
short time period
of the
velocity
of the
material
to be
tested.
Two
principal categories
are
usually distinguished:
-
"impulse"
machines, which
increase
the
velocity
of the
test
item during
the
shock.
The
initial velocity
is in
general zero.
The air
gun, which
creates
the
shock
during
the
setting
of
velocity
in the
tube,
is an
example;
-
"impact"
machines, which
decrease
the
velocity
of the
test
item throughout
the
shock and/or which change
its
direction.
6.2. Impact shock machines
Most
machines with
free or
accelerated drops belong
to
this last category.
The
machine itself allows
the
setting
of
velocity
of the
test
item.
The
shock
is
carried
out by
impact
on a
programmer which formats
the
acceleration
of
braking according
to the
desired shape.
The
impact
can be
without
rebound when
the
velocity
is
zero
at the end of the
shock,
or
with rebound when
the
velocity
changes
sign during
the
movement.
The
laboratory machines
of
this type consists
of two
vertical guide rods
on
which
the
table carrying
test
item (Figure 6.3) slides.
The
impact velocity
is
obtained
by
gravity,
after
the
dropping
of the
table
from a
certain height
or
using bungee
cords
allowing
one to
obtain
a
larger impact velocity.
152
Mechanical shock
Figure
6.3.
Elements
of
a
shock test machine
In
all
cases,
whatever
the
method
for
realization
of the
shock,
it is
useful
to
consider
the
complete movement
of the
test
item between
the
moment when
its
velocity starts
to
take
a
nonzero value
and
that where
it
again becomes equal
to
zero.
One
thus always observes
the
presence
of a
pre-shock and/or
a
post-shock.
Let us
consider
a free
fall
shock machine
for
which
the friction of the
shock table
on
the
guidance system
can be
neglected.
The
necessary drop height
to
obtain
the
desired impact velocity
v
i'
is
given
by:
if
M = the
mass
of the
moving assembly
of the
machine (table,
fixture,
programmer)
m
=
mass
of the
test item
g
=
acceleration
of
gravity (9.81 m/s
2
).
yielding
Standard shock machines
153
These machines
are
limited
by the
possible drop height, i.e.
by the
height
of the
columns
and the
height
of the
test
item when
the
machine
is
provided
with
a
gantry.
It
is
difficult
to
increase
the
height
of the
machine
due to
overcrowding
and
problems with
guiding
the
table.
One
can
increase, however,
the
impact velocity using
a
force complementary
to
gravity
by
means
of
bungee
cords
tended before
the
test
and
exerting
a
force
generally directed downwards.
The
acceleration produced
by the
cords
is in
general
much
higher than gravity which then becomes negligible. This idea
was
used
to
design horizontal [LON
63] or
vertical machines [LAV
69]
[MAR 65], this last
configuration
being less cumbersome.
Figure 6.4.
Use
of
elastic
cords
The
Collins machine
is an
example.
Its
principle
of
operation
is
illustrated
in
Figure 6.4.
The
table
is
guided
by two
vertical columns
in
order
to
ensure
a
good
position
of the
test
item
at
impact. When
the
carriage
is
accelerated
by
elastic cords,
the
force
applied
to the
table
is due to
gravity
and to the
action
of
these cords.
One
has
then,
if T
h
is the
tension
of the
elastic
cord
at the
instant
of
dropping
and Tj the
tension
of the
cord
at the
time
of the
impact: