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12.8 Shock Machines

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12.8.1 Main Types

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 (also, see Chapter 15). Two principal categories are

usually distinguished (Lalanne, 2002b):

* The first category is that of 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 the velocity in the tube, is an example.

* The second category is that of impact machines, which decrease the velocity of the test item

throughout the shock and/or which change its direction.

The test facilities now used are classified as follows:

* In free fall machines, the impact is made on a shock simulator (in American literature these

devices are termed “shock programmers”) adapted to the shape of the specified shock (elastomer

discs, conical or cylindrical lead pellets, pneumatic shock simulators, etc.). To increase the impact

velocity, which is limited by the drop height, that is, by the height of the guide columns, the fall

can be accelerated by the use of bungee cords.

* In pneumatic machines, the velocity is derived from a pneumatic actuator.

* In electrodynamic exciters, the shock is specified either by the shape of a temporal signal, its

amplitude and its duration, or by a SRS.

Rectangle shock pulse

Half-sine shock pulse

Velocity change

Acceleration

FIGURE 12.32 DBC comparison of half-sine and

rectangular shock pulses.

12-28 Vibration and Shock Handbook

* Exotic machines are designed to carry out shocks that are nonrealizable by the preceding methods,

generally because their amplitude and duration characteristics are not compatible with the

performances from these means. The desired shapes, not being normal, are not possible with the

shock simulators delivered by the manufacturers.

We will try to show in the following sections how mechanical shocks could be simulated on materials

in the laboratory. The facilities described are the most current, but the list is far from being exhaustive.

Many other processes were or are still used to satisfy particular needs (Nelson and Prasthofer, 1974;

Powers, 1974, 1976; Conway et al., 1976).

12.8.2 Impact Shock Machines

Most machines with free or accelerated drop

testing belong to the category of impact shock

machines. The machine itself allows the setting of

velocity of the test item.

The shock is carried out by impact, with the

help of the shock simulator (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. Laboratory machines

of this type consist of two vertical guide rods on

which the table carrying the test item slides

(Figure 12.33).

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.

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, H; to obtain the desired impact

velocity, vi, is given by

H ¼

2g ð12:19Þ

where g is the acceleration of gravity

(9.81 m/sec2).

These machines are limited by the possible drop height, that is, 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.

However, the impact velocity can be increased 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 (Lonborg, 1963) and vertical machines (Marshall et al., 1965; La Verne

Root and Bohs, 1969), this last configuration being less cumbersome.

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 simulator

(programmer).

FIGURE 12.33 Elements of a shock-test machine.

(Source: Lalanne, Chocs Mecaniques, Hermes Science

Publications. With permission.)

Mechanical Shock 12-29

12.8.2.1 Universal Shock-Test Machines

12.8.2.1.1 Impact Mode

As an example, the MRLw Company (Monterey

Research Laboratory) has marketed a machine

allowing the carrying out of shocks according to

two modes: impulse and impact (Bresk and Beal,

1966). In the two test configurations, the test item

is installed on the upper face of the table. The table

is guided by two rods that are fixed at a vertical

frame.

To carry out a test according to the impact mode

(the general case), one raises the table by the height

required by means of a hoist attached to the top of

the frame, using the intermediary assembly for

raising and dropping (see Figure 12.34). 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, as seen on the shock

simulator (programmer), the table is again

blocked to avoid a second impact.

12.8.2.1.2 Impulse Mode

The impulse mode shocks (see Figure 12.35) are

obtained while placing the table on the piston of

the shock simulator (used for the realization

of initial peak sawtooth shock pulses). The

piston of this hydropneumatic shock simulator

(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 for a second

time on the shock simulator (programmer).

12.8.3 Shock Simulators

(Programmers)

We will describe only the most frequently used shock simulators to carry out half-sine, TPS and trapezoid

shock pulses.

12.8.3.1 Half-Sine Pulse

These shocks are obtained using an elastic material interposed between the table and the solid mass

reaction.

12.8.3.1.1 Shock Duration

The shock duration is calculated by supposing that the table and the shock simulator (programmer), for

this length of time, constitute a linear mass – spring system with only one DoF. From the differential

equation of the movement (valid only during the elastomeric material compression and its relaxation, so

long as there is contact between the table and the shock simulator, i.e., during a half-period)

d2x

dt2 þ kx ¼ 0 ð12:20Þ

FIGURE 12.34 MRL universal shock-test machine

(impact mode). (Source: Lalanne, Chocs Mecaniques,

Hermes Science Publications. With permission.)

12-30 Vibration and Shock Handbook

the shock duration t can be deduced:

t ¼ p

ffiffiffiffi

ð12:21Þ

where m is the mass of the moving assembly

(table þ fixture þ test item) and k is the stiffness

constant of the shock simulator (programmer).

This expression shows that, theoretically, the

duration can be regarded as a function alone of the

mass, m; and of the stiffness of the target. It is, in

particular, independent of the impact velocity. The

mass, m; and the duration, t; being known, we

deduce from it the stiffness constant, k; of the target:

k ¼ m

t2 ð12:22Þ

12.8.3.1.2 Impact Velocity

Let us set vi as the impact velocity of the table and

vR as the velocity of rebound. The elastomeric

shock simulators often have a coefficient of

restitution, a ðvR ¼ 2aviÞ; of about 50%. In a

first approximation, we will consider that the

rebound is perfect ða ¼ 1Þ: The impact velocity is

then equal to DV =2; where DV is the velocity

change given by Table 12.1:

DV ¼

x€mt

12.8.3.1.3 Maximum Deformation of the

Shock Simulator (Programmer)

If xm is the maximum deformation of the shock

simulator (programmer) during the shock, it

becomes, by equalizing the kinetic loss of energy

and the deformation energy during the compression

of the shock simulator (programmer)

mv2

i ¼

kx2

m ð12:23Þ

yielding

xm ¼ vi

ffiffiffiffi

ð12:24Þ

12.8.3.1.4 Shock Amplitude

From Equation 12.20, one has, in absolute terms, mx€m ¼ kxm; yielding x€m ¼ xmðk=mÞ and, according to

Equation 12.24

x€m ¼ vi

ffiffiffiffi

ð12:25Þ

FIGURE 12.35 MRL universal shock-test machine

(impulse mode). (Source: Lalanne, Chocs Mecaniques,

Hermes Science Publications. With permission.)

Mechanical Shock 12-31

where the impact velocity, vi is equal to

vi ¼

ffiffiffiffiffiffi

2gH

ð12:26Þ

where g is the acceleration of gravity (1g ¼ 9.81 m/sec2) and H is the drop height.

This relation, established theoretically for perfect rebound, remains usable in practice as long as the

rebound velocity remains higher than approximately 50% of the impact velocity. Having determined

k from m and t; it is enough to act on the impact velocity, that is, on the drop height, to obtain the

required shock amplitude.

12.8.3.1.5 Characteristics of the Target

For a cylindrical shock simulator (programmer),

we have

k ¼

L ð12:27Þ

where S and L are, respectively, the cross section

and the height of the shock simulator (programmer)

and where E is Young’s modulus of material

in compression.

Depending on the materials available, that is

the possible values of E; one chooses the values of

L and S that lead to a realizable shock simulator

(by avoiding too large a height-to-diameter ratio

to eliminate the risks from buckling). When the

table has a large surface, it is possible to place

four shock simulators to distribute the effort.

The cross section of each shock simulator

(programmer) is then calculated starting from

the value of S determined above and divided

by four.

If the surface of impact is planar, a wave

created at the time of the impact is propagated

in the cylinder and makes several up and down

excursions (Figure 12.36). From it, at the

beginning of the signal the appearance of a

high frequency oscillation that distorts the

desired half-sine pulse results.

To avoid this phenomenon, the front face of the shock simulator (programmer) is designed to be

slightly conical (Figure 12.37) in order to insert the load material gradually (open module). The

shock thus created is between a half-sine and a versed-sine pulse. In addition, a good empirical rule is

to limit the maximum dynamic deformation of the shock simulator (programmer) from 10 to 15% of

its initial thickness to avoid distortion of the half-sine due to damping of the material. If this limit is

exceeded, the shape obtained risks nonlinear tendencies.

Example

Consider the realization of a half-sine shock 340 m/sec2, 9 msec. It is supposed that the mass of the

moving assembly (table þ fixture þ test item) is equal to 470 kg (test item þ fixture mass: 150 kg).

From Equation 12.22

k ¼ m

p 2

t 2 ¼ 470

p 2

ð0:009Þ2 < 5:727 £ 107 N=m

x(t)

t t

FIGURE 12.36 High frequencies at impact. (Source:

Lalanne, Chocs Mecaniques, Hermes Science Publications.

With permission.)

FIGURE 12.37 Impact module with conical impact

face (open module). (Source: Lalanne, Chocs Mecaniques,

Hermes Science Publications. With permission.)

12-32 Vibration and Shock Handbook

The impact velocity is calculated from Equation 12.25:

vi ¼ x€m

ffiffiffiffi

¼ x€m

p ¼ 340

0:009

< 0:974 m=sec

which leads to the drop height, H ¼ ðv2

i =2gÞ < 48 £ 1023 m: During the impact, the elastomeric target

will be deformed to a height equal to Equation 12.24:

xm ¼ vi

ffiffiffiffi

¼ x€m

�� 􀀐2

¼ 300

0:009

􀀏 􀀐2

< 2:79 £ 1023 m

The velocity change during the shock is equal to DV ¼ ð2=pÞx€mt ¼ ð2=pÞ340 £ 0:009 < 1:91 m=sec: It is

checked that DV ¼ 2vi:

With L being the height of the target, its diameter D is calculated from k ¼ ES=L:

D2 ¼

If the target is an elastomer of Young’s modulus, E ¼ 5 £ 107 N=m2 yielding, if L ¼ 0:015 m; D <

0:148 m: It remains to check that the stress in the material does not exceed the acceptable value.

The manufacturers provide cylindrical modules made up of an elastomer sandwiched between two metal

plates. The shock simulator (programmer) is composed of stacked modules of various stiffnesses (Figure

12.38). A relatively low number of different modules allows the covering of a broad range of shock durations

by combinations of these elements (Brooks, 1966; Brooks and Mathews, 1966; Gray, 1966; Bresk, 1967).

The modules are in general distributed between the bottom of the table and the top of the solid mass of

reaction to regularly distribute the load at the time of the shock in the lower part of the table. One thus

avoids exciting its bending mode at lower frequency and amplifying the vibrations due to resonance of

the table.

The shock simulators for very short duration shock are made up of a high strength and high Young’s

modulus thermoplastic material. The selected plastic is highly resilient and very hard. It is used within its

yield stress and can thus be useful almost indefinitely. Reproducibility is very good.

The shock simulator (programmer) is composed of a cylinder of this material attached to a planar

circular plate screwed to the lower part of the table of the shock machine.

Drop table

Modules of different thickness

and hardness bolted together.

Addition of modules increases duration.

Removing modules decreases duration.

Machine base

Open face

shaped modules

FIGURE 12.38 Distribution of the modules (half-sine shock pulse). (Source: Lalanne, Chocs Mecaniques, Hermes

Science Publications. With permission.)

Mechanical Shock 12-33

12.8.3.2 Terminal Peak Sawtooth Shock Pulse

To generate a TPS shock pulse, any target made up of an inelastic material (crushable material) with a

curve dynamic deflection-load which follows a cubic law is thus appropriate (McWhirter, 1961). This

curve is approximated by using shock simulators of conical shape.

The material generally used is lead or honeycomb. The cones can be calculated as follows:

* Crushed length:

xm ¼

x€mt2

3 ð12:28Þ

yielding the height of the cone, h . 1:2 xm (to allow material to become deformed to the necessary

height).

* Force maximum:

Fm ¼ Smscr ¼ mx€m ð12:29Þ

where Sm is the cross section of the cone at height xm and scr is the crush stress of material

constituting the target yielding:

Sm ¼

mx€m

scr ð12:30Þ

When all the kinetic energy of the table is dissipated by the crushing of the lead, acceleration decreases

to zero. The shock machine must have a very rigid solid mass of reaction, so that the time of decay to zero

is not too long and satisfies the specification. The speed of this decay to zero is a function of the mass of

reaction and of the mass of the table: if the solid mass of reaction has a nonnegligible elasticity, the time,

already nonzero because of the imperfections inherent in the shock simulator (programmer), can become

too long and unacceptable.

For lead, the order of magnitude of scr is 760 kg/cm2 (7.6 £ 107 N/m2 ¼ 76 MPa). The range of

possible durations lies between approximately 2 and 20 msec.

For each machine and each shock, it is necessary to carry out preliminary tests to check that the

shock simulator (programmer) is well calculated. The shock simulators are destroyed with each test. It is

thus a relatively expensive method. One prefers to use, if possible, a Universal Programmer (Section

12.8.3.4).

Example

TPS shock pulse, 340 m/sec2, 9 msec (example of Section 12.5.2.5)

Unit table mass: 320 kg

Fixture þ test item mass: 150 kg

Conical lead shock simulator (scr ¼ 760 kg=cm2 ¼ 7:6 £ 107 N=m2Þ

The impact velocity is calculated from Table 12.1:

DV ¼ vi ¼

x€mt

2 ¼

340 £ 0:009

< 1:53 m=sec

which leads to the theoretical drop height H ¼ ðv2

i =2gÞ < 0:119 m: During the impact, the target will be

deformed to a height equal to Equation 12.28:

xm ¼

x€mt2

3 ¼

340 £ 0:0092

< 9:18 £ 1023 m

yielding the height of the target h $ 1:2xm < 1:2 £ 9:18 £ 1023 < 0:011 m:

12-34 Vibration and Shock Handbook

The cross section of the cone at height xm is equal to Equation 12.30

Sm ¼

mx€m

scr ¼

470 £ 340

7:6 £ 107 < 2:1 £ 1023 m2

corresponding to a diameter (at height xm) D < 0:052 m:

12.8.3.3 Rectangular Pulse – Trapezoidal Pulse

This test is carried out by impact. A cylindrical shock simulator (programmer) consists of a material

which is crushed with constant force (lead, honeycomb) or using the Universal Shock simulator

(programmer). In the first case, the characteristics of the shock simulator (programmer) can be

calculated as follows:

* The cross section is given according to the shock amplitude to be realized using the relation

Fm ¼ mx€m ¼ Sscr ð12:31Þ

yielding

S ¼

mx€m

scr ð12:32Þ

* Starting from the dynamics of the impact without rebound, the length of crushing is equal to

xm ¼

x€mt 2

2 ð12:33Þ

and that of the shock simulator (programmer) must be at least equal to 1:4xm in order to allow a

correct crushing of the matter with constant force.

The shock amplitude is controlled by the cross section of the shock simulator (programmer), the crush

stress of material, and the mass of the total carriage mass. The duration is affected only by the impact

velocity.

This method produces relatively disturbed signals, because of the impact between two plane surfaces.

They are adapted only for shocks of short duration, because of the limits of deformation. A long duration

requires a plastic deformation over a big length, but it is difficult to maintain the constant force of

resistance on such a stroke. The honeycombs lend themselves better to the realization of a long duration

shock (Gray, 1966).

Example

Rectangular shock pulse, 340 m/sec2, 9 msec

Unit table mass: 320 kg

Fixture þ test item mass: 150 kg

Cylindrical lead shock simulator ðscr ¼ 760 kg=cm2 ¼ 7:6 £ 107 N=m2Þ

The impact velocity is calculated from Table 12.1:

DV ¼ vi ¼ x€mt ¼ 340 £ 0:009 ¼ 3:06 m=sec

which leads to the theoretical drop height H ¼ ðv2

i =2gÞ < 0:477 m: During the impact, the target will be

deformed to a height equal to Equation 12.33:

xm ¼

x€mt 2

2 ¼

340 £ 0:0092

< 13:8 £ 1023 m

yielding the height of the target h $ 1:4xm < 1:4 £ 13:8 £ 1023 < 0:019 m:

Mechanical Shock 12-35

The cross section of the cylinder is equal to Equation 12.32

Sm ¼

mx€m

scr ¼

470 £ 340

7:6 £ 107 < 2:1 £ 1023 m2

corresponding to a diameter D < 0:052 m:

Table 12.8 recapitulates the main relations allowing the predimensioning of targets for generating halfsine,

sawtooth and rectangular shock pulses.

12.8.3.4 Universal Shock Simulator (Programmer)

MTSw1 has manufactured a shock simulator (programmer), known as Universal, still used in many

laboratories, to produce half-sine, TPS, and trapezoidal shock pulses after various adjustments.

This shock simulator (programmer) consists of a cylinder fixed under the table of the

machine, filled with a gas under pressure, and, in the lower part of a piston, a rod and a head

(Figure 12.39).

12.8.3.4.1 Generating a Half-Sine Shock Pulse

The chamber is put under sufficient pressure so that, during the shock, the piston cannot move

(Figure 12.39). The shock pulse is thus formatted only by the compression of the stacking of elastomeric

cylinders (modular shock simulators), placed under the piston head. One is thus brought back to the case

of Section 12.8.3.1.

12.8.3.4.2 Generating a Terminal Peak Sawtooth Shock Pulse

The gas pressure (nitrogen) in the cylinder is selected so that, after compression of elastomer during

duration, t; the piston, assembled in the cylinder as indicated in Figure 12.40, is suddenly released for a

force corresponding to the required maximum acceleration, x€m:

The pressure that was exerted before separation over the whole area of the piston applies only after

separation to one area equal to that of the rod, producing a negligible resistant force.

Acceleration thus passes very quickly from x€m to zero, as shown in Figure 12.41. The rise phase is not

perfectly linear, but corresponds rather to an arc of versed-sine (since if the pressure were sufficiently

strong, one would obtain a versed-sine by compression of the elastomer alone).

TABLE 12.8 Characteristics of the Target for the Half-Sine, Sawtooth, and Rectangular Pulses

Half-Sine TPS Rectangle

Maximum deformation of the shock simulator (programmer) xm ¼

x€mt 2

p 2 xm ¼

x€mt 2

xm ¼

x€mt 2

Shock simulator (programmer) cross section at height xm

h ¼

p 2 m

Et 2 Sm ¼

mx€m

scr

S ¼

mx€m

scr

Shock simulator (programmer) height h $ 1:2

x€mt 2

h $ 1:4

x€mt 2

Impact velocity vi ¼

x€mt

vi ¼

x€mt

vi ¼ x€mt

Free fall height H ¼

1Registered trademark of MTS Systems Corporation.

12-36 Vibration and Shock Handbook

12.8.3.4.3 Trapezoidal Shock Pulse

The assembly here is the same as that of the half-sine pulse (Figure 12.39). At the time of the impact,

there is:

* Compression of the elastomer until the force exerted on the piston balances the compressive force

produced by nitrogen (this phase gives the first part [rise] of the trapezoid).

* Up and down displacement of the piston in the part of the cylinder of smaller diameter,

approximately with constant force, since volume varies little (this phase corresponds to the

horizontal part of the trapezoid).

* Relaxation of elastomer: decay to zero acceleration.

The rise and decay parts are not perfectly linear for the same reason as in the case of the TPS pulse.

12.8.4 Limitations

12.8.4.1 Limitations of the Shock Machines

The limitations are often represented graphically by straight lines plotted in logarithmic

scales, delimiting the domain of realizable shocks (amplitude, duration). The shock machine is

FIGURE 12.39 MTSw Universal shock simulator (half-sine and rectangle pulse configuration). (Source: Lalanne,

Chocs Mecaniques, Hermes Science Publications. With permission.)

Mechanical Shock 12-37

limited by (IMPAC 6060F Operating Manual;

Figure 12.42):

* The allowable maximum force on the table.

To carry out a shock of amplitude x€m; the

force generated on the table, given by

F ¼ ½mtable þ mprogrammer þ mfixture

þ mtest item􀀉x€m ð12:34Þ

must be lower than or equal to the acceptable

maximum force, Fmax: Knowing the total

carriage mass, the relation (Equation 12.34)

allows calculation of the possible maximum

acceleration under the test conditions

ðx€mÞmax ¼ Fmax=½mtable þ mprogrammer þ mfixture þ mtest item􀀉 ð12:35Þ

FIGURE 12.40 MTSw Universal shock simulator (TPS pulse configuration). (Source: Lalanne, Chocs Mecaniques,

Hermes Science Publications. With permission.)

Versed-sine

T.P.S.

x(t)

t t

FIGURE 12.41 Realization of a TPS shock pulse.

(Source: Lalanne, Chocs Mecaniques, Hermes Science

Publications. With permission.)

12-38 Vibration and Shock Handbook

This limitation is represented on the abacus

by a horizontal line constant, x€m:

* This emphasizes maximum free fall

height, H; or the maximum impact

velocity, that is the velocity change, DV

of the shock pulse. If vR is the rebound

velocity, equal to a percentage a of the

impact velocity, we have

DV ¼ vR 2 vi ¼ 2ð1 þ aÞvi

¼ 2ð1 þ aÞ

ffiffiffiffiffiffi

2gH

ðt

x€ðtÞdt ð12:36Þ

yielding

H ¼

DV 2

2gð1 þ aÞ2 ð12:37Þ

where a is a function of the shape of the shock and of the type of shock simulator (programmer)

used. In practice, there are losses of energy by friction during the fall and especially in the shock

simulator (programmer) during the realization of the shock. Taking account of these losses is

difficult to calculate analytically and so one can set:

H ¼ b

DV 2

2g ð12:38Þ

where b takes into account at the same time losses of energy and rebound. As an example, the

manufacturer of machine IMPAC 60 £ 60 (MRL) gives Table 12.9, according to the type of

shock simulators (IMPAC 6060F Operating Manual).

The limitation related to the drop height can be represented by parallel straight lines on

a diagram giving the velocity change, DV ; as a function of the drop height in logarithmic scales.

The velocity change being, for all simple shocks, proportional to the product x€mt; we have

DV ¼ lx€mt ¼

ffiffiffiffiffiffiffiffi

2gH=b

ð12:39Þ

Some typical values for the amplitude £ duration product are given in Table 12.10.

On logarithmic scales ðx€m; tÞ; the limitation relating to the velocity change is represented by parallel,

inclined straight lines (Figure 12.42).

Table acceleration limit

Velocity

change

limit

Stroke limit

Shock duration (ms)

Maximum acceleration (m/s2)

Force limit

on elastomer

FIGURE 12.42 Abacus of the limitations of a

shock machine. (Source: Lalanne, Chocs Mecaniques,

Hermes Science Publications. With permission.)

TABLE 12.9 Loss Coefficient b

Shock Simulator (Programmer) Value of b

Elastomer (half-sine pulse) 0.556

Lead (rectangle pulse) 0.2338

Lead (TPS pulse) 1.544

Source: Lalanne, Chocs Mecaniques, Hermes Science

Publications. With permission.

Mechanical Shock 12-39

12.8.4.2 Limitations of Shock Simulators

Elastomeric materials are used to generate shocks of:

* Half-sine shape (or versed-sine with a conical frontal module to avoid the presence of high

frequencies).

* TPS and rectangular shapes, in association with a Universal shock simulator.

Elastomer shock simulators are limited by the allowable maximum force, a function of Young’s

modulus, and their dimensions (Figure 12.42). This limitation is in fact related to the need to maintain

the stress lower than the yield stress of the material, so that the target can be regarded as a pure stiffness.

The maximum stress, smax; developed in the target at the time of the shock can be expressed according to

Young’s modulus, E; to the maximum deformation, xm; and to the thickness, h; of the target according to

smax ¼ E

h ð12:40Þ

with, for an impact with perfect rebound, xm ¼ x€mt 2=p 2: It is necessary that, if Re is the elastic ultimate

stress

Ex€mt 2

hp 2 , Re ð12:41Þ

that is

h .

Ex€mt 2

Rep 2 ð12:42Þ

Taking into account the mass of the carriage assembly, this limitation can be transformed into

maximum acceleration ðFm ¼ mx€mÞ: With four shock simulators used simultaneously, the maximum

acceleration is naturally multiplied by four. This limitation is represented on the abacus of Figure 12.42

by the straight lines of greater slope.

The Universal shock simulator is limited (MRL 2680 Operating Manual):

* By the acceptable maximum force.

* By the stroke of the piston: for each waveform, the displacement during the shock is always

proportional to the product x€mt 2:

This limitation is provided by the manufacturer.

In short, the domain of the realizable shock pulses is limited on this diagram by straight lines

representative of the conditions given in Table 12.11.

TABLE 12.10 Amplitude £ Duration Limitation

Waveform Shock Simulator (Programmer) ðx€mt_Þmax (m/sec)

Half-sine Elastomer 17.7

TPS Lead cone 10.8

Universal shock simulator (programmer) 7.0

Rectangle Universal shock simulator (programmer) 9.2

Source: Lalanne, Chocs Mecaniques, Hermes Science Publications. With

permission.

TABLE 12.11 Summary of Limitations on the Domain of Realizable Shock Pulses

x€m ¼ constant Acceptable force on the table or on the

Universal shock simulator

x€mt ¼ constant Drop height (DV)

x€mt2 ¼ constant Piston stroke of the Universal shock simulator

x€mt4 ¼ constant Acceptable force for elastomers

Source: Lalanne, Chocs Mecaniques, Hermes Science Publications. With permission.

12-40 Vibration and Shock Handbook

12.8.5 Pneumatic Machines

Pneumatic machines in general consist of

a cylinder separated into two parts by a plate

bored to let pass the rod of a piston located lower

down (Figure 12.43). The rod crosses the higher

cylinder, comes out of the cylinder, and supports a

table receiving the test item.

The surface of the piston subjected to the

pressure is different according to whether it is on

the higher face or the lower face, as long as it is

supported in the higher position on the Teflonw2

seat (Thorne, 1964).

Initially, the moving piston, rod, and table rose

by filling the lower cylinder (reference pressure).

The higher chamber is then inflated to a pressure

of approximately five times the reference pressure.

When the force exerted on the higher face of the

piston exceeds the force induced by the pressure of

reference, the piston releases. The useful surface

area of the higher face increases quickly and the

piston is subjected in a very short time to a

significant force exerted towards the bottom. It

involves the table, which compresses the shock

simulators (elastomers, lead cones, etc.) placed on

the top of the body of the jack.

This machine is assembled on four rubber

bladders filled with air to uncouple it from the

floor of the building. The body of the machine is

used as a solid mass of reaction. The interest

behind this lies in its performance and its

compactness. An industrial pneumatic shock

machine is shown in Figure 12.44.

12.8.6 High Impact Shock Machines

The first machine was developed in 1939 to simulate the effects of underwater explosions (mines) on the

equipment onboard military ships. Such explosions, which generally occur at large distances from the

ships, create shocks that are propagated in all the structures.

The procedure consisted of specifying the machine to be used, the method of assembly, the adjustment

of the machine and so on, and not of a SRS or a simple shape shock.

Two models of machines of this type were built to test lightweight and medium weight

equipment.

12.8.6.1 Lightweight High Impact Shock Machine

The lightweight high impact shock machine, the first built, consists of a welded frame of standard steel

sections and two hammers, one sliding vertically, the other describing an arc of a circle in a vertical plane,

according to a pendular motion (Figure 12.45).

FIGURE 12.43 The principle of pneumatic machines.

(Source: Lalanne, Chocs Mecaniques, Hermes Science

Publications. With permission.)

2Registered trademark of E.I. du Pont de Nemours & Company, Inc., Wilmington, DE.

Mechanical Shock 12-41

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 (Conrad,

1952). The target is a plate of steel of 86 cm £ 122

cm £ 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.

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

1 msec and the amplitudes range between 5000

and 10,000 m/sec2.

12.8.6.2 Medium Weight High Impact

Shock Machine

This machine was designed to test equipment

whose mass, including the fixture, is less than

2500 kg (Figure 12.46). It consists of a hammer

weighing 1360 kg that swings through an arc of a

circle at an angle greater than 1808 and comes 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

(Vigness, 1947, 1961a; Conrad, 1951; Lazarus,

1967) by stops that halt 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.

FIGURE 12.44 Benchmarkw SM 105 pneumatic shock

machine. SM 105 and Benchmark are registered trademarks

owned by Benchmark Electronics, Hunstville, Inc.

(courtesy Benchmark Electronics).

12-42 Vibration and Shock Handbook

The shocks obtained are similar to those produced with the machine for light equipment (Lazarus,

1967).

The shocks carried out on all these facilities are not very reproducible and are 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; Vigness, 1961b).

These machines can also be used to generate simple shape shocks such as half-sine or TPS pulses

(Vigness, 1963), while inserting either an elastic or a plastic material between the hammer and the anvil

carrying the test item. One thus obtains durations of about 10 msec at 20 msec for the half-sine pulse and

10 msec for the TPS pulse.

FIGURE 12.45 High impact shock machine for lightweight equipment. (Source: Lalanne, Chocs Mecaniques,

Hermes Science Publications. With permission.)

FIGURE 12.46 High impact machine for medium weight equipment. (Source: Lalanne, Chocs Mecaniques, Hermes

Science Publications. With permission.)

Mechanical Shock 12-43

12.8.7 Specific Test Facilities

When the impact velocity of standard machines is

insufficient, one can use other means to obtain the

desired velocity. For example:

* One can use drop testers, equipped with

two vertical (or inclined) guide cables

(McWhirter, 1963; Lalanne, 1975). The

drop height can reach a few tens of meters.

It is wise to make sure that the guidance is

correct and, in particular, and that friction

is negligible. It is also desirable to measure

the impact velocity (using photoelectric cells or any other device).

* One can also use gas guns, which initially use the expansion of a gas (often air) under

pressure in a tank to propel a projectile carrying the test item towards a target equipped with

a shock simulator fixed at the extremity of a gun on a solid reaction mass (McWhirter, 1961;

McWhirter, 1963; Yarnold, 1965; Lazarus, 1967; Lalanne, 1975). One finds the impact mode

to be as above. It is necessary that the shock created at the time of the velocity setting in the

gun is of low amplitude with regard to the specified shock carried out at the time of the

impact. Another operating mode consists of using the phase of the velocity setting to

program the specified shock, the projectile then being braked at the end of the gun by a

pneumatic device, with a small acceleration with respect to the principal shock. A major

disadvantage of guns is related to the difficulty of handling cables instrumentation, which

must be wound or unreeled in the gun, in order to follow the movement of the projectile.

* Alternatively, one can use inclined-plane impact testers (Vigness, 1961a; Lazarus, 1967).

These were especially conceived to simulate shocks undergone during too severe handling

operations or in trains. They are made up primarily of a carriage on which the test item

is fixed, traveling on an inclined rail and coming to run up against a wooden barrier

(Figure 12.47).

The shape of the shock can be modified by using elastomeric “bumpers” or springs. Tests of this type

are often named “CONBUR tests.”

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