Lalanne C. Mechanical Vibrations and Shocks: Mechanical Shock Volume II

94

Mechanical shock

Under

certain conditions,

one can try to

center

a

signal presenting

a

zero

shift

constant

or

variable according

to

time,

by

addition

of a

signal

of the

same shape

as

this

shift

and of

opposite sign [SMI 85]. This correction

is

always

a

delicate

operation which

supposes

that only

the

average value

was

affected during

the

disturbance

of

measurement.

In

particular

one

should ensure that

the

signal

is not

saturated.

Figure 3.26.

Zero

shift

influence

on

positive

and

negative

SRS

Chapter

4

Development

of

shock test specifications

4.1. General

The

first

tests

of the

behaviour

of

materials

in

response

to

shocks were carried

out

in

1917

by the

American Navy [PUS

77] and

[WEL 46].

The

most significant

development started

at the

time

of the

World

War II

with

the

development

of

specific

free

fall

or

pendular hammer machines.

The

specifications

are

type

of

machine

and its

adjustments (drop

height, material constituting

the

programmer, mass

of the

hammer). Given certain

precautions, this

process

ensures

a

great

uniformity

of the

tests.

The

demonstration

is

based

on the

fact

that

the

materials, having undergone this

test

successfully

resist

well

the

real

environment which

the

test

claims

to

simulate.

It is

necessary

to be

certain that

the

severity

of the

real shocks does

not

change

from one

project

to

another.

It is to be

feared

that

the

material thus designed

is

more

fashioned

to

resist

the

specified

shock

on the

machine than

the

shock

to

which

it

will

be

really

subjected

in

service.

Very

quickly specifications appeared imposing contractually

the

shape

of

acceleration signals, their amplitude

and

duration.

In the

mid-1950s, taking into

account

the

development

of

electrodynamic exciters

for

vibration

tests,

and the

interest

in

producing mechanical shocks,

the

same methods were developed

(it was

that

time that simulation vibrations

by

random vibrations under

test

real conditions

were

started). This testing

on a

shaker, when possible, indeed presents

a

certain

number

of

advantages [COT 66]; vibration

and

impact

tests

on the

same device,

the

possibility

of

carrying

out

shocks

of

very diverse shapes, etc.

96

Mechanical

shock

In

addition

the

shock

response

spectrum

became

the

tool

selected

for the

comparison

of the

severity

of

several shocks

and for the

development

of

specifications,

the

stages being

in

this last case

the

following:

-

calculation

of

shock spectra

of

transient signals

of

the

real environment;

-

plotting

of

the

envelope

of

these spectra;

-

searching

for a

signal

of

simple shape (half-sine,

saw

tooth etc)

of

which

the

spectrum

is

close

to the

spectrum envelope. This operation

is

generally delicate

and

cannot

be

carried

out

without requiring

an

over-test

or an

under-test

in

certain

frequency

bands.

In

the

years 1963/1975

the

development

of

computers gave

way to a

method,

consisting

of

giving directly

the

shock spectrum

to be

realized

on the

control system

of the

shaker. Taking into account

the

transfer

function

of the

test machine (with

the

test item),

the

software

then generates

on the

input

of the

test item

a

signal versus

time

which

has the

desired shock spectrum. This makes

it

possible

to

avoid

the

last

stage

of the

process.

The

shocks measured

in the

real environment

are in

general complex

in

shape;

they

are

difficult

to

describe simply

and

impossible

to

reproduce accurately

on the

usual shock machines.

These

machines

can

generate only simple shape shocks such

as

rectangle, half-sine, terminal peak

saw

tooth pulses. Several methods

have

been

proposed

to

transform

the

real signal into

a

specification

of

this nature.

4.2. Simplification

of the

measured signal

This method consists

of

extracting

the first

peak,

the

duration being

defined

by

time

when

the

signal x(t)

is

cancelled

for the first

time,

or

extraction

of the

highest

peak.

Figure

4.1. Taking into account

the

largest

peak

Development

of

shock test specifications

97

The

shock

test

specification

is

then described

in the

form

of an

impulse

of

amplitude

equal

to

that

of the

chosen peak

in the

measured signal,

of

duration equal

to

the

half-period thus defined

and

whose shape

can

vary, while approaching

as

early

as

possible that

of the first

peak (Figure 4.1).

The

choice

can be

guided

by the use of an

abacus making

it

possible

to

check

that

the

profile

of the

shock pulse remains within

the

tolerances

of one of the

standardized

forms

[KIR 69].

Another

method consists

of

measuring

the

velocity change associated with

the

shock

pulse

by

integration

of the

function

x(t) during

the

half-cycle

with greater

amplitude.

The

shape

of the

shock

is

selected

arbitrarily.

The

amplitude

and the

duration

are fixed in

order

to

preserve

the

velocity change [KIR

69]

(Figure 4.2).

Figure

4.2.

Specification

with same velocity change

The

transformation

of a

complex shock environment into

a

simple shape shock,

realizable

in the

laboratory,

is

under these conditions

an

operation which utilizes

in

an

important

way the

judgement

of the

operator.

It is

rare,

in

practice, that

the

shocks observed

are

simple, with

a

form easy

to

approach,

and it is

necessary

to

avoid

falling

into

the

trap

of

over-simplification.

Figure

4.3.

Difficulty

of

transformation

of

real shockpulses

98

Mechanical shock

In

the

example

in

Figure 4.3,

the

half-sine signal

can be a

correct approximation

of

the

relatively

"clean"

shock

1; but the

real shock

2,

which contains several

positive

and

negative peaks, cannot

be

simulated

by

just

one

unidirectional wave.

It

is

difficult

to

give

a

general empirical rule

to

ensure

the

quality

of

simulation

in

laboratory carried

out

according

to

this

process

and the

experimental quality

is

important.

It is not

shown that

the

criterion

of

equivalence chosen

to

transform

the

complex signal

to a

simple shape shock

is

valid.

It is

undoubtedly

the

most serious

defect.

This method lends itself little

to

statistical analysis which would

be

possible

if

one had

several measurements

of a

particular event

and

which would make

it

possible

to

establish

a

specification covering

the

real environment with

a

given

probability.

In the

same way,

it is

difficult

to

determine

a

shock enveloping various

shocks measured

in the

life

profile

of the

material.

4.3.

Use of

shock response spectra

4.3.1.

Synthesis

of

spectra

The

most complex

case

is

where

the

real environment, described

by

curves

of

acceleration against time,

is

supposed

to be

composed

of p

different

events (handling

shock,

inter-stage

cutting shock

on a

satellite launcher), with each

one of

these

events

itself

being characterized

by r

i

successive measurements.

These

r

i

measurements allow

a

statistical description

of

each event.

The

folowing

procedure

consists

for

each one:

- To

calculate

the

shock

response

spectrum

of

each signal recorded with

the

damping

factor

of the

principal mode

of the

structure

if

this value

is

known,

if not

with

the

conventional value 0.05.

In the

same way,

the frequency

band

of

analysis

will

have

to

envelop

the

principal resonance

frequencies of the

structure (known

or

foreseeable frequencies).

- If the

number

of

measurements

is

sufficient,

to

calculate

the

mean spectrum

m

(mean

of the

points

at

each

frequency) as

well

as the

standard deviation spectrum,

then

the

standard deviation/mean ratio, according

to the frequency; if it is

insufficient,

to

make

the

envelope

of the

spectra.

- To

apply

to the

mean spectrum

or the

mean spectrum

+ 3

standard deviations

a

statistical

uncertainty coefficient

k,

calculated

for a

probability

of

tolerated

maximum

failure

(cf

Volume

5), or

contractual

(if one

uses

the

envelope).

Development

of

shock test

specifications

99

Each event thus being synthesized

in

only

one

spectrum,

one

proceeds

to an

envelope

of all the

spectra obtained

to

deduce

a

spectrum

from it

covering

the

totality

of the

shocks

of the

life

profile.

After

multiplication

by a

test factor

(Volume

5),

this spectrum

will

be

used

as

reference 'real environment'

for the

determination

of the

specification.

Table

4.1.

Process

of

developing

a

specification

from

real

shocks

measurements

The

reference spectrum

can

consist

of the

positive

and

negative spectra

or the

envelope

of

their absolute value (maximax spectrum).

In

this last case,

the

specification

will

have

to be

applied according

to the two

corresponding half-axes

of

the

test item.

4.3.2. Nature

of

the

specification

According

to the

characteristics

of the

spectrum

and

available means,

the

specification

can be

expressed

in the

form

of:

-A

simple shape signal according

to

time realizable

on the

usual shock

machines

(half-sine,

T.P.S.,

rectangular pulse). There

is an

infinity

of

shocks having

a

given response spectrum.

The

fact

that this transformation

is

universal

is

its

very great loss

of

information, since

one

retains only

the

largest value

of the

response according

to

time

to

constitute

the SRS at

each natural

frequency. One can

thus

try to

find

a

shock

of

simple

form,

to

which

the

spectrum

is

closed

to the

reference

spectrum, characterized

by its

form,

its

amplitude

and its

duration.

It is in

Event

#1

Handling

shock

r

1

measured

data

Event

#2

Landing

shock

T

2

measured

data

Event

#p

Ignition

shock

r_

measured

data

Calculation

of

r

1

S.RS.

Calculation

of

T

2

S.RS.

Calculation

of

r

p

S.R.S.

-

Mean

and

standard

deviation

spectra

or

envelope

Mean

and

standard

deviation

spectra

or

envelope

Mean

and

standard

deviation

spectra

or

envelope

Envelope

X

Test

factor

-

k (m + 3 s)

or

k

env.

k (m + 3 s)

or

k

env.

k (m + 3 s)

or

k

env.

Envelope

—

100

Mechanical shock

general desirable that

the

positive

and

negative spectra

of the

specification

respectively cover

the

positive

and

negative spectra

of the field

environment.

If

this

condition cannot

be

obtained

by

application

of

only

one

shock (particular shape

of

the

spectra, limitations

of the

facilities),

the

specification will

be

made

up of two

shocks,

one on

each half-axis.

The

envelope must

be

approaching

the

real

environment

as

well

as

possible,

if

possible

on all the

spectrum

in the frequency

band retained

for the

analysis,

if not in a frequency

band surrounding

the

resonance

frequencies

of

the

test item

(if

they

are

known).

- A

shock response spectrum.

In

this last case,

the

specification

is

directly

the

reference SRS.

4.3.3. Choice

of

shape

The

choice

of the

shape

of the

shock

is

carried

out by

comparison

of the

shapes

of

the

positive

and

negative spectra

of the

real environment with those

of the

spectra

of

the

usual shocks

of

simple shape (half-sine, TPS, rectangle) (Figure 4.4).

Figure 4.4.

Shapes

of

the SRS

of

the

realizable shocks

on the

usual machines

Development

of

shock

test

specifications

101

If

these

positive

and

negative

spectra

are

nearly symmetrical,

one

will

retain

a

terminal peak

saw

tooth, whilst remembering, however, that

the

shock which will

be

really applied

to the

tested equipment will have

a

non-zero decay time

so

that

its

negative spectrum will tend

towards

zero

at

very high

frequencies.

This

disadvantage

is not

necessarily onerous,

if for

example

a

preliminary study could

show

that

the

resonance

frequencies of the

test item

are in the frequency

band where

the

spectrum

of the

specified shock envelops

the

real environment.

If

only

the

positive spectrum

is

important,

one

will

choose

any

form,

the

selection criterion being

the

facility

for

realization,

or the

ratio between

the

amplitude

of the first

peak

of the

spectrum

and the

value

of the

spectrum

at

high

frequencies:

approximately

1.65

for the

half-sine pulse

(Q =

10), 1.18

for the

terminal peak

saw

tooth pulse,

and no

peak

for the

rectangular pulse.

4.3.4.

Amplitude

The

amplitude

of the

shock

is

obtained

by

plotting

the

horizontal straight line

which

closely envelops

the

positive reference

SRS at

high

frequency.

This

line cuts

the

y-axis

at a

point which gives

the

amplitude sought (one uses

here

the

property

of the

spectra

at

high

frequencies,

which tends

in

this zone towards

the

amplitude

of the

signal

in the

time domain).

4.3.5. Duration

The

shock duration

is

given

by the

coincidence

of a

particular point

of the

reference

spectrum

and the

reduced spectrum

of the

simple shock selected above

(Figure

4.6).

Figure

4.5. Determination

of

the

amplitude

of

the

specification

102

Mechanical shock

One

in

general

considers

the

abscissa

f

01

of the first

point

which

reaches

the

value

of the

asymptote

at the

high frequencies

(amplitude

of

shock).

Table

4.2

joins

together

some

values

of

this

abscissa

for the

most

usual

simple

shocks

according

to

the

Q

factor [LAL 78].

Table

4.2.

Values

of

the

dimensionless

frequency

corresponding

to the first

passage

of

the

SRS by the

amplitude

unit

Q

2

3

4

5

6

7

8

9

10

15

20

25

30

35

40

45

50

00

£

0.2500

0.1667

0.1250

0.1000

0.0833

0.0714

0.0625

0.0556

0.0500

0.0333

0.0250

0.0200

0.0167

0.0143

0.0125

0.0111

0.0100

0.0000

f

01

Half-sine

0.413

0.358

0.333

0.319

0.310

0.304

0.293

0.295

0.293

0.284

0.280

0.277

0.276

0.275

0.274

0.273

0.272

0.267

Versed-sine

0.542

0.465

0.431

0.412

0.400

0.392

0.385

0.381

0.377

0.365

0.360

0.357

0.354

0.353

0.352

0.351

0.350

0.344

IPS

/

0.564

0.499

0.468

0.449

0.437

0.427

0.421

0.415

0.400

0.392

0.388

0.385

0.383

0.382

0.380

0.379

0.371

Rectangle

0.248

0.219

0.205

0.197

0.192

0.188

0.185

0.183

0.181

0.176

0.174

0.173

0.172

0.171

0.170

0.167

Figure 4.6.

Determination

of

the

shock

duration

Development

of

shock

test

specifications

103

NOTES:

1.

If

the

calculated duration must

be

rounded

(in

milliseconds),

the

higher value

should always

be

considered,

so

that

the

spectrum

of the

specified

shock remains

always

higher

or

equal

to the

reference

spectrum.

2. It is in

general

difficult

to

carry

out

shocks

of

duration lower than

2 ms on

standard shock machines.

This

difficulty

can be

circumvented

for

very

light

equipment

with

a

specific

assembly associated with

the

shock machine

(dual

mass

shock

amplifier,

Section 6.2).

One

will validate

the

specification

by

checking

that

the

positive

and

negative

spectra

of the

shock thus determined

are

well enveloped

by the

respective

reference

spectra

and one

will verify,

if the

resonance

frequencies

of the

test

item

are

known,

that

one

does

not

over-test

exaggeratedly

at

these frequencies.

Example

Let us

consider

the

positive

and

negative

spectra

characterizing

the

real

environment plotted (Figure 4.7) (result

of a

synthesis).

Figure 4.7.

SRS

of

the

field

environment

Lalanne C. Mechanical Vibrations and Shocks: Mechanical Shock Volume II

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