The ASTM D4169-16 applies to shipping containers

and systems. This standard is composed of three

level types and each one follows a definite duration to

complete the test sequence. According to the

distribution cycle and to the packaging system the

test sequence can be repeated on several sides.

The real truck PSD has been raised in order to be at the same

level as the ASTM D4169-16 PSD. The raising coefficient has

been determined by calculating𝐺𝑅𝑀𝑆𝑜𝑣𝑒𝑟𝑎𝑙𝑙 𝐴𝑆𝑇𝑀 𝐷4169−16

𝐺𝑅𝑀𝑆𝑟𝑒𝑎𝑙 𝑡𝑟𝑢𝑐𝑘 = 7.58

1,00E-06

1,00E-05

1,00E-04

1,00E-03

1,00E-02

1,00E-01

1,00E+00

1,00E+00 1,00E+01 1,00E+02

Pow

er S

pect

ral D

ensi

ty (

g²/H

z)

Frequency (Hz)

ASTM D4169-16 VS real truck

High Level - GRMS=0.70 G Medium Level - GRMS=0.54 G

Low Level - GRMS=0.40 G PSD real truck - GRMS=0.062 G

PSD real truck raised - GRMS=0.47 G

Result of the

three levelsModified Gaussian equation:

a=1.04

b=0.40

For the experiment, a 20-minute-duration test has been applied to the system

(composed of the recorder stuck to the vibration table). The test duration

proportionality between the levels has been saved.

𝐹𝑊𝐻𝑀𝑚𝑜𝑑𝑖𝑓𝑖𝑒𝑑 𝐺𝑎𝑢𝑠𝑠𝑖𝑎𝑛 = 2𝑏(2𝑙𝑛2)1𝑐= 0.95

Severity factor:

𝐹𝑊𝐻𝑀𝐺𝑎𝑢𝑠𝑠𝑖𝑎𝑛 = 2σ(2𝑙𝑛2)12= 1.04

𝑆 =𝐹𝑊𝐻𝑀𝑚𝑜𝑑𝑖𝑓𝑖𝑒𝑑 𝐺𝑎𝑢𝑠𝑠𝑖𝑎𝑛

𝐹𝑊𝐻𝑀𝐺𝑎𝑢𝑠𝑠𝑖𝑎𝑛

c=1.82

x0=0.03 (noise)S tends to 1 when the distribution tends to a Gaussian distribution.

If S<1 the occurrence probability of very low acceleration values is higher and the

severity is weaker.

FWHM (Full Width at Half Maximum):

𝑆 = 0.91 < 1

-0,1

0,1

0,3

0,5

0,7

0,9

1,1

1,3

-3,00E+00 -2,00E+00 -1,00E+00 0,00E+00 1,00E+00 2,00E+00 3,00E+00

Pro

babi

lity

dens

ity

Acceleration (G)

ASTM D4169-16

1min 40s ASTM D4169-16 high 5min ASTM D4169-16 medium

13min 20s ASTM D4169-16 low ASTM D4169-16 all profiles

a indicates the occurrence probability of very low

acceleration values

b indicates the values dispersion

c indicates the slope of the curve extremities and

gives the curve a leptokurtic style when c<2

𝑝(𝑥) = 𝑎𝑒−0,5

𝑥−𝑥0

𝑏

𝑐

Determination coefficient : r²=0.99

Introduction

Everyone knows that the aim of a packaging is to protect the product it contains. However during the packaging’s life cycle many constraints can occur, especially

during handling and transport. That is why each packaging has to be tested before any launching. Standards have been developed in order to simulate transport in

laboratory and one of these standards has recently changed. Indeed the ASTM International (American Society for Testing and Materials International) D4169

standard, which simulates the vibrations during transport by truck over the packaging, among other things, has evolved so as to be closer to an actual transport by

truck. In terms of acceleration probability density, an actual transport by truck is not a Gaussian[1], in fact it approximates a modified Gaussian[2]. The present work

shows in which way the current standard represents an actual transport by analysing its PSD, its acceleration probability density and by comparing them to those of

the former standard and of an actual transport by truck. Moreover in each case the severity factors will be calculated based on the method of S. OTARI[2].

As we observed at the beginning of this study, the ASTM D4169-16 PSD is more likely to approximate an actual transport by truck than the ASTM D4169-14 one. This

statement is confirmed by the study of the probability densities: an actual transport by truck is characterized by a modified Gaussian and the current standard is closer

to a modified Gaussian than the former one, which is composed of Gaussians. In conclusion the ASTM D4169-16 is more likely to represent the constraints

encountered during transport. However the severity factor of the ASTM D4169-16 is equal to 0.91 while the actual transport’s one is equal to 0.41. Therefore a small

improvement can be brought to the current standard so as to get closer to an actual transport severity factor. For example the levels durations can be adjusted in order

to fit to one particular transport type.

Experimental set-up

Sampling frequency = 500 Hz

Continuous recording over the z axis

Full scale = 20.0 G

Filter = 250 Hz

Recorder: SAVER 3X90 Vibration table: LANSMONT 10 000 TTVII

x

zy

ASTM D4169-14 and ASTM D4169-16 Truck Protocol Vibration Comparison

Anne-Sophie BONNINa,b,c, Victor HUARTa, Nicolas KRAJKAa, Jean-Baptiste NOLOTc, Serge ODOFb,c and Damien ERREb,c

aMETROPACK 30-32 rue du Capitaine Georges Madon ZAC Croix Blandin, 51100 REIMS, FRANCEbGRESPI/Université de Reims Champagne-Ardenne, REIMS, FRANCE

cESIREIMS-ESIEC École nationale Supérieure d’Ingénieurs de Reims, REIMS, FRANCE

3 esplanade Roland Garros, 51100 REIMS, FRANCE

Level Duration (1 hour) T=12t

Low 40 minutes 8t

Medium 15 minutes 3t

High 5 minutes t

Level Duration

Low13 minutes

20 seconds

Medium 5 minutes

High1 minute

40 seconds

PSD (Power Spectral Density)

Probability Densities

[1]ROUILLARD V. “On the Non-Gaussian Nature of Random Vehicle Vibrations”, Proceedings of the World Congress on Engineering 2007, Volume II, July 2-4, 2007[2]OTARI S. “Statistical Characterization of Acceleration Levels of Random Vibrations during Transport”, Packaging Technology and Science, 2011. DOI: 10.1002/pts.926

The ASTM D4169-14 level II has been

chosen for the comparison because

its coefficient of determination is

higher than those of levels I or III.

r²level I=0.90

r²level II=0.99

r²level III=0.98

yi

y'i

𝑟2 =σ𝑖(𝑦𝑖 − ത𝑦)(𝑦′𝑖 − ഥ𝑦′)

σ𝑖(𝑦𝑖 − ത𝑦)² ∗ σ𝑖(𝑦′𝑖 − ഥ𝑦′)²

2

-0,1

0,1

0,3

0,5

0,7

0,9

1,1

1,3

-3,00E+00 -2,00E+00 -1,00E+00 0,00E+00 1,00E+00 2,00E+00 3,00E+00

Pro

babi

lity

dens

ity

Acceleration (G)

ASTM D4169-16 VS ASTM D4169-14

ASTM D4169-16 all profiles ASTM D4169-14 level I

ASTM D4169-14 level II ASTM D4169-14 level III

The ASTM D4169-16’s profile is less severe than a Gaussian’s.

For the experiment, the three levels

have been applied separately to the

system (composed of the recorder

stuck to the vibration table). Each

test sequence lasts 20 minutes.

-0,1

0,1

0,3

0,5

0,7

0,9

1,1

1,3

-3,00E+00 -2,00E+00 -1,00E+00 0,00E+00 1,00E+00 2,00E+00 3,00E+00

Pro

babi

lity

dens

ity

Acceleration (G)

ASTM D4169-14

Level I

Level II

Level III

σlevel I=0.70

σlevel II=0.50

σlevel III=0.35

The severity factor S has been calculated

for level II by using σlevel II and GRMSlevel II.

Slevel II=0.96

ASTM D4169-16 VS stricter real transport at the same GRMS

𝑆 = 0.41

Adjusted real transport modified Gaussian

coefficients:

a=0.71

b=0.36

c=1.02

x0=0.03 (noise)

The truck recording was made on several types of roads, the recorder was fixed directly on the floor of the truck.

Determination coefficient :

r²=0.99

-0,2

0,0

0,2

0,4

0,6

0,8

1,0

-3,00E+00 -2,00E+00 -1,00E+00 0,00E+00 1,00E+00 2,00E+00 3,00E+00

Pro

babi

lity

dens

ity

Acceleration (G)

Adjusted real transport ASTM D4169-16 all profiles

aASTM D4169-16>aadjusted real transport: less low

acceleration values in the adjusted real

transport than with the standard

bASTM D4169-16>breal transport: the values are more

dispersed with the standard than in a real

transport, but the difference is quite thin

The ASTM D4169-14 applies to shipping containers

and systems. Three levels are available to test the

system: level I, level II or level III. Only one level is

applied to the system during the test sequence. The

test duration and the sides tested depend on the

distribution cycle.

The truck recording was made on several types of

roads, the recorder was fixed directly on the floor of

the truck.

1,00E-06

1,00E-05

1,00E-04

1,00E-03

1,00E-02

1,00E-01

1,00E+00 1,00E+01 1,00E+02

Pow

er S

pect

ral D

ensi

ty (

g²/H

z)

Frequency (Hz)

ASTM D4169-14 VS real truck

PSD real truck - GRMS=0.062 G Level I - GRMS=0.73 G

Level II - GRMS=0.52 G Level II - GRMS=0.37 G

GRMSoverall ASTM D4169-16=0.47 G