Lesson 12
Shock,Vibration,and
Compression
第 12课 冲击、振动和受压
Shock
? Defined as an impact,characterized by a sudden
and substantial change in velocity,
? Shocks in the distribution environment,
Accidental and deliberate drops during manual
handling
Drops from chutes,conveyors,and other machinery
Falls from pallet loads
Sudden arrests on conveyors
Impacts occurring when vehicles hit potholes,curbs,
or railroad tracks
Shock
Impacts occurring when a package is rolled or tipped
over
Shock due to rail shunting
Shock Resulting from Drops,
? can be treated as manual drops,
? typical manual handling patterns (Figure 12.1)(the
basic predictability of package handling),
Shock
Figure 12.1 Cumulative percentage and drop height in next day air
parcel delivery for United States Postal Service
Shock
? generalized drop probability curves (Figure 12.2)
illustrating another predictable feature of manual
handling,the lighter the package,the higher the
probable drop height,
Shock
Figure 12.2 Generalized drop-height probability curves,The curves
flatten out at the point where mechanical handling predominates,
Shock
? Purposes,1.probable drop height a given package
should be designed to withstand,
2,being the basis of preshipment test
procedures and
3,provide information for the development
of protective packaging systems,
? Fundamental lessons are as follows,
The probability that a package will be dropped
from a height greater than 1 meter (40 inches) is
minimal,
Shock
Packages receive many drops from low heights,
while few receive more than one drop from greater
heights,
Skidded,wrapped,or otherwise unitized loads are
subject to fewer drops than individual packages,
There is little control over drop orientation with
small packages,With larger packages,about half of
the drops are on the base,
A heavier package has a lower probable drop
height,
Shock
The larger or bulkier the package,the lower the
probable drop height,
Handholds reduce the probable drop height by
lowering the container relative to the floor,
Cautionary labeling (fragile,this side up,handle
with care) has only a minor effect,Cautionary labeling
is no substitute for sound packaging practice,
Address labels tend to orient the drop to a label-
up position regardless of other instructions,
Shock
? The usual results of drops and shocks fall into two
categories,
protective or containment qualities are reduced
bending,distortion,or,ultimately,breakage
Shock During Rail Transport,
Railcar coupling,boxcars assembled into trains
by moving individual cars; The average shunting
speed is 8.4 kilometres per hour,This is the average
speed; some of the impacts are at greater speeds!
(Figure 12.3)
Shock
Figure 12.3 Distribution of rail coupling speeds
Shock
? Shipper experience suggests that damage is greater
for rail than for truck shipment,
? The high damage rates attributed to rail are probably
due not so much to the actual shock forces as to load
shifts and the effects of dynamic compression,
? Good loading and bracing and securing (dunnage)
practices can substantially reduce rail damage,
? TOFC shipping may be gentler than regular boxcar
shipping,
Shock
Other Shock Conditions,
? occurs during the bumps and bangs,typical of
mechanical handling and transport; not as great as
that experienced during manual handling and free-fall
drops; i.e.,a package that will withstand manual
handling shocks will survive mechanical handling,
?,Repetitive shock”,the low-frequency bouncing or
rattling; not likely to cause typical shock damage;
however,abrasion can occur,and if the product is in
resonance with the input frequency,various forms of
mechanical damage may develop (vibration-induced
damage),
Shock
Quantifying Shock Fragility,
? protection against shock damage provided and a
knowledge of how,fragile” or,sturdy” the product is,
? cushioning system based on the product's quantified
ability to withstand shock,
? quantifying shock fragility in terms of drop height is
useful only if no additional protection is anticipated,for
products that may experience drops in their use
environment,cell telephones,consumer electronics
and laptop computers,
Shock
? Fragility factor:,critical acceleration”,or,G,” levels to
describe an object's tendency to break when
subjected to shock,An object will break if subjected to
a force greater than its structure can bear,
Newton’s second law,
F = ma
G =
? Since mass is constant for a given packaging problem,
force is directly proportional to G,
[Example] for a cup,m=200 gram,h=1m
g r a v i t y ofon a c c e l e r a t i
ona c c e l e r a t i o b s e r v e d
Shock
1,if (hitting onto floor),then a= 2200
m/sec2,G=224
At the moment of impact,the cup would,in
effect,weigh 224 times normal (44.8 kilograms),
Unless it was a very unusual cup,breakage could be
guaranteed,
2,if ( rubber pad),then a= 554 m/sec2,
G=56
s e c/43.42 mghv i ??
s a f t er v t 0 0 2.00 ?? ?
s a f t er v t 0 0 8.00 ?? ?
Shock
3,if (sponge layer),then a= 443 m/sec2,
G=44
Adding still more layers would eventually reduce
the G level to the point where the cup would not break,
This would be one way of determining what cushioning
protection the cup needed to protect it from a 1 m drop,
It can be seen from the cup example that time is
needed over which to dissipate the impact velocity and
that this time is gained by the deflection of a resilient
cushioning material,This is the basic principle of
cushioning against shock,
s a f t e r v t 01.00 ?? ?
Shock
? A quick estimate of cushion material thickness can be
made if the cushion material is treated as a linear,
undampened spring,The deflection necessary to
maintain a desired acceleration is calculated as
follows,
where D = required deflection,h = anticipated drop
height,G = fragility level (critical acceleration)
This formula provides the minimum distance over
which the deceleration must take place in order not to
exceed the critical acceleration,
)2( 2?? G hD
Shock
[Example] for a product with a fragility factor of 40 G
and an anticipated 1 m drop,
The 53 mm deflection distance is the minimum
stopping distance consistent with maintaining 40 G or
less,Stopping in any lesser distance would raise
acceleration to over 40 G and cause damage,The 53
mm deflection is the theoretical deflection distance,
not the cushion thickness,To determine actual
cushion thickness,it is necessary to know how far the
mm) m ( 5 3 053.02-40 12 ??? mD
Shock
proposed material will compress before reaching
maximum strain,or,bottoming out”,
?,Static stress working range” refers to the load per
unit area that will cause a resilient material to deflect,
but not to flatten out completely,
typical optimum strains for three commonly used
cushion materials are on the order of the following,
Expanded polystyrene (EPS) 40%
Polyethylene foam (or EPE) 50%
Polyurethane(PUR) 70%
Shock
[Example]
The theoretical deflection distance,.i.e.,the
required thickness for the three different materials,132
mm (EPS),106 mm (EPE),or 76 mm (PUR),
? More accurate estimates of cushioning thickness can
be made using dynamic cushioning curves that are
available for most cushioning materials,The
information necessary to make these calculations
using dynamic cushioning curves is,
·Product size and mass,
Shock
·Product fragility,expressed in G,
·Anticipated drop height,
[Example]
Using a dynamic cushioning curve (Figure 12.4),
Shock
Figure 12.4 An example of a dynamic cushioning curve
Shock
Table 12.1 Typical fragility factor classes,A manufacturer would be
advised to consider redesign of any product with a fragility level of
less than about 30 G,
G Factor Classed as Examples
15-25 G Extremely fragile Precision instruments,first-
generation computer hard drives
25-40 G Fragile Benchtop and floor-
standinginstrumentation and
electronics
40-60 G Stable Cash registers,office equipment,
desktop computers
60-85 G Durable Television sets,appliances,printers
85-110 G Rugged Machinery,durable appliances,
power supplies,monitors
110 G Portable Laptop computers,optical readers
150 G Hand held Calculators,telephones,
microphones,radios
Shock
? Fragility may be greatly dependent on how the force
is transmitted to the product,
An egg on a flat surface has a fragility of 35 to 50
G,depending on the axis of impact,If the egg is
supported in a conforming surface,its fragility can
exceed 150 G,
(Cautionary Note,The explanations for shock
provided in this text are simplified,Proper
consideration of shock and shock protection takes into
account not only peak G but also velocity change,
Shock
These two factors are usually represented by
a“damage boundary curve”,The proper method of
quantifying shock fragility is through the use of a shock
test machine,This device is capable of providing a
shock pulse of an accurately defined amplitude,
duration,and shape),
Cushioning Against Shock,
? Any material that will deflect under an applied load can
act as a cushioning material,
? By deflecting,the cushioning material attenuates the
peak G level experienced by the product,
Shock
compared with the shock pulse at the package surface
(Figure 12.5),
Figure 12.5 A cushioning material attenuates the initial shock pulse
at the package's surface so that the product's response takes
place over a longer period of time,The areas under the curves
represent energy
Shock
? Cushioning and volume,
Premolded shapes (high-volume production)
Fabricated shapes,those cut and assembled
from flat planks (intermediate volume)
Loose fill,foam-in-place,and bubble pads (low-
volume,nearly every shipment is unique)
Cushioning materials,
1,Cellulose-based cushioning materials (the most
economical),
cellulose wadding excelsior fill corrugated
inserts
Shock
molded pulp indented kraft newspaper
Features,
shock absorption,resiliency,and cleanliness
characteristics
corrosive (not be used with bare metal parts)
hygroscopic and the risk of corrosion at high
humidity
quite abrasive
reduced effectiveness after one major
shock(i.e.,corrugated fiberboard and rigid
foams)
Shock
2,Polymeric-based cushioning materials,
EPE EPP EPS PS loose fill
air bubble sheet EPUR foam foam-in-place PUR
Features,
wide design latitude(densities and resiliencies)
clean
little or no corrosive
static problems
dramatic change in the resiliency with temperature
and altitude
Shock
not hygroscopic
some open-celled foams (typically PUR) absorb
liquid if wetted
-loose fills,used for random product packing;difficult to
get under large overhangs; subject to settling during
transport; loose fills based on popcorn and expanded
starches (attract rodents and other vermin)
-Foam-in-place urethane,by mixing two reactive liquid
chemicals (an isocyanine and a glycol); two materials
react almost immediately and begin to expand into a
foam-like structure,
Shock
During the foaming stage,the urethane is soft and
pliable,but it quickly stiffens to a more semi-rigid state,
Versatile,custom-made; form-fitting shapes easily
fabricated; labor-intensive process,
Vibration
? Definitions,
vibration,an oscillation or motion about a fixed
reference point
amplitude,the distance moved about the reference
point
frequency,the number of oscillations per second(Hz)
? Vibration is associated with all transport modes
typically,the higher the frequency,the lower the
amplitude
frequencies above 100 Hz are of little concern to most
packagers
Vibration
the most troublesome frequencies are below 30 Hz
? Vehicle vibrations come from many sources
Truck vibrations (Figure 12.6),at the natural
frequencies of ① the load on the suspension system,
② of the unsprung mass of the tires against the
suspension system,and of ③ the trailer and body
structure,They are excited by the condition and
irregularities of the roadbed,the engine and drive train,
tire and wheel imbalance,and the dynamics of the
lading,or freight,
Vibration
Figure 12.6 Typical source of truck-bed vibrations
Vibration
Vibration Damage Due to Relative Motion,
? Vibrational damage can take several forms,
1.scuffing and abrasion (particularly objectionable on
labels and graphics)
Approaches,
reducing or eliminating relative motion(tight shipping
case dimensions); recessed label areas; hard surface
varnishes; soft,nonabrasive plastic or cellulose wraps;
wax coating,
Vibration
2,an open void at the tops of boxes and bottles( an
underfill)
Approaches,
shipped inverted so that the settling and compaction
take place against the container top
Vibration Resonance,
? The spring/mass relationship between an input
vibration and the response of a mass can have three
outcomes,
Output = input direct coupling
Vibration
Output> input resonance
Output < input Isolation
?,Resonance”,the condition where a vibration input is
amplified,is the key packaging concern,
? Resonance occurs whenever the forcing (input)
frequency= the natural frequency of the product and/or
the package system,
? How to identify resonance points,by subjecting the
product to a range of frequencies and observing the
frequencies at which a resonance condition occurs
Vibration
(a typical resonance search might sweep the
frequencies between 3 Hz and 100 Hz at 0.5 to 1.0
octave per minute (refer to ASTM D 999)
? Hazards resulted from resonance,
· Fatigue and finally fracture metal cans and pails
· Flex and crack delicate circuits on circuit boards
· Disintegrate or otherwise alter the texture of food
products
· Separate and settle granular components in a food
product or settle loose protective fill
Vibration
· Aggravate scuffing and abrasion problems by several
orders of magnitude
· Cause individual containers or components to bang
into one another
· Disturb pallet patterns or dunnage (load-securing)
systems
· Initiate stack resonance
· Unscrew bottle caps and threaded fasteners
? Damage caused by resonance vibration can be
difficult to resolve,all cushioning materials are resilient
Vibration
(while acting to attenuate shock,also acting as a
spring in response to vibrational input; for many
applications,designing a vibration-isolation cushioning
system,
Stack Resonance,
? each succeeding container goes into resonance with
the previous container until the entire stack is
bouncing,creating conditions of extraordinary
destructiveness (Figure 12.7),
Vibration
Figure 12.7 In stack resonance,the entire stack is bouncing,
creating a destructive condition
Vibration
[For example] if a truck bed ’s A = 5 mm and the
bottom container goes into resonance(A1=10 mm);
when the second container in the stack goes into
resonance(A2=20 mm); …,,until the top container
actually bounces off the top of the load,
Results,the dynamic load on the bottom container
can be several orders of magnitude greater than the
actual weight resting on it; the top container is
subjected to extremes of repetitive shock and
vibrations of considerable amplitude; skew the entire
pallet load to one side (Figure 12.8),
Vibration
Figure 12.8 Skewing of a load may cause boxes in adjacent
loads to interlock
Vibration
Isolating Vibration,
? An ideal vibration-isolation material provides isolation
in the 3 to 100 Hz range
? Vibrational response curves are available for many
resilient materials,
? A material with the characteristics shown in Figure
12.9 could be used effectively to isolate vibrational
inputs over 100 Hz,The amplification between 40 and
100 Hz is not necessarily a problem,provided the
Vibration
Figure 12.9 Vibration response curve for 175-pound,C-flute pad at
0.5 psi static load,The three conditions-direct coupling,
amplification,and isolation-can be clearly identified
Vibration
product has no response in this zone,If by bad choice
this is where the product resonates,damage is almost
certain,Below 40 Hz there is direct coupling,and the
product will not see any worse vibration than the input
level,
? A properly selected isolation material resonates at an
input frequency that is less than half of the product's
resonance frequency,For example,if a product has a
major resonance at 48 Hz,the isolation material
should resonate at less than 24 Hz,
Compression
Static and Dynamic Compression,
? Most products are stacked during warehousing and
shipping,
? Static compression is determined by mechanically
applying a load at a slow rate or by conducting dead-
load stacking tests,
? Dynamic compression describes a condition where the
compression load is applied at a rapid rate,
i.e.,during clamp-truck operation
rail shunting
Compression
stack resonance
during normal transit conditions
? Apparent compression strength is affected by the load
application rate,standardized to 12.7 mm/min.,2.5
mm/min,
Compression Strength and Warehouse Stack
Duration,
? To predict safe warehouse stack duration or to
evaluate new container designs
? The warehouse condition is one of static loading over
time,
Compression
? The laboratory compression test is completed within
minutes; it is a dynamic test,
? Compression strength (a dynamic value) is not the
load that can safely be applied in the warehouse,
? Stacking strength (a static value) for a given situation
can be estimated from Figure 12.10,
Compression
Figure 12.10 The compression strength of corrugated board falls off
with time,This graph relates dynamic compression (laboratory) to
static compression (warehouse)
Compression
Compression Strength and Humidity,
? A change in relative humidity from 40 to 90% can
result in a loss of about 50% of a corrugated
container's stack strength,Corrugated containers
destined for very humid conditions need excess stack
strength to allow for this loss,
? Figure 12.11 contains a chart for estimating the
compression strength of corrugated board at different
moisture levels,
Compression
Figure 12.11 Chart for estimating compression strengths at different
board moisture contents
Compression
Other Factors Influencing Box Stack Strength,
? Compression strength is mostly a function of the wall
perimeter,with the greatest contribution made by the
four corners (Figure 12.12),
? A box will fail at loads far below the measured
compression strength if the loads are applied unevenly
at points away from the corners or in a concentrated
area,Thus,in addition to the total compressive load,
one mustalso consider the load per unit perimeter
length and the load distribution,
Compression
i.e.,clamp-truck handling creases container side
panels
a cord used to unitize or secure the pallet load that
cuts into the edges of all corner boxes
Result,dramatically reduces available load-bearing
ability,
? Higher initial compression strength is needed where
warehousing follows a long journey or rough handling,
since the containers will have experienced attrition
factors that will have an accumulated effect on load-
bearing ability,
Compression
? Lower initial compression strengths can be used only
in those instances where the product has a short
distribution cycle,
? Most pallets are decked with boards,and therefore the
bottom container does not have full support over its
base,
Single-face pallet stringers produce a much greater
unit area load on the topmost container of the lower
pallet (Figure 12.13),
Compression
Single-face pallet
stringers create
high local loads
when double-
stacked
Figure 12.13 Crushing loads from a single-face pallet,
Compression
? Most shipping containers are designed to provide
maximum vertical stack strength,since this is the
common warehouse condition,Dynamic compression
by clamp trucks and rail shunting is in the longitudinal
direction,normally the container's weaker axis,
? Each palleting pattern has a different total stacking
strength,
vertical column,The best possible use of container
load-bearing ability,unfortunately,the least stable
technique
Compression
other stacking patterns,used to provide better load
stability or cube utilization,
? Pallet overhang is often deliberate but is rarely a good
idea,Inadvertent overhang can occur internally
because of pallet board geometries relative to the
container size,Typical loss of available compression
strength to overhang is shown in Figure 12.14,
Compression
Figure 12.14 Effect of overhang on compression stack strength
Compression
Contents’ Effect on Compression Strength,
? Contents sometimes increase apparent compression
strength,The usual reason is that the contents prevent
the container sidewalls from buckling inward,thus
delaying the failure point,
? The asymmetrical nature of the oil bottle shown in
Figure 12.15 can result in overhang of the major load-
bearing bottle wall segment,The available bottle
compression strength is a fraction of the measured
value,
Compression
Figure 12.15 Overhang of asymmetrical supporting contents can
have a major impact on a container's calculated ability to hold a
load
Compression
? It is generally assumed that stack forces are acting on
a vertical wall of a corrugated box,
? However,flexible primary packages and bag-in-box
systems containing liquids or semisolids exert varying
degrees of hydrostatic pressure perpendicular to the
vertical container wall,thus reducing compression
strength,
? Hydrostatic pressure appears as an outward bulge
slightly below the midpoint and is greatest at the
bottom of the enclosing box,with a corresponding loss
of compression strength (Figure 12.16),
Compression
Figure 12.16 Bag-in-box systems reduce compression strength by
bowing out the side walls
Compression
? Where various components contribute to total
compression strength,good design calls for the
individual
components to act collectively,Maximum strength is
gained when all components have the same failure
point,e.g.,if a plastic bottle and a partition are
expected to contribute to a corrugated container's
overall compression strength,the three should be
sized so that they fail as a single unit (Figure 12.17),
Compression
Figure 12.17 The highest compression strength in a multicomponent
system is achieved when all components act together,Top
example shows separate failures,while the bottom example
shows simultaneous failure at a higher compression
Compression
Plastic Bottle Stacking Factors,
? With plastic,as with corrugated board,the dynamic
compression strength must be related to static
warehouse conditions,
? Stack duration for PE bottles can be estimated using
the bottle load ratio shown in Figure 12.18,
Compression
Figure 12.18 Warehouse stacking and load ratios for polyethylene
bottles
Compression
load ratio, expected load/compression strength,
[Example] A bottle with a compression strength of 10
kilograms and loaded with 3.1 kilograms would have a
load ratio of 0.31,It could be expected to last about
180 days under this loading,
- The design of plastic container,
avoiding sharp corners,edges,or small-radius curves
since they act as stress concentrators and promote
flex cracking,
circular cross sections,large finish surfaces to spread
the load,and shallow-angled transitions to distribute
the load from the finish to the container walls,
Compression
Estimating Required Compression Strength,
? Assessing all of the factors discussed above and
calculating a reasonable stack strength requirement
for corrugated or plastic shipping units requires
judgment and experience,
? Typically,containers should be designed to have a
compression test value 3 to 7 times greater than the
stacking load anticipated during warehousing,referred
to as the,stacking factor” or the,safety factor”,
Compression
? Deciding what stacking factor to use is initially an
intuitive assessment of a specific distribution
environment (Table 12.2),
Compression
Table 12.2 Recommended stacking factors,These should be
regarded only as starting points,Actual required stacking factors
should be calculated for each application
Condition Stacking Factor
Column stack,no overhang,minimum warehousing 3.5
Column stack,no overhang,normal warehousing 4.0
Interlock stack,no overhang,normal warehousing 5.5
Column stack,overhang,normal warehousing 5.5
Column stack,no overhang,freezer storage 5.5
Interlock stack,overhang,normal warehousing 6.0
Interlock stack,extended distribution and warehousing 7.0
Shock,Vibration,and
Compression
第 12课 冲击、振动和受压
Shock
? Defined as an impact,characterized by a sudden
and substantial change in velocity,
? Shocks in the distribution environment,
Accidental and deliberate drops during manual
handling
Drops from chutes,conveyors,and other machinery
Falls from pallet loads
Sudden arrests on conveyors
Impacts occurring when vehicles hit potholes,curbs,
or railroad tracks
Shock
Impacts occurring when a package is rolled or tipped
over
Shock due to rail shunting
Shock Resulting from Drops,
? can be treated as manual drops,
? typical manual handling patterns (Figure 12.1)(the
basic predictability of package handling),
Shock
Figure 12.1 Cumulative percentage and drop height in next day air
parcel delivery for United States Postal Service
Shock
? generalized drop probability curves (Figure 12.2)
illustrating another predictable feature of manual
handling,the lighter the package,the higher the
probable drop height,
Shock
Figure 12.2 Generalized drop-height probability curves,The curves
flatten out at the point where mechanical handling predominates,
Shock
? Purposes,1.probable drop height a given package
should be designed to withstand,
2,being the basis of preshipment test
procedures and
3,provide information for the development
of protective packaging systems,
? Fundamental lessons are as follows,
The probability that a package will be dropped
from a height greater than 1 meter (40 inches) is
minimal,
Shock
Packages receive many drops from low heights,
while few receive more than one drop from greater
heights,
Skidded,wrapped,or otherwise unitized loads are
subject to fewer drops than individual packages,
There is little control over drop orientation with
small packages,With larger packages,about half of
the drops are on the base,
A heavier package has a lower probable drop
height,
Shock
The larger or bulkier the package,the lower the
probable drop height,
Handholds reduce the probable drop height by
lowering the container relative to the floor,
Cautionary labeling (fragile,this side up,handle
with care) has only a minor effect,Cautionary labeling
is no substitute for sound packaging practice,
Address labels tend to orient the drop to a label-
up position regardless of other instructions,
Shock
? The usual results of drops and shocks fall into two
categories,
protective or containment qualities are reduced
bending,distortion,or,ultimately,breakage
Shock During Rail Transport,
Railcar coupling,boxcars assembled into trains
by moving individual cars; The average shunting
speed is 8.4 kilometres per hour,This is the average
speed; some of the impacts are at greater speeds!
(Figure 12.3)
Shock
Figure 12.3 Distribution of rail coupling speeds
Shock
? Shipper experience suggests that damage is greater
for rail than for truck shipment,
? The high damage rates attributed to rail are probably
due not so much to the actual shock forces as to load
shifts and the effects of dynamic compression,
? Good loading and bracing and securing (dunnage)
practices can substantially reduce rail damage,
? TOFC shipping may be gentler than regular boxcar
shipping,
Shock
Other Shock Conditions,
? occurs during the bumps and bangs,typical of
mechanical handling and transport; not as great as
that experienced during manual handling and free-fall
drops; i.e.,a package that will withstand manual
handling shocks will survive mechanical handling,
?,Repetitive shock”,the low-frequency bouncing or
rattling; not likely to cause typical shock damage;
however,abrasion can occur,and if the product is in
resonance with the input frequency,various forms of
mechanical damage may develop (vibration-induced
damage),
Shock
Quantifying Shock Fragility,
? protection against shock damage provided and a
knowledge of how,fragile” or,sturdy” the product is,
? cushioning system based on the product's quantified
ability to withstand shock,
? quantifying shock fragility in terms of drop height is
useful only if no additional protection is anticipated,for
products that may experience drops in their use
environment,cell telephones,consumer electronics
and laptop computers,
Shock
? Fragility factor:,critical acceleration”,or,G,” levels to
describe an object's tendency to break when
subjected to shock,An object will break if subjected to
a force greater than its structure can bear,
Newton’s second law,
F = ma
G =
? Since mass is constant for a given packaging problem,
force is directly proportional to G,
[Example] for a cup,m=200 gram,h=1m
g r a v i t y ofon a c c e l e r a t i
ona c c e l e r a t i o b s e r v e d
Shock
1,if (hitting onto floor),then a= 2200
m/sec2,G=224
At the moment of impact,the cup would,in
effect,weigh 224 times normal (44.8 kilograms),
Unless it was a very unusual cup,breakage could be
guaranteed,
2,if ( rubber pad),then a= 554 m/sec2,
G=56
s e c/43.42 mghv i ??
s a f t er v t 0 0 2.00 ?? ?
s a f t er v t 0 0 8.00 ?? ?
Shock
3,if (sponge layer),then a= 443 m/sec2,
G=44
Adding still more layers would eventually reduce
the G level to the point where the cup would not break,
This would be one way of determining what cushioning
protection the cup needed to protect it from a 1 m drop,
It can be seen from the cup example that time is
needed over which to dissipate the impact velocity and
that this time is gained by the deflection of a resilient
cushioning material,This is the basic principle of
cushioning against shock,
s a f t e r v t 01.00 ?? ?
Shock
? A quick estimate of cushion material thickness can be
made if the cushion material is treated as a linear,
undampened spring,The deflection necessary to
maintain a desired acceleration is calculated as
follows,
where D = required deflection,h = anticipated drop
height,G = fragility level (critical acceleration)
This formula provides the minimum distance over
which the deceleration must take place in order not to
exceed the critical acceleration,
)2( 2?? G hD
Shock
[Example] for a product with a fragility factor of 40 G
and an anticipated 1 m drop,
The 53 mm deflection distance is the minimum
stopping distance consistent with maintaining 40 G or
less,Stopping in any lesser distance would raise
acceleration to over 40 G and cause damage,The 53
mm deflection is the theoretical deflection distance,
not the cushion thickness,To determine actual
cushion thickness,it is necessary to know how far the
mm) m ( 5 3 053.02-40 12 ??? mD
Shock
proposed material will compress before reaching
maximum strain,or,bottoming out”,
?,Static stress working range” refers to the load per
unit area that will cause a resilient material to deflect,
but not to flatten out completely,
typical optimum strains for three commonly used
cushion materials are on the order of the following,
Expanded polystyrene (EPS) 40%
Polyethylene foam (or EPE) 50%
Polyurethane(PUR) 70%
Shock
[Example]
The theoretical deflection distance,.i.e.,the
required thickness for the three different materials,132
mm (EPS),106 mm (EPE),or 76 mm (PUR),
? More accurate estimates of cushioning thickness can
be made using dynamic cushioning curves that are
available for most cushioning materials,The
information necessary to make these calculations
using dynamic cushioning curves is,
·Product size and mass,
Shock
·Product fragility,expressed in G,
·Anticipated drop height,
[Example]
Using a dynamic cushioning curve (Figure 12.4),
Shock
Figure 12.4 An example of a dynamic cushioning curve
Shock
Table 12.1 Typical fragility factor classes,A manufacturer would be
advised to consider redesign of any product with a fragility level of
less than about 30 G,
G Factor Classed as Examples
15-25 G Extremely fragile Precision instruments,first-
generation computer hard drives
25-40 G Fragile Benchtop and floor-
standinginstrumentation and
electronics
40-60 G Stable Cash registers,office equipment,
desktop computers
60-85 G Durable Television sets,appliances,printers
85-110 G Rugged Machinery,durable appliances,
power supplies,monitors
110 G Portable Laptop computers,optical readers
150 G Hand held Calculators,telephones,
microphones,radios
Shock
? Fragility may be greatly dependent on how the force
is transmitted to the product,
An egg on a flat surface has a fragility of 35 to 50
G,depending on the axis of impact,If the egg is
supported in a conforming surface,its fragility can
exceed 150 G,
(Cautionary Note,The explanations for shock
provided in this text are simplified,Proper
consideration of shock and shock protection takes into
account not only peak G but also velocity change,
Shock
These two factors are usually represented by
a“damage boundary curve”,The proper method of
quantifying shock fragility is through the use of a shock
test machine,This device is capable of providing a
shock pulse of an accurately defined amplitude,
duration,and shape),
Cushioning Against Shock,
? Any material that will deflect under an applied load can
act as a cushioning material,
? By deflecting,the cushioning material attenuates the
peak G level experienced by the product,
Shock
compared with the shock pulse at the package surface
(Figure 12.5),
Figure 12.5 A cushioning material attenuates the initial shock pulse
at the package's surface so that the product's response takes
place over a longer period of time,The areas under the curves
represent energy
Shock
? Cushioning and volume,
Premolded shapes (high-volume production)
Fabricated shapes,those cut and assembled
from flat planks (intermediate volume)
Loose fill,foam-in-place,and bubble pads (low-
volume,nearly every shipment is unique)
Cushioning materials,
1,Cellulose-based cushioning materials (the most
economical),
cellulose wadding excelsior fill corrugated
inserts
Shock
molded pulp indented kraft newspaper
Features,
shock absorption,resiliency,and cleanliness
characteristics
corrosive (not be used with bare metal parts)
hygroscopic and the risk of corrosion at high
humidity
quite abrasive
reduced effectiveness after one major
shock(i.e.,corrugated fiberboard and rigid
foams)
Shock
2,Polymeric-based cushioning materials,
EPE EPP EPS PS loose fill
air bubble sheet EPUR foam foam-in-place PUR
Features,
wide design latitude(densities and resiliencies)
clean
little or no corrosive
static problems
dramatic change in the resiliency with temperature
and altitude
Shock
not hygroscopic
some open-celled foams (typically PUR) absorb
liquid if wetted
-loose fills,used for random product packing;difficult to
get under large overhangs; subject to settling during
transport; loose fills based on popcorn and expanded
starches (attract rodents and other vermin)
-Foam-in-place urethane,by mixing two reactive liquid
chemicals (an isocyanine and a glycol); two materials
react almost immediately and begin to expand into a
foam-like structure,
Shock
During the foaming stage,the urethane is soft and
pliable,but it quickly stiffens to a more semi-rigid state,
Versatile,custom-made; form-fitting shapes easily
fabricated; labor-intensive process,
Vibration
? Definitions,
vibration,an oscillation or motion about a fixed
reference point
amplitude,the distance moved about the reference
point
frequency,the number of oscillations per second(Hz)
? Vibration is associated with all transport modes
typically,the higher the frequency,the lower the
amplitude
frequencies above 100 Hz are of little concern to most
packagers
Vibration
the most troublesome frequencies are below 30 Hz
? Vehicle vibrations come from many sources
Truck vibrations (Figure 12.6),at the natural
frequencies of ① the load on the suspension system,
② of the unsprung mass of the tires against the
suspension system,and of ③ the trailer and body
structure,They are excited by the condition and
irregularities of the roadbed,the engine and drive train,
tire and wheel imbalance,and the dynamics of the
lading,or freight,
Vibration
Figure 12.6 Typical source of truck-bed vibrations
Vibration
Vibration Damage Due to Relative Motion,
? Vibrational damage can take several forms,
1.scuffing and abrasion (particularly objectionable on
labels and graphics)
Approaches,
reducing or eliminating relative motion(tight shipping
case dimensions); recessed label areas; hard surface
varnishes; soft,nonabrasive plastic or cellulose wraps;
wax coating,
Vibration
2,an open void at the tops of boxes and bottles( an
underfill)
Approaches,
shipped inverted so that the settling and compaction
take place against the container top
Vibration Resonance,
? The spring/mass relationship between an input
vibration and the response of a mass can have three
outcomes,
Output = input direct coupling
Vibration
Output> input resonance
Output < input Isolation
?,Resonance”,the condition where a vibration input is
amplified,is the key packaging concern,
? Resonance occurs whenever the forcing (input)
frequency= the natural frequency of the product and/or
the package system,
? How to identify resonance points,by subjecting the
product to a range of frequencies and observing the
frequencies at which a resonance condition occurs
Vibration
(a typical resonance search might sweep the
frequencies between 3 Hz and 100 Hz at 0.5 to 1.0
octave per minute (refer to ASTM D 999)
? Hazards resulted from resonance,
· Fatigue and finally fracture metal cans and pails
· Flex and crack delicate circuits on circuit boards
· Disintegrate or otherwise alter the texture of food
products
· Separate and settle granular components in a food
product or settle loose protective fill
Vibration
· Aggravate scuffing and abrasion problems by several
orders of magnitude
· Cause individual containers or components to bang
into one another
· Disturb pallet patterns or dunnage (load-securing)
systems
· Initiate stack resonance
· Unscrew bottle caps and threaded fasteners
? Damage caused by resonance vibration can be
difficult to resolve,all cushioning materials are resilient
Vibration
(while acting to attenuate shock,also acting as a
spring in response to vibrational input; for many
applications,designing a vibration-isolation cushioning
system,
Stack Resonance,
? each succeeding container goes into resonance with
the previous container until the entire stack is
bouncing,creating conditions of extraordinary
destructiveness (Figure 12.7),
Vibration
Figure 12.7 In stack resonance,the entire stack is bouncing,
creating a destructive condition
Vibration
[For example] if a truck bed ’s A = 5 mm and the
bottom container goes into resonance(A1=10 mm);
when the second container in the stack goes into
resonance(A2=20 mm); …,,until the top container
actually bounces off the top of the load,
Results,the dynamic load on the bottom container
can be several orders of magnitude greater than the
actual weight resting on it; the top container is
subjected to extremes of repetitive shock and
vibrations of considerable amplitude; skew the entire
pallet load to one side (Figure 12.8),
Vibration
Figure 12.8 Skewing of a load may cause boxes in adjacent
loads to interlock
Vibration
Isolating Vibration,
? An ideal vibration-isolation material provides isolation
in the 3 to 100 Hz range
? Vibrational response curves are available for many
resilient materials,
? A material with the characteristics shown in Figure
12.9 could be used effectively to isolate vibrational
inputs over 100 Hz,The amplification between 40 and
100 Hz is not necessarily a problem,provided the
Vibration
Figure 12.9 Vibration response curve for 175-pound,C-flute pad at
0.5 psi static load,The three conditions-direct coupling,
amplification,and isolation-can be clearly identified
Vibration
product has no response in this zone,If by bad choice
this is where the product resonates,damage is almost
certain,Below 40 Hz there is direct coupling,and the
product will not see any worse vibration than the input
level,
? A properly selected isolation material resonates at an
input frequency that is less than half of the product's
resonance frequency,For example,if a product has a
major resonance at 48 Hz,the isolation material
should resonate at less than 24 Hz,
Compression
Static and Dynamic Compression,
? Most products are stacked during warehousing and
shipping,
? Static compression is determined by mechanically
applying a load at a slow rate or by conducting dead-
load stacking tests,
? Dynamic compression describes a condition where the
compression load is applied at a rapid rate,
i.e.,during clamp-truck operation
rail shunting
Compression
stack resonance
during normal transit conditions
? Apparent compression strength is affected by the load
application rate,standardized to 12.7 mm/min.,2.5
mm/min,
Compression Strength and Warehouse Stack
Duration,
? To predict safe warehouse stack duration or to
evaluate new container designs
? The warehouse condition is one of static loading over
time,
Compression
? The laboratory compression test is completed within
minutes; it is a dynamic test,
? Compression strength (a dynamic value) is not the
load that can safely be applied in the warehouse,
? Stacking strength (a static value) for a given situation
can be estimated from Figure 12.10,
Compression
Figure 12.10 The compression strength of corrugated board falls off
with time,This graph relates dynamic compression (laboratory) to
static compression (warehouse)
Compression
Compression Strength and Humidity,
? A change in relative humidity from 40 to 90% can
result in a loss of about 50% of a corrugated
container's stack strength,Corrugated containers
destined for very humid conditions need excess stack
strength to allow for this loss,
? Figure 12.11 contains a chart for estimating the
compression strength of corrugated board at different
moisture levels,
Compression
Figure 12.11 Chart for estimating compression strengths at different
board moisture contents
Compression
Other Factors Influencing Box Stack Strength,
? Compression strength is mostly a function of the wall
perimeter,with the greatest contribution made by the
four corners (Figure 12.12),
? A box will fail at loads far below the measured
compression strength if the loads are applied unevenly
at points away from the corners or in a concentrated
area,Thus,in addition to the total compressive load,
one mustalso consider the load per unit perimeter
length and the load distribution,
Compression
i.e.,clamp-truck handling creases container side
panels
a cord used to unitize or secure the pallet load that
cuts into the edges of all corner boxes
Result,dramatically reduces available load-bearing
ability,
? Higher initial compression strength is needed where
warehousing follows a long journey or rough handling,
since the containers will have experienced attrition
factors that will have an accumulated effect on load-
bearing ability,
Compression
? Lower initial compression strengths can be used only
in those instances where the product has a short
distribution cycle,
? Most pallets are decked with boards,and therefore the
bottom container does not have full support over its
base,
Single-face pallet stringers produce a much greater
unit area load on the topmost container of the lower
pallet (Figure 12.13),
Compression
Single-face pallet
stringers create
high local loads
when double-
stacked
Figure 12.13 Crushing loads from a single-face pallet,
Compression
? Most shipping containers are designed to provide
maximum vertical stack strength,since this is the
common warehouse condition,Dynamic compression
by clamp trucks and rail shunting is in the longitudinal
direction,normally the container's weaker axis,
? Each palleting pattern has a different total stacking
strength,
vertical column,The best possible use of container
load-bearing ability,unfortunately,the least stable
technique
Compression
other stacking patterns,used to provide better load
stability or cube utilization,
? Pallet overhang is often deliberate but is rarely a good
idea,Inadvertent overhang can occur internally
because of pallet board geometries relative to the
container size,Typical loss of available compression
strength to overhang is shown in Figure 12.14,
Compression
Figure 12.14 Effect of overhang on compression stack strength
Compression
Contents’ Effect on Compression Strength,
? Contents sometimes increase apparent compression
strength,The usual reason is that the contents prevent
the container sidewalls from buckling inward,thus
delaying the failure point,
? The asymmetrical nature of the oil bottle shown in
Figure 12.15 can result in overhang of the major load-
bearing bottle wall segment,The available bottle
compression strength is a fraction of the measured
value,
Compression
Figure 12.15 Overhang of asymmetrical supporting contents can
have a major impact on a container's calculated ability to hold a
load
Compression
? It is generally assumed that stack forces are acting on
a vertical wall of a corrugated box,
? However,flexible primary packages and bag-in-box
systems containing liquids or semisolids exert varying
degrees of hydrostatic pressure perpendicular to the
vertical container wall,thus reducing compression
strength,
? Hydrostatic pressure appears as an outward bulge
slightly below the midpoint and is greatest at the
bottom of the enclosing box,with a corresponding loss
of compression strength (Figure 12.16),
Compression
Figure 12.16 Bag-in-box systems reduce compression strength by
bowing out the side walls
Compression
? Where various components contribute to total
compression strength,good design calls for the
individual
components to act collectively,Maximum strength is
gained when all components have the same failure
point,e.g.,if a plastic bottle and a partition are
expected to contribute to a corrugated container's
overall compression strength,the three should be
sized so that they fail as a single unit (Figure 12.17),
Compression
Figure 12.17 The highest compression strength in a multicomponent
system is achieved when all components act together,Top
example shows separate failures,while the bottom example
shows simultaneous failure at a higher compression
Compression
Plastic Bottle Stacking Factors,
? With plastic,as with corrugated board,the dynamic
compression strength must be related to static
warehouse conditions,
? Stack duration for PE bottles can be estimated using
the bottle load ratio shown in Figure 12.18,
Compression
Figure 12.18 Warehouse stacking and load ratios for polyethylene
bottles
Compression
load ratio, expected load/compression strength,
[Example] A bottle with a compression strength of 10
kilograms and loaded with 3.1 kilograms would have a
load ratio of 0.31,It could be expected to last about
180 days under this loading,
- The design of plastic container,
avoiding sharp corners,edges,or small-radius curves
since they act as stress concentrators and promote
flex cracking,
circular cross sections,large finish surfaces to spread
the load,and shallow-angled transitions to distribute
the load from the finish to the container walls,
Compression
Estimating Required Compression Strength,
? Assessing all of the factors discussed above and
calculating a reasonable stack strength requirement
for corrugated or plastic shipping units requires
judgment and experience,
? Typically,containers should be designed to have a
compression test value 3 to 7 times greater than the
stacking load anticipated during warehousing,referred
to as the,stacking factor” or the,safety factor”,
Compression
? Deciding what stacking factor to use is initially an
intuitive assessment of a specific distribution
environment (Table 12.2),
Compression
Table 12.2 Recommended stacking factors,These should be
regarded only as starting points,Actual required stacking factors
should be calculated for each application
Condition Stacking Factor
Column stack,no overhang,minimum warehousing 3.5
Column stack,no overhang,normal warehousing 4.0
Interlock stack,no overhang,normal warehousing 5.5
Column stack,overhang,normal warehousing 5.5
Column stack,no overhang,freezer storage 5.5
Interlock stack,overhang,normal warehousing 6.0
Interlock stack,extended distribution and warehousing 7.0
