GSB 570 - Problem Sets Flashcards
(1) T/F – Because the forces placed on a product are much greater in shock than vibration,
damage occurs much more often during drops than transportation.
False, for a certified package usually the expected shocks are already considered in the
designing portion of package development. Fatigue caused due to vibration is, however,
more unpredictable and hence difficult to simulate in a lab and hence damage may occur
due to fatigue caused by continuous small level shocks
(1) What do you expect the outside temperature and pressure to be on top of a mountain
(10,000’)?
Lapse Rate: for every 1000 feet increase in elevation, the pressure drops 0.5 psi and the
temperature drops by 3.5 °F.
So at 10,000 feet elevation, the temperature will be 10,000 *
- 5/1000 = 35 °F below that at the foot of the mountain and the pressure will be 10,000 *
- 5/1000 = 5 psi below that at the foot of the mountain.
(1) T/F – Static charge build up occurs more often during compression than vibration.
False, static charge build up occurs more due to vibration and occurs more during winter
due to low relative humidity conditions.
(1) How would you explain the presence of rust on engine blocks which are loaded rust-free on
rail cars in Canada in the winter and arrive in Florida in this condition?
Due to condensation and also possibly due to “green pallets”
(1) Are the various ASTM, ISO, DOT and ISTA standards voluntary or required?
All the standards mentioned are voluntary, except for DOT since it relates to hazardous
materials.
(1) Explain the meaning of all the letters and numbers in the following test standard: ASTM D
3833/D 3833M-88 (93)Є1
ASTM: American Society for Testing and Materials D: Committee D-10 which deals specifically with packaging 3833: number designation, 3833M: metric equivalent 88: year adopted (93): year revised Є1: footnote for the standard
(1) “Conditioning” of samples for ASTM tests almost always takes place at what temperature and
relative humidity?
Standard conditioning according to ASTM is done at 73 °F and 50% RH
(1) What is the meaning of the following “error” terms found in many ASTM standards:
repeatability
reproducibility
bias?
Repeatability: variation in results when using same operator, equipment, procedure and materials
Reproducibility: different operators and equipment (maybe)
Bias: when test method affects results e.g., clamp pressure in thickness measurement
(1) In general, do you expect packaging costs for hazardous materials to be more or less than for non-hazardous ones? For individually shipped product (LTL) to be more or less than for a unit load (TL)?
Packaging cost would be more for hazardous materials and for LTL shipments
(1) How does instrumentation during performance testing help to economize the design?
Instrumentation helps identify maximum loads packages may experience. Hence packaging requirements may be adjusted.
(1) Describe a simple way to check the calibration of a compression tester.
A compression tester acts somewhat similar to a weighing scale. Place a calibrated weight on the platen with the load cell (on top of the bottom platen in our lab) and compare the force value displayed. The two values should match.
(1) Would you expect to use a load tracker to simulate a dead load more for a plastic bottle or aluminum can?
A load tracker continuously monitors the output from the load cell and then automatically
starts the platen moving again if it senses a drop in the load. Due to relaxation tendencies
being greater in plastic than metal, a load cell would be required more for it.
(1) You perform a compression test on a package without using a load tracker. You find that
when you stop the machine once it gets to 500 lbs, the load falls off over time to 450 lbs. if
you wanted to maintain a level of 500 lbs, you could overshoot the mark and then wait for
the load to relax to 500 lbs. How much would you overshoot the 500 lb mark before you stop
the machine?
Retention = 450/500 = 0.9 or 90%
Overshoot to 500/0.9 = 556 lb
(1) What is the purpose of a “preload” when compression testing boxes according to ASTM
D642?
Preload: reference point for zero deflection, allows definite contact between sample and
platen
(1) If we are interested in whole package (box and product together) compression strength, then
why not test the whole package as is, instead of testing the box and product separately?
Testing the box and product separately provides information needed to redesign the box
for optimum headspace thereby allowing for maximum compression strength.
(1) If you put large handholds in opposite ends of a box whose compression strength is 600 lbs, potentially how much are you reducing its compression strength to?
The sides the handholds are cut into theoretically do not contribute anything to the overall
compression strength. Each face contributes 1/12 of the compression strength, hence we lose 2x1/12 = 1/6 the CS or 1/600 = 100 lb of the CS. This reduces the overall CS to 500
lb
(1) What is the absolute maximum height to which you can stack 50 lb packages whose compression strength is 430 lbs? Under what conditions is your answer valid?
(430/50) + 1 = 9.6 ~ 9
Answer valid at standard conditions (see 7)
(1) Look at the table of box humidity factors: specifically H = 110% @ RH = 25%. How can a
box be stronger because of humidity?
A humidity factor ‘H’ of 100% is assigned to a RH of 50% because the lab test for
compression strength is done at 50% RH and therefore serves as a reference for other
RH’s. A decrease in RH (hence the moisture content in the box) is what gives us a higher
strength value.
(1) At what RH does a box have only half of its CS under standard test conditions? How long
does it take for a box to lose half of its CS compared to standard conditions?
~ 90% RH, 1 year (look up the tables for RH and time respectively)
(1) Can you use the retention factors for paperboard cartons? For plastic bottles? For metal cans?
Retention analysis factors only apply to paper based packaging materials and hence do
not apply to plastic bottles and metal cans
(1) A 15” x 10” x 8” box contains a product which is not intended to support any of the load in
compression. The product is a high volume, average priced item and the limiting height on a
stack of these 25 lb packages is the height of the truck, 92”. According to ASTM D4169, at
what test level in lbs should this box be capable of withstanding?
The height of the truck is 92” and the box height is only 8”, hence you can only fit 92/8 =
11.5 ~ 11 boxes on the truck. Hence, H = 8” * 11 = 88”. Also remember, 15” * 10” * 8”
represents L * W * H of the box. Select the safety factor appropriately from the table
based on the information provided in the question. Here we get F = 4.5.
L=W(H-h/h)F
L=25(88-8/8)4.5 = 1125.lbs
(1) A 22” x 15” x 12” box contains twenty 3 lbs cans side by side. This inexpensive product is
designed to support the load in compression. The boxes will be stacked 6 high in a
warehouse. You want to compression test a single package to simulate the environment.
What test level (lbs) do you recommend if no information on climate conditions or storage
time is available?
For both problems 16 and 17, we could not use the retention analysis method since the distribution environment conditions were not specified. W in this problem = 20 * 3 = 60 lbs. h = 12” and H = 12” * stacked 6 high = 72”. Safety factor from table = 1.5 (product isinexpensive)
L=W(H-h/h)F
L=60(70-12/12)1.5=450lbs
(1) What is the highest safety factor possible according to retention analysis?
For this problem look at the worst possible conditions for all retention factors and
substitute in the retention analysis equation.
F=1/HTPPPOV
F=1/.29.46.05.51.67 = ~ 44
(1) How many drops are likely to occur in the life of an average package?
According to ASTM 6-12 and ISTA - 10
(1) How do you suppose drop heights versus package weight tables are created?
Data recorders, actual observations by supervisors/managers
(1) Shock Fragility
How do you explain the fact that a DVD player dropped from 24” onto a cushion does not
break whereas the same DVD player dropped from 12” onto a pallet does?
Deceleration = ∆V/∆t. A cushion allows the shock to last longer than a pallet and absorbs
most of it rather than the product.
(1) Shock Fragility
A bare product dropped onto the ground from 24” will have an impact velocity of 136 in/sec.
If it slows to a stop in 5 ms, what is the deceleration in G’s? A soft cushion allows the
product to slow down over a longer time period, say about 50 ms. What does this do to G?
Deceleration = ∆V/∆t.
1. Deceleration = 136/0.005 = 27,200 in/s = 27200/386.4 = 70.4 G;
- Deceleration = 136/0.05 = 2,720 in/s = 2720/386.4 = 7.04 G
(1) Shock Indicators/Acceleromoters
Why should the object you want to mount the accelerometer on be at least ten times as
heavy as the accelerometer itself?
So that it does not cause any interference (such as rotation) with the natural motion of the fall
(1) Shock Pulse Information
What is the typical range of shock durations found in packaging situations?
2-100 ms
(1) Shock Pulse Information
An accelerometer is mounted sideways in a package and placed between other packages in a
railcar. The accelerometer records the shock pulse below during railcar coupling. The railroad
claims that railcars are never coupled at velocities greater than 7 mph. Do you believe that
this is the case? Assume triangular shape factors.
Here all we need to find out is the impact velocity, Vi, since we are looking at the coupling velocity only. So, from the left part of the shock pulse,
Vi = .0540/100018*386.4 = 139.4in/s
Need to convert to MPH
139.4in/s3600s/1hr1ft/12in*1mile/5280 feet =
7.9 mph
So the railroad’s claim is false
(1) Shock Pulse Information (See Image)
If the velocity change for a package dropped from 10” is 125 in/sec, what would the velocity change be for a drop from 40” onto the same surface?
250in/s
See Solution Set
(1) Shock Pulse Information
Under what conditions are the average and peak G’s the same?
When the shock pulse is trapezoidal or square in shape
(1) Shock Pulse Information
If the drop height is 10”, what is the typical range for the rebound height in a packaging
situation?
.9 < hr < 2.5
See Solution Set
(1) Shock Pulse Information
If “e” is less than 1, then the energy is not conserved in the impact. Where does the energy
go?
Floor, product, air, changing shape of objec
(1) What does the “seismic” mass on a shock machine do?
Isolates the shock, immobilizes impact surface
(2) Why is the velocity change defined to be the sum of impact and rebound velocities instead of the
difference as the name “change” suggests?
ΔV = Vi – (-Vr) = Vi + Vr.
The two velocities are in opposite direction.
(2) Drop Height Sensors (See Image)
The three separate shocks from the tri-axial accelerometer are combined into one called the
“resultant,” from which the drop height is calculated in the usual manner. What is the drop height
for the resultant shock pulse below? The measured free fall time just before impact is 250 ms. Was
this a toss or a simple drop? (See Image)
Shock Pulse Analysis h ≈ 11 in
Free Fall time = 12 in
Since the two drop heights calculated appear to be very close to each other, this was a simple drop.
See Solution Set
(2) Drop Test Machines
Look at the shock machine calibration chart. On the plastic programmers, what shock machine drop
height is equivalent to a 24” free fall?
Look up the closest value of ΔV = 136 on the calibration table for plastic programmers. The answer is 11
inches.
See Solution Set
(2) Drop Test Machines
A cushioned product is strapped to the table of a shock machine and dropped from 10” onto the
plastic programmers. The coefficient of restitution between the shock table and the programmers is
0.4. What is the equivalent free fall drop height?
Table impact velocity (Vi) = 2gh = 2386.410 = 88 in/s
e = Vr/Vi, Vr = 0.4*88 = 35 in/s
DeltaV = Vr + Vi = 123 in/s
Max free fall Vi = Shock table DeltaV
Max free fall Vi = 123 in/s = (sq root)2gh
Therefore free fall drop height = 19.6 in
(2) Drop Test Machines
You plan to simulate a 30” free fall on a shock machine using plastic programmers. The test object is a boxed and cushioned TV monitor. From what height should you drop the shock table? (“e”
between the table and the programmers is 0.4)
h = 15.3
See Solution Set
(2) Damage Boundary Curve
A product gets damages when dropped using plastic programmers from 10 inches and a second
sample gets damaged when dropped using gas programmers at 450 psi. Construct a neatly drawn and labeled DBC.
a. Will a 75 G, 20 ms, half sine shock received by the product damage it?
b. Will a 150 G, 3 ms, triangular shock received by the product damage it?
A. Will Damage
B. No Damage
See Solution Set
(2) Cushioning Materials
A 15” x 12” x 8” product is encased in a 3” thick 2 pcf cushioning material and then placed in a box.
What are the box dimensions? How much weight does the cushion add to the package?
Box dimensions = 21” x 18” x 14”
(add 2 times 3” for all dimensions)
Cushion volume = (21” x 18” x 14”) – (15” x 12” x 8”) = 3852 in3
= 2.23 ft3
(2) Cushioning Materials
Which type of cushion is more likely to have lower coefficient of restitution, open-cell or closed-cell?
. Open-cell
(2) Cushion Design
The corner of a product can penetrate far enough into a cushion during impact to crack the cushion,
especially if the cushion is brittle, like EPS. What can you do to take care of this?
Cut a chunk out at the corner
(2) Cushion Design
A block shaped product is dropped from 12” without a cushion. The G level is likely to be the
greatest in which of the following cases?
a. Perfect corner drop
b. Perfect edge drop
c. Perfect flat drop onto the largest face
d. Perfect flat drop onto the smallest face
c. Perfect flat drop onto the largest face.
(2) Cushion Design
What is the thinnest Arcel 512 cushion you can use to protect a 50 lb product (10” x 10” x 5”) with a
fragility of 50 G in multiple drops from 48” if the product is cushioned under its entire base?
Static stress = 50/(10 * 10) = 0. 5 psi, won’t work
Try different cushion or orientation
Static stress = 50/(10 * 5) = 1 psi → 4 in
(2) Cushion Design
A 15 lb product measuring 15” x 10” x 5” is encased in polyurethane foam using the same thickness
on each face, and placed in a box measuring 21” x 16” x 11”. If dropped from 30” onto any face,
what is the largest G the product will experience?
Cushion thickness = 3 in
a. Drop on 10 in x 15 in face: Static stress = 15lb/ (10” x 15”) = 0.1 psi. from cushion curve, G = 25
b. Drop on 5 in x 15 in face: Static stress = 15lb/ (5” x 15”) = 0.2 psi. From cushion curve, G = 50
c. Drop on 5 in x 10 in face: Static stress = 15lb/ (5” x 10”) = 0.3 psi. From cushion curve, G = 85
See Image
(2) Cushion Design
Suppose you want to design a block style cushion made from 2 pcf Arcel 512 foam for a 35 lb
product. The product measures 10” x 7” x 5” and has a fragility of 30 G. What is the expected drop
height for this product? What should the thickness of the cushion be for flat-drop protection if the
product needs to be supported under its entire base? What should the thickness and the bearing area be if it does not need full base support?
. W = 35 lb, 10” x 7” x 5”, fragility = 30G, Expected drop height = 24”
Follow example as solved in class.
(3) Spring-Mass Model
A 20lb product placed on top of a cushion causes it to compress 0.1”. What is the spring constant for the cushion? What would the cushion compression be if an additional 10lbs were placed on top?
Case 1: dst = W/k or k = W/dst = 20/0.1 = 200 lb/in Spring constant, k, is a constant property of a spring i.e. it does not change for changing applications
Case 2: dst = W/k = 30/200 = 0.15 inches
(3) Spring-Mass Model
A 30 lb product on a 100 lb/in cushion is dropped from 24”. What are the peak G, dynamic
deflection and shock duration? Repeat for a 48” drop height
G = 12.6
Dynamic Deflection = 3.8 inches
Shock Duration = 87 ms
(3) Natural Frequency
A sinusoidal waveform is shown below. What are the period and natural frequency
f = 3.5 cycles/0.07 s = 50 Hz period = 1/f = 1/50 = 0.02 s or 20 ms
(3) Natural Frequency
A horizontal square plate is supported at its four corners. The natural frequency is 20 cps.
Does placing an additional support at the center of the plate raise or lower the natural
frequency
More support = increased stiffness = higher fn
(3) Natural Frequency
A fully loaded truck trailer weighs 50,000 lbs (trailer plus load) and has a natural frequency
of 2 cps on its suspension. An empty trailer has a natural frequency of 8 Hz. Estimate the
weight of the empty trailer
Loaded Truck = 2.45 in
Empty Truck = .153 in
(3) Natural Frequency
Estimate the peak G to a packaged product in a 24” drop if the cushion gives the product a
natural frequency of 10 cps
fn = .097 G = 22.2
(3) Natural Frequency
A product on a cushion is placed in a box. An accelerometer attached to the product records
a peak G of 20 in a flat drop from 36”. Estimate the natural frequency of the product on its
cushion
G = .18 in fn = 7.4 Hz
(3) Natural Frequency
Estimate the range of G levels likely to be encountered by trucks going over a 2” high bump
Truck frequency range = 2-8 Hz
2 Hz = .82
8 Hz = 13.08
(3) Resonance
True or False? The natural frequency of a packaged product is more important than its
weight in determining its response during transportation
True: The natural frequency of a packaged product is more important than its weight in
determining its response during transportation
(3) Resonance
Describe how you can find the natural frequency of a circuit board in a TV set using a
vibration table
See methods 3 & 4 from class notes for “Estimating Natural Frequency
(3) Transportation Environment
. At what location(s) on the floor of a truck trailer is the shock to a package likely to be the
greatest?
Tail end and over the rear axles
(3) Transportation Environment
Besides the suspension, name other sources of vibration present in a random vibration
signal taken off the floor of a truck trailer
Suspension, tires, structural, engine, wheel imbalance
(3) Transportation Environment
What is the natural frequency of a truck trailer on its suspension if the truck is carrying a
medium load
Frequency range for truck suspension = 2 Hz (loaded) – 8 Hz (empty), therefore medium
load can be estimated to be 4 Hz
(3) Transportation Environment
The vibration signal recorded off the floor of a truck is shown below. Is this a heavily loaded
truck or a lightly loaded one
2.5 cycles/0.75 s = 3.33 Hz
3.33 Hz is closer to 2 Hz than 8 Hz when looking at the truck trailer frequency range of 2-8 Hz
Hence, it is a heavily loaded truck
(3) Transportation Environment
What are the two frequencies present in the portion of the random vibration signal shown
below
- 5 cycles/0.3 sec = 5 Hz (suspension)
6. 5 cycles/0.3 sec = 22 Hz (most likely tires)
(3) Vibration Damage
Explain how vibration can cause a screw‐on lid on a plastic bottle to loosen up during
transportation
Flexing causes thread-to-thread contact to break for brief intervals
(3) Vibration Damage
In a stack of packages on a truck, which location in the stack (top or bottom) generally
causes the most product damage and why? Which location causes the most package damage
and why
Product damage on top of stack due to more movement, package damage on bottom of stack
due to dynamic compression
(3) Vibration Damage
Is flex cracking likely to be more of a problem at high or low temperature?
low temperature
(3) Performance Testing
What is the main difference in the motion of the vibration table when testing according to
ASTM D999 and ASTM D4728?
D999 = sinusoidal vibration, D4728 = random vibration
(3) Performance Testing
What can a random vibration test potentially do to a product that a single frequency test
cannot?
Excite multiple components at the same time
(3) Performance Testing
Using ASTM D4169, you do a performance test on an expensive 30 lb product packaged in a
box. The package is shipped as a single unit. What distribution cycle do you use?
Leave it to the students
