### UN38 3 T4 Options

1
Considerations About UN38.3 T4 Test, and its
Applicability to Large Lithium Batteries.
How to improve this test?
T4 Constant Acceleration Test – Force vs Mass
Currently, the UN38.3 T4 test is based on constant acceleration, which means
higher force is applied to larger battery mass.
Batteries over 6200Wh (approximately 120kg) are not required to be tested at all.
Force
UN38.3 T4 Shock Test Force vs Mass
F  ma
50G
Cell
Test
Only
150G
12kg
50kg
Mass
~120kg
Does a bigger battery
actually experience
higher force during
transport?
>120kg (>6200Wh)
But do larger batteries actually experience higher forces, or constant accelerations under
actual shipping conditions?
Let’s consider a case of large shock in shipping  Battery Drop from Height, and compare it
to the constant acceleration of UN38.3 T4. Let’s study one battery of mass m and one
battery 10x that mass.
2
3
T4 Constant Acceleration Test – Force vs Mass
Constant acceleration would require the ratio of velocity change over time to be
constant for all masses of batteries tested to the constant acceleration. UN38.3 T4
test is for 50G acceleration for 12kg<X<6200Wh batteries.
But is this representative of the actual physics of battery transportation?
Acceleration is a measure of velocity change
over time.
dv
dt
50G acceleration is similar to stopping a mass
travelling at 50m/s and stopping on 0.1s, or
travelling at 10m/s and stopping in 0.02s.
What is the actual situation? How
much does a battery pack
accelerate? What is the force?
dV - Velocity Change - m/s
a
Velocity Change vs Impact Time for 50G
Impact
60
50
40
30
20
10
0
0
0.02
0.04
0.06
0.08
dt - Impulse Time - Seconds
0.1
4
Consider a Drop Test – Constant Velocity
Compare it to a drop test.
Large Mass
=10xSmall Mass
Small Mass
Mass=m
Mass=10m
mg
mg
d
An object in freefall will have a
velocity related to the distance
of freefall.
v
2 gd
For a given height of freefall, d,
both a large mass and a small
mass will have the same
velocity at impact.
But is the acceleration on
impact the same?
Semi Rigid Surface
5
Consider a Drop Test – Constant Velocity
Small Mass
v
Large Mass
=10xSmall Mass
2 gd
Momentum p=mv
Kinetic Energy=1/2mv2
Momentum p=10mv
Kinetic Energy=1/210mv2
Semi Rigid Surface
The momentum of an object in motion is its mass x its velocity. The energy is the mass x
velocity squared. The velocity for the small mass and large mass dropped from the same
height is the same!
When the object in motion strikes another object, the momentum is transferred to that
other object (conservation of momentum principle), and the energy is conserved
(conservation of energy principle).
Impact Deformation  Longer Impact Time
Small Mass
v
2 gd
Large Mass
=10xSmall Mass
Momentum p=mv
Kinetic Energy=1/2mv2
Elastic deformation of impact surface and mass
due to small momentum. Energy  Elastic
Deformation.
6
Plastic Deformation of
mass shape.
Momentum p=10mv
Kinetic Energy=1/210mv2
Elastic + Plastic Deformation of impact
surface due to large momentum. Energy 
Elastic + Plastic Deformation.
Semi Rigid Surface
For a small mass and a large mass dropped from a height, the change in velocity, dv, is
the same. Both are brought to rest and the momentum goes to zero. The kinetic energy
is distributed through elastic deformation (like a spring) and plastic deformation
(physical permanent damage to both surfaces). The higher the momentum, the more
deformation.
But the force acting on a small mass and a large mass is not proportional to the
difference in mass, because the impact time is different due to the magnitude of the
deformation!
Impact Deformation  Longer Impact Time
Small Mass
v
2 gd
Large Mass
=10xSmall Mass
I=Fsdts=mdv
Elastic deformation of impact surface and mass
due to small momentum. Energy  Elastic
Deformation. Short Impact Time.
Plastic Deformation of
mass shape.
I=FLdtL=10mdv
Elastic + Plastic Deformation of impact surface
due to large momentum. Energy  Elastic +
Plastic Deformation. Long Impact Time!
Semi Rigid Surface
For a change in momentum, an object must undergo an Impulse.
Impulse is the Acting Force x Impact Time = Change in Momentum.
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Impact Deformation  Longer Impact Time
Small Mass
v
2 gd
I=Fsdts=mdv
Large Mass
=10xSmall Mass
I=FLdtL=10mdv
Semi Rigid Surface
Since the large mass is deformed by the semi-rigid surface more than the small mass,
and the semi-rigid surface is deformed by the large mass more than the small mass, the
resulting Impulse time is longer. (it takes more time for the large mass to travel through
the deformation)
Small Mass Impact Time < Large Mass Impact Time
dts<dtl
If the difference between the Small Mass impact time and the large mass
impact time is Dt, then dtl=dts+Dt
8
Longer Impact Time  Lower Force and Acceleration
Small Mass
v
2 gd
Large Mass
=10xSmall Mass
I=Fsdts=mdv
Small Mass Force x Small Mass Impulse Time =
Small Mass x Change in Velocity.
Impulse
Momentum Change
F s dt s  mdv
Fs 
mdv
dt s
 ma s
Let’s consider the difference
between the Small Force, FS,
and the Large Force, FL.
I=FLdtL=10mdv
Large Mass Force x Large Mass Impulse Time =
Large Mass x Change in Velocity.
Impulse
Momentum Change
dt L F L  10 mdv
FL 
10 mdv
FL 
10 mdv
dt L
dt S  D t
 10 ma L
m
10 dv
dt S  D t
9
Longer Impact Time  Lower Force and Acceleration
Ratio of Small Force
to Large Force
mdv
FS
dt s

FL
m
10 dv
dt S  D t
Fs

FL
dt S  D t
10 dt s
10 dt s F s  F L ( dt S  D t )
mdv
FS
FL
dt s

m
Even though the
large mass is 10x
the small mass,
because Dt>0, the
large force is not
10x the small force.
10 F s  F L (1 
10 dv
Dt
dt S
dt S  D t
10
(1 
Dt
dt S
Fs  FL
)
)
The longer the Dt,
the smaller the
impact force.
(This is why we design cars
to crush in impact – to lower
the impulse force!)
Since Dt>0,
FL<10FS
10
Longer Impact Time  Lower Force and Acceleration
10
(1 
Dt
Fs  FL
)
T4 treats all size from 12kg to 6200Wh with the
same acceleration.
dt S
10
(1 
Dt
Now let’s consider the acceleration, aS for the
small mass and aL for the large mass.
ma S  10 ma L
)
But…
dt S
1
(1 
Dt
dt S
aS  aL
)
Since Dt>0, aL is always less than aS.
The larger battery experiences smaller
acceleration.
Therefore under T4 with a constant acceleration
for different masses, larger batteries are subjected
to a higher force then necessary.
Another way to look at it is again to compare to a drop test…
11
T4 Constant Acceleration Test  Higher Drop
Acceleration G vs Impact time for Item Dropped from Height
100000
Acceleration G
10000
Graph showing lines of constant height
drop test and resulting acceleration G
for a given impulse time.
UN38.3 T4 gives 0.011s impulse time for
50G shock.
1000
150g
Drop Test Height
1m
2m
20m
200m
Constant Acceleration Line
100
50g
10
But larger mass needs larger force to generate
0.011s pulse. It doesn’t reflect real world!
1
0.0001
0.001
0.01
0.1
dt - Impulse Time - Seconds
1
10
12
T4 Constant Acceleration Test  Higher Drop
Acceleration G vs Impact time for Item Dropped from Height
100000
Acceleration G
10000
Since the larger mass has longer
impulse time…
Increasing Impulse Time
1000
150g
Drop Test Height
1m
2m
20m
200m
Constant Acceleration Line
100
50g
10
1
0.0001
using a test of constant G is similar to
increasing the height of a drop test for
larger mass objects!
0.001
0.01
0.1
dt - Impulse Time - Seconds
1
10
13
T4 Constant Acceleration Test – Force vs Mass
• So we have established two things:
– Larger battery assemblies experience lower accelerations than smaller
batteries during shock events in transportation due to the
deformations in the system under load.
• Therefore the constant acceleration test exposes larger batteries to
disproportionally larger forces than they would experience in reality.
– Battery Assemblies of higher mass experience forces in transportation
that are not proportionally higher than batteries of smaller mass.
• Therefore reduction in force from the constant acceleration line of T4 is
warranted.
• And the corollary of this is that the surface that an item is
attached to for transport can only impart a maximum force on
that item before it deforms under load.
– An airplane floor, for instance, will deform significantly under the force
that is necessary to accelerate a large battery assembly, thereby
reducing the acceleration and the magnitude of the force.
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T4 Constant Acceleration Test – Force vs Mass
There are two descriptions of conditions to relieve testing below in current publication...
<The last paragraph of 38.3>
When batteries that have passed all applicable tests are electrically connected to form a
battery assembly in which the aggregate lithium content of all anodes, when fully
charged, is more than 500 g, or in the case of a lithium ion battery, with a Watt-hour
rating of more than 6200 Watt-hours, that battery assembly does not need to be tested
if it is equipped with a system capable of monitoring the battery assembly and
preventing short circuits, or over discharge between the batteries in the assembly and
any overheat or overcharge of the battery assembly.
<P903 in Model Regulations>
Proposal of the addition of the paragraph below into T.4 Shock
Shock test for battery assembly with (test 1 or 2) can be applied if the battery assembly is
contained in a strong, impact resistant outer casing and is equipped with a system capable of
monitoring the battery assembly and preventing short circuits, or over discharge between
the batteries in the assembly and any overheat or overcharge of the battery assembly.
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16
T4 Constant Acceleration Test – Drop Test?
So, the basic rationale for the T4 shock test needs to be clarified.
 Does it represent an object dropping onto a rigid surface from a given height? Or a
crash from a given speed?
UN38.3 T4 Shock Test By Drop Test
 Then Option 1
Option 1) Change the criteria from an Acceleration
G based test to a Drop Test from a height, or a
sled test from a corresponding velocity.
Basic Problem: What height? What surface?
PGII test requires 1.2m
PGI test requires 1.8m
SAEJ2464 tests at 2m
(What height?
What velocity?
What surface?)
ma
d
(Option 1 is more favorable as test
equipment is more widely available)
Proposal of the addition of the paragraph below into T.4 Shock
Shock test for battery assembly with drop from height X can be applied if the battery
assembly is contained in a strong, impact resistant outer casing and is equipped with a
system capable of monitoring the battery assembly and preventing short circuits, or over
discharge between the batteries in the assembly and any overheat or overcharge of the
battery assembly.
17
T4 Constant Acceleration Test – Force Test?
 Does it represent a certain force that can act on the object? For instance,
a surface can only impart a maximum force before it deforms.
 Then Option 2
Option 2) Change the criteria from an
Acceleration G based test to a
Force Based test.
UN38.3 T4 Shock Test Force vs Mass
Basic Problem: What force? Should it be
[email protected] or something else?
Force
F  ma
Maximum Force
(How to define?)
50G
Cell
Test
Only
150G
12kg
50kg
Mass
~120kg >120kg (>6200Wh)
Proposal of the addition of the paragraph below into T.4 Shock
Shock test for battery assembly with constant F can be applied if the battery assembly is
contained in a strong, impact resistant outer casing and is equipped with a system capable of
monitoring the battery assembly and preventing short circuits, or over discharge between
the batteries in the assembly and any overheat or overcharge of the battery assembly.