t4 constant acceleration test – force vs mass

Considerations About UN38.3 T4 Test, and its Applicability to Large Lithium Batteries.

How to improve this test?

1

Mass

Forc

e

12kg 50kg ~120kg >120kg (>6200Wh)

150G

50G

Cell Test Only

UN38.3 T4 Shock Test Force vs Mass

maF Does a bigger battery actually experience higher force during transport?

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.

T4 Constant Acceleration Test – Force vs Mass2

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.

Acceleration is a measure of velocity change over time.

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.

Velocity Change vs Impact Time for 50G Impact

0

10

20

30

40

50

60

0 0.02 0.04 0.06 0.08 0.1

dt - Impulse Time - Seconds

dV

- V

elo

cit

y C

ha

ng

e -

m/sdt

dva

What is the actual situation? How much does a battery pack accelerate? What is the force?

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?

An object in freefall will have a velocity related to the distance of freefall.

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?

mg

gdv 2

d

Semi Rigid Surface

Small Mass

Large Mass=10xSmall Mass

mg

Compare it to a drop test.

4

Consider a Drop Test – Constant Velocity

Mass=m Mass=10m

Small Mass Large Mass=10xSmall Mass

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).

5

Consider a Drop Test – Constant Velocity

Momentum p=mvKinetic Energy=1/2mv2

Momentum p=10mvKinetic Energy=1/210mv2

gdv 2

Small Mass

Elastic deformation of impact surface and mass due to small momentum. Energy Elastic Deformation.

Elastic + Plastic Deformation of impact surface due to large momentum. Energy Elastic + Plastic Deformation.

Semi Rigid SurfaceFor 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!

6

Impact Deformation Longer Impact Time


Plastic Deformation of mass shape. gdv 2

Momentum p=mvKinetic Energy=1/2mv2

Momentum p=10mvKinetic Energy=1/210mv2

Small Mass

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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gdv 2

I=FLdtL=10mdvI=Fsdts=mdv

Plastic Deformation of mass shape.

Elastic deformation of impact surface and mass due to small momentum. Energy Elastic Deformation. Short Impact Time.

Elastic + Plastic Deformation of impact surface due to large momentum. Energy Elastic + Plastic Deformation. Long Impact Time!

Small Mass

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)

8



gdv 2

Small Mass Impact Time < Large Mass Impact Timedts<dtl

If the difference between the Small Mass impact time and the large mass impact time is t, then dtl=dts+t

I=FLdtL=10mdvI=Fsdts=mdv

Small Mass

I=FLdtL=10mdv

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Longer Impact Time Lower Force and Acceleration


gdv 2

ss

s

ss

madt

mdvF

mdvdtF

LL

L

LL

madt

mdvF

mdvFdt

1010

10

tdt

dvm

tdt

mdvF

SSL

1010

Small Mass Force x Small Mass Impulse Time = Small Mass x Change in Velocity.

Large Mass Force x Large Mass Impulse Time = Large Mass x Change in Velocity.

Impulse Momentum Change

I=Fsdts=mdv

Impulse Momentum Change

Let’s consider the difference between the Small Force, FS, and the Large Force, FL.

10


tdtdv

m

dtmdv

F

F

tdtdv

m

dtmdv

F

F

S

s

L

S

S

s

L

S

10

10

Ls

S

SLs

SLss

s

S

L

s

FF

dtt

dt

tFF

tdtFFdt

dt

tdt

F

F

)1(

10

)1(10

)(10

10

Since t>0, FL<10FS

Ratio of Small Force to Large Force Even though the

large mass is 10x the small mass, because t>0, the large force is not 10x the small force.

The longer the t, the smaller the impact force.

(This is why we design cars to crush in impact – to lower the impulse force!)

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LS

S

LS

S

Ls

S

aa

dtt

mama

dtt

FF

dtt

)1(

1

10)1(

10

)1(

10 Now let’s consider the acceleration, aS for the small mass and aL for the large mass.

T4 treats all size from 12kg to 6200Wh with the same acceleration.

But…

Since t>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…

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T4 Constant Acceleration Test Higher Drop

Acceleration G vs Impact time for Item Dropped from Height

1

10

100

1000

10000

100000

0.0001 0.001 0.01 0.1 1 10


Ac

ce

lera

tio

n G

1m

2m

20m

200m

50g50g

150g150g

Drop Test HeightDrop Test Height

Constant Acceleration LineConstant Acceleration Line

Graph showing lines of constant height Graph showing lines of constant height drop test and resulting acceleration G drop test and resulting acceleration G for a given impulse time. for a given impulse time. UN38.3 T4 gives 0.011s impulse time for UN38.3 T4 gives 0.011s impulse time for 50G shock.50G shock.

But larger mass needs larger force to generate But larger mass needs larger force to generate 0.011s pulse. It doesn’t reflect real world! 0.011s pulse. It doesn’t reflect real world!

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T4 Constant Acceleration Test Higher Drop

Acceleration G vs Impact time for Item Dropped from Height

1

10

100

1000

10000

100000

0.0001 0.001 0.01 0.1 1 10


Ac

ce

lera

tio

n G

1m

2m

20m

200m

50g50g

150g150g

using a test of constant G is similar to using a test of constant G is similar to increasing the height of a drop test for increasing the height of a drop test for larger mass objects!larger mass objects!

Drop Test HeightDrop Test Height

Constant Acceleration LineConstant Acceleration Line

Since the larger mass has longer Since the larger mass has longer impulse time… impulse time…

Increasing Impulse TimeIncreasing Impulse Time

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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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>

<The last paragraph of 38.3>

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.

Proposal of the addition of the paragraph below into T.4 Shock

There are two descriptions of conditions to relieve testing below in current publication...

T4 Constant Acceleration Test – Force vs Mass15

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?

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.

(What height? What velocity?What surface?)

d

ma

UN38.3 T4 Shock Test By Drop Test

16

T4 Constant Acceleration Test – Drop Test?

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.


Basic Problem: What height? What surface?PGII test requires 1.2mPGI test requires 1.8mSAEJ2464 tests at 2m (Option 1 is more favorable as test

equipment is more widely available)

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.

Mass

Forc

e

12kg 50kg ~120kg >120kg (>6200Wh)

150G

50G

Cell Test Only

UN38.3 T4 Shock Test Force vs Mass

maF

Maximum Force(How to define?)

Basic Problem: What force? Should it be 12kg@50G or something else?

17

T4 Constant Acceleration Test – Force Test?

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.


t4 constant acceleration test – force vs mass

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