Automotive E-coat Paint Process Simulation Using FEA
This paper was presented at the NAFEMS Ninth International Conference in Orlando, FL, USA on May 29,
Frederick Hess, UFS Corporation, Valparaiso, IN, USA
Ulises Gonzalez, Ph.D., ALGOR, Inc., Pittsburgh, PA, USA
Finite element analysis (FEA) is widely utilized
in the automotive industry to study a variety of engineering design
activities such as crash test simulations and optimization of
manufacturing processes. One of the latest areas to benefit from FEA
technology is the E-coat paint process. E-coat paint provides for
excellent corrosion resistance and is the first of several different
protective paint layers applied to an automotive body. During the
E-coat paint process, an entire automotive body is immersed in a
liquid bath. By applying an electrical current, a thin paint film
forms over all the surfaces in contact with the liquid, including
those surfaces in recessed portions of the body.
The E-coat paint process deposits a thin paint film on the
automotive body under the influence of a voltage gradient of about
200 to 300 volts. The water-based E-coat paint bath is conductive
with an array of anodes that extends into the bath delivering a DC
current. The paint film that forms has physical properties that
resist corrosion (these appear only after the automotive body has
been cured in an oven). However, as the paint film forms, its
electrical resistance increases.
In the past several years, two-dimensional (2-D) FEA models of
the E-coat paint process have been developed for specific or limited
applications. In this paper, we discuss a general three-dimensional
(3-D) FEA method using ALGOR software. This method can simulate the
formation of the E-coat film and can thus predict its thickness at
any point on the surface of the automotive body. Operational variables,
such as voltages and process duration, are used to simulate the
time-dependent interaction among the automotive body, the increasing
paint layer and the liquid within the E-coat bath.
The method is based on a quasi-static technique that accounts for
the changing material properties of the paint layer. A quasi-static
approach is appropriate because the time required for the electric
field to be established is much smaller than the duration of the
paint deposition process. The actual time is simulated by considering
a series of time steps, each of which requires an electrostatic
solution. The E-coat film thickness is updated during each time
A primary concern is how to model the changing FEA geometry due
to the growth of the E-coat film. Technology has been developed that
is capable of generating a film of specified thickness (as a function
of position) on the automotive body.
Because of symmetry along the longitudinal axis of the automotive
body, only half the body was modeled. In addition, an enclosing box
was constructed around the automotive body and features were created
for the possible anode locations. Generally, there is little
electrical interaction between two adjacent automotive bodies. Any
net electrical current that flows into the leading and trailing
surfaces of the enclosing box is considered negligible. The space
between the outside of this box and the automotive body will be
considered as the E-coat paint bath. Furthermore, the growth of the
E-coat film is assumed to be perpendicular to the surface of the
automotive body at all times.
Laboratory experiments can establish an accurate estimate of the
deposition coefficient of the E-coat film that forms in response to
the flow of electrical current. The result of interest is the flow
of DC electrical current that causes the E-coat film to form. The
growth of the E-coat film is dependent on the number of Coulombs that
are delivered. In each iteration, the FEA model is solved for
electrical current flow from which the E-coat film thickness can
then be calculated. The material properties for each of the
elements where the E-coat film develops are also changed in
response to the growth in the E-coat film thickness.
Another feature of a typical automotive E-coat paint system is
the use of multiple voltage zones and differing locations where
the anodes are placed in the E-coat bath. These factors affect the
application of voltages in the FEA model. The appropriate voltage
values must be added or updated for each new iteration as required.
The primary use of the method is to predict how, as the paint
layer forms, the effective electrical resistance increases, which
prompts the current to seek out less resistive paths. Even though
the paint film that forms has drastically reduced conductivity
compared to the surrounding E-coat paint bath, it is not enough to
stop its continued growth past the optimum thickness which is
generally about 25 μ.
A 3-D FEA model of the E-coat paint process would not only help
the designers of a new automotive body obtain a more uniform paint
distribution, but could be advantageous to existing assembly
plants, as they explore means to reduce costs as well as make
improvements to existing designs. It is well known that the layout
of the anodes and the automotive body have a significant impact on
the overall electrical resistance of the system, and thus the
amount of current that must be delivered. In some circumstances,
assembly plants are faced with the challenge of obtaining an
adequate E-coat paint thickness on exposed parts of the automotive
body, while avoiding an insufficient thickness in recessed regions.
The standard solution is to increase the overall voltage, which
results in greater energy and material costs. The resulting
E-coat paint thickness achieved on the exposed parts of the body
is particularly costly because it provides for no additional
Using the method discussed in this paper, engineers can
perform a variety of optimization exercises without incurring
the high costs or risks of making operational modifications to
the existing E-coat paint process at an assembly plant.
E-coat paint is an organic polymer applied to a conductive
automotive body under the presence of medium-range voltage and
relatively high electrical current. It only takes approximately
10 – 15 μ of film thickness to afford corrosion protection. While
the E-coat film may be very thin, annual E-coat paint material
usage can be $2–4 million (USD) for an automotive plant. Thus,
even small percentage reductions in usage can yield significant
annual savings for the plant.
Simulation techniques are now in widespread use in most other aspects
of automotive design, plant layout and assembly optimization. The
benefits for adopting E-coat FEA simulation are substantial for the
The theme of this paper will be to establish the framework of how
FEA can be used to construct a simulation model appropriate for the
E-coat paint process.
BENEFITS OF USING FEA SIMULATION
Up to this point, computer simulation was not available for a
process like E-coat painting. E-coat and other "soft" processes
did not have the analytical tools that have been applied to other
automotive design disciplines such as strength and materials,
vibration, thermodynamics and so on.
As an example of what E-coat FEA simulations can provide to an
automotive plant, consider the following scenario – an automotive
plant produces 1400 cars per day; operates for 220 days per year,
and the annual E-coat paint expenditures are $4 million (USD).
If the plant can reduce its E-coat paint material usage by 2%,
it can save over $0.26 (USD) per body. This would be a significant
cost reduction effort. Table A shows what the per-body cost reduction
would be for other material reduction targets.
In addition, E-coat FEA simulation will provide automotive
OEMs with new virtual tools to better evaluate new designs
and capital equipment changes that can lead to optimization of
new body designs and reduction of E-coat paint, energy
consumption and chilled water.
Variable Cost Savings Potential
Plants operate on QA recommendations for: 1) the state of the
equipment used in the E-coat machine; and 2) the results the
machine is producing. They have very few tools to help them
evaluate new cost-saving projects. As shown earlier, there
can be significant cost savings for even small reductions in
material usage. In addition, energy and cooling costs can
creep up ever so slowly while the plant focuses on other matters.
More support can be given to projects that offer substantial
reduction in electrical resistance (i.e., replacing Membrane
Electrode [ME] Cells for example) since the plant has
confidence that the simulation shows reasonable results.
In some cases, simulation will be used to improve quality
and, in these cases, the E-coat material consumption may be
increased slightly to provide for the minimum requirements.
Optimize E-coat Film in Design Stage
The adage of "push quality decisions forward" towards
the design stage in a manufacturing business such as
automotive is very true. Decisions made on the CAD
workstations defining the body designs have a significant
impact on operations at the plant level two years later
when the body is near launch and the plant is scrambling
to produce the units for the first time. It is often too
late to raise the quality level from the back of the assembly
Body designers benefited with the introduction of
CAD and FEA tools for the "hard" aspects of body design.
Now "soft" processes such as E-coat paint can be simulated
and the body designer can make changes that will benefit
the OEM and improve the corrosion resistance characteristics
of the body.
TYPICAL AUTOMOTIVE E-COAT PAINT SYSTEM
Modern plants typically have design limits of
approximately 1400 cars per day. If the work day is
considered to be 20 hours, then the hourly throughput
is 70 bodies per hour. The surface area of a body can
range from a small-size body of 35 m2 to a large-size
body of 100 m2.
For most automotive plants, the automotive body is
fabricated from sheet steel on site or from sub-assemblies
provided by other plants. The assembled body is then
transferred to the paint shop. In the paint shop, the
first step is to degrease and clean the body of most
of the oils, weld balls and other loose metal slag.
The body shown in Figure 1 does not yet have its doors,
hood or trunk attached. It is common for those to be
installed before the body is sent to the E-coat bath.
Many E-coat machines have 10 or more individual
stages or different process baths. The E-coat bath
is one of these stages. Prior to the E-coat machine
is the pretreatment system which creates a zinc
crystalline structure on the surfaces of the sheet
steel of the automotive body. After the E-coat bath
is the post rinse, which recycles the excess E-coat
paint and the oven, which melts the polymer and
creates the tough corrosion protection.
This is the second major step of the E-coat machine
wherein the body is fully submerged while the coating
is being applied. E-coat paint as it is used in
automotive plants is very different from electrostatic
paint applications where extremely high voltages and
very small electrical currents are used to apply top
coats to conductive wares. Electrostatic application
occurs through the air while E-coat paint is applied
to an object immersed in a liquid bath.
Figure 2 shows the entrance to an automotive E-coat
bath that has a continuous moving conveyor. The tank
is about 3 m wide x 3 m tall x 30 m long. The Side ME
Cells are arranged along the side walls of the tank,
typically placed on 30 cm center-to-center spacing.
The ME Cells are responsible for the delivery of
electrical current into the E-coat bath.
Visible above where the top of the body would be
held are the Roof ME Cells. These are generally
placed near the middle of the process to avoid
defects on the upper horizontal surfaces of the
body. Floor ME Cells can be seen in the middle of
the E-coat bath. The use of Roof and Floor ME Cells
reduces the overall system resistance and allows
for the application of the E-coat paint at lower
voltages, compared to using only Side ME Cells.
The time required to apply the E-coat paint is
usually less than 4 minutes and the process begins
at a voltage of approximately 200 volts. About halfway
through the process, the voltage is increased by
approximately 50 to 100 volts. The extra voltage is
required to penetrate further into the body and coat
those regions furthest away from the ME Cells in the
second half of the E-coat paint cycle.
There are a multitude of E-coat process variables,
each with their own operating window. Each one of
these has an impact on the quality of the E-coat film
as well as the all-important film thickness, used as a
main parameter for long-term durability of the
corrosion-free steel body.
Sheet Steel Types
There are many different types of sheet steel that
can be used in the construction of a body. In fact,
there can be many different sheet steel types used on
the same body.
||Sheet typically used
Some of the newer sheet steel materials such as
galvaneal offer cost advantages over those with the
more costly traditional galvanized treatment.
However, these newer materials are more sensitive to
E-coat film defects caused from hydrogen gas trapped
in the quickly forming E-coat film. Special attention
must be paid when these materials are being used.
Car body differentiation can be achieved by using
more costly sheet steel types and more 2-sided
galvanized sheet steel on the higher-end bodies.
Jobs per Hour
High-production automotive assembly plants use a
continuous motion type conveyor system with a capacity
as high as 70 jobs per hour. At lower volume plants,
the jobs per hour can be 12 – 15. They typically use an
indexing type conveyor that is smaller and does not
require as much floor space.
In nearly 80% of the automotive plants in the world,
one or two different bodies are processed. An example is
Ford Chicago Assembly (Illinois, USA) that produces the
Taurus Sedan and the Taurus Wagon. The similarity in the
body styles reduces the difficulty of optimizing the
E-coat film thickness on the two different bodies.
Other plants produce as many as 4 or 5 different body
styles. Their optimization challenge is substantially
greater as the difference in size between the smallest
and largest body can be as much as 60% to 80%.
The DC rectifier provides the voltage gradient necessary
to deliver the electrical current to the cathode, which
causes the organic polymer to fall out of solution and form
on the cathode. Generally, the highest voltage used is less
than 450 V DC. The total current capacity for many automotive
E-coat systems is above 2000 amps.
Cathodic Paint Reactions
Paint solids account for only about 20% of the E-coat bath
and the remainder is deionized water. The organic resin
molecule has an inherently positive charge and so, as shown
in Figure 3, it moves toward the cathode under the presence
of a voltage gradient.
There are four basic electro-chemical reactions simultaneously
occurring. These reactions are: hydrolysis of water,
electrophoresis, electrodeposition and electro-endosmosis.
Hydrolysis of Water
A voltage gradient is applied across two electrodes submerged
in the liquid E-coat bath and the water is broken down at both
the anode and cathode. Electrons are exchanged and they are
circulated in a loop by the DC rectifier causing the electrical
current to flow and work to be performed. As seen in Figure 3,
oxygen gas is generated at the anode and hydrogen gas is
given off at the cathode.
Since there are two opposing electrical poles in the E-coat
bath and an electrical current flow has been established, any
charged particles in the bath will begin to move. The movement
of charged particles in a liquid bath under the presence of a
voltage gradient is called electrophoresis. In the E-coat
process, the polymer resin has a positive charge and is
repelled at the anode so it moves toward the cathode, which
is negative. Negatively charged acetate ions typically move
in the opposite direction and are attracted to the positive
Electrodeposition occurs as the polymer molecule enters the
highly caustic region surrounding the cathode. Usually the
polymer is neutralized by joining with an acid group.
However, when this pairing gets close enough to the cathode,
the acid group is stripped away and the polymer forms on the
As the E-coat film forms and grows in thickness, the
increasing resistive material property of this thin film
becomes a very important factor. Since there are regions
that do not have any film, electrical current seeks out
these "lower" resistance paths until all regions of the
cathode have at least some film.
At some point, the cathode current density falls to a
point where electrodeposition can no longer take place,
generally less than 1 mA/cm2. The voltage gradient would
have to be increased for additional E-coat paint to be
Electro-endosmosis is the removal of the water and
other matter from the interior of the forming E-coat film
as long as the cathode current density is above the
critical minimum value. As the water moves away from the
film, the film has a high degree of porosity and thus more
electrical conductivity compared to when the E-coat film
is better developed and has far less porosity.
Different Voltage Zones
Most automotive E-coat paint systems allow for 2 or 3
different voltage zones in use at the same time. The
exterior of the body is painted first since it is closest
to the ME Cells. The recessed regions of the body are
farther away and, therefore, pose more resistance to the
flow of electrical current. Hence 50 to 100 volts more is
required in the second or later voltage zone. Ideally, a
third DC rectifier can be used for the Floor and Roof ME
Cells to further optimize the E-coat film distribution on
Membrane Electrode System
Figure 4 shows a body in the E-coat bath with its doors
and trunk held slightly open to make it easier for the
paint to form inside the body. The ME Cells provide the
electrical connections that deliver the current into the
E-coat bath so work can be performed.
ME Cell Construction
The electrode is kept separate from the E-coat bath
by an ion-exchange membrane that allows only negatively
charged particles to enter into the ME Cell. These
particles are attracted to the anode and are able to
recombine with free H+ to form common organic compounds.
As shown in Figure 5, the typical TECTRON™ ME Cell
is comprised of a stainless steel electrode (anode),
an ion-exchange membrane and a means to circulate an
electrolytic fluid between the inside face of the
ion-exchange membrane and the exterior surface of the
electrode. The conductivity of this fluid is generally
1 or 2 times that of the E-coat bath. The electrolytic
fluid is also responsible for cooling the surface of
the electrode and keeping its temperature to
approximately 3 – 5 °C above that of the E-coat bath.
The ion-exchange membrane contributes to the overall
electrical resistance and performance of the E-coat
system, especially as it accumulates wear.
The automotive body is designed by an individual or
team that is principally responsible for strength and
rigidity as well as minimization of vibration or
harmonics. E-coat film distribution is not a prime design
input and is generally considered as an afterthought.
Every new body must be submitted for federal
crashworthiness testing. The design team knows this is
an important test and makes every effort to provide the
proper strength as required. Weight savings are important
to fuel economy and so they also attempt to reduce the
overall mass of the design.
E-coat Film Trials
For each new car body, the manufacturer usually spends
up to $500,000 (USD) for the production of 4 to 6
prototype bodies. These bodies will be used for E-coat
paint trials and a process will have to be developed for
the body to meet and surpass the OEM’s quality standards.
If deficiencies are discovered at this stage, then it is
normally not practical to alter the body design to correct
the problems. The plant will have to work around the
issue, which usually means higher costs.
Figure 1 showed what a prototype body, called a "body
in white", could look like. The plant that is designated
to produce the new body would receive several of these
for testing and evaluation purposes. One of the important
tests is a test run through their E-coat paint system.
Afterward, the prototype body is torn down so the E-coat
film in the recessed regions can be measured.
Rocker Panel Structure
The rocker panels typically represent the most difficult
portion of the body to adequately coat during the E-coat
process. This is a recessed region that has one or more
compartments and must be very strong to provide for the
rigidity of the body. Figure 6 shows a rocker panel that
has been opened up to inspect the E-coat film distribution.
If the quality audit reveals a problem, it is too late
to convince the body designer to add more access holes for
paint solids and electrical current to more easily enter
and pass through.
Thus, an assembly plant must usually increase voltage
to drive current into these regions at the expense of
higher variable expenses in terms of extra paint
consumption for the side verticals of the body. An
alternative is to increase the level of galvanization
on the particular part or portion, which is also costly.
Another alternative is to apply a layer of heavy wax in
the recessed region to keep moisture off its surface and
delay the onset of corrosion.
The real issue is that the body designer can only make
educated guesses, based upon previous work for other
similar bodies, about what the E-coat film thickness will
be. Ideally, any E-coat film problems should be addressed
at the same time that the strength, rigidity and
crashworthiness of the body are being designed and
A surprising fact is how much of the total surface
area of a body is located in recessed and difficult to
reach areas. Table C shows the approximate split of
exterior vs. interior/recessed regions for a typical
passenger body – as much as ľ of the total surface
area. These areas are more difficult to adequately
paint without applying too much E-coat paint on the
|Region of body
||Percent of total
surface area (%)
A practical minimum for the E-coat film thickness
is approximately 13 μ in order to afford long-term
corrosion protection. The normal requirement for the
E-coat film thickness is approximately 25 μ. There
is no additional benefit beyond a certain E-coat film
thickness, so any extra E-coat paint thickness is
Uneven E-coat Film Distribution
High E-coat material consumption leads to higher
costs and is something the plant examines to develop
changes in their process or equipment that can lead to
variable cost reductions. Too much E-coat film on the
exterior side verticals and not enough on the exterior
roof or somewhere in the interior is bound to lead to
higher annual variable costs.
Higher Energy Consumption
As the ion-exchange membrane of the ME Cell ages,
its resistivity increases. If the automotive plant wants
to keep all the production levels the same, this means
the voltage set point of the DC rectifier(s) will have
to be increased. In this fashion, the same number of
Coulombs (i.e. same number amps as long as the line
speed did not increase) will be delivered, but the
voltage will have to be increased to accomplish this.
This "extra" voltage does nothing but lead to more
heat rejection into the E-coat bath. This extra heat
must then be removed by the heat exchanger, requiring
more chilled water. In addition, the energy consumption
for the E-coat machine will increase by the increase in
the voltage set point. Using the production figures from
Table A, 2000 amps is required; and if the plant uses
electric-driven chillers, then the refrigeration cost
will be about the same (or even a little more) than the
heat it is trying to remove from the E-coat bath in the
first place. For a 50 V increase, the cost to purchase
the additional energy to remove the excess heat from
the E-coat bath is shown in Table D.
As an example, the increase for the energy cost is
50 V x 2000 amps = 100 W, at $0.05 (USD)/kW-hr. This
is an extra $5.00 (USD) per hour. The cooling costs
will be the same since electric motors are used to
provide chilled water. So the increase in variable
energy costs is $10.00 (USD) per hour. If 70 bodies
are produced an hour, then the per-unit cost increase
is $0.14286 (USD).
Presently, the plants have very few tools to
optimize energy (and E-coat paint) consumption in
order to reduce variable operating costs. Simulation
can provide the tool that assembly plant managers have
E-COAT FEA SIMULATION
In situations where the body is in continuous motion
as it moves through the E-coat bath, it may be
beneficial to take advantage of symmetry between the
body of interest and the body immediately in front and
immediately behind. The geometry could extend ahead of
the body ˝ the distance of the body in front and also
extend backwards ˝ the distance of the body to the
rear. The use of this symmetry technique requires that
the bodies in front and to the rear are the same.
If all three bodies are not the same, then the
geometry of the E-coat bath needs to be lengthened to
accommodate two or more bodies.
If the body comes to a stop ("at rest") during the
E-coat paint cycle, then the entire E-coat bath needs
to be modeled. Figure 7 shows a body being lowered
vertically into an E-coat bath. These tanks are common
at low-volume automotive plants that, in many cases,
have to produce a wide range of bodies.
The ME Cells define the placement of the voltage
loads. Since there are different types of ME Cells
in use at different times, the FEA model will have to
be altered and re-meshed at certain times as the
simulation progresses. In addition, the magnitude of
the voltage loads will change, even if the spatial
relationship between the ME Cells and body do not
change. Thus, the model must be able to reflect this
Typical Cell Placement
Side ME Cells begin about ˝ the distance of the
overall length of the body (in front of the body).
They are placed on 30 cm centers. Typically, the body
is under the influence of Side ME Cells during the
entire E-coat paint cycle.
Floor and Roof ME Cells can either be placed
perpendicular to the travel of the body or parallel.
These are usually only employed later in the E-coat
paint cycle, so the model will have to be updated at
the appropriate elapsed time to create additional
voltage loads as they are required.
Automotive Body Geometry
The body designer will have a preliminary design
that was built using the OEM's CAD platform. This
design can be transferred to the ALGOR FEMPRO software
via ALGOR's CAD support options, which include direct
CAD/CAE data exchange with leading CAD solid modelers
and support for CAD universal files such as ACIS, IGES
The body may need styling features removed that do
not provide for the strength and rigidity of the body,
nor adversely impact the formation of the E-coat film.
Keep in mind that the E-coat FEA simulation will take
place before the body design is submitted to the federal
system for crashworthiness testing. The thickness of the
body can be made uniform since the relative differences
in the thicknesses of the various sheet steels are
insignificant when compared to the overall width or
length of the automotive body.
Figure 8 shows some of the complexity that has to be
rationalized in order to reduce the size of the body
file. It is a Taurus front fender and there are numerous
bolt holes where the fender is secured to other portions
of the body. These holes can be eliminated for two
reasons. First, these holes are near an edge and the
backside of the fender will not be affected if the hole
is removed. Second, when the fender is attached (as it
will be when the entire body is painted), a bolt will
occupy this space.
Features such as openings in the rocker panel, for
example, should not be changed in any way. Other
features that cannot be changed include the separation
of partitions, panels or other structural elements of
a recessed region. Openings and narrow channel spacing
are critical paths that E-coat paint and electrical
current must flow into and around. Thus, these need to
be accurately represented in the FEA geometry.
If more than one type of sheet metal is used, each
can be modeled separately as part of the solid body.
Different sheet steel materials do have different
electrical conductivities; so more than one material
will have to be utilized when making the solid body
Typical units for electrical conductivity are
Where k is the material electrical conductivity and
is the material resistivity, which is expressed as -cm
for a sample size of a 1 cm cube.
E-coat Paint Bath
Like many FEA problems, the crux of the problem is
an accurate estimate of what the real material
properties are and how they change as a function of
time, temperature, etc. It is easy to set up a test
and measure the ending resistance of the E-coat film
by knowing the voltage and current. You can use Ohm’s
Law to solve for an estimate of what the resistance
is at the time the voltage and current were measured.
Refer to Figure 5 for a cut-away view of the
typical TECTRON™ ME Cell. The electrical current
source is connected to the metal electrode above
the liquid level of the E-coat paint. The electrode
rests inside the ion-exchange membrane, which acts
like a diaphragm to keep the E-coat bath material
from touching the surface of the electrode and it
only allows anion species to pass. The electrolytic
fluid inside the ion-exchange membrane has a very
low pH and its conductivity is usually 2,500 µS/cm.
Measurement of the actual ME Cell in operation
will have to be taken when the E-coat paint system
is shut down and voltage has been locked out in
accordance with the plant safety protocol.
The ion-exchange membrane is approximately
0.5 mm thick and has a very low electrical
resistivity () on the order of 1–10 -cm when new.
With age, this material property can increase by
2 or 3 orders of magnitude or more.
The anode material is typically 316L stainless
steel alloy and is made from a Schedule 40 pipe.
Thus, the geometry of the ME Cell will consist
of at least three different parts. The first is
the 316L stainless steel anode, the second is the
annular space that is filled with electrolytic
fluid and the third is the ion-exchange membrane.
EXAMPLE FEA SIMULATION
The body was a piece of sheet steel with a width
of 10 cm and a thickness of 2 mm. It was submerged
about 26 cm (the portion of the body that extends out
of the E-coat bath was not modeled since there was no
current flow). The cathode was made only 5 cm wide
since there was a symmetry plane at its midpoint.
A solid model file was produced with these dimensions
and a mesh size of ˝ x ˝ was applied to the two major
surfaces. From this, a solid mesh was created. This
was considered the first part. The result can be
visualized in Figure 14 and is "inside" the E-coat
E-coat Film Geometry
The inside face of the E-coat film solid elements
shared the same face as the exterior of the body.
The other side shared a face with the E-coat bath.
Space was reserved for the creation of the E-coat
film elements after the first iteration. Each of the
nodes of the body was mapped to another "future" node,
whose position was away from the body in the normal
Thus, a pairing was created for each of the nodes
on the body. This would then allow for the creation
of a second part. This second part would displace
the E-coat bath as the simulation progressed.
E-coat Bath Geometry
A wireframe (Figure 9) of the E-coat bath was made
to which a surface mesh of ˝ x ˝ was applied.
Afterwards, a copy of the outer surface of the body
was made and inserted into the E-coat bath wireframe.
Then, the volume inside of the wireframe and outside
of the body was meshed with solid elements.
A low-voltage load of 0 volts was applied to the
entire surface of the body. The high-voltage load
of 250 volts was applied to the appropriate portion
of the E-coat bath wireframe. This was only 2.5 cm
wide and the same 26 cm as was the body. The
thickness of the electrode (anode) was ignored and
no ion-exchange membrane was included in the test
The Ford SRL E-coat test lab was modeled using a
symmetry plane (for y = 0) that bisected the anode
and cathode at their midpoint. The conductivity of
the E-coat bath was 0.0028 S/cm and the electrical
resistivity of the E-coat film was 5.0e8 –cm.
Even though the material property of the E-coat
film is known (i.e., as measured at the end point),
the software must be calibrated to the actual E-coat
paint conditions before a simulation can be performed.
As shown in Figure 10, these elements will be
extremely thin, especially at the beginning of the
simulation. The maximum thickness will be as much as
50 µ and the minimum may be as much as 2 or 3 orders
of magnitude smaller.
This is generally an important topic with a
classical strength and materials problem that FEA is
used to solve every day. However, this is not the same
case in electrostatics. Generally, the resistance is
governed only by the distance the electric travels.
Since the current only wants to travel the shortest
possible distance, this direction will be considered
normal to the surface of the cathode (automotive body).
Where R is the resistance, is the material property,
L is the distance the current travels and A is the area
through which the current is traveling.
An FEA experiment was performed to see if the electrical
current changes when the thickness of a brick element is
altered from a length of 1 cm to 0.0001 cm. For both cases,
the voltage gradient is 10 V and the material conductivity
is 1 S/cm. There was no difference in the current results
between the two different models, one of which was a single
brick (cube) with length of 1 and the other model was made
up of 10,000 thin bricks.
Once the geometry, voltages and materials are established,
electrostatic analysis from ALGOR solves for the resulting
Using a parametric language developed by ALGOR to allow
users to automate tasks, an automated loop of the iterative
process was defined. In addition, script (or macro) files
can be made to automate such tasks as creating FEA loads,
changing geometry, etc. The combination of the parametric
language and script file capabilities made the development
of the iteration code a straightforward process.
Quasi-Static Current Analysis
The flow of electrical current is central to the
simulation of the E-coat paint process. The processor
accepts the geometry, material and voltages and solves
for the electrical current flow resulting from the inputs.
While each iteration is processed as an "electrostatics"
condition, the threading together of many of these
iteration steps is termed quasi-static analysis.
Flow Chart of the Automation Loop
A series of routines was prepared that created
the ability to run the electrostatic analyses. The
electrical current distribution is used to calculate
the E-coat film thickness that developed as a result
of the electrical current flow. Databases are used
to keep results from each iteration, so the total
E-coat film thickness is maintained. The material
properties of the brick elements that comprise the
E-coat film elements are then adjusted (i.e.
electrical conductivity is reduced). See Figure 11
for a summary of the program flow chart.
For a given FEA model, electrical currents are
calculated. For the given time step, an estimate
of the incremental E-coat film thickness can be
made based on a deposition coefficient and
specific gravity of the deposited E-coat film.
Preparation is made for the next iteration,
which could involve: removing a high-voltage
load, changing the magnitude of the high-voltage
load, etc. Once this is done, the FEA processor
is activated again and the next iteration is
performed. The outputs are the nodal electrical
current flows and these are used to repeat the
calculation of the incremental growth of the
E-coat film thickness.
At this point, visualizations of the simulations
can be made for the end user to quickly pick up
the salient results. For example, the lower limit
could be 13 microns. Therefore, the visualization
would highlight where this condition (or these
conditions) may exist.
Total Cycle Time
The total elapsed time of the Ford SRL test was
87 seconds. Hence, the calibration trials
(simulations testing for the appropriate
coefficients) were also stopped after 87 seconds.
Figure 12 shows the voltage profile at time
equal to zero. Note the anode is on the middle
to lower, left side of the model. At this point,
the current is concentrated between the shortest
line from the high-voltage load to the low-voltage
load. Later on as the resistance begins to increase
on the front side of the body, the voltage profile
will change and begin to wrap around the body as
the current seeks out "lower" resistance paths.
Figure 13 shows the voltage profile after
approximately 87 seconds and indeed the voltage
distribution has been altered in a way that
is consistent with more electrical current
flowing towards the far side of the body.
Figure 14 shows the body current density for
the first iteration. As expected, the lower
right hand corner of the cathode has received
the most current. This is for two reasons:
the first is that an exposed corner is an
attractive target for current, and the second
is current can flow around both the side
(away from reader) and under the body.
In Figure 15, the elapsed time is
approximately 87 seconds and there is more
electrical current activity now than in the
first iteration. The most activity is on the
lower exposed corner and gradually the current
falls off as you move closer to the top and
to the symmetry plane.
After several calibration trial runs, the
E-coat film thickness profile follows in
Table E. For each of the locations below,
there are 3 entries. The first one is closest
to the symmetry plane and then moving out
towards the exposed edge of the body.
||E-coat Film Thickness (µ)
||4, 11, 15
||2, 6, 13
||5, 13, 18
||3, 7, 15
||6, 15, 20
||4, 11, 18
The E-coat film thicknesses are as expected.
Notice that all the thicknesses on the front
side are more than those on the back side.
In addition, the E-coat film thicknesses are
also greatest near the exposed edge and least
near the symmetry plane as one would expect.
Lastly, the E-coat film thicknesses near the
bottom are greater than those near the top;
again this is as expected since the bottom
edge is also exposed and more electrical
current will flow to this region of the body.
Efficient, Realistic Simulation
Future applications of FEA for simulating
the automotive E-coat paint process will
involve developing an efficient method for
analyzing more complicated 3-D models based
on actual geometry. Ways must be found to
include smaller features of the CAD geometry
in the FEA model without causing the number
of elements and the analysis run time to
increase beyond the point of practicality.
This is an important factor to consider
since the typical current versus time plot
for an E-coat paint cycle has a severe peak
current several seconds after the voltage
gradient is established. E-coat paint solids
move toward the cathode and are deposited
on the closest portions of the body. The
resistance presented by the E-coat film
begins to take hold and there is a rapid
fall off approximately 1/3 of the way
through the E-coat paint cycle.
The current decay continues, but the slope
flattens out after the halfway point. The
E-coat film continues to form as long as
the cathode current density stays above the
The in-rush of electrical current during
the first several seconds results in very
significant temperature changes. These
temperature changes affect material
properties of both the E-coat film
and the E-coat bath.
The output of the electrostatic analysis
should be coupled with a heat transfer
analysis and regions near the body need to
account for the amount of heat input caused
by the IR heating.
The output from the heat transfer analysis
is then used to change the material properties
of the affected elements.
In this paper, it was shown that the E-coat
paint process is a widely used technique at
every automotive plant. However, it has lacked
simulation tools up to now and that has hampered
optimization efforts and led to increased
variable costs for the automotive OEMs.
In this paper, a method has been shown for
performing a 3-D FEA simulation of the E-coat
paint process on an automotive body. Adoption
of this FEA simulation method will lead to
improvements and enhancements as practice is
gained and automotive OEMs take advantage of
its use and application.
ULSAB.org for Figure 1.
VW Mexico for Figure 2.
PPG Industries for Figure 3.
General Motors Ecuador for Figure 7.
Ford Motor Company for Figure 9.
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