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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, 2003.

Frederick Hess, UFS Corporation, Valparaiso, IN, USA
Ulises Gonzalez, Ph.D., ALGOR, Inc., Pittsburgh, PA, USA

EXTENDED ABSTRACT

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 step.

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 corrosion protection.

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.

INTRODUCTION

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 automotive OEMs.

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.

Table A
E-coat material
reduction (%)
Cost reduction
(USD/body)
0.5 0.06493
1.0 0.12987
2.0 0.25974
3.0 0.38961

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.

Improving Quality

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 line.

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.

E-coat Machine

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.

Figure 1

Multi-step Processing

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.

E-coat Bath

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.

Figure 2

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.

Process Variables

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.

Table B
Location Sheet typically used
Roof Cold-rolled
Side member 1-sided galvanized
Rocker panel 2-sided galvanized

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.

Body Style

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%.

DC Rectifier

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.

Figure 3

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.

Electrophoresis

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 anode.

Electrodeposition

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 cathode.

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 formed.

Electro-endosmosis

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 the body.

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.

Figure 4

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.

Figure 5

The ion-exchange membrane contributes to the overall electrical resistance and performance of the E-coat system, especially as it accumulates wear.

AUTOMOTIVE BODY

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.

Testing

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.

Figure 6

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 simulated.

OPTIMIZATION CHALLENGE

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 external surfaces.

Table C
Region of body Percent of total
surface area (%)
Exterior total 25
Horizontal
5
Vertical
20
Interior total 75
Exposed
20
Recessed
55

Corrosion Protection

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 waste.

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.

Table D
Energy cost
(USD/kW-hr)
Cost increase
(USD/body)
0.05 0.14286
0.06 0.17143
0.7 0.20000
0.8 0.22857

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 needed.

E-COAT FEA SIMULATION

Tank Length

Continuous Motion

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.

At Rest

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.

Figure 7

ME Cells

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 change.

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 and STEP.

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.

Figure 8

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 geometry.

Material Properties

Typical units for electrical conductivity are Siemens/cm.

Eq 1

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.

Eq 2

ME Cells

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

Body Geometry

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 film elements.

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 direction.

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.

Figure 9

Voltage Loads

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 apparatus.

Material Properties

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.

Brick Elements

Thin Bricks

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.

Figure 10

Aspect Ratio

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).

Eq 3

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.

Electrostatic Analysis

Once the geometry, voltages and materials are established, electrostatic analysis from ALGOR solves for the resulting current flow.

Automation

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.

Figure 11

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.

Results

Voltage

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 12

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 13

Current Distribution

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.

Figure 14

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.

Figure 15

Preliminary Results

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.

Table E
  E-coat Film Thickness (µ)
Location Front Side Back Side
Top 4, 11, 15 2, 6, 13
Middle 5, 13, 18 3, 7, 15
Bottom 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.

FUTURE APPLICATION

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.

Thermal Conditions

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 critical value.

IR Heating

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.

CONCLUSION

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.

ACKNOWLEDGEMENTS

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.

REFERENCES

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