Today in automotive
industry, the programming of a spray painting robot by paint application
specialists requires three to five months. This programming time
is a critical bottleneck in "concept to consumer" timeline--the
time required to bring a new vehicle from design to market. This process
requires so much time because the application specialist essentially prescribes
a sequence of way points, one point at a time, for the robot to
follow. These way points describe a path that completely covers the car
body while attempting to ensure uniform paint thickness; such a task is
very difficult for a person to do and today paint specialists have no
sufficient software tools to assist in the program phase -- everything
is done manually. The first goal of this work is to automate the
programming process allowing the paint specialist to finish the significantly
quicker while at the same time allowing the application specialist to
focus on higher level issues.
The uniformity of paint deposition
on the automobile surfaces is one of the important factors in consumer's
approval. Therefore, today's car market demands uniform paint thickness
on the auto bodies. However, the paint distribution coming out of the
spray gun has a complex form and ensuring uniform coverage is challenging
even on the simplest of the target surfaces such as a planar sheet.
Additionally, the paint deposition pattern interacts with the complex
auto surface geometry and produces different paint distributions at
different points on the target surface according to the local curvature.
Moreover, the paint deposition pattern from electrostatic rotating bell
(ESRB) atomizers, one of the most popular type of spray gun mechanisms,
has a relatively large size compared to typical automotive surfaces.
These factors make the task of automated generating of spray gun trajectories
for uniform coverage even more challenging.
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| Figure 2(a):
The deposition pattern (that is, the deposition d(x,y) at a given
point on the deposition plane) is modeled using two revolved 1-dimensional
Gaussians g_1 and g_2, and a two-dimensional Gaussian f. |
Figure 2(b):
The deposition pattern obtained by fitting our model to the experimental
data from painting a flat panels using ESRB atomizers. |
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As a first step towards automated
trajectory generation for spray painting applications, we first developed
a mechanism to determine the resultant paint deposition for a given
spray-gun trajectory on arbitrary curved surfaces in simulation. Our
approach first fits out deposition model (see Figure 2 (a) and 2(b))
to experimental data from 3-pass tests on flat panels (with both horizontal
and vertical orientation of passes). For typical ESRB atomizers, the
shape of the deposition pattern is like an asymmetrical volcano. Once
we determine the deposition pattern on the flat deposition model plane,
we proceed to determine the paint deposition in simulation on any arbitrary
surface painted using the same spray gun. We assume that the paint particles
flow along a prescribed path (along a straight line in Figure 3(a)).
We then determine a local mapping at a given point on the target surface
between the deposition model plane and the target surface. Using the
concept of area magnification from differential geometry and the law
of conservation of mass, we then determine the deposition at the given
point on the target surface.
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Figure
3(a): Linear Projection Model: To determine paint deposition on
any point on the target surface, we assume that paint particles
flow along straight lines after leaving the nozzle.
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Figure 3(b):
The equation for deposition D(s,o) at point s on the target
surface, when the spray gun emission point is at point o. Here,
(x,y) is the point on the deposition plane where the straight
line joining s and o intersects the deposition plane,
Omega is the distance between the emission point and the deposition
plane, e is a unit vector along so, n is unit surface
normal, z is unit vector along spray gun axis. L is
the length of segment so. |
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Finally, once the deposition
model is available, given the target surface CAD model, our software
tools generate the spray gun trajectory on the target surface automatically
using procedures described in constrained
controlled coverage. Figure 4 shows a Ford Excursion door painted
using trajectories generated by our planning tools.
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