Effect of Direct Slicing on Geometric Tolerances in Additive
Manufacturing Process
A Barari
Faculty of Applied Science and Engineering
University of Ontario Institute of Technology
Oshawa, Ontario, Canada
INTRODUCTION
Additive Manufacturing (AM) parts and surfaces
are inherently subject to stair case effect which
can be quantified by cusp height. Cusp height of
a layer is the maximum distance measured
along a surface normal between the ideal
surface and the produced layer. Although
calculation of local cusp high is a simple task but
estimating the overall deviation zone of the
produced surface is a highly nonlinear and
complicated problem. This paper presents a
practical approach to predict the actual profile
tolerances of the surfaces. This prediction is
used to allocate profile tolerances for the
additive manufacturing processes. Also the
methodology can be used to select the optimum
uniform layer thicknesses that compromise
between the number of layers and the desired
accuracy of the final surfaces. The unified
developed methodologies are capable to
analyse complex surfaces and geometries.
Variety of experiments is carried out to study the
effectiveness and practicality of the presented
methodology. The developed methodology can
be employed efficiently during design of rapid
prototyping parts to compromise between final
part accuracy and prototyping cost.
FIGURE 1. Cusp height and staircase effect
The actual cusp height can be calculated
be by geometric analysis
of the two
consecutive layers and the ideal Geometry, .
As it can be seen in Figure 1, for any corner
intersection point,
, of i-th layer and i+1-th
layer in any given orientation two corresponding
intersection points, and
,of the two layers
and the ideal geometry can be found. The
corresponding cusp height in the plan specified
by three points of
,
, and
is
calculated by:
(1)
Problem Definition
The slicing process is a highly critical stage
in Rapid Prototyping manufacture. As it can be
seen in Figure 1, large thickness of slices
generally incorporates for rough surface quality
due to the stair-case effect and its corresponding
cusp
height
in
layered
manufacturing.
Alternatively, utilizing very small thickness of
layers takes much longer time to finish a part
and is costly. Although the desired layer
thickness can be selected in majority of today’s
RP machines, but usually it remains constant for
the entire model.
where
the
operator
specifies
the
Euclidian distance of point, , to the geometry,
, in a plane that the point, , forms with two
points of
and
. As it can be seen, large
thickness of layers generally incorporates for
rough surface quality due to the stair-case effect
and its corresponding cusp height in layered
manufacturing. Alternatively, utilizing very small
thickness of layers takes much longer time to
finish a part and is costly. These two
contradictions have led to research toward
optimizing the layer thickness and improving the
slicing techniques. However, the cusp height
always depends on the surface tangent of the
ideal geometry and the slicing techniques need
to be developed and customized based on the
specifications of the ideal geometry.
Cusp height is commonly addressed in the
literature as a major indicator of the accuracy of
the final AM surfaces [1-5]. However, it can be
used to study the local deviations of the points
from the ideal geometry but understanding the
global deviation zone of the produced surfaces
need additional study.
A method to estimate the profile deviation
zone for accurate allocation of the profile
tolerances of the RP produced surfaces is
presented in this paper. It is also shown that by
the results of this methodological analysis can
be used to select the optimum uniform layer
thickness for the RP process. The presented
methodologies are implemented for a unified
solution using Non-Uniform Rational B-Spline
(NURBS) representation of the surfaces. This
will allows application of the developed
procedure for both primitive as well as the
sculptured surfaces. Case study of a NURBS
surface is used for demonstration of the process
and validation of the process.
Implementation
Varity of experiments are conducted to test and
validate the developed methodology. In order to
demonstrate the implementation of the
presented methodology and for validation a
case-study is presented here.
The ideal surface geometry is defined as a
uniform, non-periodic NURBS surface generated
by a control net including 36 control points
defined identically in the two parametric
directions. The degrees of NURBS surface in
the parametric directions are identical and are
equal to three (forth order polynomials). The
designed NURBS surface is presented in Figure
2.
FIGURE 2. NURBS representation of the
desired geometry
Figure 3 presents the results of the analysis:
FIGURE 3. Estimated Distribution of the detailed
Minimum Deviation Zone
CONCLUSION
Using the developed methodology the actual
minimum deviation zone can be calculated and
used directly to allocate profile tolerances for the
designed surfaces. This methodology also can
be adopted by the rapid prototyping slicing
software to select the most appropriate uniform
layer thickness that although doesn’t increase
the number of layers significantly, but it provides
a much higher product’s accuracy comparing to
slicing with maximum layer thickness.
REFERENCES
1. Denis, C., Kittinan, U., and Ezat, S.,
2000, "Specifying Non-Uniform Cusp
Heights as a Potential Aid for Adaptive
Slicing," Rapid Prototyping Journal, 6(3),
pp. 204.
2. Justin, T., and Jan Helge, B., 1998,
"Local Adaptive Slicing," Rapid
Prototyping Journal, 4(3), pp. 118.
3. A.Barari, and M.T.Ahmadian, 1999,
"Optimum Slicing of Model for Rapid
Prototyping," eds., Tehran, Iran, pp.
218-228.
4. Sabourin, E., Houser, S. A., and Bohn,
J. H., 1997, "Accurate Exterior, Fast
Interior Layered Manufacturing," Rapid
Prototyping Journal, 3(2), pp. 44.
5. A. Barari, “Sources of uncertainty in
coordinate metrology of automotive
body,” CD Proc. of 2nd CIRP
International Conference on Assembly
Tech. and Systems, 2008