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CIRP Journal of Manufacturing Science and Technology xxx (2014)
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CIRPJ-264; No. of Pages 8
Contents lists available at ScienceDirect
CIRP Journal of Manufacturin
.e1. Introduction
In many industrial applications, like in the automotive or
theaerospace industry, deep drawing is an important
productionprocess [9]. Thermally sprayed abrasive-wear resistant
tungstencarbide (WC-Co) hard material coatings can be applied in
order toincrease the endurance of the forming tools in the process
[18]. Aninvestigation of the simulation of the grinding of such
coatedsurfaces was presented on the 3rd CIRP Conference on
ProcessMachine Interactions [14]. The previous work is extended by
thispaper.
In order to use the coated tools for deep drawing,
severalconditions have to be met. The material ow of the sheets in
theprocess is inuenced by the topology of the tool surface.
Forexample, a high surface roughness can inuence the quality of
theformed sheets negatively, because fractures can occur
[16].Another challenge is the achievement of a constant layer
thicknesswith thermal spraying processes [17]. Especially on
free-formedsurfaces, deviations are likely to occur. The required
geometry ofthe blank holder and the dies is determined with great
precision inthe tool design process in order to enable a precise
forming of theworkpieces. To accomplish this, the shape of the
coated tools mustbe kept within sufciently small tolerances. It is
necessary to nishthe hard material coatings to take these aspects
into account.
Grinding on machining centers is exible method for this
purpose[13].
The production of coated deep drawing tools can be optimizedby
simulating the whole process chain, including every necessarystep:
the milling of the substrates [21], the deposition of the
hardmaterial coatings [19] and the nal grinding. In the following,
thesimulation of the grinding process is described. Grinding
processeshave already been modeled and simulated in different ways
[5].Macroscopic geometric-kinematic approaches can be used
toestimate the process forces during the NC grinding of
free-formedsurfaces [10]. In this approach, the tool shape is
represented bybasic primitives like spheres or cylinders. In order
to predict theresulting topography and to provide a more accurate
forceestimation, it is possible to model individual grains of the
grindingtool [1]. These can be used to estimate the surface
roughness,which is of interest for the deep drawing application.
The abrasionsimulation with individual grains can be achieved by
FiniteElement Analysis (FEA) [5] or Smooth Particle
Hydrodynamics(SPH) [15], for example. The complexity of these
approachesrestricts the amount of grains and the maximum workpiece
sizewhich can be simulated with limited computational resources
andsimulation time.
A simulation of every grain of a grinding tool is possible
withgeometric-kinematic solutions. This is done by the
simulationsystem KSIM [2], which uses the chip cross sections of
theindividual grains to estimate the process forces with an
adaptedKienzle equation [8]. In the previous work by [14], which
isextended by this paper, a geometric-kinematic approach is
applied
* Corresponding author. Tel.: 49 2317555819.E-mail address:
[email protected] (T. Siebrecht).
Hard material coating
Process force
2014 CIRP.
1755-5817/$ see front matter 2014
CIRP.http://dx.doi.org/10.1016/j.cirpj.2014.01.001Grinding process
simulation of free-forcoated surfaces on machining centers udexel
representations
T. Siebrecht *, S. Rausch, P. Kersting, D. Biermann
Institute of Machining Technology, TU Dortmund University,
Baroper Str. 301, 44227 D
A R T I C L E I N F O
Article history:
Available online xxx
Keywords:
Grinding
Simulation
Geometric modeling
A B S T R A C T
Deep drawing tools are us
tools, thermally sprayed
respect to the shape accu
nished. A suitable machi
paper, a geometric simula
with constructive solid ge
sampled dexels. Validatio
forces in different engage
jou r nal h o mep age: w wwPlease cite this article in press as:
Siebrecht, T., et al., Grinding proceson machining centers using
poisson-disk sampled dexel
representatiohttp://dx.doi.org/10.1016/j.cirpj.2014.01.001ed WC-Co
hard materialng poisson-disk sampled
und, Germany
n various production processes. In order to increase the life
cycle of these
sive-wear resistant WC-Co hard material coatings can be applied.
With
and surface quality of the forming tools, the coated surfaces
have to be
process to meet these conditions is grinding on machining
centers. In this
model for this grinding process based on the modeling of
individual grains
try techniques is presented. The workpiece is represented by
poisson-disk
xperiments show a good match of the simulated and measured
process
t situations.
g Science and Technology
l s evier . co m/lo c ate /c i rp js simulation of free-formed
WC-Co hard material coated surfacesns. CIRP Journal of
Manufacturing Science and Technology (2014),
-
as well. The grinding forces are directly calculated based on
thechip thickness. Instead of a complex grain model like
trianglemeshes, a Constructive Solid Geometry (CSG) [7] based
approach isused. In addition to the representation of workpieces by
a grid-likearrangement of dexels (height elds) or multi-dexel
boards [10], apoisson-disk sampling [6] based distribution of
dexels on thesurface of the workpiece is analyzed. The experimental
investiga-tion of the force model is extended by the machining
andsimulation of convex and concave surfaces.
grinding simulations. This includes discrete displacement eldson
triangle meshes [3] and CSG based workpiece models [12].
Incontrast, dexel based models provide a exible and potentiallymore
efcient solution [14]. A dexel can be dened by its positiondp,
direction dd and height dh. The surface point represented by
thedexel is given by dp + dddh. This way, material cutting
correspondsto a reduction of dh. If undercuts have to be modeled as
well, it ispossible to store more than one height value for every
dexel, which
Fig. 3. Microscopic images of diamond grains.
T. Siebrecht et al. / CIRP Journal of Manufacturing Science and
Technology xxx (2014) xxxxxx2
G Model
CIRPJ-264; No. of Pages 8The modeling of grinding tools,
including the shape ofindividual grains, is described in Section
2.1. In Section 2.2, themodeling of the workpiece surface is
explained and a process forcemodel is presented in Section 2.3. The
experimental investigationof the simulation of the grinding process
is shown in Section 3.
2. Simulation of the NC grinding process
The goal of the simulation is the replication of the
wholeproduction process chain for coated deep drawing tools. For
thisreason, the simulation of NC grinding is integrated into an
existingsoftware tool, which is already used to simulate the NC
milling ofthe uncoated substrate [20]. This allows an effortless
exchange ofthe workpiece shapes. Additionally, many software
components,like the NC program evaluation or the graphical user
interface, canbe reused in the simulation of both processes. The
simulatedkinematic movement of the tool is based on the same NC
programused to control the machine tool. This allows the comparison
of thesimulated values to the real process without further effort
[14].Ideal material removal is assumed within the simulation
model.Effects like ploughing, friction or elastic deformations
areneglected.
The considered forming tools consist of free-formed surfaces
aswell as at areas. Fig. 1 shows an example of a segment of a
free-formed deep drawing tool. Varying contact situations occur
atdifferent locations on the surface. To take this into
account,different grinding tool shapes can be used for an efcient
grindingprocess. This includes cylindrical tools for at areas or
sphericaltools for curved surfaces.
2.1. Modeling of grinding tools
The modeling of individual grains of the grinding tool requires
aprior analysis of possibly occurring grain shapes. For the
grindingof the WC-Co coatings, diamond grains are used.
Syntheticdiamonds can be shaped like hexahedrons, octahedrons or
acombination of both [4]. In order to represent these diamondshapes
in the simulation system, a CSG [7] based approach isapplied. The
resulting shapes of the grains are given by theintersection of
hexahedrons and octahedrons with varying sizes, asshown in Fig. 2.
The numbers represent an index which can beassigned to the
different grain shapes [4]. This allows an efcientclassication of
grains on a real grinding tool. The index rangesfrom 0
(representing a plain hexahedron) to 8 (representing a
plainoctahedron). Fig. 3 shows microscopic images of diamond
grains.
In order to simulate the behavior of real grinding tools,
theshapes and the distribution of the grains on the tool surface
have to
Fig. 1. Shape of a segment of a free-formed deep drawing
tool.Please cite this article in press as: Siebrecht, T., et al.,
Grinding proceson machining centers using poisson-disk sampled
dexel representatiohttp://dx.doi.org/10.1016/j.cirpj.2014.01.001be
modeled. In the presented approach, the positions andorientations
of the grains are chosen randomly until a speciedamount of grains
is placed. The distance between a new grain andevery existing grain
has to be longer than the sum of their radii.This way, the
generation of overlapping grains is prevented. Inaddition to the
distribution and amount of grains, the sizes, shapesand protrusion
heights have a major inuence on the result of thegrinding process
simulation. The values of these properties aregenerated using
normal distributions, which are parameterizedbased on
representative microscopic images. Due to the neglectionof tool
wear, grains completely inside the bond are never in contactwith
the workpiece. Therefore, only grains on the tool surface haveto be
modeled. Assuming ideal material removal, only the grainsare used
to cut the workpiece and the bonding system is neglectedduring the
process simulation. The modeled tool topography isdepicted in Fig.
4.
2.2. Workpiece modeling
Workpieces can be represented with different models in
Fig. 2. Geometric model of diamond grains as intersections of an
octahedron and ahexahedron.s simulation of free-formed WC-Co hard
material coated surfacesns. CIRP Journal of Manufacturing Science
and Technology (2014),
-
the difference between the maximum dexel height hI before the
cutand the minimum dexel height hII after the cut is used to
estimate
Fig. 4. Simulated grains on a cylindrical tool with a diameter
of 15 mm and a height
Fig. 6. Slices of a grain.
T. Siebrecht et al. / CIRP Journal of Manufacturing Science and
Technology xxx (2014) xxxxxx 3
G Model
CIRPJ-264; No. of Pages 8represent different points on the
workpiece surface. This isespecially necessary for milling
processes and can often beneglected for grinding, because no
undercuts occur. Dependingon the shape of the workpiece, different
arrangements of the dexelsare possible. If only a at surface has to
be ground, it is usuallysufcient to arrange them as a dexel board
in a grid-like manner, asshown in Fig. 5a. For free-formed
surfaces, multi-dexel models canbe used [20]. These consist of
three perpendicular dexel boards.This is shown in Fig. 5b for a
two-dimensional case.
Both of these workpiece representations have differentadvantages
and disadvantages. Using a height eld, it is difcultto model
free-formed surfaces, especially if there are perpendicu-lar faces.
This is true for the deep drawing tool shown in Fig. 1.Resulting
from the grid-like arrangement of dexels, anotherproblem occurs. In
this case, the simulated process forces areslightly inuenced by the
cutting direction. This is analyzed inSection 2.3 in more detail.
Multi-dexel models have the samedrawback, since each of the three
participating dexel boards isstructured as a grid as well. Another
disadvantage is theinhomogeneous density of the points representing
the surface.This can be seen in Fig. 5b, where the points are
distributed evenlyon the at surface areas, but non-uniformly in the
curved region. Apossible solution for this is a poisson-disk
sampled distribution ofdexels along the surface, which is described
in Section 2.4.
2.3. Force prediction
The calculation of the process forces is based on the
simulatedchip thickness. Due to the shape of the grains, the depth
of cutvaries along the grain width perpendicular to the cutting
direction.To take this into account, the grains are divided into
small cuttingslices along the perpendicular direction, as shown in
Fig. 6. In everysimulation step, the process forces are estimated
for each of theseslices.
The process forces are expressed as vectors in the direction
ofthe grain face normals in the corresponding cutting slices.
The
of 10 mm.force affecting a grain is given by the superposition
of the forcesacting on the individual slices. For the calculation
of these forces,
Fig. 5. Dexel based representations of a workpiece.
Please cite this article in press as: Siebrecht, T., et al.,
Grinding proceson machining centers using poisson-disk sampled
dexel representatiohttp://dx.doi.org/10.1016/j.cirpj.2014.01.001the
chip thickness. A schematic view of this procedure is shown inFig.
7. The calculation includes the following steps:
1 kinematic grain movement according to the process
parametersand the given NC program,
2 determination of the set of dexels being cut by each slice,3
calculation of the maximum dexel height hI before the cut withinthe
set,
4 reduction of the dexel heights to simulate the material
removal,5 calculation of the minimum dexel height hII after the cut
withinthe set,
6 calculation of the grain immersion depth d = hI hII,7
projection d0 of the immersion depth onto the normal n of
thecutting grain face,
8 and nally the estimation of the process forces using d0 and
n.
In the last step, an adopted Kienzle equation is used for the
forceestimation [14,8]:
f n kc;sim b d0d0
d0
1mc;sim; (1)
where kc,sim and mc,sim are the force model parameters,
whichrequire a prior calibration, b is the width of the slice, and
d0 is 1mm.The width b is necessary to ensure the independence of
theresulting force values of the slice size. In this force model,
thedirection of the force vector directly depends on the direction
ofthe orientation of the cutting grain surface.
In the previous investigations, the ratio between the forces
innormal and tangential direction was comparable in the
simulatedFig. 7. Calculation of the process forces [14].
s simulation of free-formed WC-Co hard material coated
surfacesns. CIRP Journal of Manufacturing Science and Technology
(2014),
-
heights. As shown in Fig. 9b, this results in negative values,
becausethe directions are facing outward and the surface points are
movedinward.
For the simulation of the grinding of coated surfaces,
thisrepresentation can be used to store the local thickness of
thecoating in an implicit way. If the dexels are placed on the
uncoatedsurface and the initial height is set to the local
thickness, theresulting positions represent the coated surface.
When a dexelheight is reduced to a negative value during the
grinding processes,the coating is completely removed at that point.
This is shown inFig. 10. Additionally, the dexel heights after the
process directlyshow the remaining thickness of the coating.
Fig. 8. Top view of a single grain cutting a dexel board in two
different directions.
Fig. 9. Placement of dexels on a surface before and after
cutting.
T. Siebrecht et al. / CIRP Journal of Manufacturing Science and
Technology xxx (2014) xxxxxx4
G Model
CIRPJ-264; No. of Pages 8and experimental results [14]. Using
other types of abrasive grainswith different grain sizes, this
correspondence turned out to beinvalid in some cases. Therefore,
the force model was extended byan additional set of Kienzle
parameters. The rst parameter set isused to estimate the force in
the direction of the surface normal(Fn) and the second set for the
force in cutting direction (Ft):
Fn xn kc;sim;n b d0d0
d0
1mc;sim;n; (2)
Ft xt kc;sim;t b d0d0
d0
1mc;sim;t; (3)
where xn and xt are unit vectors in normal and tangential
direction.The individual calibration of the different parameter
sets ensures acorrect ratio between Fn and Ft.
The described force model is calibrated by estimating the
fourparameters kc,sim,n, mc,sim,n, kc,sim,t, and mc,sim,t. Process
forces forthis purpose can be measured by carrying out at
grindingprocesses. Due to the non-linear correlation between the
chipthickness and the process forces, experiments with varying
processparameters are necessary. For each of these parameter sets,
tworevolutions of the grinding tool are simulated. The rst
revolutionis necessary to prepare the topography of the workpiece
surface.During the second revolution, the process forces are
predicted fordifferent values of mc,sim,n/t, assuming kc,sim,n/t =
1. Afterwards,suitable values of kc,sim,n/t are determined by
linear regression. Foreach simulated value of mc,sim,n/t, the mean
deviation from themeasured process forces is calculated. Finally,
the force model iscalibrated by using the Kienzle parameter set
with the lowestdeviation.
In simple cases like the grinding of at surfaces with
cylindricaltools, the dexel board can be aligned with the cutting
region asshown in Fig. 8a. This means that a grain slice can be
directlyassigned to a row of dexels. The size of the slice is then
equal to thedistance between the dexels. In case of a rotation
between thecutting direction and the orientation of the dexel
board, as shownin Fig. 8b for an angle of 458, a more complicated
way of deningthe slices and determining the set of dexels cut by
each slice has tobe found. This can be done by assigning each cut
dexel to the slice itis located in. All dexels of a slice are then
projected onto a planewhich is dened by the cutting direction and
average dexeldirection in the cutting area. This reduces the
problem to twodimensions, allowing the application of the
previously presentedforce calculation model. The width of the
slices has to be chosenlarge enough to contain a sufcient amount of
cut dexels in eachsimulation step. If the width is too small, some
slices could beempty or contain a small amount of dexels only,
leading to a poorprecision of the cutting depth estimation. To meet
this require-ment, the density of the dexel distribution on the
surface has to betaken into account. A homogeneous distribution is
helpful for thedenition a globally well performing slice size.
2.4. Poisson-disk dexel distribution
The previous approaches of representing the workpiece havethe
disadvantage of an inhomogeneous distribution of dexels alongthe
surface. To solve this problem, the dexels can be placed directlyon
the surface, instead of arranging them as a grid with
varyingheights as shown in Fig. 5a. This can been seen in Fig. 9a,
where asurface is represented by equally spaced dexels. The
direction ofeach dexel is oriented with the local normal vector of
the surface.Due to the placement of the dexels on the workpiece,
the heightsare initially set to zero. The material removal
resulting from thegrinding process can be expressed as a reduction
of the dexelPlease cite this article in press as: Siebrecht, T., et
al., Grinding proceson machining centers using poisson-disk sampled
dexel representatiohttp://dx.doi.org/10.1016/j.cirpj.2014.01.001s
simulation of free-formed WC-Co hard material coated surfacesns.
CIRP Journal of Manufacturing Science and Technology (2014),
-
process on C45 warm working steel. The small particle size of
range210 mm in combination with the high particle velocity leads to
alamellar layer structure and low porosity of the coating.
Theworkpiece was ground with a cylindrical, resin-bonded
grindingtool with a diameter of approximately 14 mm. Diamond was
usedas cutting material due to the high hardness of the coating
of
Fig. 12. Simulated grinding of a at workpiece at different
orientations using a grid-like and a poisson-disk dexel
placement.
T. Siebrecht et al. / CIRP Journal of Manufacturing Science and
Technology xxx (2014) xxxxxx 5
G Model
CIRPJ-264; No. of Pages 8Poisson-disk sampling [6] provides a
suitable method for theplacement of the dexels on the workpiece
surface. Randomsamples of the surface are subsequently generated.
For every newsample, the minimum distance to any of the previously
generatedsamples is calculated. If it is less than a minimum value
r, a newsample is generated. This process terminates when no valid
samplecan be found within a specied amount of tries. Fig. 11 shows
thedistribution of dexels on a at area of 2 mm 2 mm with
differentdexel distances.
For a verication of the applicability of the new
poisson-diskbased dexel distribution, the grinding of a at
workpiece of5 mm 5 mm was simulated with both methods. In case of a
458rotation, the pattern of the grid-like dexel distribution (Fig.
12a andb) is different along the cutting direction. In contrast,
the randomdexel distribution of the poisson-disk sampling does not
show thiseffect (Fig. 12c and d). In order to analyze the inuence
of theorientation on the simulated process forces, both approaches
werecarried out with the two different cutting directions.
Thesimulation was performed with a dexel distance of 3mm in
bothcases. The resulting process forces in normal direction are
shown inFig. 13. It can be seen that both approaches lead to
approximatelyequal process forces. Due to the random distribution
of dexels inthe poisson-disk approach, the forces contain slightly
more noise,but the deviation resulting from the different
orientations seems tobe neglectable in both cases. The average
force difference betweenthe two orientations was 0.06 N for the
poisson-disk approach and0.21 N for the grid-like approach. As
expected, the difference issmall, but the grid-like approach leads
to slightly biased results.
In summary, both approaches are applicable for the simulationof
grinding processes. The major advantage of the poisson-diskbased
approach is the homogeneous distribution of dexels on atand curved
surfaces. This can be seen in Fig. 14, which shows afree-formed
surface represented by a multi-dexel board and apoisson-disk
distribution.
3. Experimental investigation
Fig. 10. Dexels representing a coated surface.The coatings
analyzed in the presented investigations are basedon tungsten
carbide in a cobalt/chrome binder matrix. The materialwas deposited
by a High Velocity Oxy-Fuel (HVOF) spraying
Fig. 11. Poisson-disk sampled dexel distribution on a at area of
2 mm 2 mm.
Please cite this article in press as: Siebrecht, T., et al.,
Grinding proceson machining centers using poisson-disk sampled
dexel
representatiohttp://dx.doi.org/10.1016/j.cirpj.2014.01.001approximately
1300 HV0.3.The experimental validation was performed on a Deckel
Maho
DMU50 eVolution ve-axis machining center. In order to
calibratethe parameters of the process force model, a Design of
Experiments(DoE) based on a Latin Hypercube Design (LHD) [11] was
used bygrinding a at surface with different process parameters.
Thecutting speed vc was set to a constant value of 10 m s1 and
thedepth of cut ae, feed speed v f and width of cut ap were varied
(ae:1020 mm, v f : 200800 mm min
1, ap: 2.03.3 mm). Overall, 20experiments with 16 distinct
parameter sets were performed. Theprocess parameters are shown in
Table 1. For each of theseFig. 13. Simulated process forces in
normal direction.
s simulation of free-formed WC-Co hard material coated
surfacesns. CIRP Journal of Manufacturing Science and Technology
(2014),
-
T. Siebrecht et al. / CIRP Journal of Manufacturing Science and
Technology xxx (2014) xxxxxx6
G Model
CIRPJ-264; No. of Pages 8parameter sets, the resulting process
forces were measured insurface normal direction (Fn) and feed
direction (Ft) by a three-component dynamometer Kistler 9257B. The
fourth measurement representing the center of the parameter space
was repeatedfour times to determine the standard deviation of the
processforces. The mean values were 10.46 N in normal direction
and4.12 N in tangential direction with standard deviations of 0.21
Nand 0.08 N. A Design and Analysis of Computer Experiments(DACE)
model [11] was generated based on the measured forces.The
coefcients of determination R2 were 93.24% for Fn and 93.17%for Ft.
Fig. 15 shows the normal and tangential forces for varyingvalues of
depth of cut ae and feed speed v f , and a xed width of cutap = 3.2
mm, as predicted by the generated DACE model.
Fig. 14. Comparison of multi-dexel board and poisson-disk
representation of thefree-formed surface shown in Fig. 1. The
density of the point distribution is more
homogeneous in case of poisson-disk sampling.
Table 1Calibration experiments based on a latin hypercube design
[14].
# ae(mm)
v f(mm min1)
ap(mm)
# ae(mm)
v f(mm min1)
ap(mm)
1 14 790 2.7 11 13 480 2.0
2 11 560 2.5 12 19 370 2.3
3 13 750 2.2 13 19 710 2.6
4 15 520 2.6 14 15 520 2.6
5 17 600 2.1 15 15 520 2.6
6 12 330 3.0 16 18 670 3.1
7 15 250 2.2 17 16 400 3.2
8 15 520 2.6 18 15 520 2.6
9 20 440 2.9 19 10 290 2.4
10 11 630 3.0 20 17 210 2.8
Please cite this article in press as: Siebrecht, T., et al.,
Grinding proceson machining centers using poisson-disk sampled
dexel representatiohttp://dx.doi.org/10.1016/j.cirpj.2014.01.001In
order to estimate the Kienzle parameters for the process
forcemodel, as described in Section 2.1, the at surface grinding
processwas simulated as well. The grinding tool was modeled as a
cylinderwith a height of 3.2 mm. 3000 grains with a mean diameter
of182 mm, a mean shape index of 5.9 (Fig. 2), and a mean
protrusionheight of 76 mm were distributed on the surface of the
tool. For thegiven experimental setup, the calibrated Kienzle
parameters werekc,sim,n = 64.93 and mc,sim,n = 1.05 for the force
in normal directionand kc,sim,t = 59.8 and mc,sim,t = 0.95 in
tangential direction.
For the evaluation of the applicability of the
developedsimulation system on free-formed surfaces, the process
forceswere measured while grinding a curved workpiece with a
coatedsurface. Fig. 16 shows the shape of this workpiece, which
containsconvex as well as concave surface areas. The experimental
setup isshown in Fig. 17. Due to the different curvatures, the
contactsituation of the cylindrical tool varies along a single
overrun.Therefore, it is expected that the resulting process forces
vary aswell. The process was performed with a feed speed of v f
=1000 mm min1, a depth of cut of ae = 10 mm, and a width of cut
of
Fig. 15. DACE model of the normal and tangential forces for a
width of cut of3.2 mm.
Fig. 16. Coated workpiece with convex and concave surface
areas.
s simulation of free-formed WC-Co hard material coated
surfacesns. CIRP Journal of Manufacturing Science and Technology
(2014),
-
T. Siebrecht et al. / CIRP Journal of Manufacturing Science and
Technology xxx (2014) xxxxxx 7
G Model
CIRPJ-264; No. of Pages 8ap = 5 mm. Fig. 18 shows the sum of the
low-pass ltered and drift-corrected process forces along the course
of a single overrun. It can
Fig. 17. Experimental setup.
51 52 53 54 55 56 s 580
2
N
6
Process me
Processforce
sum
MeasuredSimulated
Fig. 18. Low-pass ltered measured force sum of a single overrun
and the simulatedforces at three locations on the surface.be seen
that the force is signicantly higher in the concave surfacearea
than in the convex areas. The force peaks at the beginning andthe
end of the shown interval of time correspond to the at areas atthe
edges of the workpiece.
In order to compare the simulation to the measured values,
thegrinding process was simulated at three different locations on
thecurved workpiece. One simulation was located in each of
theconvex areas and one in the middle of the concave area. At each
ofthese locations, a full tool revolution was simulated.
Thisrestriction to three local simulations is possible, because
thecutting situation is invariant as long as the curvature of
theworkpiece does not change. Therefore, the process forces
areexpected to be approximately constant within the concave
andconvex areas. Only the orientation of the resulting force vector
isdifferent. As stated before, the simulated height of the grinding
toolis 3.2 mm and the width of cut in the experimental setup is 5.0
mm.Therefore, the simulated force values were extrapolated to the
full5.0 mm according to the slope of the DACE model. The
extrapolatedsimulated force values were 2.97 N and 3.26 N in the
convexsurface areas and 5.76 N in the concave area. These forces
arevisualized as horizontal lines in Fig. 18. The average of
themeasured forces in the corresponding areas are 2.54 N, 3.12 N
and5.42 N, resulting in an average deviation of 9.2%.
4. Conclusions and outlook
In this paper, a force model for the simulation of the
grindingprocess of free-formed surfaces is presented, extending
previouswork presented on the 3rd CIRP Conference on Process
MachineInteractions by [14]. This force model calculates the
resultingprocess forces based on individual grains distributed on
the shapeof grinding tools in a geometric-kinematic simulation
approach.
Please cite this article in press as: Siebrecht, T., et al.,
Grinding proceson machining centers using poisson-disk sampled
dexel representatiohttp://dx.doi.org/10.1016/j.cirpj.2014.01.001The
grains are represented using CSG modeling techniques and
theworkpiece is modeled by dexel boards.
In order to achieve a homogeneous distribution of points on
thesurface of the workpiece, the application of a
poisson-disksampling approach has been investigated as an
alternative todexel boards or multi-dexel models. Using this method
it is easilypossible to distribute dexels uniformly on complex
surfaces. Due tothe random placement, the resulting simulated
forces are slightlymore noisy but less biased in comparison to a
grid-like dexelarrangement. This was shown for the grinding of a at
workpieceat two different orientations.
The fundamental experimental investigations on grinding
atsurfaces are extended by the machining of convex and
concavesurfaces. The experiment as well as the simulation result in
similarforces, which are higher in the concave area. This shows
that thepresented force model can be used for varying
engagementsituations as well.
In further research, the developed process model will be used
tosimulate the grinding of free-formed surfaces with
differentlyshaped tools. Additionally, currently neglected effects
like tooldeection and wear will be integrated into the process
simulation.
Acknowledgments
The investigations and scientic results described in this
paperare based on the research project A5 Simulation supported
NC-shape grinding as a nishing operation of thermally coated
deepdrawing tools, which is kindly funded by the German
ResearchFoundation (DFG) within the Collaborative Research Center
(SFB)708 3D-Surface Engineering of Tools for Sheet Metal Forming
Manufacturing, Modeling, Machining.
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T. Siebrecht et al. / CIRP Journal of Manufacturing Science and
Technology xxx (2014) xxxxxx8
G Model
CIRPJ-264; No. of Pages 8Please cite this article in press as:
Siebrecht, T., et al., Grinding proceson machining centers using
poisson-disk sampled dexel
representatiohttp://dx.doi.org/10.1016/j.cirpj.2014.01.001s
simulation of free-formed WC-Co hard material coated surfacesns.
CIRP Journal of Manufacturing Science and Technology (2014),
Grinding process simulation of free-formed WC-Co hard material
coated surfaces on machining centers using poisson-disk sampled
dexel representationsIntroductionSimulation of the NC grinding
processModeling of grinding toolsWorkpiece modelingForce
predictionPoisson-disk dexel distribution
Experimental investigationConclusions and
outlookAcknowledgmentsReferences