Grinding Process Simulation of Free Formed WC Co Hard Material Coated Surfaces on Machining Centers...

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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

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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

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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.


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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.


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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.



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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.



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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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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

Grinding Process Simulation of Free Formed WC Co Hard Material Coated Surfaces on Machining Centers...

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