Measurement 45 (2012) 1396–1405

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Measurement

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3-Dimensional kinematics simulation of face milling

Nikolaos Tapoglou, Aristomenis Antoniadis ⇑Technical University of Crete, Department of Production Engineering & Management, University Campus, Kounoupidiana, Chania, Crete 73100, Greece

a r t i c l e i n f o

Article history:Received 22 June 2011Received in revised form 10 February 2012Accepted 21 March 2012Available online 29 March 2012

Keywords:Face millingCutting forcesCAD based simulation

0263-2241/$ - see front matter � 2012 Elsevier Ltdhttp://dx.doi.org/10.1016/j.measurement.2012.03.02

⇑ Corresponding author. Tel.: +30 28210 37293.E-mail address: antoniadis@dpem.tuc.gr (A. Anto

a b s t r a c t

Face milling is currently the most effective and productive manufacturing method forroughing and finishing large surfaces of metallic parts. Milling data, such as surface topo-morphy, surface roughness, non-deformed chip dimensions, cutting force components anddynamic cutting behavior, are very helpful, especially if they can be accurately produced bymeans of a simulation program. This paper presents a novel simulation model which hasbeen developed and embedded in a commercial CAD environment. The model simulatesthe true tool kinematics using the exact geometry of the cutting tool thus accurately fore-casting the resulting roughness. The accuracy of the simulation model has been thoroughlyverified, with the aid of a wide variety of cutting experiments. The proposed model hasproved to be suitable for determining optimal cutting conditions for face milling. The soft-ware can be easily integrated into various CAD–CAM systems.

� 2012 Elsevier Ltd. All rights reserved.

1. Introduction

The kinematics of face milling is widely known and issimilar to conventional milling. As presented in Fig. 1 thekinematics of the process of face milling consists of a rota-tion and a translation of the tool. The rotation has an axisof revolution parallel to axis Z, while the translation ismade along the X axis of the part and depends on the feedper tooth (fz). Each pass cuts a specific depth of cut (tz) as itcan be illustrated in the middle picture of Fig. 1.

The process is affected by a series of parameters, whichcan be divided into two categories. The first category in-cludes the geometrical characteristics of the cutting tool,while the second contains the cutting process parameters.Some of the above parameters are the cutter diameter (D),the number of teeth of the cutter (z), the feed per tooth (fz),cutting speed (vc), the axial depth of cut (tz), the radialdepth of cut (txy), the axial rake angle (ca), the radial rakeangle (cr) and the shift of the cutting edge (s).

This paper presents a novel simulation program, theso-called FaceMill code, which is able to determine theproduced surface, the resulting surface roughness and

. All rights reserved.6

niadis).

the cutting forces, for every possible milling strategy andcutting tool. The completeness of the simulating softwarehas been thoroughly verified with the aid of a wide varietyof cutting experiments. Hereby, several roughness and cut-ting forces measurements were carried out on workpieceswhich had been cut using a 3-axes milling center. In a stepforward, the proposed model was proved suitable to deter-mine optimal cutting conditions.

2. State of the art

Face milling process has been studied by manyresearchers. The main research subjects are cutting forces,surface roughness, search of optimal parameters and toolwear. An area of great interest is the optimization of cut-ting parameters where researchers [1,2] have developedoptimization models based on genetic algorithms for theselection of the optimal cutting parameters for multipassface milling. Another approach in this area was suggestedby Lin [3], who used Taguchi’s method with multiple per-formance characteristics in order to optimize a series ofcharacteristics of stainless steel, produced with face mill-ing. Some other works made in the field of face millinginclude the development of models that predict the burrformation and suggest the optimal parameters which

Fig. 1. Face milling kinematics.

Fig. 2. FaceMill simulation algorithm.

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minimize its formation [4,5] as well as studies on thebehavior of burr [6]. As for the tool wear in the face milling,in-process models are used in order to measure cuttingforces and determine the wear of the cutting tool [7–9].In their study Sampath et al. [10] used an acoustic finiteelement model to predict the cutting noise produced bythe face milling process. Wu [11] investigated the effectof milling strategy on the produced part while face millinglarge surfaces. Machining experiments are usually con-ducted in order to observe the influence of cutting param-eters on tool wear, tool life, cutting forces, surfaceroughness or chip morphology [12–15]. Li et al. [16,17]and Zheng et al. [18] used analytical models in order topredict cutting forces with cutter runout. In their workPatel and Joshi [19] and Baro et al. [20] used also analyticalforce prediction models for face milling cutters, with self-propelled inserts. Another approach was made by Aykutet al. [21] who used an artificial neural network to predictthe cutting forces in face milling of stellite 6 cobalt alloy. Inthe field of surface roughness Baek et al. [22] and Sastry

et al. [23] developed models that optimize the cuttingparameters in order to minimize the effect of run-out onthe roughness of the final workpiece. Saï and Bouzid [24]used a mathematical model to predict surface roughness,using an experimental system method. Similar modelsbut with the use of another objective function was devel-oped by Bagci and Aykut [25], who used Taguchi’s optimi-zation method and Lela et al. [26], who used regressionanalysis, support vector machines and Bayesian neural net-work for this task’s. Benardos and Vosniakos [27] also usedneural networks and the Taguchi design of experiments inorder to predict the surface roughness of machined parts.Franco et al. [28,29] developed a geometric model that pre-dicts the surface roughness and profile in the process offace milling with round insert cutting tools. Their workwas focused on axial and radial runouts. The experimentsthat they conducted were with 1 and 4 cutting inserts.

The development of cutting force models is the mainsubject of many researches. Chang [30] and Zheng et al.[31] developed a mechanical model with empirical

Fig. 3. Cutting edge description.

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constants and analytical model in order to predict the cut-ting forces in face milling. Engin and Altintas [32] proposeda more complete, generalized mathematical model whichcan predict cutting forces, vibrations, surface topomorphyand stability lobes in inserted cutters.

Most of the above mentioned works fail to develop aunified model that can deal with the face milling processin a unified way calculating surface topomorphy andcutting forces at the same time.

3. FaceMill simulation process

As it is presented in Fig. 2, when all the input datashown on the left side of the figure have been defined,the initial workpiece is constructed in the CAD environ-ment. Then the cutting edge of the cutter is created andplaced throughout the 3D trajectory, which this toothcovers during one rotation. This procedure leads to thecreation of the 3D surface that the tooth covers in onerevolution. The surface is positioned in the 3D space, alongwith the workpiece. After combining the above and withthe help of Boolean operations, the non-deformed chip

geometry and the geometry of the workpiece after thatpass are obtained. This process is repeated for all the cut-ting teeth of the cutter, until all the required rotationsare simulated.

After the end of the simulation, the output data are: thesolid geometry of the workpiece in every step of the simu-lation, the non-deformed chip solid geometry in every step,the cutting forces, the surface topomorphy in any sectionparallel or vertical to the feed as well as the roughnessparameters in these sections.

3.1. FaceMill formulation

In the simulation model that is presented the twomovements involved in the process are transferred tothe cutting edge. This way, the workpiece has a steadyglobal XYZ system. The first step of the simulation pro-cess is the creation of the solid workpiece. This can beeither a solid rectangular block created from the simula-tion program or any solid part which can be supportedby the parent CAD program. In the case of the rectangularblock, the XYZ global system is located on the front left

Fig. 4. Creation of 3D solid chip and workpiece.

Fig. 5. Chip development in entry phase.

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upper point of the part, like the one shown on the leftpicture of Fig. 1.

As illustrated in Fig. 3, the next step of the simulationmodel is the description of the 3D cutting tooth geometryand the correct positioning of it in the 3D space. From thecutting tool geometry, like the one shown on the top leftpicture of this figure, the cutting edge geometry is obtainedas a 2D sketch. The geometry of the cutting edge is fully de-fined by this 2D sketch and the angles and the displace-ments that position it on the 3D space. The developedsimulation model supports two angles: axial rake and ra-dial rake, and one displacement of the cutting edge for-ward and backwards in the cut (radial shift). Therotations have axes of revolution, v1 and v2, which passthrough the tip of the cutting edge which is the local zeroof the sketch. The movements and rotations are made insuch a way that the distance between the tip of the cuttingedge, located on the origin of the 2D cutting edge’s posi-tioning system, and the center of the cutter is equal tothe cutter radius.

The following step of the simulation involves the crea-tion of the 3D trajectory of the cutting edge during onerevolution. The 3D cutting tooth geometry is placedthroughout this trajectory. Furthermore, a 3D-Spline isused for the modeling of the trajectory, in order to increasethe accuracy of the produced path. The points of the 3D-Spline are produced by the set of equations that describea motion of this kind and are presented in the followingequations:

x ¼ D2� cosð/Þ þ fz ð1Þ

y ¼ D2� sinð/Þ ð2Þ

The data obtained from the previous step is combinedin order to create the 3D surface which represents themovement of the cutting edge in the 3D space as presentedin Fig. 4. The surface is positioned in the 3D space alongwith the solid workpiece, taking into consideration the off-sets measured from the workpiece’s global XYZ system.

Fig. 6. Experimental setup.

Fig. 7. Experimental results of cutting Ck-60.

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After combining the above and with the help of Booleanoperations the non-deformed chip geometry and the

geometry of the workpiece after that pass are obtained.The workpiece that is obtained is assembled with the 3D

Fig. 8. Experimental results of cutting St52-3.

Fig. 9. Force calculation algorithm.

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Fig. 10. Cutting force results of cutting Ck-60.

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surface of the next tooth until all the teeth cut the work-piece. This procedure is repeated until the required finalpoint of the simulation is reached.

After the end of the simulation, sections can be made onplanes parallel or vertical to the direction of the feed. Theroughness parameters Ra, Rz and Rt are calculated at a gi-ven region within the profile. Furthermore, the profile ofthe section can be exported in text and CAD formats.

3.2. Simulation results

The 3D-solid geometries of 22 chips in the entry phaseof face milling from the simulation of this process withFaceMill are presented in the bottom side of Fig. 5. More-over, the solid geometry of the final workpiece is also illus-trated. The development of the length of the top front edgeof all chips is presented on the top right side of the figure.The reason why this edge was selected is because this edgecan be measured during all the steps of the simulation. Incontrast, the bottom ones cannot be measured during thefirst steps of the cutting process because the cutting edgehas not been fully entered into the cut.

4. Verification

A series of face milling experiments were carried out inorder to verify the accuracy of the developed simulationmodel. Moreover, the experiment results of Franco et al.[28] were used in this process. The experimental setupused can be seen in Fig. 6. The experiments were con-ducted in a DMU50 Universal CNC milling machine usingKennametal’s KSHR40D03R50B25SHN09 cutter head

which can be seen in the top left and center pictures. Thecutting insert was HNGJ535ANENLD grade KC725 M.

The workpiece material used was carbon steel St52-3and Ck60. In order to measure the cutting force, the work-piece was mounted on a Kistler 9257BA three-componentpiezoelectric dynamometer. The force measuring setupwas completed with Kistler’s 5233A amplifier, a PC witha 2855A3 data collection board and Kistler’s Dynowaredata collection and analysis program. After the end of thecutting process, the parts were measured using Asmeto’sprofilometer, diavite compact VHF with SH tracer. Themeasuring arrangement, as it can be seen in the bottomleft picture of Fig. 6, consisted of the profilometer, a sup-porting base and a PC equipped with Diasoft basic programfor the collection and processing of the data acquired.

4.1. Verification experiments part one

The first set of experiments was made in order to exam-ine if the simulated surface topomorphy is similar to themachined one. This set of machining experiments wasmade on a Ck-60 carbon steel plate. In Fig. 7 the machined,as well as the simulated surface are illustrated. Moreover, asection on the center of the simulated model was made toshow the surface topomorphy. In the top row of pictures inFig. 7, the results for feedrate 1 mm/rev,tooth are pre-sented. The machined surface is presented through a pho-tograph on the left taken using an optical stereoscope. Thearea where the picture was taken is near the front end ofthe cut. This means that the marks on the photographare created from the front cutting action of the cutter.The picture in the center shows the surface topomorphy,

Fig. 11. Experimental and simulation results.

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as it is shown on the CAD program. A section of the simu-lated surface can be seen on the right side; this section wasmade on the plane parallel to the XZ plane that passesthrough the center of the cutter. We can see in this picturethat the distance between two successive peaks is equal tothe programmed feedrate and the distance between twosuccessive marks. This is also the case in the other threefeedrates. As expected, the distance between two succes-sive marks decreases as the feedrate decreases. Moreover,the height of the roughness profile is decreased as the fee-drate is decreased, getting from 6.6 lm to 0.8 lm. As it canbe clearly illustrated, the feed marks are consistent withthe programmed feed under all conditions, on both ma-chined and simulated model.

The second set of experiments was conducted on St52-3 with the same conditions. Profilometry tests were con-ducted on the machined surfaces in order to measurethe deviation between the machined and the simulatedsurface. Fig. 8 sums up the results of these experiments.The profilometries were executed in the front region ofthe machined surface in order to acquire a profile createdonly from the cutting action of the front part of the cutter.On the first row, the results for feedrate 1 mm/rev,toothare presented. On the left side the machined surface isshown along, overlapped by the simulated one. As it canbe easily noticed the simulated profile is very similar tothe machined one, both in form and height. Similar resultscan be seen in feeds 0.8–0.4 mm/rev,tooth. As it can beseen, the simulated results have greater accuracy in high-er feeds. The variation between the simulated and the ma-chined surface is a result of a series of parameters thataffect the process, some of which are the tearing of theworkpiece material during the chip removal, built-upedge, vibrations in the milling cutter or the workpiece

and defects in the homogeneity of the workpiece material[28].

The cutting forces obtained from the first set of experi-ments must be compared to the simulated ones. In order tocalculate the cutting forces, a series of sections are made inthe non-deformed chip like the one presented on the leftpicture of Fig. 9. Every section is made in the plane of thecutter according to the geometric characteristics of it, likeaxial and radial rake angle and radial shift. Each section,like the one seen in the right picture of Fig. 9, has a localcoordinate system XeYeZe which rotates with the rotationof the cutter. In every section the cutting edge is insertedin the same way that it was created. The area of the non-deformed chip is divided into a number of elementaryareas. These areas have sides that are perpendicular tothe cutting edge. In every elementary area, the width andlength of this area (b, h) are calculated. Next, the cuttingforces are calculated accordingly to Kienzle–Victor’s equa-tions [33] shown in Eq. (3). The elementary force has 3components Fr, Fs and Fv. The first is parallel to the cuttingedge, the second parallel to the cutting speed vector andthe last perpendicular to the prior two. Every elementaryforce is rotated with the help of rotation matrixes to the lo-cal system of the cutting edge XeYeZe and then rotatedagain to the global system XgYgZg. The forces of each ele-ment of the section are then added up and the process ofcalculation of cutting forces on that section is over. Thisprocess is repeated for a series of sections throughout thechip.

Fi ¼ bi � Ki1;1 � h1�mii for i ¼ r; s; v ð3Þ

where Ki1,1 is the specific cutting resistance, bi is the widthof cut and h the non-deformed chip thickness.

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The force calculation model analyzed above was veri-fied through the experiments made with Ck-60. The resultsof the experiments, as well as the calculated ones, are illus-trated in Fig. 10. As it can be seen, in all four cutting con-ditions the developed model can predict with very goodaccuracy, the prediction made predicts not only the formof the cutting forces but also the magnitude of the forces.

4.2. Verification experiments part two

The second part of the verification was conducted usingexperimental data taken from Franco et al. [28]. The exper-iments they conducted were executed with a cutting toollike the one shown in Fig. 11. As it can be seen, the cuttingtool has four round inserts. During the series of theirexperiments, one and four cutting inserts were used. Thecase that was used was the one with one cutting edge.The results of their experiments can be seen on the top fourgraphs of Fig. 11. The machined surface along with the pro-duced profile, as it was exported from a series of simula-tions made in FaceMill, is presented on these four graphs.As it can be seen, the simulated data in this case is alsovery close to the measured ones. This can also be illus-trated with a comparative graph at the bottom of Fig. 11,which presents the surface roughness of the part simulatedand machined.

5. Conclusion

A novel simulation model which has been developedand embedded in a commercial CAD environment was pre-sented in this paper. The model simulates precisely thetool kinematics and considers the effect of the cuttinggeometry on the resulting roughness. The accuracy of thesimulation model has been thoroughly verified, with theaid of a wide variety of cutting experiments. Moreoverthe cutting forces of this process were also calculatedand verified.

Acknowledgment

The authors wish to thank the Research Committee ofthe Technical University of Crete for their financial support(via basic research project 2008).

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