09-1256_Virtual Process Systems for Part Machining Operations

CIRP Annals - Manufacturing Technology 63 (2014) 585–605

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CIRP Annals - Manufacturing Technology

journal homepage: http: / /ees.elsevier.com/cirp/default .asp

Virtual process systems for part machining operations

Y. Altintas (1)a,*, P. Kersting b, D. Biermann (2)b, E. Budak (1)c, B. Denkena (1)d,
I. Lazoglu (2)e
a Manufacturing Automation Laboratory, University of British Columbia, Canadab Institute of Machining Technology (ISF), Technische Universitat, Dortmund, Germanyc Manufacturing Research Laboratory, Sabanci University, Istanbul, Turkeyd Institute of Production Engineering and Machine Tools (IFW), Leibniz Universitat, Hannover, Germanye Manufacturing and Automation Research Center, Koc University, Istanbul, Turkey

A R T I C L E I N F O

Keywords:

Virtual

Machining

CAM

A B S T R A C T

This paper presents an overview of recent developments in simulating machining and grinding processes

along the NC tool path in virtual environments. The evaluations of cutter–part-geometry intersection

algorithms are reviewed, and are used to predict cutting forces, torque, power, and the possibility of

having chatter and other machining process states along the tool path. The trajectory generation of CNC

systems is included in predicting the effective feeds. The NC program is automatically optimized by

respecting the physical limits of the machine tool and cutting operation. Samples of industrial turning,

milling and grinding applications are presented. The paper concludes with the present and future

challenges to achieving a more accurate and efficient virtual machining process simulation and

optimization system.

� 2014 CIRP.

1. Introduction

The current trend is to develop digital models of the manufactur-ing chain from conceptual design to engineering analysis andmanufacturing processes. Conceptual design has been practicedsince the 1960s with the introduction of Computer Aided Design(CAD) and Computer Aided Manufacturing (CAM) methods.Engineering analysis has also accompanied design via ComputerAided Engineering (CAE) tools such as Finite Element (FE) Analysis.The concept of digital machines has also been widely implemented inindustry by utilizing computer graphics and animation technologies.Machine tools are designed using solid models with integrated FEanalysis systems that predict the mode shapes and their dynamicstiffness at the cutting tool–workpiece interface, which leads to aprediction of the machine’s maximum material removal limitsduring design [5]. The geometric removal of material on a machinetool is graphically simulated to check the collision and kinematiccorrectness of the tool path. Virtual geometric simulations of thematerial removal and machine tool motions are now commonly usedin industry. The dynamics of the servo drives, trajectory generation,tool change and part handling mechanisms are simulated in virtualenvironments [15]. The interaction between the manufacturingprocesses and machine tools has also been analyzed using digitalmodels as presented in [1,5,31]. However, the virtual machining ofparts by considering the physics of the manufacturing processes hasrecently been evolving, and the progress being made in this field issubject of this keynote paper.

* Corresponding author.

http://dx.doi.org/10.1016/j.cirp.2014.05.007

0007-8506/� 2014 CIRP.

The virtual machining concept is illustrated in Fig. 1. The CADmodel of the part is used to generate NC programs in a CAMenvironment where the process planners design tool pathstrategies and select cutting conditions based on their experience.

The NC program is tried on a physical machine, and if the processis found to be faulty, the trial and error cycle between the CAM andphysical machining steps is repeated until a satisfactory result isobtained. The aim of the virtual machining is to reduce or eveneliminate physical trials by simulating the physical operations indigital environments ahead of costly production as introduced byAltintas in 1991 [13]. There has been progress toward virtualmachining by simulating the cutting forces and optimizing the feedalong the tool path in three-axis peripheral [76,131] and three-[74,91] to five-axis ball-end milling of dies and molds [104].

The virtual machining system requires sound mathematicalmodels of metal cutting and grinding processes, the dynamics ofmachine kinematics and CNC servo drives, and cutter–partgeometry engagement conditions along the tool path. Themechanics [20,82] and dynamics of cutting [16], drilling [123]and grinding [34,121] processes have been investigated for almosta century, and the progress in their mathematical modeling hasbeen reported in the cited keynote papers and will not be repeatedhere. This paper presents the integration of cutting and grindingprocess models into CAM systems for the simulation of partmachining operations in virtual environments.

Henceforth, the paper is organized as follows. The identificationmethods for tool–workpiece engagement conditions along the toolpath are summarized in Section 2. The computationally efficientmathematical modeling of metal-cutting and grinding processmechanics that are relevant to virtual machining are presented in

[(Fig._1)TD$FIG]

Fig. 1. Architecture of a virtual machining system (UBC MAL).

Fig. 3. Example of a CSG-based composition: combining two primitives (here: cube

and sphere) using set operations: union, difference, and intersection respectively

(ISF).

Y. Altintas et al. / CIRP Annals - Manufacturing Technology 63 (2014) 585–605586

Section 3. The kinematics and dynamics of machines that govern therelative motion between the tool and workpiece are given in Section4. The optimization criteria for NC programs are given in Section 5with the presentation of industrial applications in Section 6. Thepaper concludes by highlighting the current research challenges thatneed to be resolved before fully utilizing manufacturing processsimulation and optimization tools in CAM environments.

2. Tool–workpiece-engagement identification algorithms

Machining process simulation and optimization requires thegeometric modeling of the engagement of the cutter with theworkpiece at discrete intervals along the tool path [116,117]. Thecutter–workpiece engagement (CWE) will lead to the variation inchip thickness, and axial and radial depth of cut which are needed toevaluate force [11,27,115], torque, power, vibration [98,99] and otherprocess states along the tool path [68,134]. Various geometricmodeling techniques are known in the literature for the description ofthe engagement between a tool and a workpiece, which are reviewedas follows.

2.1. Solid-model-based systems

Solid modeling techniques, such as Constructive Solid Geome-try (CSG) or Boundary Representation (B-Rep), are used to modelthree-dimensional objects [108]. These techniques were designedin the mid-1960s when CAD/CAM-systems required modelscontaining the geometric dimensions of the parts.

The method of describing solid objects by their boundaries, i.e.,surface patches, edges and vertices, is called B-rep [26]. It supportsvarious mathematical descriptions [77] such as Bezier, Spline, orNURBS (NonUniform Rational B-Splines) techniques [72]. B-rep offersdesign flexibility and high reproducibility of free-form surfaces [26],and allows a continuous and accurate representation of the sweepvolume [130] of a moving cutter envelope as shown in Fig. 2 [57,133].[(Fig._2)TD$FIG]

Fig. 2. Example of a boundary representation of a tool-workpiece engagement. (a)

Initial (P1) and final (P2) configuration of the cutter. (b) Sweep volume of the moving

cutter envelope. (c) Raw stock material and generated sweep volume. (d) Result of the

Boolean operation of the sweep volume and the raw stock material [133].

However, the computation of the intersection between therepresented surfaces (Fig. 2d) is a difficult and computationallytime-consuming task.

In contrast to the B-rep technique, the CSG (Constructive SolidGeometry) representation allows an easy description of thecomposition of individual components [72]. The idea of the CSGtechnique is to combine solid objects, e.g., spheres, cones, cuboids,using Boolean operations, like union, difference or intersection asshown in Fig. 3 [1,128].[(Fig._3)TD$FIG]

2.2. Wire-frame-based systems

The shape of a 3D object can also be represented by points andlines. These models do not provide any information about theinside and outside of the component, but allow a fast and simplevisualization of the components as shown in Fig. 4, although not assmooth as in solid model representation of parts.[(Fig._4)TD$FIG]

Fig. 4. Example of a wire-frame-based system: The tool and the workpiece are

depicted by lines (ISF).

2.3. Voxel-, dexel-, and Z-buffer-based systems

Modeling techniques based on z-buffer, dexels or voxels arediscrete representations of objects [72]. Using a voxel-basedsystem, the volume is approximated using small, uniform cuboids(Fig. 5) which are called voxels (volume element/volumetricpixel). Voxels are either filled with a material or kept empty. Sincethe number of voxels (n) depends on the resolution by O(n3) [128],the drawback of this easy-to-implement modeling technique is ahigh demand of memory and computation time when theresolution of the model is increased.

[(Fig._5)TD$FIG]

Fig. 5. Example of a milling simulation using a voxel-based workpiece model [119].

[(Fig._7)TD$FIG]

Fig. 7. Concept of the dexel-based technique (ISF).

Y. Altintas et al. / CIRP Annals - Manufacturing Technology 63 (2014) 585–605 587

The basic idea of dexel (depth element)-based systems is todiscretize an object not by using cuboids, but parallel linesegments, which are arranged on a regular grid. These linesegments can have different lengths defined by their start andend points. If the elements are only used in one direction andshare the same start value [73,134], the method is called z-buffer technique (Fig. 6), which is named after the renderingtechnique in graphic processor units [129]. This approach isvery easy to implement and has a low computation time.However, only convex shapes (without undercuts) can bemodeled, and each line has to be replaced by a list of linesegments [128].[(Fig._6)TD$FIG]

Fig. 6. Example of modeling the surface of a honing tool [83] using z-buffer method

(ISF).

In order to improve the accuracy of the z-buffer model, threedexel models – each aligned along one of the Cartesian axes – canbe used (Fig. 7). In contrast to the voxel-based technique, the dexelmodel has less memory demand of O(n2).

[(Fig._8)TD$FIG]

Fig. 8. Different possibilities to model

2.4. Point-based methods

Point-based methods discretize an object using single points(Fig. 8 [85]). For example, the basis for element-free techniques,like SPH (Smooth Particle Hydrodynamics [93]), or methods usingbackground meshes, e.g., MPM (Material Point Method [19]) areused. These techniques are adapted from computer science inorder to overcome the disadvantages of finite element models, e.g.,a strong distortion of finite elements resulting in a low computa-tion accuracy or high computational costs for re-meshing [19].

2.5. Analytical methods

Besides discretization and solid modeling techniques, analyticalapproaches have also been used in calculating tool–workpieceengagement. Such approaches mainly depend on the approxima-tion of the workpiece surface information by use of the cutterlocation (CL) file itself as shown in [126]. The cutting parameterssuch as step over, cutting depth, lead and tilt angles are calculatedusing the analytical difference between consecutive CL points, toolaxis vector and the approximated workpiece surface (Fig. 9).Although such methods are fast, their application is limited tospecial machining cases such as ball end milling of blades due tothe geometrical definition requirements for the features on thepart.

2.6. Discussions

The choice of the models for the workpiece and the tool (Fig. 8)depends on the focus of the simulation, the required accuracy ofthe results and the demand on the computation time. Additionally,if particular simulation systems or commercial software are used,the kind of model is generally predetermined. The approach forcalculating the material removal process and for the tool–workpiece-engagement identification depends on the chosenmodels. Generally, the machining processes are simulated usinga time [133] or displacement discretization of the tool path[97,115] (Fig. 10).

the workpiece and the tool (ISF).

[(Fig._9)TD$FIG]

Fig. 9. Analytical calculation of cutting parameters [105].

[(Fig._10)TD$FIG]

Fig. 10. Discretization of the tool movement [133]. (a) Tool at different NC positions.

(b) Approximated sweep surface.

Fig. 12. Geometric model of the current chip shape Cn based on the CSG technique

(ISF).


Since discrete models (voxel-, dexel-, z-buffer-based systems)are easy to implement, they are most commonly used for therepresentation of tools or workpieces [24,25,28,56]. The simplestand fastest approach is the z-buffer technique, which is, forexample, used in (Fig. 6) to model the honing process [83].However, z-buffer models are insufficient for use in the five-axismachining of free-form surfaces, where dexel- or voxel-basedsystems are preferred (Fig. 11). Due to the discrete sampling, thesemodeling techniques are subject to aliasing errors, which can bereduced by increasing the number of elements (dexel or voxel) butat the expense of higher computation loads and larger memorydemands, i.e. O(n3) for voxel and O(n2) for dexel boards. If a moreprecise model is needed, solid modeling techniques such as CSG orB-rep methods, should be used [92].[(Fig._11)TD$FIG]

Fig. 11. Example of dexel-based workpiece and a CSG-based tool model. Simulation

of the (a) NC-milling process, (b) NC-grinding, (c) drill grinding (ISF).

Using the CSG technique, the material removal process and thecurrent chip shape Cn can be easily described by the following

equation:

Cn ¼W0

[n�1

i¼1

Ti

0BBBB@

1CCCCA\ Tn (1)

where W0 is the model of the stock material and Ti is the envelopeof the tool model at the position of the nth cut (Fig. 12 [118]). SinceBoolean operations can be defined easily and accurately, the CSGtechnique is a popular model for high-precision engagementcalculations [85].[(Fig._12)TD$FIG]

The visualization of the material removal on the part is also anessential feature in virtual machining. Although a CSG representa-tion of the workpiece can be updated in constant time, it iscomputationally costly to directly render this model using ray-tracing techniques [115]. Therefore, an alternative visualizationmodel is often used in combination with the CSG model [118].

3. Metal cutting process models

The main objective in simulating part machining operations in avirtual environment is to predict the maximum cutting forces,torque, power, vibration amplitudes and dimensional surfaceerrors left on the part in short computational time windows. As aresult, the micro-mechanics of cutting which aims to predict thetemperature, stress, residual stresses and strain distribution intool–chip interface zones are not considered in the virtualmachining of parts. However, the micro-analysis at the cuttingzone is still possible by freezing the tool at a particular location andsimulating the process in detail if needed. The details of micro-mechanics models, which are not used by NC programmers but byprocess design specialists, can be found in the past CIRP keynotepapers [20,82].

3.1. Mechanics of orthogonal cutting

The macro mechanics of orthogonal cutting can be simplified byassuming a thin shear plane with an average shear angle (fc) andshear yield stress (ts) as shown in Fig. 13 [4]. The sticking andsliding friction zones between the chip and rake face are simplifiedby having an average Coulomb friction coefficient (ma). Thefundamental orthogonal cutting parameters (fc, ts, ma) can beobtained from orthogonal cutting tests and stored in a materialdata base as an experimentally calibrated function of uncut chipthickness (h), cutting velocity (V) and tool rake angle (gr) [4].Alternatively, the orthogonal cutting parameters can be predictedfrom micro-metal cutting mechanics methods such as FiniteElement or slip line field analysis [136,137]. The chip thickness (h)has a static part (hcs) which is dependent on the tool geometry andkinematics of the cutting operation, and a dynamic part (hcd) due toregenerative vibrations [9,16,37].

Since a number of metal cutting operations such as turning,drilling, and milling occur in machining a part on CNC machiningcenters, the mechanics of cutting for a variety of tool geometriesmust be handled by the virtual machining system. The cutting edge

[(Fig._13)TD$FIG]

Fig. 13. Mechanics of orthogonal cutting with thin shear plane [4].

[(Fig._14)TD$FIG]

Fig. 14. Tool-in-hand planes and motion directions (adapted from ISO 3002) and the

definition of normal rake angle [81].

[(Fig._15)TD$FIG]

Fig. 15. Mechanics of oblique cutting [84].


geometry is first defined according to ISO 3002 [81] standards. Thenormal rake, cutting edge and oblique angles, which are needed inmodeling the mechanics of cutting, are evaluated from the toolgeometry and cutting velocity direction [84]. The tool referenceplane (Pr) is oriented perpendicular to the primary motion (cuttingvelocity) vector and parallel to the tool axis (Fig. 14a). The toolcutting edge plane (Ps) is tangential to the cutting edge at theselected point and perpendicular to Pr. The cutting velocity vector(v0) is transformed to design coordinates (Frame D) after the insertis oriented on the cutter body (Fig. 14b) [84]. The tool with anoblique angle of cut (ls) and the normal rake angle (gn) is defined inthe oblique cutting mechanics frame (Fig. 14) as a function of theorientation of the cutting edge with respect to the cutting velocitydirection and the cutter body. The details of geometric transfor-mations can be found in [84].

The generalized mechanics model requires the evaluation of thefriction force on the rake face (Fu), which is aligned with the chipflow angle (h) and the normal force (Fv) described in chip flowcoordinates, as shown in Fig. 15. A differential cutting edge thatproduces a chip with an area (dAc) and length (dS) creates thefollowing friction and normal forces:

dFuðkdzÞ ¼ KucðkdzÞdAcðkdzÞ þ KuedSðkdzÞdFvðkdzÞ ¼ KvcðkdzÞdAcðkdzÞ þ KvedSðkdzÞ (2)

where Kuc and Kvc are the friction and normal cutting forcecoefficients, and Kue and Kve are the edge force coefficients inoblique cutting for each insert and differential segment (k) with dz

height. The chip area and width are evaluated as

dAcjðkdzÞ ¼ h jðkdzÞ � dS jðkdzÞ and dS jðkdzÞ ¼ dz

sin k�r j

where hj (kdz) is the local chip thickness cut by tooth j. Cuttingcoefficients in friction and normal directions can be evaluatedusing orthogonal to oblique transformation methods such asproposed by Armarego et al. [21] as follows:

Kuc ¼ts

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1� tan2h sin2 bn

q

cos ls sin fn

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffifficos2ðfn þ bn � gnÞ þ tan2h sin2 bn

q sin ba;

Kvc ¼ts

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1� tan2h sin2 bn

q

cos ls sin fn

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffifficos2ðfn þ bn � gnÞ þ tan2h sin2bn

q cos ba:

(3)

[(Fig._16)TD$FIG]

Fig. 16. Turning operation [9].[(Fig._17)TD$FIG]

Fig. 17. Multiple teeth boring [84].

[(Fig._18)TD$FIG]

Fig. 18. Drilling operation [9].


The shear stress (ts), shear angle (fn), average friction angle(ba = tan�1 ma) and edge coefficients (Kue and Kve) are evaluatedfrom the orthogonal cutting model as described in [21]. Theprojection of the friction angle on the cutting edge normal plane isshown as (Pn), is bn = tan�1(ms cos h), where h is the chip flow anglewhich can be assumed to be equal to oblique angle h � ls using theStabler rule [48] for simplistic force analysis. Alternatively, thecutting force coefficients (Kuc, Kvc) can be mechanisticallycalibrated from dedicated cutting tests conducted with each toolgeometry. Both methods are widely used in creating a cutting forcecoefficient data base for various materials. The edge forcecoefficients (Kue, Kve) are highly dependent on the radius of thecutting edge and flank wear. They need to be identified eitherexperimentally, or by using Finite Element [20,137] or slip linefield [136] models. The thermo-mechanical behavior of thematerial can be modeled using the Johnson–Cook material modelwhere strain, strain rate and temperature effects can be consideredin Finite Element or slip line field models when predicting thecutting force coefficients [38,101]. A sample mechanistic cuttingforce coefficient identified from the flow stress and frictionparameters of a material as a nonlinear function of chip thickness(h) and cutting edge radius (r) from Finite Element and slip linefield simulations is given as [17]:

Kt h; rð Þ ¼ Kt1 hð Þ þ Kt2 h; rð Þ ¼ athdt þ bth

pt rqt : (4)

Once the differential friction (dFu) and normal (dFv) forces onthe rake face are identified from the material properties andcutting edge geometry (Eqs. (2) and (3)), they can be integratedalong the width of cut (b) to find the total cutting (Fu, Fv) forces onthe rake face of the cutting edge.

3.2. Transformations to machining coordinates

In a virtual machine tool, the chip thickness must be calculatedas a function of feed, tool geometry, the kinematics of themachining operation, and relative vibrations between the cuttingtool and workpiece. There are several coordinate systems in theprocess chain, but the fundamental base is the rake face of the toolwhere the chip leaves the part.

The rake face coordinates (u, v) are transformed into cuttingedge coordinates (x, y, z-RTA coordinate system I) from Fig. 15 as[84]:

x y zf gTI ¼ T1U u vf gT (5)

T1U ¼cosðgnÞcosðhÞ

sinðlsÞsinðhÞ þ cosðlsÞsinðgnÞcosðhÞ�cosðlsÞsinðhÞ þ sinðlsÞsinðgnÞcosðhÞ

24

�sinðgnÞcosðlsÞcosðgnÞsinðlsÞcosðgnÞ

35:

The RTA coordinates define the cutting edge, which can betransformed to a machine coordinate system (0) as a function ofeach machining operation:

x y z cf gT0¼

T0R � TRI

0 Rt 0

� �x y zf gT

I (6)

where Rt is the moment arm for the force in y direction creating thetorque in direction c. The transformation matrices TOR and TR1 areunique for each machining operation. TOR matrix is represented as:

TOR ¼sin ðc jÞ �cos ðc jÞ 0cos ðc jÞ sin ðc jÞ 0

0 0 1

24

35; (7)

where the location angle (cj) and TR1 depend on the cutting toolorientation for each operation as shown in Figs. 16–18.

The chip thickness is measured perpendicular to the cuttingedge and defined by the following general expression:

h jðt; kdzÞ ¼ c j sin k�r ðkdzÞ � sin f jðt; kdzÞ þ ecdj ðt; kdzÞ �DqðtÞ (8)

where cj is the feed rate for tooth j. The engagement angle timevaries with the time in milling (fj = cj) and the constant forturning (fj = p/2) operations.

[(Fig._20)TD$FIG]

Fig. 20. Cutters with arbitrary geometry [10].

Fig. 19. Milling operation [9].


The vibrations in lateral (x, y) and axial (z) directions are definedin machine coordinates as [9]:

qðtÞ ¼ f xðtÞ yðtÞ zðtÞ gT (9)

The effect of regenerative vibrations ðDq ¼ qðtÞ � qðt � TÞÞ isconsidered by orienting them into the direction of the chipthickness with the transformation vector:

e jðt; kdzÞ ¼ �1 0 0f g T0R � TR1ð ÞT : (10)

The cutting forces on the rake face (Eq. (2)) are transformed toRTA coordinates using Eq. (5) which have cutting, ploughing andprocess damping parts as follows [59]:

dF jðt; kdzÞ ¼ dFcjðt; kdzÞ

|fflfflfflfflfflfflffl{zfflfflfflfflfflfflffl}cutting

þ dFesj ðt; kdzÞ

|fflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflffl}ploughing

þ dFedj ðt; kdzÞ

|fflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflffl}process damping

;

Fðt; kdzÞ ¼ Fx Fy Fz Tc

� �T

0¼XN

j¼1

XK

k¼1

gðt; kdzÞdF jðt; kdzÞ;(11)

where g (t, kdz) = 1 when the cutting edge is in cut and g (t, kdz) = 0otherwise. The cutting component ðdFc

j Þ of the forces is divided intostationary ðdFcs

j Þ and dynamic ðdFcdj Þ parts as:

dFcjðt; kdzÞ ¼ dFcs

j ðt; kdzÞ þ dFcdj ðt; kdzÞ;

dFcsj ðt; kdzÞ ¼ T0R � TRI

0 RtðkdzÞ 0

� �T1U

KucðkdzÞKvcðkdzÞ

� c jsinf jðt; kdzÞ dz;

dFcdj ðt; kdzÞ ¼ T0R � TRI

0 RtðkdzÞ 0

� �T1U

KucðkdzÞKvcðkdzÞ

� ecd

j ðt; kdzÞDqðtÞ dz:

(12)

The ploughing forces are given as:

dFesj ðt; kdzÞ ¼ T0R � TRI

0 RtðkdzÞ 0

� �T1U �

KueðkdzÞKveðkdzÞ

� 1

sinðk�r ðkdzÞÞ dz(13)

Process damping forces are found as [9]:

dFedj ðt; kdzÞ ¼ T0R � TRI

0 RtðkdzÞ 0

� �Ks pLw

2

4vcP

e pdj ðt; kdzÞ

sinðk�r ðkdzÞÞdz (14)

where P ¼ 1 m 0f gT and m is the Coulomb friction coefficient.Ksp is the material-dependent contact force coefficient; Lw is flankwear land width of the tool and vc is the cutting speed. The totaldynamic forces that affect the stability of cutting become:

FdðtÞ ¼ FcdðtÞ þ FedðtÞ: (15)

The effects of run-out, variable pitch and helix, and serratededge can also be added to the overall cutting forces [59,95].

3.3. Specific machining operations

The generalized force models can be adapted to various chipremoval operations by simply transforming the forces from RTA(cutting edge) coordinates to the coordinates of the specificmachining operation. Only the operation and tool-geometryspecific engagement angle (c) and transformation matrices(TR1,e) are needed as described in Figs. 16–18 [9].

3.3.1. Single point turning operations

Single point turning and boring operations have the samegeometry, and the fundamental parameter is the side cutting edgeangle ðk�r Þ as shown in Fig. 16. The rotational matrices TOR and TRI

are automatically transformed to predict cutting forces in turning.

3.3.2. Boring heads and drilling operations

Drilling and boring heads have multiple cutting edges but withidentical kinematics as shown in [22,23]. The tool rotates andmoves axially along the hole axis, and the correspondingtransformation parameters are set as shown in Figs. 17 and 18[9,84].

3.3.3. Milling operations

Milling cutters have multiple teeth but the direction of feed isperpendicular to the plane formed by the spindle (Z8) and normalto the feed (X8) directions, as shown in Fig. 19. If the cutter has anarbitrary geometry with different inserts along each flute as in Fig.20, the cutter is subdivided into small differential disk elements[7,10]. The contributions of all differential cutter elements to forcesare calculated and summed digitally to find the total forces, torqueand power contributed by the total cutter engaged with theworkpiece [60,61].[(Fig._19)TD$FIG]

An example of simulated milling forces predicted by consider-ing the thermo-mechanical properties of the material is shown inFig. 21 [38]. Instead of simulating the periodic states such asmilling forces and torque at discrete time intervals, Altintas et al.[11] argued that the maximum force, torque, power anddimensional surface errors are the most crucial information forprocess planners. The maximum values of the process states mustnot exceed the machine limits or the tolerance of the part. Theydeveloped analytical, closed form formulas to predict themaximum and minimum values of process states at each discrete

[(Fig._21)TD$FIG]

Fig. 21. Comparison of simulated and measured forces using the thermo-

mechanical model [38].

[(Fig._23)TD$FIG]

Fig. 23. Vibration amplitude under process damping effect [41].

[(Fig._22)TD$FIG]

Fig. 22. Time domain milling simulation. (a) Visualization of surface location errors

during the simulation of the machining process. (b) Analyzing the chip shape using

scanning rays (ISF).


tool position along the tool path [98,99]. The closed form solutionsgive the exact values of maximum states directly and accuratelythus avoiding the time marching solutions. They argued that a timemarching simulation can still be conducted if the process needs tobe interrogated at an unsafe tool path position.

3.4. Time-domain simulation of machining processes

As the tool travels along the tool path, the cutter–partengagement boundaries are evaluated at each discrete pathsegment by one of the methods presented in Section 2. Thecutter–workpiece engagement maps contain the axial depth of cutand width of cut along the cutting edge engaged with the material.There are various approaches in simulating the process states suchas forces and vibrations. The time marching methods revolvethe spindle and move the tool along the tool path at discretetime intervals and simulate the process states as a function of time[114]. The process equations (Eq. (11)) are solved at eachtime interval as demonstrated in boring [22,23,88], five axismilling [51,89,109]. Such methods are computationally costly, andfine sampling intervals (i.e. 0.2 ms to capture 5000 Hz vibrationmarks) are needed in order to simulate the maximum values offorces in periodic processes like milling.

However, there have been efforts to improve the computationalspeed of time domain simulations. Surmann et al. [118] developeda time-domain simulation system for the milling process, in whichit is not necessary to explicitly solve the process equations. Bymodeling the tool and the workpiece using CSG (Section 2.1), animplicit model of the chip is obtained for each tooth feed. Theprocess forces are then calculated by analyzing this chip shapeusing scanning rays for the determination of the undeformed chipthickness (Fig. 45b), and subsequently applying an empirical forcemodel. In order to predict the tool vibrations, the process forces areapplied to a system of single-degree-of-freedom oscillators, whichis used to describe the dynamic behavior of the cutting tool [118].This approach was extended and applied for the modeling ofworkpiece vibrations by Kersting et al. [86,87]. The resulting tooland workpiece deflections are added to a CSG model of the tool–workpiece engagement that generates the chip shape in thesubsequent tooth period in order to consider the regenerativeeffect [135]. The numerical simulation thereby provides aprediction of cutting forces, relative vibrations between the tooland workpiece, and dimensional form errors left on the finishsurface as shown in Fig. 22 [29,30]. The computational speed ofthis approach can be further increased by avoiding the remodeling

and analysis of the chip geometry if the cutter–part engagementconditions do not change along the path [117].

Alternatively, the delayed differential equations can be solvedat discrete time intervals using the semi-discretization method[14], which leads to a prediction of chatter stability, cutting forces,dimensional surface errors and vibrations along the tool path [59].The process damping reduces the vibration amplitudes at lowerspeeds and increases the stability demonstrated by Budak et al.[41,42]. Although the depth of cut is the same, the vibrationamplitudes are reduced significantly at the lower cutting speeddue to the process damping effect, as in Fig. 23. The processdamping, which affects the prediction of surface quality at lowerspeeds [124,125], can be easily considered in time-domainsimulation models, as shown in Eq. (11).

3.5. Grinding operations

Grinding processes can be simulated similarly to metal cuttingby evaluating the engagement geometry between the grindingwheel and the workpiece along the tool path as presented inSection 2. An overview of the grinding process modeling andsimulation techniques is given by Tonshoff et al. [121], Brinksmeieret al. [34] and Brecher et al. [31]. Besides analytical methods,process simulation models based on geometric-kinematicapproaches, finite element analysis and molecular dynamics arewidely used.

In contrast to the previously described metal cutting processes,the cutting edges are not specified in abrasive processes due to thelarge amount of grains and the variation of their sizes, shapes,distribution and orientations. Unlike in metal cutting where thecutting edges are defined and have a line contact with the material,the grinding wheel has a contact surface which can be quite complexin multi-axis machining where free-form surfaces are generated

[(Fig._25)TD$FIG]Y. Altintas et al. / CIRP Annals - Manufacturing Technology 63 (2014) 585–605 593

[122]. In addition to the workpiece material properties, wear anddeflections of the wheel strongly influence the grinding process [78].

In analytical approaches, which can be used for the simulationof process forces and operation states such as the resultingmaximum height of profile in surface grinding, the tool andworkpiece material properties are described by empiricallydetermined constants [121]. The specific normal force F 0n, perunit width of cut (ap), can be expressed for surface grindingprocesses (Fig. 24a) as [34]:

F 0n ¼ cw pcgwv f

vc

�e1

ae2e de3

eq ; (16)[(Fig._24)TD$FIG]

Fig. 25. Geometric-kinematic simulation of a flat surface grinding process. (a)

Distribution of the grains on the grinding tool and the topography of the ground

surface. (b) Dexel-based representation of the workpiece with a dexel distance of

3 mm (ISF).

Fig. 24. Engagement situation of tool and workpiece in (a) longitudinal surface

grinding (IFW) and (b) NC grinding (ISF).

[(Fig._26)TD$FIG]

Fig. 26. Simulated single grain engagement (ISF).

where ae is the depth of cut, deq is the equivalent grinding wheeldiameter which reflects the wheel engagement, and vc and vf are thecutting speed and the feed velocity, respectively. Additionally, thecoefficients cwp for the workpiece material, cgw for the grinding wheeland e1, e2 and e3 for the process parameters have to be determinedempirically from experiments. An extended version of these modelshas been applied to other grinding operations such as internal orexternal grinding, which require the contact area between the wheeland the workpiece [34]. However, the applicability of analyticalmodels to grinding operations with varying contact conditions (e.g.profile grinding [55,88,132]) is limited.

Geometric-kinematic simulation models offer a flexible solutionfor the determination of the tool engagement with the workpiece insuch grinding operations (Fig. 24b)[132]. The basic shapes of thegrinding tools can be represented with solid modeling techniques(e.g. CSG) as described in Section 2. The contact area or the materialremoval rate can be calculated by intersecting the tool and theworkpiece models [34,112]. Similar to the analytical approaches,process forces can be calculated using empirical methods, and theinfluence of the distribution and shapes of the grains are consideredby the calibration of empirical constants.

Instead of an implicit representation of the cutting grains, thegeometry of the individual grains on the grinding tool can bemodeled [28,113]. These grains can be generated based on statisticaldistributions [34,113] or measured tool topographies [78]. Theextended model can be used to estimate the topography of theworkpiece after finishing (Fig. 25a) or to determine characteristic

values of grinding processes [24]. In order to calculate the processforces acting on the tool, two different methods can be applied [113].In the first method the engaged chip cross sectional areas Acu have tobe summed and multiplied by an empirically determined specificcutting force coefficient kc,sim [24] (Fig. 24):

FðtÞ ¼ kc;sim

XN

i¼1

Acu;iðtÞ: (17)

For the second force model, the undeformed chip thicknesseshave to be determined within the simulation system [113]. Theforce model for each grain can be expressed as:

F ¼ nkc;simbd0d0

d0

�1�mc;sim

(18)

where n is the normal direction of the cutting grain face, b thewidth of a considered segment of the cutting edge and d theundeformed chip thicknesses. The coefficients kc,sim and mc,sim haveto be separately determined empirically for the calculation ofnormal and tangential forces.

For example, by applying the simulation to drill-grindingprocesses, the material removal per individual grain was analyzedin order to allow improvement of the tool layout and thereby toavoid material clogging [28]. The same basic approach was utilizedfor simulating the NC grinding of free-formed surfaces [113]. Byanalyzing the chip shape for each cutting grain, it is possible tocalculate the process forces, which can be used to adapt the tool pathfor keeping the grinding forces at a desired level. For the definitionand calibration of the process force model, the geometric-kinematicapproach was coupled with a finite element simulation [112].

However, these extended simulation models are computation-ally costly due to small simulation time steps which are necessaryto evaluate the changing process conditions during the rotation ofthe grinding tool. Moreover, high resolutions of the workpiecemodels are necessary due to the small contact area of theindividual grains (Fig. 26).

[(Fig._28)TD$FIG]

Fig. 28. Trajectory generation profile with jerk continuity [63].


4. Machine dynamic models

The dynamics of the machine tool are modeled by the rigid bodykinematics, CNC system and structural dynamics of the multi-axismachine system. The NC tool path is followed by the machine at afeed velocity governed by the kinematics and control of themachine used by the CNC system. Any change in the feed along thetool path affects the chip load, and hence the cutting process.

4.1. CNC and trajectory generation models of machines

A detailed review of CNC systems, their architecture andfunctional modules has been presented in previous CIRP keynotepapers [15,107]. The virtual design and simulation of CNC systems[66], which include trajectory generation [63], drive dynamics [64]and servo control [65] have also been presented in detail byAltintas’s research group [139,140]. Here, only the kinematics ofmulti-axis machines and trajectory generation are briefly summa-rized since they are most relevant to the prediction of chipthickness, forces and vibrations in the virtual machining of a part.

NC programs contain the tangential feed velocity, tool tip andorientations on the part coordinate (P) system as shown in Fig. 27.The tool motions are transformed into axes commands in themachine tool coordinate system (M) by the inverse kinematics of themachine tool. The tangential feed commanded by the NC programhas to go through acceleration, constant feed and deceleration stageswithout saturating the torque limits of each drive, while preservingjerk continuity in order to have the smooth velocity profile as shownin Fig. 28 [4]. The feed varies during the acceleration anddeceleration stages, and may not even reach the programmedvalues in the 3- to 5-axis machining of sculptured surfaces if the pathsegments are short and the drives do not have high accelerations (i.e.torque) [111]. For example, if the jerk is constant (J0), theacceleration will linearly increase, stay constant, and linearlydecrease when the feed reaches a desired, cruising velocity. Themachine will start decelerating by following the reverse phases ofacceleration. As a result, the feed will have seven distinct variationzones within one NC block in the part program as follows [4]:

f ðtÞ ¼

f s þJ0t2

2zone 1h i

f 1 þ At 2h i

f 2 þ At � J0t2

23h i

f 3 ¼ f 4 4h i

f 4 �J0t2

25h i

f 5 � At 6h i

f 6 � At þ J0t2

27h i

8>>>>>>>>>>>>>>>><

>>>>>>>>>>>>>>>>:

(19)

[(Fig._27)TD$FIG]

Fig. 27. Kinematics of five-axis machine tool [141].

Correct feed must be calculated by considering the trajectoryprofile of the CNC so that the chip loads, and hence the cuttingloads, are estimated accordingly. If the jerk is a second ordercontinuous system, the feed changes in nine distinct zones duringthe machining of one NC block, which has to be considered inpredicting the process in virtual environments [4]. Including theeffect of the servo dynamics will not drastically improve theevaluation of feedrates, i.e. chip loads, and hence it can bedisregarded for virtual machining process simulations.

4.2. Stability inspection of machining processes

Process planners must select chatter-free global cutting speedsand cutting conditions in preparing NC programs. However, sincethe tool-part engagement conditions vary continuously along thetool path, the virtual machining system must alert the planner tothe possibility of having chatter at specific locations. Instead ofpredicting the chatter-free stability lobes, virtual machining mustinspect the presence of chatter and change the spindle speed, ifpossible, or alert the planner to modify the process.

The transfer function of the structural dynamics of the machinemeasured at the tool–workpiece contact zone can be constructedin Laplace domain in the machine coordinates as:

F ¼ Ft þFw p ¼FxxðsÞ FxyðsÞ FxzðsÞ

FyyðsÞ FyzðsÞsym: FzzðsÞ

24

35: (20)

The corresponding relative vibrations between the tool andworkpiece can be predicted by applying the total cutting force (Eq.(11)) on the machine at the tool–workpiece interface:

q3�1 ¼ F3�3F3�1 (21)

where q3�1 represents the relative vibrations between the tool andworkpiece:

q ¼ qt þ qw p (22)

The vibrations (Eq. (21)) and total dynamic cutting forces(Eq. (11)) cannot be directly solved in time domain due to the

Fig. 29. FE-based structural modification. (a) FE mesh of workpiece and stock, (b)

element determination [52].

Fig. 30. Geometry of simultaneous turning and milling [49].


regenerative term ðDqðtÞ ¼ qðtÞ � qðt � TÞÞ with the time delay(t � T) in the dynamic cutting force (Eq. (12)). The process caneither be solved in time domain using numerical integrationmethods [100], or by converting the delayed dynamic equationinto an analytical, semi-discrete form [14,80]. However, it is morepractical to check whether the cutting system is stable or unstableat the particular tool path position in the frequency domain asfollows.

The critical stability of the system can be determined by settingthe displacements and forces as:

qðtÞ ¼ qðvcÞeivc t; FðtÞ ¼ FðvcÞeivct (23)

where vc is the chatter frequency and q and F are the amplitudes ofdisplacement and force vectors, respectively. Similarly, the delayeddisplacement vector can be expressed as:

qðt � TÞ ¼ qeivc te�ivcT : (24)

Some of the machining operations, such as milling and boringwith an uneven number of inserts on the cutter, have time periodiccoefficients in their dynamic cutting forces (Eq. (11)). By averagingthe periodic coefficients in tooth passing or spindle periods [6], thedynamic cutting force with regenerative and process dampingparts that affect the chatter stability [9,138] can be described as:

FðtÞffi A0ð1� expð�ivcTÞÞ þ C0ð Þdz½ �qeivc t (25)

where the averaged directional matrix (A0) is given as [35,36]

A0 ¼VZ 1=V

0

XN

j¼1

f ðtÞdt ¼ 1

2p

Z 2p

0

XN

j¼1

f ðcÞdc: (26)

Since the cutter is engaged only when it is between entry (fst)and exit (fex) angles (fst <c < fex), Eq. (26) can be simplified as:

A0 ¼1

2p

Zfex

fst

XN

j¼1

XK

k¼1

T01

KrcðkdzÞKtcðkdzÞKacðkdzÞ

8<

:

9=

;e jðt; kdzÞ

sinðk�r ðkdzÞÞ

24

35 � dc

¼ N

2p

XK

k¼1

Zfex

fst

T01

KrcðkdzÞKtcðkdzÞKacðkdzÞ

8<

:

9=

;e jðc; kdzÞ

sinðk�r ðkdzÞÞ dc

264

375 ¼

N

2p1

2A

(27)

Similarly, the process damping matrix (C0) in Eq. (25) isevaluated by averaging as [59]:

C0 ¼1

2p

Z fex

fst

XN

j¼1

XK

k¼1

Ks pL2w

4vcT01P

e jðt; kdzÞsinðk�r ðkdzÞÞ

� �dc

¼ N

2p

XK

k¼1

Z fex

fst

Ks pL2w

4vcT01P

e jðc; kdzÞsinðk�r ðkdzÞÞ dc

" #¼ N

2pKs pL2

w

4vcC

(28)

The generalized A0 and C0 matrices become constant and timeinvariant, but dependent only on the geometry of the tool and thekinematics (A, C) of each operation as in the case of general forcemodels. Although considering time varying, periodic coefficients inmulti-frequency [35,96] or semi-discrete [14,80] solutions leads tomore accurate stability solutions when the radial depth of cuts aresmall, they are computationally more costly to use in virtualmachining applications. By substituting Eq. (21) into Eq. (25), thestability of machining operations is reduced to the following,generalized eigenvalue problem:

I� ð1� e�ivcTÞA0 þ C0

h iFðvcÞdz

n oFeivct ffi0 (29)

which leads to the following characteristic equation:

det I� 1� e�ivcT�

A0 þ Ch i

FðvcÞdzn o

¼ 0: (30)

The chatter-free critical depth of cut and spindle speeds can bedirectly predicted in frequency domain for milling [3,6], turning[103] and drilling [110,120]; the form errors can be predicted andconstrained for process planning during NC tool path generation in

CAM systems [40,45,46]. However, since Eq. (30) is speed dependentdue to process damping, and the depth of cut is already assigned, thestability is solved using the Nyquist criterion [68,69]. For a specificspindle speed, the critical stable depth of cut is identified byincreasing the depth of cut ða ¼ K � dzÞ until the cutting systembecomes critically stable. If the depth of cut identified from thecutter–part engagement module of the virtual machining system isgreater than the predicted critical depth, a chatter alert is sent to theprocess planner at the analyzed tool path location [11].

The structural dynamics of the system may vary along the toolpath either due to the kinematic configuration of the machine tool,structural changes in the part or removal of the mass from the thinwalled parts. It is possible to attach specific FRFs at each tool locationalong the NC tool path in virtual environments [12,30], and to checkthe corresponding chatter stability. However, if the dynamicschange rapidly, the part machining needs to be simulated in timedomain, and the FRF of the structure must be updated as the chipsare removed from the part. Budak et al. [52] proposed an FRFupdating scheme based on a matrix inversion method [102]. The FRFof the final part shape after machining is predicted with the FEmethod and used as a core model. The mass [M], structural damping[H] and stiffness [K] matrices are identified a priori. Instead ofremoving machined elements from the part, un-machined elementswith their incremental mass [DM], damping [DH], and stiffness [DK]are added at each tool path location and the FRF is updated as:

g½ � ¼ ½½K� þ ½DK�� v2½½M� þ ½DM�� þ i½½H� þ ½DH�� 1

(31)

where [g] is the receptance matrix and v is the vibration frequencyin rad/s. The method was applied in virtual, five-axis ball-endmilling of turbine blades as shown Fig. 29.[(Fig._29)TD$FIG]

It is common to use multi-functional machines such as mill-turnsin industry. While the simulation of the process forces, power andtorque of such operations can be simply done by superposing processstates, their chatter stability inspection differs due to the couplingbetween them. A parallel turning system shown in Fig. 30 has thefollowing coupled dynamics [39,49]:[(Fig._30)TD$FIG]

z1ðtÞz2ðtÞ

� �¼ z1

z2

� �eivct;

F1ðtÞF2ðtÞ

� �¼ F1

F2

� �eivct (32)

[(Fig._33)TD$FIG]Y. Altintas et al. / CIRP Annals - Manufacturing Technology 63 (2014) 585–605596

The stability analysis leads to optimal metal removal conditionswithout violating the chatter limits of both tools used in theoperation, see Fig. 31. Since multi-functional machines are morewidely used, the chatter stability of combined turning, milling,drilling and grinding operations must be further developed todetect the abnormalities along the tool path in the virtualmachining environment.[(Fig._31)TD$FIG]

Fig. 31. Stability diagram for a parallel turning operation with two tools.

Experimental results are shown by markers [39].

Fig. 33. Flow chart of the optimization procedure [UBC MAL].
5. Virtual optimization of machining operations
Machining parameters such as speeds, feedrates and depthsof cut need to be selected properly in order to improve theprocess efficiency and quality of the finished product. Anoptimization strategy is proposed to determine the mostefficient machining parameters based on the process physics[99]. The machining constraints include the cutting forces, chipthickness, spindle torque-power, form errors on the workpieceand system stability. The objective of the optimization is tomaximize the Material Removal Rate (MRR), which is defined as[97]:

MRR ¼ a B c n N (33)

where a is the axial depth of cut, B is the radial width of cut, c is thefeed per tooth, n is the spindle speed, and N is the number of fluteson the milling cutter, as depicted in Fig. 32.
[(Fig._32)TD$FIG]
Fig. 32. Milling process with design variables [99].

The optimization strategy is divided into a pre-process andpost-process optimization as illustrated in Fig. 33.

5.1. Pre-process optimization

Pre-process optimization provides an upper bound of thecutting parameters to obtain an efficient machining operationduring the process planning stage. Since the cutter is chosen beforeselecting the cutting conditions and generating the tool path, thenumber of teeth of the tool (N) is known prior to the optimization.The spindle speed (n) is selected based on tool life and chatter

stability. Therefore, the objective function of the pre-processoptimization reduces to [99]:

f ob j ¼ a B c: (34)

5.1.1. Chatter stability constraint

Selection of the depth of cut, width of cut and spindle speedshould lead to stable cutting conditions, which is determined bythe stability lobe. Fig. 34(a) shows the stability lobe with a constantwidth of cut (B), and Fig. 34(b) shows the stability lobe with aconstant depth of cut (a) when the width of cut is normalized withrespect to the tool diameter. By locating the optimum spindlespeed from these two figures, the design space shown as Fig. 34(c)is formed by extracting a maximum stable depth and width of cutat a constant spindle speed [98].

Stability limits increase drastically with the effect of processdamping at low cutting speeds [8]. Although its accuratemathematical modeling is still an ongoing research topic, thecutting edge geometry, flank wear, work material’s contactresistance, vibration frequency and cutting speed highly affectthe stability with process damping [138] as shown in Fig. 35 [124].The inclusion of process damping in selecting a chatter-free,optimal depth of cut is therefore crucial in machining thermalresistant alloys in the aerospace industry.

5.1.2. Machine tool torque/power constraint

In order to avoid spindle stall, the torque/power limit of themachine tool should not be exceeded. Both torque and power aredependent on tangential cutting force Ft (w) as [97]:

Torque ðfÞ ¼ Ftð’ÞD

2Nm

Power ð’Þ ¼ Ftð’ÞDpn

60

�1:34102� 10�3 hp

8>><

>>:(35)

where D is in (m), n is in (rev/min), and Ft is in (N). An analyticalsolution of the tangential force for a cylindrical end mill is derivedas a function of an angular position w [99].

The critical angular positions ’tmin and ’t

max corresponding toglobal minimum and maximum tangential forces are obtained. Inorder to prevent the violation of torque/power constraints, the

[(Fig._34)TD$FIG]

Fig. 34. Chatter stability lobes for constant axial depth of cut, constant radial depth

of cut and constant speed [99].

[(Fig._35)TD$FIG]

Fig. 35. Effect of cutting parameters on process damping and stability in turning (MRL).


cumulative average torque and power, which are defined as:

qcav ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiqð’t

minÞ2 þ qð’t

maxÞ2

2

" #vuut

q ¼ fTorque; Powerg

: (36)

must not exceed the machine tool torque/power limitations of themachine tool at spindle speed n:

Torquecav TmoðnÞ; Powercav PmoðnÞ (37)

where Tmo and Pmo are machine tool torque and power curvesprovided by a manufacturer as shown in Fig. 36.[(Fig._36)TD$FIG]

Fig. 36. Torque-power characteristics of a machine tool [99].

5.1.3. Chip thinning constraint

When the width of cut is smaller than the radius of the tool (i.e.b < 0.5), the maximum chip thickness does not reach thecommanded feed per tooth. A very small chip thickness leads toa low material removal rate and to ploughing of the cutting edge onthe workpiece instead of cutting. The chip limit must bemaintained by manipulating the feed rate as the width of cutvaries. The feedrate cmax, which generates the desired maximumchip load hmax, is calculated as:

cmax ¼hmax

2ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffibð1� bÞ

p i f 0< b 0:5

hmax otherwise

8<

:

9=

;: (38)

The constraints are identified ahead of optimizing the NCprograms as the tool traverses along the tool path.

5.2. Post-process optimization

Once the NC program is generated, the width and depth of cut,i.e., the NC tool path, are defined. However, since the part geometryvaries along the tool path, the desired depth of cut and width of cutcannot be maintained, which leads to a variation in the cuttingprocess. The cutter–part engagement boundaries along the toolpath are identified at desired displacements along the tool path,and the feed and speed are optimized by respecting the physicalconstraints of the process as outlined in the previous section. Theconstraints include the maximum chip load, the resultant force onthe tool, form errors left on the part, and the torque/powercharacteristics of the machine tool.

5.2.1. Feedrate optimization

The majority of the process output is linearly dependent on thefeedrate in the following form, provided that the cutting forcecoefficients are independent of the feedrate:

Fqð’Þ ¼ Aq0ð’Þ þ Aq

1ð’Þcðq x; y; z; t; r; trq; pwrÞ (39)


where subscripts x, y, z, t, r are the cutting forces in the feed,perpendicular to feed, axial, tangential, and radial directions; andtrq, pwr are the spindle torque and power, respectively. Bynumerically solving the angular position ’q

max at which the processoutput becomes the maximum defined as Fq,max, the maximumallowable feedrate is solved as:

cqmax ¼

Fq;max � Aq0ð’

qmaxÞ

Aq1ð’

qmaxÞ

: (40)

The maximum resultant force in the xy plane is a quadraticfunction of the federate [99], shown as:

Fresð’Þ ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiAres

0 ð’Þ þ Ares1 ð’Þc þ Ares

2 ð’Þc2q

: (41)

The maximum feedrate is obtained by solving the root ofEq. (41) when the resultant force is equal to the user-definedmaximum Fres,max.

Considering the form errors in milling, the maximum allowablefeedrate for a user-defined deflection constraint dd fl

max is solved as:

cd flmax ¼ c1 þ ðc2 � c1Þ

dmax � d1

d2 � d1(42)

where c1, c2 are two arbitrary feed rates, and d1, d2 are thecorresponding calculated deflections.

5.2.2. Feedrate and spindle speed optimization

The optimization of spindle speed is based on the constraints ofthe torque-power characteristics of the machine and the stabilitylimit. For a fixed depth of cut, the feasible spindle speed is in therange that results in a stable cutting condition as:

n nmax;i

� �; ð�n �nmin;iÞ (43)

where nmin,i and nmax,i are the lower and upper spindle speedsunder a critically stable condition for the ith lobe. The graphicalrepresentation of the design space considering the nonlineartorque and power constrains is shown in Fig. 37. The spindle speedand feedrate corresponding to the optimum solution (maximumMRR) are obtained at the limits of the constraints, which is markedwith a star in the Fig. 37.[(Fig._37)TD$FIG]

Fig. 38. Simulated and machined free-form surface and optimized tool path in 3D.

Fig. 37. Graphical representation of design space [98].

[(Fig._39)TD$FIG]

Fig. 39. Stability of finishing and multi-level finishing.

5.2.3. CL file updating

The original cutter location (CL) file is used to obtain the cutter–workpiece engagement along the tool path, then the feedrate andspindle speed are adjusted based on the user-defined constraints.The optimization process might generate highly fluctuating feed

rates due to the continuously varying workpiece geometry, andresult in the saturation of axis motors and undesired feed marks onthe finished surface; therefore, optimized feed rates are filtered byconsidering the trajectory generation parameters of the CNCsystem as described in the machine dynamics section. It isparticularly important to achieve smooth feed changes to avoidmarks on the finish surface without violating the jerk andacceleration limits of the drives [67,111].

5.2.4. Tool path optimization

Tool path selection is one of the critical parameters in planningmachining processes. In the commercial CAM packages, tool pathsare selected from standard path libraries by considering only thegeometry of the part. New approaches are needed to generateoptimized tool-paths for complex free-form surfaces. In recentstudies [90,94], the physical relationship between the meanresultant forces, cycle times and scallop heights were introduced.Since the three critical process outputs conflict with each other, theoptimal path strategy was identified by using the objectiveweighting algorithm. Moreover, the method allows for observationof the trade-off between each criterion, and determination of thecorresponding toolpath for each solution. A sample three-dimensional free-form surface generated with the optimized toolpath strategy is shown in Fig. 38.[(Fig._38)TD$FIG]

The cycle times can be considerably long in the finishmachining of highly flexible gas turbine blades [47]. The structuraldynamics of the blade varies both, in the axial and along the toolpath as shown in Fig. 39. The blade is far more flexible than thetool, and it becomes more rigid as the tool moves from the tip to the

[(Fig._41)TD$FIG]Y. Altintas et al. / CIRP Annals - Manufacturing Technology 63 (2014) 585–605 599

hub of the blade. As a result, the stability limits and naturalfrequencies vary along the blade surface as the cutting toolremoves the material [52]. A multi-level cutting strategy for bladefinishing is found to be more feasible in a virtual machiningenvironment, as opposed to the commonly used constant cuttingdepth strategy (see Fig. 39). The blade surface is divided into foursegments along the axial direction. For each segment the spindlespeed and cutting depth are selected according to the largeststability pocket of the corresponding segment. By changing thecutting depth in the multi-level finishing strategy, the cycle time isdecreased from 35 minutes to 19 minutes while still respecting thepart quality requirements.

6. Virtual part machining examples

Typical virtual machining software is shown in Fig. 40. Thesystem reads the standard CL file from a CAM system, parses the NCprogram and separates the operations by identifying tool changecommands, and either simulates or optimizes the process bypredicting/optimizing the maximum forces, torque, power, formerrors and chip loads along the tool path. The system automaticallybreaks large tool paths into smaller segments by respecting theCNC’s trajectory generation profile and gives a new CL file withoptimized feed commands. The original NC tool path geometry isunchanged. There are few commercially available virtual machin-ing systems, and they all operate in a similar fashion except thattheir process models and optimization strategies may differ. Theprediction accuracy of virtual machining systems is most affectedby the cutting force coefficients, the mathematical model of thephysical processes and cutter–workpiece engagement conditions[50]. Any error in these three modules will reflect directly on theaccuracy of the virtual prediction and optimization of NCprograms. The cutting force coefficients can be mechanisticallycalibrated for each cutter–work material couple to minimize theireffect on the prediction accuracy for the mass production of parts,but generalized orthogonal-to-oblique cutting transformationmethods would be less costly for small batch production [2]. Itis ideal to digitize the cutter–part engagement conditions at feedrate increments so that any small change in part geometry can bedetected along the tool path. However, a densely digitized toolpath may unnecessarily increase the computation time and makethe virtual machining system unfeasible to use in production.[(Fig._40)TD$FIG]

Fig. 40. A sample view of a virtual machining system.

(Courtesy of Sandvik Coromant and MAL Inc.).

Fig. 41. Virtual machining of a stamping die, predicted maximum cutting forces

with MACHPROTM and measured forces along the tool path

(Courtesy of Sandvik Coromant and MAL Inc.).

6.1. Metal cutting applications

A sample three-axis milling of a stamping die with circularinserts is shown in Fig. 41. The accuracy of the simulation systemwas verified by comparing the predicted and measured maximumcutting forces along the tool path. The process had an experience of

severe chip thinning at sharp curvatures, which was eliminatedwhile decreasing the machining time by 25% with the feedregulation. Virtual machining is most crucial in manufacturingvery costly aerospace parts, since their trial- and error-basedoptimization may be cost prohibitive. A sample optimization of ajet engine impeller is shown before and after virtual machining inFig. 42. The cutter was a taper helical ball end mill, whose pitchangles are designed to maximize the chatter-free depth of cuts atthe desired cutting speeds [18,43,44]. The virtual processoptimization parameters included maximum stress at the toolshank to avoid tool failure, chip load and torque limit on thespindle and feed drives [47,70,71].

Virtual machining with process forces and deflections can becomplemented with visualization by updating the part geometryusing solid modeling methods. The result of simulating theperipheral milling of a turbine blade with modeled workpiece andtool vibrations is shown in Fig. 43a. Both spherical end mill andworkpiece geometries were modeled by CSG where the workpieceand tool deflections were applied by altering the CSG model of thetool for each tooth feed. This allows the visualization of thevibration marks on the finish surface by rendering with ray-tracing

[(Fig._43)TD$FIG]

Fig. 43. Simulated surface structures. (a) Simulation of the machining of a turbine

blade taking workpiece vibrations into account [29]. (b) Simulation surface location

errors, (c) simulation of structures generated during face milling [32].

[(Fig._44)TD$FIG]

Fig. 44. Toolpath and the broken tool (MRL).

[(Fig._42)TD$FIG]

Fig. 42. Five axis flank milling of a jet engine impeller before and after optimizing

with virtual machining system. The cycle time is reduced by 62% and the surface

finish is improved by 8.4 fold.

(Courtesy of Pratt & Whitney Canada).

[(Fig._45)TD$FIG]

Fig. 45. Roughing toolpath and kinematic profiles for a sample pass, resultant

cutting forces and cycle time comparison [67].


techniques (Fig. 43b) [29,118]. For the modeling of the surfacesgenerated during face milling, another modeling technique has tobe applied. Since the tool is constantly engaged with theworkpiece, an altered CSG model for each tooth feed is notsufficient. For the simulation of this process, the geometry of thecutting edge can be approximated by an open traverse line, whosepoints are adjusted corresponding to the tool deflections. Byconnecting the lines from subsequent time steps, a triangulatedsweep surface is obtained, which can be projected directly onto aheight field in order to visualize the surface structure (Fig. 43c).Another approach allows the direct modeling and visualization ofthe surface location error without the need for ray-tracing ortriangulation techniques. It is based on the combination of the CSGtechnique for the determination of the process forces and thedynamic behavior, and a dexel-based workpiece model for thevisualization of surface location errors. Each time a dexel is cut, theintersection points can be displaced by the projected vibrationamplitude. This applied displacement also corresponds directly tothe surface location error (Fig. 43b). The combination of the twodifferent workpiece models also permits the identification ofconstant engagement situations for the optimization techniquedescribed in Section 3.4. Alternatively, it is possible to estimate theerrors left on the finish surface by correlating the measured forcesand stiffness of the system in a virtual environment as well [54].

A problematic tool path for roughing of an integrally bladedrotor, which leads to frequent breakage of a serrated tool at its ballend, is shown in Fig. 44. The multi-axis virtual machining software

indicated that the axial cutting force increased from 150 N to 450 Nas seen in Fig. 44, where the tool was digging into the material dueto a negative effective lead angle [58]. The problem was solved byre-orienting the tool axis vector that minimized the indentation ofthe tool into the material [126,127]. The effect of tool orientation,i.e. lead and tilt angles, on the process mechanics is quite important


as presented by Ozturk et al. [106] who reported that the lead angleof about +10 degrees would be most suitable as demonstrated inthis application.

Once the optimal feed is identified from the process, a furtherreduction in machining time can be achieved by optimizing thetrajectory profiles in three- to five-axis machining of free-formsurfaces. The CNC systems may not be able to achieve thecommanded feeds when the paths have sharp curvatures,demanding high torque and acceleration from feed drives. It ispossible to reduce the machining cycle time by re-shaping thetrajectory commands along the curved paths without violating thefeed drive limits and process-imposed federate along the tool path.Erkorkmaz et al. [67] and Sencer et al. [111] demonstrated that upto a 65% reduction can be achieved in the machining of free-formparts via trajectory optimization. The tool path for a free-formsurface shown in Fig. 45 was generated with 0.04 mm tolerance,leading to 11,186 CL points for the complete operation. Processingby the solid modeler, applying the B-rep method, took 482 s andconsumed 1.2 GB of memory. In feed planning, the resultant forcelimit was set to 250 N. A Mori Seiki NMV 5000DCG machiningcenter was used in the cutting tests. The drives’ velocity,acceleration and jerk limits were identified by inspecting thecorresponding registers in the CNC. The process was firstoptimized by varying the feed while keeping the cutting force at250 N [62]. At the second step, the feed was optimized again byrespecting the acceleration and jerk limits of the drives, which ledto a further 17% reduction in machining time [67].

6.2. Grinding applications

When grinding complex parts such as airfoils and bladeretention slots as shown in Fig. 46, the complex wheel/workpiecegeometry and multi-axis motion result in variable wheel–workpiece contact. All grinding process parameters such as depthof cut, wheelspeed, workspeed, forces and temperature will varyalong the wheel axis and grinding path. Optimizing such grinding[(Fig._46)TD$FIG]

Fig. 46. Grinding of jet engine impellers with tapered ball ended tools (a) and form

grinding (b) of turbine blade retention slots.

(Courtesy of United Technologies Research Center).

processes requires detailed knowledge about the distributions ofthese process parameters. A virtual environment is developed tosimulate and optimize five-axis grinding with complex wheel andwork geometries [75]. Boolean intersection algorithms are used todetermine the shape and geometrical characteristics of the wheel–workpiece contacts at any instant. The contact geometry is thenanalyzed as a stack of discrete sub-wheels for which the physicalprocess parameters such as forces, power and temperature arepredicted using the contact data. Grinding examples show that thegrinding process parameters vary significantly along the wheelaxis at any instant and along the grinding path. The grindingprocess is far from optimal if a constant workspeed is used. Multi-constraint optimization is then applied to optimize the workspeedto reduce cycle time while maintaining grinding forces, power andtemperature below the specified limits as shown in Fig. 46. Theoptimization leads to about a 40% cycle time reduction, while themaximum power is reduced by >30% and the maximum forcereduced by about 35% [75].

A good example of a virtual grinding application is themanufacturing of tungsten carbide end mills. Due to the hardnessof tungsten carbide, cutting tools are manufactured using deepgrinding processes with diamond or CBN-grains. Because of thelarge grinding forces, the flexible end mill which has varyingstiffness along its axis, experiences static deflections and vibra-tions. The deflections lead to geometrical errors and poor cuttingedge grinding quality which need to be optimized through virtualsimulations. The virtual model considers the kinematics of the 8-axis tool grinding machine, the discrete removal of material andthe tool-grinding wheel engagement zone, which are used topredict the grinding process [53] (Fig. 47).[(Fig._47)TD$FIG]

Fig. 47. Calculated material removal rate Qwa(i) (mm3/s) and (b) calculated

equivalent chip thickness heq (mm) for a tool grinding process (vft = 30 mm/min,

d = 10 mm, R = 62.0 mm) [53].

The workpiece discretization is based on dexel grids in all threecoordinate directions. The cylindrical grinding wheel is approxi-mated by a non-rotating polyhedron which is reduced to a piesegment. During each simulation step, the grinding wheel movesin a step-wise linear motion, and the intersection of the sweepvolume and workpiece is calculated to estimate grinding forces. Tomap values to different areas, the grinding tool is divided into slicesalong the tool axis. By dividing the removed volume of each dexel


at discrete simulation time steps and mapping it to thecorresponding slice, the distribution of the material removal rateQwa (Fig. 47a) and equivalent chip thickness heq (Fig. 47b) can bedetermined for each element. A constant cutting speed is assumed,which is reasonable due to the cylindrical shape of the grindingwheel.

To parameterize an empirical grinding force model, flatgrinding experiments using a cylindrical grinding wheel and arectangular workpiece have been carried out on a WalterHelitronic Power tool grinding machine. The resulting forces fordifferent depths of cut have to be related to geometric parameters,which can both be evaluated in the 3D dexel simulation. The factorheq/dlg relates the equivalent chip thickness heq to the local contactlength dlg for each segment of the contact area. This dimensionlessvalue replaces the factors for feed speed, cutting speed andgrinding wheel diameter, which are commonly used in grindingforce models [121].

The grinding forces are applied on the position-dependentstructural model of the ground end mill at each simulation step.Since a deflection directly affects the contact conditions andtherefore the acting grinding forces, the coupled process–structureinteraction is handled with an iterative model. The algorithmdetermines the deformation of the workpiece and machinestructure during grinding at a static equilibrium of the grindingforce, and the spring-back force of the workpiece until thedeformations calculated in the previous and current stepsconverge within a defined tolerance. Subsequently, the materialis removed, the current shape is defined and the calculation step isrepeated. Once the deflections are predicted by the virtual grindingmodel, the original tool path is modified to compensate them. Theiterative simulation process is repeated until the predictedworkpiece geometry and the ground end mill match with thedesired geometry within its specified tolerance as shown in Fig. 48.The deflections of the ground end mill are reduced from 163 mm to35 mm as shown in [53,55].[(Fig._48)TD$FIG]

Fig. 48. Comparison of resulting workpiece cross-sections with uncompensated NC-

program (left) and compensated tool path (right) [53].

For optimizing the grinding of wear-resistant coated free-formed surfaces on machining centers using abrasive mountedpoints, a simulation system based on multi-dexel boards and CSG-techniques is used [113]. Due to the inhomogeneus thickness of thethermally sprayed coating and the varying contact areas betweenthe grinding tool and the free-formed workpiece surface (Fig. 49),the grinding forces vary along the NC path. These variations can[(Fig._49)TD$FIG]

Fig. 49. Process simulation of grinding of wear-resistant coated free-formed

surfaces on machining centers using abrasive mounted points (ISF).

lead to shape and dimensional errors as well as surface defects. Inorder to counteract these effects, the NC path can be adjustedbased on the simulation results. The process force model uses theengagements of the individual grains, as described in Section 3.5. Inaddition to the calculated forces, the generated surface roughnesscan be approximated within the simulation system.

7. Uncertainties in virtual machining

Virtual machining is based on the mathematical modeling ofpart-tool engagement geometry, machining process physics,structural and rigid body kinematic motion of the machine andwork material properties. The accuracy of the prediction will bedependent not only on how well the mathematical modelsapproximate the complex machining process physics, but alsoon how accurately the input parameters are entered to the virtualmachining system. The accuracy of mathematical models havebeen well reported in previous dedicated metal cutting [2,20],grinding [79,121], chatter stability [16] and virtual machine tool[5] key note articles. The effects of uncertainties in the key inputparameters are summarized as follows.

7.1.1. Geometric variations

Assuming that the part is accurately placed on the fixture andmachine, the key source of uncertainties originate from casting,forging and semi-finish tolerances. The unexpected extra stock lefton the part results in an under-prediction with the sameproportion, i.e. 5% extra stock leads to 5% less magnitudes inpredicted force, power and torque. The mesh size in the cutter–workpiece engagement affects the prediction results similar to theforging errors.

7.1.2. Cutting process models

The key uncertainties originate from the cutting forcecoefficients, which depend on the tool geometry (rake angle, helixangle, nose radius, cutting edge radius and inclination angle), andmaterial properties such as temperature-dependent hardness andflow stress, tool wear and lubrication (i.e. Coulomb friction). Errorsin the cutting force coefficient affect the cutting forces, torque andpower in the same proportion. Changes in the material’s yieldshear stress directly and linearly affect the cutting force coefficient.For example, if the tangential cutting force coefficient for AISI steelis 1500 MPa with �10% uncertainty, the prediction of cutting forces,torque and power will also have the same uncertainty (�10%). Theeffect of uncertainties in tool geometry varies. While the effect of rakeand helix angles is about 2% per degree, the cutting edge radius andgrain size of the grinding wheel have a major effect, especially infinish machining where the chip loads can have the same magnitude.It is recommended that the cutting force coefficients are calibratedagainst the edge radius, grain size and lubricant for each material asexplained in [121,139].

7.1.3. Machine dynamic models

The forced and chatter vibrations between the tool center pointand workpiece depend on the relative dynamic stiffness betweenthe two and the process forces. The chatter stability is linearlyproportional to the dynamic stiffness (2k ). If the measurement ofthe dynamic stiffness has an error of +10%, the chatter-free depth ofcut will be underestimated by �10%. If the natural frequencies ofthe machine tool structure varies along the tool path due tokinematic and cross coupling effects [33], the stability pockets willalso shift. One Hz error in the natural frequency measurement willresult in a chatter-free spindle speed shift of 60 rev/min/N where N

is the number of teeth on the tool. Often, the structural dynamics ofthin-walled parts change significantly during machining, whichneed to be carefully mapped to the tool path as discussed in thedynamic section.


7.1.4. CNC models

The positioning errors of CNC models have a negligibly smalleffect on process simulation in virtual machining. However, thechip loads in cutting and grinding are direct functions of feedsalong the tool path. If the tool path is curved, especially in three-and five-axis machining of free-form surfaces, the feed changescontinuously as a function of path curvature, acceleration and jerksettings of the CNC (i.e. trajectory generation). Although thetrajectory generation settings of the CNC are considered in virtualmachining [11,67,99], any uncertainty in the acceleration and jerkhave a third and second order polynomial relationship with thefeed, hence the forces as explained in the paper. Typically, 10–15%errors may originate from the approximated trajectory models ofthe CNC systems in virtual machining of free-form surfaces.

8. Conclusion

The modeling of machining operations has been evolving as animportant engineering tool to simulate operation physics ahead ofcostly production trials of parts used in industry.

Virtual machining technology has three important componentswhich affect the accuracy of prediction, computational speed andvisualization of the operation by the process planners.

The first step is the evaluation of cutter–workpiece engagementconditions along the tool path. The tool and workpiece geometriesare extracted from the CAM systems, and various solid modelingmethods have been developed with varying computationalefficiency, accuracy and visualization. The accuracy of virtualmachining is directly related to the identification of the cutter–workpiece engagement conditions. Accurate engagement predic-tions lead to impractically long simulation times for industry, andrough engagement predictions lead to inaccuracies in processsimulations. Further research is needed to improve both theaccuracy and computational efficiency of cutter–workpieceengagement conditions.

The mathematical models of metal cutting and grindingprocesses must be well developed with computational efficiencyand accurate physics. There have been major advances inpredicting the micro-mechanics of cutting (i.e. stress, temperature,white layer characteristics of the finish surface, thermo-mechani-cal behavior of the material) as well as the macro-mechanics ofcutting (i.e. forces, torque, power, vibrations, part deformationerrors). While the micro-mechanics models are used to design theprocess and to analyze the operation at specific part locations, themacro-mechanics are used to optimize the general machiningoperation in CAM environments. There are still challenges inachieving computationally efficient but accurate modeling ofcutting forces, structural deformations and chatter stability whencomplex cutting tools are used in NC programs.

The third component of the virtual machining system is tomodel the rigid body kinematic motion of the machine and itsposition-dependent structural dynamics. The tangential feedvelocity between the workpiece and tool varies as a function ofthe machine’s kinematic and CNC configuration, which has to beincluded in predicting the chip loads along the tool path. Thestructural dynamics of both the machine and workpiece may alsochange along the tool path, and they need to be incorporated intothe virtual machining system in order to predict deflections andvibration marks imprinted on the finish surface of the part.Furthermore, machine tools have volumetric errors which arereflected on the part. The volumetric errors of the machine toolmust be integrated into virtual machining systems to predict thesemetrology errors.

Although a significant amount of research still must beconducted to achieve highly efficient and accurate virtualmachining systems, the current know-how is already useful inminimizing scrap rates and maximizing production efficiency inindustry.

Acknowledgement

The following co-workers have assisted in preparing themanuscript: Murat Kilic, Dr. Xioliang Jin and Dr. Doruk Merdol(MAL, University of British Columbia), Dr. Volker Boß (IFW, LeibnizUniversitat Hannover), Dr. Taner Tunc (MRL, Sabanci University),Dr. G. Guo (United Technologies Research Center), MikaelLundblad (Sandvik Coromant Engineering Center).

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09-1256_Virtual Process Systems for Part Machining Operations

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