Cutting force integration at the CAM stage in the high-speed milling of ...

International Journal of Computer Integrated Manufacturing, Vol. 18, No. 7, October – November 2005, 586 – 600

Cutting force integration at the CAM stage in the high-speed milling of complex surfaces A. LAMIKIZ*, L. N. LO´PEZ DE LACALLE, J. A. SAŃCHEZ and M. A. SALGADO Department of Mechanical Engineering, University of the Basque Country, ETSII, c/Alameda de Urquijo s/n, 48013 Bilbao, Spain High-speed milling (HSM) technology has been rapidly absorbed by the die and mould manufacturing industry and by the aeronautical sector. The new cutting tools can withstand much higher machining conditions than 10 years ago. Last-generation, highspeed machining centres are equipped with high-frequency spindles with hybrid ball bearings, leading to rotational speeds over 18 000 r/min. Multiaxis machining can be effectively carried out in five-axis machining centres of different architecture. These new and advanced machining processes are much more complex and provide the final component with a higher added value. However, the reliability of the whole process must be reconsidered, since collisions, tool breakage and dynamic problems can result in expensive machine repairs and some parts may be impossible to recover. In order both to minimize the above problems and increase machining performance, a new machining approach based on two ideas has been developed. First, virtual verification of the NC programs, avoiding collisions or tool – machine interferences that may arise during the machining of complex surfaces. Second, toolpath optimization in the machining of complex surfaces. For this purpose a utility to estimate the cutting forces before machining has been integrated in the computer-aided manufacturing (CAM) planning process stage. The estimation of cutting force uses a semi-empirical approach, in which the pair tool/ material is characterized by six specific cutting force coefficients. The force model introduces the effect of part slope in calculations, just with tool geometry, cutting conditions, and material. The value of cutting force is used as an estimator for selecting the best cutting toolpaths for a complex surface. In this way a more accurate, betterfinished surface is machined, and a reduced tool wear is withstood. The global CAM process is applied to three examples that are discussed. They are representative of a highly efficient high-speed process, without any risks of tool collisions, surface machined errors and low cutting forces. Keywords: High-speed machining; Complex surfaces; Process integration; Intelligent CAM

*Corresponding author. Email: [email protected] International Journal of Computer Integrated Manufacturing ISSN 0951-192X print/ISSN 1362-3052 online ª 2005 Taylor & Francis http://www.tandf.co.uk/journals DOI: 10.1080/09511920500069309

High-speed milling of complex surfaces

Notation ac ap CAM c

EDM F Ft, Fa, Fr

fz i0 HRC HSM Krc, Ktc, Kec, Kre, Kte, Kae N P, ae Ra Vc y k

c

f

chip thickness axial depth of cut computer-aided manufacturing cusp height, similar to the maximum theoretical roughness Rth electrodischarge machining machine tool linear feed components of cutting force in the tool tangential, axial and radial directions feed per tooth nominal helix angle Rockwell C hardness high-speed milling specific cutting force coefficients rotary speed of the spindle transversal step over or radial depth of cut mean roughness cutting speed spindle rotation angle positioning angle of the main cutting edge of each cutting edge element positioning angle of each cutting edge element of the j flute angle gap between the i cutting edge element and the tool point

processing. The CNC programs for the complex parts are made with special-purpose computer-aided manufacturing (CAM) software (Hock and Jajenski 1996), with new features and functions. Hence HSM is currently a technology in full industrial use, and research is being carried out into certain problems especially relative to the machining in different industrial sectors, such as mould construction and aeronautical parts. Moulds are made in hardened steels (more than 40 Rockwell C hardness (HRC)) and present very complex sculptured surfaces. Tool wear and lack of part accuracy are common problems. European, Japanese and American mould makers see this technology as one of their main interests. Of those polled, 25 % of ascribe great importance to it (Thonsoff 1998), while 35% attach great importance to CAM, which is highly related to HSM. Bagard (1997) asserted that the use of HSM can result in savings in time and cost of at least 20%, on occasion even 50%, depending on the type and size of the mould to be manufactured. Companies like Boeing had made commercial studies in which they previewed a future manufacturing of 13 000 new aircrafts over the next twenty years (Makino Inc. 2000). Other firms with large quantities of orders, i.e. Airbus in Europe developing the new Airbus 380 also back these perspectives. In many modern aircraft, the skin and parts of the framework are made from a single piece of material, a so-called ‘monolithic part’. Today’s alternative to produce these monolithic structures is the HSM technology, which provides a high productivity. One example is the production of the F-16, where some parts which were machined at 3000 r/min, are now being machined at 15 000 r/min, reducing the time of milling, as a consequence of a dramatic increase in removal rate (Makino Inc. 2000). Today’s research efforts are focused on proposing a more reliable manufacturing process. There are various consequences of a higher reliability: 1.

1. Introduction The technology of high-speed milling (HSM) had its highest rate of growth during the second half of the 1990s. An important part of this success has been based on the development of new tool materials (Dewes and Aspinwall 1997) that can withstand very high cutting speeds. This brings the necessity of developing new highspeed spindles, with rotational speeds up to 25 000 r/min. The high engine speed resulted in faster machine feeds. When applied in complex paths these feeds need accurate and rapid computer numerical controls (CNC). The continuous path changes imply high acceleration of machine axis and, therefore, a good structural analysis of machines. These new machines, named ‘high-speed machining centres’ led to new possibilities in material

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2.

3.

There will be a reduction in the number of machine breakdowns and of unrecoverable workpieces. A new generation of new hard tools made of ceramics, or synthetic materials such as polycrystalline cubicboron nitride (PCBN) or P polycrystalline diamond (PCD) can be used to machine difficultto-cut materials for a greater number of hours. However, todatetheyhaveonlybeenusedoccasionally because of their low toughness, breaking when sudden changes occur in the chip section, as may happen with programs that have not been previously checked. The high-speed spindles, the weakest component of the machining centres because of their ceramic ball hybrid bearings (with steel races), are protected against breakdowns. In some companies such as Boeing (Seattle), more than six spindles are changed every year because of bearing failures.

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The modelling of cutting processes can help in different points such as tool design, machine-tool design, machine drives selection, etc. Planning of machining operations can also benefit from modelling. Quite a lot of research work has been done on this subject (Van Luttervelt et al. 1998) and the ‘STC-C Committee’ of the CIRP (Centre International for Production Research) has a group dealing with modelling. If cutting forces are to be predicted, empirical models are the useful approach. For their application, empirical coefficients must be experimentally obtained, and they depend upon material properties, friction, tool geometry and material. This kind of model directly relates cutting parameters to cutting forces. Since the geometry of the tool edge is complex, it is normally considered as a finite number of discrete simple elements. The empirical model is applied to each of these elements, and then integration along the edge is carried out to obtain the resulting cutting force (Altintas and Lee 1996, Feng and Menq 1994). Meng and Menq (1997) propose a new approach for the milling of sculptured surfaces based on the use of cutting force calculation in user-selected control points. In the present paper an integrated approach to the HSM process, aiming to maximize process reliability and to reduce production lead times, is introduced. The CAM stage integrates a cutting force estimator utility with the best selection of toolpath programming for complex

surfaces. A stability analysis utility for rough and thin-wall machining is also proposed. The integrated approach is applied to three examples: a forging die five-axis machine, a five-axis aluminium injection mould and a stamping die testpart. 2. The integrated planning process for HSM Figure 1 presents the global complex parts machining process, in which CAM and related steps are included. These stages are explained below. 2.1. Part design As a result of the part design, a computer aided design (CAD) model is made with all the geometry features of the complex part. The quality of this CAD model is of primary importance (Diehl 1996); problems at the joint of surfaces and defects of trimming must be avoided. The joint between surfaces must always be tangential. The presence of gaps or misalignments between surfaces may lead to the generation of machining marks on the work surface. The advantages produced by the use of solid modelling instead of surfaces must be considered. Thus, a part modelled as a solid closes a certain volume, so that the zones in which material may be present can be easily defined. On the other hand, a fillet radius can be easily introduced.

Figure 1. Process stages in the HSM of complex surfaces and parts.

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The main drawback is related to the problems when dealing with very complex surfaces, such as sculptured surfaces. This is the reason why most companies working in the mould and die industry commonly use surface modelling, which allows the user to have a higher control over the geometry. It should be taken into account that the systems based on solid modelling can also use surface representation if the user so requires, offering both types of modelling. Once part geometry has been defined, this is directly introduced in the CAM, if it is the same commercial CAD/ CAM package. If this is not the case, standard interchange files must be used (IGES, VDA, STEP, STL, etc.). The use of standard files results in problems in the definition of the geometry in many cases, and a thorough study of the CAD model is absolutely necessary. 2.2. CAM process There are three stages in the generation of CAM cutting paths, according to the type of operation: (a) roughing, (b) semifinishing and (c) finishing. Roughing is of critical importance in HSM. The aim is to achieve not only productivity but also a highly uniform stock allowance, which will be removed in the course of finishing (Hock and Jajenski 1996). In roughing there are two possibilities, each very much related to the size and hardness of the workpiece: 1.

2.

If the material does not exceed 40 HRC and the pieces are large, then interchangeable round insert cutters can be used. The strategy most suitable and used is the Z-level, i.e. machining in planes parallel to the XY, at constant Z. Furthermore it is necessary to use such techniques as bitangencies and rest milling, which remove material from the concave edges of the workpiece, the aim being to avoid an uncontrolled increase in chip thickness in areas accessible to large tools. If the part material exceeds 50 HRC and the volume for removal is high, then the strategies followed should be of trochoidal type. In this case roughing is achieved via orbital finishing, with a deep axial cutting.

The object of finishing is to achieve a roughness and tolerance specified by the client for each surface. The traditional strategy is zig-zag, but in this case the main drawback is that it intercalates two different cutting types: downmilling (also called climb milling) and upmilling. A solution may be to cut in one direction (zig), either downmilling (the most commonly used) or upmilling, but not both. The high maximum rapid feed rates of some machines equipped with linear motors currently make this cutting method cost-effective in a few cases. However, the

best option is the use of milling strategies more closely suited to each part zone and its geometry, depending on factors such as control of the cusp and consequently the maximum roughness Rth, by varying the radial depth of the cut in accordance with the workpiece slope. The cusp height is geometrically established as P¼

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 8Rc 4c2 cosðaÞ

ð1Þ

where P is the step, c is the cusp height to be held constant and a is the slope angle of surface. At the definition of cutting parameters stage, two developed utilities, explained in section 2.2, are available to assist in the selection of its right values. These utilities are applied after the selection of the recommended cutting conditions given by toolmakers, directly obtained from links to the commercial applications and databases of this companies. 2.3. Virtual simulation A check stage is included for the NC programs, using an ad hoc software utility such as Vericutª, NC-Verifyª or NC-Simulª. Even commercially well-known CAM packages such as Unigraphicsª or Himillª are integrating the virtual machining module into new products. This software allows the user to perform a virtual simulation of the process previous to actual machining, in which different problems can be effectively detected. These problems include: 1. 2. 3.

collisions, machining outside of the machine work volume, problems owing to tool gauging into the workpiece.

A virtual environment is divided into three parts: 1. 2. 3.

the representation of the machine itself, including its kinematics and moving elements, the control of the machine (NC program, spindle rotation, etc.), virtual simulation including process data, tool holder, tool, workpiece and initial raw block.

An example is shown in figure 2, in this case the machining in five axes of a honeycomb. 2.4. Post-processor The post-processor translates the program to a specified machine and control. In three-axis machines, post-processing consists only of a translator from the standard APT (output of the CAM system) and the CNC language syntax.

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Figure 2. Five-axis HSM of an aeronautical complex part.

In the case of five-axis machines, however, the two angular axes may both be located in the spindle, both in the table or one in the spindle and the other in the table; this information must be taken into account by the postprocessor. This is the reason why the same program might be completely different under other circumstances, depending on the machine on which it will be executed. 2.5. Machining Each material and part has its own characteristics, but two main groups of HSM applications can be identified: hardened steels and structural aeronautical pieces. 2.5.1. Hardened steels. Before the advent of HSM (prior to 1997) the technology employed in the manufacture of moulds was a combination of conventional milling and electrodischarge machining (EDM). From 1997 to 1999 the procedure (marked as A in figure 1) was to carry out roughing and semifinishing with conventional machines. Subsequently heat treatment was applied, and then finishing was at high speed in the new high-speed machining centres. There were two reasons for such a sequence. First, roughing, which was subject to few precision requirements, was performed on a machine that cost one fifth of what a high-speed machine would cost; second, tool consumption was slight owing to the low hardness level of the material. Most of the spindles in high-speed machines were unable to deliver sufficient torque at less than 1500 r/min, and roughing was impossible. High-speed machining was performed only in the finishing of parts. In 2001 the improvements made to spindles and their control resulted in their having the capacity to deliver torque to low speeds. Roughing with high-speed machines

therefore became possible. The new procedure was to start with a block initially heat treated (marked as B in figure 1) and to carry out all operations in the same HSM machine. The major advantage of this simpler process was the short time to launch a mould, because only one set-up for all operations was required. The use of high-speed roughing currently depends on economic criteria and the evaluation of process times; both aspects are related to part size. 2.5.2. Structural aeronautical pieces. Monolithic aeronautical components are obtained by machining a homogeneous aluminium raw block (alloy 7075T6 or similar), removing as much as 95% of the initial material as chips. A high-strength and light component is thus produced. The design of monolithic components shows forms as stiffeners and pockets, as shown in figure 3. The objective of HSM application in this case is to maximize productivity, and this is achieved by machining near the borders of stability of the process (see section 2.1). 2.6. Part measurement and manual polishing Machined components must be measured in order to quantify their accuracy and surface finishing. The main goal of HSM, when applied to the finishing operations of moulds and dies, is the reduction of the maximum surface roughness down to 10 microns or even less (Schulz 1997; Fallbo¨hmer 1998), always taking into account that an agreement must be achieved between machining times (and, therefore, cost per hour of the machine) and the final surface finish of the component. Owing to the fact that the feed rate can be 5 to 10 times that of conventional machining, it becomes possible to increase the number of passes by the same factor. Consequently, the surface finish


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Figure 3. Two different designs of a structural part, showed at Ingersol Inc. booth, EMO Hannover, 2001.

is greatly improved, reducing manual polishing, which may account for up to 30% of the total time spent in the die manufacturing process and 10% in injection moulds. On the other hand, aeronautical components have less accuracy and roughness requirements than moulds. Surface polishing is never needed after HSM.

3. Process optimization 3.1. Stability analysis Milling can induce vibrations, resulting in machine tool excitation, or local dynamic phenomenon on the piece. In the case of self-excited vibration, it is the cutting process that generates the oscillations. The origin of these oscillations, called ‘chatter’, is the dynamic excitation produced by the periodic irregular surfaces of the piece generated by the precedent tooth (Scott Smith 1987). The subsequent behaviour of these oscillations depends on the whole system machine – tool – piece. Parameters involving that phenomenon are the static and dynamic rigidity of the system, and material mechanical properties. The stability of chatter vibrations is analysed using the so-called ‘lobe diagram’. Altintas (2000) obtains this diagram by means of an analytical method. Chatter can appear by other means (Altuzarra et al. 2002) because the piece is vibrating instead of the machine. In the case of low rigidity structures this is a usual problem, because the dynamic stiffness of the thin wall is lower than that of the machine. The relative movement between the wall and the tool, caused by the cutting force, produces auto-induced vibration. Whatever the case, the analysis of stability is a very important problem when rough machining aluminium and when finishing very thin walls. This must be taken into account when choosing the machining parameters, but the analysis is beyond the scope of this work. At present there are some commercial utilities based on estimation of

lobe diagrams through a modal analysis of machine – tool and tools, such us CUTPROª or MILLSIMª. A similar software has been developed using Matlab (Altuzarra 2002). 3.2. Cutting force estimation For the optimization of the ball-end HSM process of complex surfaces, a cutting force analysis utility has been developed. Sculptured surfaces are milled after a CAM toolpath optimization stage. The developed model is based on Altintas and Lee (2000), and it is explained in detail by Lamikiz et al. (2002). The cutting force is divided into two components. 1.

2.

The component from the shear force inherent to the chip formation mechanism: this component is assumed to be proportional to the chip thickness (ac). The component from the friction forces of tool and chip: this component is assumed to be proportional to the cutting edge length.

The resulting forces will be the addition of the two components. The contribution of each component is ruled by empirical coefficients, which depend on the workpiece material and the tool geometry. The three projections of the cutting force are 8 dFt ðy; zÞ ¼ Kte dS þ Ktc ac ðC; y; kÞdb > > < dFr ðy; zÞ ¼ Kre dS þ Krc ac ðC; y; kÞdb > > : dFa ðy; zÞ ¼ Kae dS þ Kac ac ðC; y; kÞdb

ð2Þ

where Krc, Ktc, Kec, the so-called ‘shearing coefficients’, are in N/mm2. Kre, Kte, Kae, the ‘friction coefficients’ are in N/mm and ac is in mm.

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In the calculation of the three projections it is necessary to develop a geometric model of the tool cutting edges. Figure 4 details the calculation steps.

3.2.1. Tool geometric model. The ball-end mills for the die and mould machining have a small number of flutes (2 – 4)

with a nominal helix angle (io) ranging from 15 to 458. This angle is constant for one tool, but not in the spherical end part of it. Here the local helix angle decreases down to 08 at the tool tip. In figure 5 the geometry of one flute is shown. This figure also shows one of the cutting edge discrete elements. The position of the different discrete elements of the cutting edge will be a function of the ball-end mill radius

Figure 4. Cutting force estimation steps.

Figure 5. Position angle definition and cutting edge element detail.


(Ro), the nominal helix angle (io) and position angle turned by the spindle (y). Finally, the elements of the flutes can be obtained by the following expressions (Lamikiz et al. 2002)

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Nevertheless, these expressions are only valid for horizontal machining. A coordinate transformation is applied to obtain the chip thickness and the discrete cutting edge length (dS) in slope machining conditions, which is the typical situation in die and mould machining, as explained below.

X ¼ RðcÞ sin ðCÞ Y ¼ RðcÞ cos ðCÞ c R0 Z¼ tan ði0 Þ

ð3Þ

cj ðzÞ ¼ y þ ð j 1Þ fp

z tan ðio Þ R0

For a Z value a circle with radius R(c) will be obtained, expressed as sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2ffi c RðcÞ ¼ R0 1 1 tanði0 Þ

ð4Þ

Thus, the positioning vector of each element on the edge is obtained. The length of each element is obtained by differentiating with respect to the variable c. R0 ðcÞ ~ k^ rðcÞ ¼ RðcÞ sinðCÞ^ i þ cosðCÞ^ j þ tanði0 Þ sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi R20 dðcÞ dS ¼ kd~ r k ¼ ½R0 ðcÞ2 þ R2 ðcÞ þ tan2 ði0 Þ

ð5Þ

Once the position of the flute discrete elements is defined, the undeformed chip thickness (ac) is calculated. Undeformed chip thickness is a function of the flute position (C) and feed per tooth ( fz). As shown in figure 6, chip thickness can be expressed mathematically as: ac ðC; y; kÞ ¼ fz sinðCÞ sinðkÞ

3.2.2. Machining of slope surfaces. When sculptured surfaces are machined it is necessary to take into account the effect of the surface inclination on the cutting forces. The slope is calculated using a tangent plane, which contains the tool – surface contact point. Once the angle is known, a coordinate transformation is used to obtain the valid expressions for slope machining. The positions of the cutting edge elements (x, y, z) are known from the first coordinate system X1Y1Z1, with the origin in the tool tip and the Z1 axis in the tool axis direction. The X1 direction is given by the feed direction projected in a normal to Z1 plane; this system is shown in figure 5. On the other hand, chip thickness (equation (6)) is valid when the X axis direction coincides with the feed direction and Z axis is normal to the machined surface. The X2Y2Z2 coordinate axis is defined in this way. Therefore, it is necessary to make a coordinate transformation from X2Y2Z2 to X1Y1Z1 to obtain the valid value of the undeformed chip thickness and the discrete flute element length for each slope machining case. In figure 7, both coordinate systems (X1Y1Z1 and X2Y2Z2) are represented together with the most important angles involved in the coordinate transformation. The inputs are the surface slope(a) and the machining angle (r), defined as the actual value of angle of the toolpath with respect to horizontal plane, measured in a vertical plane containing the tangent line to the toolpath.

ð6Þ

where k ¼ arcsin

RðcÞ R0

ð7Þ

Figure 6. Non-deformed chip thickness calculation in a discrete cutting edge element.

Figure 7. Main angles and coordinate system used in the model.

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The change of coordinate system in the case of upward milling (figure 7) is shown in the following expressions. 8 9 0 18 0 9 1 0 0 > > < X2 > = = B C Y2 ¼@ 0 sinðbÞ cosðbÞ A Y0 > > : > ; : 0> ; 0 cosðbÞ sinðbÞ Z2 Z 8 09 0 18 00 9 cosðrÞ 0 sinðrÞ > > = = B C 0 ¼@ 0 1 0 A Y00 Y > > : 0> ; : 00 > ; sinðrÞ 0 cosðrÞ Z Z 9 8 00 9 8 9 8 > = = > = > < Ro sinðaÞ cosðwÞ > < X1 > Ro sinðaÞ sinðwÞ Y00 ¼ Y1 þ > > ; ; > ; > : : 00 > : > Ro þ Ro cosðaÞ Z Z1

ð8Þ

The first step is a rotation around the X2 axis until the axis is parallel to the horizontal plane. Once this rotation is complete, auxiliary X’Y’Z’ axes are obtained. When this transformation is finished, a new rotation is needed around the Y’ axis to obtain a new X’’ axis parallel to the horizontal plane. After this rotation, auxiliary X 00 Y 00 Z 0 ’ axes are obtained. These axes are parallel to the X1Y1Z1 axes. Finally, a translation has to be carried out to finish the transformation. Thus, chip thickness can be calculated as a function of discrete cutting edge elements position (x,y,z), using X1Y1Z1 axes. After the calculation of chip thickness in the tool reference system X1Y1Z1, integration of equation (2) is performed, using a general integration procedure based on Lobato’s quadratic method. 3.2.3. Material characterization. After programming the model, experimental tests are performed to obtain material/ tool coefficients. Real forces are measured with a Kistler

9255B dynamometric table installed in a three-axis HSM Centre Kondia HS-1000. The signals from piezoelectrics are amplified and stored in a Intel Pentium III 600 PC with a data acquisition card with up to 800 kHz sampling frequency. Tests were made in an aluminium alloy (Al 7075 - T6) and in type hardened steel commonly used in moulds (52 HRC). The cutting force components were measured using different cutting conditions in a few horizontal machining tests. Once the cutting tests were finished, the coefficients for each pair tool/material were obtained using a reverse methodology based on a least squares approach. A first approximation was made with constant cutting coefficients. However, this approximation is only valid for end mills. When ball-end mills are used, variable cutting coefficients along the cutting edge have to be used (Feng and Menq 1994). After some tests, polynomial coefficients have been defined as quadratic (Kc = a0+a1z+a2z2) and linear (Kc = a0+a1z); Ke are constant. Figure 8 shows quadratic and linear cutting coefficients for a tool steel commonly used for moulds (52 HRC). Its values are shown in table 1. Table 1. Edge and shear cutting coefficients for AISI H13 52 HRC tempered tool steel/ball-end mill HM K10 + TiAlN, 308 nominal helix angle and 08 rake angle. Linear

Quadratic

Ktc: 4254.9 + 2822.7 Z

Ktc: 72411.5 + 23555Z 7 11359 Z2

Krc: 8030.6 7 2225.4 Z

Krc: 7574.3 + 28126Z 7 12407 Z2

Kac: 73344.1 + 1438.9 Z

Kac: 9489.9 7 14177Z + 6652.1 Z2

Kte: 4.2919

Kte: 5.3245

Kre: 6.1777 Kae: 1.3115

Kre: 4.8567 Kae: 1.9345

Figure 8. Cutting coefficients for the 1.2344 tool steel (52HRC) and a ball end mill of Ø 8 mm.


The validity of the obtained coefficients was tested by comparing the actual cutting force (as measured in the characterization tests) with the simulated cutting force (as predicted by the coefficients and proposed method). B. 3.3. Experimental validation of cutting force model Once the cutting coefficients have been obtained, slopemachining tests are carried out. In these tests, the cutting forces are measured over a period of time using different cutting strategies and different cutting parameters. One illustrative result is shown in figure 9. The fit between measured and simulated forces, not only values but also the shape of the wave can be observed. Errors between the actual and the predicted forces are less than 10% in most of the cases. The errors can be attributed to two main sources: the run-out (eccentricity) of tool teeth and electrical distortions in the Kistler device owing to lack of ground isolation. 4. Cutting force integration in the CAM stage Once the model for the cutting force prediction had been developed and validated, and the characteristic coefficients of mould steels were available from experiments, the model was integrated in a CAM system. The aim was to calculate optimum toolpaths from the point of view of the cutting force. Two approaches are possible at this point. A.

The model can be used a posteriori. In this case, the objective would be the validation of a previously programmed toolpath: a maximum admissible value

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for the cutting force is set, and the programmed toolpath is accepted if force is kept below this maximum value. This is shown in the examples 1 and 2 given in section 5 of this paper. The model can be used to evaluate a priori the performance of different possible machining strategies at some user-defined control points on the surface. The optimum toolpath will be the one that minimizes the value of the cutting force on those points. This option allows a ‘scientific’ selection of the best machining strategy, and can be seen in example 3, given in section 5 of this paper.

Figure 10 shows the methodology for the implementation of the a priori option. Projecting a grid onto the surface of the workpiece (figure 10 step A), defines a number of control points. The excess of material that must be machined in each point is calculated and then the model for the prediction of the cutting forces is applied. Results are obtained at every 158 (24 directions in each control point) in both the downmilling and the upmilling cases (figure 10 step B). When studying the results, the best machining strategy is established (figure 10 step C). This method can be applied in the case of sculptured surfaces and/or free surfaces. In very sharp forms, or those with very little curvature, there are other considerations to be taken into account, such as avoiding unexpected material stocks owing to previous operations, or the rational succession of milling operations. Therefore this methodology is absurd for, for example, pocket milling.

Figure 9. Validation test in hardened steel 1.2344 (52 HRC), slope 158, slotting operation.

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4.1. Input data As stated previously, the user must define a number of control points on the work surface. A grid is projected onto the surface but points (not included in the grid) can be defined by the user. Data relating to the slope are obtained from the CAD model in directions at 158 (in the horizontal projection). Using a windows-like user-friendly interface, the user defines the cutting conditions, i.e. the axial and radial

depth of cut, up- or downmilling case, programmed feedrate, rotational speed of tool. The excess of material to be removed is obtained from the file generated by the CAM program for the semifinishing operation. 4.2. Output data and results The cutting forces are predicted for each control point at different directions, as shown in figure 11. The length of the

Figure 10. Integration of cutting force estimation in the CAM stage. (A) Selection of control points; (B) estimation each 158; (C) selection of the minimum force toolpath.

Figure 11. Cutting force representation for one point, in downmilling and upmilling.


lines represents the value of the force and the small dot represents where material is still unremoved and, therefore, whether it is a case of downmilling or upmilling (tool always rotate in M03 case). The numerical value of the force for a tool rotating in M03 (clockwise) can also be displayed, as it is shown in figure 11 in upmilling in two directions. Once the representation is available for all the control points, the optimum toolpath can be selected in a semiautomatic way, with a b-spline utility. 5. Examples Examples 1 and 2 are representative of the option described in option A in section 4 i.e. both are applied in a five-axis machining process. First a cutting method is selected to generate a programmed toolpath, which is then studied using the cutting force estimation tool. If the maximum force is less than a desired value, then the defined toolpath is accepted. It is therefore inferred that those programmed are good toolpaths.

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Example 3 is, however, representative of a priori estimation of the cutting force, option B in section 4. Consequently the final selected toolpath is that which causes the minimum cutting force in all control points. Thus it can be deduced that this toolpath is the best. In the three examples outlined below, the stability analysis is not necessary, because the low axial depth of cut of the finishing operation. 5.1. Five-axis HSM of forging die The zone marked as ‘central slide’ (see figure 12) was machined using a simultaneous four-axis strategy, keeping a constant lead angle of 108, with a maximum cutting force perpendicular to the tool axis of 22 N, estimated using the new model. The machine tool was the five-axis one shown in figure 2, with a high-speed spindle up to 18 000 r/min, and 1G acceleration in all linear axes. Tool overhang length was 30 mm when the tool measured 6 mm in diameter, that is, the (L3/D4) tool slenderness was 20.8 mm71. Doing the same workpiece in a three-axis machining centre the tool

Figure 12. (a) Material. (b) Tool and holder. (c) Machining operations, cutting parameters and machining times. (d) CAD geometry and name of programs. (e) Final result.

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overhang ought to be 70 mm, that is, a tool slenderness of value 264.6 mm71, an as consequence, tool deflection is non admissible (more than 264.6/20.8 = 12.7 times tool deflection), applying the cantilever beam model for the tool: d¼

64F L3 3pE D4

ð9Þ

The ‘shoulder’ was a part of the machine with a constant part orientation with respect to a tool axis of 188, using a spiral toolpath. In this case a maximum cutting force of 20 N was calculated, and a very good finishing was achieved. The zone ‘Slot 5’ was also machined with a constant part orientation, and the estimated cutting force was always less than 27 N. ‘Slot 3’ is the same, with a maximum force of 22 N. All programs were checked with previous virtual simulation, and no tool collisions and part cut mistakes were recorded. 5.2. Five-axis high-speed machined injection mould In this case a plastic injection mould made in 35 HRC steel has been analysed and machined in the same HSM five-axis centre as the above example. Figure 13 shows geometry, cutting conditions and the bull-nose tool (thoroidal tool with a radius of 2 mm). Part flanks have been machined using a z-level simultaneous five-axis strategy, finishing them in only 6 min, and with a maximum cutting force perpendicular to tool axis of 35 N. The floor was machined with a downmilling spiral strategy, with cutting force less than 27 N.

Part quality, precision and machining times are very good. Virtual machining of this part was also performed. 5.3. Three-axis HSM of stamping die The last example shows an application of the force prediction, integrated in a CAM system (Unigraphics V18). This testpiece, a portion of a stamping die for a car door, is made of cast iron GGG70. In this case a HSM centre with three axis and a spindle up to 25 000 r/min has been used. A number of control points are projected from a userselected grid. The component of the cutting force perpendicular both to the tool axis and to the machined surface has been calculated for these points. Both downmilling and upmilling situations have been studied (shown in figures 14(a) and (b), respectively). The first possibility was selected owing to its more common use in the die industries, from which the toolpaths shown in figures 14(c) and (d) have been generated. The cutting conditions were fz 0.1 mm, ap 0.6 mm, ae 0.4 mm, using a two-teeth solid tool of 16 mm diameter coated with TiALN, and S = 15 000 r/min. At these conditions the maximum cutting force perpendicular to tool axis is 75 N in 08 and 38 N is the component of the cutting force perpendicular both to the tool axis and to a 458 inclined plane. The transition between the master toolpaths associated with control points is carried out by a curve fitting procedure. In this case, since the work surface is rather smooth, the discontinuities between toolpaths are negligible. After machining, the test part has been measured in a coordinate measuring machine. Accuracy results are

Figure 13. (a) Mould material. (b) Tool (bull nose (12). (c) Machining operations, cutting parameters and machining times (d) CAD geometry. (e) Workpiece fixing. (f ) Final result.


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Figure 14. Application of minimum cutting force criterion for the selection of the toolpath in a stamping die test piece. (a) Calculation of force in control points in downmilling case. (b) Same in upmilling. (c) Perspective of toolpaths. (d) Top view.

Figure 15. Machined testpiece and its measurement in a coordinate measuring machine. presented in a colour map (as shown in figure 15). As it can be seen, good accuracy and dimensional tolerance have been achieved. 6. Conclusions A new model for cutting force calculation based on a mechanistic approach has been presented. Not only spherical geometry, but also the machined surface slope

have been taken into account. The presented model is useful in die and mould machining with ball-end mills, and in flank machining of inclined surfaces with end mills. Linear coefficients for material/tool characterization have been used because the resulting forces were close to the measured forces and the number of tests needed to achieve them is small. Measured cutting forces of tests are compared with those predicted by the model. The fit between them is good.

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Results are valid for different slopes, cutting strategies and cutting parameters. Cutting force is calculated in two examples for a previous toolpath programmed with a commercial CAM software. In many cases this is enough to assess a predefined level of accuracy in complex surfaces. The estimation of cutting forces has also been integrated as a utility in commercial CAM software to the best selection of the toolpaths in the HSM of complex surfaces. In each control point, selected by users, an estimation of forces is carried out at every 158, selecting that toolpath for which the maximum cutting force in the direction both perpendicular to tool axis and surface is minimum. In the examples presented, very good surface accuracy just with machining times has been achieved. No spindle crashes or part machining errors have occurred. This has been attained using the proposed CAM methodology based on the virtual simulation of machining and the toolpath optimization through the estimation of cutting forces. Acknowledgements The authors are very grateful to Eduardo Sasia, David Grijalba and Julen Munõa for assistance rendered in the three machining examples, and to Fundacioń Tekniker for its full assistance in the first example. This paper was sponsored by the projects MICYT DPI2002-04167-C02-02 (Spanish Government) and UPV/EHU 145.345-TB7923/ 2000. References Altintas, Y., Manufacturing Automation: Metal Cutting Mechanics Machine Tool Vibrations and CNC Design, 2000 (Cambridge University Press: Cambridge). Altintas, Y. and Lee, P., A general mechanics and dynamics model for helical end mills. Annals of the CIRP, 1996, 45(1), 59 – 64.

Altuzarra, O., Bravo, U., Lo´pez de Lacalle, L. N. and Rivero, A., Static and dynamic problems in the high speed machining of low rigidity monolithic structures. DAAAM International Scientific Book, 2002, pp. 7 – 15 (DAAAM Publishers, Wien). Bagard P., Tooling and complex shapes: technical – economic reports between HSM, conventional machining and electro erosion, CETIM Sensils DPM-SU, 1st French and German Conference on HSM, 1997, Metz. Dewes, R. C. and Aspinwall, D. K., A review of ultra high speed milling of hardened steels. Journal of Materials Processing Technology, 1997, 69, 1 – 17. Diehl, L., Machining methods for complex models, Modern Machine Shop, 5 July 1996. Available online from: http://www.mmsonline.com/ articles/ Fallbo¨hmer, P., Advanced cutting tools for the finishing of dies and moulds. Technical report of IFW, 1998 (VDI Verlag, Du¨sseldorf ). Feng, H. and Menq, C., The prediction of cutting forces in the ball end milling process – I. Model Formulation and Model building procedure. International Journal of Machine Tools and Manufacture, 1994, 34(5), 697 – 710. Hock, L. and Jajenski. J., NC programming for HSM. Modern Machine Shop, 1996, 5. Available online from: http://www.mmsonline.com/ articles/. Lamikiz, A., Lo´pez de Lacalle, L. N. and Salgado, M. A., Estimation of cutting forces in the ball end machining of complex surfaces. DAAAM International Scientific Book, 2002, pp. 329 – 343 (DAAAM Publishers, Wien). Makino Inc., Thin Wall Machining, 2000. Available online from: http:// www.makino.com. Accessed: 12/01/2001. Meng, E. and Menq, C., Integrated planning for precision machining of complex surfaces. Part 1: Cutting-path and feedrate optimisation. International Journal of Machine Tools and Manufacture, 1997, 37(1), 61 – 75. Schulz, H., Hochgeschwindigkeitsbearbeitung (High Speed Machining), 1997 (Carl Hanser Verlag, Germany). Scott Smith, K., Automatic selection of the optimum spindle speed in highspeed milling, PhD Thesis, University of Florida, 1987. To¨nshoff, H. K., Technologie des Werkzeug- und Formenbaus im internationalen Vegleich (International technology of machining and forming), 1998 (IFW Hannover). Van Luttervelt, Childs, T.H.C., Jawahir, I. S., Klocke, F. and Venuvinod, P. K., Present situation and future trends in modeling of machining operations. Annals of the CIRP, 1998, 47, 587 – 626.