Development of a reference cutting force model for rough milling feedrate scheduling using FEM analysis

ARTICLE IN PRESS

International Journal of Machine Tools & Manufacture 47 (2007) 158–167 www.elsevier.com/locate/ijmactool

Development of a reference cutting force model for rough milling feedrate scheduling using FEM analysis Han-Ul Lee, Dong-Woo Cho Department of Mechanical Engineering, Pohang University of Science and Technology, San 31 Hyoja-dong, Nam-gu, Pohang, Kyungbuk 790-784, Republic of Korea Received 19 May 2005; received in revised form 7 February 2006; accepted 9 February 2006 Available online 4 April 2006

Abstract Recently developed feedrate scheduling systems regulate cutting forces at the desired level by changing the feedrate to reduce the machining time and to avoid undesirable situations. For effective scheduling, an optimized criterion is required to adjust the feedrate. In this study, a method to obtain the most appropriate reference cutting force for rough milling was developed. The reference cutting force was determined by considering the transverse rupture strength of the tool material and the area of the rupture surface. A finite element method analysis was performed to accurately calculate the area of the rupture surface. Using the analyzed results, the effect of various cutting parameters on the chipping phenomenon was determined. The calculation method for the reference cutting force considered the area of the rupture surface, the effect of the rake angle, and the axial depth of the cut. The reference cutting force calculated using the developed model was applied to feedrate scheduling for pocket machining. The experimental results clearly show that the reference cutting force obtained from the proposed method met the desired constraints that guarantee higher productivity without tool failure. r 2006 Elsevier Ltd. All rights reserved. Keywords: Reference cutting force; Feedrate scheduling; FEM analysis; Transverse rupture strength; Rupture surface

1. Introduction The manufacturing paradigm has changed from mass production to mass customization. To adapt to this transition, many industries require new technologies that can increase their production rate and decrease their production costs. The cutting process accounts for a large portion of the development and manufacturing of most products. Thus, by reducing the time required for the cutting process, higher productivity and shorter development periods for new products can be achieved. For this purpose, feedrate scheduling systems that regulate the material removal rate [1–3] or cutting force [4–10,12] to the desired level have been developed. These systems change the feedrate to reduce the machining time. In rough milling, machining time is the most important factor that affects productivity. In this case, feedrate scheduling is focused on reducing the machining time. Corresponding author. Tel.: +82 54 279 2171; fax: +82 54 279 5889.

E-mail address: [email protected] (D.-W. Cho). 0890-6955/$ - see front matter r 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijmachtools.2006.02.007

However, there is a trade–off between the machining time and cutting stability. The faster the feedrate, the larger the cutting force; an increased cutting force introduces various problems, such as machining chatter, tool wear, and breakage. In finish milling, on the other hand, dimensional tolerance is the dominant factor that affects productivity. There is a similar trade-off between the machining time and the machined surface error. A slower feedrate causes a longer machining time while it can introduce small tool deflections, which are the main source of machined surface errors. Thus, selecting the most appropriate reference cutting force is very important for effective feedrate scheduling. Previous research has focused on designing a feedrate scheduling model to regulate the cutting force. To improve the cutting performance, Tarng et al. [4] applied a geometric modeling system to an in-process simulation of the cutting geometry for pocket machining. The area of the cut chip was identified; then the corresponding cutting performance was evaluated and optimized. Lim and Menq [5] created an integrated planner for machining complex

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surfaces that optimized the cutting path and feedrate. Bae et al. [8] proposed an automatic feed adjustment method that calculated the adjusted feedrate using a simplified cutting force model. This model obtained the cutting force from a non-parametric Bezier surface that was constructed from experimental cutting data. In their work on feedrate scheduling, Guzel and Lazoglu [9] adjusted the feedrate during ball-end milling to decrease the cycle time for sculpture surface machining. However, a reference or constraint for their cutting force was selected by experimental methods. Some researchers have used arbitrary values for the reference cutting force [5,8,9]; others have applied maximum values of measured cutting forces in non-scheduled machining [4]. Fussell et al. [6] developed a feedrate process planner for complex sculptured end milling cuts from mechanistic and geometric end milling models. A cantilever beam model of the tool was used to relate the vector force to the allowable tool deflection or tool bending stress. Thus, they set the desired constraint force of 133 N to a maximum 0.25 mm tool deflection. Ko and Cho [10] presented an analytical model of offline feedrate scheduling for three-dimensional ball-end milling based on a cutting force model that used cuttingcondition-independent coefficients. They also defined the transverse rupture strength (TRS) of the tool to determine the reference cutting force that must be considered to avoid breakage of the tool shank and edge. The reference cutting force was calculated by several equations determined from cutter geometry and rupture surface position. The rupture surface position, however, has to be defined by the user, which can be considered as a very difficult task by itself. Therefore, a new method that calculates the exact area of rupture surface in various cutting conditions is required. In our earlier work [7], a feedrate scheduling system was proposed, based on an improved cutting force model that could predict the cutting force accurately for general end milling situations. However, the cutting force was regulated at a safe level, which was the maximum allowable value for non-scheduled cutting. To increase the efficiency of the feedrate scheduling, a reference cutting force model was developed in this study. The reference cutting force was determined considering the TRS of the tool material proposed by Ko and Cho [10]. To predict the exact point at which tool breakage and chipping would occur, the area of the rupture surface and other effects were calculated using a finite element model (FEM) and the results from a mathematical analysis. The developed reference cutting force model makes it possible to determine the maximum level of force that a cutter can resist. 2. FEM analysis The reference cutting force was derived considering the TRS of the tool material. The TRS is the stress required to break a specimen and is calculated from the flexure formula [11]. It has been used by tool makers to determine the strength of tool material. Using the TRS, the reference

159

cutting force can be determined as follows [10]: RFb ¼ TRS  S b ; RFc ¼ TRS  S c ;

(1)

where RFb and RFc represent the reference cutting forces that mark the onset of tool breakage and chipping, respectively, and Sb and Sc are the cross-sectional areas of the tool shank and edge. The reference cutting force is a minimum value between RFb and RFc. Sb can be easily calculated from the tool geometric data. However, the chipping mechanism must be understood to determine Sc because most chipping occurs at the end of a tooth and the area of the rupture surface cannot be calculated using only the tool geometry. Therefore, FEM analysis was performed to understand the tool chipping mechanism and calculate the area of the rupture surface. Using the analyzed results, various cutting parameters, such as the cutting conditions and tool geometry, were considered to calculate the reference cutting force. 2.1. FEM analysis When a cutting force is inflicted on a rake surface, the internal stress is concentrated into an arbitrary region. If the concentrated stress is above a critical level, then chipping occurs in this region. This region was defined as the rupture surface. To calculate the area of the rupture surface, the distribution of the internal stress of the tool was computed using ANSYS. The following assumptions were made in the analysis. (1) The chipping occurs due to the normal pressure cutting force on the rake surface of the tool. The frictional cutting force is negligible in the chipping mechanism. (2) The normal pressure cutting force is distributed regularly on the engaged rake surface. (3) The width of the engaged rake surface is equal to the uncut chip thickness, and it is a fixed value regardless of the axial position. In general, the TRS is determined by subjecting the specimen to a uniformly increasing transverse load. The inflicted load, which provokes the rupture of the specimen, is applied parallel to the specimen cross-section or the rupture surface. During the cutting process, the frictional cutting force is perpendicular to the rupture surface. Thus, only the normal pressure cutting force was used in this analysis, as described by the first assumption and illustrated in Fig. 1. From the second assumption, an arbitrary pressure was inflicted on the engaged rake surface instead of a force. Inflicting a force on limited points can produce incorrect analytical results because the cutting force is distributed over the entire engaged rake surface. As illustrated in Fig. 1, a constant value was used for the width of the engaged rake surface. Because of the helix angle, the uncut chip thickness varied with the axial position. From

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Normal pressure cutting force

Axial depth of cut

cutter radii reduce the error. Thus, the third assumption is reasonable for various cutting conditions. To describe the actual cutting state in the FEM analysis, the inflicted normal pressure cutting force was determined from experimental results. From Fig. 2, the normal vector at an arbitrary cutting edge location angle on the rake surface can be defined as [13] nðfÞ ¼

cos yh cos yh sin yh cosðf  ar Þi þ sinðf  ar Þj  cos ar k, sin ytk sin ytk sin ytk

(3) Uncut chip thickness

Fig. 1. Schematic diagram of the assumptions for the FEM analysis.

where cos ytk ¼ sin ar  sin yh , and ar is the rake angle of the tool. Thus, the normal pressure cutting force can be determined from the dot product of the measured cutting force and the normal vector, F n ðfÞ ¼

cos yh cos yh sin yh cosðf  ar ÞF x ðfÞ þ sinðf  ar ÞF y ðfÞ  cos ar F z ðfÞ, sin ytk sin ytk sin ytk

(4)

rake surface

αr κ h Z

Tc τ c

Y b

r1

r2

n

a

h tc X

where F x ðfÞ, F y ðfÞ, and F z ðfÞ are the measured cutting forces at the arbitrary angle, f. The calculated normal pressure cutting force from the experimental results was 5.52 MPa; this value was used throughout the FEM analysis. A tungsten carbide two-flute flat end mill was used for the analysis. The tool material and geometry used for the computations are listed in Table 1. Tetrahedron elements were selected to mesh the model; the smallest mesh size was 0.005 mm.To determine the effects of the cutting conditions and tool geometry, the FEM analysis was executed for various axial depths, uncut chip thicknesses, and rake angles, as listed in Table 2.

feed direction

Y



R2

2.2. Analytical results The stress concentration curve for each simulation had the same shape, regardless of the axial depth, uncut chip

αr

R

X

φ

 κ

Fig. 2. Cutter geometry, coordinate system, and unit vectors on the rake surface [13].

Table 1 Cutter information

Cutter geometry

the coordinate system illustrated in Fig. 2, the uncut chip thickness at an arbitrary axial position can be described by   tan yh tc ¼ f t sin f þ pa , (2) R where ft is the feed per tooth, f is the cutting edge location angle, pa is the axial position, yh is the helix angle, and R is the cutter radius. From Eq. (2), the calculated uncut chip thickness error is less than 10% when the axial depth, radial depth, helix angle, and cutter radius are 1, 0.5 mm, 301, and 5 mm, respectively. Larger radial depths and

Cutter material properties

Type

Flat end mill

Radius (mm) Number of flutes Helix angle (deg.) Rake angle (deg.)

5 2 30 22, 11, 5, 1, 5, 11, 22 13 1 30

Primary clearance angle (deg.) Primary clearance width (mm) Secondary clearance angle (deg.) Secondary clearance width (mm) TRS (MPa) Elastic modulus (GPa) Shear modulus (GPa) Poisson’s ratio

1 3000 540 270 0

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Table 2 FEM analysis conditions No.

Uncut chip thickness (mm)

Axial depth of cut (mm)

Rake angle (deg.)

Pressure (MPa)

1

0.02

11

5.52

2-1 2-2 2-3 3-1

0.01, 0.02, 0.03, 0.04, 0.05, 0.06, 0.07, 0.08, 0.09, 0.10 0.01, 0.02, 0.03, 0.04, 0.05, 0.06, 0.07, 0.08, 0.09, 0.10 0.01, 0.02, 0.03, 0.04, 0.05, 0.06, 0.07, 0.08, 0.09, 0.10 0.02

0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0 1.0 1.0 1.0 1.0

5.52 5.52 5.52 5.52

3-2

0.05

1.0

11 1 11 22, 11, 5, 1, 5, 11, 22 22, 11, 5, 1, 5, 11, 22

5.52

d e

Prism part

Rupture surface

C

B

b

l

h

FEM analysis result

c

a r A Tetrahedron part

Fig. 3. Schematic diagram of the rupture surface.

thickness, or rake angle. If there are not any cracks, chipping will normally occur in this portion of the tool, and the rupture surface will be a boundary surface between this portion and the rest of the tool. This portion of the tool can be divided into the prism and tetrahedron parts, as illustrated in Fig. 3. Most of the inflicted normal pressure cutting force is distributed over the range of the uncut chip thickness because the direction of the load is perpendicular to the rake surface. Thus, most of the stress is concentrated on the prism part. However, because of the helix angle, the load accumulates on the bottom surface of the tool, and the shape of the stress concentration curve becomes a tetrahedron. From the analytical results, it was shown that the length of ‘e’ in Fig. 3, the width of prism part on the rake surface, is identical to uncut chip thickness, and the stress concentrated on the boundary between prism part and the rest of the tool is of an almost same value as the average stress of the entire tool. Therefore, this average

value was used to identify the rupture part of the tool. That is, if the concentrated stress on an arbitrary region is larger than this average value, the region belongs to the rupture part. The effect of the axial depth of the cut was determined from the simulation results of Group 1 in Table 2. The height of the prism part increased with respect to the axial depth of the cut. However, there were no changes in the size of the tetrahedron part and the cross-section of the prism part. When the end mill was assumed to be a group of disk elements, the axial depth of the cut did not affect the distribution or magnitude of the stress on an arbitrary disk. Thus, a large axial depth of cut did not chip the tool; rather, it contributed only to the wear or breakage of the tool. From an analysis of the simulation results of Group 2, the uncut chip thickness was the main factor that determined the size of the rupture surface. Fig. 4 shows

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162

a

b

c

d

0.3

30

0.25

25

0.2 0.15

15 10

0.05

5

0.02

0

0.04 0.06 0.08 Uncut chip thickness (mm)

0.1

0.12

Fig. 4. The size of rupture surface with respect to the uncut chip thickness.

a

0.21

b

c

d

0.18

Size (mm)

0.15 0.12 0.09

-25

average

20

0.1

0

max

35

Stress (GPa)

Size (mm)

0.35

-20

-15

-10

0 0 5 -5 Rake angle (deg.)

10

15

20

25

Fig. 6. The maximum and average von Mises stresses with respect to the rake angle from the FEM analysis.

(2) The size of both the prism and tetrahedron parts increases in proportion to the uncut chip thickness. (3) The depth of cut affects only the height of the prism part. It does not affect the cross-section of either the prism or the tetrahedron part. (4) The rake angle affects the concentrated stresses of each part, not the size of the rupture surface.

0.06 0.03

3. Reference cutting force

0 -30

-20

-100

0

10

20

30

Rake angle (deg.)

Fig. 5. Size of rupture surface with respect to the rake angle.

the simulation results of Groups 2–3. The size of both the prism and tetrahedral parts increased proportionally with the uncut chip thickness. However, the height of the prism part was not affected by this factor. The area of the rupture surface of the tetrahedron part was determined by the uncut chip thickness. Thus, the size of the chipping was also determined by the uncut chip thickness because chipping generally occurs on the end of a tooth. Usually, the rake angle is a dominant factor for chipping as well as the uncut chip thickness. However, the size of each part was not affected by the rake angle, as illustrated in Fig. 5. The size of the rupture surface was almost constant, regardless of variations in the rake angle. Thus, the area of the rupture surface can be determined using the analytical results for any rake angle condition. From the simulation results of Group 3, the rake angle affected the concentrated stresses of each part, not the size of the rupture surface. The maximum and average von Mises stresses increased with the rake angle, as depicted in Fig. 6. Thus, a tool with a larger rake angle is more likely to chip. Based on the analysis of the FEM results, the following conclusions can be drawn. (1) The stresses are concentrated on the prism and tetrahedron parts of the tool.

The effects of the cutting conditions and tool geometry were determined from analyzing the FEM simulations, and the exact area of the rupture surface was calculated for various cutting conditions. The reference cutting force model was developed considering this information and validated using experimental results. 3.1. Reference cutting force model There are two types of reference cutting force given by Eq. (1): one that defines the onset of tool breakage, and one that defines the onset of tool chipping. The first reference cutting force can be determined easily using Eq. (1). The rupture surface of the tool shank can be calculated from an equivalent cross-sectional area of the tool. Considering the equivalent cross-section, the reference cutting force for tool breakage is RFb ¼ TRS  pR2 rc ,

(5)

where rc is the ratio of the actual cross-section and the cross-section of the outer circle of the tool. This value can be determined from the tool geometry data. Generally, if the number of teeth is two, four, or six, then the ratios of the cross-sections are 0.5, 0.6, and 0.7, respectively. The reference cutting force that defined the onset of chipping was calculated from the TRS and the area of the rupture surface. However, the cutting conditions and tool geometry determined from the FEM analysis must be considered to obtain correct calculations. After integrating

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the areas, the reference cutting force is qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi da 1 þ K 2f , RFc ¼ TRS  S r f r f c l

(6)

where Sr is the area of the rupture surface, fr and fc are the factors for the rake angle and the critical uncut chip thickness, respectively, l and da are the height of the rupture surface and the axial depth of the cut, and Kf is the frictional cutting force coefficient. The area of the rupture surface is determined from the analytical results. Most chippings occur at the end of the tooth, that is, the tetrahedron part, and only the uncut chip thickness affects the size of the tetrahedron part. The axial depth and the rake angle merely affect the height of the prism part and the concentrated stress, respectively, and do not affect the size of the tetrahedron part. Thus, the area of the rupture surface can be obtained from a function of the uncut chip thickness as follows: S r ¼ 1=4

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðA þ B þ CÞðA þ B þ CÞðA  B þ CÞðA þ B  CÞ,

A2 ¼ a2 þ c2  2ac cos ar , B2 ¼ a2 þ b2  2ab cos yh , C 2 ¼ b2 þ c 2 ,

ð7Þ

where A, B, and C are the three side of a cross-section triangle in the tetrahedron part, as illustrated in Fig. 3. They can be calculated from the flank (a), rake (b), and bottom (c) chip sizes. Using the curve-fitted results of Fig. 4, a ¼ 2:9046tc þ 0:0035; b ¼ 2:1833tc  0:0098; c ¼ 1:0964tc þ 0:001:

(8)

These values can be used for any cutting conditions and tool geometries because the uncut chip thickness is a unique variable of the size of the rupture surface. The ISO 8688-2 standard recommends defining a tool-life end-point criterion when the flank wear is greater than an average value of 0.3 mm or a local value of 0.5 mm [14]. The maximum allowable chip size is the same as the local wear criteria of 0.5 mm.In this paper, the flank chip size (A), which was the largest chip size at 0.3 mm, was used to calculate the reference cutting force because the reference cutting force was not used to determine the end of a tool’s life but rather to ensure that the cutting force remained in the safe region. Thus, from Eq. (8), the critical uncut chip thickness (tc,c) that gives the largest allowable chip is 0.102 mm. The maximum allowable amount of chipping occurs when an arbitrary cutting force (F) generated in an uncut chip thickness of tc is equal to the load that makes the maximum allowable chipping and tc the same as tc,c. If the workpiece is a hard material such as very hard steel, then the cutting force becomes the same for smaller uncut chip thickness values, and smaller chips form. However, if the workpiece is a soft material, such as aluminum or brass,

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then the pressure inflicted on the critical uncut chip thickness area is less than the pressure that causes the chipping. In this case, ideally, there will be no chipping for any cutting conditions because the cutting force increases according to the uncut chip thickness. However, because of unpredictable factors such as errors in the cutter geometry, irregularities in the cutter material, and loads generated by the chip flow, increases to the reference cutting force must be restricted. Therefore, we introduced a critical uncut chip thickness factor as follows: ( 1; tc  tc;c ; (9) fc ¼ tc =tc;c ; tc 4tc;c : Using this factor, the reference force increases proportionally when the current uncut chip thickness is greater than the critical uncut chip thickness. As depicted in Fig. 6, the concentrated stress increases with the rake angle when the pressure is maintained at a constant value. That is, larger cutting forces must be inflicted on the tooth for chipping to occur if the rake angle is small or a negative value. To reflect this characteristic, a rake angle factor was introduced, given by the maximum von Mises stress ratio of an arbitrary rake angle to a standard rake angle. If the current rake angle is greater than the standard rake angle, the allowable load increases by this ratio. For the opposite case, the reference cutting force decreases by this ratio. An elastic calculation method is used to calculate the maximum stress for an arbitrary rake angle. The cross-section of the cutter tooth can be assumed to be a wedge shape. For plane stress conditions, the solution for the stress field is [15]: w w ðsin 2y þ 2y cos 2fÞ þ , 2 2 ðsin 2y  2f cos 2fÞ w w ðsin 2y þ 2y cos 2fÞ sy ¼   , 2 2 ðsin 2y  2f cos 2fÞ w ðcos 2y  cos 2fÞ try ¼ , 2 ðsin 2y  2f cos 2fÞ sr ¼ 

ð10Þ

where f and w are the wedge angle divided by two and the inflicted load, respectively. The von Mises stress can be expressed in terms of the stress components [16], qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi syp ¼ s2r  sr sy þ s2y þ 3t2ry . (11) The rake angle factor is then given by syp;s fr ¼ syp;c

(12)

where syp,s and syp,c are the von Mises stresses for the standard rake angle and the current rake angle, respectively. In this study, a 5-degree rake angle was selected to correspond to a standard rake angle in experiments. Fig. 7 shows the calculated maximum von Mises stress with respect to the rake angle. Since Eqs. (8) and (9) were derived from the plane stress condition, the absolute values of the calculated results were not the same as the analytical results from the FEM. However, the relative values for the

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-30

-20

-10

Elastical calculation

1.5

15

1.2

12

0.9

9

0.6

6

0.3

3

0

0 10 Rake angle (deg.)

20

to rupture. In this paper, 0.8 was chosen for the critical scaling value based on experimental results.

18

0 30

Fig. 7. Calculated maximum von Mises stress and stress ratio from the FEM analysis.

standard rake angle stresses were quite similar, as depicted in Fig. 7. Thus, this method of calculating rake angle stresses based on the stress of the plane wedge produces reasonable results. The reference force calculated using the above parameters gives the necessary feedrate scheduling criteria for the tetrahedron part of the tooth. As mentioned before, the depth of the cut does not affect the size of the tetrahedron part. Thus, the reference force for the entire axial depth range can easily be determined once the number of tetrahedron parts that can be included in the axial depth range is known. The thickness of the tetrahedron (l) can be calculated from l ¼ b sin yh .

(13)

Since the reference cutting force is the normal pressure cutting force, it must be transformed into the x, y, and zdirectional cutting forces. The frictional cutting force (Ff) is determined by the normal pressure cutting force and a frictional cutting force coefficient (Kf as follows [13]: kF f k ¼ K f kF n k.

(14)

Because the normal pressure cutting force and the frictional cutting force are perpendicular, the resultant cutting force is given by qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi F ¼ kF n k 1 þ K 2f . (15) Using Eq. (15), the final form of the reference cutting force, which is the resultant value of the normal and the frictional reference cutting forces, can be determined. Finally, the minimum value between RFb and RFc is selected as the reference cutting force as follows: RF ¼ CS minðRFb ; RFc Þ,

(16)

where CS is a critical scaling value. The tool starts to rupture when the critical scaling value is 1. The objective of the reference cutting force is to avoid this damage. Thus, the critical scaling value was introduced to reduce the reference cutting force from the point where the tool begins

3.2. Model validation The calculated reference cutting forces about a flat end mill, which had a diameter of 10 mm and a helix angle of 301 with respect to the rake angle, are shown in Fig. 8. The cutting conditions used were axial depths of 1 and 1.5 mm and a standard rake angle of 51. To verify the performance of the developed model, the critical scaling value was not used. To validate the developed reference cutting force model, cutting forces were measured over a wide range of cutting conditions. Experiments were performed on a vertical machine tool (Daewoo Heavy Industries and Machinery Ltd., ACE-V30) using flat end mills that had various rake angles. The workpiece material was SKD41, which has a hardness of HRC 30. The instantaneous three-dimensional cutting forces were measured with a tool dynamometer (Kistler, Dyn.9257A). The width of the cut was 1 mm and the spindle speed was 1000 rpm.The other cutting conditions, measured maximum resultant cutting forces, and calculated reference cutting forces for each test are listed in Table 3. There were only two tests in which chipping occurred. In Test 4, the measured cutting force was greater than the calculated cutting force and chipping occurred after 4 s, as shown in Fig. 9(a). After chipping occurred, the cutting force suddenly rose because the end of the tooth was no longer sharp. In Test 7, the measured cutting force was greater than the cutting force of Test 4. However, there was no chipping because the axial depth of the cut was greater, which increased the reference cutting force as described by Eq. (6). When the rake angle was set to 31, only the cutting force of Test 11 exceeded the reference cutting force; chipping occurred under this condition, as depicted in Fig. 9(b). In the figure, the initial cutting force is almost the same as the reference cutting force, and the cutting force increases after chipping occurs. This demonstrates that the developed model can accurately predict the onset of tool failure. Thus, the critical scaling value given by Eq. (16) 1500 Reference cutting force (N)

FEM 1.8avg.

Stress ratio

FEM max.

Stress (MPa)

164

1.0mm da

1.5mm da

1200 900 600 300 0

-30

-20

-10

0 10 Rake angle (deg.)

20

30

Fig. 8. Calculated reference cutting forces with respect to the rake angle.

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Table 3 Experimental cutting conditions, measured maximum resultant cutting forces, and calculated reference cutting forces under each condition No.

Rake angle (deg.)

Axial depth of cut (mm)

Feedrate (mm/min)

Max. resultant cutting force (N)

Reference cutting force (N)

Chipping

1 2 3 4 5 6 7 8 9 10 11 12 13 14

13 13 13 13 13 13 13 3 3 3 3 3 3 3

1 1 1 1 1.5 1.5 1.5 1 1 1 1 1.5 1.5 1.5

100 300 500 700 100 300 500 100 300 500 700 100 300 500

101 236 241 441 135 325 468 150 303 414 515 200 423 567

380 380 380 380 569 569 569 514 514 514 514 771 771 771

N N N Y N N N N N N Y N N N

must be used when calculating the reference cutting force for feedrate scheduling. 4. Feedrate scheduling An appropriate reference cutting force permits more effective feedrate scheduling and improves productivity. To evaluate the proposed reference cutting force model, it was applied to a feedrate scheduling problem for a rectangularshaped pocket machining operation. Three critical scaling values, 0.5, 0.8, and 1.0, were used to confirm the relevance of this parameter. 4.1. Feedrate scheduling method The developed reference cutting force model was installed in the feedrate scheduling system that was developed in our earlier research [7]. This feedrate scheduling system, which is based on an improved cutting force model that can accurately predict the cutting forces for general machining situations, can regulate the cutting force to a specified level [17]. The feedrate scheduling begins by loading the NC code, after which each block in the NC code is simulated one by one. After calculating the cutting forces in each block, the original block of the NC code is divided into smaller blocks with optimized feedrates that adjust the peak value of the cutting forces to the reference cutting force. The reference cutting force is calculated using the tool geometry information and the calculated cutting configurations, and is then used to calculate the optimized feedrate. 4.2. Experimental Results Feedrate scheduling for rectangular-shaped pocket machining was performed. Fig. 10 shows the tool path and workpiece geometry. The spindle speed was 1000 rpm

and the original feedrate was 100 mm/min. The workpiece material and tool geometry were the same as used in the experiment to validate the developed model. The tool had a rake angle of 31, and the axial depth and width of the cut were 2 and 1 mm, respectively. The offset value for the tool path was set to 1 mm.The cutting forces were measured during machining and compared with the simulated results. Fig. 11 shows a comparison between the measured and predicted cutting forces at the initial feedrate. The predicted maximum resultant cutting forces are in good agreement with the measured values. Feedrate scheduling was performed for three different reference cutting forces: 440, 704, and 881 N. These were calculated using the developed model for critical scaling values of 0.5, 0.8, and 1.0, respectively. The scheduled feedrates are depicted in Fig. 12. Fig. 13 compares the maximum resultant cutting forces obtained with the initial and scheduled feedrates using the different reference cutting forces. The cutting forces were clearly regulated to the desired level. The total machining time was reduced by between 57% and 76%. When the reference cutting force was set to 881 N using the critical scaling value of 1.0, chipping occurred at the end of the tooth, as shown in Fig. 13(a). However, when the reference cutting force was calculated using a critical scaling value of 0.8 or 0.5, chipping did not occur, as depicted in Fig. 13(b) and (c). The chipping on the flank surface (FC region in Fig. 13) is not caused by the cutting force but by the initial cracks. If there is no initial crack, the inflicted cutting force cannot make the chipping on flank surface without the chipping in the end of a tooth because the largest stress is concentrated on the tetrahedron part. A load of 880 N or slightly less causes chipping to occur; therefore, a load less than 704 N provides safe cutting conditions. These results show that the developed reference cutting force model can determine the exact chipping load and the selected critical scaling value is an optimum value that prevents tool failure.

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1st 2nd 3rd 4th

16 Fig. 10. Tool path and machined workpiece geometry.

500

Measured cutting force

Predicted cutting force

Cutting Force (N)

400

300

200

100

0 0

3

6

9 12 Time (sec.)

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Fig. 11. Comparison between measured and predicted maximum resultant cutting force for the third loop of tool path.

RF440N(CS0.5)

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700 600 500 400 300 200 100 0 0

1

2

3 3 Time (sec.)

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Fig. 12. Scheduled feedrates using the various reference cutting forces.

Fig. 9. Measured maximum resultant cutting forces and tool failures.

5. Conclusions In this paper, a reference cutting force model was developed to increase the efficiency of feedrate scheduling. The model was derived considering the TRS of the tool material. The area of the rupture surface and other effects were calculated using a FEM analysis to predict the exact

point at which tool breakage and chipping would occur. By analyzing the results, the effects of various cutting parameters on the chipping phenomenon were determined. The calculation method for the reference cutting forces considered the area of the rupture surface, effect of the rake angle, and axial depth of the cut. The reference cutting force calculated using the developed model was applied to feedrate scheduling for pocket machining. The total machining time was reduced from 21 to 6 s, saving 71% of the cutting time without causing any chipping. The

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Fig. 13. Comparison of maximum resultant cutting force at the initial and scheduled feedrates using different reference cutting forces.

reference cutting force calculated by the developed model provides an effective criterion for a feedrate scheduling system that regulates cutting force at a given criterion. Therefore, safer and more productive cutting operation can be achieved using this system. Acknowledgements The financial support obtained from the National Research Laboratory Program of the Ministry of Science and Technology is greatly appreciated. References [1] W.P. Wang, Solid modeling for optimizing metal removal of threedimensional NC end milling, Journal of Manufacturing Systems 7 (1) (1998) 57–65. [2] D.J. Jang, K.S. Kim, J.M. Jung, Voxel-based virtual multi-axis machining, International Journal Advanced Manufacturing Technology 16 (10) (2000) 709–713. [3] D.M. Sheen, C.H. Lee, S.D. Noh, K.W. Lee, A process planning system for machining of dies for auto-body production—operation planning and NC code post-processing, International Journal of Precision Engineering & Manufacturing 2 (3) (2001) 69–78. [4] Y.S. Tarng, Y.Y. Shyur, B.Y. Lee, Computer-added generation of the cutting condition in pocket machining, Journal of Materials Processing Technology 51 (1995) 223–234. [5] E.M. Lim, C.H. Menq, Integrated planning for precision machining of complex surface, Part 1: cutting-path and feedrate optimization, Int. J. Mach. Tools & Manufacture 37 (1) (1997) 61–75.

[6] B.K. Fussell, R.B. Jerard, J.G. Hemmett, Robust feedrate selection for 3-axis NC machining using discrete models, Journal of Manufacturing Science and Engineering 123 (8) (2001) 214–224. [7] H.U. Lee, D.W. Cho, An intelligent feedrate scheduling based on virtual machining, International Journal of Advanced Manufacturing Technology 22 (2003) 873–882. [8] S.H. Bae, K.H. Ko, B.H. Kim, B.K. Choi, Automatic Feedrate Adjustment for Pocket Machining, Computer-Aided Design 35 (2003) 495–500. [9] B.U. Guzel, I. Lazoglu, Increasing Productivity in Sculpture Surface Machining via Off-line Piecewise Variable Feedrate Scheduling Based on the Force System Model, International Journal of Machine Tools & Manufactures 44 (2004) 21–28. [10] J.H. Ko, D.W. Cho, Feed rate scheduling model considering transverse rupture strength of a tool for 3d ball-end milling, International Journal of Machine Tools & Manufactures 44 (2004) 1047–1059. [11] S.M. Lee, Dictionary of Composite Materials Technology, Technomic Pub. Co.,1989. [12] K.W. Kim, Predicting cutting forces in face milling with the orthogonal machining theory, International Journal of Precision Engineering and Manufacturing 6 (3) (2005) 13–18. [13] W.S. Yun, D.W. Cho, K.F. Ehmann, Determination of constant 3d cutting force coefficients and runout parameters in end milling, Transactions of NAMRI/SME 27 (1999) 87–92. [14] ISO 8688-2, Tool Life Testing in Milling, Part 2: End Milling, 1989, pp. 1–26. [15] R. Richards Jr., Principle of Solid Mechanics, CRC Press LLC, 2001. [16] A. R. Ragab, S. E. Bayoumi, Engineering Solid Mechanics, CRC Press LLC, 1999. [17] J.H. Ko, W.S. Yun, D.W. Cho, K.F. Ehmann, Development of a virtual machining system, Part 1: approximation of the size effect for cutting force prediction 42 (2002) 1595–1605.