Prediction of Cutting Forces in Milling Stainless Steels Using Chamfered Main
Cutting Edge Tool
Chung-Shin Chang
*
Abstract
To study the cutting forces, the carbide tip’s surface temperature, and the mechanism of secondary
chip and main chip formation of face milling stainless steel with a chamfered main cutting edge has been
investigated.
Theoretical values of cutting forces were calculated and compared to the experimental results
with SUS 304 stainless steel plate as a workpiece material.
Force data from these tests were used to
estimate the empirical constants of the mechanical model and to verify its prediction capabilities.
comparison of the predicted and measured forces shows good agreement.
A
A preliminary discussion is also
made for the design of special tool holders and their geometrical configurations.
Next, the tips mounted in
the tool holders are ground to a chamfered width and the tool dimensions are measured by using a toolmaker
microscope.
Key Words: Face milling, oblique cutting, chamfered main cutting edge, stainless steel
*
Professor, Dept. of Mechanical Engineering, National Ilan University, I-Lan, Taiwan, 26014, R.O.C.
I. Introduction
The practical application of alloy steels in modern mechanical manufacturing is quite popular and most
of these alloy steels are difficult to cut, especially stainless steel.
The variety of structures and compositions
currently available in stainless steels provides a range of mechanical properties and corrosion resistance,
which affords a high degree of design versatility [1].
for the production of flat surfaces.
Face milling is a machining process used extensively
Intermittent cutting and high productivity rates characterize it.
simple and complex workpiece shapes can be face milled by [2, 3].
Both
Lin [4] showed from the stand-point of
tool life by chipping on face milling stainless steel, the feed-rate range can be cataloged into three regions: in
the high-feed rate region, the cutting edge of the tool is chipped with built-up edge; in the medium feed-rate
region, the cutting edge of the tool is chipped with no built-up edge; whilst in the low feed-rate region
chipping rarely occurs.
It was also observed that a cutting speed of 85m/min is optimum to remove the
maximum volume of metal.
However, the main failure mechanism of the cutting tool is wear than chipping
when face-milling stainless steel.
good finish machined surface.
Recently, in the interest of increased productivity, heavy cuts can produce
The cutting efficiency could increase significantly if a high power machine
tool and cutting tools are selected properly.
A good tool needs sufficient hardness and the appropriate
geometry. Shaw [5] demonstrated silver-white chip (SWC) tools could decrease energy by 15 %, and
prolongs tool life by 20%, compared with that of conventional tools, but tool wear inevitable.
Hoshi [6]
studied extensively the characteristics of the built-up edge (BUE) and developed SWC tool in face milling
method.
The method involved tool geometries that produce a BUE which flows away continuously in the
form of a separated secondary chip. For an understanding of the cutting dynamics, Kim and Ehmann [7]
showed the knowledge of the cutting forces is one of the most fundamental requirements.
These
knowledges also give important information for cutting design, machine tool design and detection of tool
wear and breakage.
There have been many analyses of the three-dimensional cutting forces [8, 9].
Compared with the other factors, cutting force has a great effect on the dynamics of the cutting process as
well as the machine tool structure; therefore a full understanding of cutting force variation is crucial.
Usui
et al. [10] have presented a basic model with a single point tool and a nose-radius tool, applying the energy
approach method to predict the cutting force.
For predicting the correct cutting forces, however, shear plane
areas must be cooperated with the wear effects of tool edge during the cutting process.
Young [11] had arranged a special experiment set-up, and performed a series of experiments.
showed that a good correlation between the milling and turning was obtained for the same conditions.
It
He
concluded that to the use of steady state intermitted cut operation such as face milling is recommended.
Chang [12] has presented that milling of medium carbon steel with chamfered main cutting edge tools could
improve cutting efficiency.
from his discussion.
However, the effects of tool with face milling stainless steel were excluded
In this paper, the effects of sharp inserts on milling forces and the shape of chips are
examined to predict the theoretical milling forces.
Theoretical results will compare with experimental
cutting forces for the chamfered main cutting edge tool in milling of stainless steel plate.
II. Methods of Solution
Pandey and Shan [13] employed a single shear plane model to develop an analytical force model for
face milling.
A force model for face milling stainless steel with chamfered main cutting edge tools which
deal with the realities of more complicated machining situations should be systematically organized and
computerized.
Nakayama [14] et al. investigated the relationship between the cutting forces, temperatures,
surface roughness and BUE; the results indicated that the cutting forces were low when BUE was present.
A chamfered main cutting edge tool, which can produce a secondary chip, reduces the cutting force and aids
thermal dissipation. The results indicated that, for ease of chip flow, the lead angle C s should fall in the
range of 20 ° to 40 ° .
The edge of the negative radial angle α r 1 lightly contacts the workpiece and
participates in the cutting action.
according to Eq. (1).
Once C s , α r 1 , α r 2 and R were determined, the cut depth was selected
The choice of the width of chamfer,We , the value of the negative radial angle, α r 1 ,
positive radial angle, α r 2 , and the value of C s will greatly affect the ease of chip flow and the resulting
surface roughness of the workpiece.
We<f cos Cs, where f represents the feedrate, and C s denotes the lead angle of the tool
(1)
Based on the experimental results of Hoshi [6], and Chang [12], the basic force model for a sharp corner
tool with a chamfered main cutting edge ( R = 0) shown in Fig. 1 was derived as follows:
(i) The energy method to predict cutting force
U=Us+Uf
The shear energy (U s ) and the friction energy (U f ) were proposed by Usui [10] as:
V cos α e
τ s sin β cos α e QV
(3), and U f = Ft Vc = f t ∫0B1 dbVc =
U S = FS V S = FS
cos(φ e − α e )
[cos(φ e + β − α e ) cos(φ e − α e )]
(2)
(4)
Where ∫0B1 db is the integral width of chip flow direction along the tool face, (Fig. 2). B1 is the width
measured in the direction orthogonal to the chip flow, db is an increment of integration in that direction, as
shown in Fig. 2.
FS = τ S A,
ft =
(5), and V S =
V cos α e
cos (φ e − α e )
(6)
τ s t1 sin β
, (notation: f t is the frictional force in orthogonal cutting for unit width of
[cos(φ + β − α ) sin φ ]
cut and t 1 is the undeformed chip thickness (Fig. 2))
V sin φ e
,
Vc =
cos(φ e − α e )
(7)
The relation between η ' c and η c on the tool face is:
η ' c = tan −1 [(tan η c − sin α r 2 tan α a cos α a cos α r 2 ]
(8)
According to this equation, the shear plane can be verified by changing η c over a small number of
values ∆η c , and
sin α e = sin −1 (sin α r 2 cosα a cos η c + sin η c sin α a )
(9)
where the symbol α e represents the effective rake angle (rad), α a denotes the axial angle (rad), φe
is the effective shear angle and equals to 0.581 α e -1.139 (rad), β is the friction angle (rad) which equals to
exp (0.848 α e -0.416) [10], τ s is the shear stress which equals to 571 - 19.9 α e ( MN m 2 ) [15], and η c is
the chip flow angle which is determined by minimizing the total cutting energy U .
The constitution of the shear plane area, A, and the friction area, Q, is plotted in Fig. 1, and they will be
obtained from the following equations:
(ii) The shear areas in the cutting process for sharp tool
A = A1 + A 2 + A s
A1 =
t3
2
{
4 cos 2 α e
4 cos α r 2 sin φ e cos η c
2
2
2
− [1 +
cos 2 α e
sin φ e cos η c
2
2
−
1
[sin2 ηc + ( sinα e +
cos 2 ηc
1
cos α e cot φ e ) 2 − 2 sin η c ⋅ sin α a (sin α e + cos α e ⋅ cot φ e )]] 2 } 2 (the area of triangle BCE);
(10)
t tan η c
2b
)
− 3
1
cos α a
cos α r 2
2
A2 =
× {cos 2 α e − sin 2 φ e [sin η c − (sin α e + cos α e cot φ e ) sin α a ] } 2 (the area of
2 sin φ e cos α r 2 cos η c
t3 (
trapezoid CEFD),
(11)
and
As =
(W e cos α r 1 ) 2 tan C s
2( cos α a sinφ e )
(the area of triangle D' YJ )
(12)
A1 + A2 is the area of main chip, and As is the area of secondary chip, which is a triangule in Fig. 1.
The area of the projected cross section Q is equal to Q1 + Q2 + Q3 .
t3
1 b +b
Q1 = ( 2
(the area of the trapezoid LBCD );
)
2 cos α a cos α r 2
t b
Q2 = 2 2 (the area of the rectangle CC ' DD' );
cos α a
We cos α r1 tan C s
(the area of triangle DD' Y )
2 cos α a
(13)
(14)
2
Q3 =
(15)
where coefficients of t1 , t 2 , t 3 , f 1 , b, b2 and b4 are described in Appendix A.
According to the above investigations, the cutting force is a function of parameters α r 1 ,α r 2 ,α a , d ,
W e ,θ ref ,C S ,C e , f ,V and ηc .
formation can be determined.
Once η c had been determined, then α e , φe ,τ s and β that describe chip
By changing the value of η c in the developed computer program, the
cutting force can be calculated.
energyU min .
The angle η c can be determined by considering the minimum
The calaulation procedure for the cutting force is shown in Fig. 3.
The cutting force, F H , can be determined by applying the equation by Reklaitis et al. [16] as:
U min = V ( FH ) U min ,
(16); where U min = U s + U f
and F H is the cutting force and V is the cutting speed. Therefore,
τ cos α e A
τ s sin β cos α e Q
U
FH = ( FH )U min = min = { s
+
}
V
cos(φ e − α e ) [cos(φ e + β − α e ) cos(φ e − α e )]
(17)
(18)
and
( R t ) H = N t cos α r 2 cos α a + ( Ft ) U min sin α e = ( FH ) U min
where Ft =
τ s sin β cos α e Q
[cos(φ e + β − α e ) sin φ e ]
Hence, N t can be rewritten as
[(FH )U min − (Ft )U min sin α e ]
Nt =
(cos α r 2 cos α a )
(19)
(20)
(21)
In Eq. (19) ( Rt ) H is the horizontal cutting force in the horizontal plane, N t is the normal force at the
tip surface with minimum energy. Therefore, transverse cutting force, FT , and vertical cutting force, FV ,
can be expressed by the following:
FT = − N t cos α r 2 sin α a + Ft (sin η c cos α a − cos η c sin α r 2 sin α a )
(22)
FV = − N t ⋅ sinα r 2 + Ft cos η c ⋅ cos α r 2 .
(23)
Due to the size effects, a modified cutting force is presented in this paper to get more precise results.
Besides the horizontal force F H , the plowing force F p due to the effects of the tool edge and the wear
force FW due to the effects of flank wear [12] are considered in the prediction of the modified horizontal
cutting force, ( FH ) M , as illustrated in Fig. 4.
(iii) Modified force model
(FH )M = (FH )U min + FW + FP
That is
(24), F p = HB ⋅ r ⋅ L f
(25), and FW = τ y L f Vb
(26)
where HB is the Brinell hardness of the workpiece, r is the radius on the main cutting edge between the
face and flank. Vb is flank wear of tips and for simplification, the value of Vb is set to be 0.05mm. L f is
the contact length between the cutting edge and the workpiece and L p is the projected contact length
between the tool and the workpiece, as referred to [12], can be determined according to the following
conditions.
Lf =
f 1 ⋅ cos C s
f 1 ⋅ cos C s ⋅ cos C e
d
d
) sinC s +
(28)
+
(27),and L p = (
cos C s
[cos α r 2 ⋅ cos (C s − C e )]
cos C s [cos (C e − C s ) ⋅ cos α r 2 ]
The modified transverse cutting force (FT
degree of tool wears.
)M
is equal to FT (Eq. 21) plus a thrust force caused by the
This thrust force can be estimated ( L pVb ) by the yield strength of the workpiece σ y .
The (FT )M is shown in Eq. (29). The modified vertical cutting force ( FV ) M is equal to, FV (from Eq. 23)
plus a shear force caused by tool wears.
of the workpiece τ y .
(FT )M
This shear force can be estimated (Vb L p ) and the shear strength
The expression of ( FV ) M is shown in Eq. (30).
= FT + L p ⋅V b ⋅ σ y ,
(29), and ( FV ) M = FV + L pVbτ y
(30)
If the Brinell hardness of the workpiece, HB , is given, the expression of σ y and τ y , are given by
Cook [17]
τ s = σ y 2 , σ y = HB π .
(31)
Based on Fig.5, the final modified cutting force, FHH , FTT and FVV can be calculated by
FHH = (FH )M
(32), and FTT = (FT )M cos C s + (FV )M sin C s ,
FVV = (FV )M cos C s − ( FT ) M sin C s (fo r Cs ≠ 0° )
(33)
(34)
Face milling is one of the most important machining processes, which inherently have a high metal
removal rate due to multitooth cutting. In Fig. 6, each tooth of the cutter has an entry angle and exit angle,
and both vary with the workpiece and cutter diameter, the values will alter at θ X = 0 o ~ 180o . To
understand the whole process of the cutting force pulsation, the complete process ( θ i = 0 o , θ f = 180o ) will
be presented in this paper.
motion.
In face milling, the cutter has a rotary motion and the workpiece has a plane
By contrast with the turning operation, as shown in Fig. 7, the workpiece carries out a rotary
motion and the tool has a plane motion. But as long as the feedrate is small, the cutting velocity, the radial
angle ( α r ), the axial angle ( α a ), the undeformed chip thickness, and the normal rake angle, which all vary
by less than 5% [18], so that the path can be approximated as a circle without much loss in accuracy. The
tooth path of a face-milling cutter is a cycloid as shown in Fig. 6. The comparison of tool geometry
between the face milling cutter and turning tool is shown in Fig. 7. Where the radial angle, α r 2 , the axial
angle, α a , and lead angle of face milling cutter are equal to the second normal side rake angle, α s 2 , the back
rake angle, α b and the side cutting edge angle, C s , repectively.
As shown in Fig. 6, the undeformed chip
thickness of the tooth path is divided into a series of elements, 10 degrees in each element, in which
undeformed chip thickness ( t 1 ) is the central cross section between both sides. Comparing the chip cross
section with the turning process, it is realized that the f (feed per tooth) and d of face milling are equal to
f
(feed per revolution) and d (cutting depth) in turning, so that the undeformed chip thickness and
cutting width W in face milling process are calculated by the following equations:
t1 = fθ cos Cs
(35), fθ = f sin θ X
(36), and W = d cos Cs
(37)
where f = feedrate (rev ⋅ per ⋅ tooth) .
Figure 7 shows the unit chip cross section and various cutting force components exerted on workpiece
at cutting edge where FHH , FVV and FTT are equal to the cutting force components in turning. Since the
directions and magnitudes of the elemental oblique cutting force components FHH , FVV and FTT will vary
from element to element, these can be resolved into the fixed and practical directions X , Y and Z .
cutting forces are given by
FX = FHH cosθ X + FVV sin θ X
(38), FY = FHH sin θ X − FVV cosθ X
(39), and FZ = FTT
Thus the
(40).
(iv) Experiment method and procedure
In previous sections, the cutting force model for various cutting conditions and tool geometries were
derived. To verify these force models, experiments were conducted using the set-up in Fig. 8; a sampling
rate of 1024 samples sec was found to be sufficient for the experiments. The experiments were on a
vertical machining center using a plate face milling process without using any cutting fluids. It was
required to measure the cutting force components FHH , FVV and FTT (Figs. 5 and 6) for a range of cutting
conditions and tool geometrical factors.
The machine tool used for the tests was a leadwell vertical
machining center (MCV-OP) having a variable feed range with 1~10000mm/min, motor with
speeds 60 ~ 6000rpm, rating up to 3. 7 5.5 kW . In measuring the cutting forces a Kistler type 9257B,
three-component piezoelectric dynamometer was used with a data acquisition system that consisted of Kistler
type 5807A charge amplifiers, all measured data were recorded by a data acquisition system (Keithley Metro
byte-DAS1600) and analyzed by the control software (Easyest).
checked constantly by repeating the experiments.
The reliability of the measurement data was
Since the manufacturers do not provide tools with
selected combinations of lead, radial, axial and inclination angles, special tool holders were designed and
manufactured in house.
The cutting tool used in the experiment was Sandvik P10 [19] and the workpieces were SUS 304.
The
experimental conditions were maintained the same for all tests as follows:
(1) dry cutting; (2) cutting velocity,V = 75 m min( N = 250 rpm ) ; (3) cutting depth: d = 0.5 and d = 1
mm; (4) rate of feed: f = 50 mm min ; (5) the tool holder was vertical to the workpiece.
Oblique milling tests were carried out for each tool.
In the test for each tool geometry the workpiece
was milled 170 mm in the feed direction, while the data were recorded three times at different depths.
results were then averaged.
The
The cutting force, the shapes of chips and tips wear were observed and
discussion in sections III.
III. Results and Discussion
(i) Shape of chips
The milling tests were described in the previous section.
Fig. 9 shows photographs of the chips
obtained with the three tool holders (6 tips) when the nose radius of the tips was 0.03 mm and the lead angle
was 20 o , 30o and 40 o .
It can be observed from the resulting chips that:
1. Due to the larger effective shear angles and smaller friction angles (revealed by the aid of the flow chart in
Fig. 3), the secondary chip was formed more obviously and flowed more easily under the situations of
α r1 = −30o and α r 2 = 30 o , and shown in Figs. 9(a)-9(f). Therefore, α r1 = −30° and α r 2 = 30° are the ideal
radial angles to produce secondary chips.
2. During the milling process, it is easier for the secondary chip to flow out, as a lead angle ( C s ) of the
chamfered main cutting edge milling tool was 30o .
3. Regardless of the value of the nose radius, a secondary chip forms for α r1 = −30o , α r 2 = 30° and
C s = 30 o .
This result leads to the conclusion that C s , α r1 and α r 2 affect the formation of the secondary
chip but not R .
(ii) The cutting forces and current consumption
From Eqs. (10)-(15), the shear area A and projected area Q were calculated. After the shear area (A)
and projected area (Q) were obtained, the shear energy per unit time ( U s ) and the friction energy per unit
time ( U f ) were calculated from Eqs. (3)-(4). The theoretical principal component of the cutting force
( FH )U min was then obtained from Eqs. (16)-(18); the vertical theoretical cutting force ( FV ) and the
transverse theoretical cutting force ( FT ) were obtained from Eqs. (19)-(23).
The flank wears and plowing
force must be taken into account in order to obtain the modified three-axis turning forces FHH , FVV and
FTT (Fig. 4) that were obtained from Eqs. (24)-(34) and the three axis milling forces FX , FY and FZ that
were obtained from Eqs. (35)-(40) respectively. The values of the theoretical, modified and experimental
results for FX , FY and FZ are plotted respectively in Figs. 10-14. The following conclusions were
obtained from these results.
1. Fuh and Chang showed that increasing the side rake angles α s 1 and α s 2 , decreases the cutting
forces F HH , FVV and FTT as Ref. [15]. Similarly in this study, for a constant lead angle C s ,
and nose radius R=0 mm, Fig. 10-12, that increasing the radial angles α r 1 and α r 2 , decreases the
cutting forces F X , FY
and F Z .
Because the contact length between the chip and the tips is
shortened, the effective radial angle and effective shear angle are increased but the friction angle is decreased.
The symbols α r 1 ( α s 1 ), α r 2 ( α s 2 ), F HH , FVV … FY and F Z are shown in Figs. 5-7. (Note: The
side rake angle in the papers of Fuh and Chang [15] is denoted by α s , here we use α r , which is
shown in Table 1 too.)
2. In Figs. 10-14, we find that in the case of a constant radial angles ( α r1 and α r 2 ), the increase of the lead
angle, C s , from 20 ° to 30 ° , will induce a decrease in the cutting force because the chip flows more easily
and the secondary chip is produced more clearly.
chip and the tip is decreased.
Especially in this situation, the contact length between the
However, if the lead angle is increased from 30 ° to 40 ° , the cutting force
will increase because the contact length between the chip and the cutter is increased [12].
3. In Figs. 10-14, the theoretical values and the experimental values for chamfered R = 0 (R<f), and
unchamfered milling tool show good agreement.
4. In Figs. 10-14, a face-milling tool with a chamfered main cutting edge decreases the cutting force about
20% more than an unchamfered main cutting edge milling tool. This is because the shear area of chamfered
main cutting edge milling tools is smaller than that of unchamfered main cutting edge milling tools, as
simulated from the flow chart of cutting force prediction in Fig.3, thus leading to the unstable cutting forces.
5. If the flank wear and the plowing force were taken into consideration, the final modified theoretical cutting
forces will be closer to the experimental values.
6. Figs. 10-12, show that FX , FY and FZ increase greatly with tooling on unchamfered main cutting edge.
(iii) Tip wear
The unchamfered main cutting edge with sharpness milling tool ( R = 0 ) has the most wear among the
various tested tools, as shown in Fig. 15, because the tools with the largest cutting force produce a secondary
chip with more difficulty.
IV. Conclusions
A new model has been constructed to predict the cutting forces of face milling, for the cases of
chamfered, R = 0 ( R < f ), and unchamfered sharpness tool ( R = 0 ). The predicted cutting forces for
face milling are in agreement with those obtained by experiments. With the increase of the first and second
radial angles, the cutting forces FX , FY and FZ decrease. But when Cs = 30o , and α r1 = α r 2 = 30o , the
cutting forces are at the lowest levels, so this is an ideal tool geometry because the areas of shear and friction
are the smallest.
Using chamfered main cutting edge milling tools under suitable cutting conditions, the
chips flow away more easily.
This effect can also increase the impact value and the strength of tips, as well
as avoiding the tool fracture.
A new tool model is successful to calculate the variation of shear areas using
the energy approach and can predict the three-dimensional face milling cutting forces when the tool is either
chamfered or unchamfered.
Acknowledgements
The National Science Council, Taiwan, R.O.C. supported the work under grant No. NSC-91-2212-E-197-001
Normcultures
A:
area of shear plane ( mm 2 )
FH :
theoretical horizontal cutting force (N)
Ft :
friction force (N)
Fs :
shear force(N)
FT :
theoretical transversal cutting force (N)
FV :
theoretical vertical cutting force (N)
FX :
milling force in X-axis direction (N)
FY :
milling force in Y-axis direction (N)
FZ :
milling force in Z-axis direction (N)
fθ :
feed rate of cutting position
i:
inclination angle (rad)
r:
main cutting edge radius (mm)
R:
nose radius(mm)
V :
Vc :
cutting velocity (m/min)
chip velocity (m/min)
Vs :
shear velocity (m/min)
We :
chamfering width (mm)
α :
αa :
rake angle (rad)
θi :
axis direction angle (rad)
entry angle (rad)
θf :
exit angle (rad)
θX :
alter entry angle (rad)
θ ref :
φ :
side relief angle (rad)
σy :
yield normal shear stress ( N / mm 2 )
shear angle in orthogonal cutting (rad)
τy :
yield shear stress ( N / mm 2 )
τs :
shear stress ( N / mm 2 )
Appendix A
A.
Variables for the tool with a sharp corner, Fig. 1 ( R = 0 )
t 1 = f cos C s
(A1), t 2 =W e ⋅ cos α r 1
(A2) and t 3 = t 1 − t 2
f1 = f −W e ⋅ cos α r 1 (A4), b = d cos C s (A5), b4 = t 2 ⋅ tan C s (A6), and b 2 = b − b 4
(A3)
(A7).
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Single-Point Oblique Cutting Tools with Other than Single Straight Cutting Edges and Milling and
Experimental Verification," Ph. D., Universities of New Wales, Australia (1986)
[19] Brookes, K. J. A., World Dictionary, Handbook of Hard metals and Hard Materials, Int. Carbide Data
Handbook, UK, pp. 10-12 (1992).
Table 1 Tool geometry specifications
Fig. 1 Detail model of the shear plane A(A=A1+A2+AS) and the projected area Q(Q= Q1+Q2+Q3) with the chamfered main cutting
edge, f>R, R=0,(αr : radial angle, φe: shear angle, ηc : chip flow angle)
Fig. 2 Calculation of friction forces on the tool face, f>R, R=0 (αr : radial angle, αb=αa, αb: parallel back angle, β: friction angle, φe: shear
angle, ηc: chip flow angle, t1=undeformed chip thickness)
Fig. 3
Fig. 4
Flow chart of cutting force prediction
The composition of modified (FH)M
Fig. 5 Rotation of main cutting edge and positive
directions of force components (final force)
Fig. 6 Cutting forces model of face milling
and cutting geometric relationships
Fig. 7 Tool geometric angles between (a) turning
and (b) milling cutter
Fig. 8
experimental set-up
(a) αr1=-10˚, αr1=-10˚
(d) αr1=-30˚, αr1=-30˚
(b) αr1=-30˚, αr1=-30˚
(c) αr1=-10˚, αr1=-10˚
(e) αr1=-10˚, αr1=-10˚
(f) αr1=-30˚, αr1=-30˚
180
160
140
120
100
80
60
40
20
700
600
500
400
300
200
100
0
-100
-200
0
Fig. 9 Chip shapes with: (a)(b) CS=20˚; (c)(d) CS=30˚; and (e)(f) CS=40˚;of chamfered cutting edge tools at f>R, R=0,
f=45mm/min, d=0.5mm and V=75m/min
Fz: theoretical values (unchamfer edge, R=0mm)
Fy: theoretical values (chamfer edge, sharp,R=0)
Fx: theoretical values (chamfer edge, sharp,R=0)
Fx: theoretical values (unchamfer edge, R=0mm)
Fy: theoretical values (unchamfer edge, R=0mm)
Fz: theoretical values (chamfer edge, sharp,R=0)
Fig. 10 Theoretical cutting forces: horizontal (FX), transverse (FY) and vertical (FZ) vs rotating angles (˚ ) for unchamfered and
chamfered (f>R, R=0) tool at Cs=20˚, αr1=-30˚ and αr2=30˚, f=45mm/min, d=0.5mm and V=75m/min (stainless steel)
650
550
450
350
250
150
0
0
0
0
0
18
16
14
12
10
80
60
40
0
-50
-150
20
50
-250
Fx: theoretical forces(chamfer edge, sharp, R=0)
Fy: theoretical forces(chamfer edge, sharp, R=0)
Fz: theoretical forces(chamfer edge, sharp, R=0)
Fx: theoretical forces (unchamfer edge, R=0mm)
Fy: theoretical forces (unchamfer edge, R=0mm)
Fz: theoretical values (unchamfer edge, R=0mm)
Fig. 11 Theoretical cutting forces: horizontal (FX), transverse (FY) and vertical (FZ) vs rotating angles (˚ ) for unchamfered and
chamfered (f>R, R=0) tool at Cs=30˚, αr1=-30˚ , αr2=30˚, f=45m/min, d=0.5mm and V=75m/min(stainless steel)
750
650
550
80
10
0
12
0
14
0
16
0
18
0
60
40
0
-50
-150
-250
20
450
350
250
150
50
Fx: theoretical values (chamfer edge,sharp, R=0)
Fy: theoretical values (chamfer edge, sharp, R=0)
Fz: theoretical values (chamfer edge, sharp, R=0)
Fx: theoretical values (unchamfer edge, R=0mm)
Fy: theoretical values (unchamfer edge, R=0mm)
Fz: theoretical values (unchamfer edge, R=0mm)
Fig. 12 Theoretical cutting forces: horizontal (FX), transverse (FY) and vertical (FZ) vs rotating angles (˚ ) for
unchamfered and chamfered (f>R, R=0) tool at Cs=40˚, αr1=-30˚ and αr2=30˚, f=45mm/min, d=0.5mm and
V=75m/min (stainless steel)
(a) (FX) unchamfered tool
(d) (FY) chamfered tool
(b) (FX) chamfered tool
(c) (FY) unchamfered tool
(e) (FZ) unchamfered tool
(f) (FZ) chamfered tool
Fig. 13 Experimental cutting forces: (a) (b) horizontal (FX) ; (c)(d) transverse (FY) ; and (e)(f) vertical (FZ), vs cutting time(sec) for an
unchamfered and chamfered (f>R, R=0) tool at CS=20˚, αr1=-30˚ and αr2=30˚, f=45mm/min, d=0.5mm and V=75m/min (stainless steel)
(a) (FX) unchamfered tool
(b) (FX) chamfered tool
(d) (FY) chamfered tool
(e) (FZ) unchamfered tool
(c) (FY) unchamfered tool
(f) (FZ) chamfered tool
Fig. 14 Experimental cutting forces: (a) (b) horizontal (FX); (c)(d) transverse (FY) ; and (e)(f) vertical (FZ), vs cutting time(sec) for an
unchamfered and chamfered (f>R, R=0) tool at CS=30˚, αr1=-30˚ and αr2=30˚, f=45mm/min, d=0.5mm and V=75m/min(stainless steel)
top view
top view
front view
front view
(a) unchamfered tool
(b) chamfered tool
Fig. 15 The wear of tips (a) an unchamfered (R=0) and (b) a chamfered (f>R, R=0) main edge tool at CS=30˚, αr1=-30˚ and αr2=30˚,
f=45m/min, d=0.5mm and V=75m/min (stainless steel)