Proceedings of COBEM 2005
Copyright © 2005 by ABCM
18th International Congress of Mechanical Engineering
November 6-11, 2005, Ouro Preto, MG
ANALYSYS OF THE DYNAMIC STABILITY OF HIGH SPEED FINISHING
END MILING AND BALL-END MILLING
Walter Lindolfo Weingaertner
Universidade Federal de Santa Catarina, Departamento de Engenharia Mecânica, Laboratório de Mecânica de Precisão, Campus
Universitário, Caixa Postal 476, EMC - CEP 88010-970, Florianópolis/SC - Brasil
e-mail: wlw@emc.ufsc.br
Rolf Bertrand Schroeter
Universidade Federal de Santa Catarina, Departamento de Engenharia Mecânica, Laboratório de Mecânica de Precisão, Campus
Universitário, Caixa Postal 476, EMC - CEP 88010-970, Florianópolis/SC - Brasil.
e-mail: rolf@lmp.ufsc.br
Milton Luiz Polli
Centro Federal de Educação Tecnológica do Paraná, Departamento Acadêmico de Mecânica, Av. Sete de Setembro, 3165 - CEP
80230-901, Curitiba/PR – Brasil.
e-mail: polli@cefetpr.br
Jefferson de Oliveira Gomes
Centro Integrado de Manufatura e Tecnologia, ITA-CTA, Praça Marechal Eduardo Gomes, 50 - CEP 12228-900, Vila das Acácias
São José dos Campos /SP – Brasil.
email: gomes@ita.br
Abstract. Finishing milling operation is characterized by high interruptions during the cut. The time the tool spend
cutting is just a fraction of one rotation period. The phenomena related to the process dynamic are different from
those found in roughing operations. The influence of the cutting parameters and the system dynamics (tool, tool holder
and spindle) on the stability of high-speed end milling and ball-end milling are investigated in this work. The system
dynamics are identified by impact tests. The workpieces are considered to be rigid. The stability evaluation is based on
the workpiece texture parameters and the analysis of sound pressure measured during the process. In finishing end
milling operations the highest limitation are the regenerative vibrations. Best results are found for the spindle
rotations, whose tooth-passing frequency are close but lower than the natural frequency of the most flexible mode.
Forced vibrations exert higher influence on the results for finishing ball-end milling. Due to the small machining
sections the contact region between tool and workpiece is reduced, and consequently occurs a minimization of the
effects of phase difference between the ondulations left by consecutive teeth, and get more importance the periodic
excitation of the interrupted cut. Best results are found when the harmonics of the tooth passing frequency have a
distance from the natural frequency.
Keywords: high speed milling, end milling, ball-end milling, vibrations.
1. Introduction
In finishing end milling the tool geometry and cutting parameters are chosen in such way to attempt the project
requirements related to surface finish and dimensional precision. Endmills are used to finish plane surfaces, while ballendmills are recommended for finishing of tapered and free form surfaces (Stemmer, 1995). Small radial depth of cuts
leads to a condition of smaller engagement between tool and workpiece. This process is characterized by high
interruptions during the cut. The time the tool spend cutting is just a fraction of one tool rotation period. The
phenomena related to the process dynamic are different from those found in roughing operations (Polli, 2005). The
relative vibrations between tool and workpiece, which arise during the operation, may achieve unacceptable levels and
deteriorate the surface finish and reduce tool life, especially in situations, that demands the use of tools with high
lengths to machine deep cavities, as the ones commonly found in die and mold industries (Tlusty, 1993).
The influence of the cutting parameters and the system dynamics (tool, tool holder and spindle) on the stability of
high-speed end milling and ball-end milling are investigated in this work. The system dynamics are identified by impact
tests. The workpieces are considered to be rigid. The stability evaluation is based on the workpiece texture parameters
and the analysis of sound pressure measured during the process.
2. Metodology
Cutting tests were conduced on a high-speed milling center with a 16000 rpm, 15 kW power spindle and maximum
slide-speed of 30 m/min. The workpiece material was ABNT P20 steel. Six flutes, 12 mm diameter endmills and four
flute, 8 mm diameter ball-endmills were used in the cutting tests. The cutting tool material was cemented carbide with
TiAlN coating. All tests were conducted using fresh tools under dry conditions. The stability evaluation was based on
the workpiece surface finish and the sound pressure measured during the process.
The frequency response functions for each tool were obtained by attaching an accelerometer to the end of the tool,
striking the tool in the direction of the accelerometer with an instrumented hammer and recording the signals
simultaneously by using a signal analyzer.
The surface roughness was used as a relative measure for the process stability. A stable process was characterized
by a relatively fine finished surface, while an unstable process was associated with a deteriorated one. Measurements
were made using the same cut-off (0.8 mm), enabling comparative analysis of the results.
A microphone was chosen as a sensor to detect vibrations during the process because it has an adequate frequency
band and it is able to detect vibrations signal from the tool, workpiece or machine-tool. The system used to measure the
sound pressure was composed by the following elements: ½” free field microphone, sensor signal conditioner, signal
acquisition board, microcomputer and signal analyzer software. The signal acquisition rate was 10 kHz.
3. Results and discussion
3.1. Finishing end milling
The graph in figure 1 shows a Frequency Response Function (FRF) measured at the end of an endmill. The peak of
magnitude occurs in the natural frequency (fn) and corresponds to 1585 Hz.
Magnitude (m/N)
6.0E-06
Tool: Endmill
Diameter (D) [mm]: 12
Length (L) [mm]: 72
Number of teeth (z): 6
Machine: Hermle C800 U
4.0E-06
2.0E-06
0.0E+00
1000
1250
1500
1750
2000
2250
2500
Frequency (Hz)
Figure 1. FRF measured at the end of an endmill
Figure 2 shows a graph of the surface roughness parameter Rz as a function of the spindle rotation for down-milling
and up-milling cuts.
Dow
n-milling
Concordante
Workpiece material: ABNT P20 steel
Up-milling
Discordante
Toll: Endmill
Diameter (D) [mm]: 12
Length (L) [mm]: 72
Number of teeth (z): 6
Surface roughness ((µm)
m)
12
9
Axial depth of cut (ae) [mm]: 2.5
Radial depth of cut (ae) [mm]: 0.25
Feed per tooth (fz) [mm]: 0.05
6
3
0
5000
7500
10000
12500
Spindle rotation (rpm )
15000
17500
Down-milling
Figure 2. Surface roughness as a function of the spindle rotation
Up-milling
Proceedings of COBEM 2005
Copyright © 2005 by ABCM
18th International Congress of Mechanical Engineering
November 6-11, 2005, Ouro Preto, MG
The curves have very close values. There are peaks representing considerably high values for some spindle
rotations. These peaks are the result of vibrations during the process. In these cases, the depth of cut used in the tests
was greater than the limit for a stable cut.
Figure 3 shows the surface profile for a stable condition (n = 13750 rpm). Due to the tool run-out and the forced
vibrations, the distance between the marks observed in the profile corresponds manly to the feed per revolution.
4.0
Workpiece material:
ABNT P20 steel
Profile (µ m)
3.0
2.0
1.0
Down-milling
n = 13750 rpm
ae = 0.25 mm
ap = 2.5 mm
fz= 0.05 mm/tooth
0.0
-1.0
-2.0
-3.0
-4.0
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
5 mm
Length (mm)
Figure 3. Surface profile for a down-milling stable cut
Figure 4 shows the surface profile for a condition next to the resonance (n = 16000 rpm). The depth of wave is
almost 60 µm and the distance between the marks are five times greater than the feed per revolution. The marks tend to
be closer a vertical line because the difference between the tool-passing frequency and the regenerative vibration one is
small.
50.0
Workpiece material:
ABNT P20 steel
Profile (µm)
40.0
30.0
Up-milling
n = 16000 rpm
ae = 0.25 mm
ap = 2.5 mm
fz= 0.05 mm/tooth
20.0
10.0
0.0
-10.0
-20.0
-30.0
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
Length (mm)
5 mm
Figure 4. Surface profile for an unstable cut
The graph of figure 5 shows the sound pressure spectra measured during the down-milling cuts.
For stable cuts, which resulted in lower surface roughness values, the spectra are dominated by the tool-passing
frequency (ft) and its harmonics that have relative low magnitudes. For unstable conditions, the highest peak does not
occur in the tool-passing frequency, but in the regenerative vibration frequency (fv). One exception occurs for n = 16000
rpm, where the magnitude of the tool-passing frequency is higher than the regenerative vibration frequency one.
ft
fv
Workpiece material: ABNT P20 steel
Sound pressure (Pa)
fv
Toll: Endmill
Diameter (D) [mm]: 12
Length (L) [mm]: 72
Number of teeth (z): 6
3
2
1
Down-milling
Axial depth of cut (ae) [mm]: 2.5
Radial depth of cut (ae) [mm]: 0.25
Feed per tooth (fz) [mm]: 0.05
0
2.000
1.500
15.000
12.500
1.000
FrFere
qüque
ên n
500
cia cy
[H (H
z z)
m)
()rp
10.000
7.500
0
m
] pn
rpotm
a(trio
oçr[ão
ã
ç
a
e
t
l
a
R
inod
Sp
5.000
Figure 5. Sound pressure spectra for down-milling cuts
The graph of figure 6 shows the sound pressure spectra measured during the up-milling cuts. There are few
differences in comparison to the spectra of the down-milling cuts. The peaks of the unstable conditions were less
prominent for up-milling cuts. For the stable condition n = 15000 rpm, the peak correspondent to the tooth-passing
frequency was higher, but it did not reflected on the surface roughness value. For the conditions n = 5000 rpm and n =
6250 rpm, the magnitude in the regenerative vibration frequency is lower than the magnitudes of the tooth-passing
frequency and its harmonics for both cutting directions, what indicates the beginning of the instability. In these cases,
the vibrations amplitudes were smaller than the other unstable cases, and they have fewer consequences on the surface
finish.
ft
Workpiece material: ABNT P20 steel
fv
Pressão
[Pa](Pa)
Sound sonora
pressure
fv
Toll: Endmill
Diameter (D) [mm]: 12
Length (L) [mm]: 72
Number of teeth (z): 6
3
2
Up-milling
Axial depth of cut (ae) [mm]: 2.5
Radial depth of cut (ae) [mm]: 0.25
Feed per tooth (fz) [mm]: 0.05
1
0
2.000
15.000
1.500
1.000
FFrereq
qü ue
ên nc
500
cia y (
[H H
z
z] )
12.500
)
pm
n] (r
o
i
t
m
ota[rp
7.500
le r o
inodta çã
p
S R
10.000
0
5.000
Figure 6. Sound pressure spectra for up-milling cuts
Best results were found for the spindle rotations, whose tooth-passing frequencies approach the natural frequency,
but do not exceed this value. The same occurred when the tooth-passing frequency approaches the half of the natural
frequency. The spindle rotation n = 7500 rpm, whose tooth-passing frequency was close but lower than the natural one,
resulted in a stable cut and relative low surface roughness value. While for the spindle rotations n = 8750 rpm e n =
10000 rpm, the cuts were unstable and the surface roughness deteriorated.
Proceedings of COBEM 2005
Copyright © 2005 by ABCM
18th International Congress of Mechanical Engineering
November 6-11, 2005, Ouro Preto, MG
3.2. Finishing ball-end milling
The graph of figure 7 shows the FRF measured at the end of a ball-endmill. The natural frequency (fn) is 1425 Hz.
Magnitude (m/N)
2.5E-05
Tool: Ball-endmill
Diameter (D) [mm]: 8
Length (L) [mm]: 64
Number of teeth (z): 4
Machine: Hermle C800 U
2.0E-05
1.5E-05
1.0E-05
5.0E-06
0.0E+00
750
1000
1250
1500
1750
2000
Frequency (Hz)
Figure 7. FRF measured at the of a endmill
Figure 8 shows a graph of the surface roughness parameter Rz as a function of the spindle rotation for down-milling
e and up-milling for a surface inclination of 45˚.
Surface roughness R z [µ m]
Dow n-milling
Concordante
Up-milling
Discordante
Up-milling
Workpiece material: ABNT P20 steel
10
Tool: Ball-endmill
D = 8 mm
L = 64 mm
z = 4 teeth
8
6
α = 45°
aet = 0.2 mm
aen = 0.2 mm
fz= 0.05 mm/tooth
Machine: Hermle C800 U
4
2
0
5000
7500
10000
12500
15000
θ = 45º
75°
vf
17500
Spindle rotation [rpm]
Figure 8. Surface roughness as a function of the spindle rotation for ball-end milling
There are differences between the values found for down-milling comparing to the up-milling ones. However, there
are some regions with peaks and other with valleys, in a similar way for both cutting directions. The peaks are related to
spindle rotations whose tool- passing frequencies are close to 1/2 or 1/3 of the natural frequency. The lowest surface
roughness values are found to the spindle rotation n = 16000 rpm, which permitted the highest peripheral speed and
corresponded to 3/4 of the natural frequency.
Figure 9 shows the measured profile for a stable cut. In this case the distances between the marks correspond to the
feed per revolution or half of this value.
4.0
Workpice material:
ABNT P20 steel
Profile (µm)
3.0
2.0
Down-milling
n = 16000 rpm
α = 45°
aet = 0.2 mm
aen = 0.2 mm
fz= 0.05 mm/tooth
1.0
0.0
-1.0
-2.0
-3.0
-4.0
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
Length (mm)
5 mm
Figure 9. Surface profile for a stable condition
Figure 10 shows the surface profile for an unstable condition, which the tooth-passing frequency corresponded to
the half of the natural frequency of the system. Due to the high vibration amplitudes the distance between the highest
crest are close to six times the feed per revolution. Marks of the feed per revolution overlapped to the big ones are still
visible.
Profile (µm)
10.0
8.0
6.0
Workpice material:
ABNT P20 steel
4.0
2.0
0.0
-2.0
-4.0
Down-milling
n = 10688 rpm
α = 45°
aet = 0.2 mm
aen = 0.2 mm
fz= 0.05 mm/tooth
-6.0
-8.0
-10.0
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
Length (mm)
4.0
5 mm
Figure 10. Surface profile for an unstable condition
The graph of figure 11 shows the sound pressure spectra measured during the down-milling cuts. The highest peaks
are related to the spindle rotations whose tooth-passing frequencies (ft) were close to 1/2 or 1/3 of the natural frequency
(fn). They correspond to the harmonics of the tooth-passing frequency closer to the natural of the system. Hence, the
forced vibrations are the major limitation to this process.
Proceedings of COBEM 2005
Copyright © 2005 by ABCM
18th International Congress of Mechanical Engineering
November 6-11, 2005, Ouro Preto, MG
Workpiece material: ABNT P20 steel
2 ft = fn
Tool: Ball-endmill
D = 8 mm
L = 64 mm
z = 4 teeth
Pressão sonora [Pa]
Sound pressure (Pa)
3 ft = fn
0,8
Down-milling
α = 45°
aet = 0.2 mm
aen = 0.2 mm
fz= 0.05 mm/tooth
Machine: Hermle C800 U
0,4
0
2.000
1.500
15.000
Fre
1.000
Frqeu
qeünc
êny
ci(aH
[zH)
z]
12.500
)
pm
n ](r
o
m
i
t
p
r
rãoota[
10.000
500
7.500
0
5.000
le ç
indo ta
Sp R
Figure 11. Sound pressure spectra for down-milling cuts
The graph of figure 12 shows the sound pressure spectra measured during the up-milling cuts. The highest peaks are
related to the same spindle rotations similarly to the down-milling cuts. Therefore, it is confirmed the presence of the
forced vibrations and discarded the regenerative ones. There is no other significant frequency besides the tooth-passing
frequency and its harmonics.
2 ft = fn
Workpiece material: ABNT P20 steel
Pressão sonora [Pa]
Sound pressure (Pa)
3 ft = fn
Tool: Ball-endmill
D = 8 mm
L = 64 mm
z = 4 teeth
1,2
Up-milling
α = 45°
aet = 0.2 mm
aen = 0.2 mm
fz= 0.05 mm/tooth
Machine: Hermle C800 U
0,6
0
2.000
1.500
15.000
1.000
FFr
reeqq
üuêe
n nc c
iay (
[HHz
z] )
12.500
10.000
500
7.500
0
5.000
omn]
ta[ rtpi
m)
(rp
ãro
leç
inodta
SpR
Figure 12. Sound pressure spectra for up-milling cuts
Best results are found for the spindle rotation n = 16000 rpm, whose tooth-passing frequency is close to 3/4 of the
natural frequency. This is the condition where the harmonics of the tooth passing frequency have a distance from the
natural frequency. Hence, the system has a smaller response to the periodic forces of the ball-end milling process. These
results are similar to the ones found by Werner (1992) who made finishing ball-end milling experiments of horizontal
and vertical surfaces.
The major difference between the surface roughness values for up-milling and down-milling occurred to n = 7125
rpm, whose tooth-passing frequency corresponded to 1/3 of the natural frequency. Despite the high magnitude in the
spectrum for down-milling, the surface roughness value was relative low. However, for a spindle rotation a little bit
higher (n = 7500 rpm), the amplitude was high enough to deteriorate the surface finish.
For up-milling, the peaks of the surface roughness curve follow the peaks of magnitude in the spectrum. The values
increase for the spindle rotations whose harmonics of the tooth passing frequency are close to the natural frequency, and
decrease for those whose harmonics of the tooth passing frequency have a distance from this value.
The fact that the forced vibrations are more critical to finishing ball-end milling is related to its engagement
condition. Due to the small machining sections the contact region between tool and workpiece is reduced, and
consequently occurs a minimization of the effects of phase difference between the undulations left by consecutive teeth,
and get more importance the periodic excitation of the interrupted cut.
According to Janovsky (1996), the phase difference between the excitation force and the displacement which occurs
in conditions next to the resonance leads to considerable dimensional errors, mainly to contact conditions where the
surface generation occurs in the end of the tool contact.
4. Conclusions
In finishing end milling operations the highest limitation are the regenerative vibrations. For unstable cuts the sound
pressure spectrum is dominated by the regenerative vibration frequency. Best results are found for the spindle rotations,
whose tooth-passing frequency are close but lower than the natural frequency of the most flexible mode. Forced
vibrations exert higher influence on the results for finishing ball-end milling. The highest peaks in the sound pressure
spectrum are related to the spindle rotations whose tooth-passing frequency harmonics were closer to the natural of the
system. Due to the small machining sections the contact region between tool and workpiece is reduced, and
consequently occurs a minimization of the effects of phase difference between the undulations left by consecutive teeth,
and get more importance the periodic excitation of the interrupted cut. Best results are found when the harmonics of the
tooth passing frequency have a distance from the natural frequency.
5. Acknowledgements
The authors would like to thanks to Kennametal do Brasil, Capes and Fapesb.
6. References
Janovsky, D., 1996, “Einfluβ der Technologie auf Maβgenauigkeit und Prozeβsicherheit beim
Hochgeschwindingkeitsfräsen im Werkzeug und Formembau”, Ph.D. Thesis, TU, Darmstadt, Germany, 153 p.
Polli, M. L., 2005, “Análise da Estabilidade Dinâmica do Processo de Fresamento a Altas Velocidades de Corte”, Ph.D.
Thesis, UFSC, Florianópolis, Brazil, 214 p.
Stemmer, C. E., 1995, “Ferramentas de corte II”, Editora da UFSC, Florianópolis, Brazil, 216 p.
Tlusty, J., 1993, “High-Speed Machining”, Annals of the CIRP, Vol. 42, No. 2, pp. 733-738.
Werner, A., 1992, “Prozeßauslegung und Prozeßsicherheit beim Einsatz von schlanken Schaftfräsern”, RWTH, Aachen,
Germany, 147 p.
7. Responsibility notice
The authors are the only responsible for the printed material included in this paper.