il chatter e le vibrazioni nelle macchine utensili · il chatter e le vibrazioni nelle macchine...
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IL CHATTER E LE VIBRAZIONI NELLE
MACCHINE UTENSILI
Origine e modalità di riduzione
04/12/2013
Ing. Massimo Goletti
Ing. Paolo Albertelli
• Machine Tools performance
• Vibration Issues
• Cutting process instability
• Stability Lobes Estimation
• Experimental procedure
• Uncertainty in SDL estimation
• Structural optimization with metal foams
• Vibration Mitigation strategies and Spindle Speed Variation (SSV)
• SSV in turning operations
▫ Vibration and cutting forces mitigation effectiveness
▫ Industrial feasibility: promising applications
• SSV in milling operations
▫ Vibration and cutting forces mitigation effectiveness
▫ SSSV parameter selection
Agenda
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Machine tool performances
“Material Removal Rate” maximization
Finishing operations
Complex geometry components
(3 or more axes)
Roughing operations
Components require high cutting capability
High feed rates and 3D trajectories precision (tracking requirements)
HSM: High Speed MachiningHigh roughing operation (hard materials)
High performances axes dynamics
Forces vibrations andauto-regenerative chatter
3
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Effects of vibrations in machine tools
Undesired effects
• Poor surface finish quality
• Increased tool wear and chipping probability
• High spindle bearings load
4
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Effects of vibrations in machine tools
Undesired effects
• Poor surface finish quality
• Increased tool wear and chipping probability
• High spindle bearings load
Commonly accepted approach to reduce vibration effects
Cutting parameter reduction: depth of cut and spindle speed
Productivity limitation
5
Forced vibrations Regenerative vibrations
• Directly related to machine dynamics
• Technological signature (waviness) on machine surface
• Linked to the machine dynamics
• Related to the interaction between successive tooth pass’ waviness
• The chip thickness has an unstable dynamic component
Classification of vibration in machine cutting
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3 4 5 6 7 8 9 10-0.02
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
tempo [s]
vib
razi
on
i [m
m]
0.5 1 1.5
4
5
6
7
8
9
10
11
x 10-3
tempo [s]
vib
razi
on
i [m
m]
6
• Machine tool is not a rigid system
• Cutting forces deforms the machine
tool
• Real tooth position can be defined
studying the dynamic compliance of
the system
• Tooth j-1 leaves a waviness on the
machined surface
• Tooth j leaves a waviness that interacts
with the previous one
• Chip thickness is modulated
Tooth pass and surface waviness
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Tooth j
x
y
kx
bx
kyby
Tooth j-1
Tooth j
7
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Chip thickness modulation
-
=
Rigid system
-
=
Compliant system(Forced vibrations)
Phase shift ε=0
-
=
Auto-regenerativevibrations
Phase shift ε≠0
8
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Chip thickness modulation
Cutting forces are proportional to chip thickness
Vibrations are proportional to cutting forces
Successive tooth vibrations affects surface waviness
Chip thickness is proportional to
surface waviness -
=
Auto-regenerativevibrations
Phase shift ε≠0
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Estimation of the stability lobes diagram
Stabilitylobes
diagram
φ
z
FRFTool
FRFWorkpiece
Ks
n [rpm]
ap [mm]
ωc [Hz]
y
x
𝑑𝐹𝑡 ,𝑗 𝜑, 𝑧 = 𝐾𝑡𝑠 ∙ ℎ𝑗 𝜑𝑗 𝑧 +𝐾𝑡𝑒 ∙ 𝑑𝑧
𝑑𝐹𝑟 ,𝑗 𝜑, 𝑧 = 𝐾𝑟𝑠 ∙ ℎ𝑗 𝜑𝑗 𝑧 + 𝐾𝑟𝑒 ∙ 𝑑𝑧
𝑑𝐹𝑎 ,𝑗 𝜑, 𝑧 = 𝐾𝑎𝑠 ∙ ℎ𝑗 𝜑𝑗 𝑧 + 𝐾𝑎𝑒 ∙ 𝑑𝑧
10
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Cutting coefficient determination
• The select force model is the mechanicistic one
• Mean cutting forces are estimated as a function of az
• A regression of the mean forces as a function of the az allows to
determine the cutting coefficients
x
y
az
feedn
φst
φex
φj
dFt
dFr
x
y
z
φj
jth tooth
dzKzhKzdF
dzKzhKzdF
dzKzhKzdF
aejjasja
rejjrsjr
tejjtsjt
,
,
,
,
,
,
zazh jzjj sin
11
• The dynamic compliance at the tool allows to describe system behavior
• There are two ways for Frequency Response Function (FRF) determination
Determination of structure dynamics
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(1) Experimental measurement (2) Finite Element Modeling
12
Two typologies of measurement
• Impact test: instrumented hammer and accelerometers
• Measurement with actuators: complex function with force sensor and actuator
Experimental FRF measurement
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(1.1) Impact testing (1.2) Measurement with actuator
13
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Impact testing
Solicitation
Acceleration
Displacement
FRF
(double integration)
Frequency Response Function
estimation
14
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Stability lobes diagram
100 200 300 400 500 600 700 800
0.5
1
1.5
2
2.5
3
3.5
4
velocità del mandrino, n [rpm]
pro
fon
dit
à d
i p
as
sa
ta, b
[m
m]
UNSTABLE
REGION
3 4 5 6 7 8 9 10-0.02
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
tempo [s]
vib
razi
on
i [m
m]
STABLE
REGION0.5 1 1.5
4
5
6
7
8
9
10
11
x 10-3
tempo [s]
vib
razi
on
i [m
m]
1
K0 K0 K0 K0 K0 K0
K0 K0 K0 K0 K0 K0 K0 K0 K0 K0 K0
K0 K0 K0 K0 K0 M0 M0
K0 K0 K0 K0
K0 K0 K0 K0 K0 K0 K0 K0 K0 K0 K0
K0 K0 K0 K0 K0
K0 K0 K0 K0 K0 K0 K0 K0 K0 K0 K0 K0 K0 K0 K0 M0 M0
K0 K0 K0 K0 K0
K0 K0 K0 K0 K0 K0 K0 K0 K0 K0 K0 K0 K0 K0 K0 M0 M0
K0 K0 K0 K0 K0 K0 K0 K0 K0 K0
K0 K0 K0 K0 K0 M0 M0 K0 K0 K0 K0 K0 K0 K0 K0 K0 K0
K0 K0 K0 K0 K0 M0 M0
M0
M0 K0 K0 K0 K0 K0 K0
M0
M0
M0 M0
M0
XY
Z
SEP 6 2007
12:51:43
ELEMENTS
Virtual Model
Instrumentedhammer
Accelerometer
FRF
15
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Experimental modal analysis
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
2021
2223
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
5354
5556
57
5859
60
616263
6465
66
6768
69
16
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Why the Lobes Diagram is not widely applied?
Comments
• The Stability Lobes Diagram (SLD) is not reliable
• Whenever used it is experimentally verified
Needs
• Quantify the “errors” on SLD estimation
• Quantify the errors is SLDalgorithm
Proposed approach
• Propagation of uncertainty
17
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Propagation of uncertainty
• Uncertainty of y is calculated as the composition of uncertainties of the various inputs xi
• The combined uncertainty is computed as follows:
1
1 11
2
2
2 ,22N
i
N
ij
ji
ji
N
i
i
i
c xxux
f
x
fxu
x
fyu
Nxxxfy ,,,1 21
• This equation is the law of propagation of uncertainty
UNI CEI ENV 13005:2000. Guida all’espressione dell’incertezza di misura. Milano: UNI – CEI, 2000.
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Multivariate propagation of uncertainty
• The covariance matrix of the output variables (matricial version of the law of propagation of uncertainty) is:
𝑢2 𝑦
1 ⋯ 𝑢 𝑦
1, 𝑦
𝑀
⋮ ⋱ ⋮
𝑢 𝑦𝑀, 𝑦
1 ⋯ 𝑢2 𝑦
𝑀 =
𝜕𝑓
1
𝜕𝑥1⋯
𝜕𝑓1
𝜕𝑥𝑁⋮ ⋱ ⋮
𝜕𝑓𝑀
𝜕𝑥1⋯
𝜕𝑓𝑀
𝜕𝑥𝑁
∙ 𝑢2 𝑥1 ⋯ 𝑢 𝑥1, 𝑥𝑁
⋮ ⋱ ⋮
𝑢 𝑥𝑁, 𝑥1 ⋯ 𝑢2 𝑥𝑁 ∙
𝜕𝑓
1
𝜕𝑥1⋯
𝜕𝑓𝑀
𝜕𝑥1⋮ ⋱ ⋮
𝜕𝑓1
𝜕𝑥𝑁⋯
𝜕𝑓𝑀
𝜕𝑥𝑁
𝑀 ∗ 𝑀 𝑀 ∗ 𝑁 𝑁 ∗ 𝑁 𝑁 ∗ 𝑀
• The uncertainty region in a plane of two correlated factor is an ellipse (with normality assumption)
𝜃
Re 𝑧
Im 𝑧 𝑠 𝑢
𝑠 𝑣
Im
Re’
Im’
𝜃 𝜃 =
1
2∙ atan2
2𝑠 𝑥 ,𝑦
𝑠2 𝑥 − 𝑠2 𝑦
19
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Analysis of the input and output variables
• Uncertainty affected input quantities▫ Cutting coefficients
▫ Frequency Response Functions
• Output quantities (with uncertainty)▫ Depth of cut
▫ Spindle speed
• Independent variable (without uncertainty)▫ Chatter frequency
Re
Im
1Re2 2
t
climKN
a 1tan2
kzTzn c
2
26060
20
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Uncertainty for cutting coefficients
• A regression of mean forces as a function of az is needed
• Uncertainty of the predictors can be estimated with regression
xezxsx FaFF
Feed Regression
Source DF SS MS F
Regression 1 1465502,7 1465502,684 122,5613
Error 16 191316,9 11957,306
Total 17 1656819,6
• From the cutting force model it is possible to estimate the cutting coefficients with uncertainty
• Hypothesis testing must be done after regression analysis
Cutting coefficient
Kts= 1911±53 [N/mm2]
Krs= 747,7±19 [N/mm2]
Kas= 7,696±12 [N/mm2]
Kte= 17,18±9,3 [N/mm]
Kre= 65,04±3,4 [N/mm]
Kae= -21,07±1,6 [N/mm]
21
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Uncertainty in Frequency Response Function estimation
• Frequency Response Function is the result of a series of repeated measurements
• The quantities F(t), s(t) are noise affected
• Estimators minimize these measurement noises
• The coherence function shows the linearity of the measure as a function of frequency
Linear system
+ +
F(t) s(t)
e1(t)
e2(t)x(t) y(t)
xx
xy
G
GH
ˆ
ˆˆ
1
yx
yy
G
GH
ˆ
ˆˆ
2
yyxx
xy
GG
G
ˆˆ
ˆˆ
2
2
22
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Uncertainty in Frequency Response Function estimation
1
2
1 H2
1H
dn
dn2
1sinH
21
1
• There is a formulation for the estimation of uncertainty for H1 FRF estimator as a function of coherence function
23
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Stability Lobes Diagram with uncertainty (HSM)
24
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Stability Lobes Diagram with uncertainty (example)
Kts= 575,8±27 [N/mm2]
Krs= 74,79±4,2 [N/mm2]
Kas= -10,01±5,4 [N/mm2]
Kte= 24,94±4,1 [N/mm]
Kre= 21,37±0,64 [N/mm]
Kae= 13,84±0,67 [N/mm]
• Spindle speed 3000 rpm
• Axial depth of cut 1.5 mm
• Slot milling on aluminum
• Three different milling testswith az: 0.1 - 0.2 - 0.3 mm/z
25
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Stability Lobes Diagram with uncertainty (example): performed tests
26
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Receptance Coupling Substructure Analysis (RCSA)
• Need to save time: complex industrial productive scenarii
• A lot of research have been done but the RCSA technique still shows important limitation due to the dynamics prediction accuracy
• Different RCSA techniques were developed
+
Kn
ow
n c
ase
:
Finite Element Analysis (FEA)
Coupling dynamic systemss
s
ss
27
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Tool tip dynamic prediction properties: RCSA evaluation
s
s
ss
500 1000 1500 2000 2500 3000 3500 4000 4500 5000 550010
-8
10-6
10-4
m/N
500 1000 1500 2000 2500 3000 3500 4000 4500 5000 5500-200
-100
0
100
200
de
g
hz
tool1 H
11
tool2 H11
tool2 H11
RCSA
tool1
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Stability Lobes Prediction: RCSA evaluation
2 2.5 3 3.5 4 4.5 5
x 104
0
1
2
3
4
[rpm]
axia
l d
ep
th o
f cu
t [m
m]
axial depth of cut
2 2.5 3 3.5 4 4.5 5
x 104
0
1000
2000
3000
4000
5000chatter frequency
[rpm]
[Hz]
tool1-measured tool tip compliance
tool2 -measured tool tip compliance
tool2 - predicted tool tip compliance (RCSA)
29
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Facing regenerative chatter
lobe 0
lobe 1lobe j
Axia
ld
epth
of
cut
[mm
]
Spindle speed
Stable Cutting
Unstable Cutting
• Cutting parameters (spindle speed) selection• Regenerative chatter modelling and stability
prediction accuracy (process damping, low millengagement)
• Stability Lobes Diagram (SLD) uncertainties• Fast SLD prediction-Receptance Substructuring
Analysis
• Improve the Machine Tool dynamics• cutting process oriented MT and components
design• increase structural damping
• Active or passive damping solutions• Smart materials• Metal foams
• Spindle Speed Modulation
s
s
1/f
A
Ω0
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Machine tool Performance enhancement
Cutting performance prediction and parameters selectionStability Lobes estimation•Uncertainty and SLD estimation•Receptance Coupling Sub-structuring Analysis
lobe 0
lobe 1lobe j
Axi
ald
epth
of
cut
[mm
]
Spindle speed
Stable Cutting
Unstable Cutting
s
s
Machine Tool Dynamics improvement through subsystems dynamic interaction exploitation
•Spindle-Machine Tool Structure interaction•Spindle-Control Interaction
X
Z
Y
A axis
b
1
X
Y
Z
RAM_Z_ACCIAIO
0.015122
.030243.045365
.060486.075608
.090729.105851
.120972.136094
MAR 18 2010
17:59:17
NODAL SOLUTION
STEP=1
SUB =3
FREQ=293.227
USUM (AVG)
RSYS=0
DMX =.136094
SMX =.136094
Spindle Speed Variation and vibration controller•SSV turning•SSV milling
1/f
A
Ω0
Innovative MaterialsIncrease the machine tool structural damping (metal foams)
Machine Toolsperformance enhancement
&chatter vibration mitigation
31
04/12/2013Vibrations in machine tools
10 20 30 40 50 60 70
-4
-3
-2
-1
0
1
2
3
4
x 10-7
X: 23
Y: 7.679e-008
real[m
/N]
FRF: tool tip dynamic compliance
hz
A axis locked
X
Z
Y
A axis
b
Machine Tool Structure – Control interaction
Is it possible to exploit the regulator tuning to improve the cutting process stability?a) increase the damping (loop velocity)b) introduce a quasi-static compliance contribute
Milling Parameter Value
Tool diameter [mm] 32
Radial immersion ae[mm] 32
Feed rate az[mm/rev tooth] 0.9
Tooth number z 5
A axis Locked (2 brakes)
Titanium milling
Machine Tool Dynamics improvement through subsystems dynamic interaction exploitation
32
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Goal: Define some tuning criteria to enhance the cutting stability
spin
dle
&A
transm
ission
Ftool tip
m1dof
c1 k1
mach
ine
Jeq
Real part[m/N]
dominant eigenmode
Residual
frequency(hz)
mach
ine
spin
dle
&A
trasmissio
n
Ftool tip
Aaxis controller Aaxis controller
𝜔𝑛 1 + 2𝜉
Machine Tool Dynamics improvement through subsystems dynamic interaction exploitation
33
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Machine Tool Dynamics improvement through subsystems dynamic interaction exploitation
2
11
/21
4100%
)(
)(
100%bJ
M
F
Xreal
F
Xreal
A
dofdof
global
tool
tool
rAcontrolle
tool
tool
101
102
-1
0
1
2
x 10-7
X: 24.72
Y: -1.665e-007
tool tip dynamic compliance (A axis controller tuning effects)
X: 24.46
Y: -1.133e-007
Rea
l [m
/N]
101
102
-4
-3
-2
-1
0
1x 10
-7
hz
Imag
inar
y [m
/N]
tool tip dyn. compliance (structural contribute)
tool tip dyn. compliance (global - optimized tuning)
tool tip dyn. compliance (controller contribute - optimized)
tool tip dyn. compliance (controller contribute - standard tuning)
tool tip dyn. compliance (global - standard tuning)
Contribute linked to the regulator
Tool compliance:
identified from experimental tests
Tool compliance:
Computed using the identified criteria
100 200 300 400 500 600 700
1
1.5
2
2.5
Depth
of
Cut
[mm
]
Stability Lobes Diagramm: Cutting Stability oriented A axes control tuning
100 200 300 400 500 600 70020
25
30
35
40
Spindle Speed [rpm]
Chatt
er
Fre
q.
[Hz]
A blocked
Cutting Stability Oriented tuning (A axes controller )
34
04/12/2013Vibrations in machine tools
Spindle Speed Variation
Spindle Speed Variation
0
2 fRVF
0
ARVA
)()( 000 tRVFsenRVAt
SSV
• Infinite acceleration values are not required
• Can be easily tracked by Numerical Control systems
W0 = nominal spindle speed
RVA = 0 ÷ 40%RVF = 0 ÷ 40%
Sinusoidal Spindle Speed Variation (SSSV)
1/f
A
Ω0
reasonable values
35
04/12/2013Vibrations in machine tools
Experimental set-up description
design of a specific workpiece with a calibrated compliance
steel turning, d=110mm, axial freq=85Hz
flexible reeds
internal shaft
Externalhollow cylinder
fixing washers
sensorized toollaser beam
displacement sensor
60 80 100 120 140 160
-6
-4
-2
0
2
4
x 10-4
X: 86
Y: -0.0006471
frequency, f [Hz]
Re
(FR
F)
[mm
/N]
AXIAL WORKPIECE COMPLIANCE
X: 88.15
Y: -0.0004496
FEM MODEL
EXPERIMENTAL
85Hz
The SSSV seems to be effective for high dominant frequency/nominal spindle speed
Spindle Speed Variation
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04/12/2013Vibrations in machine tools
Turning Model Validation
9.6 9.605 9.61 9.615 9.62 9.625 9.63 9.635 9.64 9.645 9.65
0
0.2
0.4
[mm
]TEST 1 - CSM: unstable cutting
10 10.5 11 11.5 12 12.5 130
0.05
0.1
0.15
[mm
]
TEST 2 - SSSV (RVA=30% RVF=10%): stable cutting
10.48 10.485 10.49 10.495 10.5 10.505 10.51
0
0.1
0.2
0.3
[mm
]
TEST 3 - SSSV (RVA=10% RVF=30%): unstable cutting
10 10.2 10.4 10.6 10.8 11 11.2 11.4 11.6 11.8 120
0.05
0.1
0.15
[s]
[mm
]
TEST 4 - SSSV (RVA=30% RVF=30%): stable cutting
experimental
simulated
experimental
simulated
experimental
simulated
experimental
simulated
Chip thickness reconstruction: from laser measurementTool disengagement
Spindle Speed Variation
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04/12/2013Vibrations in machine tools
Turning: simulation results
Spindle Speed Variation
spindle speed [rpm]
de
pth
of
cu
t [m
m]
Force reduction [%]: CSM Vs (RVA=0.3,RVF=0.1)
550 600 650 700 750 800 850 900 9500.5
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
-2
-1
0
1
2
3
4
5
6
7
8
7%
-1%
4%
1.2%
-2%
spindle speed [rpm]
de
pth
of
cu
t[m
m]
Vibration reduction [%]: CSM Vs (RVA=0.3,RVF=0.1)
550 600 650 700 750 800 850 900 9500.5
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
0
10
20
30
40
50
60
70
92%
-2%
91%
86%
• Tool load force (Root Mean Square)• Surface quality Workpiece vibration (Root Mean Square)• RVA=0.3, RVF=0.1
spindle speed [rpm]
de
pth
of
cu
t [m
m]
Force reduction [%]: CSM Vs (RVA=0.3,RVF=0.1)
550 600 650 700 750 800 850 900 9500.5
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
-2
-1
0
1
2
3
4
5
6
7
8
7%
-1%
4%
1.2%
-2%
spindle speed [rpm]
de
pth
of
cu
t[m
m]
Vibration reduction [%]: CSM Vs (RVA=0.3,RVF=0.1)
550 600 650 700 750 800 850 900 9500.5
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
0
10
20
30
40
50
60
70
92%
-2%
91%
86%
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04/12/2013Vibrations in machine tools
Turning: simulation results
Spindle Speed Variation
spindle speed [rpm]
de
pth
of
cu
t[m
m]
Vibration reduction [%]:CSM Vs (RVA=0.1,RVF=0.3)
550 600 650 700 750 800 850 900 9500.5
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
0
10
20
30
40
50
60
70
26%
spindle speed [rpm]
de
pth
of
cu
t [m
m]
Force reduction [%]: CSM Vs (RVA=0.1,RVF=0.3)
550 600 650 700 750 800 850 900 9500.5
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
0
1
2
3
4
5
6
7
8
2%
-0.6%
• Tool load force (Root Mean Square)• Surface quality Workpiece vibration (Root Mean Square)• RVA=0.1, RVF=0.3
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04/12/2013Vibrations in machine tools
Milling application
Spindle Speed Variation
inserts
Xm:feed Zm
3 axial accelerometer
microphone
dynamometer
Experimental set-up
Analog ouputs
insert
Tool type
Tool lenght 270mm
Tool diameter 80mm
Z 6
Insert Walter P27275-3R WTL71
Mechaniclhead
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Head Vibration (Resultant RMS value): CSM Vs (RVA=0.1,RVF=0.3)
Spindle Speed Variation
360 380 400 420 440 460 480 5000.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
RMS vibration
n [rpm]
b [
mm
]
CSM
RVA=0.1,RVF=0.3
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Interesting cases
Spindle Speed Variation
n=455rpmb=1.5mmRVA=0.1, RVF=0.3
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04/12/2013Vibrations in machine tools
Iteresting cases
Spindle Speed Variation
n=500rpmb=1.5mmRVA=0.1, RVF=0.3
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Mandelli
Spindle Speed Variation
CN&
DRIVES
Additional Sensors
on machine
signals from the NC
Feed and Speedregulation EPC main tasks
• Machine Tool “state” & Tool “state” reconstruction• Process quality estimation• Cutting process parameters automatic regulation• Chatter vibration techniques (i.e. SSV) implementation• Active vibration damping system (workpiece) control• Data logging
Additional Sensors
on workpiece/fixture
EPC
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Vibration Mitigation Strategies
Spindle Speed Variation
Regenerative chatter S parameter
lobe 0lobe 1
lobe j
Axi
al d
epth
of
cut
[mm
]
Spindle speed
Spindle Speed regulation
Spindle Speed regulation: automatic spindle speed tuning algorithm definition (robustness)
Forced Vibration feed parameter regulation
Spindle Speed Variation
Lobe 5
Spindle Speed variation: continuously spindle speed modulation parameter selection(Sinusoidal Spindle Speed Variation)
+Process damping
SSV can be a vibration suppression solution @ low spindle speeds (even if process damping exists).It is more flexible than variable pitch tools. SSV probably is non effective when high feed tools are used.
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Control strategy development on updated modelsThe model reproduces well the real behaviour
Spindle Speed Variation
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04/12/2013Vibrations in machine tools
Control strategy development on updated models
Spindle Speed Variation
Rms cutting forces Rms tool vibratiojn
SSSV parameters: RVA=0.3; RVA=0.1
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Control strategy development on updated models
Spindle Speed Variation
Rms (moving window) cutting forces Rms tool (moving window) vibration
SSSV parameters: RVA=0.3; RVA=0.1
Considering also the pulsing vibrations
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Control strategy development on updated models
Spindle Speed Variation
SSSV parameters selection Optimization
Rms tool (moving window) vibration Optimal parameters map
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Representation of the machin-tool control logic
Spindle Speed Variation
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Numerical Results
Spindle Speed Variation
0 1 2 3 4 5
-6000-4000-2000
02000
Fe
ed
Fo
rce
[N
]
0 1 2 3 4 5-500
0
500
Fe
ed
Acc. [m
/s2]
0 1 2 3 4 50
500
1000
Time [s]
Sp
ind
le V
el. [rp
m]
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Control action tested on the updated numerical model
Spindle Speed Variation
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State flow implementation control action (SSSV) – results resuming
Spindle Speed Variation
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Metal Foams
3 min 4 min 5 min 6 min 7 min 8 min 9 min2 min1 min
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Ing. Massimo Goletti [email protected]
Ing. Paolo Albertelli [email protected]
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