IL CHATTER E LE VIBRAZIONI NELLE MACCHINE UTENSILI · IL CHATTER E LE VIBRAZIONI NELLE MACCHINE UTENSILI Origine e modalità di riduzione 04/12/2013 Ing. Massimo Goletti Ing. Paolo

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

04/12/2013Vibrations in machine tools 2

04/12/2013Vibrations in machine tools

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


Effects of vibrations in machine tools

Undesired effects

• Poor surface finish quality

• Increased tool wear and chipping probability

• High spindle bearings load

4


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


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


Tooth j

x

y

kx

bx

kyby

Tooth j-1

Tooth j

7


Chip thickness modulation

-

=

Rigid system

-

=

Compliant system(Forced vibrations)

Phase shift ε=0

-

=

Auto-regenerativevibrations

Phase shift ε≠0

8


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

9


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


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


(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


(1.1) Impact testing (1.2) Measurement with actuator

13


Impact testing

Solicitation

Acceleration

Displacement

FRF

(double integration)

Frequency Response Function

estimation

14


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


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


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


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.

18


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


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


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


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


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


Stability Lobes Diagram with uncertainty (HSM)

24


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


Stability Lobes Diagram with uncertainty (example): performed tests

26


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


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

28


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


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

30


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


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


32


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


33



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


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


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


36


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


37


Turning: simulation results


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]


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%

38


Turning: simulation results


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]


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

39


Milling application


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

40


Head Vibration (Resultant RMS value): CSM Vs (RVA=0.1,RVF=0.3)


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

41


Interesting cases


n=455rpmb=1.5mmRVA=0.1, RVF=0.3

42


Iteresting cases


n=500rpmb=1.5mmRVA=0.1, RVF=0.3

43


Mandelli


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

44


Vibration Mitigation Strategies


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


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.

45


Control strategy development on updated modelsThe model reproduces well the real behaviour


46


Control strategy development on updated models


Rms cutting forces Rms tool vibratiojn

SSSV parameters: RVA=0.3; RVA=0.1

47




Rms (moving window) cutting forces Rms tool (moving window) vibration

SSSV parameters: RVA=0.3; RVA=0.1

Considering also the pulsing vibrations

48




SSSV parameters selection Optimization

Rms tool (moving window) vibration Optimal parameters map

49


Representation of the machin-tool control logic


50


Numerical Results


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]

51


Control action tested on the updated numerical model


52


State flow implementation control action (SSSV) – results resuming


53


Metal Foams

3 min 4 min 5 min 6 min 7 min 8 min 9 min2 min1 min

54

Ing. Massimo Goletti [email protected]

Ing. Paolo Albertelli [email protected]

04/12/2013Vibrations in machine tools 55

mailto:[email protected]

mailto:[email protected]

Documents

IL CHATTER E LE VIBRAZIONI NELLE MACCHINE UTENSILI · IL CHATTER E LE VIBRAZIONI NELLE MACCHINE UTENSILI Origine e modalità di riduzione 04/12/2013 Ing. Massimo Goletti Ing. Paolo