IL CHATTER E LE VIBRAZIONI NELLE

IL CHATTER E LE VIBRAZIONI NELLE MACCHINE UTENSILI Origine e modalità di riduzione Ing. Massimo Goletti Ing. Paolo Albertelli

2 Agenda 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

3 Machine tool performances 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) Material Removal Rate maximization High performances axes dynamics HSM: High Speed Machining High roughing operation (hard materials) Forces vibrations and auto-regenerative chatter

4 Effects of vibrations in machine tools Undesired effects Poor surface finish quality Increased tool wear and chipping probability High spindle bearings load

5 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

6 Classification of vibration in machine cutting Forced vibrations Regenerative vibrations x 10-3 0.16 11 0.14 10 0.12 vibrazioni [mm] 9 8 7 6 vibrazioni [mm] 0.1 0.08 0.06 0.04 5 0.02 4 0 0.5 1 1.5 tempo [s] -0.02 3 4 5 6 7 8 9 10 tempo [s] 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

7 Tooth pass and surface waviness Machine tool is not a rigid system b y k y k x Tooth j-1 Tooth j Cutting forces deforms the machine tool Real tooth position can be defined y b x x Tooth j 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

8 Chip thickness modulation Rigid system Compliant system (Forced vibrations) Auto-regenerative vibrations - - - = = = Phase shift ε=0 Phase shift ε 0

9 Chip thickness modulation Cutting forces are proportional to chip thickness Auto-regenerative vibrations Chip thickness is proportional to surface waviness Vibrations are proportional to cutting forces - Successive tooth vibrations affects surface waviness = Phase shift ε 0

10 Estimation of the stability lobes diagram x y df t,j φ, z = K ts h j φ j z + K te dz df r,j φ, z = K rs h j φ j z + K re dz df a,j φ, z = K as h j φ j z + K ae dz φ z K s FRF Tool Stability lobes diagram n [rpm] a p [mm] ω c [Hz] FRF Workpiece

11 Cutting coefficient determination dft dfr df, j, j a, j, z Kts hj j z, z K rs hj j z, z K h z h j as j j K K te K z a sin z j z j re ae dz dz dz z y φ j j th tooth x feed n a z y φ st φ j φ ex df r df t x The select force model is the mechanicistic one Mean cutting forces are estimated as a function of a z A regression of the mean forces as a function of the a z allows to determine the cutting coefficients

12 Determination of structure dynamics The dynamic compliance at the tool allows to describe system behavior There are two ways for Frequency Response Function (FRF) determination (1) Experimental measurement (2) Finite Element Modeling

13 Experimental FRF measurement Two typologies of measurement Impact test: instrumented hammer and accelerometers Measurement with actuators: complex function with force sensor and actuator (1.1) Impact testing (1.2) Measurement with actuator

14 Impact testing Solicitation Displacement (double integration) Frequency Response Function estimation FRF Acceleration

15 Stability lobes diagram FRF 1 ELEMENTS Virtual Model K0 M0 K0 SEP 6 2007 12:51:43 K0 K0 M0 M0 K0 K0 M0 K0 M0 K0 K0 K0 K0 M0 K0 M0 M0 M0 K0 M0 K0 K0 Z Y X K0 K0 Instrumented hammer Accelerometer profondità di passata, b [mm] 4 3.5 3 2.5 2 1.5 1 0.5 UNSTABLE REGION STABLE REGION vibrazioni [mm] x 10-3 11 10 9 8 7 6 5 4 vibrazioni [mm] 0.16 0.14 0.12 0.1 0.08 0.06 0.04 0.02 0-0.02 3 4 5 6 7 8 9 10 tempo [s] 0.5 1 1.5 tempo [s] 100 200 300 400 500 600 700 800 velocità del mandrino, n [rpm]

Vibrations in machine tools Experimental modal analysis 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 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 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 16

17 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

18 Propagation of uncertainty Uncertainty of y is calculated as the composition of uncertainties of the various inputs x i The combined uncertainty is computed as follows: N N1 2 2 2 u 2, c y u xi u xi x j i1 f x y f x, x,, 1 1 2 i 2 x N N i1 ji1 f x i f x j 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.

19 Multivariate propagation of uncertainty The covariance matrix of the output variables (matricial version of the law of propagation of uncertainty) is: f 1 u 2 f f 1 1 y 1 u y 1, y M x 1 x N u 2 f M x 1 u x 1, x N x 1 x 1 = u y M, y 1 u 2 y f M M f M u x N, x 1 u 2 x f N 1 f M x 1 x N x N x N M M M N N N N M The uncertainty region in a plane of two correlated factor is an ellipse (with normality assumption) Im Im Im z s u s v θ Re θ = 1 2 atan2 2s x, y s 2 x s 2 y θ Re z

20 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 a lim c Re N K Im Re 2 2 t 1 n 2 tan 60 z T 1 60 2c z 2k

21 Uncertainty for cutting coefficients A regression of mean forces as a function of a z is needed Uncertainty of the predictors can be estimated with regression 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 F x F xs a z F xe Cutting coefficient K ts = 1911±53 [N/mm 2 ] K rs = 747,7±19 [N/mm 2 ] K as = 7,696±12 [N/mm 2 ] K te = 17,18±9,3 [N/mm] K re = 65,04±3,4 [N/mm] K ae = -21,07±1,6 [N/mm] From the cutting force model it is possible to estimate the cutting coefficients with uncertainty Hypothesis testing must be done after regression analysis

22 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 F(t) e 1 (t) ˆ 2 Linear system s(t) + + x(t) e 2 (t) y(t) H ˆ1 H ˆ2 Gˆ Gˆ Gˆ Gˆ Gˆ xx xy xx yy yx Gˆ xy Gˆ yy 2

23 Uncertainty in Frequency Response Function estimation There is a formulation for the estimation of uncertainty for H 1 FRF estimator as a function of coherence function H 1 sin 1 2 1 2n d 1 2 H1 H1 2n d

24 Stability Lobes Diagram with uncertainty (HSM)

25 Stability Lobes Diagram with uncertainty (example) Spindle speed 3000 rpm Axial depth of cut 1.5 mm Slot milling on aluminum Three different milling tests with a z : 0.1-0.2-0.3 mm/z K ts = 575,8±27 [N/mm 2 ] K rs = 74,79±4,2 [N/mm 2 ] K as = -10,01±5,4 [N/mm 2 ] K te = 24,94±4,1 [N/mm] K re = 21,37±0,64 [N/mm] K ae = 13,84±0,67 [N/mm]

26 Stability Lobes Diagram with uncertainty (example): performed tests

Known case: Vibrations in machine tools 27 Receptance Coupling Substructure Analysis (RCSA) Need to save time: complex industrial productive scenarii + s s s s Coupling dynamic systems Finite Element Analysis (FEA) 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

28 Tool tip dynamic prediction properties: RCSA evaluation s s 10-4 m/n 10-6 s s tool 1 10-8 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 5500 200 100 tool1 H 11 tool2 H 11 tool2 H 11 RCSA deg 0-100 -200 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 5500 hz

29 Stability Lobes Prediction: RCSA evaluation [Hz] axial depth of cut [mm] 4 3 2 1 axial depth of cut 0 2 2.5 3 3.5 4 4.5 5 [rpm] chatter frequency x 10 4 5000 4000 3000 2000 1000 tool1-measured tool tip compliance tool2 -measured tool tip compliance tool2 - predicted tool tip compliance (RCSA) 0 2 2.5 3 3.5 4 4.5 5 [rpm] x 10 4

Axial depth of cut [mm] Vibrations in machine tools 30 Facing regenerative chatter Cutting parameters (spindle speed) selection Regenerative chatter modelling and stability prediction accuracy (process damping, low mill engagement) 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 lobe j lobe 1 lobe 0 Stable Cutting Unstable Cutting Spindle speed A Ω 0 s s 1/f

Axial depth of cut [mm] Vibrations in machine tools 31 Machine tool Performance enhancement Cutting performance prediction and parameters selection Stability Lobes estimation Uncertainty and SLD estimation Receptance Coupling Sub-structuring Analysis s s lobe j lobe 1 lobe 0 Stable Cutting Unstable Cutting Spindle speed Machine Tool Dynamics improvement through subsystems dynamic interaction exploitation Spindle-Machine Tool Structure interaction Spindle-Control Interaction 1 A axis b Y Z X NODAL SOLUTION STEP=1 SUB =3 FREQ=293.227 USUM (AVG) RSYS=0 DMX =.136094 SMX =.136094 Z Y X MAR 18 2010 17:59:17 0 RAM_Z_ACCIAIO.015122.030243.045365.060486.075608.090729.105851.120972.136094 Machine Tools performance enhancement & chatter vibration mitigation Spindle Speed Variation and vibration controller SSV turning A SSV milling Innovative Materials Increase the machine tool structural damping (metal foams) Ω 0 1/f

32 Machine Tool Dynamics improvement through subsystems dynamic interaction exploitation Machine Tool Structure Control interaction Z 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 A axis b Y X x 10-7 FRF: tool tip dynamic compliance real[m/n] 4 3 2 1 0-1 -2-3 -4 X: 23 Y: 7.679e-008 A axis locked Titanium milling Milling Parameter Value Tool diameter [mm] 32 Radial immersion a e [mm] 32 Feed rate a z [mm/rev tooth] 0.9 Tooth number z 5 10 20 30 A axis 40 50 60 Locked (2 brakes) 70 hz

machine machine spindle&a trasmission spindle&a transmission Vibrations in machine tools 33 Machine Tool Dynamics improvement through subsystems dynamic interaction exploitation c 1 k 1 Real part[m/n] dominant eigenmode m 1dof A axis controller A axis controller J eq Residual frequency(hz) F tool tip F tool tip ω n 1 + 2ξ Goal: Define some tuning criteria to enhance the cutting stability

34 Machine Tool Dynamics improvement through subsystems dynamic interaction exploitation Depth of Cut [mm] 2.5 Real [m/n] Chatter Freq. [Hz] Imaginary [m/n] 2 1.5 2 1 Tool compliance: 1-1 x 10-7 X real F % 100 X real F tool tool tool tool ( ) ( ) Acontroller global 1dof 4 % 100 1 2 tool tip dynamic compliance (A axis controller tuning effects) M J 1dof 2 A / b 100 0 200 300 400 500 600 700 identified from experimental tests X: 24.46 Y: -1.133e-007 40 10 1 X: 24.72 tool tip dyn. compliance (structural contribute) 10 2 Y: -1.665e-007 tool tip dyn. compliance (global - optimized tuning) 35 30 0-1 25-2 1 x 10-7 Stability Lobes Diagramm: Cutting Stability oriented A axes control tuning tool tip dyn. compliance (controller contribute - optimized) tool tip dyn. compliance (controller contribute - standard tuning) tool tip dyn. compliance (global - standard tuning) 20-3 100 200 300 400 500 600 700-4 Spindle Speed [rpm] 10 1 10 2 hz A blocked Cutting Stability Oriented tuning (A axes controller ) Contribute linked to the regulator Tool compliance: Computed using the identified criteria

35 Spindle Speed Variation SSV Sinusoidal Spindle Speed Variation (SSSV) Infinite acceleration values are not required Can be easily tracked by Numerical Control systems ( t) 0 RVA sen( 0 0 RVF t ) W 0 = nominal spindle speed RVA A 0 2 f RVF 0 A Ω 0 reasonable values RVA = 0 40% RVF = 0 40% Spindle Speed Variation 1/f

36 Experimental set-up description flexible reeds fixing washers internal shaft x 10-4 External hollow cylinder AXIAL WORKPIECE COMPLIANCE design of a specific workpiece with a calibrated compliance 4 FEM MODEL EXPERIMENTAL sensorized tool laser beam displacement sensor 2 Re(FRF) [mm/n] 0-2 85Hz steel turning, d=110mm, axial freq=85hz The SSSV seems to be effective for high dominant frequency/nominal spindle speed Spindle Speed Variation -4-6 X: 88.15 Y: -0.0004496 X: 86 Y: -0.0006471 60 80 100 120 140 160 frequency, f [Hz]

37 Turning Model Validation Chip thickness reconstruction: from laser measurement [mm] TEST 1 - CSM: unstable cutting 0.4 0.2 Tool disengagement experimental simulated [mm] 0 9.6 9.605 9.61 9.615 9.62 9.625 9.63 9.635 9.64 9.645 9.65 TEST 2 - SSSV (RVA=30% RVF=10%): stable cutting 0.15 experimental 0.1 simulated 0.05 [mm] 0 10 10.5 11 11.5 12 12.5 13 0.3 0.2 0.1 0 TEST 3 - SSSV (RVA=10% RVF=30%): unstable cutting experimental simulated [mm] 0.15 0.1 0.05 10.48 10.485 10.49 10.495 10.5 10.505 10.51 TEST 4 - SSSV (RVA=30% RVF=30%): stable cutting experimental simulated Spindle Speed Variation 0 10 10.2 10.4 10.6 10.8 11 11.2 11.4 11.6 11.8 12 [s]

38 Turning: simulation results Tool load force (Root Mean Square) Surface quality Workpiece vibration (Root Mean Square) RVA=0.3, RVF=0.1 1.5 Vibration reduction [%]: CSM Vs (RVA=0.3,RVF=0.1) 70 1.5 Force reduction [%]: CSM Vs (RVA=0.3,RVF=0.1) 8 1.4 60 1.4 7 1.3 1.3 6 1.2 50 1.2 5 depth of cut[mm] 1.1 1 0.9 0.8 0.7 0.6 86% 91% 92% -2% 0.5 550 600 650 700 750 800 850 900 950 spindle speed [rpm] 40 30 20 10 0 depth of cut [mm] 1.1 1 0.9 0.8 0.7 0.6 1.2% 7% 4% -2% -1% 0.5 550 600 650 700 750 800 850 900 950 spindle speed [rpm] 4 3 2 1 0-1 -2 Spindle Speed Variation

39 Turning: simulation results Tool load force (Root Mean Square) Surface quality Workpiece vibration (Root Mean Square) RVA=0.1, RVF=0.3 1.5 Vibration reduction [%]:CSM Vs (RVA=0.1,RVF=0.3) 70 1.5 Force reduction [%]: CSM Vs (RVA=0.1,RVF=0.3) 8 1.4 60 1.4 7 1.3 1.2 50 1.3 1.2 6 depth of cut[mm] 1.1 1 0.9 26% 40 30 depth of cut [mm] 1.1 1 0.9 2% 5 4 3 0.8 0.7 0.6 20 10 0.8 0.7 0.6 2 1 0.5 550 600 650 700 750 800 850 900 950 spindle speed [rpm] 0-0.6% 0.5 550 600 650 700 750 800 850 900 950 spindle speed [rpm] 0 Spindle Speed Variation

40 Milling application microphone dynamometer Experimental set-up inserts Mechanicl head 3 axial accelerometer Xm:feed Zm Tool type Tool lenght 270mm Tool diameter 80mm Z 6 Insert Walter P27275-3R WTL71 Spindle Speed Variation Analog ouputs insert

41 Head Vibration (Resultant RMS value): CSM Vs (RVA=0.1,RVF=0.3) 2 1.8 RMS vibration CSM RVA=0.1,RVF=0.3 1.6 1.4 b [mm] 1.2 1 0.8 0.6 Spindle Speed Variation 0.4 360 380 400 420 440 460 480 500 n [rpm]

42 Interesting cases n=455rpm b=1.5mm RVA=0.1, RVF=0.3 Spindle Speed Variation

43 Iteresting cases n=500rpm b=1.5mm RVA=0.1, RVF=0.3 Spindle Speed Variation

44 Mandelli CN & DRIVES Additional Sensors on machine Additional Sensors on workpiece/fixture signals from the NC Feed and Speed regulation Spindle Speed Variation EPC 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

Axial depth of cut [mm] Vibrations in machine tools 45 Vibration Mitigation Strategies Regenerative chatter S parameter Spindle Speed Variation Spindle Speed regulation Forced Vibration feed parameter regulation lobe j lobe 1 lobe 0 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. +Process damping Lobe 5 Spindle speed Spindle Speed regulation: automatic spindle speed tuning algorithm definition (robustness) Spindle Speed variation: continuously spindle speed modulation parameter selection(sinusoidal Spindle Speed Variation) Spindle Speed Variation

46 Control strategy development on updated models The model reproduces well the real behaviour Spindle Speed Variation

47 Control strategy development on updated models SSSV parameters: RVA=0.3; RVA=0.1 Rms cutting forces Rms tool vibratiojn Spindle Speed Variation

48 Control strategy development on updated models Considering also the pulsing vibrations SSSV parameters: RVA=0.3; RVA=0.1 Rms (moving window) cutting forces Rms tool (moving window) vibration Spindle Speed Variation

49 Control strategy development on updated models SSSV parameters selection Optimization Rms tool (moving window) vibration Optimal parameters map Spindle Speed Variation

50 Representation of the machin-tool control logic Spindle Speed Variation

51 Numerical Results Feed Force [N] 2000 0-2000 -4000-6000 0 1 2 3 4 5 Feed Acc. [m/s 2 ] 500 0-500 0 1 2 3 4 5 Spindle Vel. [rpm] 1000 500 0 0 1 2 3 4 5 Time [s] Spindle Speed Variation

52 Control action tested on the updated numerical model Spindle Speed Variation

53 State flow implementation control action (SSSV) results resuming Spindle Speed Variation

54 Metal Foams 1 min 2 min 3 min 4 min 5 min 6 min 7 min 8 min 9 min

55 Ing. Massimo Goletti Ing. Paolo Albertelli massimo.goletti@musp.it paolo.albertelli@musp.it