Analysis of milling stability based on cutting force signal processing

Time- frequency analysis approaches, specifically short time Fourier transform,continuous wavelet transform and Hilbert-Huang transform, were utilized to give an utterlydifferent perspec

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Abstract

The milling operation is the most common form of machining Because the action ofeach cutting edge and workpiece is intermittent and periodical, the chip thickness variesperiodically This could lead to self-excited vibrations and unstable cutting which is calledchatter vibration Chatter causes machining instability and reduces productivity in the metalcutting process It has negative effects on the surface finish, dimensional accuracy, tool lifeand machine life Chatter identification is therefore necessary to control, prevent, oreliminate chatter and to identify the stable machining condition A dynamic cutting forcemodel of the end-milling process with tool runout error was established in this research tounderstand the underlying mechanism of chatter The accuracy of the cutting force model inboth time and frequency domains was evaluated by comparing to experimental forcesignals Time- frequency analysis approaches, specifically short time Fourier transform,continuous wavelet transform and Hilbert-Huang transform, were utilized to give an utterlydifferent perspective of chatter from the conventional Fourier spectrum which is insufficient

in analyzing the signals of rich nonlinear characteristics By comparing the simulation withexperimental result, chatter frequency was found to consist of two major components,frequency modulation alongside tooth passing frequency caused by the increased toolrunout error and the non-stationary high frequency from the regenerative vibration.Moreover, dimensionless chatter indicators, defined by the standard deviation and energyratio of the specific intrinsic mode function, could identify the occurrence of chattereffectively The analysis result was then validated by the workpiece surface topography,surface roughness and the stability lobe diagram

Keywords: Milling process, Chatter detection, Time-frequency analysis, Wavelet

transform, Hilbert Huang transform

Acknowledgement

I would like to thank all the people who helped me to finish this thesis First of all, Iwould like to express my deep gratitude to my academic advisors: Professor Chun-HuiChung and Professor Meng-Kun Liu for their valuable guidance, encouragement, andsupport throughout my work towards this thesis Without their help and guidance, this workwould not be possible

I also would like to thank Mr Yi-Wen Qui who provided his experimental datawhich was used to verify my methodology in this thesis I would like to thank all of mylabmates who have supported me a lot with laboratory facilities so that I could conduct myexperiments I thank my friends who always give me encouragements and supports during

my research

Finally, I would like to thank my parents who always give me love, encouragement,and support throughout my life I would specially thank my wife and my son for theirpatience and support during my study I am very grateful for their love

differential radial cutting force (N)

differential tangential cutting force

z

the end (mm)

F si

F ex

simulated cutting force (N)

experimental cutting force (N)

b axial depth of cut (mm) c chatter frequency (rad/s)

h instantaneous chip thickness (mm)  spindle speed (rpm)

 cutting force angle (deg)  runout of cutting edge (mm)

radial and tangential cutting

K n , K t

國 國 .i

Abstract .ii

Acknowledgement iii

Nomenclature iv

Contents

v Chapter 1 1

Introduction

1 1.1 Background 1

1.2 Objective and Scope 2

1.3 Outlines and Contribution of the Chapters 3

Chapter 2 .

4 Literature Review .

4 2.1 Chatter Vibrations in Milling 4

2.2 Signal Analysis Approaches 6

Chapter 3 .

10 Dynamic Cutting Force Model .

10 3.1 Regenerative Chatter Model 10

3.2 Dynamic Cutting Force Model 15

Chapter 4 .

17

Experimental Setup and Model Verification .

17

4.1 Overview and Aim 174.2 Experimental Setup 17

4.2.1 Machine, Cutter and Workpiece 17

4.2.2 Cutting Force Measurement Equipment 19

4.2.3 Surface Topography Measurement Equipment 20

4.2.4 Surface Roughness Measurement Equipment 20

4.3 Cutting Force Coefficients 21

4 4 Experimental Design Parameters 25

4.5 Tool Tip Dynamics 27

4.5.1 Impact Testing 27

4.5.2 Modal Analysis 27

4.5.3 Stability Lobe Diagram 31

4.6 Simulation and Experimental Results 33

Chapter 5 36

Chatter Detection Methodology 36

5.1 Short-Time Fourier Transform Analysis 36

5.2 Continuous Wavelet Transform Analysis 38

5.3 Time-Frequency Analysis Based on HHT 41

5.3.1 Chatter Detection Methodology 41

5.3.2 Results and Discussions 44

5.3.3 Dimensionless Indexes for Chatter Identification 50

5.3.4 Method Verification 51

5.4 Chatter Identification in Small Size of End Mill 54

5.4.1 Overview and Aim 54

5.4.2 Experimental Setup 54

5.4.3 Chatter Identification by Time-Frequency Analysis 57

Chapter 6 60

Conclusions and Future Works 60

6.1 Conclusions 60

6.2 Future Works 60

Bibliography 61

viii viii

List of Figures

Figure 2.1 Milling regenerative chatter 4

Figure 2.2 Stability lobe diagram 6

Figure 2.3 Time-frequency resolution of STFT [9] 8

F i g u re 3.1 T h e model of h e l i ca l end mi l l g e o m e t r y 10

Figure 3.2 Dynamic cutting force model 11

Figure 3.3 Flow chart of dynamic cutting force 16

Figure 4.1 The three- axis CNC milling machine at NTUST 18

Figure 4.2 A carbide end mill 18

Figure 4.3 Kistler Dynamometer 19

Figure 4.4 Experimental setup 19

Figure 4.5 Olympus BX51 at NUTST 20

Figure 4.6 A Mitutoyo portable surface roughness tester 21

Figure 4.7 The modeling of slot milling 21

Figure 4.8 Measured cutting forced signal at feed rate of 0.03 mm/tooth in (a) x direction and (b) y direction 23

Figure 4.9 Relationship between feet per tooth and mean force 25

Figure 4.10 Setup of the impact testing 27

Figure 4.11 Relative frequency response in x direction 28

Figure 4.12 Relative frequency response in y direction 29

Figure 4.13 Direct FRF in x direction

31 Figure 4.14 Direct FRF in y direction

32 Figure 4.15 Stability lobe diagram and experimental design parameters 33

Figure 4.16 Cutting force in (a) x direction and (b) y direction at spindle speed of 1500 rpm and 1.4 mm depth of cut 34

Figure 4.17 Cutting force in x direction at spindle speed of 5250 rpm when (a) DOC =0.8mm (b) DOC = 1.4mm 35Figure 4.18 Fourier spectrum of the force signals at spindle speed of (a) 5250 rpm, DOC=0.8 mm and (b) 5250 rpm, DOC =1.4 mm 35Figure 5.1 Hanning window 36Figure 5.2 Short time Fourier transform by Hanning window at spindle speed of 5250 rpm, DOC = 0.8 mm (a) Simulation and (b) experimental force signal 37

Figure 5.3 Short time Fourier transform by Hanning window at spindle speed of 5250 rpm, DOC = 1.4 mm (a) Simulation and (b) experimental force signal 37

Figure 5.4 Morlet Wavelet 39Figure 5.5 Continuous Wavelet Transform 2-D in case of spindle speed of 5250 rpm and 0.8

mm depth of cut 40

Figure 5.6 Continuous Wavelet Transform 2-D in case of spindle speed of 5250 rpm and 1.4

mm depth of cut 40

Figure 5.7 Flow chart of the chatter identification method 41Figure 5.8 Cutting force signal 42Figure 5.9 Ensemble empirical mode decomposition 43Figure 5.10 The first eight IMFs of the filtered signal at spindle speed of 5250 rpm with 0.8

mm depth of cut 45

Figure 5.11 The first eight IMFs of the filtered signal at spindle speed of 5250 rpm with 1.4

mm depth of cut 46

Figure 5.12 Instantaneous frequency of IMFs at spindle speed of (a) 5250 rpm, DOC= 0.8

mm (stable condition) and (b) 5250 rpm, DOC =1.4 mm (unstable condition) 48

Figure 5.13 Hilbert-Huang spectrum of IMF2 at (a) stable condition and (b) unstable

condition

49 Figure 5.14 Stability lobe diagram and the stability determined by proposed method 52

Figure 5.15 Microscopic of the surface machined with different spindle speed and constant depth of cut of 1.4 m

52 Figure 5.16 Five-axis CNC milling machine 55

Figure 5.17 A carbide end mill 56

Figure 5.18 Experimental setup 56

Figure 5.19 Machined surface topography 59

xi i

List of Tables

Table 4-1 Machine features 18

Table 4-2 Parameters of Tool 19

Table 4-3 Cutting parameters for cutting force coefficients

22 Table 4-4 Average cutting forces 23

Table 4-5 Specific cutting force coefficients 25

Table 4-6 Experimental design parameters 26

Table 4-7 Model parameters in x direction 30

Table 4-8 Model parameters in y direction 30

Table 5-1 IMF Property of force signal at spindle speed of 5250 rpm 47

Table 5-2 The energy ratio values of IMF2s 50

Table 5-3 The standard deviation values of IMF2s 51

Table 5-4 Surface roughness measured along the feed direction at different cutting conditions

53 Table 5-5 Machine’s features 55

Table 5-6 Parameters of Tool 56

Table 5-7 Experimental design parameters 57

Table 5-8 The standard deviation values of IMF2s 58

Table 5-9 The energy ratio values of IMF2s 58

of chip thickness [2] There are two kinds of vibration: (1) forced vibrations caused by theperiodic cutting forces acting on the machine structure and (2) chatter vibration which isself- excited machining behavior Machine tool chatter causes machining instability Itresults in noise, poor surface roughness, increase of tool wear, reduction of tool life andproductivity in machining [3, 4] This phenomenon should be detected and avoided duringthe cutting process in order to avoid machining instability and to improve the productivity.Regenerative chatter in milling is because the previous and current cuts are out of phase.The instantaneous chip thickness is variable, it governs the cutting force which, in turn,affects subsequent tool vibrations [2] Therefore, dynamic cutting force model plays animportant role in analyzing and predicting chatter vibration The accurate model could beused to analyze the machining process and optimize the cutting parameter.

A stability lobe diagram based on regenerative chatter theory is generally a simpleand useful way to predict and control chatter [2-4] This approach was however based onthe restrictive assumption that the dynamics of spindle-tool system has not changed over thespindle speed range [5] The stability lobe diagram may inevitably misinterpret theimportant attributes of the machining processes which in fact always contain rich nonlinearcharacteristics [6, 7] Both time and frequency responses hence have to be monitoredsimultaneously

In order to distinguish whether chatter occurred, some machining process signalshave to be measured by using different techniques such as in-process real-time techniquesbased on force and displacement signals or off-line machined surface characterization [8].The Fourier transform (FT) that can transform time domain signal into frequency domainsignal is suitable for the stationary signal process, especially when the feature components

of signals are obvious in magnitude For non-stationary signal, the wavelet transform (WT)known as a flexible method is suitable for detection of a sudden frequency change in asignal [9] Another time-frequency approach, Hilbert-Huang transform (HHT) has beenwidely used to investigate machining vibration This method is a powerful tool fortime -frequency analysis of nonlinear and non-stationary signals due to performing atime adaptive decomposition operation on signals and no uncertainty principle limitation

on time or frequency resolution [10]

A dynamic cutting force model with tool runout error was established in thisresearch to fit the cutting force signal properly and analyze the chatter identification Time-frequency analysis approaches based on cutting force signal, specifically short time Fouriertransform, continuous wavelet transform and Hilbert-Huang transform, were utilized to give

an utterly different perspective of chatter from the conventional Fourier spectrum which isinsufficient in analyzing the signals of rich nonlinear characteristics

1.2 Objective and Scope

The stability of the process was investigated by the time-frequency analysis All three

of short time Fourier transform, WT and HHT approaches were used for processing thecutting force signals The difference between stable and unstable conditions was clearlydistinguished from the analysis Most of the energy concentrated at tooth passing frequency

in stable cutting condition, while a large amount of energy emerged at high frequency whenchatter occurs In order to detect chatter efficiently whether it is highly nonlinear behavior

or not, dimensionless indexes such as standard deviation and energy ratio of intrinsic modefunctions (IMF) of the cutting force signals were proposed and studied in this research

1.3 Outlines and Contribution of the Chapters

The thesis is organized into six chapters as follows Chapter 1 introduces background,objectives, methods, and contributions of the present work A literature review related to theresearch is described in Chapter 2 In chapter 3, dynamic cutting force model regardingrunout error is presented Model verification is provided in chapter 4 in which experimentaldesign parameters, tool tip dynamics, and comparison of simulated and experimental resultsare presented In chapter 5, chatter detection methodologies including short time Fouriertransform, continuous wavelet transform analysis and time-frequency analysis based onHHT are given The results and discussions are also presented in this chapter Finally, thesummarizations and future works of this thesis are carried out in chapter 6

Chapter 2

Literature Review

2.1 Chatter Vibrations in Milling

Regenerative chatter in milling is self-excited vibration This mechanism isassociated with the phase shift between vibration waves on both sides of the chip left byprevious cutting tooth and current tooth This phenomenon was firstly explained by Tlustyand Polacek (1963), and then by Schmitz and Smith, S (2008); Altintas and Yusuf (2012).Figure 2.1 shows that the wavy surface left by tooth 1 is removed by tooth 2 and so on Thisgain provides a feedback mechanism because the instantaneous chip thickness depends onboth current vibration and surface left by the previous tooth passing When the vibrationsfrom one cutting edge to the next are in phase, the chip thickness varies as the cycloidalpath This causes forced vibration only, and the cutting is stable On the other hand, the out

of phase shows a less favorable phase relationship, chip thickness variation is significant Itresults in chatter vibration in milling When chatter occurs, it could cause negative effects

on the process such as producing noise, poor surface roughness, increasing tool wear,reducing tool life and productivity [2-4] Chatter prediction is therefore critically importantfor determining stable cutting parameters such as spindle speed, depth of cut (DOC), andfeed rate

Figure 2.1 Milling regenerative chatter

Dynamic cutting force model has played an important role in analyzing andpredicting chatter vibration The accurate model could be used to analyze the machiningprocess and optimize the cutting parameter The orthogonal chatter theory was morecomplicated to apply in the milling process due to the changing thickness direction, therotating cutting force, and the intermittent cutting periods [3, 4] The engagement betweencutter and workpiece was referred to the instantaneous chip thickness and was considered as

a function of cutting force in the cutting force mechanism The force modeling for thecutting process was first presented

by Martellotti [11], in which the chip thickness was calculated by a simple expression of

h  ft sin  A mechanistic model for the force system in end milling was developed byKline et al [12] This model is based on chip load, cut geometry, and the relationshipbetween cutting forces and chip load, the uncut chip thickness was reportedly proportional

to the cutting force Tsai proposed a predictive force model in end-milling processbased on geometrical analysis [13] A generalized geometric model of milling cutters wasreported in [14] During milling operation, tool runout has negative effects on theperformance of the cutting operations There are some possibilities leading to cutter runout[2]: axis of rotation errors of the spindle, an offset between the holder centerline and spindleaxis of rotation an offset between the tool centerline and holder centerline, and radiivariation between cutter teeth The average chip thickness was increased corresponding tothe presence of runout for those teeth actually engaged in the cut, the effects of runout errors

on dynamic chip thickness were investigated to improve the accuracy of the model [15, 16].The basics of chatter vibration in orthogonal cutting operations described by an accuratemodel were proposed by Tobias [17]

A stability lobe diagram based on regenerative chatter theory is generally aprevailing method to predict and control chatter Figure 2.2 represents an example ofstability lobe diagram The diagram was divided into stable and unstable zones by astability boundary generated by a series of intersected stability lobes [2, 3] Stablemachining conditions with higher material removal rates could be thus achieved by usingthis method [18, 19] The development of stability lobe diagram was however based on therestrictive assumption that the dynamics of spindle-tool system has not changed over the

spindle speed range [5].

Figure 2.2 Stability lobe diagram [2]

The stability lobe diagram may inevitably misinterpret the important attributes of themachining processes which in fact always contain rich nonlinear characteristics [6, 7] Bothtime and frequency responses hence have to be monitored simultaneously

2.2 Signal Analysis Approaches

The methods used generally for evaluating the vibration signals involved thetransformation of the cutting force signals from time to frequency domain are Fast FourierTransform (FFT), Short-Time Fourier Transform (STFT), and Continuous WaveletTransform (CWT) Through these methods, it was possible to view properties orcharacteristic

information of the cutting process hidden in the time domain [20] Fourier transform (FT)transforms the signal

(2-1)

Fourier transform considered as the basis of modern signal processing is well known

to process the stationary signals, especially when the feature components of signals areobvious in magnitude [21, 22] There are a lot of studies using FFT to identify chattervibration in metal cutting Chatter frequencies are often high non-integer multiples offrequency with the higher magnitudes appeared in the Fourier spectrum, which wasanalyzed and shown in the previous literature [7, 23] The Fourier-based methods arenonetheless based on the assumption that the analyzed signal is stationary in the timedomain The globally inclusive of information makes it difficult to provide any informationabout individual frequency event of the signal It is accordingly not suitable for many non-stationary systems when their transient responses are analyzed

Previous research was reported that the proper method for processing time-varyingnon-stationary signal is time–frequency analysis, which includes STFT, Wigner–Villedistribution, Gabor transform, WT, wavelet packet transform, and HHT They are effectivetime–frequency analysis methods To overcome this limitation of FFT, Gabor introduced asliding window function to the FT and obtained a localized time–frequency [9] Equation 2-

2 represents the resultant transform named short-time Fourier transform

2.3, it can be concluded that high resolution both in frequency and time cannot be attained atthe same time (The uncertainty principle) This is one of the most restrictive in STFT

Figure 2.3 Time-frequency resolution of STFT [9]

Continuous and discrete wavelet transform (WT) were recognized by manyresearchers as flexible and effective tools for processing both stationary and non-stationarysignals, particularly in machining [25] Wavelet is advantageous for the analysis of non-stationary time series data arisen from metal cutting according to Kunpeng et al [26]because it possesses better resolution capabilities in both time and frequency domains.Decomposed signals were usually obtained by choosing proper wavelet coefficients forfeature extraction in order to detect chatter [27] The sudden amplitude change ofdecomposed vibration signals could be considered as a valid evidence to identify chatter[7] By applying FT to the decomposed signals, their Fourier spectrum revealed clearpresence of chatter [28] Support vector machine and wavelet transform were used by Peng

et al [29] to detect chatter They reported that once chatter occurs, the correspondingvibration signal generally exhibited non- stationarity, and the frequency components of thesignal varied over time The behavior of the detail coefficients from WT was used todetermine the presence of chatter [30] Nevertheless, WT is still difficult to determine thesuitable wavelet function and decomposition levels to carry out the chatter fingerprint Inaddition, the decomposed signal might be distorted and result in limited accuracy

Hilbert-Huang transform (HHT) has recently become a superior tool to investigatemachining vibration This method is a powerful tool for time-frequency analysis ofnonlinear and non-stationary signals due to a time adaptive decomposition operation on thesignals It

is moreover not limited by uncertainty principle because of its precise time and frequencyresolutions [10, 31] The complex time series signals were decomposed into a set of intrinsicmode functions (IMFs) which represent simple oscillatory modes [32] The instantaneousfrequency (IF) could be consequently obtained by applying Hilbert transform to each IMF.Fourier spectrum of IMFs and the marginal spectrum obtained by HHT could be used toobserve the main frequencies of the signal among those moments with chatter, as reported

by Wei et al [6] and Peng et al [33] The approach, however, was still burdensome to selectIMFs that contain rich chatter information for analyzing signals Wavelet packets wereutilized by Cao et al [34] to decompose the signal into a set of narrow bands in order toenhance the result of HHT The dimensionless chatter indicators defined by the mean valueand standard deviation of Hilbert-Huang spectrum were reported as effective tools forchatter detection This method is nevertheless troublesome to determine the suitable waveletdecomposition level and to select optimal mother wavelet The nonlinear dimensionlessindicators, complexity and power spectral entropy were utilized as chatter indicators afterbeing processed with ensemble empirical mode decomposition (EEMD) [35]

A dynamic cutting force model with tool runout error in the end-milling process wasproposed to generate the force signals in this study The stability of the process was theninvestigated by the time-frequency analysis All three of STFT, WT and HHT were used forprocessing the cutting force signals The difference between stable and unstable conditionswas clearly distinguished from the analysis Most of the energy concentrated at toothpassing frequency in stable cutting condition, while a large amount of energy emerged athigh frequency when chatter occurs The standard deviation and energy ratio of IMFs weredefined as dimensionless indicators for detecting the presence of chatter effectively, eventhough the cutting forces are known as non-stationary signals and changed in differentstates The proposed method was validated by the stability lobe diagram created by impacttesting and the machined surface topography along with surface roughness

Chapter 3

Dynamic Cutting Force Model

3.1 Regenerative Chatter Model

This section presents a dynamic cutting force mode in which the cutting edges aredecomposed into a set of elements by discretizing along tool axis The geometry of generalend mill with its schematic representation is provided in Fig 3.1

Figure 3.1 The model of helical end mill geometry

A model of the end mill which has two orthogonal degrees of freedom in x and ydirections is considered in Fig 3.2 The vibration normal to the cut surface is used todetermine the instantaneous chip thickness The trajectory of the cutter is assumed to be acircular path

Figure 3.2 Dynamic cutting force model

The tool vibration in x and y directions must be projected into surface normal

direction in order to evaluate chip thickness Those displacements can be represented

h(i, j, k )   f t sin(i , j ,k )  n(t  )  n(t)  g(i ,

j ,k )

(3-5)

 K K bh(

disk

h(i, j, k)   f t sin(i , j ,k )  n(t  )  n(t)  (i, j, k)  (i, j 1, k) 

g(i , j ,k )

(3-6)

and

and equals to zero otherwise:

h  f t sin j and   (i, j, k )   (i, j 1, k

)

are neglected The chip thickness in normal

direction is therefore become as Eq (3-8)

characteristic equation can be written as in Eq (3-23).



 xx yy xx yy xy yx  xx xx yy yy

The limiting chip width or critical depth of cut is evaluated from the real and imaginary part

The phase shift between subsequent tooth passages, the tooth passing periods, and spindle

  

 ph    2

 Re 

of this method is presented in the following sections.

3.2 Dynamic Cutting Force Model

The instantaneous chip thickness including tool runout errors was presented in Eq 6) The different cutting forces in radial, axial, and tangential directions regarding effects ofplowing are written as [2]:

 cos( j ) dF n (i, j, k )

The whole process to predict dynamic cutting force is shown in Fig 3.3, in whichthe input parameters of the process including model dynamic parameters, cutting forcecoefficients, cutting parameter, cutting conditions, cuter parameters and geometry Chipthickness then can be calculated following chip thickness model, Cutting forces in the globalcoordinate frame are finally determined using Eq (3-32) Once the model was verified bythe experiments, the force signals were used for signal processing in order to investigate the

machining stability.

Figure 3.3 Flow chart of dynamic cutting force

16

Chapter 4

Experimental Setup and Model Verification

4.1 Overview and Aim

The accuracy of the cutting force model which has been investigated in previoussection was evaluated by experiments This chapter introduces the machines and equipmentused to conduct the experiments Three experiments were conducted Firstly, a set ofexperiments was conducted to find specific cutting force coefficients and cutting forceangle Secondly, impact testing was carried out in order to investigate the tool tip dynamics

in the system Finally, a series of end milling experiments was conducted to examine thedynamic force model and to investigate the proposed methodology for chatter detection All

of the experimental setups are also described in detail for each kind of experiment

4.2 Experimental Setup

4.2.1 Machine, Cutter and Workpiece

Machining experiments were performed in a 3-axis CNC milling machine MV-154(with Heidenhain TNC620 controller) as shown in Fig 4.1 The machine features areprovided in Table 4-1 The workpiece was a block of Al6061-T6 with the size of30x30x40mm Figure 4.2 represents an uncoated carbide end mill cutter used in theexperiments Its diameter is 12 mm, with helix angle of 26° and two flutes The cutting toolparameters in detail are shown in Table 4-2

Table 4-1 Machine features

Max Speed Max

Power

Axis travel

x y zrpm KW mm mm mm

8000 15 762 530 560

Figure 4.1 The three- axis CNC milling machine at NTUST

Figure 4.2 A carbide end mill

Table 4-2 Parameters of ToolTool company Model Tool diameter

(mm)

Flutes Cutting edge length

(mm)Lasting

Victory LV9932WW2 12 2 30

4.2.2 Cutting Force Measurement Equipment

Figure 4.3 illustrates a Kistler dynamometer (type 9129AA) which used to measurethe cutting force signals directly The dynamometer was mounted between the workpieceand workbench Figures 4.4 shows the experimental setup

Figure 4.3 Kistler Dynamometer

Figure 4.4 Experimental setup