Analysis of milling stability based on cutting force signal processing

國立臺灣科技大學

機械工程系

碩士學位論文

學號：M10403802

以切削力訊號分析銑削加工穩定性

Analysis of Milling Stability Based on

Cutting Force Signal Processing

(Draft)

研究生：Tran Minh Quang

指導教授：Chun-Hui Chung, Meng-Kun Liu

中華民國 一零六 年 六月 三十日

i

摘要

銑削加工是一種非常常見的成型加工方法，而在銑削加工的過程中，不

適當的加工參數會使刀具產生顫震，其顫震原因來自於刀刃與工件之間呈現週

期性的不連續切削行為，造成切屑厚度週期性的變化，使得刀具產生自激性的

震動以及不穩定的切削行為，而顫震會使銑削加工的不穩定性以及降低切削效

率，造成尺寸精度、刀具壽命以及表面完整性的下降，因此本研究主要目標為

建立完整之刀具壽命下，開發端銑刀的動態切削力模組，對於銑削加工潛在的

顫震進行探討。以模組的方式模擬出之切削立，與實際切削所獲得之切削力進

行時間及頻率域比較，我們發現時域、頻率域、短時距傅立葉變換、連率小波

轉換以及希爾伯特-黃轉換進行顫震訊號分析，相較於使用傅立葉變換光譜法

所獲得之結果是徹底地不同，傅立葉變換光譜法在應用於大量的非線性訊號效

率極低，進行動態切削力模組模擬之訊號與實驗所獲得之切削力訊號比較，發

現顫震頻率主要由兩個現象之頻率所構成，為刀刃通過工件時之頻率以及顫震

造成的不穩定高頻，此外，以 standard deviation 以及本質模態函數方式所獲

得之能量比，可有效率的辦別出刀具顫震，最後通過工件表面形貌、表面粗糙

度和穩定性波瓣圖驗證其分析結果。

關鍵字：銑削加工、刀具顫震、時頻分析、小波分析、希爾伯特-黃轉換

ii

Abstract

The milling operation is the most common form of machining. Because the action of

each cutting edge and workpiece is intermittent and periodical, the chip thickness varies

periodically. This could lead to self-excited vibrations and unstable cutting which is called

chatter vibration. Chatter causes machining instability and reduces productivity in the metal

cutting process. It has negative effects on the surface finish, dimensional accuracy, tool life

and machine life. Chatter identification is therefore necessary to control, prevent, or eliminate

chatter and to identify the stable machining condition. A dynamic cutting force model of the

end-milling process with tool runout error was established in this research to understand the

underlying mechanism of chatter. The accuracy of the cutting force model in both time and

frequency domains was evaluated by comparing to experimental force signals. Time￾frequency analysis approaches, specifically short time Fourier transform, continuous wavelet

transform and Hilbert-Huang transform, were utilized to give an utterly different perspective

of chatter from the conventional Fourier spectrum which is insufficient in analyzing the

signals of rich nonlinear characteristics. By comparing the simulation with experimental

result, chatter frequency was found to consist of two major components, frequency

modulation alongside tooth passing frequency caused by the increased tool runout error and

the non-stationary high frequency from the regenerative vibration. Moreover, dimensionless

chatter indicators, defined by the standard deviation and energy ratio of the specific intrinsic

mode function, could identify the occurrence of chatter effectively. 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.

iii

Acknowledgement

I would like to thank all the people who helped me to finish this thesis. First of all, I

would like to express my deep gratitude to my academic advisors: Professor. Chun-Hui

Chung and Professor. Meng-Kun Liu for their valuable guidance, encouragement, and support

throughout my work towards this thesis. Without their help and guidance, this work would

not be possible.

I also would like to thank Mr. Yi-Wen Qui who provided his experimental data which

was used to verify my methodology in this thesis. I would like to thank all of my labmates

who have supported me a lot with laboratory facilities so that I could conduct my experiments.

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 their patience

and support during my study. I am very grateful for their love.

iv

Nomenclature

db

discretized axial depth of cut (mm)

, K K ne te

radial and tangential edge

coefficients (N/mm)

n

dF

differential radial cutting force (N)

Nt

number of flutes

t

dF

differential tangential cutting force

(N)

r

edge radius (mm)

x

dF

differential cutting force in x-direction

(N)

x y,

displacement in x and y directions

(mm)

y dF

differential cutting force in y direction

(N)

z

absolute value of the distance from

the end (mm)

t

f

feed per tooth (mm/flute)



helix angle (deg)

F

s

sampling rate frequency (Hz)



immersion angle (deg)

Fsi

simulated cutting force (N)

e

exit angle (deg)

F

ex

experimental cutting force (N)

s

start angle (deg)

b

axial depth of cut (mm)

c

chatter frequency (rad/s)

h

instantaneous chip thickness (mm)



spindle speed (rpm)

K

s

specific cutting force coefficient (N)



position angle (deg)



cutting force angle (deg)



runout of cutting edge (mm)

, K Kn t

radial and tangential cutting

coefficients (N/mm2

)



time for one rotation (sec)

v

Contents

摘要 ..........................................................................................................................................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......................................................................................................17

4.2. Experimental Setup.....................................................................................................17