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Modelling the effect of flank wear on machining thrust stability

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Abstract

This paper discusses an analytical assessment of the effect of cutting tool flank wear on machining stability along the thrust direction in a turning operation based on an analysis of frequency band root-mean-square (RMS) level of the accelerometer signals. The energy content of machining at the tool-tip/workpiece interface along the flank is represented by the RMS signal level, in comparison to the random vibration of the cantilever portion of the tool holder. The RMS signals measured from a tool-post accelerometer in stable machining with tool wear effect are calculated using the frequency band RMS method at the first natural frequency of the cantilever portion of the tool holder. Increasing flank wear results in increasing stability and decreasing RMS in the thrust direction in machining. For model validation, a series of machining experiments were performed under the condition of various flank wear/land widths, while the RMS signals from a tool-post accelerometer were collected and studied. It was found that theoretical predictions were shown to be in agreement with experimental results.

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Abbreviations

c :

Viscous damping constant

c′ :

Effective damping constant, c +k c T+k f

F w :

Contact force in the x direction

f 1 :

Lower frequency of band pass filter

f 2 :

Higher frequency of band pass filter

G x (f):

One-sided power spectral density function of the signal x(t)

H(w):

Complex frequency response function

k′ :

k m

k m :

Spring constant

k c :

Cutting coefficient

k f :

Penetration rate constant

k sp :

Specific contact force

l w :

Tool wear width

ψ(x):

Variation of chip thickness in the direction normal to the primary cutting edge, ψ(x)=[x(t−T)−x(t)]

m :

Mass

m′ :

Effective mass, \(m - k_{c} \frac{{T^{2} }} {2}\)

n(t):

Random force

n′(t):

Random acceleration

p(x):

Power spectral density function

S (w):

Mean square spectral density

S o :

Spectral density

T :

Delay time (1/spindle speed)

T p :

Time period

t :

Time

V :

total volume of displaced material

v :

cutting speed

W oc :

Width of cut

w :

frequency, rad/s

w oc :

Width of cut

w n :

Natural frequency, (k′/m′)1/2

ζ :

Damping ratio, c′/2m’w n

x :

Displacement of the mass

\( \ifmmode\expandafter\bar\else\expandafter\=\fi{x} \) :

Mean

\( \dot{x} \) :

Velocity

\(\ifmmode\expandafter\ddot\else\expandafter\"\fi{x}\) :

Acceleration

σ :

Standard deviation

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Authors and Affiliations

  1. Applied Engineering Technology, Goodwin College, Drexel University, Philadelphia, PA 19104, USA

    R. Y. Chiou

  2. Department of Mechanical Engineering, Jeonju Technical College, Jeonju, Korea

    Y. K. Kwon

  3. The Georgia W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA

    S. Y. Liang

Authors
  1. S. Y. Liang
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  2. Y. K. Kwon
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  3. R. Y. Chiou
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Correspondence to S. Y. Liang.

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Liang, S.Y., Kwon, Y.K. & Chiou, R.Y. Modelling the effect of flank wear on machining thrust stability. Int J Adv Manuf Technol 23, 857–864 (2004). https://doi.org/10.1007/s00170-003-1756-1

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