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Prediction of stable depth of cuts in turning and milling operations: a new probabilistic approach

  • M. Alper SofuoğluEmail author
Technical Paper
  • 10 Downloads

Abstract

Chatter vibration in turning and milling operations is one of the most critical problems that causes low workpiece quality and manufacturing efficiency. Therefore, the determination of stable cutting depths is crucial for these operations. Several vibrational characteristics [natural frequency (ωn), stiffness coefficient (k), and damping coefficient (s)] affect stable cutting depths. The vibration characteristics of these operations show randomness for every setup condition. For this reason, the randomness of the vibration characteristics should be modeled. In this study, a probabilistic approach and regression model are combined for turning operation. Also, a probabilistic approach and analytical model are integrated for milling operation. The purpose of these models is to establish confidence intervals for stability diagrams. As a result, the operators can work in a secure region during the operations.

Keywords

Chatter vibrations Stable cutting depths Stochastic approach Turning operation Milling operation 

List of symbols

alim

Axial depth of cut (chatter-free)

CNC

Computer numerical control

D

Test statistic for Kolmogorov–Smirnov test

Ei

Expected frequency of ith data

F

Theoretical cumulative distribution of the distribution

FOSM

First-order second-moment method

k

Stiffness coefficient

kx

Stiffness coefficient in the x-direction

ky

Stiffness coefficient in the y-direction

K

Imaginary part of eigenvalue/real part of the eigenvalue

Kt

Radial cutting constant

N

The number of data

Nt

The number of teeth

Oi

Observed frequency of ith data

s

Damping coefficient

sx

Damping coefficient in the x-direction

sy

Damping coefficient in the y-direction

S

Test statistic for Anderson–Darling test

ωn

Natural frequency

ωn x

Natural frequency in the x-direction

ωn y

Natural frequency in the y-direction

χ2

Test statistic for Chi-square test

α

Significance level

λr,i

Eigenvalue (real and imaginary parts)

Notes

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Copyright information

© The Brazilian Society of Mechanical Sciences and Engineering 2019

Authors and Affiliations

  1. 1.Mechanical Engineering DepartmentEskişehir Osmangazi UniversityEskisehirTurkey

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