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

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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.

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Abbreviations

a lim :

Axial depth of cut (chatter-free)

CNC:

Computer numerical control

D :

Test statistic for Kolmogorov–Smirnov test

E i :

Expected frequency of ith data

F :

Theoretical cumulative distribution of the distribution

FOSM:

First-order second-moment method

k :

Stiffness coefficient

k x :

Stiffness coefficient in the x-direction

k y :

Stiffness coefficient in the y-direction

K :

Imaginary part of eigenvalue/real part of the eigenvalue

K t :

Radial cutting constant

N :

The number of data

N t :

The number of teeth

O i :

Observed frequency of ith data

s :

Damping coefficient

s x :

Damping coefficient in the x-direction

s y :

Damping coefficient in the y-direction

S :

Test statistic for Anderson–Darling test

ω n :

Natural frequency

ω n x :

Natural frequency in the x-direction

ω n y :

Natural frequency in the y-direction

χ 2 :

Test statistic for Chi-square test

α :

Significance level

λ r,i :

Eigenvalue (real and imaginary parts)

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Authors and Affiliations

  1. Mechanical Engineering Department, Eskişehir Osmangazi University, Eskisehir, Turkey

    M. Alper Sofuoğlu

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Sofuoğlu, M.A. Prediction of stable depth of cuts in turning and milling operations: a new probabilistic approach. J Braz. Soc. Mech. Sci. Eng. 41, 206 (2019). https://doi.org/10.1007/s40430-019-1706-y

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  • DOI: https://doi.org/10.1007/s40430-019-1706-y

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