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

  • M. Alper SofuoğluEmail author
Technical Paper


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.


Chatter vibrations Stable cutting depths Stochastic approach Turning operation Milling operation 

List of symbols


Axial depth of cut (chatter-free)


Computer numerical control


Test statistic for Kolmogorov–Smirnov test


Expected frequency of ith data


Theoretical cumulative distribution of the distribution


First-order second-moment method


Stiffness coefficient


Stiffness coefficient in the x-direction


Stiffness coefficient in the y-direction


Imaginary part of eigenvalue/real part of the eigenvalue


Radial cutting constant


The number of data


The number of teeth


Observed frequency of ith data


Damping coefficient


Damping coefficient in the x-direction


Damping coefficient in the y-direction


Test statistic for Anderson–Darling test


Natural frequency

ωn x

Natural frequency in the x-direction

ωn y

Natural frequency in the y-direction


Test statistic for Chi-square test


Significance level


Eigenvalue (real and imaginary parts)



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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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