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Chatter reliability prediction of side milling aero-engine blisk

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Abstract

Reliability analysis of a dynamic structural system is applied to predict chatter of side milling system for machining blisk. Chatter reliability is defined as the probability of stability for processing. A reliability model of chatter was developed to forecast chatter vibration of side milling, where structure parameters and spindle speed are regarded as random variables and chatter frequency is considered as intermediate variable. The first-order second-moment method was used to work out the side milling system reliability model. Reliability lobe diagram (RLD) was applied to distinguish reliable regions of chatter instead of stability lobe diagram (SLD). One example is used to validate the effectiveness of the proposed method and compare with the Monte Carlo method. The results of the two approaches were consistent. Chatter reliability and RLD could be used to determine the probability of stability of side milling.

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Abbreviations

ϕex, ϕst :

Cutter entrance and exit angles

N t :

Tooth number of cutter

hj(t):

Dynamic chip thickness

ϕj(t):

Cutter rotation angle

(x(t), y(t)):

Dynamic displacement of the current cutter tooth at the present time t

(x(t-T), y(t-T)):

Dynamic displacement of the previous current cutter tooth period

T :

The tooth passing interval

(Δx, Δy):

Dynamic displacement difference

g(ϕj(t)):

A unit step function that determines whether the tooth is in or out of cut

F(t):

The cutting forces excite in the X- and Y-direction

b:

The axial cutting depth

KT,KR :

The tangential and radial cutting force coefficients

aXX(t), aXY(t), aYX(t), aYY(t):

The time-varying directional dynamic milling force coefficients

ϕ p :

The pitch angular

G(iω):

The transfer function matrix of the cutter-workpiece contact zone

Δt :

The regeneration displacement vector

S c :

Chatter frequency

Λ:

The eigenvalue

Λr :

The real part of eigenvalue

Λi :

The imaginary part of eigenvalue

d lim :

The critical axial depth of cut

m :

Mass

k :

Stiffness

c:

Damp

S :

Spindle speed

ω n :

Inherent frequency

ξ :

Damping ratio

fx(x):

The limit state function of the milling system

d :

The axial depth of cut

R S :

The reliability of the model

X :

The random variables vector

Z :

The limit state function of milling system

ρ :

The correlation matrix for milling system

ρ xixj :

The correlation coefficient between variable xi and xj.

ζ xixj :

The standard deviation between variable xi and Xj

D:

The covariance matrix of milling system

Y :

The independent random variables

μ :

The mean value of the random variables

ζ :

The standard deviation of the random variables

X* :

The mean value of random variables vector X

Y* :

The original value of random variables vector Y β

δ Yi :

The sensitivity coefficient of variable Yi

P r :

Reliability probability of the milling system

W:

Effective work

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Acknowledgments

This work was supported by the National Natural Science Foundation of China (71761030 and 51965051), China, the Natural Science Foundation of Inner Mongolia (2019LH07003 and 2019LH05029), China, and the Scientific Research Project of High Educational Institution of Inner Mongolia (NJZY19085), China.

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Authors and Affiliations

  1. School of Mechanical Engineering, Inner Mongolia University of Technology, Hohhot, 010051, China

    Guang-Jun Jiang, Dong-Wei Wu, Nan Zhang, Jian-Xin Wu & Ying Wang

Authors
  1. Guang-Jun Jiang
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  2. Dong-Wei Wu
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  3. Nan Zhang
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  4. Jian-Xin Wu
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  5. Ying Wang
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Corresponding author

Correspondence to Nan Zhang.

Additional information

Guang-Jun Jiang is a Professor of Mechanical Engineering at Inner Mongolia University of Technology. He received a Ph.D. in Management Science and Engineering from China University of Mining & Technology, Beijing in 2011. His research interests include reliability analysis, reliability evaluation and system reliability model.

Dong-Wei Wu is a Master’s candidate in Mechanical Engineering at Inner Mongolia University of Technology. His research fields include machining parameter optimization, condition monitoring, residual life prediction, deep learning and reliability analysis.

Nan Zhang is an Associate Professor of Mechanical Engineering at Inner Mongolia University of Technology. She received the Ph.D. in Mechatronic Engineering from Northwestern Polytechnical University in 2020. Her research fields include machining mechanism, condition monitoring, residual life prediction and system reliability.

Jian-Xin Wu is a Professor of Mechanical Engineering at Inner Mongolia University of Technology. He received a Ph.D. in Solid Mechanics from Inner Mongolia University of Technology, Hohhot in 2007. His research fields include mechanical and electrical equipment, wind turbine maintenance and reliability evaluation.

Ying Wang is an Associate Professor of Mechanical Engineering at the Inner Mongolia University of Technology. She received a Ph.D. in Electrical and Information Engineering from University of Duisburg-Eisen in Germany in 2014. Her research fields include control system fault diagnosis, reliability analysis, reliability evaluation and system reliability.

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Jiang, GJ., Wu, DW., Zhang, N. et al. Chatter reliability prediction of side milling aero-engine blisk. J Mech Sci Technol 34, 4005–4013 (2020). https://doi.org/10.1007/s12206-020-2211-z

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  • DOI: https://doi.org/10.1007/s12206-020-2211-z

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