Skip to main content

Damping Ratio and Natural Frequency of Dynamic System in Milling

  • Conference paper
  • First Online:
Proceedings of the 4th International Conference on Industrial Engineering (ICIE 2018)

Part of the book series: Lecture Notes in Mechanical Engineering ((LNME))

Included in the following conference series:

  • 122 Accesses

Abstract

The problem of the machine tool stability in metalworking has existed since the first machine tool was created. Stability plays an important role in investigations dedicated to machining quality improvement, wear decrease, and, on the other hand, productivity increase. The identification of dynamic parameters such as modes, damping, and stiffness is a part of a stability problem. There are two groups of techniques to find the dynamic parameters: experimental modal analysis and operational modal analysis (OMA). In this study, OMA is used to identify the dynamic parameters of the system in milling. Responses (accelerations) are stored via three-axis accelerometer mounted on the spindle. Furthermore, power spectral density matrix of output responses is estimated. The estimation of natural frequencies and damping ratios is based on the analysis of a power spectral density matrix. A simulation model of milling is created, and some experimental tests are done to verify the suggested approach. The results are discussed as well.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 259.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 329.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Bandat J (2010) Random data, analysis and measurement procedures, 4th edn. Wiley, New York

    Book  Google Scholar 

  2. Brincker R, Ventura CE, Anderson P (1999) Modal identification of output-only systems using frequency domain decomposition. Smart Mater Struct 10:441–445

    Article  Google Scholar 

  3. Shih CY, Twuei YG, Allemang RJ et al (1988) A frequency domain global parameter estimation method for multiple reference frequency response measurements. Mech Sys Sig Proc 2:349–365. https://doi.org/10.1016/0888-3270(88)90059-3

    Article  MATH  Google Scholar 

  4. Peeters B, De Roeck G (1999) Reference-based stochastic subspace identification for output-only modal analysis. Mech SysSig Proc 13:855–878. https://doi.org/10.1006/mssp.1999.1249

    Article  Google Scholar 

  5. Van Overschee P, De Moor B (1993) Subspace algorithms for the stochastic identification problem. Automatica 29:649–660. https://doi.org/10.1016/0005-1098(93)90061-W

    Article  MathSciNet  MATH  Google Scholar 

  6. Zhang L-M, Yao Y-X, Lu M-F (1987) An improved time domain polyreference method for modal identification. Mech Sys Sig Proc 1:399–413. https://doi.org/10.1016/0888-3270(87)90097-5

    Article  MATH  Google Scholar 

  7. Leuridan JM, Brown DL, Allemang RJ (1986) Time domain parameter identification methods for linear modal analysis: a unifying approach. Trans ASME J Vib AcoustStress Reliab 108:1–8. https://doi.org/10.1115/1.3269298

    Article  Google Scholar 

  8. Ewins DJ (2000) Modal testing: theory, practice and application, 2nd edn. Wiley, New York

    Google Scholar 

  9. Krasil’nikov AYa, Kravchenko KYu (2013) Analytical approaches for stability analysis of milling process as a delay system, handbook. Eng J 9:23–31

    Google Scholar 

  10. Krasil’nikov AYa, Kravchenko KYu (2013) Research of stability of delayed systems, describing milling process, in case of one degree of freedom. Bull Mech Eng 9:67–75

    Google Scholar 

  11. Krasil’nikov AYa, Kravchenko KYu (2016) Determining the stability regions in end milling. Russ Eng Res 36:294–299. https://doi.org/10.3103/s1068798x16040080

    Article  Google Scholar 

  12. Krasil’nikov AYa, Kravchenko KYu (2016) Application of analytical approach and simulation for determining of stability lobe diagram of end milling. Bull. Mech. Eng 1:79–84

    Google Scholar 

  13. Kravchenko KYu, Kugaevsky SS, Zhuravlev MP et al (2017) Natural frequencies estimation using operational modal analysis. Bull PNRPU Mech Eng Mater Sci 2:21–35. https://doi.org/10.15593/2224-9877/2017.2.02

    Article  Google Scholar 

  14. James OH III, Carne TG (1995) The natural excitation technique (NExT) for modal parameter extraction from operating structures. Int J Anal Exp Modal Anal 10:260–277

    Google Scholar 

  15. James GH, Carne TG, Lauffer JP et al (1992) Modal testing using natural excitation. In: Proceedings of the 10-th IMAC, San Diego, USA, 3–7 February 1992

    Google Scholar 

  16. Brincker R, Ventura CE, Andersen P (2001) Damping estimation by frequency domain decomposition. In: A conference on structural dynamics, Kissimmee, Florida, 5–8 February 2001

    Google Scholar 

  17. Juang J-N, Pappa RS (1985) An eigensystem realization algorithm for modal parameter identification and model reduction. J Guid Control Dynam 8:620–627. https://doi.org/10.2514/3.20031

    Article  MATH  Google Scholar 

  18. Juang J-N, Cooper JE, Wright JR (1988) An eigensystem realization algorithm using data correlation (ERA/DC) for modal parameter identification. Control-Theory Adv Technol 4:5–14

    MathSciNet  Google Scholar 

  19. Edwin R (2012) System identification methods for (operational) modal analysis: review and comparison. Arch Comput Methods Eng 19:51–124. https://doi.org/10.1007/s11831-012-9069-x

    Article  MathSciNet  MATH  Google Scholar 

  20. Melnikov A, Soal K, Bienert O (2017) Determination of static stiffness of mechanical structures from operational modal analysis. In: 7-th international operational modal analysis conference, Ingolstadt, Germany, 10–12 May 2017

    Google Scholar 

Download references

Acknowledgements

The work was supported by Ministry of Education and Science of the Russian Federation, contract № 02.G25.31.0148.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to K. Yu. Kravchenko .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Kravchenko, K.Y., Kugaevskii, S.S., Zhuravlev, M.P. (2019). Damping Ratio and Natural Frequency of Dynamic System in Milling. In: Radionov, A., Kravchenko, O., Guzeev, V., Rozhdestvenskiy, Y. (eds) Proceedings of the 4th International Conference on Industrial Engineering. ICIE 2018. Lecture Notes in Mechanical Engineering. Springer, Cham. https://doi.org/10.1007/978-3-319-95630-5_23

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-95630-5_23

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-95629-9

  • Online ISBN: 978-3-319-95630-5

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics