Skip to main content
SpringerLink
Log in

Dynamics of Miniature and High-Compliance Structures: Experimental Characterization and Modeling

  • Research paper
  • Published:
Experimental Mechanics Aims and scope Submit manuscript

Abstract

Background

The dynamic behavior of miniature and high-compliance structures is critical for their performance. However, their low stiffness and inertia bring significant challenges to the experimental characterization and modeling of their dynamics. Traditional modal testing techniques cannot produce the required low noise, high-bandwidth dynamic models with sufficiently low forces to prevent damage to the fragile structures.

Objective

The objective of this work is to develop a new iterative approach that enables effective dynamic characterization of miniature and high-compliance structures.

Methods

The iterative approach consists of a combination of model-based simulations and experimentation. An impact excitation system (IES) with a flexure-jointed cantilever controls the motions of an instrumented impact tip to enable specifying the bandwidth and force magnitude of the impact excitations. Successful application of the IES requires determination of the IES-parameters that produce the desired (broad) bandwidth and (limited) force magnitudes. However, for high-compliance and miniature structures, this requires the knowledge of the dynamics of the sample (the structure), which is not known a priori. To address this, the simulations use both the dynamic model of the IES and an approximate model of the sample dynamics obtained from the previous iteration in order to identify a set of favorable IES parameters for the current iteration.

Results

Two case studies involving a miniature blade of a jet engine turbine and a high-compliance load cell are presented to demonstrate the approach. Only a few iterations were sufficient for converging to a favorable set of parameters that produce high-bandwidth (e.g., 31 kHz) and reproducible dynamic models in the form of frequency response functions (FRFs). As compared to manual impact testing, the use of the new approach expands the bandwidth by as much as 50 times while reducing the test repetitions by more than ten times.

Conclusions

The presented iterative framework based on the impact excitation system addresses the shortcomings of traditional modal testing techniques and enables effective dynamic characterization and modeling of miniature and high-compliance structures.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

References

  1. Filiz S, Ozdoganlar OB (2008) Microendmill dynamics including the actual fluted geometry and setup errors-Part II: Model validation and application. J Manuf Sci Eng 130(3):031120

  2. Filiz S, Ozdoganlar OB (2010) A model for bending, torsional, and axial vibrations of micro- and macro-drills including actual drill geometry Part II: Model validation and application. J Manuf Sci Eng 132(4)

  3. Bediz B, Ozdoganlar OB (2019) Rotational dynamics of micro-scale cutting tools. Precis Eng 60:1–11

    Article  Google Scholar 

  4. Bediz B, Kumar U, Schmitz TL, Ozdoganlar OB (2012) Modeling and experimentation for three-dimensional dynamics of endmills. Int J Mach Tools Manuf 53(1):39–50

  5. Bediz B, Arda Gozen B, Korkmaz E, Ozdoganlar OB (2014) Dynamics of ultra-high-speed (UHS) spindles used for micromachining. Int J Mach Tools Manuf 87:27–38

    Article  Google Scholar 

  6. Filiz S, Xie L, Weiss LE, Ozdoganlar OB (2008) Micromilling of microbarbs for medical implants. Int J Mach Tools Manuf

  7. Samuel J, Jun MBG, Ozdoganlar OB, Honegger A, Vogler M, Kapoor SG (2020) Micro/Meso-scale mechanical machining 2020: A two-decade state-of-the-field review. J Manuf Sci Eng 142(11)

  8. Kim NI, Lee J (2017) Coupled vibration characteristics of shear flexible thin-walled functionally graded sandwich I-beams. Compos Part B Eng 110:229–247

    Article  Google Scholar 

  9. Lundstrom T, Sidoti C, Jalili N (2015) Dynamic modeling of stacked, multi-plate flexible systems. Exp. Mech. 55(8):1551–1568

    Article  Google Scholar 

  10. Tokhi MO, Mohamed Z, Shaheed MH (2001) Dynamic characterisation of a flexible manipulator system. Robotica 19(5):571–580

    Article  Google Scholar 

  11. Salumäe T, Chambers LD, Megill WM, Kruusmaa M (2014) Modelling of a biologically inspired robotic fish driven by compliant parts. Bioinspir Biomim

  12. Li Y (2011) Optimal design of a 3-PUPU parallel robot with compliant hinges for micromanipulation in a cubic workspace. Robot Comput Integr Manuf

  13. Phan CN, Aureli M, Porfiri M (2013) Finite amplitude vibrations of cantilevers of rectangular cross sections in viscous fluids. J Fluids Struct 40:52–69

    Article  Google Scholar 

  14. Rubio WM, Silva ECN, Bordatchev EV, Zeman MJF (2009) Topology optimized design, microfabrication and characterization of electro-thermally driven microgripper. J Intell Mater Syst Struct 20(6):669–681

    Article  Google Scholar 

  15. Kim HS, Kim JH, Kim J (2011) A review of piezoelectric energy harvesting based on vibration. Int J Precis Eng Manuf 12(6):1129–1141

    Article  Google Scholar 

  16. Tang L, Yang Y, Soh CK (2010) Toward Broadband Vibration-based Energy Harvesting. J Intell Mater Syst Struct 21(18):1867–1897

    Article  Google Scholar 

  17. Arrieta AF, Delpero T, Bergamini AE, Ermanni P (2013) Broadband vibration energy harvesting based on cantilevered piezoelectric bi-stable composites. Appl Phys Lett 102(17):173904

  18. Tang X, Zuo L (2011) Enhanced vibration energy harvesting using dual-mass systems. J Sound Vib 330(21):5199–5209

    Article  Google Scholar 

  19. Zhou W, Penamalli GR, Zuo L (2012) An efficient vibration energy harvester with a multi-mode dynamic magnifier. Smart Mater Struct 21(1):15014

  20. Ewins DJ (1986) Modal testing: Theory and practice. J Vib Acoust Stress Reliab Des 108:109

    Article  Google Scholar 

  21. Ozdoganlar OB, Hansche BD, Carne TG (2005) Experimental modal analysis for microelectromechanical systems. Exp Mech 45(6):498–506

    Article  Google Scholar 

  22. Filiz S, Ozdoganlar OB (2008) Experimental modal analysis of microdrills. In: Transactions of the North American Manufacturing Research Institution of SME, vol 36. pp 185–192

  23. Korkmaz E, Bediz B, Gozen BA, Ozdoganlar OB (2014) Dynamic characterization of multi-axis dynamometers. Precis. Eng. 38(1):148–161

    Article  Google Scholar 

  24. Chen W, Korkmaz E, Gozen BA, Ozdoganlar OB (2019) Measurement of high-bandwidth nanonewton forces in a low-compliance configuration. Sensors and Actuators, A: Physical 299:111474

  25. Gozen BA, Ozdoganlar OB (2012) A method for open-loop control of dynamic motions of piezo-stack actuators. Sensors and Actuators, A: Physical 184:160–172

    Article  Google Scholar 

  26. Gozen BA, Ozdoganlar OB (2012) Design and evaluation of a mechanical nanomanufacturing system for nanomilling. Precis Eng 36(1):19–30

    Article  Google Scholar 

  27. Gozen BA, Ozdoganlar OB (2012) Characterization of three-dimensional dynamics of piezo-stack actuators. Mech Syst Signal Process 31:268–283

    Article  Google Scholar 

  28. Shekhar S, Nahata S, Ozdoganlar OB (2020) The effect of spindle dynamics on tool-tip radial throw in micromachining. J Manuf Process 56:1397–1403

    Article  Google Scholar 

  29. Brüggemann T, Biermann D, Zabel A (2015) Development of an automatic modal pendulum for the measurement of frequency responses for the calculation of stability charts. Procedia CIRP 33:587–592

    Article  Google Scholar 

  30. Hosoya N, Kato J, Kajiwara I (2019) Spherical projectile impact using compressed air for frequency response function measurements in vibration tests. Mech Syst Signal Process 134:106295

  31. Norman P, Jung G, Ratcliffe CP, Crane RM, Davis CH (2012) Development of an Automated Impact Hammer for Modal Analysis of Structures

  32. Maierhofer J, Mahmoudi AE, Rixen DJ (2020) Development of a low cost automatic modal hammer for applications in substructuring. Dynamic Substructures, vol 4. Springer International Publishing, Cham, pp 77–86

    Google Scholar 

  33. Shekhar S, Ozdoganlar OB (2020) Reproducible modal testing using a flexure-based impact excitation system. Topics in Modal Analysis & Testing, vol 8. Springer International Publishing, Cham, pp 349–352

    Google Scholar 

  34. Bediz B, Korkmaz E, Ozdoganlar OB (2014) An impact excitation system for repeatable, high-bandwidth modal testing of miniature structures. J Sound Vib 333(13):2743–2761

    Article  Google Scholar 

  35. Korkmaz E, Gozen BA, Bediz B, Ozdoganlar OB (2017) Accurate measurement of micromachining forces through dynamic compensation of dynamometers. Precis Eng 49:365–376

    Article  Google Scholar 

  36. Yagci B, Filiz S, Romero LL, Ozdoganlar OB (2009) A spectral-Tchebychev technique for solving linear and nonlinear beam equations. J Sound Vib 321(1–2):375–404

    Article  Google Scholar 

  37. Filiz S, Ozdoganlar OB (2008) Microendmill dynamics including the actual fluted geometry and setup errors Part I: Model development and numerical solution. J Manuf Sci Eng 130(3)

  38. Filiz S, Ozdoganlar OB (2010) A model for bending, torsional, and axial vibrations of micro- and macro-drills including actual drill geometry part I: Model development and numerical solution. J Manuf Sci E T ASME 132(4):1–8

    Google Scholar 

  39. Filiz S, Ozdoganlar OB (2011) A three-dimensional model for the dynamics of micro-endmills including bending, torsional and axial vibrations. Precis Eng 35(1):24–37

    Article  Google Scholar 

  40. Filiz S, Bediz B, Romero LA, Ozdoganlar OB (2012) A spectral-Tchebychev solution for three-dimensional vibrations of parallelepipeds under mixed boundary conditions. J Appl Mech 79(September 2012):051012

  41. Filiz S, Bediz B, Romero LA, Ozdoganlar OB (2014) Three dimensional dynamics of pretwisted beams: A spectral-Tchebychev solution. J Sound Vib 333(10):2823–2839

    Article  Google Scholar 

  42. Bediz B, Aksoy S (2018) A spectral-Tchebychev solution for three-dimensional dynamics of curved beams under mixed boundary conditions. J Sound Vib 413:26–40

    Article  Google Scholar 

  43. Bediz B (2018) A spectral-Tchebychev solution technique for determining vibrational behavior of thick plates having arbitrary geometry. J Sound Vib 432:272–289

    Article  Google Scholar 

  44. Serhat G, Bediz B, Basdogan I (2020) Unifying lamination parameters with spectral-Tchebychev method for variable-stiffness composite plate design. Compos Struct 242:112183

  45. Anamagh MR, Bediz B (2020) Free vibration and buckling behavior of functionally graded porous plates reinforced by graphene platelets using spectral Chebyshev approach. Compos Struct 253:112765

  46. Lankarani HM, Nikravesh P (1994) Continuous contact force models for impact analysis in multibody systems. Nonlinear Dyn 5(2):193–207

    Google Scholar 

  47. Johnson, K. (1985). Normal contact of elastic solids – Hertz theory. In Contact Mechanics. Cambridge University Press. pp 84-106.

  48. Gugan D (2000) Inelastic collision and the Hertz theory of impact. Am J Phys 68(10):920–924

    Article  Google Scholar 

  49. Gilardi G, Sharf I (2002) Literature survey of contact dynamics modelling. Mech Mach Theory 37(10):1213–1239. https://doi.org/10.1016/S0094-114X(02)00045-9

    Article  MathSciNet  MATH  Google Scholar 

  50. Shekhar S, Nahata A, Ozdoganlar OB (2019) Analysis of contact dynamics using controlled impact excitations. Conference Proceedings of the Society for Experimental Mechanics Series, vol 3. Springer, New York LLC, pp 265–273

    Google Scholar 

  51. Richardson MH, Formenti DL (1982) Parameter estimation from frequency response measurements using rational fraction polynomials. Proceedings of the International Modal Analysis Conference. pp 167–182

  52. Polytec I (2010) OFV-5000 vibrometer controller user manual. https://www.polytec.com/us/vibrometry/products/single-pointvibrometers

  53. Anandan KP, Ozdoganlar OB (2013) An LDV-based methodology for measuring axial and radial error motions when using miniature ultra-high-speed (UHS) micromachining spindles. Precis. Eng. 37(1):172–186

    Article  Google Scholar 

  54. Anandan KP, Tulsian AS, Donmez A, Ozdoganlar OB (2012) A technique for measuring radial error motions of ultra-high-speed miniature spindles used for micromachining. Precis Eng 36(1):104–120

    Article  Google Scholar 

  55. Anandan KP, Ozdoganlar OB (2013) Analysis of error motions of ultra-high-speed (UHS) micromachining spindles. Int J Mach Tools Manuf 70:1–14

    Article  Google Scholar 

  56. Anandan KP, Ozdoganlar OB (2016) A multi-orientation error separation technique for spindle metrology of miniature ultra-high-speed spindles. Precis Eng 43:119–131

    Article  Google Scholar 

  57. Nahata S, Anandan KP, Ozdoganlar OB (2013) LDV-based spindle metrology for ultra-high-speed micromachining spindles. In: Transactions of the North American Manufacturing Research Institution of SME, vol 41. pp 319–324

  58. Nahata S, Onler R, Shekhar S, Korkmaz E, Ozdoganlar OB (2018) Radial throw in micromachining: Measurement and analysis. Precis Eng 54:21–32

    Article  Google Scholar 

  59. Nahata S, Onler R, Korkmaz E, Ozdoganlar OB (2018) Radial throw at the cutting edges of micro-tools when using ultra-high-speed micromachining spindles. In: Procedia Manufacturing, vol 26. Elsevier B.V., pp 1517–1526

Download references

Acknowledgements

The authors would like to acknowledge valuable discussions with Dr. Bekir Bediz and his assistance in modeling with the spectral-Tchebychev approach.

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, Carnegie Mellon University, Pittsburgh, Pennsylvania, 15213, USA

    S. Shekhar & O. Burak Ozdoganlar

  2. Department of Material Science and Engineering, Carnegie Mellon University, Pittsburgh, Pennsylvania, 15213, USA

    O. Burak Ozdoganlar

  3. Department of Biomedical Engineering, Carnegie Mellon University, Pittsburgh, Pennsylvania, 15213, USA

    O. Burak Ozdoganlar

Authors
  1. S. Shekhar
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. O. Burak Ozdoganlar
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to O. Burak Ozdoganlar.

Ethics declarations

Conflicts of Interest

The authors declare that they have no conflicts of interest.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

The contents of this article is based upon the work supported by the National Science Foundation under Grant No. 1562439 (Ozdoganlar).

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Shekhar, S., Ozdoganlar, O.B. Dynamics of Miniature and High-Compliance Structures: Experimental Characterization and Modeling. Exp Mech 62, 299–312 (2022). https://doi.org/10.1007/s11340-021-00788-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11340-021-00788-5

Keywords

Search

Navigation