The use of modal derivatives in determining stroke-dependent frequencies of large stroke flexure hinges

Mieke van den Belt, Jurnan Schilder

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

1 Citation (Scopus)
42 Downloads (Pure)

Abstract

Nowadays, a lot of use is made of large stroke flexure hinges in precision engineering. However, these large stroke flexure hinges typically lose stiffness in supporting direction during deflection. The lowest natural frequency is a commonly used measure for this property. Therefore, in shape and topology optimization, the decrease of this first parasitic frequency is often minimized. These optimizations are typically very time consuming, due to the large number of design evaluations. In this paper, a method is presented for determining stroke-dependent frequencies of large stroke flexure hinges. This method makes use of derivatives of mode shapes with respect to modal coordinates. Therefore, geometrical nonlinearities can be taken into account. Using these modal derivatives, frequency derivatives can be determined, making it possible to determine natural frequencies for any given deflection without having to linearize for every load step. For demonstration, the method is used to determine the first parasitic frequency of a single leaf spring as a function of the deflection. The results show that the decrease of this parasitic frequency has the shape of a bell-shaped curve, as commonly described in literature and found in experiments.
Original languageEnglish
Title of host publicationECCOMAS Thematic Conference on Multibody Dynamics
Subtitle of host publicationPrague, June 19-22, 2017: conference proceedings
EditorsMichael Valasek, Zbynek Sika, Tomas Vampola
PublisherCzech Technical University
Pages177-180
Number of pages4
ISBN (Electronic)978-80-01-6174-9
ISBN (Print)978-80-01-06173-2
Publication statusPublished - 2017
EventMultibody Dynamics 2017: 8th ECCOMAS Thematic Conference - Czech Technical University, Prague, Czech Republic
Duration: 19 Jun 201722 Jun 2017
Conference number: 8
http://multibody2017.cz/

Conference

ConferenceMultibody Dynamics 2017
CountryCzech Republic
CityPrague
Period19/06/1722/06/17
Internet address

Fingerprint

Hinges
Shape optimization
Derivatives
Natural frequencies
Leaf springs
Precision engineering
Demonstrations
Stiffness
Experiments

Keywords

  • Modal derivatives
  • Large stroke flexure hinges
  • Frequency derivatives
  • Floating frame of referenceq

Cite this

van den Belt, M., & Schilder, J. (2017). The use of modal derivatives in determining stroke-dependent frequencies of large stroke flexure hinges. In M. Valasek, Z. Sika, & T. Vampola (Eds.), ECCOMAS Thematic Conference on Multibody Dynamics: Prague, June 19-22, 2017: conference proceedings (pp. 177-180). Czech Technical University.
van den Belt, Mieke ; Schilder, Jurnan. / The use of modal derivatives in determining stroke-dependent frequencies of large stroke flexure hinges. ECCOMAS Thematic Conference on Multibody Dynamics: Prague, June 19-22, 2017: conference proceedings. editor / Michael Valasek ; Zbynek Sika ; Tomas Vampola. Czech Technical University, 2017. pp. 177-180
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abstract = "Nowadays, a lot of use is made of large stroke flexure hinges in precision engineering. However, these large stroke flexure hinges typically lose stiffness in supporting direction during deflection. The lowest natural frequency is a commonly used measure for this property. Therefore, in shape and topology optimization, the decrease of this first parasitic frequency is often minimized. These optimizations are typically very time consuming, due to the large number of design evaluations. In this paper, a method is presented for determining stroke-dependent frequencies of large stroke flexure hinges. This method makes use of derivatives of mode shapes with respect to modal coordinates. Therefore, geometrical nonlinearities can be taken into account. Using these modal derivatives, frequency derivatives can be determined, making it possible to determine natural frequencies for any given deflection without having to linearize for every load step. For demonstration, the method is used to determine the first parasitic frequency of a single leaf spring as a function of the deflection. The results show that the decrease of this parasitic frequency has the shape of a bell-shaped curve, as commonly described in literature and found in experiments.",
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van den Belt, M & Schilder, J 2017, The use of modal derivatives in determining stroke-dependent frequencies of large stroke flexure hinges. in M Valasek, Z Sika & T Vampola (eds), ECCOMAS Thematic Conference on Multibody Dynamics: Prague, June 19-22, 2017: conference proceedings. Czech Technical University, pp. 177-180, Multibody Dynamics 2017, Prague, Czech Republic, 19/06/17.

The use of modal derivatives in determining stroke-dependent frequencies of large stroke flexure hinges. / van den Belt, Mieke ; Schilder, Jurnan.

ECCOMAS Thematic Conference on Multibody Dynamics: Prague, June 19-22, 2017: conference proceedings. ed. / Michael Valasek; Zbynek Sika; Tomas Vampola. Czech Technical University, 2017. p. 177-180.

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

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T1 - The use of modal derivatives in determining stroke-dependent frequencies of large stroke flexure hinges

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AU - Schilder, Jurnan

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N2 - Nowadays, a lot of use is made of large stroke flexure hinges in precision engineering. However, these large stroke flexure hinges typically lose stiffness in supporting direction during deflection. The lowest natural frequency is a commonly used measure for this property. Therefore, in shape and topology optimization, the decrease of this first parasitic frequency is often minimized. These optimizations are typically very time consuming, due to the large number of design evaluations. In this paper, a method is presented for determining stroke-dependent frequencies of large stroke flexure hinges. This method makes use of derivatives of mode shapes with respect to modal coordinates. Therefore, geometrical nonlinearities can be taken into account. Using these modal derivatives, frequency derivatives can be determined, making it possible to determine natural frequencies for any given deflection without having to linearize for every load step. For demonstration, the method is used to determine the first parasitic frequency of a single leaf spring as a function of the deflection. The results show that the decrease of this parasitic frequency has the shape of a bell-shaped curve, as commonly described in literature and found in experiments.

AB - Nowadays, a lot of use is made of large stroke flexure hinges in precision engineering. However, these large stroke flexure hinges typically lose stiffness in supporting direction during deflection. The lowest natural frequency is a commonly used measure for this property. Therefore, in shape and topology optimization, the decrease of this first parasitic frequency is often minimized. These optimizations are typically very time consuming, due to the large number of design evaluations. In this paper, a method is presented for determining stroke-dependent frequencies of large stroke flexure hinges. This method makes use of derivatives of mode shapes with respect to modal coordinates. Therefore, geometrical nonlinearities can be taken into account. Using these modal derivatives, frequency derivatives can be determined, making it possible to determine natural frequencies for any given deflection without having to linearize for every load step. For demonstration, the method is used to determine the first parasitic frequency of a single leaf spring as a function of the deflection. The results show that the decrease of this parasitic frequency has the shape of a bell-shaped curve, as commonly described in literature and found in experiments.

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KW - Floating frame of referenceq

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van den Belt M, Schilder J. The use of modal derivatives in determining stroke-dependent frequencies of large stroke flexure hinges. In Valasek M, Sika Z, Vampola T, editors, ECCOMAS Thematic Conference on Multibody Dynamics: Prague, June 19-22, 2017: conference proceedings. Czech Technical University. 2017. p. 177-180