Analytical and experimental investigation of a parallel leaf spring guidance

Jacob Philippus Meijaard, Dannis Michel Brouwer, Jan B. Jonker

Research output: Contribution to journalArticleAcademicpeer-review

37 Citations (Scopus)
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Abstract

The consequences for the static and dynamic system behaviour of misalignment in an overconstrained direction are analysed. Therefore, a relatively simple parallel leaf spring guidance, which is overdetermined only once, serves as a case to gain insight. A multibody program using flexible beam theory is used to determine the change in vibration mode frequencies and stiffnesses due to misalignment. A previously developed beam element for modelling the leaf springs is shown to be able to describe these phenomena with a limited number of elements. Buckling loads and associated buckling modes are also determined analytically. An instrument has been fabricated to measure the change of vibration mode frequencies due to a rotational misalignment in the overconstrained direction. Experiments using wire spark eroded leaf springs are in good agreement with the calculations. Differences between the experimental and calculated results are attributed to the imperfections in the hardware model, in particular residual stresses, and the assumptions used for the beam element in the numerical model. A small misalignment, in this case 0.8–5.8 mrad, causes strong change of static and dynamic system behaviour. The decreased stiffnesses perpendicular to the compliant direction are disturbing, because these are designed to be large to enhance precision manipulation. The negative effects of overconstrained design are largest if relatively thin and wide leaf springs are used. If the misalignment is kept below 50% of the angle of which a bifurcation occurs, the overconstrained design of the parallel leaf spring mechanism does not significantly influence the system natural frequencies and stiffness.
Original languageUndefined
Pages (from-to)77-97
Number of pages20
JournalMultibody system dynamics
Volume23
Issue number1
DOIs
Publication statusPublished - 2010

Keywords

  • METIS-267191
  • IR-87885

Cite this

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title = "Analytical and experimental investigation of a parallel leaf spring guidance",
abstract = "The consequences for the static and dynamic system behaviour of misalignment in an overconstrained direction are analysed. Therefore, a relatively simple parallel leaf spring guidance, which is overdetermined only once, serves as a case to gain insight. A multibody program using flexible beam theory is used to determine the change in vibration mode frequencies and stiffnesses due to misalignment. A previously developed beam element for modelling the leaf springs is shown to be able to describe these phenomena with a limited number of elements. Buckling loads and associated buckling modes are also determined analytically. An instrument has been fabricated to measure the change of vibration mode frequencies due to a rotational misalignment in the overconstrained direction. Experiments using wire spark eroded leaf springs are in good agreement with the calculations. Differences between the experimental and calculated results are attributed to the imperfections in the hardware model, in particular residual stresses, and the assumptions used for the beam element in the numerical model. A small misalignment, in this case 0.8–5.8 mrad, causes strong change of static and dynamic system behaviour. The decreased stiffnesses perpendicular to the compliant direction are disturbing, because these are designed to be large to enhance precision manipulation. The negative effects of overconstrained design are largest if relatively thin and wide leaf springs are used. If the misalignment is kept below 50{\%} of the angle of which a bifurcation occurs, the overconstrained design of the parallel leaf spring mechanism does not significantly influence the system natural frequencies and stiffness.",
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Analytical and experimental investigation of a parallel leaf spring guidance. / Meijaard, Jacob Philippus; Brouwer, Dannis Michel; Jonker, Jan B.

In: Multibody system dynamics, Vol. 23, No. 1, 2010, p. 77-97.

Research output: Contribution to journalArticleAcademicpeer-review

TY - JOUR

T1 - Analytical and experimental investigation of a parallel leaf spring guidance

AU - Meijaard, Jacob Philippus

AU - Brouwer, Dannis Michel

AU - Jonker, Jan B.

PY - 2010

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N2 - The consequences for the static and dynamic system behaviour of misalignment in an overconstrained direction are analysed. Therefore, a relatively simple parallel leaf spring guidance, which is overdetermined only once, serves as a case to gain insight. A multibody program using flexible beam theory is used to determine the change in vibration mode frequencies and stiffnesses due to misalignment. A previously developed beam element for modelling the leaf springs is shown to be able to describe these phenomena with a limited number of elements. Buckling loads and associated buckling modes are also determined analytically. An instrument has been fabricated to measure the change of vibration mode frequencies due to a rotational misalignment in the overconstrained direction. Experiments using wire spark eroded leaf springs are in good agreement with the calculations. Differences between the experimental and calculated results are attributed to the imperfections in the hardware model, in particular residual stresses, and the assumptions used for the beam element in the numerical model. A small misalignment, in this case 0.8–5.8 mrad, causes strong change of static and dynamic system behaviour. The decreased stiffnesses perpendicular to the compliant direction are disturbing, because these are designed to be large to enhance precision manipulation. The negative effects of overconstrained design are largest if relatively thin and wide leaf springs are used. If the misalignment is kept below 50% of the angle of which a bifurcation occurs, the overconstrained design of the parallel leaf spring mechanism does not significantly influence the system natural frequencies and stiffness.

AB - The consequences for the static and dynamic system behaviour of misalignment in an overconstrained direction are analysed. Therefore, a relatively simple parallel leaf spring guidance, which is overdetermined only once, serves as a case to gain insight. A multibody program using flexible beam theory is used to determine the change in vibration mode frequencies and stiffnesses due to misalignment. A previously developed beam element for modelling the leaf springs is shown to be able to describe these phenomena with a limited number of elements. Buckling loads and associated buckling modes are also determined analytically. An instrument has been fabricated to measure the change of vibration mode frequencies due to a rotational misalignment in the overconstrained direction. Experiments using wire spark eroded leaf springs are in good agreement with the calculations. Differences between the experimental and calculated results are attributed to the imperfections in the hardware model, in particular residual stresses, and the assumptions used for the beam element in the numerical model. A small misalignment, in this case 0.8–5.8 mrad, causes strong change of static and dynamic system behaviour. The decreased stiffnesses perpendicular to the compliant direction are disturbing, because these are designed to be large to enhance precision manipulation. The negative effects of overconstrained design are largest if relatively thin and wide leaf springs are used. If the misalignment is kept below 50% of the angle of which a bifurcation occurs, the overconstrained design of the parallel leaf spring mechanism does not significantly influence the system natural frequencies and stiffness.

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