Optimized cross-spring pivot configurations with minimized parasitic shifts and stiffness variations investigated via nonlinear FEA

Marković, Kamenka Živčić; Zelenika, Saša

doi:10.1080/15397734.2016.1231614

Cited by 21 publications

(11 citation statements)

References 22 publications

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“…The main known cause for in-plane gravity effects on the stiffness of flexure pivots is their parasitic center shift. It is well-known that flexure pivots only approximate a rotational motion [10,15,16,[22][23][24][25] and, in the case of a flexure-pivot oscillator, their center shift displaces the center of mass (COM) of the inertial body. The action of gravity on this displaced COM results in a torque that either contributes to the restoring torque of the flexures (positive stiffness contribution) or drives the oscillator away from its equilibrium (negative stiffness contribution).…”

Section: In-plane Gravity Effects Mitigationmentioning

confidence: 99%

Gravity-Compensation Design Approaches for Flexure-Pivot Time Bases

Thalmann¹,

Gubler²,

Henein³

2022

Machines

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While flexure time bases have gained significant traction in the watchmaking industry thanks to their high quality factor and monolithic design, maintaining a stable frequency in varying orientations of wrist watches with respect to gravity remains a significant challenge. This results from the fact that the flexures play two roles simultaneously: guiding the oscillating mass along a one-degree-of-freedom pivotal motion, and providing the oscillator’s elastic restoring force. Indeed, varying stress-stiffening effects induced by the varying direction of the weight of the oscillating mass affect the pivot angular stiffness, which impacts its oscillating frequency. In order to address this issue, two design approaches are presented which, when combined, allow to reach the strict chronometric standards of mechanical watches. Firstly, the frequency differences for all vertical positions (i.e., gravity orthogonal to the rotation axis) are mitigated by designing architectures with reduced parasitic center shift, or by offsetting the center of mass (COM) along their axis of symmetry, or both. Secondly, the frequency differences between vertical and horizontal positions (i.e., gravity parallel to the rotation axis) are reduced by offsetting the COM along the rotation axis. The implementation and effectiveness of these approaches are demonstrated by numeric simulations, as well as by experimental measurements performed on watch-scale silicon etched prototypes.

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Section: In-plane Gravity Effects Mitigationmentioning

confidence: 99%

Gravity-Compensation Design Approaches for Flexure-Pivot Time Bases

Thalmann¹,

Gubler²,

Henein³

2022

Machines

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“…Analyses of the axis drift can be found for example in (Du et al, 2020; Fowler et al, 2014; Goldfarb and Speich, 1999; Linß et al, 2017; Marković and Zelenika, 2017; Xu and King, 1996). The axis drift is recorded or calculated as a function of the hinge swing angle.…”

Section: Kinematic Studies On Solid-state Hingesin Literaturementioning

confidence: 99%

Accuracy and precision: A new view on kinematic assessment of solid-state hinges and compliant mechanisms

Campanile

Kirmse

Hasse

2021

Journal of Intelligent Material Systems and Structures

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Compliant mechanisms are alternatives to conventional mechanisms which exploit elastic strain to produce desired deformations instead of using moveable parts. They are designed for a kinematic task (providing desired deformations) but do not possess a kinematics in the strict sense. This leads to difficulties while assessing the quality of a compliant mechanism’s design. The kinematics of a compliant mechanism can be seen as a fuzzy property. There is no unique kinematics, since every deformation need a particular force system to act; however, certain deformations are easier to obtain than others. A parallel can be made with measurement theory: the measured value of a quantity is not unique, but exists as statistic distribution of measures. A representative measure of this distribution can be chosen to evaluate how far the measures divert from a reference value. Based on this analogy, the concept of accuracy and precision of compliant systems are introduced and discussed in this paper. A quantitative determination of these qualities based on the eigenvalue analysis of the hinge’s stiffness is proposed. This new approach is capable of removing most of the ambiguities included in the state-of-the-art assessment criteria (usually based on the concepts of path deviation and parasitic motion).

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“…16,17 Furthermore, optimal design of the CAFP with minimal center shift and stiffness variations was investigated via nonlinear FEA. 18 A parametric model of a cylindrical CAFP was established based on the FEA results to investigate the pivot's stiffness and stress characteristics. 19 Although the FEA approach provides high accuracy and wide applicability, it offers only limited parametric insights to designers.…”

Section: Introductionmentioning

confidence: 99%

Adaptive pseudo-rigid-body model for generalized cross-spring pivots under combined loads

Wang

Sun

Wang

et al. 2014

Advances in Mechanical Engineering

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Generalized cross-spring pivots (CSPs) are widely used as revolute joints in precision machinery. However, pseudo-rigid-body (PRB) models cannot capture the parasitic motions of a generalized CSP exactly under combined loads; moreover, the characteristic parameters used in PRB methods must be recomputed using optimization techniques. In this study, we develop two simple and accurate PRB models for generalized CSPs. First, a PRB method for a beam is developed based on the beam constraint model and the instantaneous center model, where the beam is modeled as two rigid links joined at a pivot via a torsion spring. Subsequently, two PRB models of the generalized CSP, comprising a four-bar model for accuracy and a pin-joint model for stiffness, are constructed based on a kinematic analysis using the proposed PRB method. A deflection characteristic analysis is then conducted to determine the relationship between the proposed model and the existing models. Finally, the PRB models for the pivot under the action of combined loads are validated via finite element analysis. The error evaluation indicates that the proposed PRB models are more accurate than the results from existing methods. The PRB models proposed here can be used in parametric design of compliant mechanisms.

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Optimized cross-spring pivot configurations with minimized parasitic shifts and stiffness variations investigated via nonlinear FEA

Cited by 21 publications

References 22 publications

Gravity-Compensation Design Approaches for Flexure-Pivot Time Bases

Gravity-Compensation Design Approaches for Flexure-Pivot Time Bases

Accuracy and precision: A new view on kinematic assessment of solid-state hinges and compliant mechanisms

Adaptive pseudo-rigid-body model for generalized cross-spring pivots under combined loads

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