On Modeling the Bending Stiffness of Thin Semi-Circular Flexure Hinges for Precision Applications

Melgarejo, Mario André Torres; Darnieder, Maximilian; Linß, Sebastian; Zentner, Lena; Fröhlich, Thomas; Theska, René

doi:10.3390/act7040086

Cited by 12 publications

(7 citation statements)

References 27 publications

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“…The most likely reason for this is a deviation of thickness of the flexure hinges. The thin areas are difficult to manufacture, and deviations of only a few micrometers result in significant deviations (for more information on the calculation of stiffness of flexure hinges, see Torres Melgarejo et al, 2018). According to Fig.…”

Section: Experimental Investigations and Resultsmentioning

confidence: 99%

“…The calculation of the initial stiffness of the mechanism C init.FEM can be performed using finite element method (FEM) simulations or analytically C init.model with good confidence in the nominal geometry (Torres Melgarejo et al, 2018;Henning and Zentner, 2021). Deviations from the measured stiffness of prototypes are prone to manufacturing uncertainties.…”

Section: Operating Principle Of Emfc Weighing Cellsmentioning

confidence: 99%

“…( 10). The value for the initial stiffness was calculated according to Torres Melgarejo et al (2018) and was estimated at C init.model = 55.9 N m −1 . To compensate for the initial stiffness, the adjustment parameter h HG was chosen to be 3.15 mm, which is slightly less than the calculated value for h HG (C 0 = 0), in order to avoid the possibility of a negative stiffness (inverted pendulum).…”

Section: Reduction Of Initial Stiffness C Init By H Hgmentioning

confidence: 99%

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Adjustment concept for compensating for stiffness and tilt sensitivity of a novel monolithic electromagnetic force compensation (EMFC) weighing cell

Pabst

Darnieder

Theska

et al. 2022

J. Sens. Sens. Syst.

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Abstract. This paper describes the new adjustment concept of novel planar, monolithic, high-precision electromagnetic force compensation weighing cells. The concept allows the stiffness and the tilt sensitivity of the compliant mechanisms that are dependent on the nominal load on the weighing pan to be adjusted to an optimum. The new mechanism is set up and adjusted according to the developed mechanical model. For evaluation of the concept the system is tested on a high-precision tilt table and under high vacuum conditions in the environment of a commercially available mass comparator.

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Section: Experimental Investigations and Resultsmentioning

confidence: 99%

Section: Operating Principle Of Emfc Weighing Cellsmentioning

confidence: 99%

Section: Reduction Of Initial Stiffness C Init By H Hgmentioning

confidence: 99%

See 1 more Smart Citation

Adjustment concept for compensating for stiffness and tilt sensitivity of a novel monolithic electromagnetic force compensation (EMFC) weighing cell

Pabst

Darnieder

Theska

et al. 2022

J. Sens. Sens. Syst.

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“…If a flexure hinge is modeled together with adjacent deformable link segments as a bent rod with a variable height, this theory is assumed to be suitable, too. Further specific effects relevant for notch flexure hinges have to be expected especially for very thin hinges [43], but they are neglected here with regard to general design guidelines. Among them are shear deformation [44], stress concentration [45], anticlastic bending [46], or manufacturing imperfections [47].…”

Section: Nonlinear Analytical Calculationmentioning

confidence: 99%

Modeling and Design of Flexure Hinge-Based Compliant Mechanisms

Linß¹,

Henning²,

Zentner³

2019

Kinematics - Analysis and Applications

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A compliant mechanism gains its mobility fully or partially from the compliance of its elastically deformable parts rather than from conventional joints. Due to many advantages, in particular the smooth and repeatable motion, monolithic mechanisms with notch flexure hinges are state of the art in numerous precision engineering applications with required positioning accuracies in the low micrometer range. However, the deformation and especially motion behavior are complex and depend on the notch geometry. This complicates both the accurate modeling and purposeful design. Therefore, the chapter provides a survey of different methods for the general and simplified modeling of the elasto-kinematic properties of flexure hinges and compliant mechanisms for four hinge contours. Based on nonlinear analytical calculations and FEM simulations, several guidelines like design graphs, design equations, design tools, or a geometric scaling approach are presented. The obtained results are analytically and simulatively verified and show a good correlation. Using the example of a path-generating mechanism, it will be demonstrated that the suggested angle-based method for synthesizing a compliant mechanism with individually shaped hinges can be used to design high-precise and large-stroke compliant mechanisms. The approaches can be used for the accelerated synthesis of planar and spatial flexure hinge-based compliant mechanisms.

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“…However, the flexure mechanism of a conventional EMFC weighing cell has limitations of poor ruggedness and slow settling performance. To achieve a high mechanical sensitivity, the thickness of the flexure applied in the weighing cell is minimized to a fabrication limitation of about 50 µm [12], but it can be easily damaged by external disturbances or a system deadweight. To prevent the large deflection of flexure due to deadweights, a counterweight is normally applied, as shown in figure 1.…”

Section: Introductionmentioning

confidence: 99%

Electromagnetic force compensation weighing cell with magnetic springs and air bearings

Yoon

Park

Choi

2020

Meas. Sci. Technol.

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The electromagnetic force compensation (EMFC) principle is a state-of-the-art weighing method for precision mass measurement. In this method, the low stiffness of the flexure-based Roberval guide mechanism and high lever ratio of force transmission contribute to achieving extremely high weighing sensitivity. However, weak damping and the parasitic resonant frequencies of the flexure mechanism lead to a slow settling time after loading a weight. Moreover, the low ruggedness of the flexure mechanism limits the load capacity of the EMFC weighing cell and may result in fatigue failure under repeated loading. In this paper, we propose a novel precision weighing cell with Halbach array magnetic springs and air bearings instead of the flexure mechanism. The magnetic spring is designed for near-zero negative stiffness to increase the system bandwidth, as well as for gravity force compensation ability against deadweights. The air bearings ensure high ruggedness toward parasitic directions with high stiffness in the parasitic direction and a damping effect from the pressurized air film. The stiffness of the fabricated prototype weighing cell is −27.3 N m−1, which is tens of times lower than that of conventional EMFC weighing cells. The weighing repeatability of the weighing cell is 2.35 mg, as measured with a 10 g E2 class test mass, and the settling time within ±2% of its final value is 57 ms in air.

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On Modeling the Bending Stiffness of Thin Semi-Circular Flexure Hinges for Precision Applications

Cited by 12 publications

References 27 publications

Adjustment concept for compensating for stiffness and tilt sensitivity of a novel monolithic electromagnetic force compensation (EMFC) weighing cell

Adjustment concept for compensating for stiffness and tilt sensitivity of a novel monolithic electromagnetic force compensation (EMFC) weighing cell

Modeling and Design of Flexure Hinge-Based Compliant Mechanisms

Electromagnetic force compensation weighing cell with magnetic springs and air bearings

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