Energy-based method for nonlinear characteristics analysis of Belleville springs

Zheng, Enlai; Jia, Fang; Zhou, Xinlong

doi:10.1016/j.tws.2014.01.025

Cited by 21 publications

(12 citation statements)

References 9 publications

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“…According to [ 84 ], the use of the measured diameters instead of those of the neutral surface in the formulas results in a better match with characteristics determined experimentally. This measurement of the diameters is also done in the standard DIN EN 16984 [ 36 ] and by Zheng et al [ 41 ], and thus is used in the current work for Almen – Laszlo -, Curti – Orlando and Zheng -based computation. It is not used for the Kobelev -based computation [ 85 ] as the results couldn’t be improved using different diameter definitions.…”

Section: Calculation Of Spring Characteristicsmentioning

confidence: 99%

“…Equation ( 54 ) as well as Equation ( 59 ) derived above show an exemplary application of the new method introduced in Section 5.1 to adopt other algorithms to a non-rectangular cross-section with rounded edges. To show the effect of the adjustments, the method is also applied to the algorithm by Curti and Orlando [ 40 ], as well as the one by Zhang [ 41 ], by replacing the force

computed using the original Almen formula with the force

computed using Curti ’s or Zheng ’s original formulas, respectively. The algorithm by Kobelev [ 85 ] is also adapted by using the force

instead of

in the above equations and replacing the adjusted difference in radius R by the lever arm

used by Kobelev .…”

Section: Calculation Of Spring Characteristicsmentioning

confidence: 99%

“…

where the argument

denotates that the original forces need to be computed using

and

instead of

and

, in quantities defined using them or directly in the formulas below, e.g.,

is replaced by

. Note the different calculation of

and

discussed in Section 5.1 for the Kobelev -based adjustment, in which the following definition should be used instead of Equations ( 42 ) and ( 43 ):

The original forces of Almen – Laszlo [ 39 ]

, Curti – Orlando [ 40 ]

and Zheng [ 41 ]

are calculated as follows:

…”

Section: Figure A1mentioning

confidence: 99%

“…Curti and Orlando published a similar approach incorporating radial stresses [ 40 ]. An energy-based approach to compute the characteristics was published by Zheng et al [ 41 ]. Koblev [ 42 ] presents an analytical approach capable of approximating high working angle disc springs.…”

Section: Introductionmentioning

confidence: 99%

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A New Method for the Calculation of Characteristics of Disc Springs with Trapezoidal Cross-Sections and Rounded Edges

et al. 2022

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In the European standards specifying disc spring manufacturing, geometry, shape and characteristic, an edge rounding is prescribed. Common methods for the calculation of disc spring characteristics, even in these standards, are based on a rectangular cross-section. This discrepancy can lead to a considerable divergence of the computed characteristic from the characteristic determined by testing. In literature, this divergence has not yet been examined with regard to rounded edges. In this paper, a new method addressing this problem is introduced. For this purpose, the geometry of idealized disc springs is parameterized. Based on four edge radii and two angles of the inner and outer faces, equations to compute the initial cone angle and the lever arm are introduced. These equations are used to formulate an algorithm to adapt other computation methods to non-rectangular cross-sections and rounded edges. The method is applied to the formulas by Almen–Laszlo, Curti–Orlando, Zheng and those by Kobelev. FE simulations of disc springs with rounded edges and a non-rectangular cross-section were used to verify the new formulas. The results show that the introduced method can be applied to known characteristic computation methods and result in a model expansion taking cross-section variations into account. The adjusted characteristics show more accurate alignment to the FE simulation for the cross-section variations investigated. These findings not only close the geometric gap between the manufacturing guidelines and the computation on an analytical basis, they also define a new parameter space for designs of disc springs and a corresponding force computation method to optimize spring characteristics.

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Section: Calculation Of Spring Characteristicsmentioning

confidence: 99%

computed using the original Almen formula with the force

computed using Curti ’s or Zheng ’s original formulas, respectively. The algorithm by Kobelev [ 85 ] is also adapted by using the force

instead of

in the above equations and replacing the adjusted difference in radius R by the lever arm

used by Kobelev .…”

Section: Calculation Of Spring Characteristicsmentioning

confidence: 99%

“…

where the argument

denotates that the original forces need to be computed using

and

instead of

and

, in quantities defined using them or directly in the formulas below, e.g.,

is replaced by

. Note the different calculation of

and

discussed in Section 5.1 for the Kobelev -based adjustment, in which the following definition should be used instead of Equations ( 42 ) and ( 43 ):

The original forces of Almen – Laszlo [ 39 ]

, Curti – Orlando [ 40 ]

and Zheng [ 41 ]

are calculated as follows:

…”

Section: Figure A1mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A New Method for the Calculation of Characteristics of Disc Springs with Trapezoidal Cross-Sections and Rounded Edges

et al. 2022

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show abstract

“…Almen and Laszlo [2] developed a theory and derived a simple formula becoming the current standard. Recently, Zheng E [3] obtained a new analytical solution of the load deflection characteristic of the Belleville springs through energy method and Kobelev V [4] developed a closed form analytical solutions based on the common deformation hypotheses for the equations of thin-and thick-walled truncated conical disc springs with rectangular cross-section. By taking the finger part and other local structures such as rounder corner in the inner radius of the spring into consideration, the finite element method was applied to the diaphragm spring modeling and the corresponding load-deflection characteristic was obtained [5]- [7].…”

Section: Introd1uctionmentioning

confidence: 99%

Mechanism for the Forced Strengthening on the Diaphragm Spring's Load-Deflection Characteristic

Gong¹,

Zhang²

2017

IJET

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Load-deflection characteristic of the diaphragm spring during its life time may vary, which usually leads to slipping, burns and other failures in industry application. To avoiding these failures, the forced strengthening process in manufacturing of the diaphragm spring is often applied to stabilize the load-deflection characteristic of the spring by accelerating its elastic extenuation before it goes out. However the mechanism for the forced strengthening process on the diaphragm spring load-deflection characteristic is not yet completely understood. Based on the finite element method, the model of the diaphragm spring was built and the forced strengthening process was simulated. The load-deflection characteristic before and after the forced strengthening process were obtained, respectively and compared. The difference of the load-deflection characteristic was conducted. For understanding and explaining this difference, two known mechanisms for the forced strengthening process on the load-deflection characteristic of the spring, namely the geometry change of the spring structure and residual stress effects, were introduced and studied. The results show that although two mechanisms have both attribute to this change of the characteristic of the spring after forced strengthening process, the geometry-related mechanism plays a more important role as a main mechanism and the height change of the spring is the main factor among these geometry changes in geometry-related mechanism.

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Enhanced design and experimental investigation of disc spring‐based self‐centering buckling‐restrained braces with a compounded combination mode

Chen

Xie

2023

Earthq Engng Struct Dyn

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The disc spring-based self-centering energy dissipation (SCED) brace is a high-capacity resilient structural component, characterized by a flag-shaped hysteresis curve, which can provide both damping and recentering capacity to a structure. However, the conventional design method for the disc spring-based SCED brace cannot quantitatively take into account the friction effects induced by combined disc springs, which greatly limits the disc spring size selection and combination mode. To address this issue, the friction effect of the combined springs is quantified using an incremental energy method and then introduced into the existing design method. A fully assembled self-centering steel bucklingrestrained brace (SC-SBRB) consisting of an energy dissipation (ED) system and a self-centering (SC) system is proposed. The SC system employs a combination mode of stacking multi-section springs in parallel and compounding new and old springs together to provide the desired recentering capacity for the brace; however, it is distinguished by an appreciable ED capacity that is different from the SC devices in previously reported SCED braces. With the use of the energy method for the quantification of the spring friction, the differences between the mechanical properties of a group of old springs in earlier and recent tests were systematically analyzed to check their reliability and serviceability. A series of test procedures were sequentially conducted on a pure BRB brace and a pure SC brace, and then on the full SC-SBRB. A fatigue test was also performed after the damaged brace was repaired. The experimental results demonstrate that the improved design can provide accurate estimations of the spring friction in the brace design, and that the proposed brace can exhibit a stable and favorable flagshaped hysteretic response with negligible residual deformations throughout the loading protocol. The old spring used in the tests was found to have stable and reliable mechanical properties and could be reused in a brace requiring repair after an earthquake.

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Energy-based method for nonlinear characteristics analysis of Belleville springs

Cited by 21 publications

References 9 publications

A New Method for the Calculation of Characteristics of Disc Springs with Trapezoidal Cross-Sections and Rounded Edges

A New Method for the Calculation of Characteristics of Disc Springs with Trapezoidal Cross-Sections and Rounded Edges

Mechanism for the Forced Strengthening on the Diaphragm Spring's Load-Deflection Characteristic

Enhanced design and experimental investigation of disc spring‐based self‐centering buckling‐restrained braces with a compounded combination mode

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