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1

A simple formula for predicting the first natural frequency of transverse vibrations of axially loaded helical springs

Michalczyk Krzysztof, Bera Piotr

Journal of Theoretical and Applied Mechanics

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2019

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Vol. 57 nr 3

779--790

EN

A new formula that allows the first natural frequency of transverse vibrations of axially loaded steel helical springs to be determined has been presented in the paper. The relationship is easy to use and allows finding the first natural frequency of spring vibrations without the necessity of solving analytical or numerical models. According to the authors’ knowledge, this is the first such a formula and, consequently, when this frequency becomes zero, it enables determination of the critical axial force or deflection causing the buckling of the spring. The way of obtaining the described formula is presented in the paper. The results of this formula are compared with those obtained using FEM and experiments. The advantages, drawbacks and limitations of the proposed relationship are also discussed.

2

Natural transverse vibrations of helical springs in sections covered with elastic coatings

Michalczyk K.

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2017

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Vol. 65, nr 6

949--959

EN

It has been demonstrated in previous studies that local elastomer coatings covering the end coils of helical springs can efficiently reduce the amplitudes of circum-resonant vibrations in such springs. The analysis of the influence that elastic coatings have on the frequencies and modes of natural transverse vibrations of springs is presented in this paper. The concept of the equivalent beam of the Timoshenko type is utilized in calculations of the frequencies and modes of transverse vibrations. The model developed allows users to determine the frequencies and modes of symmetric as well as antisymmetric vibrations of axially loaded springs with elastic coatings of arbitrary length. A comparison of the results obtained using FEM analysis, in which the model represented the actual spring geometry, with the results obtained by means of the presented model indicates its high accuracy.

3

Analysis of lateral vibrations of the axially loaded helical spring

Michalczyk K.

Journal of Theoretical and Applied Mechanics

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2015

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Vol. 53 nr 3

745—755

EN

It is shown in this paper that the proposed concept by Krużelecki and Życzkowski (1990) of the equivalent rod can be applied in calculations of natural lateral vibrations of springs and that the obtained results will be nearer FEM results than the standard model based on the Timoshenko equivalent beam. The model, created on this base, allows one to calculate natural frequencies of the clamped-clamped spring. It is also shown that models based on the equivalent beam concept, which are easier to apply than the models treating the spring as the spatially curved rod, have only a slightly smaller accuracy. It is also indicated that in the most common practice making of manufacturing end coils of springs, the natural frequencies differ significantly from the frequencies calculated by means of all tested methods. The performed simulations show that differences between the first and the second as well as the third and the fourth natural frequency of the spring are small and, therefore, the axially symmetrical equivalent beam model can be used without a large error. The diagram allowing one to determine whether the desired frequencies are lower or higher than the cut-off frequency is developed for the presented model.