Prediction of the dynamic equivalent stiffness for a rubber bushing using the finite element method and empirical modeli
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Prediction of the dynamic equivalent stiffness for a rubber bushing using the finite element method and empirical modeling Hyun Seong Lee . Jae Kyong Shin . Sabeur Msolli . Heung Soo Kim
Received: 6 August 2017 / Accepted: 24 November 2017 Ó Springer Science+Business Media B.V., part of Springer Nature 2017
Abstract A hybrid method using an approximation that is based on the finite element analysis and empirical modeling is proposed to analyze the dynamic characteristics of a rubber bushing. The hyperelastic–viscoplastic model and an overlay method are used to obtain the hysteresis of the rubber bushing in the finite element analysis. A spring, fractional derivatives, and frictional components are used in the empirical model to obtain the dynamic stiffness in wide ranges of the excitation frequencies and amplitudes. The parameters of the proposed empirical model are determined using the hysteresis curves that were obtained from the finite element analysis. The dynamic stiffness of the rubber bushing in the wide ranges of the frequencies and amplitudes was predicted using the proposed hybrid method and was validated using lower arm bushing experiments. The proposed hybrid method can predict the dynamic stiffness of a rubber bushing without the performance of iterative experiments and the incurrence of a high computational cost, making it applicable to analyses of full-size vehicles with numerous rubber bushings under various vibrational loading conditions.
H. S. Lee J. K. Shin S. Msolli H. S. Kim (&) Department of Mechanical, Robotics and Energy Engineering, Dongguk University-Seoul, 30 Pildong-ro 1-gil, Jung-gu, Seoul 04620, Republic of Korea e-mail: [email protected]
Keywords Rubber bushing Finite element method Overlay method Empirical model Dynamic equivalent stiffness
1 Introduction Rubber bushings are used for several industrial components to transfer motion from one part to another. In automotive suspension systems, rubber bushings play the role of an isolator by reducing the external loadings and transmitted vibrations. Although the rubber bushing is a prevalent component in automobiles, it is still challenging to predict the actual behavior of the rubber bushing due to its dynamic characteristics. The dynamic characteristics of a rubber bushing are dependent on several factors such as the amplitude, frequency, temperature and so on. The dynamic stiffness of the rubber material is decreased with the increasing of the excitation amplitude. Furthermore, the associated amplitude effect is more evident regarding filled rubber compared with natural rubber, and this is due to the disintegration of the filler-matrix structures that is called the Fletcher-Gent effect (1954) or the Payne effect (1971). Medalia (1978) investigated the amplitude-dependent behavior of elastomeric material by studying the couplings between the materials and the dynamic strain. Dean et al.
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H. S. Lee et al.
(1984) studied the variation of the dynamic stiffness of carbon-black filled rubber in terms of the frequenc
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