Studying Resonant Frequencies of a Helical Spring with and Without Axial Loads
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TECHNICAL ARTICLE—PEER-REVIEWED
Studying Resonant Frequencies of a Helical Spring with and Without Axial Loads Jairo Aparecido Martins . Daniel Leite . Estaner Claro Roma˜o
Submitted: 12 December 2019 / in revised form: 20 January 2020 Ó ASM International 2020
Abstract This paper presents the resonant frequencies of a helical spring manually calculated in compliance with SAE-11 and also via numerical simulation. In both calculations, a damper rate of zero was utilized to make modeling simpler. Two numerical simulations were run, ranging in frequency from 90 to 590 Hz. The first simulation applied frequencies with no load on the spring, while a second simulation had an axial load on the spring grounded surface, perpendicular to spring centerline. In addition, the second simulation had a constraint added to the opposite grounded surface of the spring and was opposite to the load. Likewise, manual calculation and numerical simulation via COMSOLTM Multiphysics presented very similar results. But, when comparing only the simulations, both revealed high stresses for the same frequencies. However, the second simulation (spring with load applied) had very high stresses, which indicates a high risk of premature failure of the spring. Keywords Numerical simulation Fatigue Resonance Helical springs
Introduction Metallic parts exposed to dynamic systems may fail due to high cycle fatigue if the design of the product neither simulates correct load intensity and number, nor considers resonant frequencies during the movement of the parts. Several authors have shown, by either field experience or practical tests in laboratories, that most of the common J. A. Martins D. Leite E. C. Roma˜o (&) Sa˜o Paulo, Brazil e-mail: [email protected]
causes of failure under dynamic forces are near-resonant vibrations. The author [1], for example, set up a simple model for predicting vibration-induced sliding of mass and provided quantitative experimental evidence for the validity of the model. In addition, Khalily et al. [2] used a simple system also composed of a mass, which was induced to move by an applied force as opposed to the case considered in extant literature. The authors [3] showed an alternative method for calculating the high-speed motion of a cam-actuated engine valve, operating a flexible linkage. In terms of design, Lee and Thompson [4] demonstrated an efficient method for calculating the dynamic stiffness of a helical coil spring and Liu and Kim [5] a method for estimating the natural frequencies of various engine valve springs, such as constant pitch, two-step variable pitch, three-step variable pitch and progressive springs. Researchers [6] designed and investigated a synchronized system with two corotating rotors with nonlinear springs in a non-resonance system. Their proposed mechanism, adjusting the value of the coupling spring stiffness, could make two motors operate at zero phase differences, thus meeting the engineering requirements of the intensity of the force due to vibrations. The researchers [7] analyz
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