Effect of Electromagnetic Actuation on Contact Loss in a Hertzian Contact Oscillator

Bichri, Amine; Belhaq, Mohamed; Perret-Liaudet, Joël

doi:10.1115/1.4028838

Cited by 6 publications

(6 citation statements)

References 11 publications

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“…Henceforward we consider two symmetrical EA on the loss contact only on the frequency response of the Hertzian contact oscillator near the primary resonance. The model is depicted in Figure 1 and the governing equation can be written as [4,15,16]:…”

Section: Mathematical Modelmentioning

confidence: 99%

“…In the last decades, analysis of the Hertzian contact and electromagnetic actuation (EA) has been caried out in several studies since these are present in various engineering systems such as railway wheel contact [1], the automotive sector [2], gear drive [3], energy dissipation in mechanical systems, and in mechanisms transforming movements of rotations or translations [4]. EA are used in some engineering applications such as hydraulic valves, small heart pumps, electric door, power relays, etc.…”

Section: Introductionmentioning

confidence: 99%

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Analysis of the Vibro-Impact Nonlinear Damped and Forced Oscillator in the Dynamics of the Electromagnetic Actuation

et al. 2023

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In this work, the effect of vibro-impact nonlinear, forced, and damped oscillator on the dynamics of the electromagnetic actuation (EA) near primary resonance is studied. The vibro-impact regime is given by the presence of the Hertzian contact. The EA is supplied by a constant current generating a static force and by an actuation generating a fast alternative force. The deformations between the solids in contact are supposed to be elastic and the contact is maintained. In this study, a single degree of freedom nonlinear damped oscillator under a static normal load is considered. An analytical approximate solution of this problem is obtained using the Optimal Auxiliary Functions Method (OAFM). By means of some auxiliary functions and introducing so-called convergence-control parameters, a very accurate approximate solution of the governing equation can be obtained. We need only the first iteration for this technique, applying a rigorous mathematical procedure in finding the optimal values of the convergence-control parameters. Local stability by means of the Routh-Hurwitz criteria and global stability using the Lyapunov function are also studied. It should be emphasized that the amplitude of AC excitation voltage is not considered much lower than bias voltage (in contrast to other studies). Also, the Hertzian contact coupled with EA is analytically studied for the first time in the present work. The approximate analytical solution is determined with a high accuracy on two domains. Local stability is established in five cases with some cases depending on the trace of the Jacobian matrix and of the discriminant of the characteristic equation. In the study of global stability, the estimate parameters which are components of the Lyapunov function are given in a closed form and a graphical form and therefore the Lyapunov function is well-determined.

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Section: Mathematical Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Analysis of the Vibro-Impact Nonlinear Damped and Forced Oscillator in the Dynamics of the Electromagnetic Actuation

et al. 2023

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“…Vibro-impact dynamics under a Hertzian contact force is present in various engineering applications, especially in gear drive, bearing, mechanisms transforming non-resonant rotations or translations, railway wheel-rail contact, and so on [1][2][3]. The Hertzian model is just one of the existing vibro-impact models, and many different phenomena have been reported in the field of vibro-impact systems in the last 40 years, including grazing and C-bifurcations [4], Neimark-Sacker bifurcation [5], period-doubling bifurcations [6], stochastic stability [7], fractals [8], chaos [9], and many others.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of the Vibro-Impact Nonlinear Damped and Forced Oscillator under the Influence of the Electromagnetic Actuation

Herişanu

Marinca

2022

Mathematics

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The main objective of the present work is to find an approximate analytical solution for the nonlinear differential equation of the vibro-impact oscillator under the influence of the electromagnetic actuation near the primary resonance. The trigger of vibro-impact regime is due to Hertzian contact. The optimal auxiliary functions method (OAFM) is utilized to give an analytical approximate solution of the problem. The influences of static normal load and electromagnetic actuation near the primary resonance are completely studied. The main novelties of the proposed procedure are the presence of some new adequate auxiliary functions, the introduction of the convergence-control parameters, the original construction of the initial and of the first iteration, and the freedom to choose the method for determining the optimal values of the convergence-control parameters. All these led to an explicit and accurate analytical solution, which is another novelty proposed in the paper. This technique is very accurate, simple, effective, and easy to apply using only the first iteration. A second objective was to perform an analysis of stability of the model using the multiple scales method and the eigenvalues of the Jacobian matrix.

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“…Some methods of controlling this vibro-impact response were presented by Bichri and Belhaq 24 and Bichri et al. 25,26 The presented control methods utilized fast harmonic load/displacement, fast harmonic modulation of contact stiffness, or introduction of electromagnetic actuator. Xiao et al.…”

Section: Introductionmentioning

confidence: 99%

“…Hertzian contact nonlinearity is one of the primary reasons for the nonlinear jump phenomenon. Some methods of controlling this vibro-impact response were presented by Bichri and Belhaq 24 and Bichri et al 25,26 The presented control methods utilized fast harmonic load/ displacement, fast harmonic modulation of contact stiffness, or introduction of electromagnetic actuator. Xiao et al 27 used the MMS and HBM and exact method to determine the natural frequency of a mass with Hertzian contact stiffness.…”

Section: Introductionmentioning

confidence: 99%

Dynamic analysis of elastically and plastically graded spherical and cylindrical contact

Jana

Mitra

Sahoo

2019

Proceedings of the Institution of Mechanical Engineers, Part J:

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A dynamic analysis of a hemispherical and cylindrical contact, material properties of which are graded elastically and plastically along the radius, is presented. The static force–displacement behavior of a hemisphere and a semi-cylinder in contact with a rigid flat is obtained using finite element software. The force–displacement is used in a further dynamic analysis for undamped-free as well as for forced-damped vibration of the contact interface. For the undamped free vibration, variation of natural frequency w.r.t. initial displacement is furnished for different values of elastic and plastic gradation parameter. In addition, variation of maximum initial displacement for contact loss is also demonstrated. The forced-damped vibration characteristics of the spherical and cylindrical contact interfaces are presented in the form of frequency response curves with jump up and jump down frequencies. Spherical and cylindrical contact interfaces are found to exhibit softening and hardening type nonlinearity, respectively.

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Effect of Electromagnetic Actuation on Contact Loss in a Hertzian Contact Oscillator

Cited by 6 publications

References 11 publications

Analysis of the Vibro-Impact Nonlinear Damped and Forced Oscillator in the Dynamics of the Electromagnetic Actuation

Analysis of the Vibro-Impact Nonlinear Damped and Forced Oscillator in the Dynamics of the Electromagnetic Actuation

Dynamics of the Vibro-Impact Nonlinear Damped and Forced Oscillator under the Influence of the Electromagnetic Actuation

Dynamic analysis of elastically and plastically graded spherical and cylindrical contact

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