Régis Dufour

Duffing Oscillator With Parametric Excitation: Analytical and Experimental Investigation on a Belt-Pulley System

This paper is devoted to the theoretical and experimental investigation of a sample automotive belt-pulley system subjected to tension fluctuations. The equation of motion for transverse vibrations leads to a Duffing oscillator parametrically excited. The analysis is performed via the multiple scales approach for predicting the nonlinear response, considering longitudinal viscous damping. An experimental setup gives rise to nonlinear parametric instabilities and also exhibits more complex phenomena. The experimental investigation validates the assumptions made and the proposed model.

Stability control of nonlinear micromechanical resonators under simultaneous primary and superharmonic resonances

Fast effects of a slow excitation on the main resonance of a nonlinear micromechanical resonator are analytically and experimentally investigated. We show, in particular, how the bifurcation topology of an undesirable unstable behavior is modified when the resonator is simultaneously actuated at its primary and superharmonic resonances. A stabilization mechanism is proposed and demonstrated by increasing the superharmonic excitation.

Overcoming limitations of nanomechanical resonators with simultaneous resonances

Dynamic stabilization by simultaneous primary and superharmonic resonances for high order nonlinearity cancellation is demonstrated with an electrostatically actuated, piezoresistively transduced nanomechanical resonator. We prove experimentally how the combination of both the third-order nonlinearity cancellation and simultaneous resonances can be used to linearly drive a nanocantilever up to very large amplitudes compared to fundamental limits like pull-in occurrence, opening the way towards resonators with high frequency stability for high-performance sensing or time reference.

Formulation of a Hysteretic Restoring Force Model. Application to Vibration Isolation

This article focuses on the formulation of a hysteretic model used as anisolator restoring force model. The proposed model is based on operatorgoverning input and output functions that depend on the deflection andthe restoring force of the isolator. First, the mathematical formulationis demonstrated, then the hysteretic model proposed is applied toisolators having different types of behavior. The model parameters aresought using the experimental force-deflection loop of each of theisolators studied. Next, the transient response of a flexible structuremounted on an all-metal isolator is predicted by coupling the firstorder differential equation of the restoring force and the second orderdifferential equations of the structures motion. The experimentalinvestigation validates the proposed hysteretic model applied to theall-metal mount.

Parametric Instability of an Axially Moving Belt Subjected to Multifrequency Excitations: Experiments and Analytical Validation

This paper experimentally investigates the parametric instability of an industrial axially moving belt subjected to multifrequency excitation. Based on the equations of motion, an analytical perturbation analysis is achieved to identify instabilities. The second part deals with an experimental setup that subjects a moving belt to multifrequency parametric excitation. A data acquisition technique using optical encoders and based on the angular sampling method is used with success for the first time on a nonsynchronous belt transmission. Transmission error between pulleys, pulley/belt slip, and tension fluctuation are deduced from pulley rotation angle measurements. Experimental results validate the theoretical analysis. Of particular note is that the instability regions are shifted to lower frequencies than the classical ones due to the multifrequency excitation. This experiment also demonstrates nonuniform belt characteristics (longitudinal stiffness and friction coefficient) along the belt length that are unexpected sources of excitation. These variations are shown to be sources of parametric instability.

Pull-In Retarding in Nonlinear Nanoelectromechanical Resonators Under Superharmonic Excitation

In order to compensate for the loss of performance when scaling resonant sensors down to NEMS, a complete analytical model, including all main sources of nonlinearities, is presented as a predictive tool for the dynamic behavior of clamped-clamped nanoresonators electrostatically actuated. The nonlinear dynamics of such NEMS under superharmonic resonance of an order half their fundamental natural frequencies is investigated. It is shown that the critical amplitude has the same dependence on the quality factor Q and the thickness h as the case of the primary resonance. Finally, a way to retard the pull-in by decreasing the AC voltage is proposed in order to enhance the performance of NEMS resonators.

Identification of Lamination Stack Properties: Application to High-Speed Induction Motors

In order to predict the lateral rotordynamics of a high-speed induction motor, an optimization procedure is used for identifying the dynamic behavior of the magnetic core made of a lamination stack, tie rods, and short-circuit rods. Modal parameters predicted by a finite-element model based on beam elements and measured on induction motors are included in modal error functions contained in a functional. The minimization of this functional by using the Levenberg-Marquardt algorithm permits extracting the equivalent constitutive properties of the lamination stack for several rotors of different sizes. Finally, the size effect on the constitutive properties identified is discussed.

Hysteretic Behavior of a Belt Tensioner: Modeling and Experimental Investigation:

In this paper we describe the modeling of the hysteretic behavior of belt tensioners. An initial experimental device is composed only of the tensioner by using forcing frequencies, preloads and deflection amplitudes. It permits the identification of the parameters of the restoring force model used. Comparison of the measured and predicted force-deflection loops of the tensioner subjected to large deflections permits preliminary validation of the model. The second experimental device consists of a belt-tensioner system. Its non-linear modeling includes the above hysteretic model and the belt’s longitudinal characteristics. Validation of the belt-tensioner model is completed by comparing the measured and predicted belt tension. Finally, it is shown by using a parametric investigation and phase-plane portrait that the response of the belt-tensioner system increases with the frequency and the amplitude of the excitation.

Balancing of machinery with a flexible variable-speed rotor

The balancing procedure of machines composed of a flexible rotating part (rotor) and a non-rotating part (stator) mounted on suspensions is presented. The rotating part runs at a variable speed of rotation and is mounted on bearings with variable-speed-dependent characteristics. Assuming that the unbalance masses are relatively well defined, such as in the case of a crank-shaft, the procedure is based on a numerical approach using rotordynamics theory coupled with the Finite Element and Influence Coefficient Methods. An academic rotor/stator model illustrates the procedure. Moreover, the industrial application concerns a refrigerant rotary compressor whose experimental investigation permits validating the model. Assuming that the balancing planes are located on the rotor, it is shown that reducing the vibration level of both rotor and stator requires a balancing procedure using target planes on the rotor and on the stator. In the case of the rotary compressor, this avoids rotor-to-stator rubs and minimizes vibration transmission through pipes and grommets.

Steady-state dynamic behavior of an on-board rotor under combined base motions.

In the transportation domain, on-board rotors in bending are subjected not only to rotating mass unbalance but also to several movements of their base. The main objective of this article is to predict the dynamic behavior of a rotor in the presence of base excitations. The proposed on-board rotor model is based on the Timoshenko beam finite element. It takes into account the effects corresponding to rotary inertia, gyroscopic inertia, and shear deformation of shaft as well as the geometric asymmetry of disk and/or shaft and considers six types of deterministic motions (rotations and translations) of the rotor’s rigid base. The use of Lagrange’s equations associated with the finite element method yields the linear second-order differential equations of vibratory motion of the rotating rotor in bending relative to the moving rigid base which forms a non-inertial frame of reference. The linear equations of motion highlight periodic parametric terms due to the geometric asymmetry of the rotor components and time-varying parametric terms due to the rotational motions of the rotor rigid base. These parametric terms are considered as sources of internal excitation and can lead to lateral dynamic instability. In the presented applications, the rotor is excited by a rotating mass unbalance combined with constant rotation and sinusoidal translation of the base. Quasi-analytical and numerical solutions for two different rotor configurations (symmetric and asymmetric) are analyzed by means of stability charts, Campbell diagrams, steady-state responses as well as orbits of the rotor.