Régis Dufour

• Institut National des Sciences Appliquées de Lyon

This work presents an experimental investigation regarding the dynamic behavior of an onboard rotating machine in the case of disk-stator rubbing. The concept of onboard rotating machine has to do with the situation in which base excitations are considered in the mechanical modeling of the system. In the present study the system is composed of a di...

In this paper we investigate the nonlinear dynamic behavior of a rotor with an architecture targeting space turbopumps. Depending on the rotor speed of rotation, these pumps can be supported by ball bearings with a loose fit, i.e. having an outer-race housing clearance, and by annular seals providing radial fluid forces thanks to the Lomakin effect...

This paper presents a modelling of a vibroflot dynamic behaviour. Vibroflots are used by ground improvement companies to perform vibro compaction. This technic consists in deeply densifying sandy soils by vibrations in order to make stable future infrastructures. A classical vibroflot is a slender structure composed of several rotors which are not...

Meta-materials are utilized for bringing passive attenuation solution especially in the acoustics and vibration domains. Generally speaking, they are composed of an array or a chain of meta-cells. Here the vibratory energy exchanges between particles of a nonlinear meta-cell are studied. The meta-cell is composed of an outer mass which houses an in...

This paper investigates the global dynamics of an array of electrostatically coupled nonlinear MEMS resonators before and after a symmetry breaking event by means of nonlinear normal modes, nonlinear forced responses curves and bifurcation analysis. The possible coexistence of isolated solutions is explained by means of energy balance and limit poi...

Active magnetic bearing (AMB) technology provides to rotating machinery, high operating speeds, direct couplings, almost frictionless support and a reduced footprint. In case of strong base excitations, the rotor may contact its touchdown bearings (TDBs), which are used as landing and safety bearings, while AMBs still operate. The paper presents, e...

This paper addresses rotor-stator contact issues, especially the dry-whip phenomenon, as caused by base excitations. So far, this particular instability in the case of direct rub between shaft and stator was only shown by experiments to occur in response to mass unbalance excitation during run-up or run-down and/or to external disturbance such as d...

Qualification tests on the vibrations of on-board equipment depend on the ability of the shaker used to reproduce as precisely as possible the excitation profiles stipulated by standards, given that real operational conditions are generally multiaxial. Using a set of six measured linear accelerations the original method proposed permits determining...

On-board rotating machinery subject to multi-axial excitations is encountered in a wide variety of high-technology applications. Such excitations combined with mass unbalance forces play a considerable role in their integrity because they can cause parametric instability and rotor–stator interactions. Consequently, predicting the rotordynamics of s...

In the transportation domain such as automotive turbochargers and aircraft turbines, the vibrations of on-board rotors are induced not only by the mass unbalance excitation but also by various movements of their support. The dynamics of an on-board rotor mounted on hydrodynamic finite-length bearings is investigated in the presence of support motio...

During drilling operations, the bit-rock and drillstring-wellbore contacts with stick-slip phenomena, fluid-structure interaction, and mass unbalances distributed along the drillstring yield nonlinear dynamics coupling axial, torsional, and lateral vibrations. Excessive and uncontrolled vibrations may induce drilling equipment damage due to fatigue...

During drilling operations, high drillstring vibrations may originate from various sources, namely, the bit-rock interaction, drillstring-wellbore contacts, stick-slip phenomena, fluid-structure interaction, and mass unbalances. Excessive vibrations may induce drilling equipment failures (fatigue, cracking, washouts, and ruptures), which can be cos...

The drilling operations for oil or geothermic extraction use a slender structure introduced inside the drill well, hanging from a derrick and driven by a rotary table at the surface. The drilling structure consists in a series of drill-pipes and some heavy pipes at the well bottom. The drilling process involves nonlinear dynamic phenomena such as b...

In rotary drilling, a drillstring is an assembly of slender pipes. It is used to transmit the driving torque of a motor at the drilling surface to the drill bit at the bottom hole of a 3D well. Numerous vibratory phenomena are induced during the drilling: whirling, stick-slip, bit-bouncing, lateral instability, inducing in particular reduction of t...

A new reduction method is proposed to investigate the behavior stability of rotor-bearing systems subject to a multifrequency rotational motion of their base. Combining the modal analysis and the construction of specific dynamic Ritz vectors, this method is able to deal with complex rotordynamics characterics such as non-proportional damping, non-s...

The aim of this paper is to provide an efficient multi-parametric recursive continuation method of specific solution points of a nonlinear dynamical system such as bifurcation points. The proposed method explores the topology of specific points found on the frequency response curves by tracking extremum points in the successive codimensions of the...

The drilling operations use a rotary slender structure introduced inside the drill well. The nonlinear dynamics with bit-bouncing, stick-slip phenomena, and pulsating mud flow may yield the premature wear and damage of drilling equipment and should be investigated to improve the reliability of drilling operations. This work presents the beam elemen...

Rotating drilling for oil or geothermic applications uses a very slenderness structure hanging from to a derrick and made of a drill-string inside the drill well and linked to the bottom hole assembly (BHA). Vibrations provided by the nonlinear dynamics is due to the distributed unbalance masses, to well-assembly interactions, pulsating mud flow, b...

The paper investigates experimentally and numerically the nonlinear dynamics of a rotor supported by Active Magnetic Bearings (AMBs) and subjected to more or less severe motions from its support. In case of strong base excitations, the rotor can contact its touchdown bearings (TDBs) which are emergency bearings. The objective is to analyze the effe...

Oil or geothermic rotary drilling is composed with a very slenderness drill-string which is subjected in particular to the tool-bit excitations. Therefore a great number of vibratory phenomena concerned with the axial, lateral and torsional behavior are exhibited: whirling, bit bouncing, stick slip to cite just a few. In order to predict the rotord...

This paper investigates the mass sensing capability of an array of a few identical electrostatically actuated microbeams, as a first step toward the implementation of arrays of thousands of such resonant sensors. A reduced-order model is considered, and Taylor series are used to simplify the nonlinear electrostatic force. Then, the harmonic balance...

These works analyze isolated solutions in a symmetric 2-beam MEMS array designed for mass detection using Nonlinear Normal Modes (NNM) during symmetry breaking event. While symmetric, the system present two pure NNM and one mixed NNM. Then an added mass is dropped onto the MEMS array, the symmetry is broken and an isolated NNM is appearing. Particu...

This work presents a method to calculate non-conservative Nonlinear Normal Modes (NNMs) based on the conservative NNMs. A specific fictive force is added to the initial non-conservative equation of motion in order to insure the energy balance of the damped nonlinear equation. By doing so, conservative equations corresponding to Phase and Energy res...

Ce travail présente une méthode d’analyse de stabilité et de bifurcation des Modes normaux non- linéaires (MNN) utilisant la méthode d’équilibrage harmonique (HBM). Afin de lever la non-unicité de la solution, une condition de phase temporelle a été adaptée au domaine fréquentiel puis ajoutée à l’équation de mouvement autonome. Ensuite un coefficie...

This work presents a frequency-domain method based on the Harmonic Balance Method (HBM) to perform bifurcation and stability analysis of Nonlinear Normal Modes (NNM). To do so, a frequency phase condition has been adapted from time domain in order to fix the non-uniqueness of the solution of the autonomous equation of motion. Then, a small damping...

Due to their low cost, size and precision M/NEMS are efficient sensors. M/NEMS sensors are used in various domains ranging from aeronautics to medicine or telecommunication, with applications such as chemical, inertial or mass sensing. Our previous researches on mass sensing were focused on a single resonator. In this work, a symmetric array of thr...

The aim of this paper is to provide an efficient frequency-domain method for bifurcation analysis of nonlinear dynamical systems. The proposed method consists in directly tracking the bifurcation points when a system parameter such as the excitation or nonlinearity level is varied. To this end, a so-called extended system comprising the equation of...

Most studies on nanomechanical resonators in the literature are concerned with a single res-onator. In this work, an array of two nanomechanical resonators is analyzed. A quasi-analytic approach with averaging method is used to compare the beams responses with and without electrostatic coupling terms. The results show modal interactions between the...

Due to their accuracy and their size, M/NEMS resonant sensors are present in a lot of domain such as automotive, aerospace and biotechnology. They are used as accelerometers, gyroscopes for inertial navigation and also mass detection which is the target application of this investigation. The literature essentially focus on improving the sensitivity...

A frequency-domain method is proposed for tuning bifurcation points in nonlinear dy-namical systems by means of multi-parametric bifurcation tracking and optimization criteria. Introduction In the field of mechanical engineering, nonlinear phenomena introduced by large deflections, miniaturization, electro-mechanical couplings, nonlinear vibration...

A frequency-domain approach for direct parametric analysis of limit points (LPs) of nonlinear dynamical systems is presented in this paper. Instead of computing responses curves for several values of a given system parameter, the direct tracking of LPs is performed. The whole numerical procedure is based on the harmonic balance method (HBM) and can...

This paper reports the proof of concept of a nonlinear detection scheme for Nanoelectromechanical (NEMS) resonators for sensing applications. This set-up increases the dynamic range of a resonant sensor by operating it at amplitudes beyond its limit of linearity. Unlike other works in non-linear sensing, this method allows the tracking of the reson...

The proposed investigation deals with the assessment of several models for the prediction of the dynamic behaviour of turbomachinery supported by Active Magnetic Bearing when drop events occur leading the rotor to drop onto its Touch-Down Bearings (TDBs), which are emergency rolling element bearings in series with a ribbon damper. The rotor exhibit...

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...

In nonlinear rotordynamics, techniques can take advantage of the periodic steady state behavior to predict quickly and accurately the mass unbalance response to a series of parameters, especially with the presence of certain nonlinearities which leads to nonlinear dynamics and complicated responses. The method proposed here calculates the response...

In turbo-engines the sudden increase of mass unbalance, due for example to a blade-loss, can generate rotor-stator contacts in different zones of the motor architecture: turbine blade/flange, centrifugal compressor wheel/shroud, seals, stopend bearing. The aim of this paper is to analyse the influence of such rotor-stator interactions on the dynami...

This paper investigates an alternative mass-sensing technique based on nonlinear micro-/nanoelectromechanical resonant sensors. The proposed approach takes advantage of multi-stability and bifurcations of the hysteretic frequency responses of the electrostatically actuated resonator. For this purpose, a reduced-order model is considered. Numerical...

A gearshift command system is composed of a cable encapsulated in a casing. The cable transfers the motion of the gearshift lever to the gearbox selector lever. The work presented focuses on the cable-casing system and its nonlinear behavior. A first step of the analysis consists in calculating the cable-casing path starting from the boundary condi...

The non-linear dynamic behavior of an on-board rotor mounted on hydrodynamic journal bearings and subject to rigid base excitations is investigated in this work. The proposed finite element rotor model takes into account the geometric asymmetry of shaft and/or rigid disk and considers six types of base deterministic motions (rotations and translati...

The major purpose of this study is to predict the dynamic behavior of an on-board rotor mounted on hydrodynamic journal bearings in the presence of rigid support movements, the target application being turbochargers of vehicles or rotating machines subject to seismic excitation. The proposed on-board rotor model is based on Timoshenko beam finite e...

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...

The pulleys of an automotive front engine accessory drive are driven in rotation by a poly-V belt itself driven by the crankshaft pulley. This driving pulley is often used as a torsional vibration damper (TVD) for the crankshaft. Three elements compose the pulley: the hub, a rubber ring and an inertia steel ring with v-ribs on its outer diameter. A...

The correlation criterion proposed in this article and called nc²o (normalized cross complex orthogonality) is based on the bi-orthogonality properties between rotor mode shapes calculated at different speeds of rotation. This criterion is proved using an industrial laminated rotor composed of disks and two fluid film bearings, whose characteristic...

Energy harvesting from motion is presently receiving great worldwide attention as a means to power autonomous systems. Conventional linear vibration energy harvesters are usually designed to be reso-nantly tuned to the ambient dominant frequency. They have a narrow operating bandwidth that limits their application in real-world environments where t...

The aim of this paper is to investigate the influence of rotor-stator interaction on the dynamic behaviour of a rotor-bearing system. First the model of a SDOF system with two stop-ends is established. The analytical solution permits testing the stability and the robustness of the penalty contact law combined with two numerical schemes. Second, a t...

The aim of this paper is to investigate the dynamic behavior of an on-board rotor mounted on elastic bearings in the presence of rigid support movements. The proposed on-board rotor model is based on the Timoshenko beam finite elements. It takes into account the six deterministic translations and rotations of its rigid support and the geometric asy...

In ship and aircraft turbine rotors, the rotating mass unbalance and the different movements of the rotor base are among the main causes of vibrations in bending. The goal of this paper is to investigate the dynamic behavior of an on-board rotor under rigid base excitations. The modeling takes into consideration six types of base deterministic moti...

We have developed a method of measuring resonance properties of high frequency nanoelectromechanical res-onators for inertial sensor applications based on capac-itive down-mixing. The technique takes advantage of the electrostatic actuation of the resonator to use it as a mixer. It also greatly reduces the effect of the cross-talk between the detec...

The nonlinear dynamics of in-plane nanoelectromechanical cantilevers based on silicon nanowire piezoresistive detection is investigated using a comprehensive analytical model that remains valid up to large displacements in the case of electrostatic actuation. This multiphysics model takes into account geometric, inertial and electrostatic nonlinear...

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 res...

This paper describes a comprehensive non-linear multiphysics model based on the Euler–Bernoulli beam equation that remains valid up to large displacements in the case of electrostatically actuated Mathieu resonators. This purely analytical model takes into account the fringing field effects and is used to track the periodic motions of the sensing p...

Electrical rotors are usually used in rotating machinery such as in ship engine pods. Designing such rotors in bending requires careful modeling of a laminated stack prestressed by tie rods. Theoretically, steel sheets, varnish layers and prestressing make it difficult to homogenize the constitutive properties of a stack both at rest and under oper...

This paper investigates the sensitivity of the third order nonlinearity cancelation to the mixed (hardening and softening) behavior in electrostatically actuated micromechanical resonators under primary resonance at large amplitudes compared to the gap. We demonstrate the dominance of the mixed behavior due to the quintic nonlinearities, beyond the...

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 stabiliza...

Large-amplitude non-linear vibrations of micro- and nano-electromechanical resonant sensors around their primary resonance are investigated. A comprehensive multiphysics model based on the Galerkin decomposition method coupled with the averaging method is developed in the case of electrostatically actuated clamped–clamped resonators. The model is p...

In order to predict the lateral rotordynamics of a high-speed induction motor, an optimization procedure is proposed for identifying the equivalent constitutive properties especially those of the magnetic core: an assembly of lamination stack, tie rods, and short-circuit rods. Modal parameters predicted by a finite element (FE) branched model based...

Basically, a reciprocating compressor consists of three main mechanical subsets: the hermetic housing, the crankcase and the rotor-crankshaft assembly. The counterweight mass located on the rotor-crankshaft is designed to balance the eccentric masses of the slider-crank mechanism which predominate in comparison to the residual distributed unbalance...

Blade optimization is more than ever a crucial activity for helicopter manufacturers, always looking for performance improvements, noise reduction and vibratory comfort increase. Latest studies have led to design new blade concepts including a double swept plan shape, an evolutionary and increased twist angle at the tip and a new layout for interna...

In order to overcome the loss of performances issue when scaling resonant sensors down to NEMS, it proves extremely useful to study the behavior of resonators up to large displacements and hence high nonlinearities. A comprehensive nonlinear multiphysics model based on the Euler-Bernoulli equation which includes both mechanical and electrostatic no...

Predicting the dynamic behavior of laminated rotors in bending requires the identification of the bending rigidity of the laminated core. An identification of constitutive properties is proposed on the rotor at rest, which is a first step for rotordynamics prediction. Modal parameters predicted and measured are included in a functional based on a h...

A gearshift command system is composed of a cable encapsulated in a casing. The cable transfers the motion of the gearshift lever to the gearbox selector lever. The work presented focuses on the cable-casing system and its non linear behavior. A first step of the analysis consists in calculating the cable-casing path starting from the boundary cond...

In order to predict the nonlinear dynamic response of automotive equipment supported by rubber mounts, it is proposed to extend the generalized Dahl model for taking into account the visco-elastic behaviour of elastomer mount and to combine it, in a next step, with the reduced dynamic equations of the equipment supposed to exhibit a linear behaviou...

In the present paper, a compact and analytical model including the main sources of nonlinearities (mechanical and electrostatic) is presented and validated thanks to the fabrication of a resonant accelerometer and the characterization of its sensing element, an electrostatically doubly clamped beam. A perturbation technique, the averaging method, h...

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 incl...

n order to predict the lateral rotordynamics of a high speed induction motor, an optimization procedure is proposed for identifying the equivalent constitutive properties especially those of the magnetic core: an assembly of lamination stack, tie rods and short-circuit rods. Modal parameters predicted by a finite element (FE) branched model based m...

In order to compensate the loss of performances when scaling resonant sensors down to NEMS, it proves extremely useful to study the behavior of resonators up to very high displacements and hence high nonlinearities. This work describes a comprehensive nonlinear multiphysics model based on the Euler-Bernoulli equation which includes both mechanical...

Pour améliorer l'agrément de conduite, il s'agit de mieux comprendre le comportement mécanique de l'ensemble câble/gaine assurant le passage de vitesses. Le frottement gaine/câble ainsi que le parcours sont les paramètres prédominants. Un plan d'expériences établit les lois de traînée et rendement linéique pour des configurations de parcours simple...

Pour prévoir le comportement dynamique en flexion des rotors à cage d'écureuil, une procédure d'optimisation est proposée pour identifier la rigidité flexionnelle de la partie feuilletée. Les quantités modales calculées et mesurées sur un rotor feuilleté sont incluses dans une fonctionnelle basée sur un quotient de Rayleigh hybride et combinée à la...