Alain Berlioz

Dynamic Behavior and Stability of a Rotor Under Base Excitation

The dynamic behavior of flexible rotor systems subjected to base excitation (support movements) is investigated theoretically and experimentally. The study focuses on behavior in bending near the critical speeds of rotation. A mathematical model is developed to calculate the kinetic energy and the strain energy. The equations of motion are derived using Lagrange equations and the Rayleigh-Ritz method is used to study the basic phenomena on simple systems. Also, the method of multiple scales is applied to study stability when the system mounting is subjected to a sinusoidal rotation. An experimental setup is used to validate the presented results.

Dynamic Behavior of a Drill-String: Experimental Investigation of Lateral Instabilities

This paper focuses on laboratory tests concerned with the lateral behavior of a rod representative of part of drill-string in the area of rotary oil drilling. The original experimental set-up takes into account the curvature of the rod, mud, stabilizers and rotation speed. The lateral behavior of the drill-string subjected to the axial excitations of the bit is governed by time varying parameter equations due to torsionlateral and longitudinal-lateral couplings. The experimental results highlight the different kinds of lateral instabilities and they are compared either with existing experimental, or theoretical results. The experimental investigation described in this paper is included in a wide ranging study which also involves theory and the development ofa computer code, both briefly presented here.

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.

Bifurcation in a Nonlinear Autoparametric System Using Experimental and Numerical Investigations

Experimental and numerical investigations are carried out on anautoparametric system consisting of a composite pendulum attached to aharmonically base excited mass-spring subsystem. The dynamic behavior ofsuch a mechanical system is governed by a set of coupled nonlinearequations with periodic parameters. Particular attention is paid to thedynamic behavior of the pendulum. The periodic doubling bifurcation ofthe pendulum is determined from the semi-trivial solution of thelinearized equations using two methods: a trigonometric approximation ofthe solution and a symbolic computation of the Floquet transition matrixbased on Chebyshev polynominal expansions. The set of nonlineardifferential equations is also integrated with respect to time using afinite difference scheme and the motion of the pendulum is analyzed viaphase-plane portraits and Poincaré maps. The predicted resultsare experimentally validated through an experimental set-up equippedwith an opto-electronic set sensor that is used to measure the angulardisplacement of the pendulum. Period doubling and chaotic motions areobserved.

Dynamique de structures souples en mouvement transitoire. Application aux raquettes de badminton

The article concerns the planar dynamic behaviour of flexible structures subjected to a rotation law. The developed nonlinear model takes into account the softening and the stress stiffening effects and is based on the finite element method associated with a dynamic condensation technique and with the modal reduction in order to include in particular the modal damping. Two examples from the literature permit in testing the model. The experimental investigation is carried out on a rod–mass system. The motion of this system subjected to a driven torque of a brushless motor is recorded using a digital high speed camera. The comparison of the predicted and measured response is very satisfactory and permits the validation of the model. Finally, the model is applied to three different kinds of existing badminton rackets. The rotation law introduced in the model comes from the record of the players wrist motion. The comparison of the three predicted racket deflexions confirm the performance claimed by the manufacturer.

Nonlinear Model for Dynamic Behavior of Drill-String

This article is devoted to the study of the contact between the drill-string and the well during drilling operations. The study focuses on the Bottom-Hole-Assembly (BHA), which is submitted to compression. The work is motivated by the need to understand the complex behavior of such a system, in order to improve control their constructive and destructive potentials. The contact, which is supposed to be localized on the drill-collar or stabilizers, is prejudicial and involves a premature abrasive wear of the drill-string, reduction of the rate of penetration of the tool into the rock (ROP) and reduction of the mean time between failure (MTBF). The proposed mathematical model is expressed in terms of four independent degrees of freedom. They include the effects of bending and torsion; the whirling motion of the drill-string as well as the phenomena of friction between the drill-string and the well. The tangential effect is modeled by using Coulomb’s law of friction. The nonlinear equations of the movement are derived using Lagrange equations and are solved numerically to obtain the response. Specific attention is paid to the study of friction and a consistent contact model which is capable of taking into account the rolling of the drill-string, both with and without slip, is included in the model. This paper also presents a parametric study on the influence of the initial position of the string and the friction coefficient of the contact on the dynamic behavior of the structure. An experimental set-up, equipped with two optolineic devices, is used to validate the model.Copyright