Lionel Manin

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.

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.

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.

Thermal Behavior of Power Gearing Transmission, Numerical Prediction, and Influence of Design Parameters

Thermal behavior prediction of Power Gearing Transmissions during preliminary design becomes necessary in order to optimize all the parts of mechanical systems (lubrication, cooling device dimensioning, static and dynamic stress resistance, etc.). It also reduces prototype tests. The thermal network method is used to model each technological element as a thermal finite element and a nonlinear system of equations is obtained. Geometric discretization is adapted to the scale of phenomenological observation and result requirements. As assumptions have to be made for the modeling of convection heat transfer and oil flow, experimental verifications are made. The influence of gear parameters, the effect of time varying running conditions, and oil flow defaults are then studied and discussed.

Modeling the climber fall arrest dynamics

Sports and mountaineering activities are becoming more and more popular. Equipment constructors seek to develop products and devices that are easy to use and that take into account all safety recommendations. PETZL and INSA have collaborated to develop a model for the simulation of displacements and efforts involved during the fall of a climber in the “safety chain”. The model is based on the classical equations of motion, in which climber and belayer are considered as rigid masses, while the rope is considered as a series of non-linear stiffness passing through several devices as brakes and runners. The main goal is to predict the forces in the rope and on the return anchor at the first rebound of the fall. Experiments were first performed in order to observe and determine the dynamic characteristics of the rope, and then to validate results stemming from simulations. Several fall configurations are simulated, and the model performs satisfactorily. It also provides a close approximation of the phenomena observed experimentally. The model enables the assessment of the existing equipments and the improved design of the future one.Copyright

Rock Climbing Belay Device Analysis, Experiments and Modeling

Amazingly no standard exists for belay devices used in rock or ice climbing. This paper presents an analysis performed on several belay devices that permits their comparison in terms of characteristics and efficiency. The belay device characterization consists in testing the brakes in the case of a given fall arrest in a testing room. Here, a belay device is characterized by its braking coefficient, the rope slip through the brake till the arrest of the fall and the impact load on the last runner. The braking coefficient is the ratio between the rope tensions on the tight and slack sides of the belay device. A device called “virtual hand” has been developed, it tries to reproduce the belayer hand action on the rope during the fall arrest, and it also enables the measurement of the load on the brake and the control of the rope tension on the belayer hand side. The fall arrest intensity or brutality is evaluated from the measurements of the rope slip in the brake and the load on the last runner. The analysis of the three measured characteristics enables the comparison of the six belay devices tested. It appears that these three quantities are related, indeed the larger the braking coefficient the lower the rope slip and the higher the impact load. The energy of the fall is absorbed over a shorter time period for belay device having a high braking coefficient. Therefore, an efficient braking gives way to a high impact force on the climber and a more brutal arrest of the fall. A basic model for the brake has been implemented in an already developed climber fall arrest model. Comparison of experimental and numerical results is made and is satisfactorily.

Effect of Rotor-Stator Contact on the Mass Unbalance 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, stop-end bearing. The aim of this paper is to analyse the influence of such rotor-stator interactions on the dynamic behaviour of two types of academic rotors. Several contact laws combined with smoothing methods are investigated in order to implement them in rotor dynamics models. The full annular rub and a finite impact series in forward whirl are exhibited.

Power losses prediction in poly-v belt transmissions: application to front engine accessory drives

This paper presents a method that permit to estimate a map of the power losses for any multi-pulley poly-v belt transmission. First, the work identifies and models the power losses in a simple two pulleys poly-v belt transmission, it focuses on the belt losses due to: the rubber hysteretic behavior, and the pulley-belt slip. The model developed is general so that it can be applied to any belt transmission. Finally, the developed model is extended to simulate the power losses of a multi pulley transmission such as a front engine accessory drives.

An analysis of rotor-stator interaction

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 three-disk rotor in bending equipped with two bearings is subject to a disk-stator contact. The two numerical algorithms analytically validated are again used and associated to four contact models: three types of smooth penalty methods and the Lagrange multiplier method. Spectrograms of time history responses are presented and permits analysing the spectral evolution of the rotor behaviour.

Nonlinear Dynamics of a Rotary Drill-String Immersed in a 3D Geometry Well

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 rotordynamics of such a structure, the model proposed is based on Timoshenko beam elements immersed in a 3D geometry well. A constant rotation speed in imposed at the top of drill-string. A fluid-structure interaction model that takes into account the drilling mud is used. The effect of drilling mud in drill-string vibration is studied by varying the well trajectories.