Bacem Zghal

Characterization of Modal Damping of Sandwich Plates

The homogenization of the energy functional of a sandwich plate, its minimization and its discretization by finite element methods and modeling the viscoelastic core behavior by an hysteretic structural damping lead to the homogenized dynamic equation of a sandwich plate. The vibratory analysis permits the determination of the elastic eigenmodes and the characterization of the modal damping which will serve to the establishment of dynamical responses if we used the modal dynamic recombination method. The numerical results obtained show that the eigenmodes are not orthogonal to the damping matrix but are only weakly coupled. Besides, the modal damping matrix coefficients vary according to the ratio of the core thickness and the total thickness of sandwich plate and follow a second-order polynomial function of this ratio.

Modal approach for dynamical analysis of sandwich plates

The dynamic equation of a sandwich plate is presented under the hypothesis of linear longitudinal displacement fields in each layer and an hysteretic structural damping of the viscoelastic core. A modal approach is adopted to investigate sandwich plate dynamical behaviour. First, the elastic eigenmodes are used in the characterisation of the modal damping. Then, the dynamical analysis is established using the modal dynamic recombination method and the result of modal damping characterisation. The numerical results obtained show that the eigenmodes are not orthogonal with respect to the damping matrix but are only weakly coupled. Besides, the modal damping matrix coefficients vary according to the ratio of the core thickness to the total thickness of the sandwich plate following a second order polynomial function. The modal approach with hysteretic modal damping characterisation is proposed in establishing dynamical responses. The results show that dynamical responses due to the use of a hysteretic diagonal modal damping matrix are in good agreement with those obtained when a full modal damping matrix is considered.

On the Research of Extra Characteristic Frequencies in a Planetary Gearbox

Gearboxes have been investigated and monitored for decades since they present one of the important transmission power systems which have been used in navy, air and automotive sectors. One of the most adopted one is the planetary gearbox since it has an important reduction ratio within compact space. The dynamic behaviour of a such one is very complicated because it possesses several gears in mesh and differs from other types of gearboxes by the fact that planet gears can occupy different positions in one period carrier rotation which leads to an important influence on the overall vibration signal acquired by a transducer mounted one the external housing. Consequently, in a measured vibration spectrum, the pass planet frequency component is identified and its energy level is considered only as the pass planet energy. However, there is another phenomenon that increases the level of the pass planet frequency component which is the Open image in new window due to the rotation of planets. In this work, a comprehensive monitoring of a staged planetary gearbox is presented. The unbalance phenomenon is investigated in every stage. Then, an experimental validation is provided in order to support our hypothesis claiming that the Open image in new window phenomenon depends on the parity of the number of planets.

Modeling the Transmission Path Effect in a Planetary Gearbox

In such mechanical systems, as helicopters and self-propelled cranes, designers need to use gearboxes which have an important reduction ratio within compact space. Hence, planetary gearboxes are widely used. Consequently, its monitoring presents an important task for researchers and engineers either in healthy or damaged case. Many researchers are interested on the investigation of the modulation phenomenon in planetary gearbox. It is presented in a frequency representation as side-band activity near to the gear-mesh frequency component and its harmonics. In a healthy case, the origin of this phenomenon in a planetary gearbox (stationary ring) is that the transducer, which is mounted on the external housing of the ring gear, perceived signals from all components including sun-gear, ring-gear, carrier and planet-gears which can occupy different position in one carrier period rotation. Hence, when the planet comes closer to the sensor, the vibration signal increases and vice-versa. In this work, a two dimensional linear lumped parameter model is proposed to model vibration sources. A mathematical formulation of the transmission path is introduced in order to model only the amplitude modulation phenomenon due to the change of the planet-gear position since the speed of the sun is constant. A frequency representation of numerical results is presented and analyzed.

New Modeling of Planetary Gear Transmission

In a planetary gearbox, there are multiple sources of vibrations due to the complexity of the gearbox since the latter contains multiple components (Sun, Carrier, Planets, and Ring) witch all of them are in mesh. In addition, the complexity of the planets motion (two rotational motions) affects the vibration collected in experiments, because the distance between planet and the transducer is time-varying. Hence, vibrations collected have not the same level: when the planet becomes closer from the senor, vibration level increases and vice versa. In this study, a linear two-dimensional lumped parameter dynamic model is developed in order to predict modulation phenomenon in a planetary gearbox. This model is based on novel description of the vibration of different components of the planetary gear taking into account the variable vibration transmission path. Numerical simulations show the ability of this model to describe this phenomenon with clear amplitude modulation in time signal.