This article is dedicated to the study of the vibratory behavior of a rotor. The study presents a set of
scientific techniques on modeling and simulation of the vibrations of a rotor of a turbomachinery driven in torsion. This study helps to understand from the dynamic study the origin of the noise and vibration of a rotor; the study allows from the Rotorinsa software to highlight the effects of unbalance on a rotor. To develop the equations of the vibratory motion of the rotor, we used Lagrange’s energy approach. To succeed, a two wheeled model carried by a tree supported by two
hydrodynamic bearings is chosen according to the characteristics of the studied rotor. Each element of the rotor is defined by its finite element. The analytical resolution of the differential equations that characterize the vibratory behavior of the rotor is difficult manually. The numerical approach using the finite element method, programmed on Rotorinsa software allowed to perform dynamic rotor analysis.
Aerodynamics is defined as the science of handling a fluid that is often the air interacting with a structure. When simulating the flow over airfoils, transition from laminar to turbulent flow plays an important role in determining the flow features and in quantifying the airfoil performance such as lift and drag. These fluidic flows are subjected to viscous stresses and inertia which produces disordered fluctuations, so turbulence affects the behavior of the aerodynamic flow as well as the structure interacting with the fluid in a range of high Reynolds, indeed, it is obliged to control these turbulent flows in this area in order to give a good design of the structure. Several models of turbulence have been developed to facilitate the calculation of characteristic quantities to optimize the simulation of turbulent flows in aerodynamics. In this paper, we carried out a validation of a numerical simulation of a 3D transonic flow over the ONERA M6 wing for which the numerical results, performed using ANSYS/FLUENT©, will be compared with experimental data and NASA CFD results consisting on the pressure coefficient (Cp) along the upper and lower wing surfaces. The flow was obtained by solving the steady-state governing equations of continuity and momentum conservation combined with one of five turbulence models (Spalart-Allmaras (S-A), standard k-ε, k-ε RNG, standard k-ω and k-ω SST) aiming to the validation of these models through the comparison of the predictions and the free field experimental measurements for the selected wing.
Computational Fluid Dynamics (CFD) incorporates mathematical relations and algorithms to analyze and solve the problems regarding fluid flow. CFD analysis of an airfoil produces results such as lift and drag forces which determines the ability of an airfoil. In this paper a transonic flow will be modelled over a NACA 0012 airfoil for which experimental data has been published, so that a comparison can be made. The flow to be considered is compressible and turbulent and the solver used is the density based implicit solver, which gives good results for high speed compressible
flows. The results show that the predicted lift, drag and pressure coefficients are in good agreement with experimental data.
In this paper, we study extensions of the RBDO of the piezoelectric engines with travelling wave taking into account the dynamic contact between the different components (stator and rotor). Generally, the life of these engines is limited by important abrasion of the different components. So, the notion of random variables and the risk of failure must be integrated in the mechanical analysis to ensure the good working of the system. The numerical treatment of the dynamic contact inside the motor is presented with the good choice of relaxation factors. The RBDO is often formulated as a minimization of the initial structural cost under constraints imposed on the values of elemental reliability indices corresponding to various limit states. The classical RBDO leads to high computing time and weak convergence, but a hybrid method has been proposed to overcame these two drawbacks. The efficiency of the hybrid method has been demonstrated on static and dynamic cases with extension to the variability of the probabilistic model. We propose two methods: the dynamic hybrid method and the frequencies hybrid method as extension of the improved hybrid method presented in further works.
The purpose of this article is to solve the differential equations of Lagrange of a discrete system. Indeed, modeling and simulation are important steps in mechanical analysis. Modeling makes it possible to write the differential equations that describe the dynamic behavior and the simulation makes it possible to produce the resolution. We presented the Runge Kutta order 4 method under Matlab to solve the differential equations of a discrete system.
This article analyzes a numerical solution to solve the differential equations that describe the dynamic behavior of a multibody system. Mechanics suffer from high experimental costs, in some circumstances, sometimes the engineer is unable to test a model, for example in aerospace engineering, it’s hard to create the conditions under the prototype has to evolve. Simulation tools are essential and have become a competitive engineering system. The dynamic of mechanical systems play a fundamental role in establishing a relationship between the causes and the resulting reactions. In this article, we presented Lagrange’s method to establish the differential equations that describe dynamic behaviors of a multibody system, to applying them to the manipulator arm. Analytical resolution by classical methods proves difficult, numerical methods are essential; furthermore, calculation of one iteration by numerical methods can take several hours manually; the use of simulation software is essential. In this article, we have exploited Easydy software who uses the numerical method Newmark.
This paper describes the application of optimization and probabilistic methods to a hollow stem design implanted in a proximal femur. The objective is to introduce a hollow stem as a robust tool for fixation. Introducing the hollow stem and taking advantage of shape optimization with objectives in stresses, the regions where stresses shielding exists can be reduced as a conclusion. Probabilistic methods allow variations in factors which control the hole fixation of the implanted femur (the input parameters) to be taken into account in determining its performance. The probabilistic analysis is applied on the resulting hollow stem to simulate the variation factors of the bone ingrowth into holes. The fixation values are generated randomly using Monte Carlo simulation (MCS). Monte Carlo sampling techniques were applied and the maximum stress in the cancellous bone was chosen as a performance indicator. A simple 2D implant-bone study of solid and hollow stem designs is carried out with a high level of confidence 99.9% taking into account statistical uncertainties.