In this paper, we propose the interval analysis method for the dynamic response of wind turbine g... more In this paper, we propose the interval analysis method for the dynamic response of wind turbine gear system with uncertain-but-bounded parameters. We developed a lumped dynamic model with 8dofs. Lagrange formalism is used to formulate the governing equation of motion of the model. The simulation results are obtained by the interval analysis method for dynamic analysis under uncertainty. The interval analysis method results are compared with probabilistic approach results. This kind of results is coincident with the meaning of the probabilistic approach and interval analysis method.
Misalignment fault is a common source that generates strong vibrations and even dysfunction in ro... more Misalignment fault is a common source that generates strong vibrations and even dysfunction in rotating machinery. However, the characteristics of the dynamic response and the modeling of this type of defect have not been fully understood and there remains today an attractive field of research. This paper sheds the light on the modeling of vibrations and the diagnosis of coupling misalignment in a water pumping station for a dam case. Firstly, the paper presents a detailed dynamic model of a pump station using lumped elements. The model includes the motor, pump and two elastic couplings. These components are connected by shafts supported by bearings. Secondly, an approach to modeling an alignment defect, specifically parallel misalignment has been developed and presented. Thirdly, motion equations of the model were formulated and solved using Newmark' method. Finally, simulated results are presented and discussed using temporal and spectrum analysis. In parallel misalignment, it is found that multi-frequency components are obvious, static components are shown in the dynamic response. 2x rotational frequency of the motor will appear and is dominated and 1x rotational frequency is weak in the spectrum. The vibration responses of the three supporting bearing according to the radial directions with misalignment defect are investigated.
Abstract This paper addresses the dynamic response of a one stage gear system with uncertain para... more Abstract This paper addresses the dynamic response of a one stage gear system with uncertain parameters. The conventional methods dealing with stochastic systems are based on series expansion of stochastic quantities with respect to uncertain parameters, by means of either Taylor expansion or perturbation technique and evaluate the first and second order moments of the response by solving deterministic equations. Unfortunately, these methods lead to significant error when the standard deviation of uncertainties is relatively large. Herein, a first order perturbation approach is proposed. Comparisons with second-order perturbation approach and Monte Carlo simulation illustrate the efficiency of the proposed method. The results are discussed in order to investigate the influence of mass, damping and stiffness uncertainty on the dynamic response of a gear system.
European Journal of Mechanics A-solids, Sep 1, 2016
In this paper, we propose a new method for taking into account uncertainties occurring due to gea... more In this paper, we propose a new method for taking into account uncertainties occurring due to gear friction, based on the projection on polynomial chaos. The new method is used to determine the dynamic response of a spur gear system with uncertainty associated to friction coefficient on the teeth contact. The simulation results are obtained by the polynomial chaos method for dynamic analysis under uncertainty. The proposed method is an efficient probabilistic tool for uncertainty propagation. The polynomial chaos results are compared with Monte Carlo simulations.
This paper presents a three-dimensional model of two-stage straight bevel gear system. Periodic f... more This paper presents a three-dimensional model of two-stage straight bevel gear system. Periodic fluctuations of the gear meshes' stiffness are the main sources of excitation for the faultless gear system. First, dynamic response is calculated using Newmark method which is step-by-step time integration. The numerical results are presented in both the frequency and time domains. After that, we introduce some defects in the developed model such us the eccentricity defect, profile error and cracked tooth. The dynamic behavior of the defected gear system is compared with that of the faultless system. The numerical results from this work have applications in the design phase or maintenance of this type of bevel gear transmission.
Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering, May 10, 2019
Finite Element Method (FEM) is proposed to model the friction-induced vibration in the gear syste... more Finite Element Method (FEM) is proposed to model the friction-induced vibration in the gear system with a lead screw and nut. In order to validate it, the experiment was conducted by using the lead screw test setup. In the frequency spectrogram, there were two distinctively different patterns of the unstable modes: a mode where the frequency significantly changed and another where the frequency remained almost unchanged. Under a constant friction coefficient, the complex eigenvalue analysis in the FE model demonstrated that the system frequencies altered with respect to the transfer distance of the nut. The unstable modes were found to occur due to mode-coupling between the paired bending modes of the screw. Meanwhile, an unstable mode in which the frequency showed little changes in relation to the translation distance of the nut, was found to be an unstable torsion mode, which was caused by the negative friction-velocity slope.
Abstract Phase change material-based heat sinks are widely used in several industrial application... more Abstract Phase change material-based heat sinks are widely used in several industrial applications such as in the field of industrial automation and mechatronics. Nowadays, several researchers aim to obtain an optimal design of these systems in order to ameliorate its performances. Nevertheless, uncertainties are not considered for the majority of these studies. Furthermore, it has been confirmed that deterministic multi-objective optimization (DMOO) may lead to an unreliable design. In this study, a new methodology that leads to perform the Multi-Objective Reliability-Based Design Optimization (MORBDO) for thermal management of a passive cooling system is proposed. It consists in coupling the Finite Element Model (FEM), MORBDO procedures and surrogate approaches. Kriging predictor is used to construct metamodels and then validated using Cross-Validation (CV) and error predictions. A numerical investigation is carried out to study the different DMOO and MORBDO approaches. In this study, a 3D PCM-based round pin-fin heat sink is detailed. The aim of this problem is to minimize two objective functions: the cost (total volume V ) and the final cooling time t f by considering both thermal and physical constraints. For this purpose, geometrical uncertain parameters are considered such as length L , height H and ϕ pin diameter of the heat sink. This study leads to develop a well-distributed reliable Pareto solutions by combining the Robust Hybrid Method (RHM) and the Constrained Non-dominated Sorting Genetic Algorithm (C-NSGA-II). Then, the efficiency of the proposed MORBDO-RHM approach for PCM-based heat sink is verified.
Finite Elements in Analysis and Design, Sep 1, 2017
Many structures are subjected to random vibrations and those vibrations can cause a fatigue damag... more Many structures are subjected to random vibrations and those vibrations can cause a fatigue damage. So, to estimate the live time of the structure, we need to applied the fatigue multiaxial criteria at each point. Many studies demonstrate that the Sines criterion seems to give the best evaluation of the fatigue damage. But the application of this criterion need a high computing time if it's evaluated in the time domain. In this paper, we present a new methodology of calculation of the Local multiaxial fatigue damage, based on the formulation of the Sines criterion developed in the frequency domain. Each parameter of the Sines criterion will be calculated from the Power Spectral Densities of the stresses at each point of the structure. A finite element example is then used, at the end of this paper, to illustrate the application of the proposed strategy of calculation of the fatigue damage.
In this paper, the formulation of the finite element method for vibro-acoustic problem is applied... more In this paper, the formulation of the finite element method for vibro-acoustic problem is applied to a vehicle to investigate the sound pressure level inside the cabin. This study is combined with a stochastic analysis to account for variability of different parameters, considered as random variables, which are related to the characteristics of materials and boundary conditions. The results show that the Generalized Polynomial Chaos (gPC) method is more efficient compared to the direct Monte Carlo simulation (MC) without causing significant loss of accuracy. It is also shown that uncertainty levels in the input data could result in large variability in the calculated interior sound pressure level. The result of this modeling strongly depends on the order of the Polynomial Chaos. An increase in this order is accompanied by a better projection of the solution.
International Journal of Mechanical Sciences, Dec 1, 2017
Abstract In this work, an analytical formulation and numerical implementation of the response of ... more Abstract In this work, an analytical formulation and numerical implementation of the response of the coupled structure-acoustic system were performed. The acoustic pressure inside the cavity as well as the plate displacement are analyzed. This study is combined with a probabilistic analysis to account for variability of different parameters, considered as random variables, which are material properties. A reliability based design optimization (RBDO) using the generalized polynomial chaos (gPC) is addressed. In order to reduce the computational cost of the classical approach of RBDO problem, the optimum safety factor (OSF) method coupled with the gPC procedure is applied to the coupled acoustic-structure systems. Numerical examples showed the effectiveness and efficiency of the OSF based on gPC for the reliability optimization of the structural-acoustic system with probabilistic random variables.
In this paper, we propose the interval analysis method for the dynamic response of wind turbine g... more In this paper, we propose the interval analysis method for the dynamic response of wind turbine gear system with uncertain-but-bounded parameters. We developed a lumped dynamic model with 8dofs. Lagrange formalism is used to formulate the governing equation of motion of the model. The simulation results are obtained by the interval analysis method for dynamic analysis under uncertainty. The interval analysis method results are compared with probabilistic approach results. This kind of results is coincident with the meaning of the probabilistic approach and interval analysis method.
Misalignment fault is a common source that generates strong vibrations and even dysfunction in ro... more Misalignment fault is a common source that generates strong vibrations and even dysfunction in rotating machinery. However, the characteristics of the dynamic response and the modeling of this type of defect have not been fully understood and there remains today an attractive field of research. This paper sheds the light on the modeling of vibrations and the diagnosis of coupling misalignment in a water pumping station for a dam case. Firstly, the paper presents a detailed dynamic model of a pump station using lumped elements. The model includes the motor, pump and two elastic couplings. These components are connected by shafts supported by bearings. Secondly, an approach to modeling an alignment defect, specifically parallel misalignment has been developed and presented. Thirdly, motion equations of the model were formulated and solved using Newmark' method. Finally, simulated results are presented and discussed using temporal and spectrum analysis. In parallel misalignment, it is found that multi-frequency components are obvious, static components are shown in the dynamic response. 2x rotational frequency of the motor will appear and is dominated and 1x rotational frequency is weak in the spectrum. The vibration responses of the three supporting bearing according to the radial directions with misalignment defect are investigated.
Abstract This paper addresses the dynamic response of a one stage gear system with uncertain para... more Abstract This paper addresses the dynamic response of a one stage gear system with uncertain parameters. The conventional methods dealing with stochastic systems are based on series expansion of stochastic quantities with respect to uncertain parameters, by means of either Taylor expansion or perturbation technique and evaluate the first and second order moments of the response by solving deterministic equations. Unfortunately, these methods lead to significant error when the standard deviation of uncertainties is relatively large. Herein, a first order perturbation approach is proposed. Comparisons with second-order perturbation approach and Monte Carlo simulation illustrate the efficiency of the proposed method. The results are discussed in order to investigate the influence of mass, damping and stiffness uncertainty on the dynamic response of a gear system.
European Journal of Mechanics A-solids, Sep 1, 2016
In this paper, we propose a new method for taking into account uncertainties occurring due to gea... more In this paper, we propose a new method for taking into account uncertainties occurring due to gear friction, based on the projection on polynomial chaos. The new method is used to determine the dynamic response of a spur gear system with uncertainty associated to friction coefficient on the teeth contact. The simulation results are obtained by the polynomial chaos method for dynamic analysis under uncertainty. The proposed method is an efficient probabilistic tool for uncertainty propagation. The polynomial chaos results are compared with Monte Carlo simulations.
This paper presents a three-dimensional model of two-stage straight bevel gear system. Periodic f... more This paper presents a three-dimensional model of two-stage straight bevel gear system. Periodic fluctuations of the gear meshes' stiffness are the main sources of excitation for the faultless gear system. First, dynamic response is calculated using Newmark method which is step-by-step time integration. The numerical results are presented in both the frequency and time domains. After that, we introduce some defects in the developed model such us the eccentricity defect, profile error and cracked tooth. The dynamic behavior of the defected gear system is compared with that of the faultless system. The numerical results from this work have applications in the design phase or maintenance of this type of bevel gear transmission.
Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering, May 10, 2019
Finite Element Method (FEM) is proposed to model the friction-induced vibration in the gear syste... more Finite Element Method (FEM) is proposed to model the friction-induced vibration in the gear system with a lead screw and nut. In order to validate it, the experiment was conducted by using the lead screw test setup. In the frequency spectrogram, there were two distinctively different patterns of the unstable modes: a mode where the frequency significantly changed and another where the frequency remained almost unchanged. Under a constant friction coefficient, the complex eigenvalue analysis in the FE model demonstrated that the system frequencies altered with respect to the transfer distance of the nut. The unstable modes were found to occur due to mode-coupling between the paired bending modes of the screw. Meanwhile, an unstable mode in which the frequency showed little changes in relation to the translation distance of the nut, was found to be an unstable torsion mode, which was caused by the negative friction-velocity slope.
Abstract Phase change material-based heat sinks are widely used in several industrial application... more Abstract Phase change material-based heat sinks are widely used in several industrial applications such as in the field of industrial automation and mechatronics. Nowadays, several researchers aim to obtain an optimal design of these systems in order to ameliorate its performances. Nevertheless, uncertainties are not considered for the majority of these studies. Furthermore, it has been confirmed that deterministic multi-objective optimization (DMOO) may lead to an unreliable design. In this study, a new methodology that leads to perform the Multi-Objective Reliability-Based Design Optimization (MORBDO) for thermal management of a passive cooling system is proposed. It consists in coupling the Finite Element Model (FEM), MORBDO procedures and surrogate approaches. Kriging predictor is used to construct metamodels and then validated using Cross-Validation (CV) and error predictions. A numerical investigation is carried out to study the different DMOO and MORBDO approaches. In this study, a 3D PCM-based round pin-fin heat sink is detailed. The aim of this problem is to minimize two objective functions: the cost (total volume V ) and the final cooling time t f by considering both thermal and physical constraints. For this purpose, geometrical uncertain parameters are considered such as length L , height H and ϕ pin diameter of the heat sink. This study leads to develop a well-distributed reliable Pareto solutions by combining the Robust Hybrid Method (RHM) and the Constrained Non-dominated Sorting Genetic Algorithm (C-NSGA-II). Then, the efficiency of the proposed MORBDO-RHM approach for PCM-based heat sink is verified.
Finite Elements in Analysis and Design, Sep 1, 2017
Many structures are subjected to random vibrations and those vibrations can cause a fatigue damag... more Many structures are subjected to random vibrations and those vibrations can cause a fatigue damage. So, to estimate the live time of the structure, we need to applied the fatigue multiaxial criteria at each point. Many studies demonstrate that the Sines criterion seems to give the best evaluation of the fatigue damage. But the application of this criterion need a high computing time if it's evaluated in the time domain. In this paper, we present a new methodology of calculation of the Local multiaxial fatigue damage, based on the formulation of the Sines criterion developed in the frequency domain. Each parameter of the Sines criterion will be calculated from the Power Spectral Densities of the stresses at each point of the structure. A finite element example is then used, at the end of this paper, to illustrate the application of the proposed strategy of calculation of the fatigue damage.
In this paper, the formulation of the finite element method for vibro-acoustic problem is applied... more In this paper, the formulation of the finite element method for vibro-acoustic problem is applied to a vehicle to investigate the sound pressure level inside the cabin. This study is combined with a stochastic analysis to account for variability of different parameters, considered as random variables, which are related to the characteristics of materials and boundary conditions. The results show that the Generalized Polynomial Chaos (gPC) method is more efficient compared to the direct Monte Carlo simulation (MC) without causing significant loss of accuracy. It is also shown that uncertainty levels in the input data could result in large variability in the calculated interior sound pressure level. The result of this modeling strongly depends on the order of the Polynomial Chaos. An increase in this order is accompanied by a better projection of the solution.
International Journal of Mechanical Sciences, Dec 1, 2017
Abstract In this work, an analytical formulation and numerical implementation of the response of ... more Abstract In this work, an analytical formulation and numerical implementation of the response of the coupled structure-acoustic system were performed. The acoustic pressure inside the cavity as well as the plate displacement are analyzed. This study is combined with a probabilistic analysis to account for variability of different parameters, considered as random variables, which are material properties. A reliability based design optimization (RBDO) using the generalized polynomial chaos (gPC) is addressed. In order to reduce the computational cost of the classical approach of RBDO problem, the optimum safety factor (OSF) method coupled with the gPC procedure is applied to the coupled acoustic-structure systems. Numerical examples showed the effectiveness and efficiency of the OSF based on gPC for the reliability optimization of the structural-acoustic system with probabilistic random variables.
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