Simulation of the Dynamic Behaviour of a Thin-Walled Meshing Gear Using Duhamel’s Integral

2010 ◽  
Author(s):  
Costantino Carmignani ◽  
Paola Forte ◽  
Gabriele Melani ◽  
Ugo Buffa
Keyword(s):  
Dynamic Behaviour ◽  
Computational Cost ◽  
Time History ◽  
Realistic Model ◽  
Computational Effort ◽  
Design Development ◽  
Virtual Displacement ◽  
Displacement Sensors ◽  
Duhamel’S Integral

Aircraft transmissions have the peculiar characteristics of light structures and high operating speeds, therefore relatively low flexural natural frequencies and high excitation frequencies due to rotation and meshing. Resonance vibrations can create serious problems of malfunctions and even catastrophic failures. A reliable numerical model is surely a convenient means to perform preliminary simulations to identify the most critical resonance conditions and evaluate the effect of structural modifications on the dynamic behaviour of the component in the design development phase. Most numerical investigations found in the literature are carried out on simplified models of the rotating bodies likened to discs to reduce the computational effort. In this work a novel approach based on the application of Duhamel’s integral for the determination of the dynamic behaviour of a rotating gear subject to meshing forces has been developed to obtain more reliable results with a realistic model at an affordable computational cost. The gear response to dynamic excitation is obtained by the determination of its response to impulse using a single 3D finite element transient analysis taking afterwards into account the effect of the gear rotation. Subsequently, the Duhamel’s integral is applied using the tooth load time history in order to simulate as realistically as possible the gear load conditions. This paper presents the case of a real bi-helicoidal gear. A test bench was simulated measuring the displacement observed by some non-rotating virtual displacement sensors, located near the gear rim and disc. The signal was processed identifying the most critical rotating speeds on the basis of its RMS value. The numerical Campbell speed/frequency diagrams are in good agreement with experimental results.

Spectral Formulations for Vortex Induced Vibration Modal Decomposition and Reconstruction

2012 ◽  
Vol 134 (4) ◽  
Author(s):  
S. I. McNeill
Keyword(s):  
Fatigue Damage ◽  
Angular Rate ◽  
Computational Cost ◽  
Time History ◽  
Computational Effort ◽  
Measured Data ◽  
Scale Model ◽  
Mode Shapes ◽  
Modal Decomposition ◽  
Vortex Induced Vibration

Modal decomposition and reconstruction (MDR) of marine riser vortex induced vibration (VIV) is a technique where vibration is measured using accelerometers and/or angular rate sensors, the modal displacements are solved for and the stress and fatigue damage is reconstructed along the riser. Recent developments have greatly increased the accuracy and reliability of the method. However the computational burden is onerous due to stress time history reconstruction and rainflow cycle counting at every desired location along the riser. In addition, fully synchronous data are required to reconstruct the stress histories. Dirlik’s method for obtaining rainflow damage for Gaussian random stress using only spectral information (four spectral automoments) has proven to be quite accurate with a significant reduction in computational effort. In this paper two spectral formulations of MDR are introduced. The first method is applicable when all the measured data are synchronous. In this method, spectral cross moments of the modal displacements are solved from the spectral cross moments of the measured data using basis vectors consisting of normal mode shapes. The spectral automoments of stress are obtained from the modal displacement cross moments and analytical stress mode shapes. Dirlik’s method is then applied to obtain rainflow damage. The second method is a generalization of the first, where the measured data cross moments are only partially known. This method is applicable when measured data are partially synchronous or asynchronous. A numerical root-finding technique is employed to solve for the modal response cross moments. The method then proceeds in the same manner as the first. The spectral methods are applied to simulated VIV data of a full-scale deepwater riser and to Norwegian Deepwater Program (NDP) scale-model test data on a 38 m long slender riser. Comparisons of reconstructed fatigue damage versus simulated or measured damage indicate that the method is capable of estimating fatigue damage accurately for Gaussian VIV even when data are not fully synchronous. It is also shown that computational cost is greatly reduced.

Comparative Analysis of Methodologies for Uncertainty Propagation and Quantification

2017 ◽  
Author(s):  
Alessandra Cuneo ◽  
Alberto Traverso ◽  
Shahrokh Shahpar
Keyword(s):  
Engineering Design ◽  
Polynomial Chaos ◽  
Epistemic Uncertainty ◽  
Uncertainty Propagation ◽  
Computational Cost ◽  
Computational Effort ◽  
Optimization Under Uncertainty ◽  
Design Parameters ◽  
Test Case ◽  
Aleatory And Epistemic Uncertainty

In engineering design, uncertainty is inevitable and can cause a significant deviation in the performance of a system. Uncertainty in input parameters can be categorized into two groups: aleatory and epistemic uncertainty. The work presented here is focused on aleatory uncertainty, which can cause natural, unpredictable and uncontrollable variations in performance of the system under study. Such uncertainty can be quantified using statistical methods, but the main obstacle is often the computational cost, because the representative model is typically highly non-linear and complex. Therefore, it is necessary to have a robust tool that can perform the uncertainty propagation with as few evaluations as possible. In the last few years, different methodologies for uncertainty propagation and quantification have been proposed. The focus of this study is to evaluate four different methods to demonstrate strengths and weaknesses of each approach. The first method considered is Monte Carlo simulation, a sampling method that can give high accuracy but needs a relatively large computational effort. The second method is Polynomial Chaos, an approximated method where the probabilistic parameters of the response function are modelled with orthogonal polynomials. The third method considered is Mid-range Approximation Method. This approach is based on the assembly of multiple meta-models into one model to perform optimization under uncertainty. The fourth method is the application of the first two methods not directly to the model but to a response surface representing the model of the simulation, to decrease computational cost. All these methods have been applied to a set of analytical test functions and engineering test cases. Relevant aspects of the engineering design and analysis such as high number of stochastic variables and optimised design problem with and without stochastic design parameters were assessed. Polynomial Chaos emerges as the most promising methodology, and was then applied to a turbomachinery test case based on a thermal analysis of a high-pressure turbine disk.

Review of Hybrid Emissions Prediction Tools and Uncertainty Quantification Methods for Gas Turbine Combustion Systems

2017 ◽  
Author(s):  
Sajjad Yousefian ◽  
Gilles Bourque ◽  
Rory F. D. Monaghan
Keyword(s):  
Uncertainty Quantification ◽  
Gas Turbine ◽  
Kinetic Modelling ◽  
Computational Cost ◽  
Chemical Kinetic ◽  
Design Development ◽  
Deterministic Models ◽  
Prediction Tools ◽  
Gas Turbine Combustion ◽  
Combustion Systems

There is a need for fast and reliable emissions prediction tools in the design, development and performance analysis of gas turbine combustion systems to predict emissions such as NOx, CO. Hybrid emissions prediction tools are defined as modelling approaches that (1) use computational fluid dynamics (CFD) or component modelling methods to generate flow field information, and (2) integrate them with detailed chemical kinetic modelling of emissions using chemical reactor network (CRN) techniques. This paper presents a review and comparison of hybrid emissions prediction tools and uncertainty quantification (UQ) methods for gas turbine combustion systems. In the first part of this study, CRN solvers are compared on the bases of some selected attributes which facilitate flexibility of network modelling, implementation of large chemical kinetic mechanisms and automatic construction of CRN. The second part of this study deals with UQ, which is becoming an important aspect of the development and use of computational tools in gas turbine combustion chamber design and analysis. Therefore, the use of UQ technique as part of the generalized modelling approach is important to develop a UQ-enabled hybrid emissions prediction tool. UQ techniques are compared on the bases of the number of evaluations and corresponding computational cost to achieve desired accuracy levels and their ability to treat deterministic models for emissions prediction as black boxes that do not require modifications. Recommendations for the development of UQ-enabled emissions prediction tools are made.

High-resolution imaging: An approach by incorporating stationary-phase implementation into deabsorption prestack time migration

Geophysics ◽  
2016 ◽  
Vol 81 (5) ◽  
pp. S317-S331 ◽  
Author(s):  
Jianfeng Zhang ◽  
Zhengwei Li ◽  
Linong Liu ◽  
Jin Wang ◽  
Jincheng Xu
Keyword(s):  
Stationary Phase ◽  
Fresnel Zone ◽  
Computational Cost ◽  
Computational Effort ◽  
Propagation Path ◽  
Time Migration ◽  
Resolution Imaging ◽  
Prestack Time Migration ◽  
Dip Angle ◽  
Absorption And Dispersion

We have improved the so-called deabsorption prestack time migration (PSTM) by introducing a dip-angle domain stationary-phase implementation. Deabsorption PSTM compensates absorption and dispersion via an actual wave propagation path using effective [Formula: see text] parameters that are obtained during migration. However, noises induced by the compensation degrade the resolution gained and deabsorption PSTM requires more computational effort than conventional PSTM. Our stationary-phase implementation improves deabsorption PSTM through the determination of an optimal migration aperture based on an estimate of the Fresnel zone. This significantly attenuates the noises and reduces the computational cost of 3D deabsorption PSTM. We have estimated the 2D Fresnel zone in terms of two dip angles through building a pair of 1D migrated dip-angle gathers using PSTM. Our stationary-phase QPSTM (deabsorption PSTM) was implemented as a two-stage process. First, we used conventional PSTM to obtain the Fresnel zones. Then, we performed deabsorption PSTM with the Fresnel-zone-based optimized migration aperture. We applied stationary-phase QPSTM to a 3D field data. Comparison with synthetic seismogram generated from well log data validates the resolution enhancements.

Load Spectrum Compilation Based on Nonparametric Statistical Extrapolation

2013 ◽  
Vol 694-697 ◽  
pp. 271-277 ◽  
Author(s):  
Zhi Qiang Xu ◽  
Hong Jian Wang ◽  
Ming Yao Yao
Keyword(s):  
Kernel Function ◽  
Time History ◽  
Critical Issue ◽  
Extrapolation Method ◽  
Load History ◽  
Load Spectrum ◽  
Load Characteristics ◽  
Nonparametric Statistical ◽  
Function Shape

Considering the special load characteristics of the wheel loader, thispaper focus on compiling the load spectrum of the transmission of the wheelloader using the nonparametric statistical extrapolation method (NSEM). In thisprocess, the determination of the kernel function shape is the critical issue,which has been discussed in detail. Before extrapolating the sample loadspectrum, the signal denoising of the field-tested time-history load signals isperformed. After that, the sample load cycles are obtained using the rainflowcounting method and the corresponding kernel function shape is determined. Thenthe NSEM of rainflow matrix is proposed, by which the whole-life load spectrumis estimated. The proposed extrapolation method can well realize the estimationof the load cycles that do not appear in sample load cycles but may exist inthe whole-life load history.

Autogenous Shrinkage in Plain Cement Mixtures

2008 ◽  
Vol 400-402 ◽  
pp. 137-143 ◽  
Author(s):  
Vinod Rajayogan ◽  
Obada Kayali
Keyword(s):  
Experimental Determination ◽  
High Performance ◽  
High Performance Concrete ◽  
Autogenous Shrinkage ◽  
Basic Mechanism ◽  
Realistic Model ◽  
Test Method ◽  
Ongoing Research ◽  
Cement Mixtures

Determination of a realistic model for the estimation of autogenous shrinkage in plain cement mixtures has been an ongoing research among researchers in high performance concrete. While no standard test method exists for the determination of autogenous shrinkage, various researchers have designed different test methods for measurement of autogenous shrinkage. Current study involved the experimental determination of autogenous shrinkage using the test method developed by O.M.Jensen and co-workers, complimented with non-contact eddy current sensors. Measurements were conducted from as early as 1.5 hours from the time of casting. The samples were placed in a constant temperature chamber and the temperature of the sample was also monitored using a thermocouple. The study was carried out on plain cement mixtures at three water cement ratios of 0.25, 0.32 and 0.38. Measurements were also conducted on simple sealed prismatic samples but these measurements could only be collected after 24 hours of casting. The work is supplemented with CEMHYD3D simulations of the samples at similar water-cement ratios under sealed conditions so as to understand the development of the microstructure of the cement responsible for autogenous shrinkage. While experimental determination of internal relative humidity is quite difficult, data regarding chemical shrinkage, amount of water left and the development of the discontinuous capillary network from the simulations help to understand the determined experimental values of autogenous shrinkage. A detailed explanation on the causes of autogenous shrinkage and the basic mechanism responsible for it has been presented.

Development of a Fast Fluid Dynamics Model Based on PISO Algorithm for Simulating Indoor Airflow

2021 ◽  
Author(s):  
Sibo Li ◽  
Hongtao Qiao
Keyword(s):  
Fluid Dynamics ◽  
Real Time ◽  
Computational Cost ◽  
Flow Simulation ◽  
Building Design ◽  
Energy Performance ◽  
Computational Effort ◽  
Computational Method ◽  
Dimensional Case ◽  
Time Flow

Abstract Real-time or faster-than-real-time flow simulation is crucial for studying airflow and heat transfer in buildings, such as building design, building emergency management and building energy performance evaluation. Computational Fluid Dynamics (CFD) with Pressure Implicit with Splitting of Operator (PISO) or Semi-Implicit Method for Pressure Linked Equations (SIMPLE) algorithm is accurate but requires great computational resources. Fast Fluid Dynamics (FFD) can reduce the computational effort but generally lack prediction accuracy due to simplification. This study developed a fast computational method based on FFD in combination with the PISO algorithm. Boussinesq approximation is adopted for simulating buoyancy effect. The proposed solver is tested in a two-dimensional case and a three-dimensional case with experimental data. The predicted results have good agreement with the experimental results. In the two test cases, the proposed solver generates lower Root Mean Square Error (RMSE) compared to the FFD and at the same time, the proposed method reduces computational cost by a factor of 10 and 13 in the two cases compared to CFD.

Updating of Dynamic Finite Element Models Based on Experimental Receptances and the Reduced Analytical Dynamic Stiffness Matrix

1995 ◽  
Author(s):  
Stefan Lammens ◽  
Marc Brughmans ◽  
Jan Leuridan ◽  
Ward Heylen ◽  
Paul Sas
Keyword(s):  
Stiffness Matrix ◽  
Model Updating ◽  
Dynamic Stiffness ◽  
Computational Cost ◽  
Computational Effort ◽  
Reduction Scheme ◽  
Dynamic Stiffness Matrix ◽  
Simple Strategy ◽  
A Minor ◽  
Analytical Dynamic

Abstract This paper presents a model updating method based on experimental receptances. The presented method minimises the so called ‘indirect receptance difference’. First, the reduced analytical dynamic stiffness matrix is expressed as an approximate, linearised function of the updating parameters. In a numerically stable, iterative procedure, this reduced analytical dynamic stiffness matrix is changed in such a way that the analytical receptances match the experimental receptances at the updating frequencies. The updating frequencies are a set of selected frequency points in the frequency range of interest. Some considerations about an optimal selection of the updating frequencies are given. Finally, a mixed static-dynamic reduction scheme is discussed. Dynamic reduction of the analytical dynamic stiffness matrix at each updating frequency is physically exact, but it involves a great computational effort. The presented mixed static-dynamic reduction scheme is a simple strategy to reduce the computational cost with a minor loss of accuracy.

scholarly journals Refined Vehicle-Bridge Interaction Analysis Using Incompatible Solid Finite Element for Evaluating Stresses and Impact Factors

2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
Qing Xie ◽  
Wanshui Han ◽  
Yangguang Yuan
Keyword(s):  
Finite Element ◽  
Computational Efficiency ◽  
Interaction Analysis ◽  
Computational Cost ◽  
Point Contact ◽  
Time History ◽  
Analysis Method ◽  
Heavy Vehicles ◽  
Solid Element ◽  
Bridge Responses

The vehicle-bridge interaction can induce bridge vibration and consequently fatigue, durability deterioration, local damage, and even collapse of bridge structure. In this paper, a solid vehicle-bridge interaction (VBI) analysis method is developed to provide refined analysis on the bridge responses including displacement and local stress under vehicle loads. The incompatible solid finite element (FE) is introduced to model the bridge, where the element shear locking is alleviated by incompatible displacement modes without sacrificing the computational efficiency. Benchmark example shows the incompatible solid element has superior computational efficiency compared to the conventional solid element. By virtue of the mass-spring-damper vehicle model, the interaction between vehicle and bridge is simulated with point-to-point contact assumption and the coupled dynamic equations are solved via nonlinear iteration. A case study on a simply supported T-girder bridge is conducted to validate the developed solid VBI analysis method and then the dynamic impact factor (DIF) of the bridge is evaluated based on the computed stress results and compared to code values. Results show that the solid VBI analysis method yields more accurate time-history bridge responses including displacement and stress under moving vehicles than the grillage method despite higher computational cost. Particularly, it can simulate realistic stress distribution and concentration along any concerned sections as well as in local components, which can provide detail information on the bridge behavior under dynamic loads. On the other hand, the DIF based on the computed stress result generally agrees well with the code values except for heavy vehicles where the stress-based DIF is slightly higher than the value in Chinese code while lower than that of AASHTO, suggesting the value specified by Chinese code may underestimate the DIF of heavy vehicles in certain circumstances to which more attention should be paid.

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