Showing papers in "Journal of Computational and Nonlinear Dynamics in 2012"

Design, Simulation, and Testing of Energy Harvesters With Magnetic Suspensions for the Generation of Electricity From Freight Train Vibrations

Abstract: The constant spread of commercial trades on railways demand to develop alternative diagnostic systems, which are suitable to applications without electric supply and convenient for the industrial development and diffusion that means low cost, good reliability and high integrability. Similarly, it is possible to install navigation and traceability systems (for instance, by the use of GPS transmitters) to control on demand the travel history of the train and even that of each coach separately. Recent studies demonstrated the possibility to generate directly onboard the electric power needed to the supply of simple diagnostic systems based on low power sensors and integrated wireless transmission modules. The design of this kind of generators is based on the idea of converting the kinetic energy of train vibration in electric energy, through appropriate energy harvesters containing electro-mechanical transducers dimensioned ad hoc. The goal of this work is to validate the design procedure for energy harvesters addressed to the railway field. The input vibration source of the train has been simulated thorough numerical simulation of the vehicle and the final harvester prototype has been tested on a scaled roller-rig. The innovative configuration of magnetic suspended proof mass is introduced in the design to fit the input vibration spectra of the vehicle. From the coupled study of the harvester generator and the vehicle, the effective output power of the device is predicted by means of a combination of experimental and simulation tests. The generator demonstrated the ability to supply a basic sensing and transceiving node by converting the kinetic energy of a train vibration in normal traveling conditions. The final device package is 150 × 125 × 95 mm, and its output voltage and current are 2.5 V and 50 mA, respectively, when the freight train velocity is 80 km/h. The corresponding output power is almost 100 mW

Analysis of the Dynamic Behavioral Performance of Mechanical Systems With Multi–Clearance Joints

Abstract: In this investigation, the effect of revolute joints’ clearance on the dynamic performance of mechanical systems is reported. A computation algorithm is developed with the aid of SolidWorks/CosmosMotion software package. A slider-crank mechanism with one and two clearance-joints is studied and analyzed when working in vertical and in horizontal planes. The simulation results point out that the presence of such clearance in the joints of the system understudy leads to high peaks in the characteristic curves of its kinematic and dynamic performance. For a multiclearance joints mechanism, the maximum impact force at its joints takes its highest value at the nearest joint to the input link. This study also shows that, when the mechanism works in horizontal plane, the rate of impacts at each clearance-joint increases and consequently the clearance-joints and actuators will deteriorate faster.

Numerical Investigation of Abradable Coating Removal in Aircraft Engines Through Plastic Constitutive Law

Abstract: In the field of turbomachines, better engine performances are achieved by reducing possible parasitic leakage flows through the closure of the clearance distance between blade tips and surrounding stationary casings and direct structural contact is now considered as part of the normal life of aircraft engines. In order to avoid catastrophic scenarios due to direct tip incursions into a bare metal housing, implementation of abradable coatings has been widely recognized as a robust solution offering several advantages: reducing potential nonrepairable damage to the incurring blade as well as adjusting operating clearances, in situ, to accept physical contact events. Nevertheless, the knowledge on the process of material removal affecting abradable coatings is very limited and it seems urgent to develop dedicated predicting numerical tools. The present work introduces a macroscopic model of the material removal through a piecewise linear plastic constitutive law which allows for real time access to the current abradable liner profile within a time-stepping approach of the explicit family. In order to reduce computational loads, the original finite element formulation of the blade of interest is projected onto a reduced-order basis embedding centrifugal stiffening. First results prove convergence in time and space and show that the frequency content of the blade response is clearly sensitive to the presence of abradable material. The continuous opening of the clearance between the blade tip and the casing due to the material removal yields larger amplitudes of motion and new scenarios of structural divergence far from the usual linear conditions provided by the well-known Campbell diagrams.

A New Approach to Analytical Solution of Cantilever Beam Vibration With Nonlinear Boundary Condition

Abstract: This paper presents the application of novel and reliable exact equivalent function (EF) for deadzone nonlinearity in an analytical investigation of nonlinear differential equations. A highly nonlinear equation of cantilever beam vibration with a deadzone nonlinear boundary condition is used to indicate the effectiveness of this EF. To obtain the analytical solution of dynamic behavior of the mentioned system, a powerful method, called He’s parameter expanding method (HPEM) is used. Comparison of the obtained solutions using a numerical method reveals the accuracy of this analytical EF. [DOI: 10.1115/1.4005924]

Multiple Pantograph Interaction With Catenaries in High-Speed Trains

Abstract: The limitation on the top velocity of high-speed trains concerns the ability to supply the proper amount of energy required to run the engines through the catenary-pantograph interface Due to the loss of contact, not only the energy supply is interrupted, but also arching between the collector bow of the pantograph and the contact wire of the catenary occurs, leading to the deterioration of the functional conditions of the two systems An alternative would be to increase the contact force between the two systems But such force increase would lead to a rapid wear of the contact strip of the pantograph and of the contact wire with negative consequences on the durability of the systems These situations require that the dynamics of the pantograph-catenary are properly modeled and that software used for analysis, design, or to support maintenance decisions is not only accurate and efficient, but also allows for modeling all details relevant to the train overhead energy collector operation This work presents a fully three-dimensional methodology for the computational analysis of the interaction between catenary and pantographs The finite element method (FEM) is used to support the modeling of the catenary, while a multibody (MB) dynamics methodology is applied to support the pantograph modeling The contact between the two subsystems is described using a penalty contact formulation A high-speed co-simulation procedure is proposed to ensure the communication between the two methodologies In order to validate the formulation and models developed, the numerical results are compared against experimental data The proposed methodology is then applied to study the interaction of multiple pantographs of a high-speed train with the catenary The results show that the passage of the front pantograph excites the catenary, leading to the deterioration of the contact conditions on the rear one

A New Closure Strategy for Proper Orthogonal Decomposition Reduced-Order Models

Abstract: Proper orthogonal decomposition (POD) is one of the most significant reduced-order modeling (ROM) techniques in fluid mechanics. However, the application of POD based reduced-order models (POD-ROMs) is primarily limited to laminar flows due to the decay of physical accuracy. A few nonlinear closure models have been developed for improving the accuracy and stability of the POD-ROMs, which are generally computationally expensive. In this paper we propose a new closure strategy for POD-ROMs that is both accurate and effective. In the new closure model, the Frobenius norm of the Jacobian of the POD-ROM is introduced as the eddy viscosity coefficient. As a first step, the new method has been tested on a one-dimensional Burgers equation with a small dissipation coefficient 1⁄4 10 . Numerical results show that the Jacobian based closure model greatly improves the physical accuracy of the POD-ROM, while maintaining a low computational cost. [DOI: 10.1115/1.4005928]

Experimental Rotations of a Pendulum on Water Waves

Abstract: The rotations of a parametric pendulum fitted onto a suitable floating support and forced to move vertically under the action of water waves have been studied on the basis of a dedicated wave flume laboratory experiment. An extended experimental campaign has been carried out with the aim of providing insight into the mechanics of the pendulum’s response to the wave forcing and data useful as a benchmark for available theories. A large number of time histories of the pendulum’s angular position have been collected. Rotations have been detected for different values of the frequency and of the amplitude of the excitation, showing the robustness in parameter space, and for different initial conditions, showing the robustness in phase space. This experiment, suggested by the recently developed concept of extracting energy from sea waves, constitutes preliminary experimental proof of that concept’s practical feasibility.

Comparison of Methods Analyzing Bifurcation and Hunting of Complex Rail Vehicle Models

Abstract: The stability assessment is an important task in the mechanical design of railway vehicles. For a detailed model of a railway passenger coach, the hunting behavior depending on the running speed, on wheel-rail contact conditions, and on different model configurations is analyzed using two different methods: The path-following method based on a direct computation of limit cycles enables an automatic computation. However, due to the direct computation, which exploits the periodicity of the solution, this method is restricted to strictly periodic behavior. In the brute-force method, an initial disturbance limited to a certain time interval is applied to the model. This method allows the analysis of the behavior independently from the type of the solution, but requires manual intervention. The comparison of the results obtained with both methods shows a good agreement and thereby the reliability of the results and the methods.

Swing Dynamics and Input-Shaping Control of Human-Operated Double-Pendulum Boom Cranes

Abstract: Boom cranes are used for numerous material-handling and manufacturing processes in factories, shipyards, and construction sites. All cranes lift their payloads by hoisting them up using overhead suspension cables. Boom cranes move payloads by slewing their base about a vertical axis, luffing their boom in and out from the base, and changing the length of the suspension cable. These motions induce payload oscillation. The problem of payload oscillation becomes more challenging when the payload exhibits double-pendulum dynamics that produce two varying frequencies of oscillation. This paper studies the swing dynamics of such cranes. It also applies input shaping to reduce the two-mode oscillatory dynamics. Experiments confirm several of the interesting dynamic effects.

Use of the Non-Inertial Coordinates in the Analysis of Train Longitudinal Forces

Abstract: A new three-dimensional non-linear train car coupler model is established,which takes into account the geometric nonlinearity due to the coupler and car body displacements.The proposed non-linear coupler model allows for arbitrary three-dimensional motion of the car bodies and captures kinetic degrees of freedom that are not captured using existing simpler models.By assuming the inertia of the coupler components negligible compared to the inertia of the car body,the system coordinates are partitioned into two distinct sets;inertial and non-inertial coordinates.The inertial coordinates that describe the car motion have inertia forces associated with them.The non-inertial coupler coordinates,on the other hand,describe the coupler kinetics and have no inertia forces associated with them.While the developed more-detailed coupler model captures the coupler kinetic degrees of freedom,it does not lead to an increase in the number of state equations,number of the system inertial coordinates,and number of constraint equations.Furthermore,by using this approach,one avoids having a system of stiff differential equations that can arise because of the relatively small coupler mass.Numerical results of simple train models are presented in order to demonstrate the use of the formulation developed in this paper.

Use of B-Spline in the Finite Element Analysis: Comparison With ANCF Geometry

Abstract: : This paper examines the limitations of using B-spline representation as an analysis tool by comparing its geometry with the nonlinear finite element absolute nodal coordinate formulation (ANCF) geometry. It is shown that while both B-spline and ANCF geometries can be used to model non-structural discontinuities using linear connectivity conditions, there are fundamental differences between B-spline and ANCF geometries. First, while B-spline geometry can always be converted to ANCF geometry, the converse is not true; that is, ANCF geometry cannot always be converted to B-spline geometry. Second, because of the rigid structure of the B-spline recurrence formula, there are restrictions on the order of the parameters and basis functions used in the polynomial interpolation; this in turn can lead to models that have significantly larger number of degrees of freedom as compared to those obtained using ANCF geometry. Third, in addition to the known fact that B-spline does not allow for straight forward modeling of T-junctions, B-spline representation cannot be used in a straight forward manner to model structural discontinuities. It is shown in this investigation that ANCF geometric description can be used to develop new spatial chain models governed by linear connectivity conditions which can be applied at a preprocessing stage allowing for an efficient elimination of the dependent variables. The modes of the deformations at the definition points of the joints that allow for rigid body rotations between ANCF finite elements are discussed. The use of the linear connectivity conditions with ANCF spatial finite elements leads to a constant inertia matrix and zero Coriolis and centrifugal forces. The fully parameterized structural ANCF finite elements used in this study allow for the deformation of the cross section and capture the coupling between this deformation and the stretch and bending.

Pull-In Retarding in Nonlinear Nanoelectromechanical Resonators Under Superharmonic Excitation

Abstract: In order to compensate for the loss of performance when scaling resonant sensors down to NEMS, a complete analytical model, including all main sources of nonlinearities, is presented as a predictive tool for the dynamic behavior of clamped-clamped nanoresonators electrostatically actuated. The nonlinear dynamics of such NEMS under superharmonic resonance of an order half their fundamental natural frequencies is investigated. It is shown that the critical amplitude has the same dependence on the quality factor Q and the thickness h as the case of the primary resonance. Finally, a way to retard the pull-in by decreasing the AC voltage is proposed in order to enhance the performance of NEMS resonators.

Numerical and Hardware-In-the-Loop Tools for the Design of Very High Speed Pantograph-Catenary Systems

Abstract: To be competitive with other transport means for a wider distance range, high-speed trains need to increase their revenue service speed. Due to this need, improving the pantograph-catenary interaction to ensure appropriate current collection in spite of the increased dynamic effects and the larger electrical power required represents one of the most serious technical issues to be solved. The aim of this paper is to discuss the use of numerical and hybrid (hardware in the loop) simulation tools in the design of new overhead lines for a speed of 360 km/h. A validation of both simulation tools is performed using line measurements as a point of comparison; then the validated simulation approaches are used to quantitatively assess the effectiveness of some catenary design options.

Position Control of a Rehabilitation Robotic Joint Based on Neuron Proportion-Integral and Feedforward Control

Abstract: The joint of the upper limb rehabilitation robot, which is designed and built in our lab, is driven by pneumatic muscles (PMs) in an opposing pair configuration. Each PM drives the robotic joint through a steel wire with a flexible sleeve and a tension device, which causes delay and various frictions as disturbances to the robotic joint system. These factors make the rehabilitation robotic joint very complex to model and control. Especially in position control, the overshoot is difficult to deal with when the directions of the friction forces are changing. The main purpose of this paper is to enhance the position control performance of the robotic joint by neuron PI and feedforward. Neuron PI control has a powerful capability of learning, adaptation, and tackling nonlinearity, and feedforward control demonstrates good performance in dealing with frictions, which cause overshoot. The results of the experiments indicate that the proposed controller, which combines neuron PI and feedforward, can enhance the performance in position control of the robotic joint, especially on dealing with overshoot.

Nonlinear Parameter Identification in Multibody Systems Using Homotopy Continuation

Abstract: The identification of parameters in multibody systems governed by ordinary differential equations, given noisy experimental data for only a subset of the system states, is considered in this work. The underlying optimization problem is solved using a combination of the Gauss–Newton and single-shooting methods. A homotopy transformation motivated by the theory of state observers is proposed to avoid the well-known issue of converging to a local minimum. By ensuring that the response predicted by the mathematical model is very close to the experimental data at every stage of the optimization procedure, the homotopy transformation guides the algorithm toward the global minimum. To demonstrate the efficacy of the algorithm, parameters are identified for pendulum-cart and double-pendulum systems using only one noisy state measurement in each case. The proposed approach is also compared with the linear regression method. [DOI: 10.1115/1.4004885]

Denavit-Hartenberg Parameterization of Euler Angles

Abstract: Euler angles describe rotations of a rigid body in three-dimensional Cartesian space, as can be obtained by, say, a spherical joint. The rotation carried out by a spherical joint can also be expressed by using three intersecting revolute joints that can be described using the popular Denavit-Hartenberg (DH) parameters. However, the motions of these revolute joints do not necessarily correspond to any set of the Euler angles. This paper attempts to correlate the Euler angles and DH parameters by introducing a concept of DH parameterization of Euler angels. A systematic approach is presented in order to obtain the DH parameters for any Euler angles set. This gives rise to the concept of Euler-angle-joints (EAJs), which provide rotations equivalent to a particular set of Euler angles. Such EAJs can be conveniently used for the modeling of multibody systems having multiple-degrees-of-freedom joints.

Response and Stability Analysis of Periodic Delayed Systems With Discontinuous Distributed Delay

Abstract: In this paper, the analysis of delay differential equations with periodic coefficients and discontinuous distributed delay is carried out through discretization by the Chebyshev spectral continuous time approximation (ChSCTA). These features are introduced in the delayed Mathieu equation with discontinuous distributed delay which is used as an illustrative example. The efficiency of stability analysis is improved by using shifted Chebyshev polynomials for computing the monodromy matrix, as well as the adaptive meshing of the parameter plane. An idea for a method for numerical integration of periodic DDEs with discontinuous distributed delay based on existing MATLAB functions is proposed. [DOI: 10.1115/1.4005925]

A Discrete Element Approach to Model Breakable Railway Ballast

Abstract: A discrete element approach to assess degradation processes in ballast beds is presented. Firstly, a discrete element model describing strength and failure of strong rock is introduced. For this purpose a granular solid is created by bonding of adjacent particles. A method to define angular ballast stones made from the granular solid is proposed. The strength of these stones is evaluated by compression between parallel platens. Comparing these results to published experimental data yields very good qualitative and reasonable quantitative agreement. Finally, the failure of aggregates of breakable stones is investigated by simulation of oedometric compression tests and indentation of a sleeper into a ballast bed.

Influence of Track Irregularities in the Catenary-Pantograph Dynamic Interaction

Abstract: This paper presents an advanced pantograph-catenary-vehicle-track model, which allows us to analyze the vertical dynamics of the complete system. The developed model is able to evaluate the displacements and the contact force generated in the catenary-pantograph as well as the wheel-track interactions. Nevertheless, this paper focuses on the possible influence of track irregularities on the catenarypantograph dynamic interaction. From a power spectral density function of the track irregularities, 180 track profiles and their respective catenary pantograph vehicle track simulations have been generated. The wide range of results allows us to obtain some conclusions about the influence of the track profile in the catenary pantograph behavior.

Different Types of Instabilities and Complex Dynamics in Reaction-Diffusion Systems With Fractional Derivatives

Abstract: In this article we analyze conditions for different types of instabilities and complex dynamics that occur in nonlinear two-component fractional reaction-diffusion systems. It is shown that the stability of steady state solutions and their evolution are mainly determined by the eigenvalue spectrum of a linearized system and the fractional derivative order. The results of the linear stability analysis are confirmed by computer simulations of the FitzHugh-Nahumo-like model. On the basis of this model, it is demonstrated that the conditions of instability and the pattern formation dynamics in fractional activator- inhibitor systems are different from the standard ones. As a result, a richer and a more complicated spatiotemporal dynamics takes place in fractional reaction-diffusion systems. A common picture of nonlinear solutions in time-fractional reaction-diffusion systems and illustrative examples are presented. The results obtained in the article for homogeneous perturbation have also been of interest for dynamical systems described by fractional ordinary differential equations.

Study on Derailment Mechanism and Safety Operation Area of High-Speed Trains Under Earthquake

Abstract: In order to investigate the derailment mechanism and safety operation area of high-speed trains under earthquake, a coupled vehicle-track dynamic model considering earthquake effect is developed, in which the vehicle is modeled as a 35 degrees of freedom (DOF) multibody system with nonlinear suspension characteristic and the slab track is modeled as a discrete elastic support model. The rails of the track are assumed to be Timoshenko beams supported by discrete rail fasteners, and the slabs are modeled with solid finite elements. The system motion equations are solved by means of an explicit integration method in time domain. The present work analyzes in detail the effect of earthquake characteristics on the dynamical behaviors of a vehicle-track coupling system and the transient derailment criteria. The considered derailment criteria include the ratio of the wheel/rail lateral force to the vertical force, the wheel loading reduction, the wheel/rail contact point traces on the wheel tread, and the wheel rise with respect to the rail top, respectively. The present work also finds the safety operation area, the derailment area, and the warning area of high-speed trains under earthquake, and their boundaries. These areas consist of three key parameters influencing the dynamical behavior of high-speed train and track under earthquake. The three key influencing parameters are, respectively, the vehicle speed and the lateral and vertical peak ground acceleration (PGA) of an earthquake. The results obtained indicate that the lateral earthquake motion has a greater influence on the vehicle dynamic behavior and its running safety compared to the vertical earthquake motion. The risk of derailment increases quickly with the increasing of lateral earthquake motion amplitude. The lateral earthquake motion is dominant in the vehicle running safety influenced by an earthquake. While the vertical earthquake motion promotes jumping of the wheels easily, not easy is flange climb derailment. And the effect of the vehicle speed is not significant under earthquake.

Nadal’s Formula and High Speed Rail Derailments

Abstract: Several railroad vehicle derailment criteria are based on the (L/LVV) ratio where L is the lateral force and V is the vertical force acting on the wheelset. Derailment is assumed to occur if this ratio exceeds a certain limit. The (L/LVV) ratio has its roots in Nadal’s formula which was introduced more than a century ago. When a planar analysis that corresponds to zero angle of attack is used, Nadal’s formula can be derived using a geometric approach, while a Nadal-like formula can be derived using a kinetic approach. In the geometric approach, a coordinate transformation is used to define the normal and friction forces in another coordinate system. In this case, the lateral and vertical forces are interpreted as the components of a vector that defines the normal and friction forces in another coordinate system without consideration of other external forces that are applied to the wheelset. Because the geometric approach does not account for other forces, it should not be used as the basis for derailment studies. In the kinetic approach, on the other hand, the L and V forces are interpreted as the resultant of the forces excluding the normal and friction forces at the contact point. That is, in both approaches discussed in this paper, the L and V forces cannot be interpreted as the resultant forces acting on the wheelset. The condition for the wheel climb using the kinetic approach is obtained and examined. It is shown that formulas obtained in this paper are based on assumptions that do not capture the gyroscopic moments, and therefore, these formulas should not be used as the basis for general high speed rail derailment criteria. It is also shown that in the case of zero angle of attack and using single degree of freedom planar kinetic model assumptions, an increase in the lateral force L can reduce the tendency for wheel climb, while reducing L can increase the wheel climb risk. Furthermore, the single degree of freedom assumptions used to obtain the wheel climb formula presented in this paper do not allow for wheel lift, and as a consequence, wheel lift derailment scenarios that can be the result of large moment should not be investigated using Nadal’s formula or one of its derivatives that employ the same assumptions. Furthermore, since the analysis presented in this paper assumes zero angle of attack, the conclusions obtained in this investigation do not apply to the wheel climb scenarios with nonzero angle of attack. It is also important to point out that this paper is not intended as a discussion on how Nadal’s formula is interpreted by researchers and engineers; instead, the paper is mainly focused on examining the roots of this formula and the problems that can arise from the assumptions used in its derivation.