Brendan J. Chan

Treating Uncertainties in Multibody Dynamic Systems Using a Polynomial Chaos Spectral Decomposition

This study addresses the critical need for computational tools to model complex nonlinear multibody dynamic systems in the presence of parametric and external uncertainty. Polynomial chaos has been used extensively to model uncertainties in structural mechanics and in fluids, but to our knowledge they have yet to be applied to multibody dynamic simulations. We show that the method can be applied to quantify uncertainties in time domain and frequency domain.© 2004 ASME

Multibody dynamics modelling of the freight train bogie system

Previous work in the railway technology laboratory at Virginia Polytechnic Institute and State University (Virginia Tech) focused on better capturing the dynamics of the friction wedge, modelled using three-dimensional rigid body dynamics with unilateral contact conditions. The current study extends the previous work to a half-bogie model treated as an application of multibody dynamics with unilateral contact to model the friction wedge interactions with the bolster and the sideframe. The half-bogie model was derived using MATLAB and functions as a three dimensional, dynamic, and multibody dynamics model comprised of four rigid bodies: a bolster, two friction wedges, and a sideframe assembly. This expanded model allows each wedge four degrees of freedom: vertical displacement, longitudinal displacement (between the bolster and sideframe), pitch (rotation around the lateral axis), and yaw (rotation around the vertical axis). The bolster and the sideframe are constrained to have only the vertical degree of freedom. The geometry of these bodies can be adjusted for various simulation scenarios. The bolster can be initialised with a pre-defined yaw (rotation around the vertical axis) and the sideframe may be initialised with a pre-defined pitch/toe (rotation around the lateral axis). The results of the multibody dynamics in half-bogie model simulation are shown in comparison with results from NUCARS®, an industry standard in train-modelling software, for similar inputs.

A Novel Wheel-Soil Interaction Model for Off-Road Vehicle Dynamics Simulation

This work establishes a semi-empirical wheel-soil interaction model, developed in the framework of plasticity theory and equilibrium analysis, to be used in vehicle dynamics simulations. Vehicle-terrain interaction is a complex phenomena governed by soil mechanical behavior and tire deformation. The application of soil load bearing capacity theory is used in this study to determine the tangential and radial stresses on the soil-wheel interface. Using semi-empirical data, the tire deformation geometry is determined to establish the drawbar pull, tractive force, and wheel load. To illustrate the theory developed, two important case studies are presented: a rigid wheel and a flexible tire on deformable terrain; the differences between the two implementations are discussed. The outcome of this work shows promising results which indicate that the modeling methodology presented could form the basis of a three-dimensional off-road tire model. In an off-road three-dimensional tire model, the traction behavior should include shear forces arising from the surface shear with the soil as well as the bulldozing effect during turning maneuvers.Copyright

A Ray-Tracing Approach to Simulation and Evaluation of a Real-Time Quarter Car Model With Semi-Active Suspension System Using Matlab

With the advent of X-by-wire systems, more research has been done in the field of semi-active suspension systems. These systems are not only lighter and less complicated than active suspension systems but also consume less power for operation. Power economy is crucial in an X-by-wire system because all of the safety critical systems run on electrical power in an X-by-wire vehicle. In this study, a comparison will be done on the performance of a real-time non-linear semi-active control scheme versus a passive suspension scheme. This comparison is done by using Matlab graphic visualization and Simulink to generate a graphic model of both simulations and observing the performance of both systems in real time. A mathematical model is created in Simulink and the response, given a certain excitation is output into a graphic object to view the Real-Time response. The main purpose of this study is to provide a method for ride control system engineers to evaluate their design and better visualize the performance of the designed system.Copyright

A Multibody Dynamics Approach to Friction Wedge Modeling for Freight Train Suspensions

This paper presents an effort to use multi-body dynamics with unilateral contact to model the friction wedge interaction with the bolster and the side frame. The new friction wedge model is a 3D, dynamic, stand-alone model of a bolster-friction wedge-side frame assembly. It allows the wedge four degrees of freedom: vertical displacement, longitudinal (between the bolster and the side frame) displacement, toe-in and toe-out, and yaw (rotation about the vertical axis). The dedicated train modeling software NUCARS® has been used to run simulations with similar inputs and to compare — when possible — the results with those obtained from the new stand-alone MATLAB friction wedge model. The stand-alone model shows improvement in capturing the transient dynamics of the wedge better. Also, it can predict not only normal forces going into the frame and bolster, but also use the associated moments to enhance model behavior. Significant simulation results are presented and the main differences between the current NUCARS® model and the new stand-alone MATLAB models are highlighted.Copyright

Development of a 3-D quasi-steady-state tyre model for on-road and off-road vehicle dynamics simulations: Part II – off-road rigid wheel model

This study presents the development of a simplified brush-based tyre model for on-road simulation, together with a simplified off-road wheel/tyre model that has the capability to revert back to on-road trend of behaviour on firmer soils. The on-road tyre model is developed based on empirical data collected by NHSTA, while the off-road tyre model is developed based on observations of experimental data and photographic evidence collected by various terramechanics researchers within the last few decades. Using theoretical analysis and empirical data, the tyre deformation geometry is determined to establish the tractive forces in off-road operation. The first step of any off-road vehicle is to model the condition where the soil is much more deformable than the tyre, where the tyre can be modelled as a rigid wheel. This study explores the development of the rigid wheel mode of the model, using dry sandy terrain, an example of extremely deformable soil. This paper is the second of three papers on the modelling of tyres for both on and off-road operations.

Development of a 3-D quasi-static tyre model for on-road and off-road vehicle dynamics simulations: Part I – on-road flexible tyre model

The research conducted in this study deals with the development of a simplified brush-based tyre model for on-road simulation, together with a simplified off-road wheel/tyre model. The on-road tyre model is developed based on data collected by NHTSA throughout the years, while the off-road tyre model is developed based on observations of experimental data and photographic evidence collected by various terramechanics researchers within the last few decades. The principle behind the model revolves around the integration of the stresses at the contact interface and has its basis in terramechanics. The model was parameterised from test data to acquire static and dynamic friction coefficients, cornering and longitudinal stiffness, as well as camber stiffness. The results are compared with test data and show good correlation. This paper is the first of a series of three papers on the modelling tyres for both on- and off-road operations.

Three-Piece Half-Truck Multibody Dynamics Models for Freight Train Suspensions

A three-piece bogie acts as a support for the freight train car bodies so that they can run on straight and curved tracks. It also absorbs the vibrational energy generated by the track. The three main parts of a traditional three-piece bogie are two side frames and a bolster. The side frames run parallel to the rails and are connected to each other by the bolster, which runs perpendicular to the rail. The side frames are connected to the axles, which are directly connected to the wheels that run on the track through the primary suspension. The primary suspension includes the bearing adapter and pedestal roof. The secondary suspension, which includes the friction wedge and load coils, connects and provides damping on each end of the bolster at its intersection with the side frame. Moreover, the friction wedge aids in warp resistance of the bogie. Because of the wedge’s non-linear frictional characteristics and load sensitive behavior, accurately capturing its dynamics in a computational model proves difficult. Previous work at the Railway Technology Laboratory (RTL) at Virginia Tech focused on better capturing the dynamics of the friction wedge modeled as a 3D rigid body. The current study extends that work to a half-truck model treated as an application of multibody dynamics with unilateral contact to model the friction wedge interactions with the bolster and the side frame. The half-truck model created in MATLAB is a 3D, dynamic, stand-alone model comprised of four rigid bodies: a bolster, two friction wedges, and a side frame assembly. The model allows each wedge four degrees of freedom: vertical displacement, longitudinal displacement (between the bolster and side frame), pitch (rotation around the lateral axis), and yaw (rotation around the vertical axis). The bolster and the side frame have only a vertical translation degree of freedom. The geometry of these bodies can be adjusted for various simulation scenarios. The bolster can be initialized with a pre-defined static yaw (rotation around the vertical axis) and the side frame may be initialized with a predefined pitch/toe geometry (rotation around the lateral axis). The model simulation results have been compared with results from NUCARS®, an industrially used train modeling software developed by the Transportation Technology Center, Inc., for similar inputs.Copyright

Control of Mechanical Systems Using a Parameterized Spectral Decomposition Approach

This study investigates a control methodology for dynamic systems based on representing all possible system responses under all possible values of the control variables. The underlying idea is to extend the system along the “control dimension” and explicitly account for the dependence of the system state on control variables. A spectral discretization along the “control dimension” is employed. The optimal control values are chosen to obtain the desired system response. Numerical studies for the control of linear and nonlinear quarter car models riding on various terrain profiles show promising results.Copyright

Modeling and simulation of a VTOL UAV for landing gear performance evaluation

A multibody dynamics model of a Vertical Take-off and Landing (VTOL) Unmanned Aerial Vehicle (UAV) is presented in this study. The scope of the project was to investigate a lightweight landing gear which has a stable and robust landing performance. Two original designs of the landing gear for the module of interest have been modeled and analyzed in this study. Two new designs have also been developed, modeled, and analyzed. A limited analysis of the forces that occur in the legs/struts has also been performed, to account for possible failure of the members due to buckling. The model incorporates a sloped surface of deformable terrain for stability analysis of the landing scenarios, and unilateral constraints to model the ground reaction forces upon contact. The lift forces on the UAV are modeled as mathematical relations dependent on the speed of the ducted fan to enable the variation of the impact velocities and the different landing scenarios. The simulations conducted illustrate that initial conditions at landing have a big impact on the stability of the module. The two new designs account for the worst possible scenario, and, for the material properties given, end with a larger weight than the one of the original design with three legs and a ring. Simulation data from several landing scenarios are presented in this paper, with analysis of the difference in performance among the different designs.