Indiana University-Purdue University Indianapolis (IUPUI) / In this thesis, an explicit time integration code which integrates multibody dynamics (MBD) and the discrete element method (DEM) is validated using three previously published steady-state physical experiments for non-cohesive sand-type material, namely: shear-cell for measuring shear stress versus normal stress; penetroplate pressure-sinkage test; and wheel drawbar pull-torque-slip test. The test results are used to calibrate the material properties of the DEM soft soil model and validate the coupled MBD-DEM code. All three tests are important because each test measures specific mechanical characteristics of the soil under various loading conditions. Shear strength of the soil as a function of normal load help to understand shearing of the soil under a vehicle wheel contact patch causing loss of traction. Penetroplate pressure-sinkage test is used to calibrate and validate friction and shear strength characteristics of the soil. Finally the rigid wheel-soil interaction test is used to predict drawbar pull force and wheel torque vs. slip percentage and normal stress for a rigid wheel. Wheel-Soil interaction test is important because it plays the role of ultimate validation of the soil model tuned in the previous two experiments and also shows how the soil model behaves in vehicle mobility applications. All the aforementioned tests were modeled in the multibody dynamics software using rigid bodies and various joints and actuators. The sand-type material is modeled using discrete cubical particles. A penalty technique is used to impose normal contact constraints (including particle-particle and particle-wall contact). An asperity-based friction model is used to model friction. A Cartesian Eulerian grid contact search algorithm is used to allow fast contact detection between particles. A recursive bounding box contact search algorithm enabled fast contact detection between the particles and polygonal body surfaces (such as walls, penetrometer, and wheel). The governing equations of motion are solved along with contact constraint equations using a time-accurate explicit solution procedure. The results show very good agreement between the simulation and the experimental measurements. The model is then demonstrated in a full-scale application of high-speed off-road vehicle mobility on the sand-type soil.

The problem of attitude control of a flexible satellite using magnetic attitude control is investigated. The work is motivated by JC2Sat - a joint CSA and JAXA mission whose main purpose is a proof of concept of two satellites performing differential drag formation flying. The impact of additional flexible drag panels (of various sizes) on the attitude control is assessed. JC2Sat's attitude control system consists of three perpendicular magnetorquers and one reaction/bias-momentum wheel. Four Linear Quadratic Regulator controllers are compared, ranging in complexity from being time-invariant and assuming a rigid satellite, to being periodic and actively suppressing panel vibrations. These include the first controllers which use magnetic attitude control to actively suppress vibrations, and where the periodic vibration suppression controller is able to guarantee asymptotic stability of the linearized system. It was found that for larger panels, the controllers which actively suppressed the vibrations outperformed those that did not.

The problem of attitude control of a flexible satellite using magnetic attitude control is investigated. The work is motivated by JC2Sat - a joint CSA and JAXA mission whose main purpose is a proof of concept of two satellites performing differential drag formation flying. The impact of additional flexible drag panels (of various sizes) on the attitude control is assessed. JC2Sat's attitude control system consists of three perpendicular magnetorquers and one reaction/bias-momentum wheel. Four Linear Quadratic Regulator controllers are compared, ranging in complexity from being time-invariant and assuming a rigid satellite, to being periodic and actively suppressing panel vibrations. These include the first controllers which use magnetic attitude control to actively suppress vibrations, and where the periodic vibration suppression controller is able to guarantee asymptotic stability of the linearized system. It was found that for larger panels, the controllers which actively suppressed the vibrations outperformed those that did not.

The goal of this study is to present a method for deriving equations of motion capable of modeling the controlled motion of an open loop multibody structure comprised of an arbitrary number of rigid bodies and slender beams. The procedure presented here for deriving equations of motion for flexible multibody systems is carried out by means of the Principle of Virtual Work (often referred to in the dynamics literature as d'Alembert's Principle). We first consider the motion of a general flexible body relative to the inertial space, and then derive specific formulas for both rigid bodies and slender beams. Next, we make a small motions assumption, with the end result being equations for a Rayleigh beam, which include terms which account for the axial motion, due to bending, of points on the beam central axis. This process includes a novel application of the exponential form of an orthogonal matrix, which is ideally suited for truncation. Then, the generalized coordinates and quasi-velocities used in the mathematical model, including those needed in the spatial discretization process of the beam equations are discussed. Furthermore, we develop a new set of recursive relations used to compute the inertial motion of a body in terms of the generalized coordinates and quasi-velocities. This research was motivated by the desire to model the controlled motion of a flexible space robot, and consequently, we use the multibody dynamics equations to simulate the motion of such a structure, providing a demonstration of the computer program. For this particular example we make use of a new sequence of shape functions, first used by Meirovitch and Stemple to model a two dimensional building frame subjected to earthquake excitations. / Ph. D.

Multibody dynamics simulations are currently widely accepted as valuable means for dynamic performance analysis of mechanical systems. The evolution of theoretical and computational aspects of the multibody dynamics discipline make it conducive these days for other types of applications, in addition to pure simulations. One very important such application is design optimization for multibody systems. Sensitivity analysis of multibody system dynamics, which is performed before optimization or in parallel, is essential for optimization. Current sensitivity approaches have limitations in terms of efficiently performing sensitivity analysis for complex systems with respect to multiple design parameters. Thus, we bring new contributions to the state-of-the-art in analytical sensitivity approaches in this study. A direct differentiation method is developed for multibody dynamic models that employ Maggi's formulation. An adjoint variable method is developed for explicit and implicit first order Maggi's formulations, second order Maggi's formulation, and first and second order penalty formulations. The resulting sensitivities are employed to perform optimization of different multibody systems case studies. The collection of benchmark problems includes a five-bar mechanism, a full vehicle model, and a passive dynamic robot. The five-bar mechanism is used to test and validate the sensitivity approaches derived in this paper by comparing them with other sensitivity approaches. The full vehicle system is used to demonstrate the capability of the adjoint variable method based on the penalty formulation to perform sensitivity analysis and optimization for large and complex multibody systems with respect to multiple design parameters with high efficiency. In addition, a new multibody dynamics software library MBSVT (Multibody Systems at Virginia Tech) is developed in Fortran 2003, with forward kinematics and dynamics, sensitivity analysis, and optimization capabilities. Several different contact and friction models, which can be used to model point contact and surface contact, are developed and included in MBSVT. Finally, this study employs reference point coordinates and the penalty formulation to perform dynamic analysis for the passive dynamic robot, simplifying the modeling stage and making the robotic system more stable. The passive dynamic robot is also used to test and validate all the point contact and surface contact models developed in MBSVT. / Ph. D.

No description available.

A co-simulation methodology is explored whereby a finite element code and a multi-body dynamics code featuring flexible cantilevered beams can be coupled and interactively executed. The floating frame of reference formulation is used to develop the equations of motion. The floating frame is fixed at the blade root. Such a formulation results in ordinary differential equations without added algebraic constraints. A variety of loose coupling and tight coupling schemes are examined for this problem. To synchronize the coupling variables, a Gauss-Seidel type iterative algorithm is used. The resulting fixed-point iterations are accelerated using Aitken’s adaptive relaxation technique. The methodology is evaluated for FAST, a wind turbine aeroelastic simulation code developed by NREL. As with FAST, many multi-body codes which can model flexibility employ modal methods. A proposed addition for FAST to simulate flexible effects using a finite element method module offers a potential to include a variety of non-linearities and also provides possibilities for using a high-fidelity aerodynamics module. The coupling schemes are compared and their applicability and limitations for different scenarios are pointed out. Results validating the approach are provided.

This licentiate thesis deals with effective simulation of multibody dynamic systems in the product development process. Previous work to make simulation more effective has concentrated on developing faster calculation methods. Instead, this approach is to make the process of multibody dynamics simulation more effective by structuring of products, simulation models and their usage. Efforts have been made to clarify how computer tools are used in product development in industry today. Insight into the two domains of product development and multibody dynamics is given. These domains have traditionally been separated but the introduction of concurrent engineering and faster computers puts new demands on the integration of computer support and analysis in the development process. A proposal for performing the multibody dynamics methodology in a modular way in the product development process is given based on the performed work.

An important facet of creating high-quality vehicles is to create components that are quiet and smooth under operation. In reality, however, it is challenging to measure the sound that some automotive components make under load because it requires specialist facilities and equipment which are expensive to acquire. Furthermore, the motors used in testbeds drown out the noise emitted from much quieter components, such as a Power Transfer Unit (PTU). This thesis aims to solve these issues by outlining the steps required to virtually estimate the acoustic radiation of a PTU using the Transmission Error (TE) as the input excitation via multi-body dynamics (MBD). MBD is used to estimate the housing vibrations, which can then be coupled with an acoustic tool to create a radiation analysis. Thus, creating a viable method to measure the acoustic performance without incurring significant expenses. Furthermore, it enables noise and vibration analyses to be incorporated more easily into the design stage. This thesis analysed the sound radiated due to gear whine which arises due to the TE and occurs at the gear mesh frequency and its multiples. The simulations highlighted that the TE can be accurately predicted using the methods outlined in this thesis. Similarly, the method can reliably obtain the vibrations of the housing. The results from this analysis show that at 2000 rpm the PTU was sensitive to vibrations at 500, 1000 and 1500 Hz, the largest amplitude being at 1000 Hz. Furthermore, the Sound Power Level (SWL) was proportional to the vibration amplitudes in the system. Analytical calculations were conducted to verify the methods and showed a strong correlation. However, it was concluded that experiments are required to further verify the findings in this thesis. / En viktig aspekt i att skapa fordon av hög kvalitet är att skapa komponenter som är tysta och smidiga under drift. I verkligheten är det dock svårt att mäta ljudet som vissa fordonskompo- nenter ger under belastning eftersom det kräver specialanläggningar och utrustning, vilket är dyrt att skaffa. Dessutom maskerar motorerna som används i testbäddar ut bullret från mycket tystare komponenter, till exempel en kraftöverföringsenhet (PTU). Detta examensar- bete syftar till att lösa dessa problem genom att beskriva de steg som krävs för att virtuellt uppskatta den akustiska strålningen av en PTU med hjälp av transmissionsfelet (TE) som ingångsexcitation via flerkroppsdynamik (multi-body dynamics, MBD). MBD används för att uppskatta kåpans vibrationer, som sedan kan kopplas till ett akustiskt verktyg för att skapa en ljudutstrålningsanalys. Således skapas en genomförbar metod för att mäta den akustiska pre- standan utan att medföra betydande kostnader. Dessutom möjliggör det att lättare integrera ljud- och vibrationsanalyser i designfasen. Detta examensarbete analyserade ljudet som utstrålats på grund av kugghjulsljud, som uppstår på grund av TE och uppträder vid kuggingreppsfrekvensen och dess multiplar. Simuleringarna belyste att TE kan förutsägas exakt med de metoder som beskrivs i detta examensarbete. På samma sätt kan metoden på ett tillförlitligt sätt uppnå kåpans vibrationer. Resultaten från denna analys visar att vid 2000 rpm var PTU känslig för vibrationer vid 500, 1000 och 1500 Hz, den största amplituden var vid 1000 Hz. Dessutom var ljudeffektsnivån (SWL) proportionell mot vibrationsamplituderna i systemet. Analytiska beräkningar genomfördes för att verifiera metoderna och visade en stark korrelation. Dock drogs slutsatsen att experiment krävs för att ytterligare verifiera resultaten i detta arbete.

For controller design, design of experiments, and other dynamic simulation purposes there is a need to be able to predict the dynamic response and joint reaction forces of a quarter-car suspension. This need is addressed by this study through development and system identification of both a linear and a non-linear multibody dynamics McPherson strut quarter-car suspension model. Both models are developed using a method customary to multibody dynamics so that the same numerical integrator can be used to compare their respective performances. This method involves using the Lagrange multiplier form of the constrained equations of motion to assemble a set of differential algebraic equations that characterize each model's dynamic response. The response of these models to a band-limited random tire displacement time array is then simulated using a Hilber-Hughes-Taylor integrator. The models are constructed to match the dynamic response of a state-of-the-art quarter-car test rig that was designed, constructed, and installed at the Institute for Advanced Learning and Research (IALR) for the Performance Engineering Research Lab (PERL). Attached to the experimental quarter-car rig was the front left McPherson strut suspension from a 2004 Porsche 996 Grand American Cup GS Class race car. This quarter-car rig facilitated acquisition of the experimental reference data to which the simulated data is compared. After developing these models their optimal parameters are obtained by performing system identification. The performance of both models using their respective optimal parameters is presented and discussed in the context of the basic linearity of the experimental suspension. Additionally, a method for estimating the loads applied to the experimental quarter-car rig bearings is developed. Finally, conclusions and recommendations for future research and applications are presented. / Master of Science