This thesis presents the theoretical derivations and the implementation of a contact dynamics modelling system based on compliant contact models. The system was designed to be used as a general-purpose modelling tool to support the task planning process space-based robot manipulator systems. This operational context imposes additional requirements on the contact dynamics modelling system beyond the usual ones of fidelity and accuracy. The system must not only be able to generate accurate and reliable simulation results, but it must do it in a reasonably short period of time, such that an operations engineer can investigate multiple scenarios within a few hours. The system is easy to interface with existing simulation facilities. All physical parameters of the contact model can be identified experimentally or can be obtained by other means through analysis or theoretical derivations based on the material properties. Similarly, the numerical parameters can be selected automatically or by using heuristic rules that give an indication of the range of values that would ensure that the simulations results are qualitatively correct. The contact dynamics modelling system is comprised of two contact models. On one hand, a point contact model is proposed to tackle simulations involving bodies with non-conformal surfaces. Since it is based on Hertz theory, the contacting surfaces must be smooth and without discontinuity, i.e., no corners or sharp edges. The point contact model includes normal damping and tangential friction and assumes the contact surface is very small, such that the contact force is assumed to be acting through a point. An expression to set the normal damping as a function of the effective coefficient of restitution is given. A new seven-parameter friction model is introduced. The friction model is based on a bristle friction model, and is adapted to the context of 3-dimensional frictional impact modelling with introduction of load-dependent bristle stiffness and damping terms, and with the expression of the bristle deformation in vectorial form. The model features a dwell-time stiction force dependency and is shown to be able to reproduce the dynamic nature of the friction phenomenon. A second contact model based on the Winkler elastic foundation model is then proposed to deal with a more general class of geometries. This so-called volumetric contact model is suitable for a broad range of contact geometries, as long as the contact surface can be approximated as being flat. A method to deal with objects where this latter approximation is not reasonable is also presented. The effect of the contact pressure distribution across the contact surface is accounted for in the form of the rolling resistance torque and spinning friction torque. It is shown that the contact forces and moments can be expressed in terms of the volumetric properties of the volume of interference between the two bodies, defined as the volume spanned by the intersection of the two undeformed geometries of the colliding bodies. The properties of interest are: the volume of the volume of interference, the position of its centroid, and its inertia tensor taken about the centroid. The analysis also introduces a new way of defining the contact normal; it is shown that the contact normal must correspond to one of the eigenvectors of the inertia tensor. The investigation also examines how the Coulomb friction is affected by the relative motion of the objects. The concept of average surface velocity is introduced. It accounts for both the relative translational and angular motions of the contacting surfaces. The average surface velocity is then used to find dimensionless factors that relate friction force and spinning torque caused by the Coulomb friction. These latter factors are labelled the Contensou factors. Also, the radius of gyration of the moment of inertia of the volume of interference about the contact normal was shown to correlate the spinning Coulomb friction torque to the translational Coulomb friction force. A volumetric version of the seven-parameter bristle friction model is then presented. The friction model includes both the tangential friction force and spinning friction torque. The Contensou factors are used to control the behaviour of the Coulomb friction. For both contact models, the equations are derived from first principles, and the behaviour of each contact model characteristic was studied and simulated. When available, the simulation results were compared with benchmark results from the literature. Experiments were performed to validate the point contact model using a six degrees-of-freedom manipulator holding a half-spherical payload, and coming into contact with a flat plate. Good correspondence between the simulated and experimental results was obtained.

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.

This thesis deals with multibody dynamic simulation of mechanical systems in the product development process. The approach is to make the process of multibody dynamics simulation more efficient by structuring of the simulation, simulation models and their usage. Previous work has concentrated on developing faster calculation methods and more specialised simulation software. Efforts have been made to clarify how computer tools and multibody dynamic analysis methods are used in product development in industry today. Insight into the knowledge domains of product development and multibody dynamics is given together with an introduction to the area of distributed simulation, modularisation techniques and nonlinear analysis. The mentioned domains have traditionally been separated but the introduction of concurrent engineering and faster computers puts new demands on the need for integration of computer support and analysis in the development process. The performed work is to be seen as cross-functional work in order to bring different domains together for the sake of a better total product development. The applications areas used in the work are all within vehicle system dynamics. A proposal for performing the multibody dynamics methodology in a distributed and modular way in the product development process is given based on the performed work together with a prototype implementation.

The diploma thesis, which belongs to the area of vehicle dynamics, deals with the issue of suspension of trucks cabins. In particular, it focuses on the suspension of a race truck cab such as the Rally Dakar. Includes an overview of truck suspension (especially cabs), driving comfort assessment methods and the impact of vibration on human. To verify the suitability of using different cab suspension concepts, a multibody model was built in program MSC ADAMS. Suitable primary suspension has been found appropriate for this model. Cab suspension was tested for driving safety, but first for driving comfort.

We present a framework for modeling multibody systems based on the method of natural coordinates and Lagrange's equation of the first kind, resulting in a system of Differential-Algebraic Equations (DAEs). The C++ package DAETS (DAEs by Taylor Series), a robust high-index DAE solver, is utilized to solve the models. The simulation process is straightforward, with no need to derive equations of motion directly. Instead, the user supplies a Lagrangian, kinematic constraints, and if applicable, a dissipation function and external forces. A corresponding system of DAEs is formed by computing the required derivatives via automatic differentiation. DAETS primarily uses Cartesian coordinates as variables, eliminating angles and the associated trigonometric functions, which results in simplified models. Furthermore, DAETS provides direct access to the position/velocity data of any desired points or vectors as output, facilitating post-processing tasks, such as visualization. The main focus of this thesis is on establishing the viability of our framework through case studies. We simulate seven multibody systems and compare our results with those of reference models developed in the Simulink environment of MATLAB. A detailed account of the modeling process is given for each system, demonstrating the ease and intuitiveness of our approach. We also provide, from both DAETS and Simulink, the time history plots of several position coordinates to allow for direct comparison. Finally, we compute two types of errors over time. Our findings show that the results of DAETS match those of the reference models under different error tolerances for the studied systems, indicating that our framework is capable of simulating a wide variety of mechanisms with a superb degree of accuracy. / Thesis / Master of Science (MSc)

No description available.

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.

Environmental, aesthetic and political pressures continue to push for siting off-shore wind turbines beyond sight of land, where waters tend to be deeper, and use of floating structures is likely to be considered. Savings could potentially be realized by reducing hull size, which would allow more compliance with the wind thrust force in the pitch direction. On the other hand, these structures with large-amplitude motions will make dynamic analysis both more challenging and more critical. Prior to the present work, there were no existing dynamic simulation tools specifically intended for compliant wind turbine design. Development and application of a new computational method underlying a new time-domain simulation tool is presented in this dissertation. The compliant floating wind turbine system is considered as a multibody system including tower, nacelle, rotor and other moving parts. Euler's equations of motion are first applied to the compliant design to investigate the large-amplitude motions. Then, a new formulation of multibody dynamics is developed through application of the conservation of both linear momentum and angular momentum to the entire system directly. A base body is prescribed within the compliant wind turbine system, and the equations of motion (EOMs) of the system are projected into the coordinate system associated with this body. Only six basic EOMs of the system are required to capture 6 unknown degrees of freedom (DOFs) of the base body when mechanical DOFs between contiguous bodies are prescribed. The 6 x 6 mass matrix is actually composed of two decoupled 3 x 3 mass matrices for translation and rotation, respectively. Each element within the matrix includes the inertial effects of all bodies. This condensation decreases the coupling between elements in the mass matrix, and so minimizes the computational demand. The simulation results are verified by critical comparison with those of the popular wind turbine dynamics software FAST. The new formulation is generalized to form the momentum cloud method (M- CM), which is particularly well suited to the serial mechanical N-body systems connected by revolute joints with prescribed relative rotation. The MCM is then expanded to multibody systems with more complicated joints and connection types.

Virtual durability simulations have been explored in the automotive industry to complement physical testing in designing durable vehicles. Simulations are useful to check the validity of the design before even building the prototype of the vehicle. They are also useful in checking the effect of changes in vehicle design to the durability of the vehicle. Buses are designed and tested for durability before they are sold to customers. Bus manufacturers use special test tracks consisting of different kinds of maneuvers/obstacles to test the buses for durability. Proving ground durability test schedules defines the combination of different test track maneuvers/obstacles at which the bus is to be run. The test schedules are created to achieve accelerated fatigue damage in the bus comparable with the fatigue damage occurring in typical customer usage. This thesis is an attempt to check if a proving ground durability test schedule can be simulated in a computer. A Multibody dynamic model of the bus with its constituent subsystems is modeled in a multibody simulation software MSC ADAMS. Sub-systems like bus chassis frame and axle are modeled as flexible as their dynamic properties are assumed to influence the simulation results. The virtual bus is run on the virtual version of the test tracks. Loads at suspension torque rods, anti-roll bars, axles and displacement of dampers are extracted from the simulation. The load signals are post-processed to derive fatigue damage. The simulation model is compared with the test results of a single standard test track maneuver. The simulation model is tuned by adjusting the parameters to match with the test results of the given maneuver. Finally, the tuned model is used to run the bus in a test schedule. Results achieved at the end of the thesis shows that well-tuned simulation model is necessary for simulating test schedules with enough accuracy. Comparison with test results are to be treated with caution as the conditions of the test bus should be exactly same as the simulation model; which is difficult to achieve. Future extension of the work involves improving the accuracy of simulations and using simulations to iterate new kinds of maneuvers/obstacles to improve existing test schedules. / Virtuell hållfasthetsprovning utnyttjats inom fordonsindustrin för att komplettera fysisk provning med avseende att konstruera hållfasta fordon. Simuleringar är användbara för att kontrollera designen innan första prototypen har byggts men även för att kontrollera hur hållfastheten påverkas av olika fordonskoncept. Bussar utvecklas och provas så att de ska klara målen för hållfasthet innan de säljs. Busstillverkarna använder speciella provbanor bestående av olika hinder och manövrar för att testa hållfastheten. Tillsammans med speciella provningsprogram som specificerar vilka provbanehinder och manövrar som bussen ska provas enligt kan hållfastheten säkerställas. Dessa provprogram är framtagna för att den accelererade utmattningen på provbanan ska matcha den utmattning bussen utsätt för hos kund. Denna avhandling undersöker huruvida provprogram kan utvecklas digitalt via simuleringar. Multidynamiska modeller av bussens delsystem modelleras i programvaran MSC ADAMS. Delsystem som buss chassi ram och axlar modelleras som flexibla då deras dynamik egenskaper anses påverka simuleringsresultaten. Den virtuella bussen provas på en digital provbanan. Krafterna i reaktionsstag, kränghämmare, axlar och förskjutningen i stötdämpare beräknas. Dessa kraft- och förskjutningssignalser används senare för att beräkna utmattning. Simulerade resultat av ett hinder jämförs med resultat från fysisk provning för att därefter justera vissa parametrar för att virtuella resultat ska matcha fysiska. Efter att modellen är optimerad kan slutligen delskadan för ett helt provprogram simuleras. Resultat visar på att en väll optimerad simuleringsmodell är nödvändig för att simulera fram provprogram med bra noggrannhet. Att jämföra simulerade resultat med fysiska ska göras med viss aktsamhet då den fysiska bussen bör vara identisk med den virtuella; vilket är mycket svårt att uppnå. Framtida arbete inom ämnet bör innefatta förbättringar av simuleringsnoggrannheten och använda simulering för framtagandet av nya hinder/manövrar för att förbättra befintliga provprogram.