The full model of a double-wishbone suspension has more than 30 differential-algebraic equations which takes a remarkably long time to simulate. By contrast, the look-up table for the same suspension is simulated much faster, but may not be very accurate. Therefore, developing reduced models that approximate complex systems is necessary because model reduction decreases the simulation time in comparison with the original model, enables real time applications, and produces acceptable accuracy. In this research, we focus on model reduction techniques for vehicle systems such as suspensions and how they are approximated by models having lower degrees of freedom. First, some existing model reduction techniques, such as irreducible realization procedures, balanced truncation, and activity-based reduction, are implemented to some vehicle suspensions. Based on the application of these techniques, their disadvantages are revealed. Then, two methods of model reduction for multi-body systems are proposed. The first proposed method is 2-norm power-based model reduction (2NPR) that combines 2-norm of power and genetic algorithms to derive reduced models having lower degrees of freedom and fewer number of components. In the 2NPR, some components such as mass, damper, and spring are removed from the original system. Afterward, the values of the remaining components are adjusted by the genetic algorithms. The most important advantage of the 2NPR is keeping the topology of multi-body systems which is useful for design purposes. The second method uses proper orthogonal decomposition. First, the equations of motion for a multi-body system are converted to explicit second-order differential equations. Second, the projection matrix is obtained from simulation or experimental data by proper orthogonal decomposition. Finally, the equations of motion are transferred to a lower-dimensional state coordinate system. The implementation of the 2NPR to two double-wishbone suspensions and the comparison with other techniques such as balanced truncation and activity-based model reduction also demonstrate the efficiency of the new reduction technique.

Orientador: Tamotsu Hirata / Banca: José Elias Tomazini / Banca: Luiz Fernando Costa Nascimento / Resumo: Um modelo fundamentado nos sistemas multicorpos, com sete corpos rígidos e oito corpos flexíveis, com três graus de liberdade para cada um dos corpos rígidos está sendo proposto. Os corpos rígidos são providos de inércia e os corpos flexíveis trabalham como juntas e não são providos de inércia. A solução numérica do modelo foi obtida com o método Runge-Kutta. Os parâmetros de influência, curvatura inicial da espinha lombar, posições dos centros geométricos das vértebras, tórax e da sacrum-pélvis, e o ponto de aplicação da força póstero-anterior (PA), foram obtidos de radiografia digital de cada paciente. O modelo foi simulado com dados de literaturas (obtidos de experimentos in vivo e em peças anatômicas). Os resultados foram satisfatórios do ponto de vista dos terapeutas e apresentam-se em conformidade com outros modelos propostos. O modelo oferece vantagem na aplicação individualizada a cada paciente pelos terapeutas, e foi construído com a metodologia de análise das forças aplicadas e suas reações diferentemente de outros modelos que apoiam-se nos métodos de análise das energias. O objetivo principal deste trabalho será o de avaliar o comportamento dinâmico do segmento lombar da coluna vertebral humana incluindo as massas do tórax e da pelve, por um modelo não-linear da rigidez viscoelástica estabelecido a partir da relação força-deslocamento obtida por experimentação in vivo. / Abstract: Evaluate a dynamic behavior of the human lumbar spine, with non-linear viscoelastic stiffness model followed by experimental data. Many of the techniques for the clinical treatment of dysfunction acting on lumber segments of the human spine have been based in the application of a postero anterior forces. Existing models to predict the state of lumber segments are restricted to evaluate general characteristic, furthermore, they use unrealistic boundary condition for its analysis. Periodic oscillatory posteroanterior forces were applied on each vertebra with initial lordotic curvature of the lumbar spine. A model is based on the multibody system of seven rigid bodies and eight deformable bodies representing human spine composed of thoratic, lumber and sacrum-pelvis segments. On each lumber were considered three degree of freedom(posterior - anterior, axial and flexion - extension). The rigid bodies are provided with inerti and the deformable bodies, wich would as joints with no inertia provided. Numerical solution of proposed model was solved with Ringe-Kutta methods. Parameter of influence, initial lordotic curvature, positions of the geometric centers of the vertebras, thorax and of the sacrum-pelvis, and point of application of the posteroanterior force (PA) were evaluated from x-ray image of patients. Nonlinear stiffness character introducedin the model affects the motion stability when periodic posteroanterior forces are applied to one vertebra. / Doutor

The thesis deals with building and utilization of mechatronic models which are based on modeling of system of rigid and flexible bodies. Such models are then used for analysis of behavior of complex systems, for instance machine tools. The work is concentrated on analysis of self-excitation of a machine tool. The appearance of the self-excitation during the machining may be influenced by several methods described in the work. The evaluation of the appearance of the self-excitation is analyzed via so called lobe diagram. It is necessary to know transfer function describing the impact of acting forces on the deformation of the system (machine tool in this case) for compilation of the lobe diagram. The whole structure of the model shows compliant behavior which dramatically influences the transfer function thus the approach to the modeling of mechanical parts as flexible bodies is proposed. There are created models of modally reduced flexible bodies based on modified CAD models which have same modal properties as non-reduced FEM models up to the maximal excitation frequency. The reduced models have significantly lower number of degrees of freedom and it is possible to work with them in multi-body simulation tools and at the same time they contain the information about the deformations. The work utilizes Graig-Bamton method which is implemented to the ANSYS. The whole model is consequently built and analyzed in ADAMS. It is possible to export the linearized model of the system in form of state matrices which are used for writing of the transfer function. The conditions of stability of the machining process are then evaluated via the lobe diagram. The proposed thesis presents the modeling of mechatronic systems with stiff and rigid bodies. The approach may be used for analysis of machining tools as well as for development of advanced mechatronic systems with active damping, etc.

Made available in DSpace on 2014-06-11T19:34:58Z (GMT). No. of bitstreams: 0 Previous issue date: 2006-04-24Bitstream added on 2014-06-13T19:04:57Z : No. of bitstreams: 1 duque_lhm_dr_guara.pdf: 1861000 bytes, checksum: 826224c8ed71ff732f9aa6af40eab143 (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Um modelo fundamentado nos sistemas multicorpos, com sete corpos rígidos e oito corpos flexíveis, com três graus de liberdade para cada um dos corpos rígidos está sendo proposto. Os corpos rígidos são providos de inércia e os corpos flexíveis trabalham como juntas e não são providos de inércia. A solução numérica do modelo foi obtida com o método Runge-Kutta. Os parâmetros de influência, curvatura inicial da espinha lombar, posições dos centros geométricos das vértebras, tórax e da sacrum-pélvis, e o ponto de aplicação da força póstero-anterior (PA), foram obtidos de radiografia digital de cada paciente. O modelo foi simulado com dados de literaturas (obtidos de experimentos in vivo e em peças anatômicas). Os resultados foram satisfatórios do ponto de vista dos terapeutas e apresentam-se em conformidade com outros modelos propostos. O modelo oferece vantagem na aplicação individualizada a cada paciente pelos terapeutas, e foi construído com a metodologia de análise das forças aplicadas e suas reações diferentemente de outros modelos que apoiam-se nos métodos de análise das energias. O objetivo principal deste trabalho será o de avaliar o comportamento dinâmico do segmento lombar da coluna vertebral humana incluindo as massas do tórax e da pelve, por um modelo não-linear da rigidez viscoelástica estabelecido a partir da relação força-deslocamento obtida por experimentação in vivo. / Evaluate a dynamic behavior of the human lumbar spine, with non-linear viscoelastic stiffness model followed by experimental data. Many of the techniques for the clinical treatment of dysfunction acting on lumber segments of the human spine have been based in the application of a postero anterior forces. Existing models to predict the state of lumber segments are restricted to evaluate general characteristic, furthermore, they use unrealistic boundary condition for its analysis. Periodic oscillatory posteroanterior forces were applied on each vertebra with initial lordotic curvature of the lumbar spine. A model is based on the multibody system of seven rigid bodies and eight deformable bodies representing human spine composed of thoratic, lumber and sacrum-pelvis segments. On each lumber were considered three degree of freedom(posterior - anterior, axial and flexion - extension). The rigid bodies are provided with inerti and the deformable bodies, wich would as joints with no inertia provided. Numerical solution of proposed model was solved with Ringe-Kutta methods. Parameter of influence, initial lordotic curvature, positions of the geometric centers of the vertebras, thorax and of the sacrum-pelvis, and point of application of the posteroanterior force (PA) were evaluated from x-ray image of patients. Nonlinear stiffness character introducedin the model affects the motion stability when periodic posteroanterior forces are applied to one vertebra.

This diploma thesis is focused on compiling a computational model of the transmission of a Zetor Forterra HSX tractor in the Multibody software MSC ADAMS environment. It analyses the issue of creating gears in terms of vibration and noise. The thesis describes the creation of computational model which is used for simulation of the load conditions during tractor operation. The methodology is applied to a single-stage gearbox in which is verified. Then it is used on a model of a real tractor gearbox. The response of the input load conditions is projected during the forces in the engagement of the gears which are transmitted to the bearings.

This thesis deals with the hydrodynamic plain bearings tractor diesel engine. The first part is closer acquainted with the hydrodynamic bearing, its principles and materials used. The next part work deals with the multibody system adams-engine. The main part of this work is to model the crank mechanism and its storage in hydrodynamic bearings in the MBS program and the subsequent simulation under different operating conditions.

Piston rings are installed in the piston and cylinder wall, which does not have a perfect round shape due to machining tolerances or external loads e.g. head bolts tightening. If the ring cannot follow these deformations, a localized lack of contact will occur and consequently an increase in the engine blow-by and lubricant oil consumption. Current 2D computational methods can not implement such effects – more complex model is necessary. The presented master’s thesis is focused on the developement of a flexible 3D piston ring model able to capture local deformations. It is based on the Timoshenko beam theory in cooperation with MBS software Adams. Model is then compared with FEM using software ANSYS. The validated piston ring model is assembled into the piston/cylinder liner and very basic simulations are run. Finally, future improvements are suggested.

Diploma thesis aims on mechanical design of new concept of Zetor UŘ III engine with displacement increase and solves calculations of main and pin hydrodynamic bearings of crankshaft. Creo 2 CAD software is used for preparing mechanical design of this new concept. For computation and analysis of hydrodynamic bearings multibody model of crankshaft mechanism is used with flexible FEM model of crankshaft for solving dynamics of mechanism and performing hydrodynamic analysis of bearings in FEV Virtual Engine. Results of this diploma thesis demonstrate the feasibility of new concept of engine and serve as a basis for next engineering tasks before realization of concept.

Avec en perspective l’application à la robotique ou à l’étude des milieux granulaires, nous discutons la formulation des problèmes de contacts avec frottement en dynamique et pour les systèmes constitués de solides rigides. L’approche usuelle est event driven et ne permet pas d’écrire de manière systématique un problème d’évolution. Ceci a motivé l’émergence d’une nouvelle approche dans le cas sans frottement que nous généralisons au cas avec frottement. Suivant le point de vue de Lagrange sur l’équation de la dynamique, nous mettons en exergue l’usage systématique des puissances virtuelles et de la dualité. Ce parti-pris suggère de mettre l’accent sur l’effort généralisé de réaction dans la formulation et non sur les forces de réactions locales dans le monde réel, comme il est usuel. Ce point de vue permet d’échapper à des pathologies connues sous le nom de paradoxe de Painlevé. / In the view of robotics or granular media mechanics, we question the statement of the dynamical evolution problem for multibody systems with contacts and friction. The usual approach is event driven and does not allow to state an evolution problem in a systematic way. This matter of fact gave rise to a new approach in the frictionless case we generalize to the case with friction. Sticking to the point of view of Lagrange on the equation of the dynamics, we emphasize the systematic use of virtual powers and duality. This bias suggests to put emphasis on generalized reaction forces in the statement of the evolution problem and not on local reaction forces of the real world, as it is usual in practice. This point of view allows to escape from pathologies known as Painlevé paradox.

In der vorliegenden Arbeit werden mithilfe von Methoden zur numerischen Behandlung schwach besetzter Matrizen O(n³)- und O(n)-Berechnungsalgorithmen für Mehrkörpersysteme aus deren Bewegungsgleichungen abgeleitet. Durch Verwendung von Dualen Basen kann gezeigt werden, dass sich die bezüglich der Berechnungszeit effizienten Algorithmen sowohl auf Systeme mit explizit als auch implizit formulierten Bindungsgleichungen anwenden lassen. Mit diesen gewonnen Erkenntnissen wird die derzeitige Implementierung der vorgestellten Algorithmen im Sprachstandard Modelica untersucht. Es werden Ansatzmöglichkeiten aufgezeigt, mit denen ausgewählte Modelica Compiler große Mehrkörpersysteme effizienter lösen können. Zum einen wird durch eine graphentheoretische Verallgemeinerung des O(n)-Algorithmus dieser direkt in dem freien Modelica Werkzeug OpenModelica umgesetzt. Zum anderen wird die Methode der Subsysteme für den O(n)-Algorithmus vorgestellt. Sie ermöglicht es, beliebig komplexe Teilsysteme als eigenständige Modellelemente zu erstellen. Die Berechnung von kinematischen Schleifen kann auf diese Weise wesentlich beschleunigt werden. Ferner wird gezeigt, dass sich mit der Methode der Subsysteme Modellgleichungen eines idealen homokinetischen Gelenks ableiten lassen, die frei von Zwangsbedingungen sind. Dies führt ebenfalls zu einer schnelleren und robusteren Berechnung. / Using methods from sparse matrice theory, O(n³)- and O(n)-algorithms for multibody systems are derived from the equations of motion. The concept of Dual Bases reveals that efficient algorithms for explicit joint descriptions, regarding calculation time, may also be applied to systems which use implicit joint constraints. Consequently, the feasibility of implementing these results in Modelica is examined. This leads to new approaches which enable selected Modelica compilers to solve large multibody systems more efficiently. On the one hand side a graph-theoretic generalization of the O(n)-algorithm has been implemented into the OpenModelica compiler. On the other hand, a method of subsystems for the O(n)-algorithm has been devised. It allows to derive the model equations for arbitrary complex sub-systems which can be implemented as new model elements for an O(n)-algorithm library. This has been carried out for recurring kinematic loops of Mobile Machinery improving simulation speed considerably. Furthermore, it is shown that a fast and robust model of an ideal constant velocity joint can be derived that way.