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.

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.

Die Mehrkörpersimulation (MKS) kommt in immer mehr Bereichen zum Einsatz. Bis vor einigen Jahren war das Thema fast ausschließlich im Automobilbereich wichtig. Heute wird der Ansatz in fast allen Bereichen der Technik, in dem „Bewegungsabläufe“ eine Rolle spielen, eingesetzt. Im Gegensatz zur Finite Elemente (FE)-Methode, für die eine detaillierte Bauteiltopologie mit einer Vielzahl von Elementen nötig ist, können mit MKS-Systemen selbst komplexe mechanische Systeme mit einer relativ geringen Anzahl an Freiheitsgraden abgebildet werden. Das Programm Adams hat diese Entwicklung maßgeblich mit gestaltet. Neben den Erweiterungen im Bereich der Solver und anderer mathematischer Formulierungen war immer die einfache Benutzerführung, die Integration von weiteren Simulationstechnologien und auch die Entwicklung von Spezialanwendungen ein wichtiges Thema der Entwicklung. Im Rahmen dieses Vortrages wird der Einsatz von Adams an Hand von Beispielen demonstriert. Weiterer Schwerpunkt ist die Erweiterung der Modelle durch Berücksichtigung der elastischen Materialeigenschaften einzelner Bauteile. Die Kopplung zur Lebensdauerberechnung an Hand von Beispielen schließt den Beitrag ab.

Single degree-of-freedom hopping robots are typically modeled as spring loaded inverted pendulums (SLIPs). This simplified model, however, does not consider the overall leg geometry, consequently making it difficult to investigate the optimized inertial distribution of the leg for agile locomotion. To address this issue, the first part of this thesis establishes an accurate mathematical model of a DC-motor-driven, two-link hopping robot where the motors are modeled as torque sources. The equations of motion for the two distinct phases of locomotion (stance and flight) are derived using the Lagrangian approach for holonomic systems. A Simulink/Stateflow model is developed to numerically simulate the robot’s locomotion. The model is then validated with the simulation data from Simscape Multibody, which allows for accurate modeling of the environment and inertial properties for complex geometries. With the accurate model of the hopping robot, two distinct control strategies are adopted. The first strategy focuses on implementing position control while the robot is in flight to prepare for touchdown. The second control method explores implementing impedance control during stance, allowing the response to mimic that of a mass-spring-damper model. It was found that concentrating the mass of the robot in the hip allows the robot to attain larger apex heights as opposed to evenly distributing the mass throughout the leg. With plans to implement the leg on a quadruped robot, the mathematical model is easily expandable to 2 or 3 degrees-of-freedom. This allows for further stability analysis and development of control strategies of the leg.

<p>Numerical procedures for reliable wheel and rail wearprediction are rare. Recent development of simulationtechniques and computer power together with tribologicalknowledge do however suggest computer aided wear prediction.The objective of the related research field at the RoyalInstitute of Technology (KTH) is to arrive at a numericalprocedure able to simulate profile evolution due to uniformwear to a degree of accuracy sufficient for application tovehicle dynamics simulation. Such a tool would be useful formaintenance planning as well as optimisation of the transportsystem and its components.</p><p>The research contribution accounted for in this thesisincludes, in addition to a literature review, refinement ofmethods applied to uniform wheel wear simulation by inclusionof braking and improvement of the contact model. Further atentative application to uniform rail wheel simulation has beenproposed and tested.</p><p>The first part addresses issues related to braking andwheel-rail contact conditions in the context of wheel wearsimulation. The KTH approach includes Archard’s wear modelwith associated wear maps, vehicle dynamics simulation andrailway network definition. In previous work at KTH certainvariations in operating conditions have been accounted forthrough empirically estimated average scaling factors. Theobjective of the current research is to be able to include suchvariations in the set of simulations. In particular theinfluence of disc braking and varying friction and lubricationconditions are investigated. Both environmental factors likemoist and contamination and deliberate lubrication need to beconsidered. As part of the associated contact analysis theinfluence of tangential elastic deformation of the contactingsurfaces on the sliding velocity has been separatelyinvestigated and found to be essential in case of partial slipcontact conditions.</p><p>In the second part validation of the improvements related towheel wear simulation is addressed. Disc braking has beenincluded in the simulation set and a wear map for moist contactconditions based on recent tribometer tests has been draftedand tested. It has been shown that the previously used brakingfactor accounts for the combination of the contributions fromsurface elasticity and braking. Good agreement withmeasurements from the Stockholm commuter service is achieved.It is concluded that the model improvements accounted for aresufficient for adequate simulation of tread wear but thatfurther development of the flange / gauge corner contactmodelling may be needed.</p><p>In the final part a procedure for simulation of rail wearand corresponding profile evolution has been formulated. Asimulation set is selected defining the vehicles running on thetrack to be investigated, their operating conditions, andcontact parameters. Several variations of input data may beincluded together with the corresponding occurrenceprobability. Trial calculations of four non-lubricated curveswith radii from 303 m to 802 m show qualitatively reasonableresults in terms of profile shape development and difference inwear mechanisms between gauge corner and rail head. The wearrates related to traffic tonnage are however overestimated. Itis believed that model refinements in terms of environmentalinfluence and contact stress calculation are useful to improvethe quantitative results.</p> / QC 20100531

This thesis deals with aerodynamic forces and their influence on body position and ride comfort due changes in wheel loads. Simulation was made in computer program ADAMS (MSC Software TM).

The link suspension is the most prevailing suspension system for freight wagons in Central and Western Europe. The system design is simple and has existed for more than 100 years. However, still its characteristics are not fully understood. This thesis investigates the dynamic performance of freight wagons and comprises five parts: In the first part a review of freight wagon running gear is made. The different suspension systems are described and their advantages and disadvantages are discussed. The second part focuses on the lateral force-displacement characteristics of the link suspension. Results from stationary measurements on freight wagons and laboratory tests of the link suspension characteristics are presented. To improve the understanding of various mechanisms and phenomena in link suspension systems, a simulation model is developed. In the third part the multibody dynamic simulation model is discussed. The previous freight wagon model developed at KTH is able to explain many of the phenomena observed in tests. In some cases, however, simulated and measured running behaviour differ. Therefore, a new simulation model is presented and validated against on-track test results. The performance of standard two-axle freight wagons is investigated. The most important parameters for the running behaviour of the vehicle are the suspension characteristics. The variation in characteristics between different wagons is large due to geometrical tolerances of the components, wear, corrosion, moisture or other lubrication. The influence of the variation in suspension characteristics and other parameters on the behaviour of the wagon, on tangent track and in curves, is discussed. Finally, suggestions for improvements of the system are made. A majority of the traffic related track deterioration cost originates from freight traffic. With heavier and faster freight trains the maintenance cost is likely to increase. In the fourth part the possibility to improve ride comfort and reduce track forces on standard freight wagons with link suspension is discussed. The variation of characteristics in link suspension running gear is considerable and unfavourable conditions leading to hunting are likely to occur. Supported by on-track tests and multibody dynamic simulations, it is concluded that the running behaviour of two-axled wagons with UIC double-link suspension as well as wagons with link suspension bogies (G-type) can be improved when the running gear are equipped with supplementary hydraulic dampers. Finally in the fifth part the effects of different types of running gear and operational conditions on the track deterioration marginal cost — in terms of settlement in the ballast, component fatigue, wear and RCF — is investigated. Considerable differences in track deterioration cost per produced ton-km for the different types of running gear are observed. Axle load is an important parameter for settlement and component fatigue. Also the height of centre of gravity has significant influence on track deterioration, especially on track sections with high cant deficiency or cant excess. / QC 20100802

Bei Raupenfahrwerken wird das allgemeingültige Prinzip verfolgt, dass durch die scharnierbare Aneinanderreihung von Kettengliedern eine fahrzeugeigene Fahrstrecke entsteht. Dies erlaubt selbst schwere Geräte im unwegsamen, brüchigen Gelände mit großen Vortriebskräften zu mobilisieren. Jedoch wohnt, der Diskretisierung des Raupenbandes in Glieder endlicher Länge geschuldet, dem Fahrwerk eine hohe Fahrunruhe inne. Dadurch entstehen zeitvariante Lasten im Fahrwerk, welche die Lebensdauer der Kette, des Fahrwerkantriebs und der Tragstruktur des Fahrzeugs limitieren und somit regelmäßig kostenintensive Instandsetzungsmaßnahmen erzwingen. Diese Problemstellung aufgreifend beschäftigt sich die Arbeit mit der Analyse und Optimierung des fahrdynamischen Verhaltens von Raupenfahrzeugen. Zugleich werden Methoden vorgestellt, welche eine rechenzeiteffiziente Simulation von Raupenfahrzeugen und Antriebssystemen zulassen.

Numerical procedures for reliable wheel and rail wearprediction are rare. Recent development of simulationtechniques and computer power together with tribologicalknowledge do however suggest computer aided wear prediction.The objective of the related research field at the RoyalInstitute of Technology (KTH) is to arrive at a numericalprocedure able to simulate profile evolution due to uniformwear to a degree of accuracy sufficient for application tovehicle dynamics simulation. Such a tool would be useful formaintenance planning as well as optimisation of the transportsystem and its components. The research contribution accounted for in this thesisincludes, in addition to a literature review, refinement ofmethods applied to uniform wheel wear simulation by inclusionof braking and improvement of the contact model. Further atentative application to uniform rail wheel simulation has beenproposed and tested. The first part addresses issues related to braking andwheel-rail contact conditions in the context of wheel wearsimulation. The KTH approach includes Archard’s wear modelwith associated wear maps, vehicle dynamics simulation andrailway network definition. In previous work at KTH certainvariations in operating conditions have been accounted forthrough empirically estimated average scaling factors. Theobjective of the current research is to be able to include suchvariations in the set of simulations. In particular theinfluence of disc braking and varying friction and lubricationconditions are investigated. Both environmental factors likemoist and contamination and deliberate lubrication need to beconsidered. As part of the associated contact analysis theinfluence of tangential elastic deformation of the contactingsurfaces on the sliding velocity has been separatelyinvestigated and found to be essential in case of partial slipcontact conditions. In the second part validation of the improvements related towheel wear simulation is addressed. Disc braking has beenincluded in the simulation set and a wear map for moist contactconditions based on recent tribometer tests has been draftedand tested. It has been shown that the previously used brakingfactor accounts for the combination of the contributions fromsurface elasticity and braking. Good agreement withmeasurements from the Stockholm commuter service is achieved.It is concluded that the model improvements accounted for aresufficient for adequate simulation of tread wear but thatfurther development of the flange / gauge corner contactmodelling may be needed. In the final part a procedure for simulation of rail wearand corresponding profile evolution has been formulated. Asimulation set is selected defining the vehicles running on thetrack to be investigated, their operating conditions, andcontact parameters. Several variations of input data may beincluded together with the corresponding occurrenceprobability. Trial calculations of four non-lubricated curveswith radii from 303 m to 802 m show qualitatively reasonableresults in terms of profile shape development and difference inwear mechanisms between gauge corner and rail head. The wearrates related to traffic tonnage are however overestimated. Itis believed that model refinements in terms of environmentalinfluence and contact stress calculation are useful to improvethe quantitative results. / QC 20100531

Pervasive applications of the vehicle simulation technology are a powerful motivation for the development of modern automobile industry. As basic parameters of road vehicle, vehicle dynamic parameters can significantly influence the ride comfort and dynamics of vehicle, and therefore have to be calculated accurately to obtain reliable vehicle simulation results. Aiming to develop a general solution, which is applicable to diverse test rigs with different mechanisms, a novel model-based parameter identification approach using optimized excitation trajectory is proposed in this paper to identify the vehicle dynamic parameters precisely and efficiently. The proposed approach is first verified against a virtual test rig using a universal mechanism. The simulation verification consists of four sections: (a) kinematic analysis, including the analysis of forward/inverse kinematic and singularity architecture; (b) dynamic modeling, in which three kinds of dynamic modeling method are used to derive the dynamic models for parameter identification; (c) trajectory optimization, which aims to search for the optimal trajectory to minimize the sensitivity of parameter identification to measurement noise; and (d) multibody simulation, by which vehicle dynamic parameters are identified based on the virtual test rig in the simulation environment. In addition to the simulation verification, the proposed parameter identification approach is applied to the real test rig (vehicle inertia measuring machine) in laboratory subsequently. Despite the mechanism difference between the virtual test rig and vehicle inertia measuring machine, this approach has shown an excellent portability. The experimental results indicate that the proposed parameter identification approach can effectively identify the vehicle dynamic parameters without a high requirement of movement accuracy.