Hlavní cíl této práce je vyvinout pokročilý výpočtový model dynamiky pístové skupiny. Kontakt mezi pístem a válcem je zprostředkován skrz vrstvu maziva nebo pomocí kontaktu nerovností. To vede k různým režimům mazání, tudíž k různým silovým interakcím působících na plochy kontaktní dvojice. Během řešení hydrodynamiky a kontaktu nerovností, je nutné zahrnout deformaci pístu a válce do výpočtu—přirozeně iterační proces. Jelikož požadavky na výpočtovou síť kontaktních sil a deformaci těles se liší, byl navržen robustní mapovací algoritmus. Výsledky vyvinutého výpočtového nástroje jsou experimentálně verifikovány. Pro tento účel je uskutečněno měření sekundárního pohybu pístu pomocí laserových snímačů vzdálenosti. Měření je vykonáno na experimentálním motoru s bočním vedením ventilů a průhlednou hlavou válce, aby byl přítomen kompresní tlak ve spalovací komoře. Naměřený boční pohyb pístů je znehodnocen. Proto je další analýze potrobeno pouze úhlové natočení pístů. Shoda mezi naměřenými a vypočítanými výsledky variuje pro různé části pracovního cyklu. Dobrá shoda je dosažena během komprese a expanze. Naopak výrazné rozdíly nastávají, když boční síla dosahuje nízkých hodnot: sání a výfuk. Hlavní přínos této práce je vytvoření výpočtového nástroje, který je schopný zahrnout výše popisované jevy, které mají podstatný vliv na dynamiku pístové skupiny. Bohužel to vede k dlouhým výpočtovým časům, zvláště když je zahrnuta deformace. Tento problém řeší navržený paralelní výpočet. To je založeno na paralelizaci podprogramu během vyčíslování citlivostní analýzy. Tímto způsobem je řádově redukován výpočtový čas.

Cascade Drives develops electromechanical linear actuators based on multiple pinions interacting with a gear rack. With a patented load sharing mechanism, that uses flexible torsional elements, the torque is equally distributed among the pinions. The same technology was used to develop an innovative wind turbine gearbox design for a Vestas V52 wind turbine, which is more compact and consists of less parts than the current solutions. In this thesis project, this gearbox design was analyzed through software tools, in order to verify its feasibility and refine its design for improvement. In the first part of this thesis, the gearbox was analyzed using Romax, a drivetrain analysis software. From this analysis, the gearbox’s gears, bearings, shafts and housing were assessed and some design refinements were done based on the results to improve the gearbox’s safety factors and life time. In the second part of this thesis, multibody dynamic (MBD) simulations were performed for the gearbox using MSC ADAMS, to study the dynamic response of the gearbox for three load cases of interest. An MBD model was created, which included the tooth contact flexibility and the flexibility of the torsional elements. Through these simulations, the flexible torsional elements’ stiffness was tuned in order to achieve an equal torque distribution among the gears for this application. Thus, the gearbox design was verified as a feasible solution for a Vestas V52 wind turbine. / Cascade Drives utvecklar elektromekaniska linjära ställdon baserade på flera pinjonger som interagerar med ett kuggrack. Med en patenterad lastdelningsmekanism som tillåter torsion, är vridmomentet lika fördelat mellan alla pinjonger. Samma teknik har använts för att utveckla en innovativ vindkraftväxellåda för ett Vestas V52 vindkraftverk, som är mer kompakt och består av färre delar än de nuvarande lösningarna. I denna avhandling analyserades denna växellådsdesign genom mjukvaruverktyg för att verifiera dess genomförbarhet och förfina dess design. I den första delen analyserades växellådan med Romax, en mjukvara för analys av drivlinor. Från denna analys utvärderades växellådans växlar, lager, axlar och hus och vissa konstruktionsförbättringar gjordes baserat på resultaten för att förbättra växellådans säkerhetsfaktorer och livslängd. I den andra delen utfördes multikroppsdynamiska (MBD) simuleringar för växellådan med MSC ADAMS, för att studera växellådans dynamiska svar för tre belastningsfall av intresse. En MBD -modell skapades, som inkluderade kuggkontaktflexibiliteten och lastfördelningselementens flexibilitet. Genom dessa simuleringar justerades styvheten för att uppnå en jämn vridmomentsfördelning mellan växlarna för applikationen. Växellådskonstruktionen verifierades således som en genomförbar lösning för ett Vestas V52 vindkraftverk.

Previous work in the Railway Technology Laboratory 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 sideframe. The half-truck model created in MATLAB is a 3D, dynamic, multibody dynamics model comprised of four rigid bodies: a bolster, two friction wedges, and a sideframe assembly. The 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 have only the vertical degree of freedom. The geometry of these bodies can be adjusted for various simulation scenarios. The bolster can be initialized with a pre-defined yaw (rotation around the vertical axis) and the sideframe may be initialized with a pre-defined pitch/toe (rotation around the lateral axis). The multibody dynamics half-truck model simulation results have been compared with results from NUCARS®, an industry standard train modeling software, for similar inputs. The multibody dynamics models have also been extended to a variably damped full-truck model and a variably damped half-truck warping model. These models were reformulated to react dynamically to simulated truck warp inputs. The ability to better characterize truck warping properties can prevent train roll over and derailments from truck hunting. In a quarter-truck variably damped configuration the effects of a curved wedge surface has also been explored. Actual friction wedges have surfaces which are slightly curved, this iteration in the multibody dynamics friction wedge modeling attempts to draw one step closer to actual friction wedge geometry. This model lays the ground work for a contact dependant wedge wearing model based on material properties and tribology. / Master of Science

This thesis presents a theoretical application of multibody dynamics with unilateral contact to model the interaction of the damping element in a freight train suspension, the friction wedge, with the bolster and the side frame. The objective of the proposed approach is to produce a stand-alone model that can better characterize the interaction between the bolster, the friction wedge, and the side frame subsystems. The new model allows the wedge four degrees of freedom: vertical displacement, longitudinal (between the bolster and the side frame) displacement, pitch (rotation about the lateral axis), and yaw (rotation about the vertical axis). The new model also allows for toe variation. The stand-alone model shows the capability of capturing dynamics of the wedge which were not possible to simulate using previous models. The inclusion of unilateral contact conditions is integral in quantifying the behavior during lift-off and the stick-slip phenomena. The resulting friction wedge model is a 3D, dynamic, stand-alone model of a bolster-friction wedge-side frame assembly. The new stand-alone model was validated through simulation using simple inputs. 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 side frame and bolster, but also the associated moments. Significant simulation results are presented and the main differences between the current NUCARS® models and the new stand-alone MATLAB models are highlighted. / Master of Science

In multibody systems, mechanical components (bodies) can be assumed rigid (non-deformable), if their deformation is negligible. For components with non-negligible deformations several methods were developed to represent their deformation. The most widely used method is the floating frame of reference. In this formulation the deformable body is represented by a finite element model whose deformation is described with respect to a local body-fixed frame. Unfortunately, finite element models can include many degrees-of-freedom, which stand in contradiction to the requirements of multibody dynamics. System truncation is therefore inevitable to support computational efficiency. The use of modal data in representing a deformable body is well understood in the multibody community. By truncating modes associated with higher frequencies, the total degrees-of-freedom of the deformable body can be reduced while preserving its dynamic eigen-properties. However, since the finite element model may be in contact with other moving bodies, the reduction technique needs to address the issue of moving boundary conditions. The component mode synthesis reduction methods are such techniques that describe the deflection of all the nodes as a superposition of different types of modes. However, it is limited in the fact that the nodes in contact need to remain in contact throughout a simulation. In some applications these nodes may change, i.e. a node that is in contact with another body or the ground at one instant may become free at the next instant. The present methodologies in multibody modeling of a deformable body with modal data have not yet addressed the issue of changing contact nodes. This research highlights the usefulness of orientation invariant characteristics of some deformable bodies. It proposes to define orientation invariant degrees-of-freedom of the reduced model in Eulerian space, while the remaining degrees-of-freedom are defined in Lagrangian space. In some circumstances, this approach can resolve the issue of changing contact nodes. The combination of Eulerian and Lagrangian formulation for component mode synthesis reduced finite element models is a new concept in deformable multibody dynamics.

The objective of this study is to develop a high-fidelity physics-based flexible tire model that can be fully integrated into multibody dynamics computer algorithms for use in on-road and off-road vehicle dynamics simulation without ad-hoc co-simulation techniques. Despite the fact detailed finite element tire models using explicit finite element software have been widely utilized for structural design of tires by tire manufactures, it is recognized in the tire industry that existing state-of-the-art explicit finite element tire models are not capable of predicting the transient tire force characteristics accurately under severe vehicle maneuvering conditions due to the numerical instability that is essentially inevitable for explicit finite element procedures for severe loading scenarios and the lack of transient (dynamic) tire friction model suited for FE tire models. Furthermore, to integrate the deformable tire models into multibody full vehicle simulation, co-simulation technique could be an option for commercial software. However, there exist various challenges in co-simulation for the transient vehicle maneuvering simulation in terms of numerical stability and computational efficiency. The transient tire dynamics involves rapid changes in contact forces due to the abrupt braking and steering input, thus use of co-simulation requires very small step size to ensure the numerical stability and energy balance between two separate simulation using different solvers. In order to address these essential and challenging issues on the high-fidelity flexible tire model suited for multibody vehicle dynamics simulation, a physics-based tire model using the flexible multibody dynamics approach is proposed in this study. To this end, a continuum mechanics based shear deformable laminated composite shell element is developed based on the finite element absolute nodal coordinate formulation for modeling the complex fiber reinforced rubber tire structure. The assumed natural strain (ANS) and enhanced assumed strain (EAS) approaches are introduced for alleviating element lockings exhibited in the element. Use of the concept of the absolute nodal coordinate formulation leads to various advantages for tire dynamics simulation in that (1) constant mass matrix can be obtained for fully nonlinear dynamics simulation; (2) exact modeling of rigid body motion is ensured when strains are zero; and (3) non-incremental solution procedure utilized in the general multibody dynamics computer algorithm can be directly applied without specialized updating schemes for finite rotations. Using the proposed shear deformable laminated composite shell element, a physics-based flexible tire model is developed. To account for the transient tire friction characteristics including the friction-induced hysteresis that appears in severe maneuvering conditions, the distributed parameter LuGre tire friction model is integrated into the flexible tire model. To this end, the contact patch predicted by the structural tire model is discretized into small strips across the tire width, and then each strip is further discretized into small elements to convert the partial differential equations of the LuGre tire friction model to the set of first-order ordinary differential equations. By doing so, the structural deformation of the flexible tire model and the LuGre tire friction force model are dynamically coupled in the final form of the equations, and these equations are integrated simultaneously forward in time at every time step. Furthermore, a systematic and automated procedure for parameter identification of LuGre tire friction model is developed. Since several fitting parameters are introduced to account for the nonlinear friction characteristics, the correlation of the model parameters with physical quantities are not clear, making the parameter identification of the LuGre tire friction model difficult. In the procedure developed in this study, friction parameters in terms of slip-dependent friction characteristics and adhesion parameter are estimated separately, and then all the parameters are identified using the nonlinear least squares fitting. Furthermore, the modified friction characteristic curve function is proposed for wet road conditions, in which the linear decay in friction is exhibited in the large slip velocity range. It is shown that use of the proposed numerical procedure leads to an accurate prediction of the LuGre model parameters for measured tire force characteristics under various loading and speed conditions. Furthermore, the fundamental tire properties including the load-deflection curve, the contact patch lengths, contact pressure distributions, and natural frequencies are validated against the test data. Several numerical examples for hard braking and cornering simulation are presented to demonstrate capabilities of the physics-based flexible tire model developed in this study. Finally, the physics-based flexible tire model is further extended for application to off-road mobility simulation. To this end, a locking-free 9-node brick element with the curvature coordinates at the center node is developed and justified for use in modeling a continuum soil with the capped Drucker-Prager failure criterion. Multiplicative finite strain plasticity theory is utilized to consider the large soil deformation exhibited in the tire/soil interaction simulation. In order to identify soil parameters including cohesion and friction angle, the triaxial soil test is conducted. Using the soil parameters identified including the plastic hardening parameters by the compression soil test, the continuum soil model developed is validated against the test data. Use of the high-fidelity physics-based tire/soil simulation model in off-road mobility simulation, however, leads to a very large computational model to consider a wide area of terrains. Thus, the computational cost dramatically increases as the size of the soil model increases. To address this issue, the component soil model is proposed such that soil elements far behind the tire can be removed from the equations of motion sequentially, and then new soil elements are added to the portion that the tire is heading to. That is, the soil behavior only in the vicinity of the rolling tire is solved in order to reduce the overall model dimensionality associated with the finite element soil model. It is shown that use of the component soil model leads to a significant reduction in computational time while ensuring the accuracy, making the use of the physics-based deformable tire/soil simulation capability feasible in off-road mobility simulation.

Large displacement and large strain problems of mechanical systems can be solved mainly by four methods. These are Floating Frame of Reference, Incremental Finite Element, Large Rotation Vector and Absolute Nodal Coordinate Formulations (ANCF). Due to exact rigid body representation, simple mass matrix structure and non-incremental formulation, ANCF is more convenient in analyzing flexible multibody systems. However, it is limited to problems with regular boundaries, currently. The aim of the thesis is to improve the current ANCF in order to handle various problems with irregular boundaries. For this purpose, firstly meshfree ANCF has been developed to analyze flexible multibody systems. Verification of the developed meshfree formulation has been performed for beam type structures and accurate results have been obtained. Then, &ldquo / ANCF with Virtual Element Mapping Method&rdquo / has been proposed to overcome the boundary problems of the current formulations. The proposed method has been implemented to plane stress, plane strain, plate/shell and 3D solid finite elements. Verification of the proposed method has been performed by using the patch test problems available in the literature. Besides, it has been verified by various flexible multibody problems with large deformations. Additionally, shape function polynomials for thin plate assumption have been derived. It is observed that developed formulations and methods can be useful not only for flexible multibody systems but also for structural mechanics problems subjected to large deformations and/or rotations. The proposed methods and formulations are more efficient than the current formulations in the literature due to extended shape limits of finite elements.

There is a need for smaller and more economic transportation systems. Two-wheeled inverted-pendulum machines, such as the Segway, have been proposed to address this need. However, the Segway places the operator on top of a naturally unstable platform that is stabilized by means of a control system. The control stability of the Segway can be severely affected when minor disturbances or unanticipated conditions arise. In this thesis, a dynamic model of a Segway is developed and used in simulations of various conditions that can arise during normal use. The dynamic model of a general two-wheeled inverted pendulum and human rider is presented. Initial estimates of the parameters were calculated or obtained from other references. The results from numerous experiments are presented and used to develop a better understanding of the dynamics of the vehicle. The experimental data was then used to adjust the model parameters to match the dynamics of a real Segway Human Transporter. Finally, the model was used to simulate various failure conditions. The simulations provide a better understanding of how these conditions arise, and help identify which parameters play an important role in their outcome.

This thesis develops a finite element based dynamic modeling method for design and analysis of compliant mechanisms which transfer input force, displacement and energy through elastic deformations. Most published analyses have largely based on quasi-static and lump-parameter models neglecting the effects of damping, torsion, complex geometry, and nonlinearity of deformable contacts. For applications such as handling of objects by the robotic hands with multiple high-damped compliant fingers, there is a need for a dynamic model capable of analyzing the flexible multibody system. This research begins with the formulation of the explicit dynamic finite element method (FEM) which takes into account the effects of damping, complex geometry and contact nonlinearity. The numerical stability is considered by evaluating the critical time step in terms of material properties and mesh quality. A general framework incorporating explicit dynamic FEM, topology optimization, modal analysis, and damping identification has been developed. Unlike previous studies commonly focusing on geometry optimization, this research considers both geometric and operating parameters for evaluation where the dynamic performance and trajectory of the multibody motion are particularly interested. The dynamic response and contact behavior of the rotating fingers acting on the fixed and moving objects are validated by comparing against published experimental results. The effectiveness of the dynamic modeling method, which relaxes the quasi-static assumption, has been demonstrated in the analyses of developing an automated transfer system involved grasping and handling objects by the compliant robotic hands. This FEM based dynamic model offers a more realistic simulation and a better understanding of the multibody motion for improving future design. It is expected that the method presented here can be applied to a spectrum of engineering applications where flexible multibody dynamics plays a significant role.

The motivation for this thesis was the need for further development of multibody dynamics simulation packages focused on detailed contact analysis. The thesis makes contributions in three different areas: Part I summarizes the equations, algorithms and design decisions necessary for dynamics simulation of flexible bodies with moving contacts. The assumed general shape function approach is presented. Additionally, the described technique enables studies of the residual stress release during grinding of flexible bodies. The proposed set of mode shapes was also successfully applied for modeling of heat flow. Part II is motivated by the need to reduce the computation time. The availability of the new cost-efficient multiprocessor computers triggered the development of the presented hybrid parallelization framework. The framework is designed to be easily portable and can be implemented without any system level coding or compiler modifications. Part III is motivated by the need for inter-operation with other simulation tools. A co-simulation framework based on the Transmission Line Modeling (TLM) technology was developed. The framework enables integration of several different simulation components into a single time-domain simulation. The framework has been used for connecting MSC.ADAMS and SKF BEAST simulation models. Throughout the thesis the approach was to present a practitioner roadmap. The detailed description of the theoretical results relevant for a real software implementation is put in focus. The software design decisions are discussed and the results of real industrial simulations are presented. This work has been supported by SKF, SSF/ProViking, ECSEL, KK-stiftelsen.