Physics engines become more and more common due to the rapid development and increasing demand of simulations. With this comes a need of testing the engine, a way to measure its performance, not only its speed but also its accuracy and stability. The purpose of this thesis has been to create a set of benchmark tests. They aim to check the physical aspects, especially mechanics, of the engine. A strategy and export functions for the test results in order to automate the testing have also been developed. The resulting tests became a beam on piles which analyses constraint stability, an overdetermined system consisting of a static door on multiple hinges, a falling object investigating the accuracy of the integrator, a box on an inclined plane for testing the friction model, a single pendulum as well as a multibody pendulum checking constraint accuracy and energy conservation, the Earth orbiting around the Sun which tests the stability of the integrator and finally a cantilever beam that is a static test of a real scenario. After the tests are performed the results are presented on an HTML-page. A prototype of a Web application is also established as well as a set of scalar tests that can be performed continuously, in order to follow trends or compare the engine's performance from time to time. This thesis was initialized by Algoryx Simulation AB which also provided the engine, AgX Dynamics, with the numerical method called SPOOK. It mainly performed well on all tests. In order to build a fully general toolbox more tests need to be added such as material interactions, scalable test with thousands of bodies, torque tests as well as more complex scenarios, for example a scissor lift and robots. The work can also be extended with more developed export functions, both to the Web and to documents. Hopefully this thesis can be seen as a complement to the earlier efforts done in creating a general set of benchmarks and automation framework for continuous integration and testing. / Fysikmotorer blir mer och mer vanliga på grund av den snabba utvecklingen och efterfrågan på simuleringar. I och med detta ökar också behovet av att testa motorerna och ett sätt att mäta prestandan, inte bara snabbheten utan också noggrannheten och stabiliteten. Syftet med detta examensarbete har varit att skapa ett set av prestandatester. De syftar till att testa de fysikaliska aspekterna av fysikmotorn, särskilt inom mekanik. En strategi och exportfunktioner för testresultaten för att automatisera testningen har också utvecklats. De resulterande testerna blev en balk på pålar som analyserar stabiliteten hos villkoren, ett överbestämt system bestående av en statisk dörr på flera gångjärn, ett fallande objekt som granskar precisionen hos integratorn, en låda på ett lutande plan som testar friktionsmodellen, en enkel pendel samt en flerkropppspendel som kontrollerar villkorsprecisionen och energikonservering, jordens bana runt solen som testar integratorns stabilitet och slutligen en utskjutande balk som är ett statiskt test av ett verkligt fall. När testerna är genomförda presenteras resultaten på en HTML-sida. En prototyp av en webb-applikation har också utvecklats samt ett set med skalära tester som kan utföras kontinuerligt för att följa upp trender och jämföra motorns prestanda över tid. Det här examensarbetet initierades av Algoryx Simulation AB som även tillhandahållit fysikmotorn, AgX Dynamics, med den numeriska metoden SPOOK. Motorn presterade överlag bra på testerna. För att bygga en allmän verktygslåda behövs fler tester så som interaktion mellan material, skalbara tester med tusentals kroppar samt mer komplexa simuleringar, t.ex. en saxlyft och robotar. Arbetet kan också utökas med mer utvecklade exportfunktioner, både mot webben och som dokument. Förhoppningsvis kan detta ses som ett komplement till de tidigare ansträgningar som gjorts för att skapa ett generellt set av prestandatester och ett automatiskt ramverk för kontinuerlig testning.

Catamarans provide vast deck space, high thrust efficiency, and excellent transverse stability, however, in rough conditions they can be susceptible to deck slamming from head seas or bow diving in following seas and a pitch-roll coupling effect that can lead to uncomfortable corkscrew motion under bow-quartering seas. A new class of catamaran called Wave-Adaptive Modular Vessels (WAM-V™) aims to help mitigate oceanic input from the cabin by allowing for the relative motion of components not common to classic catamaran design. This thesis presents a set of multi-body dynamics simulation models created for two active WAM-Vs™ along with analysis on their suspension characteristics. Both models provide conclusive and realistic results, with the final model being validated against on-water testing data from a 12-ft unmanned prototype WAM-V. The first of these simulations serves primarily as a tool to evaluate WAM-V™ response characteristics with respect to a variety of parametric variations. The modeling environment is highlighted along with details of the parametric simulation and how it was created. The results fall in line with our expectations and are presented along with analysis of the sensitivity of each parameter at three longitudinal locations. The final simulation attempts to model the response of a 12-ft unmanned surface vessel (USV) prototype of the WAM-V™ configuration. Testing data is collected, processed, and applied to the model for validation of its prediction accuracy. The results of the sea tests indicate that the simulation model performs well in predicting USV motions at sea. Future considerations for testing WAM-Vs™ can include changes in suspension and mass parameters as well as limiting particular degrees-of-freedom by making their joints rigid. / Master of Science

Indiana University-Purdue University Indianapolis (IUPUI) / Indiana University–Purdue University Indianapolis student team Jaguar has been participating in the electric Formula SAE (FSAE) vehicle competitions in the past few years. There is an urgent need to develop a design tool for improving the performance of the vehicle. In this thesis, multibody dynamics (MBD) models have been developed which allow the student team to improve their vehicle design, while reducing the required time and actual testing costs. Although there were some studies about MBD analyses for vehicles in literature, a detailed modeling study of key parameters is still missing. Specifically, the effect of suspension system on the vehicle performance is not well studied. The objective of the thesis is to develop an MBD based model to improve the FSAE vehicle’s performance. Based on the objective and knowledge gap, the following research tasks are proposed: (1) MBD modeling of current suspension systems; (2) Modification of suspension systems, and (3) Evaluation of performance of modified suspension systems. The models for the front suspension system, rear suspension system, and full assembly are created, and a series of MBD analyses are conducted. The parameters of the vehicle by conducting virtual tests on the suspension model and overall vehicle model are studied. In this work, two main virtual tests are performed. First, parallel wheel travel test on suspension system, in which the individual suspension system is subject to equal force on both sides. The test helps understand the variation in stability parameters, such as camber angle, toe angle, motion ratio, and roll center location. Second, skid-pad test on full assembly of the vehicle. The test assists in understanding the vehicle’s behavior in constant radius cornering and the tire side slip angle variation, as it is one of the important parameters controlling alignment of the vehicle in this test. Based on the vehicle’s dynamics knowledge obtained from the existing vehicle, a modified version of the FSAE vehicle is proposed, which can provide a better cornering performance with minimum upgrades and cost possible. Based on the results from the parallel wheel travel test and skid-pad test, the lateral load transfer method is used to control the vehicle slip, by making changes to the geometry of the vehicle and obtaining appropriate roll center height for both front and rear suspension system. The results show that the stiffness in front suspension system and rear suspension system are controlled by manipulating roll center height. This study has provided insightful understanding of the parameters and forces involved in suspension system and their variations in different events influencing vehicle stability. Moreover, the MBD approach developed in this work can be readily extended to other commercial vehicles and sports vehicles.

Yes / This paper presents a multi-degrees-of-freedom non-linear multibody dynamic model of a three-axle heavy commercial vehicle tractor unit, comprising a subchassis, front and rear leaf spring suspensions, steering system, and ten wheels/tyres, with a semi-trailer comprising two axles and eight wheels/tyres. The investigation is mainly concerned with the rollover stability of the articulated vehicle. The models incorporate all sources of compliance, stiffness, and damping, all with non-linear characteristics, and are constructed and simulated using automatic dynamic analysis of mechanical systems formulation. A constant radius turn test and a single lane change test (according to the ISO Standard) are simulated. The constant radius turn test shows the understeer behaviour of the vehicle, and the single lane change manoeuvre was conducted to show the transient behaviour of the vehicle. Non-stable roll and yaw behaviour of the vehicle is predicted at test speeds .90 km/h. Rollover stability of the vehicle is also investigated using a constant radius turn test with increasing speed. The articulated laden vehicle model predicted increased understeer behaviour, due to higher load acting on the wheels of the middle and rear axles of the tractor and the influence of the semi-trailer, as shown by the reduced yaw rate and the steering angle variation during the constant radius turn. The rollover test predicted a critical lateral acceleration value where complete rollover occurs. Unstable behaviour of the articulated vehicle is also predicted in the single lane change manoeuvre.

The work presented in this thesis is dedicated to the study of transient tyre dynamics and how these influence the dynamic behaviour of the vehicle and its driveline, with the main focus being on low-to-zero speed manoeuvres such as pull-away events. The bulk of the work focuses on the amalgamation of the hitherto disparate fields of driveline modelling and detailed tyre modelling. Several tyre models are employed and their relative advantages and disadvantages analysed. The observed dynamic behaviour is correlated to the inherent structure of each tyre model in order for the most appropriate for driveline studies to be identified. The main simulation studies are split into two parts: the first comprises a study into isolated driveline dynamics; where the yaw, pitch and roll behaviours of the vehicle body are neglected. A relatively detailed driveline model with an open differential is used with tyre models of increasing complexity with the aim of determining when increased model detail fails to increase the accuracy of the results. The second part is concerned with the study of how the dynamics of the vehicle body and suspension affect tyre model performance and associated effects on the driveline behaviour. For this, the driveline and tyre models are incorporated into a full six degree-of-freedom vehicle model with full suspension effects. Frequency migration on low-μ surfaces is successfully explained via the decoupling of the vehicle and driveline inertias. Frequencies observed in FFT analyses of the simulation results correspond to those obtained through eigen-analysis of appropriately modified state-space models with varying degrees of coupling that reflect the vehicle travelling on uniform low- or split-μ surfaces. The main finding of the thesis is that this decoupling theory can also be applied to high-speed take-off manoeuvres, as it is the position along the tyre slip-force curve that dictates decoupling; i.e. if the curve has saturated. This leads to the effective traction stiffness being zero, which modifies the equations of motion and subsequently the system eigenvalues. A series of measurements are taken in order to verify the findings from the simulation work. Manoeuvres analogous to those simulated are carried out. It is found that only the simulation of split-μ conditions is necessary, as the results from the low-μ test show a similar pattern to those seen on the split-μ surface.

Automotive industry is faced with numerous power train Noise, Vibration and Harshness issues. Particularly, in the driveline area of vehicles a noise commonly referred as differential axle whine which is a tonal response and becomes apparent under cruising conditions. This is one of the key concerns in rear wheel drive commercial vehicles. Although not a failure state, it is regarded as a quality issue and a source of annoyance, which can lead to warranty concerns. The associated cost of palliation to Ford Motor Company was estimated to be $25,000,000 in 2003. There have been several ways of studying axle whine through experimentation and numerical analysis. In this thesis, a new approach for investigating axle whine is highlighted, which is more integrative and detailed. Multi-body dynamics model of a light truck s driveline is developed with all the appropriate components, using constrained Lagrangian dynamics. Component flexibility is included for driveshaft pieces, rear axle half-shafts and the suspension elements. The connectivity of the components is accurately modelled such as the floating effect of rear half-shafts, linear bushings between driveline components to chassis connections, as well as the non-linear effect of tapered roller bearings, supporting the wheel hubs and gears. Furthermore, integrated to the previously described large scale model a detailed hypoid gear pair model is devised. This incorporates micro-scale physics for tooth contact analysis to predict geometric properties and deflections for the gear pair. At the same time thermo-elastohydrodynamic lubrication theory with non-Newtonian friction is applied. All these phenomena at different physical scales, such as large displacement rigid body dynamics and analytical equations for the detailed model are solved simultaneously, all within the same modelling environment. This multi-physics, multi-scale approach has not hitherto been reported in the literature, and constitutes a significant contribution to knowledge. Comparative studies of the model predictions and detailed vehicle tests are carried out, the combination of which points to resonant conditions in system responses and flexible component behaviour, coincident with the adverse conditions in the hypoid gear meshing. It is shown that vehicle drive and coast conditions, promoting teeth pair separations lead to irregular (improper) meshing of the differential gears. Such conditions induce impulsive actions that promote the axle whine phenomenon. This is a major finding of the research and contributes to a better understanding of the axle whine problem.

Compared to conventional machine tools, industrial robots offer great advantages such as multitasking, larger workspace, and lower price. However, these advantages of robots are undermined by their high structural flexibility leading to excessive deflections, severe vibrations, and ultimately violating dimensional tolerances and poor surface finish. Modeling the dynamics of robots under machining (e.g. milling and drilling) forces is essential for reducing deflections and vibrations during the process. Although modeling the dynamics of traditional machining systems is a well-studied subject, the existing modeling approaches are not applicable to robotic manipulators because of the posture-dependent dynamics of industrial robots. Within this context, the presented thesis aims to predict the stability of vibrations during robotic machining operations through prediction of posture dependent dynamic behavior of robots. A rigid-body modeling approach is used to identify the dynamic parameters of the robotic manipulator based on least squares estimation method. Next, by adopting a rigid link flexible joint model and employing experimental modal analysis to identify the joint stiffness and damping parameters, posture dependent dynamic response prediction of the robot is achieved. Finally, the posture-dependent milling stability is presented as a function of the predicted tool center point transfer function, spindle speed, and axial depth of cut. A Staubli TX200 robot and a Kuka KR90 robot are used as experimental case studies. / Graduate

<div>Applications of electric propulsion to spaceflight in multi-body environments require a targeting algorithm to produce suitable trajectories on the ground and on board spacecraft. The two-level targeter with low thrust (TLT-LT) provides a framework to implement differential corrections in computationally-limited autonomous spacecraft applications as well as the larger design space of pre-mission planning. Extending existing two-level corrections algorithms, applications of the TLT-LT to spacecraft with a range of propulsive capabilities, from nearly-impulsive to low-thrust, are explored. The process of determining partial derivatives is generalized, allowing reduced logical complexity and increased flexibility in designing sequences of thrusting and ballistic segments. Various implementation strategies are explored to enforce constraints on time and other design variables as well as to improve convergence behavior through the use of dynamical systems theory and attenuation factors. The TLT-LT is applied to both nearly-impulsive and low-thrust spacecraft applications in the circular restricted three-body problem to demonstrate the flexibility of the framework to correct trajectories across the spectrum of thrust magnitude. Finally, parameter continuation is employed to extend a family of trajectories from a solution with nearly-impulsive thrust events to the low-thrust regime, and the characteristics of this transition are investigated.</div>

The identification of the physical parameters (mass, stiffness, and damping) of structural, mechanical, and biomechanical systems is a major challenge in many applications, especially when dealing with old systems and biological systems with heavy damping and where environmental noises are presented. This work presents a novel methodology called eigenvector phase correction (EVPHC) to solve for the physical parameters of structural and biomechanical systems even with the existence of a significant amount of noise. The method was first tested on structural/mechanical systems and showed superior results when compared with an iterative method from the literature. EVPHC was then developed and used to identify the physical parameters of supine humans under vertical whole-body vibration. Modal parameters of fifteen human subjects, in the supine position, were first identified in this work using experimentation under vertical whole-body vibration. EVPHC was then used to solve an inverse modal problem for the identification of the stiffness and damping parameters at the cervical and lumbar areas of supine humans. The results showed that the resulting physical parameters were realistically close to those presented in the literature. The proposed human model was able to predict the time histories of the acceleration at the head, chest, pelvis, and legs very closely to those of the experimental measured values. A scaling methodology is also presented in this work, where an average human model was scaled to an individual subject using the body mass properties.

Studies of human response to whole-body vibration, such those encountered in heavy machinery and ground and aerial transportation, have highlighted the critical role of the head-neck posture of seated human occupants and the role of the transport system of a supine human on the severity of the transmitted vibration to the human body. Novel passive and muscle-based models are introduced in this work to predict the biodynamical response of the human under whole-body vibration in seated and supine postures. Planar and three-dimensional models representing the human head-neck system under different seated postures and fore-aft and multiple-axis whole-body vibration are first introduced. In these models, the head-neck system is represented by rigid links connected via spring-damper components representing the soft-tissue and connecting elements between the bones. Additional muscle components are added to some models. The muscle components comprise additional mass, spring, and damper elements arranged in a special order to capture the effect of changes in the displacement, velocity, acceleration, and jerk. The results show that the proposed models are able to predict the displacement and acceleration of the head under different vibration files, with the muscle-based models showing better performance than the passive models. The second set of models is introduced in this work to investigate the effect of the underlying transport system conditions on the response of supine humans under vertical and multiple-axis whole-body vibration. In these models, the supine human body is represented by three rigid links representing the head, torso/arms, and legs. The links are connected via rotational and translational joints, and therefore, it is expected that the models can capture the coupling effects between adjacent segments. The joints comprise translational and rotational spring-damper components that represent the soft tissue and the connecting elements between the segments. The contact surfaces between the supine human and the underlying transport system were modeled using spring-damper elements. Two underlying transport systems were considered, including a rigid support and a long spinal board attached to a military litter. The results showed that the proposed models were able to predict the effect of the transport systems on the human response under different vibration conditions.