Application of mechanical micromachining for fabricating complex three-dimensional (3D) micro-scale features and small parts on a broad range of materials has increased significantly in the recent years. In particular, mechanical micromachining finds applications in manufacturing of biomedical devices, tribological surfaces, energy storage/conversion systems, and aerospace components. Effectively addressing the dual requirements for high accuracy and high throughput for micromachining applications necessitates understanding and controlling of dynamic behavior of micromachining system, including positioning stage, spindle, and the (micro-) tool, as well as their coupling with the mechanics of the material removal process. The dynamic behavior of the tool-collet-spindle-machine assembly, as reflected at the cutting edges of a micro-tool, often determines the achievable process productivity and quality. However, the common modeling techniques (such as beam based approaches) used in macro-scale to model the dynamics of cutting tools, cannot be used to accurately and efficiently in micro-scale case. Furthermore, classical modal testing techniques poses significant challenges in terms of excitation and measurement requirements, and thus, new experimental techniques are needed to determine the speed-dependent modal characteristics of miniature ultra-high-speed (UHS) spindles that are used during micromachining. The overarching objective of this thesis is to address the aforementioned issues by developing new modeling and experimental techniques to accurately predict and analyze the dynamics of micro-scale cutting tools and miniature ultra-high-speed spindles, including rotational effects arising from the ultra high rotational speeds utilized during micromachining, which are central to understanding the process stability. Accurate prediction of the dynamics of micromachining requires (1) accurate and numerically-efficient analytical approach to model the rotational dynamics of realistic micro-tool geometries that will capture non-symmetric bending and coupled torsional/axial dynamics including the rotational/ gyroscopic effects; and (2) new experimental approaches to accurately determine the speed-dependent dynamics of ultra-high-speed spindles. The dynamic models of cutting tools and ultra-high-speed spindles developed in this work can be coupled together with a mechanistic micromachining model to investigate the process stability of mechanical micromachining. To achieve the overarching research objective,first, a new three-dimensional spectral- Tchebychev approach is developed to accurately and efficiently predict the dynamics of (micro) cutting tools. In modeling the cutting tools, considering the efficiently and accuracy of the solution, a unified modeling approach is used. In this approach, the shank/taper/extension sections, vibrational behavior of which exhibit no coupling between different textural motion, of the cutting tools are modeled using one-dimensional (1D) spectral-Tchebychev (ST) approach; whereas the fluted section (that exhibits coupled vibrational behavior) is modeled using the developed 3D-ST approach. To obtain the dynamic model for the entire cutting tool, a component mode synthesis approach is used to `assemble' the dynamic models. Due to the high rotational speeds needed to attain high material removal rate while using micro tools, the gyroscopic/rotational effects should be included in predicting the dynamic response at any position along the cutting edges of a micro-tool during its operation. Thus, as a second step, the developed solution approach is improved to include the effects arising from the high rotational speeds. The convergence, accuracy, and efficiency of the presented solution technique is investigated through several case studies. It is shown that the presented modeling approach enables high-fidelity dynamic models for (micro-scale) cutting-tools. Third, to accurately model the dynamics of miniature UHS spindles, that critically affect the tool-tip motions, a new experimental (modal testing) methodology is developed. To address the deficiency of traditional dynamic excitation techniques in providing the required bandwidth, repeatability, and impact force magnitudes for accurately capturing the dynamics of rotating UHS spindles, a new impact excitation system (IES) is designed and constructed. The developed system enables repeatable and high-bandwidth modal testing of (miniature and compliant) structures, while controlling the applied impact forces on the structure. Having developed the IES, and established the experimental methodology, the speed-dependent dynamics of an air bearing miniature spindle is characterized. Finally, to show the broad impact of the develop modeling approach, a macro-scale endmill is modeled using the presented modeling technique and coupled to the dynamics of a (macro-scale) spindle, that is obtained experimentally, to predict the tool-point dynamics. Specific contributions of this thesis research include: (1) a new 3D modeling approach that can accurately and efficiently capture the dynamics of pretwisted structures including gyroscopic effects, (2) a novel IES for repeatable, high-bandwidth modal testing of miniature and compliant structures, (3) an experimental methodology to characterize and understand the (speed-dependent) dynamics of miniature UHS spindles.

<p dir="ltr">Rolling element bearings (REBs) are common components in rotating equipment. They are used to carry loads and allow for rotation and misalignments with minimal friction. There exists a wide variety of ball and roller bearings that are suited for a wide variety of applications. All varieties of REBs operate with the same fundamental principles: force transferred from the shaft is applied to the inner race of a bearing, distributed among the rolling elements, and passed on through the outer race to the bearing housing. Load distribution among the rolling elements and the dynamic performance of the bearing is dependent on the bearing’s specifications and operating conditions. Bearing-housing and inner race-shaft fit classifications also control the bearing radial internal clearance (RIC), which eventually affects the bearing performance and load transferred to the housing.</p><p dir="ltr">This thesis experimentally and analytically investigates the load distribution and dynamic performance of rolling elements and investigates roller slip, tilt, and skew in a spherical roller bearing (SRB) under various combinations of loads and speeds. In order to have better insight into the effect of flexible housing and shaft on load distribution and dynamics of REBs, it was experimentally investigated the variation of inner race-shaft and outer race-housing interfaces on load and pressure maps at the bearing-housing interface for four different varieties of rolling element bearing: deep groove ball bearings, angular contact ball bearings, cylindrical roller bearings, and spherical roller bearings. Moreover, an integrated rotor-bearing housing system model developed to examine the behaviors of the rotor, bearing, and housing operating under various conditions.</p><p dir="ltr">In order to gain a deeper understanding of the dynamic behavior of REBs, a full six degree of freedom SRB dynamic model was developed in MSC ADAMS software. C++ based ADAMS/Solver subroutines, called dynamic bearing model (DBM), were developed and incorporated in ADAMS to compute reaction forces and moments in a rolling element bearing. DBM is based on the discrete element method (DEM), which assumes each of the bearing elements (i.e., rolling elements, cage, inner race, and outer race) to be a rigid body with six degrees-of freedom (DOF) in a three-dimensional space. A novel test rig (spherical roller bearing test rig, SRBTR) was also designed and developed to investigate load distribution and roller slip, tilt, and skew in an SRB. The test rig utilized a double-row SRB and was designed to allow for direct visual access to each row using a high-speed camera. The dynamic behavior of the rollers was corroborated with the developed analytical model. The experimental and analytical results indicate that the roller tilt angle increases with axial load, remains constant with speed, and decreases with increasing radial load when the roller is located in the load zone. Furthermore, roller skew in the load zone increases with axial load and shaft speed; however, it decreases with the radial load. The results indicate that when the radial-to-axial load ratio is greater than 4, roller tilt and skew are minimized. Due to roller intermittent slip and roller cage pocket collision in the unload zone, tilt and skew become unpredictable. The magnitude of the tilt and skew in the unload zone is directly related to the roller-race and roller-cage pocket clearances, respectively. Another test rig (pressure mapping test rig, PMTR) was designed to solely investigate how bearing-housing and inner race-shaft interfaces affect the load distribution in REBs. Thin film pressure sensors were utilized and placed around the perimeter of the test bearings inside of a housing to experimentally evaluate the pressure distribution between REBs and a housing under different loads and bearing-shaft and bearing-housing interfaces. Pressure map results were used to evaluate the effect of radial internal clearance on the load distribution of different bearing types. Pressure map results confirmed that the amplitude of load variation reduces with the bearing internal clearance. The thin film sensor system was also used to investigate the circumferential load distribution on the housing.</p><p dir="ltr">Previous ADAMS bearing models have assumed the bearing outer race to be fixed to the ground and the bearing inner race to be attached to a rigid shaft. In order to develop a more realistic and versatile bearing simulation tool, ADAMS bearing models were combined with flexible housings and rotor. To achieve an integrated rotor-bearing housing system model, the ADAMS bearing model was coupled through a set of interface points using component-mode-synthesis (CMS) for the rotor and housing model. The bearing outer races were discretized into multiple nodes to compute the force and deformation at the bearing housing conformal contact as well as to minimize the computational requirements associated with the conformal contact problems. The integrated model was then utilized to investigate the effects of rotor flexibility in the bearing rotor system and the effect of bearing clearance and housing clearance on bearing dynamics. It was demonstrated that the flexibility of the rotor has a significant effect on bearing element motion and dynamics. The results also indicated that depending on the bearing type, the shaft deflection can induce a moment within the bearing that is not readily identifiable from elementary theory. The results showed that the flexible housing undergoes deformations that create ovality in the bearing housing, thus affecting bearing dynamics. The model was also used to investigate bearing performance in a miniature wind turbine main shaft, utilizing a combination of SRB and cylindrical roller bearing (CRB) ADAMS models. Results suggest that the axial-to-radial load ratio should be less than the tangent of the SRB contact angle to avoid premature failure due to rollers sliding in the SRB as well as detrimental parallel misalignment in the CRB.</p>

This master thesis concentrates on the influence of liquidity measures on the prediction of volatility and given the magic triangle phenomena subsequently on the expected return. Liquidity measures Amihud Illiquidity, Amivest Liquidity and Roll adjusted for high frequency data have been utilized. Dataset used for the modeling was consisting of 98 shares that were traded on S&P 100. The time range was from 1st January 2013 to 31st December 2014. We have found out that the liquidity truly enters into the return-volatility relationship and influences these variables - the magic triangle interacts. However, contrary to our hypothesis, the model shows up that lower liquidity signifies lower realized risk. This inference has been suggested by all three models (3SLS, 2SLS and OLS). Furthermore, we have used the realized variance and bi-power variation to separate the jump. Our second hypothesis that lower liquidity signifies higher frequency of jumps was confirmed only for one of two liquidity proxies (Roll) included in the resulting logit FE model. Keywords liquidity, risk, volatility, expected return, magic triangle, price jumps, realized variance, bi-power variation, three-stage least squares model, logit, high-frequency data, S&P 100 Author's e-mail david.brandejs@seznam.cz Supervisor's e-mail...