This is Part B of the Thesis. / <p> The design and performance of a flat emitting ring on-axis electron gun suitable for use in a small reflected beam accelerator was investigated. The design constraints include a low emittance (approximately 5π cm mrad), and a small beam size with a focus approximately 13 cm from the emitting surface.</p> <p> A suitable geometry was determined theoretically and was tested with a dispenser cathode. A beam with a focus at 12.7 ± 1 cm and an emittance of approximately 7π cm mrad was obtained. However, the dispenser cathode response time to heater current changes is too large for the required gun current control.</p> <p> Experiments were done to study the mechanical and thermal properties of flat emitting foil rings, since a directly heated foil has a fast response time. Two foils were tested: 1.27 x 10^-3 cm thick tungsten and 4.57 x 10^-4 cm thick tantalum. The present simple design requires impractically thin foils (≤ 0.25 microns thick) to reach emission temperatures at feasible heater currents.</p> / Thesis / Master of Engineering (MEngr)

The first two chapters provide the necessary prerequisites. In the third and fourth chapters we demonstrate than an affine Hjelmslev plane (or A. H. plane) is coordinatized by a biternary ring; and that given a biternary ring, one can construct an affine Hjelmslev plane. In the fifth and sixth chapters we introduce the notions of an ordering of an A. H. plane and an ordering of a biternary ring. In the seventh chapter we show that an ordering of an A. H. plane H induces an ordering on the coordinate biternary ring. In the eighth chapter we show that a given ordering of a biternary ring M induces an ordering on the A.H. plane constructed over M. In the remaining chapters we examine the associated ordinary affine plane of an A. H. plane, the case where an A. H. plane is Desarguesian, and give an example of an ordered non-Desarguesian A. H. plane. / Thesis / Master of Science (MSc)

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Interest in macrocyclic monomers can be dated back to the 1960's. The recent surge of research activities in this area is prompted by two facts: the encouraging discovery of high yield synthesis and facile ring-opening polymerization of cyclic polycarbonate; the need for a technique to solve the tough processibility problem of high performance polymers. This work was intended to address the following aspects in the cyclic poly(ether ketone) or sulfone system. The first goal was to understand the structure-property relationship of this type of macrocycles. A large number of macrocycles were synthesized by nucleophilic aromatic substitution cyclization reactions under pseudo-high dilution conditions. Pure individual macrocycles as well as cyclic mixtures were characterized by NMR, HPLC, GPC, FABMS, MALDI-TOF-MS, DSC and TGA. Comparison study suggests that the cyclic distribution is kinetically controlled. Several factors determine the melting points of individual macrocycles. The first factor is the ring size. A series of cyclic monomers for poly(ether ether ketone)s were synthesized and isolated. The melting point decreases as ring size increases. Single crystal X-ray structural results suggest that this phenomenon is related to the increased flexibility of the larger sized macrocycles. The second factor is the functional groups of the macrocycles. X-ray structural and GPC experiments reveal that the sulfone group is more rigid than the ketone group, than ether group. The effect of functional groups on melting point is in the order sulfone>ketone>ether. A third factor is the symmetry of the macrocycles. Breaking the symmetry of macrocycle through comacrocyclization dramatically decreases the melting point of individual macrocycles as well as the cyclic mixture as a whole. Based on these findings, a novel two step method was developed to control the ring size distribution, which effectively reduced the amount of the small sized macrocycle and decreased the melting point. In addition to the nucleophilic aromatic substitution cyclization, it was also demonstrated in this work that macrocycles can be synthesized by Friedel-Crafts acylation cyclization. However, this method is limited by the solubility problem. The ring-opening polymerization of macrocyclic monomers was systematically studied. Several factors were considered in this study: the nature and amount of catalyst, temperature and time. CsF; metallic phenolate and Na2S are good initiators. Conversion to near 100 % is possible under the controlled polymerization conditions. It was found that crosslinking is an inherent phenomenon. The molecular weight of the soluble fraction near complete conversion is almost independent of initiator and polymerization temperature. It is limited by the crosslinking reaction. It is demonstrated for the first time that the macrocyclic monomer techniques can be applied to more valuable semicrystalline systems. Tough polymers such as high performance poly(ether ether ketone)s were produced through ring-opening polymerization. The last chapter is devoted to the challenging synthesis of monodisperse poly(ether ether ketone)s. A convergent strategy was devised. A monofluoroaryl compound was synthesized by Friedel-crafts acylation reaction. The final monodisperse linear oligomers were generated by reacting the monofunctional compound with a bisphenol through a quantitative reaction. / Ph. D.

This work investigates steady deformations, measured spectra of quasi-static ring deformations, natural frequencies, vibration modes, parametric instabilities, and nonlinear dynamics of high-speed planetary gears with an elastically deformable ring gear and equally-spaced planets. An analytical dynamic model is developed with rigid sun, carrier, and planets coupled to an elastic continuum ring. Coriolis and centripetal acceleration effects resulting from carrier and ring gear rotation are included. Steady deformations and measured spectra of the ring deflections are examined with a quasi-static model reduced from the dynamic one. The steady deformations calculated from the analytical model agree well with those from a finite element/contact mechanics (FE/CM) model. The spectra of ring deflections measured by sensors fixed to the rotating ring, space-fixed ground, and the rotating carrier are much different. Planet mesh phasing significantly affects the measured spectra. Simple rules are derived to explain the spectra for all three sensor locations for in-phase and out-of-phase systems. A floating central member eliminates spectral content near certain mesh frequency harmonics for out-of-phase systems. Natural frequencies and vibration modes are calculated from the analytical dynamic model, and they compare well with those from a FE/CM model. Planetary gears have structured modal properties due to cyclic symmetry, but these modal properties are different for spinning systems with gyroscopic effects and stationary systems without gyroscopic effects. Vibration modes for stationary systems are real-valued standing wave modes, while those for spinning systems are complex-valued traveling wave modes. Stationary planetary gears have exactly four types of modes: rotational, translational, planet, and purely ring modes. Each type has distinctive modal properties. Planet modes may not exist or have one or more subtypes depending on the number of planets. Rotational, translational, and planet modes persist with gyroscopic effects included, but purely ring modes evolve into rotational or one subtype of planet modes. Translational and certain subtypes of planet modes are degenerate with multiplicity two for stationary systems. These modes split into two different subtypes of translational or planet modes when gyroscopic effects are included. Parametric instabilities of planetary gears are examined with the analytical dynamic model subject to time-varying mesh stiffness excitations. With the method of multiple scales, closed-form expressions for the instability boundaries are derived and verified with numerical results from Floquet theory. An instability suppression rule is identified with the modal structure of spinning planetary gears with gyroscopic effects. Each mode is associated with a phase index such that the gear mesh deflections between different planets have unique phase relations. The suppression rule depends on only the modal phase index and planet mesh phasing parameters (gear tooth numbers and the number of planets). Numerical integration of the analytical model with time-varying mesh stiffnesses and tooth separation nonlinearity gives dynamic responses, and they compare well with those from a FE/CM model. Closed-form solutions for primary, subharmonic, superharmonic, and second harmonic resonances are derived with a perturbation analysis. These analytical results agree well with the results from numerical integration. The analytical solutions show suppression of certain resonances as a result of planet mesh phasing. The tooth separation conditions are analytically determined. The influence of the gyroscopic effects on dynamic response is examined numerically and analytically. / Doctor of Philosophy / Planetary gears in aerospace applications have thin ring gears for reducing weight. These lightweight ring gears deform elastically when transmitting power. At high speed, Coriolis and centripetal accelerations of planetary gears become significant. This work develops an analytical planetary gear model that takes account of an elastically deformable ring gear and speed-dependent gyroscopic (i.e., Coriolis) and centripetal effects. Steady deformations, measured spectra of quasi-static ring deformations, natural frequencies, vibration modes, parametric instabilities, and dynamic responses of planetary gears with equally-spaced planets are investigated with the analytical model. Steady deformations refer to quasi-static deflections that result from applied torques and centripetal acceleration effects. These steady deformations vary because of periodically changing mesh interactions. Such variation leads to cyclic stress that reduces system fatigue lives. This work evaluates planetary gear steady deformations with the analytical model and studies the effects of system parameters on the steady deformations. Ring deflections measured by sensors fixed to the rotating ring gear (e.g., a strain gauge), space-fixed ground (e.g., a displacement probe), and the rotating carrier have much different spectra. The planet mesh phasing, which is determined by gear tooth numbers and the number of planets, significantly influences these spectra. Simple rules are derived that govern the occurrence of spectral content in all the three measurements. Understanding these spectra is of practical significance to planetary gear engineers and researchers. Planetary gears have highly structured modal properties due to cyclic symmetry. Vibration modes are classified into rotational, translational, and planet modes in terms of the motion of central members (sun and carrier). The central members have only rotation for a rotational mode, only translation for a translational mode, and no motion for a planet mode. Translational modes have two subtypes, rotational modes have only one subtype, and planet modes may not exist or have one or more subtypes depending on the number of planets. For each subtype of modes, all planets have the same motion with a unique phase relation between different planets and the elastic ring gear has unique deformations. Understanding this modal structure is important for modal testing and resonant mode identification in dynamic responses. Sun-planet and ring-planet mesh interactions change periodically with mesh frequency. These mesh interactions are modeled as time-varying stiffnesses that parametrically excite the planetary gear system. Parametric instabilities, in general, occur when the mesh frequency or one of its harmonics is near twice a natural frequency or combinations of two natural frequencies. Closed-form expressions for parametric instability boundaries that bound the instability region are determined from the analytical model. Certain parametric instabilities are suppressed as a result of planet mesh phasing. Near resonances, vibration can become large enough that meshing teeth lose contact. The analytical model is extended to include the tooth separation nonlinearity. Closed-form approximations for dynamic responses near resonances are determined from the analytical model, and these analytical results compare well with those from numerical simulations of the analytical model. Tooth separation conditions are analytically determined. The influences of planet mesh phasing and Coriolis acceleration on dynamic responses near resonances are investigated numerically and analytically.