Thesis (M.S.)--Virginia Polytechnic Institute, 1966. / Vita. Abstract. Includes bibliographical references (leaves 195-199). Also available via the Internet.

This thesis is a small part of a much larger work, the aim of which is to continue the transition from gear theory to gear practice. The thesis deals with some aspects of the testing and theoretical development of equiangular and plain polyangular gears respectively. Initial prototypes of the equiangular spatial involute gearing, a small subset of a general spatial involute gear set, developed in previous works are to be tested for both function and form. The tests, based on the principles of the single flank gear tester, investigate constancy of transmission ratio and use both electronic and mechanical means. The former of these highlights the shortcomings of some aspects of the experimental set up. Algebraic expressions are also developed for plain polyangular gearing, a more general form of spatial involute gearing. These equations demonstrate the links to the underlying kinematic principles and are, consequently, more robust. This is verified by their application to both the equiangular and plain polyangular cases. The expressions were checked by comparing their results to graphical and numerical models developed concurrently with the algebraic expressions. Initial investigations are also undertaken into turning the mathematical theory into gear machining theory. / Master of Engineering (Hons.)

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Abstract The interaction among the tooth wear, dynamic loads, and its corresponding frequency spectrum variation in a spur gear pair is investigated in the dissertation. A mathematical model for the dynamic responses of a profile shifting involute gear pair is derived. For simplicity, a two-step mesh stiffness model is proposed to approximate the load sharing and the time-varying stiffness effects in a mating gear pair. The analytic solutions for the dynamic responses of this simplified dynamic model are derived in both time and frequency domains. The effect of the tooth wear on the spectrum variation has been illustrated analytically. The amplitude and frequency modulations introduced from the periodic load fluctuation have also been discussed. In order to characterize the time-varying mesh stiffness, frictional coefficient, damping ratio, temperature rise and load sharing effects between engaged teeth, a computational algorithm with the quasi-linear iteration procedure is developed to include above instantaneous parameters in the teeth engagement process. The tooth wear equation proposed by Flodin and Andersson (1997) is employed to simulate the mild wear process for an engaging gear pairs. The interactions between the tooth wear and the dynamic loads for the Steel/Steel, POM/POM, Nylon/Nylon and Steel/Nylon gears pair have been studied numerically. Numerical examples indicate that the proposed models are valid for gear pairs with different materials.

The loop bandwidth of a fractional-N PLL is a desirable parameter for many applications. A wide bandwidth allows a significant attenuation of phase noise arising from the VCO. A good VCO typically requires a high Q LC oscillator. It is difficult to build an on-chip inductor with a high Q factor. In addition, a good VCO also requires a lot of power. Both these design challenges are relaxed with a wide loop bandwidth PLL. However a wide loop bandwidth reduces the effective oversampling ratio (OSR) between the update rate and loop bandwidth and makes quantization noise from the ΔΣ modulator a much bigger noise contributor. A wide band loop also makes the noise and linearity performance of the phase detector more significant. The key to successful implementation of a wideband fractional-N synthesizer is in managing jitter and spurious performance. In this dissertation we present a new PLL architecture for bandwidth extension or phase noise reduction. By using clock squaring buffers with built-in offsets, multiple clock edges are extracted from a single cycle of a sinusoidal reference and used for phase updates, effectively forming a reference frequency multiplier. A higher update rate enables a higher OSR which allows for better quantization noise shaping and makes a wideband fractional-N PLL possible. However since the proposed reference multiplier utilizes the magnitude information from a sinusoidal reference to obtain phases, the derived new edges tend to cluster around the zero-crossings and form an irregular clock. This presents a challenge in lock acquisition. We have demonstrated for the first time that an irregular clock can be used to lock a PLL. The irregularity of the reference clock is taken into account in the divider by adding a cyclic divide pattern along with the ΔΣ control bits, this forces the loop to locally match the incoming patterns and achieve lock. Theoretically this new architecture allows for a 6x increase in loop BW or a 24dB improvement in phase noise. One potential issue associated with the proposed approach is the degraded spurious performance due to PVT variations, which lead to unintended mismatches between the irregular period and the divider pattern. A calibration scheme was invented to overcome this issue. In simulation, the calibration scheme was shown to lower the spurs down to inherent spurs level, of which the total energy is much less than the integrated phase noise. A test chip for proof of concept is presented and measurements are carefully analyzed. / text

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This thesis investigates the characteristics of static torsional mesh stiffness, load sharing ratio, and transmission errors of gears in mesh with and without a localised tooth crack.Gearing is perhaps one of the most critical components in power transmission systems. The transmission error of gears in mesh is considered to be one of the main causes of gear noise and vibration. Numerous papers have been published on gear transmission error measurement and many investigations have been devoted to gear vibration analysis. There still, however, remains to be developed a general non-linear Finite Element Model capable of predicting the effect of variations of gear torsional mesh stiffness, transmission error, transmitted load and load sharing ratio. The primary purpose of this study was to develop such a model and to study the behaviour of the static torsional mesh stiffness, load sharing ratio, and transmission error over one completed cycle of the tooth mesh.The research outlined in this thesis considers the variations of the whole gear body stiffness arising from the gear body rotation due to tooth bending deflection, shearing displacement, and contact deformation. Many different positions within the meshing cycle were investigated and then compared with the results of a gear mesh having a single cracked tooth.In order to handle contact problems with the finite element method, the stiffness relationship between the two contact areas must be established. Existing Finite Element codes rely on the use of the variational approach to formulate contact problems. This can be achieved by insertion of a contact element placed in between the two contacting areas where contact occurs. For modelling of gear teeth in mesh, the penalty parameter of the contact element is user-defined and it varies through the cyclic mesh. A simple strategy of how to overcome these difficulties is ++ / also presented. Most of the previously published finite element analysis with gears has involved only partial teeth models.In an investigation of gear transmission errors using contact elements, the whole body of the gears in mesh must be modelled, because the penalty parameter of the contact elements must account for the flexibility of the entire body of the gear not just the local stiffness at the contact point.

The investigation of numerical methods for modelling the mechanism properties ofinvolute spur gears in mesh, over the mesh cycle, forms the major part of this thesis.Gearing is perhaps one of the most critical components in power transmission systemsand the transmission error of gears in mesh is considered to be one of the main causes ofgear noise and vibration. Numerous papers have been published on gear transmissionerror measurement and many investigations have been devoted to gear vibration analysis.There still, however, remains to be developed a general Finite Element Model capable ofpredicting the effect of variations in rigid body gear tooth position, in which the criticalstage is the prediction of gear behaviour with profile modifications (including tip-relief).In this thesis, FEA results have been obtained by using various techniques including: (a)adaptive re-mesh with contacts using quad (2D) and brick (3D) elements and (b) theelement birth and death option. Tooth profile modifications can affect the behaviour ofthe gear meshing including the T.E., ratio of local deformation and load-sharing ratioresults, etc, providing an alternative method for gear design. In the high order end, theelastic strains of the gear-shaft system have also been investigated. The results in thisthesis have shown the potential for using strain-vibration relationships to monitor orcontrol the transmission system.The investigations have also included some analysis with non-metallic gears, anapplication area that is rapidly growing. The results achieved here are at a fundamentalstage, and further research would necessitate applying a coupled field analysis (structuraland thermal).

Thesis (award) -- University of Western Sydney, 2005. / Includes bibliography.