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Title: Nonsmooth models of gear rattle in Roots booster pumps
Author: Mason, Joanna
ISNI:       0000 0004 2671 5266
Awarding Body: University of Bristol
Current Institution: University of Bristol
Date of Award: 2008
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This thesis is concerned with the study of gear rattle in Roots blower booster pumps. The pumps exhibit several hallmarks of nonlinearity, including intermittency and a sensitive dependence on parameters. Chapter 1 introduces the general problem background. In Chapter 2, it is described how imperfect (eccentric) gear mounting can introduce a time-dependent forcing term that operates at the same rotation rate as the gears. A second-order nonsmooth ordinary differential equation to describe the dynamics of the pump is derived, where the nonlinearity arises from the backlash clearance between the gear teeth. A piecewise linear stiffness model and a simpler infinite stiffness impacting limit are introduced. In addition, the methodologies for the calculation of linear 'silent' solutions, and the construction of noisy rattling solutions are outlined. It is found that noisy solutions can coexist with silent ones, providing a possible explanation of why these systems can rattle intermittently. The model is examined in more detail in Chapter 3 where basins of attraction are computed using cell-to-cell mapping techniques. Rich and delicate dynamics are revealed, and some of the transitions in the system's behaviour are analysed in terms of both smooth and discontinuity-induced bifurcations. The intricate stretching and folding of phase space is illustrated via computations of the grazing curve, and its preimages, and via manifold computations of basin boundaries using DsTool (Dynamical Systems Toolkit). Chapters 4 and 5 develop and analyse more complicated models for design innovations which attempt to reduce the gear rattle. The effects of (i) breaking the symmetry of the machine, (ii) mounting the driving gear on its shaft by means of a torsional spring, and finally, (iii) the addition of a type of tuned vibration absorber are investigated. A blend of both linear and nonlinear techniques are used and the relative merits of each design solution are compared. Finally, Chapter 6 presents conclusions and outlines areas for future work.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available