The Effect of Suspension on Parametric Stability and Bifurcation of Geared Systems in Permanent Contact Regime
Author
Azimi, MohsenIssue Date
2022Keywords
GearHopf bifurcation
Parametric stability
Permanent contact regime
Pitchfork bifurcation
System of equations with strong coupling
Advisor
Enikov, Eniko
Metadata
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The University of Arizona.Rights
Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction, presentation (such as public display or performance) of protected items is prohibited except with permission of the author.Abstract
Gears are known to be one of the most common mechanical parts used in rotary machinery and power transmission systems. Originally, gears are designed to remain in permanent contact regime, where the teeth in mesh do not separate during operation. But because of the clearance between the teeth in mesh, for bad range of parameters, or poor operational conditions, separation of the teeth can occur. This results in free play mode, where the teeth are no longer in contact. The separation of the teeth results in different impact phases when the teeth come back into contact; in the worst case, it results in the rattling phenomenon.To date, many analytical and numerical works have studied the dynamic characteristics of gears with rigid mountings, specifically under constant speed operational conditions. These studies show that for these models, the separation of the teeth and rattling occur in the vicinity of the unstable tongues. Under these conditions, the clearance between the teeth in mesh is the main source of nonlinearity, expressed by a non-smooth piece-wise linear function or approximated by a third-order polynomial or Fourier series. The goal of this work is to investigate the effect of small deformation of the shafts upon the number of unstable tongues, and the nonlinear behavior of gears under constant speed and heavy-load operational conditions where the permanent contact condition holds. The lumped parameter analysis method is used to formulate and analyze the normalized three Degrees of Freedom (DOF) dynamic model of a one-stage spur gear pair with nonlinear suspension. There is great similarity between the governing system of equations of gears with nonlinear suspension and the well-known Mathieu equation with cubic nonlinear term (also known as the Mathieu-Duffing equation), which have been studied extensively in different works. Here, the existing techniques used in the dynamic analysis of linear and nonlinear Mathieu equations are modified according to the applications in this study. The same approach is then used to study the governing system of equations of gears with linear suspension, where the nonlinearity of the suspension is neglected. Finally, the results of the first two analyses are employed to analyze the governing system of equations of gears with nonlinear suspension.Type
textElectronic Dissertation
Degree Name
Ph.D.Degree Level
doctoralDegree Program
Graduate CollegeMechanical Engineering