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Nonlinear dynamics of multi-mesh gear systems

Liu, Gang
http://rave.ohiolink.edu/etdc/view?acc_num=osu1196222009

Abstract Details

2007, Doctor of Philosophy, Ohio State University, Mechanical Engineering.
Multi-mesh gear systems are used in a variety of industrial machinery, where noise, quality, and reliability lie in gear vibration. The dynamic gear mesh forces are the source of vibration and result from parametric excitation and contact nonlinearity. The primary goal of this work is to develop mathematical models for multi-mesh gearsets with nonlinear, time-varying elements, to conduct numerical and analytical studies on nonlinear gear dynamic behaviors, such as parametric instabilities, frequency response, contact loss, and profile modification, and to provide guidelines for practical design and troubleshooting. First, a nonlinear analytical model considering dynamic load distribution between individual gear teeth is proposed, including the influence of variable mesh stiffnesses, profile modifications, and contact loss. This model yields better agreement than two existing models when compared against nonlinear gear dynamics from a finite element benchmark. Perturbation analysis finds approximate frequency response solutions for providing guidance for optimizing system parameters. The closed-form solution is validated by numerical integration. Second, the nonlinear, parametrically excited dynamics of idler and counter-shaft gear systems are examined. The periodic steady state solutions are obtained using analytical and numerical approaches. With proper stipulations, the contact loss function and the variable mesh stiffness are reformulated into a form suitable for perturbation. The closed-form solutions from perturbation analysis expose the impact of key parameters on the nonlinear response. The analysis for this strongly nonlinear system compares well to separate harmonic balance/continuation and numerical integration solutions. Finally, this work studies the influences of tooth friction on parametric instabilities and dynamic response of a single-mesh gear pair. A mechanism whereby tooth friction causes gear tooth bending is shown to significantly impact the dynamic response. A dynamic model is developed to consider this mechanism together with the other contributions of tooth friction and mesh stiffness fluctuation. Perturbation analysis finds approximate solutions that predict and explain the parametric instabilities. The effects of time-varying friction moments about the gear centers and friction-induced tooth bending are critical to parametric instabilities and dynamic response. The impacts of friction coefficient, bending effect, contact ratio, and modal damping on the stability boundaries are revealed.
Robert Parker (Advisor)
238 p.
Engineering, Mechanical
Multi-Mesh Gear; nonlinear dynamics; perturbation

Recommended Citations

Citations

  • Liu, G. (2007). Nonlinear dynamics of multi-mesh gear systems [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1196222009

    APA Style (7th edition)

  • Liu, Gang. Nonlinear dynamics of multi-mesh gear systems. 2007. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1196222009.

    MLA Style (8th edition)

  • Liu, Gang. "Nonlinear dynamics of multi-mesh gear systems." Doctoral dissertation, Ohio State University, 2007. http://rave.ohiolink.edu/etdc/view?acc_num=osu1196222009

    Chicago Manual of Style (17th edition)

osu1196222009
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© 2007, all rights reserved.
This open access ETD is published by The Ohio State University and OhioLINK.
Release 3.2.12