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Analytical Study On Compound Planetary Gear Dynamics

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2011, Doctor of Philosophy, Ohio State University, Mechanical Engineering.

Noise and vibration are major concerns in applications of compound planetary gears, and dynamic analysis is essential to their reduction. This work conducts a series of analytical investigations on several problems in compound planetary gear dynamics. A purely rotational model for compound planetary gear is developed, and the unique modal properties for the natural frequency spectra and vibration modes are presented and analytically proved. This model aims to simplify subsequent analyses on compound planetary gear dynamics while keeping the main dynamic behavior generated by tooth mesh forces. A systematic study on general compound planetary gear eigensensitivities is performed by utilizing the rotational-translational model in cite{G003}. The eigensensitivities are derived in compact, closed-form expressions for all parameter variations in both tuned (each stage in the system retains cyclic symmetry) and mistuned systems. The resultant formulae also suggest that modal strain and kinetic energy distribution plots are effective and straightforward means to identify the system parameters that have the greatest impact on adjusting the related natural frequency.

Compound planetary gear natural frequency veering and crossing phenomena are also systematically examined. By grouping all system parameters into tuned and mistuned parameters, the veering/crossing patterns with respect to each system parameter are determined. These patterns provide critical information on dramatic mode shape changes when tuning a compound planetary gear during the design stage.

Gear mesh phases that are critical for analytical or computational study on compound planetary gear dynamics are defined and calculated analytically. All the mesh phases are grouped into a hierarchical structure of system-level, stage-level, and train-level mesh phases to simplify the subsequent analytical investigations. In addition to providing a complete procedure to determine all the necessary relative phases, the specific relations between train-level relative phases are derived by applying the assembly conditions of compound planetary gears. Such relations, together with the systematically defined mesh phases, provide the foundation for the general rules to suppress selected dynamic responses of a general compound planetary gear through proper mesh phasing. The resultant mesh phasing rules are crucial for the troubleshooting of the vibration and noise problems in compound planetary gear applications.

Compound planetary gear parametric instabilities caused by mesh stiffness variations are analytically explored. Systems with single or multiple mesh frequencies are investigated. The instability boundaries are derived for different cases depending on the degeneracy of the natural frequencies. Application of the well-defined modal properties yields simple, closed-form expressions for instability boundaries. Some instability boundaries vanish under specific mesh phasing conditions.

The back-side mesh stiffness variation is inspected in this work to address the needs for gear vibration models that consider the gear tooth contacts on the back side. The results reveal the inherent relationship between the back-side and drive-side mesh stiffnesses. The impact of backlash on the back-side mesh stiffness variation function is also quantified.

Robert G. Parker, PhD (Advisor)
Daniel A. Mendelsohn, PhD (Advisor)
Stephen E. Bechtel, PhD (Committee Member)
Sandeep M. Vijayakar, PhD (Committee Member)
245 p.

Recommended Citations

Citations

  • Guo, Y. (2011). Analytical Study On Compound Planetary Gear Dynamics [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1312289370

    APA Style (7th edition)

  • Guo, Yichao. Analytical Study On Compound Planetary Gear Dynamics. 2011. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1312289370.

    MLA Style (8th edition)

  • Guo, Yichao. "Analytical Study On Compound Planetary Gear Dynamics." Doctoral dissertation, Ohio State University, 2011. http://rave.ohiolink.edu/etdc/view?acc_num=osu1312289370

    Chicago Manual of Style (17th edition)