Master of Science, The Ohio State University, 2019, Mechanical Engineering

Noise and vibration performance of a gear system is critical in any industry. Vibrations caused by the excitations at the gear meshes propagate to the transmission housing to cause noise, while also increasing gear tooth stresses to degrade durability. As such, gear engineers must seek gear designs that are nominally quiet with low vibration amplitudes. They must also ensure that this nominal performance is robust in the presence of various manufacturing errors. This thesis research aims at an experimental investigation of the influence of one type of manufacturing error, namely random tooth spacing errors, on the vibratory responses of spur and helical gear pairs. For this purpose, families of spur and helical gear test specimens having intentionally induced, tightly controlled random spacing error sequences are fabricated. These specimens are paired and assembled in various ways to achieve different sequences of composite spacing errors. Static and dynamic motion transmission error measurements from these tests are compared to the baseline case of “no error” gear to quantify the impact of random spacing errors on the dynamic response. These comparisons show that there is a significant, quantifiable impact of random spacing errors on both spur and helical gear dynamics. In general, vibration amplitudes of gear pairs having random spacing errors are higher than those of the corresponding no-error gear pairs. In the frequency domain, gears having random spacing errors exhibit broad-band spectra with significant non-mesh harmonics, pointing to potential noise quality issues.

Committee: Ahmet Kahraman (Advisor); David Talbot (Committee Member) Subjects: Engineering; Mechanical Engineering

PhD, University of Cincinnati, 2012, Engineering and Applied Science: Mechanical Engineering

This dissertation research focuses on evaluating the nonlinear dynamics of driveline systems employed in motor vehicles with emphasis on characterizing the excitations and response of right-angle, precision hypoid-type geared rotor structure. The main work and contribution of this dissertation is divided into three sections. Firstly, the development of an asymmetric and nonlinear gear mesh coupling model will be discussed. Secondly, the enhancement of the multi-term harmonic balance method (HBM) is presented. Thirdly and as the final topic, the development of new dynamic models capable of evaluating the dynamic coupling characteristics between the gear mesh and other driveline structures will be addressed. A new asymmetric and nonlinear mesh model will be proposed that considers backlash, and the fact that the tooth surfaces of the convex and concave sides are different. The proposed mesh model will then be fed into a dynamic model of the right-angle gear pair to formulate the dimensionless equation of motion of the dynamic model. The multi-term HBM will be enhanced to simulate the right-angle gear dynamics by solving the resultant dimensionless equation of motion. The accuracy of the enhanced HBM solution will be verified by comparison of its results to the more computationally intensive direct numerical integration calculations. The stability of both the primary and sub-harmonic solutions predicted by applying multi-term HBM will be analyzed using the Floquent Theory. In addition, the stability analysis of the multi-term HBM solutions will be proposed as an approximate approach for locating the existence of sub-harmonic and chaotic motions. In this dissertation research, a new methodology to evaluate the dynamic interaction between the nonlinear hypoid gear mesh mechanism and the time-varying characteristics of the rolling element bearings will also be developed. The time-varying mesh parameters will be obtained by synthesizing a 3-dimensional loaded tooth conta (open full item for complete abstract)

Committee: Teik Lim PhD (Committee Chair); Sundaram Murali Meenakshi PhD (Committee Member); Dong Qian PhD (Committee Member); David Thompson PhD (Committee Member) Subjects: Mechanics

Doctor of Philosophy, The Ohio State University, 2022, Mechanical Engineering

Vibro-impacts of gears are common in various automotive geared drivetrains used in engines and transmissions, causing excessive rattle noise. External torque fluctuations lead to contact loss at gear mesh interfaces of such systems to result in sequences of impacts. Further, gear root and contact stresses might be elevated due to these impact events bringing durability concerns upfront. An experimental methodology is developed in this study to investigate such gear rattle problems observed in various powertrain applications formed by a single gear pair as well as multimesh gear trains. This test methodology allows one to simulate real-life gear rattle problems in a lab environment by imposing the external torque fluctuations at desired shapes and amplitudes within a wide range of operating speed through its servo motors. The rattle set-up is used to develop a new rattle severity index defined by gear impact velocities. Rattle severity index predicted using a torsional model within wide ranges of system parameters is compared to measured sound pressure level to demonstrate its effectiveness in predicting noise outcome solely from torsional dynamics of the drivetrain. A discrete torsional dynamic model of a single gear pair along with a computationally efficient piecewise-linear solution methodology is developed to conduct extensive parametric studies. Predictions of this model are compared to actual measurements from the rattle test machine for its complete validation. A no-rattle criterion that defines a boundary between no-impact and impacting motions is defined. A wide array of nonlinear behavior is demonstrated through presentation of periodic and chaotic responses in the forms of phase plots, Poincare maps, and bifurcation diagrams. The overall nonlinear response is characterized through parameter maps that showed bands of periodic responses with n and n +1 coast-side impacts per excitation period separated by bands of chaotic motions, with ty (open full item for complete abstract)

Committee: Ahmet Kahraman (Advisor) Subjects: Mechanical Engineering

Master of Science, The Ohio State University, 2021, Mechanical Engineering

Nonlinear dynamic behavior of a spur gear pair has been a major topic in both gear dynamics and nonlinear vibration fields. A spur gear pair can exhibit a wide range of nonlinear behavior primarily due to its backlash and periodically time-varying mesh stiffness. While a number of theoretical studies pointed to the possibility of severe subharmonic resonances at integer multiples of the primary resonance of the gear pair, past experimental investigations focused overwhelmingly on the behavior within the speed ranges where primary and super-harmonic resonance peaks occur. There has been very little experimental evidence of such subharmonic resonances, perhaps because such investigations require very high-speed experiments pushing the limits of test machine and measurement system capabilities. In this study, a test gear pair design is implemented to reduce the primary resonance frequency significantly such that the first three subharmonic resonances can be studied using an existing test machine and a conventional gear transmission error measurement method. Transient and steady-state data are collected at different transmitted torque values to show softening type of nonlinear behavior at super-harmonic and primary resonance peaks along with a well-defined first subharmonic resonance peak dictated by period-2 motions. Other subharmonic motions up to period-4 are also demonstrated experimentally. At the end, two different dynamic models, a discrete torsional model and a deformable-body model, are employed to simulate the experiments, focusing on the subharmonic resonance regions. Both models are shown to be effective in correlating to experiments.

Committee: Ahmet Kahraman (Advisor); David Talbot (Committee Member) Subjects: Mechanical Engineering

Doctor of Philosophy (PhD), Wright State University, 2017, Engineering PhD

Gears are vital power transmitting mechanical components, in both automotive and aerospace applications, and commonly operate within relatively high rotational speed ranges. Therefore, the dynamic behavior of gears is inevitable and can be quite significant under certain circumstances. The gear dynamics introduces not only noises and vibrations, but also large tooth force amplitudes, and consequently large amplitudes of bending stresses and contact stresses, and high surface temperatures, promoting the failures of tooth bending fatigue, contact fatigue, and scuffing. This study focuses on the mechanism by which the gear dynamic responses affect the flash temperature rise and contact fatigue life using a gear tribo-dynamic formulation. The significance of this work is that it connects the gear dynamics and gear tribology disciplines and shows the importance of dynamic response on the two critical failure modes; scuffing and pitting. A six degree-of-freedom transverse-torsional discrete gear dynamics equation set is coupled with a thermal mixed elastohydrodynamic lubrication formulation to include the interactions between the gear dynamics and the gear tribological behavior. The flash temperature rises are quantified within a wide speed range under the different operating and surface conditions. The results indicate evident deviations of flash temperature rise between quasi-static condition and tribo-dynamic condition especially in the vicinities of the resonances. The interactive model of gear dynamics and gear tribological behavior is bridged through an iterative numerical scheme to determine the surface normal pressure and tangential shear under the tribo-dynamic condition. The resultant multi-axial stress fields (from these surface tractions) on and below the surface are then used to assess the fatigue damage. A comparison between the tribo-dynamic and quasi-static life predictions is performed to demonstrate the important role of the gear tribo-dynamics in (open full item for complete abstract)

Committee: Sheng Li Ph.D. (Advisor); Joseph Slater Ph.D. (Committee Member); Ahmet Kahraman Ph.D. (Committee Member); Ha-Rok Bae Ph.D. (Committee Member); Nikolai Priezjev Ph.D. (Committee Member) Subjects: Mechanical Engineering

Master of Science, The Ohio State University, 2017, Mechanical Engineering

This paper complements recent investigations [Handschuh et al. (2014), Talbot et al. (2016)] of the influences of tooth indexing errors on dynamic factors of spur gears by presenting data on changes to the dynamic transmission error. An experimental study is performed using an accelerometer-based dynamic transmission error measurement system incorporated into a high-speed gear tester to establish baseline dynamic behavior of gears having negligible indexing errors, and to characterize changes to this baseline due to application of tightly-controlled intentional indexing errors. Spur gears having different forms of indexing errors are paired with a gear having negligible indexing error. Dynamic transmission error of gear pairs under these error conditions is measured and examined in both time and frequency domains to quantify the transient effects induced by these indexing errors. These measurements are then compared against the baseline, no error condition, as a means to quantify the dynamic vibratory behavior induced due to the tooth indexing errors. These comparisons between measurements indicate clearly that the baseline dynamic response, dominated by well-defined resonance peaks and mesh harmonics, are complemented by non-mesh orders of transmission error due the transient behavior induced by indexing errors. In addition, the tooth (or teeth) having indexing error imparts transient effects which dominate the vibratory response of the system for significantly more mesh cycles than the teeth having errors are in contact. For this reason, along with the results presented in Talbot et al. (2016), it was concluded that spur gears containing indexing errors exhibit significant deviations from nominal behavior, at both a system and time-domain level.

Committee: Ahmet Kahraman (Advisor); David Talbor (Committee Member) Subjects: Engineering; Mechanical Engineering

PhD, University of Cincinnati, 2017, Engineering and Applied Science: Mechanical Engineering

Hypoid and bevel gears are widely used in the rear axle systems for transmitting torque at right angle. They are often subjected to harmful dynamic responses which cause gear whine noise and structural fatigue problems. In the past, researchers have focused on gear noise reduction through reducing the transmission error, which is considered as the primary excitation of the geared system. Effort on the dynamic modeling of the gear-shaft-bearing-housing system is still limited. Also, the noise generation mechanism through the vibration propagation in the geared system is not quite clear. Therefore, the primary goal of this thesis is to develop a system-level model to evaluate the vibratory and acoustic response of hypoid and bevel geared systems, with an emphasis on the application of practical vehicle powertrain system. The proposed modeling approach can be employed to assist engineers in quiet driveline system design and gear whine troubleshooting. Firstly, a series of comparative studies on hypoid geared rotor system dynamics applying different mesh formulations are performed. The purpose is to compare various hypoid gear mesh models based on pitch-cone method, unloaded and loaded tooth contact analysis. Consequently, some guidelines are given for choosing the most suitable mesh representation. Secondly, an integrated approach is proposed for the vibro-acoustic analysis of axle systems with right-angle geared drive. The approach consists of tooth contact analysis, lumped parameter gear dynamic model, finite element model and boundary element model. Then, a calculation method for tapered roller bearing stiffness matrix is introduced, which is based on the Finite Element/Contact Mechanics model of axle system with right-angle geared system. The effect of rigid bearing support and flexible bearing support is studied by comparing the flexible axle system model with rigid supported gear pair model. Other important system dynamic factors are also investigated, such as (open full item for complete abstract)

Committee: Teik Lim Ph.D. (Committee Chair); Michael Alexander-Ramos Ph.D. (Committee Member); Jay Kim Ph.D. (Committee Member); Manish Kumar Ph.D. (Committee Member) Subjects: Mechanical Engineering; Mechanics

MS, University of Cincinnati, 2013, Engineering and Applied Science: Mechanical Engineering

Hypoid and bevel gears are widely used in the rear axles of both on and off-highway vehicles, and are often subjected to harmful dynamic responses which cause gear whine noise and structural fatigue problems. The primary goal of this thesis is therefore to develop a more realistic mesh and dynamic model to predict the vibratory response of hypoid and bevel geared systems, and study the effect of different working conditions, e.g. operating speed, torque load, on the dynamic responses of those systems. First, a multi-point hypoid gear mesh model based on 3-dimensional loaded tooth contact analysis is incorporated into a coupled multi-body dynamic and vibration hypoid gear model to predict more detailed dynamic behavior of each tooth pair. To validate the accuracy of the proposed model, the time-averaged mesh parameters are applied to linear time-invariant (LTI) analysis to calculate the dynamic responses, such as dynamic mesh force and dynamic transmission error, which demonstrates good agreement with those predicted by using single-point mesh model. Furthermore, a nonlinear time-varying (NLTV) dynamic analysis is performed considering the effect of backlash nonlinearity and time-varying mesh parameters, such as time-varying mesh stiffness, transmission error, mesh point and line-of-action. One of the advantages of the multi-point mesh model is that it allows the calculation of dynamic responses for each engaging tooth pair, and simulation results for an example case are given to show the time history of the mesh parameters and dynamic mesh force for each pair of teeth within a full engagement cycle. This capability enables the analysis of durability of the gear tooth pair and more accurate prediction of the system response. Secondly, to have more insights on the load dependent mesh parameters and dynamic responses of the hypoid and spiral bevel geared systems, a load dependent mesh model is developed by using 3-dimensional loaded tooth contact analysis (LTCA). T (open full item for complete abstract)

Committee: Teik Lim Ph.D. (Committee Chair); J. Kim Ph.D. (Committee Member); David Thompson Ph.D. (Committee Member) Subjects: Mechanics

MS, University of Cincinnati, 2010, Engineering and Applied Science: Mechanical Engineering

Hypoid and spiral bevel gears, used in the rear axles of cars, trucks and off-highway equipment, are subjected to harmful dynamic response which can be substantially affected by the structural characteristics of the shafts and bearings. This thesis research, with a focus on gear-shaft-bearing structural analysis, is aimed to develop effective mathematical models and advanced analytical approaches to achieve more accurate prediction of gear dynamic response as well as to investigate the underlying physics affecting dynamic response generation and transmissibility. Two key parts in my thesis are discussed below. Firstly, existing lumped parameter dynamic model has been shown to be an effective tool for dynamic analysis of spiral bevel geared rotor system. This model is appropriate for fast computation and convenient analysis, but due to the limited degrees of freedom used, it may not fully take into consideration the shaft-bearing structural dynamic characteristics. Thus, a dynamic finite element model is proposed to fully account for the shaft-bearing dynamic characteristics. In addition, the existing equivalent lumped parameter synthesis approach used in the lumped parameter model, which is key to representing the shaft-bearing structural dynamic characteristics, has not been completely validated yet. The proposed finite element model is used to guide the validation and improvement of the current lumped parameter synthesis method using effective mass and inertia formulations, especially for modal response that is coupled to the pinion or gear bending response. Secondly, a new shaft-bearing model has been proposed for the effective supporting stiffness calculation applied in the lumped parameter dynamic analysis of the spiral bevel geared rotor system with 3-bearing straddle-mounted pinion configuration. Also, based on 14 degrees of freedom lumped parameter dynamic model and quasi-static three-dimensional finite element tooth contact analysis program, two typical s (open full item for complete abstract)

Committee: Teik Lim PhD (Committee Chair); Ronald Huston PhD (Committee Member); David Thompson PhD (Committee Member) Subjects: Mechanical Engineering

PhD, University of Cincinnati, 2010, Engineering and Applied Science: Mechanical Engineering

Hypoid and bevel gears that are widely used in both on and off-highway vehicles have the potential of producing excessive vibrations and noise. The goal of this dissertation research is to establish more effective mathematical model and analytical techniques to characterize the mesh and dynamic behavior, predict vibratory response, and reveal the underlying physics of the hypoid and bevel geared rotor system. The multi-body and multiple-degree-of-freedom (MDOF) dynamic modeling scheme is adopted and the key issues addressed in this dissertation are discussed below. Firstly, since gear mesh and dynamic characteristics are highly dependent on the torque load, a series of comparative studies and parametric analysis under different nominal torque levels are performed. The purpose is to identify critical factors and applicability of different assumptions for the MDOF hypoid and bevel geared rotor system model. In addition, a dynamic load dependent mesh model is proposed to characterize the potential interaction between dynamics and gear tooth contact. Secondly, in order to simulate the interaction between the small-displacement gear vibration and the large-angular-displacement driveline torsional dynamics, a coupled multi-body dynamic and vibration model is proposed primarily for nonlinear or transient simulation. This modeling technique possesses the capability of obtaining more realistic response and simulating a wide variety of operating conditions as well as the potential to be applied in the multi-body dynamic analysis of more complete driveline system. Thirdly, a series of important dynamic and geometric (primarily due to manufacturing error) effects are modeled and analyzed respectively to quantify and/or qualify their influence. For gyroscopic effect as a critical rotor dynamic factor, the study emphasizes their influence on hypoid gear pair vibration as well as the role of rotor inertia distribution on this issue. For assembly errors i.e. misalignments, their (open full item for complete abstract)

Committee: Teik Lim PhD (Committee Chair); Ronald Huston PhD (Committee Member); David Thompson PhD (Committee Member); J. Kim PhD (Committee Member) Subjects: Mechanical Engineering

Doctor of Philosophy, The Ohio State University, 2012, Mechanical Engineering

Planetary gear vibration causes undesirable noise. It may also excite structural resonances or shorten the life of bearings and other drivetrain components. Extensive theoretical research highlights the interest in this topic, but limited experimental data is available to direct and improve these analytical tools or provide practical design guidance to engineers who face increased pressure to reduce transmission noise. This research provides experimental data that has already confirmed, improved, and suggested new directions for analytical modeling. It is hoped that this intentionally broad effort will continue to show its usefulness in the literature. Experimental methods--including stationary modal analysis and spinning vibration tests--are applied to characterize the planar dynamic behavior of two spur planetary gears. Rotational and translational vibrations of the sun gear, carrier, and planet gears are measured. Natural frequencies, mode shapes, and dynamic response obtained by modal vibration testing are compared to the results from lumped-parameter and finite element models. Both models accurately predict the natural frequencies and modal properties established by experimentation. Rotational, translational, and planet mode types presented in published mathematical studies are confirmed experimentally. Two qualitatively different classes of mode shapes in distinct frequency ranges are observed in the experiments and confirmed by the lumped-parameter model, which considers the accessory shafts and fixtures to capture all of the natural frequencies and modes. The natural frequencies in the high-frequency range tend to gather into clusters (or groups). This behavior is first observed in the experiments and studied in further detail with numerical analysis. There are three natural frequency clusters. Each cluster contains one rotational, one translational, and one planet mode type. The clustering phenomenon is robust, continuing through parameter variations of sev (open full item for complete abstract)

Committee: Robert G. Parker (Advisor); Robert A. Siston (Committee Member); Daniel A. Mendelsohn (Committee Member); Mark E. Walter (Committee Member) Subjects: Mechanical Engineering

Doctor of Philosophy, The Ohio State University, 2012, Mechanical Engineering

This work aims to advance the understanding of nonlinear dynamics of planetary gears and the influence of the key system parameters on dynamic response. Analytical solutions of nonlinear dynamic model are mainly used to conduct investigations on interesting nonlinear dynamic behaviors. An analytical lumped-parameter model, which is parametrically excited by time-varying mesh stiffness and includes tooth separation, shows nonlinear dynamic response. The accuracy of the model is correlated against a benchmark finite element analysis over broad mesh frequency ranges. The nonlinear dynamic model is analytically solved by perturbation analysis. Concise, closed-form expressions of planetary gear dynamic response are obtained for various resonances. The analytical solution is validated by numerical integration and the harmonic balance method. The rapid calculation of dynamic response with acceptable accuracy demonstrates that the analytical solutions are effective for performing parametric studies. The explicit inclusion of key system parameters in the analytical solution shows the impact of the system parameters on planetary gear nonlinear vibration. Mesh stiffness discontinuity from tooth contact loss is considered for the analytical solution that gives nonlinear vibrations. Correlation between the external torque and vibration amplitude proves that tooth contact loss can occur even under large torque. Resonances at multiple harmonics of the mesh frequency are distinguished by different excitation sources. Nonlinear subharmonic resonance characterized by response jump phenomena on both sides of the mesh frequency range where resonance occurs is examined. The impact of system parameters on planetary gear vibrations is investigated by using a generalized planetary gear model including bearing stiffness and relative mesh phase. Use of the well-defined modal properties and closed-form expressions of resonant response confirm the existing mesh phasing rules to suppress s (open full item for complete abstract)

Committee: Robert G. Parker PhD (Advisor); Donald R. Houser PhD (Committee Member); Brian D. Harper PhD (Committee Member); Sandeep M. Vijayakar PhD (Committee Member) Subjects: Mechanical Engineering

Doctor of Philosophy, The Ohio State University, 2010, Mechanical Engineering

The primary goal of this work is to develop mathematical models for planetary gears having an elastic ring gear to conduct numerical and analytical studies to understand the modal properties, parametric instability, and nonlinear gear dynamic behaviors. First, natural frequencies and vibration modes are determined as closed-form expressions for a ring having a circumferentially varying foundation of very general description through perturbation and Galerkin analyses. The simple eigensolution expressions explicitly show the parameter dependencies, lead to natural frequency splitting rules for degenerate unperturbed eigenvalues at both first and second orders of perturbation, and identify which nodal diameter Fourier components contaminate a given n nodal diameter base mode of the free ring. As an application and as the motivating problem for the study, the natural frequencies and vibration modes of a ring gear used in helicopter planetary gears with unequally spaced planets are investigated. Second, the distinctive modal properties of equally spaced planetary gears with elastic ring gears are analytically studied through perturbation and a candidate mode method based on an elastic-discrete model. Two perturbations are used to obtain closed-form expressions of all the eigenfunctions. In the Discrete Planetary Perturbation (DPP), the unperturbed system is a discrete planetary gear with a rigid ring. In the Elastic Ring Perturbation (ERP), the unperturbed system is an elastic ring supported by the ring-planet mesh springs; the sun, planet and carrier motions are treated as small perturbations. All vibration modes are classified into rotational, translational, planet and purely ring modes. The well defined properties of each type of mode are analytically determined. All modal properties are verified numerically. Also the modal properties of planetary gears having diametrically opposed planets and an elastic ring gear are studied through the candidate mode method. Two t (open full item for complete abstract)

Committee: Robert Parker Professor (Advisor); Daniel Mendelsohn Professor (Committee Co-Chair); Chia-Hsiang Menq Professor (Committee Member); Ahmet Kahraman Professor (Committee Member) Subjects: Mechanical Engineering

Doctor of Philosophy, The Ohio State University, 2008, Mechanical Engineering

This study examines the salient effects of sliding friction on spur and helical gear dynamics and associated vibro-acoustic sources. First, new dynamic formulations are developed for spur and helical gear pairs based on a periodic description of the contact point and realistic mesh stiffness. Difficulty encountered in existing discontinuous models is overcome by characterizing a smoother transition during the contact. Frictional forces and moments now appear as either excitations or periodically-varying parameters, since the frictional force changes direction at the pitch point/line. These result in a class of periodic ordinary differential equations with multiple and interacting coefficients. Predictions match well with a benchmark finite element/contact mechanics code and/or experiments. Second, new analytical solutions are constructed which provide an efficient evaluation of the frictional effect and a more plausible explanation of dynamic interactions in multiple directions. Both single- and multi-term harmonic balance methods are utilized to predict dynamic mesh loads, friction forces and pinion/gear displacements. Such semi-analytical solutions explain the presence of higher harmonics in gear noise and vibration due to exponential modulations of periodic parameters. This knowledge also analytically reveals the effect of the tooth profile modification in spur gears under the influence of sliding friction. Further, the Floquet theory is applied to obtain closed-form solutions of the dynamic response for a helical gear pair, where the frictional effect is quantified by an effective piecewise stiffness function. Analytical predictions are validated using numerical simulations. Third, an improved source-path-receiver vibro-acoustic model is developed to quantify the effect of sliding friction on structure-borne noise. Interfacial bearing forces are predicted for the spur gear source sub-system given two whine excitations (static transmission error and sliding frict (open full item for complete abstract)

Committee: Rajendra Singh (Advisor) Subjects: Engineering, Mechanical

Doctor of Philosophy, The Ohio State University, 2007, 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 dyn (open full item for complete abstract)

Committee: Robert Parker (Advisor) Subjects: Engineering, Mechanical