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

Master of Science, The Ohio State University, 2018, Mechanical Engineering

In this study, a two-dimensional model is proposed for determining theoretical contact lines, tooth separation, and approximated loaded transmission error with frequency spectra thereof, as well as various other output variables such as instantaneous center distance, operating pressure angle, and instantaneous contact ratio when circular runout error is applied to either or both gears in a spur or helical gear pair. As an addendum, a method for calculating off-line of action tooth separation using this model is described for spur gears. Additionally, a three-dimensional model is proposed for determining theoretical contact lines and tooth separation when any combination of circular runout or wobble error are applied to either or both gears in a spur or helical gear pair. Sample analyses are shown for spur and helical gear pairs with runout error applied using the two-dimensional model, and a helical gear pair with various combinations of runout and wobble error applied using the three-dimensional model. The results are discussed qualitatively with respect to the expected effects the applied errors would have on the tooth separation and related variables.

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

Master of Science, The Ohio State University, 2014, Mechanical Engineering

Lubrication systems used in gear trains are intended to serve two distinct purposes: (i) provide the quantities of oil to gear mesh contact interfaces to allow formation of a healthy elastohydrodynamic fluid film and (ii) help remove heat generated at gear mesh contact interfaces. Failure of the lubrication system in either of these tasks often results in a temperature induced contact failure, called scuffing. This study investigates the effectiveness of various lubrication methods in preventing scuffing. A new high-speed gear test set-up is developed specifically for investigating the scuffing performance of high-speed, high-load helical gears operating at realistic oil temperature conditions. The objective of this study is to experimentally characterize the scuffing performance of the helical gears as a function of various lubrication methods and parameters defining each method. Sets of scuffing experiments are performed using the test methodology developed and lubrication methods that successfully prevented scuffing of the gears are identified. The test matrix includes two different automotive drivetrain lubricants and different lubrication methods of forced (jet) lubrication, dip lubrication and mist lubrication. The test specimens consist of gears having three surface finishes, (i) ground–honed gears which were identified as the baseline, (ii) super-finished gears and (iii) phosphate coated gears. The effects of parameters such as jet flow rate, jet velocity and impingement depth on scuffing are investigated and tabulated using the results from the jet lubricated tests. The impact of gear micro-geometry and edge-loading effects on scuffing initiation are also investigated.

Committee: Ahmet Kahraman Ph.D (Advisor); George Staab Ph.D (Committee Member) Subjects: Mechanical Engineering

Master of Science, The Ohio State University, 2009, Mechanical Engineering

In this study, a test methodology for measuring load-dependent (mechanical) and load-independent power losses of helical gear pairs is developed. A high-speed four-square type test machine is adapted for this purpose. Several sets of helical gears having varying module, pressure angle and helix angle are procured, and their power losses under jet-lubricated conditions are measured at various speed and torque levels. The experimental results are compared to a helical gear mechanical power loss model from a companion study to assess the accuracy of the power loss predictions. The validated model is then used to perform parameter sensitivity studies to quantify the impact of various key gear design parameters on mechanical power losses and to demonstrate the trade off that must take place to arrive at a gear design that is balanced in all essential aspects including noise, durability (bending and contact) and power loss.

Committee: Ahmet Kahraman PhD (Advisor); Donald Houser PhD (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, 2005, Mechanical Engineering

In this study, a general methodology is proposed for the prediction of friction-related mechanical efficiency losses of gear pairs. This methodology incorporates a gear contact analysis model and a friction coefficient model with a mechanical efficiency formulation to predict the gear mechanical efficiency under typical operating conditions. The friction coefficient model uses a new friction coefficient formula based on a non-Newtonian thermal elastohydrodynamic lubrication (EHL) model. This formula is obtained by performing a multiple linear regression analysis to the massive EHL predictions under various contact conditions. The new EHL-based friction coefficient formula is shown to agree well with measured traction data. Additional friction coefficient formulae are obtained for special contact conditions such as lubricant additives and coatings by applying the same regression technique to the actual traction data. These coefficient of friction formulae are combined with a contact analysis model and the mechanical efficiency formulation to compute instantaneous torque/power losses and the mechanical efficiency of a gear pair at a given position. This efficiency prediction methodology is applied to both parallel axis (spur and helical) and cross-axis (spiral bevel and hypoid) gears. In the case of hypoid gears, both face-milling and face-hobbing processes are considered, and closed-form expressions for the geometric and kinematic parameters required by the efficiency model are derived. The efficiency prediction model is validated by comparing the model predictions to a set of high-speed spur gear efficiency measurements covering several gear design and surface treatment variations. The differences between the predicted efficiency values and the measured ones are consistently within 0.1 percent. Influence of basic gear design parameters, tooth modifications, operating conditions, surface finish and treatments, lubricant properties, and manufacturing and assembly erro (open full item for complete abstract)

Committee: Ahmet Kahraman (Advisor) Subjects: Engineering, Mechanical

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

This work aims to provide insight into the three-dimensional vibration of gears by investigating the mechanisms of excitation and nonlinearity coming from the gear tooth mesh. The focus is on gear pairs and planetary gears. The forces and moments generated at the gear tooth mesh cause three-dimensional relative displacements of contacting gear tooth, which disengage portions of gear tooth surface (partial contact loss) nominally designed to be in contact. While complete tooth disengagement is the most commonly recognized nonlinearity in gears, partial contact loss is also a source of nonlinearity. A three-dimensional lumped-parameter gear mesh model produces the net force and moment at the gear mesh due to an arbitrary load distribution on the gear tooth surface using a translational and twist spring. Thus, the three-dimensional lumped-parameter model, named the equivalent stiffness model, concisely captures the nonlinear behavior. Both translational and twist stiffnesses depend strongly on spatial displacements at the gear mesh, and so are highly nonlinear and time-dependent. The twist moment periodically fluctuates over a mesh cycle, causing twist vibrations. With gear pairs, there is a twist vibration mode, where the twist stiffness is active, and a mesh deflection mode, where the translational stiffness is active. The dynamic response is nonlinear due to partial and total contact loss. The dynamic displacements distorts the instantaneous dynamic contact loads compared with the static design contact loads. To quantitatively assess nonlinear vibrations of gear pairs, a method is developed to give a closed-form analytical expression of the frequency-amplitude curve. Partial contact loss is captured with quadratic and cubic nonlinear terms. The vibration excitation comes from the time-dependent fluctuations due to periodic tooth engagement. The closed-form solution, found using the method of multiple scales, enables immediate calculation of nonlinear dynamic respons (open full item for complete abstract)

Committee: Robert Parker PhD (Advisor); Gary Kinzel PhD (Committee Member); Henry Busby PhD (Committee Member); Sandeep Vijayakar PhD (Committee Member) Subjects: Mechanical Engineering

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

This work aims at developing linear mathematical models of single-mesh spur and helical gears mounted on compliant parallel shafts, and single span of a serpentine belt with pulleys also mounted on parallel compliant shafts. Both the geared shaft models are hybrid discrete-continuous ones where the gears modeled as rigid disks along with the mesh spring form the discrete elements while the elastic shafts having transverse as well as torsional flexibility constitute the continuous elements. The non-dimensional governing equations along with the natural boundary conditions are developed using the Hamilton's principle. The governing equations of the flexural and torsional shafts vibrations and the equations of motion of the disks are written in an extended operator form to prove the self-adjointness of the system. The assumed modes method is used to discretize the system equations where the matching conditions are incorporated with the use of Lagrange multipliers. Orthonormal global basis functions for flexure and torsion are chosen from separate families forming complete sets. The sensitivities of the natural frequencies of different modes to mesh stiffness, torsional and flexural rigidities of the shafts, and lengths of the shafts are examined and the results are correlated with the modal energy distributions. Excitation in the form of the loaded static transmission error at the gear mesh is identified and converted to the discretized form and the response for the same is calculated. Torsional spring at the gear mesh in the helical gear-shaft model accounts for the energy stored due to the relative tilting of the gears. The rotation speed is high and therefore, the gyroscopic effect is non-negligible. Hamilton's principle is used to obtain the non-dimensional governing equations and the equations of motion of the disks. Excitation in the form of the loaded static transmission error at the gear mesh is incorporated in the equations of motion. The extended operator fo (open full item for complete abstract)

Committee: Prof. Rama Yedavalli PhD (Advisor); Prof. Daniel Mendelsohn PhD (Advisor); Prof. Ahmet Kahraman PhD (Committee Member); Prof. Gary Kinzel PhD (Committee Member) Subjects: Engineering

Master of Science, The Ohio State University, 2013, Mechanical Engineering

In this study, load-independent (spin) power losses of a gearbox operating under dip-lubrication conditions are investigated experimentally. A family of final drive helical gear pairs from an automotive transmission is considered as the example for this investigation. A dedicated gearbox is designed and fabricated to operate a single gear or a gear pair under given speed conditions. The test gearbox is incorporated with a high-speed test bed with power loss measurement capability. A test matrix that consists of sets of tests with (i) single spur, helical gears, or disks with no teeth, and (ii) helical gear pairs of varying gear ratios is executed with three different transmission fluids at various temperatures and immersion depths. Power losses from single gear and gear pair tests at identical operating conditions are compared to break down the total spin loss to its main components, namely gear drag loss, gear mesh pocketing loss, and bearing/seal loss. In addition, the space around the gears within the gearbox will be altered to quantify any influences of enclosures and peripheral shrouds on the spin losses of a rotating gear.

Committee: Ahmet Kahraman Dr. (Advisor); Donald Houser Dr. (Committee Member) Subjects: Mechanical Engineering