Dynamics of hypoid and bevel geared rotor systems

This dissertation research is primarily focused on the development of an analytical multiple-degrees of freedom vibration model for analyzing hypoid or bevel geared rotor systems with emphasis on automotive applications. The focuses are on the modeling of the gear meshing mechanism and development of the basic understanding of the generation of gear whine response related to the vibratory characteristics of the geared rotor system.; First, the spiral bevel and hypoid gear tooth surfaces in three-dimensional space are defined analytically and generated numerically by the simulation of the cutting process. Kinematic mesh simulation is developed to predict the unloaded kinematic transmission error and the theoretical contact path of idealized hypoid gear designs. An exact spatial mesh position and force vector theory is explicitly derived. Then, a generic three-dimensional coupled translation-rotational vibratory model for analyzing hypoid and bevel geared rotor systems is developed. The mesh formulation is based on the geometric characteristics and mechanics of contact cells on the gear tooth surface. The formulation applies the loaded transmission error as the primary excitation source, and includes the effects of gear backlash, friction, load, time-varying mesh position and force vectors. The modal properties and force transmissibility are computed using a reduced linear time-invariant dynamic model by assuming stationary mesh stiffness and load vectors. The effect of pinion offset and spiral angle on the system vibratory response is analyzed. Furthermore, a translation-torsional coupled non-linear time-varying mesh dynamic model based on the loaded contact analysis of hypoid gears is studied numerically. The effects of the gear backlash non-linearity and friction force are also included. This study investigated the effect of time varying mesh vectors on the cross-axis gear vibration for the first time. An experiment was conducted to provide a glimpse of the complex gear noise and vibration phenomena. The measured response is also used to partially verify the proposed model.