Recent Advances in the Analysis of Spiral Bevel Gears
A review of recent progress for the analysis of spiral bevel gears will be described. The foundation of this work relies on the description of the gear geometry of face-milled spiral bevel gears via the approach developed by Litvin. This methodology was extended by combining the basic gear design data with the manufactured surfaces using a differential geometry approach, and provides the data necessary for assembling three-dimensional finite element models. The finite element models have been utilized to conduct thermal and structural analysis of the gear system. Examples of the methods developed for thermal and structural/contact analysis are presented.
Nonlinear mesh stiffness model using slice coupling for straight bevel gear considering axial mesh force component and extended tooth contact
As one of the most important dynamic excitation sources of the gear system, time-varying mesh stiffness (TVMS) is a key parameter of the gear system dynamics model. To calculate the mesh stiffness of straight bevel gears, a semi-analytical model for calculating the single mesh stiffness (SMS) was proposed based on the infinitesimal method and energy equivalence theory, considering the real transition surface of the tooth root, elastic coupling effects between tooth segments, and nonlinear contact between tooth pairs. Based on the principle of deformation compatibility and force balance and considering the extended tooth contact, which is the phenomenon of the incoming tooth pair coming in contact ahead of the theoretical start of contact and the outgoing tooth pair coming out of contact later than the theoretical end of contact, a semi-analytical calculation model of TVMS was established. Based on the analytical model, the TVMS with different torques and gear parameters was compared with that obtained from the finite element method (FEM). The causes of errors were then analyzed to verify the validity of the semi-analytical method. The results show that the mesh stiffness calculated by the semi-analytical model is in good agreement with that calculated by the FEM, and the calculation efficiency is considerably higher than that of the FEM. Finally, the influence of the gear parameters on the mesh stiffness is analyzed. This study is expected to be helpful in further enriching and developing the calculation theory of gear stiffness and providing a theoretical tool for gear dynamics research.
A Basis for the Analysis of Surface Geometry of Spiral Bevel Gears
Geometrical procedures helpful in the fundamental studies of the surface geometry of spiral bevel gears are summarized. These procedures are based upon: (1) fundamental gear geometry and kinematics as exposited by Buckingham, et al; (2) formulas developed from differential geometry; and (3) geometrical concepts developed in recent papers and reports on spiral bevel gear surface geometry. Procedures which characterize the geometry so that the surface parametric equations, the principal radii of curvature, and the meshing kinematics are systematically determined are emphasized. Initially, the focus in on theoretical, logarithmic spiral bevel gears as defined by Buckingham. The gears, however, are difficult to fabricate and are sometimes considered to be too straight. Circular-cut spiral bevel gears are an alternative to this. Surface characteristics of crown circular cut gears are analyzed.