Advanced Techniques for Numerical Contact Analysis in Spiral Bevel Gears

The research presented in this dissertation treats the subject of efficient gear contact simulation and is applied to the contact analysis of spiral bevel gears.

Within the current development cycle of mechanical transmissions, computerized tooth contact analysis (TCA) has proven to be an invaluable tool to predict a gear pair’s key contact performance characteristics, while reducing the need for expensive physical prototyping and labor-intensive experimental testing. However, the geometrical complexity of the gear teeth still pose significant computational challenges to the tooth contact simulation for spiral bevel gears. Correctly capturing the spatial nature of the motion transfer and the resulting contact load distribution requires a three-dimensional gear contact model. Finite element method (FEM) based contact simulations are usually conducted, especially in an industrial context, while various tailor-made solutions also exist. When performing the contact detection, many of these solutions tend to apply a general contact detection method (e.g. node-to-surface) that treats the contacting gear teeth flanks as arbitrary surfaces. Not realizing that the gear flanks are designed to transmit motion in a near-conjugate way, leads to inefficient contact searches for which the associated computational cost not only limits TCA’s application to static component-level analysis but also hinders extension towards full-system level analysis or dynamic gear contact simulation.

Building upon the existing concept of the surface of roll angles to efficiently detect contact, this dissertation develops a new penetration-based contact model to compute the three-dimensional contact loads from the actual position and orientation of the real tooth surfaces, whether misaligned or not. The proposed methods show to correctly predict component behavior at a computational cost that enables further application in system-level or dynamic analyses.

An accurate description of the spiral bevel gear tooth surfaces is deep-rooted in the presented methodologies, since this proves vital to precisely describe the gear pair kinematics but also to correctly include all the relevant complex contact phenomena. However, a reference tooth profile, similar to the involute for cylindrical gears, does not exist for spiral bevel gears. Therefore, a mathematical model that simulates the cutting kinematics of the manufacturing process, proves to be indispensable to correctly capture both the gear teeth’s macro- and microgeometry. In this work the five-cut face-milling cutting process is adopted to create a representative geometry of a face-milled spiral bevel gear set.

Contact detection based on the tooth flank’s surface of roll angles, combined with the ease-off topography, has been proposed in the gear literature to reduce the computational load, associated with the contact search. Yet, the ease-off topography, which quantifies the geometrical mismatch of a pair of contacting gear tooth surfaces, shows to hold limitations when moving beyond component-level contact analysis, as it is sensitive to the instantaneous gear pair installment. With the underlying idea of potential application of the presented methodologies within multibody system simulation, the usage of ease-off topography concept for contact detection is abandoned and replaced by a penetration-based contact model. An analytical compliance model is formulated to translate the detected penetrations into appropriate contact loads. The compliance model separates the linear gear tooth deflection components from a tooth pair’s local nonlinear deformation, which arises around the contact zone.

The developed gear contact model with surfaces of roll angles, computed for the gear pair’s actual tooth flanks in the absence of misalignments, is then shown to be well capable of predicting a misaligned gear pair’s contact performance. In contrast, ease-off based contact models would require an update of the (misaligned) ease-off topography, each time the gear pair’s configuration changes (e.g. due to system-induced deflections), reducing their otherwise excellent computational efficiency. The proposed penetration-based gear contact model identifies the contact locations based on the surface of roll angles but computes the flank mismatch based on the instantaneous position and orientation of the real gear tooth surfaces, showing to be more robust to configurational changes. Finally, a strategy to parametrically redefine the gear contact model’s surfaces of roll angles in function of the instantaneous misaligned state of the gear pair, is proposed to further increase the accuracy of the contact detection.

A prototype toolchain is created around the presented techniques for contact modeling, covering the various analyses for unloaded and loaded tooth contact analysis that are an essential part of today’s spiral bevel gear design process. Automated finite element model creation routines are developed to support the validation of the methods against nonlinear FEM-based contact simulations. These tools will greatly support future research into methodological advances