• adaptive meshing
• contact analysis
• rack and pinion drives
• tooth generation

This thesis presents an automated procedure for the generation, meshing, and tooth contact analysis of rack and pinion drives with variable transmission ratio, commonly employed in steering systems. Various strategies were studied to achieve these tasks and a collection of MATLAB scripts and functions was developed throughout the work, conceived as a key component for a further automated optimization process of rack and pinion design.
The present work takes as its main input 3D teeth geometries generated through a novel hybrid analytical/Boolean approach and subsequently interpolated using NURBS surfaces.
Efficient contact regions detection is achieved through iterative algorithms based on KD-trees, a data structure widely used in computer graphics. This pre-processing step is crucial for the automated generation of the following FEM models. The process begins with the definition of mapped 2D meshes on tooth flanks, featuring progressive refinement, which are the basis to the 3D solid meshes of the entire gearset. This approach enables precise control over mesh characteristics.
An automated FEM model construction strategy is implemented using Ansys Parametric Design Language (APDL), with a focus on contact elements settings to ensure accurate and efficient analysis. Finally, the results of the automated meshing, pre-processing, and FEM analysis are presented for a test case.