Mathematically Simulated Conventional Measurement of Spur Gear Tooth Thickness using 3D Reconstruction

Dimensional measurements are performed to insure adequate performance and functionality of mechanical elements and engineering components. A large variety of well-established and special purpose conventional and contact measuring instruments are designed for different dimensional measurements. However, conventional measuring techniques have some limitations such as sensitivity to environmental conditions, unavailability, cost, time consumption, and part size limitations. In this work, it is suggested to mathematically simulate conventional measuring techniques when they are not applicable. These simulations can be applied on a 3D reconstructed model of the part of interest. In this work the 3D model of a spur gear was reconstructed using photogrammetry. A mathematical model was developed to simulate the well-established measurement of spur gear tooth thickness at both pitch line and constant chord. The proposed approach was applied on different gear teeth and sections. A conventional measuring instrument was used to measure the teeth thickness of the same gear. Simulated and actual measurements were compared to their corresponding nominal values and were all in good agreement. The proposed approach provides an adequate non-contact measurement technique well suited for in-situ measurements of part dimensions with diverse sizes and complexities.