Fast and numerically stable circle fit

We develop a new algorithm for fitting circles that does not have drawbacks commonly found in existing circle fits. Our fit achieves ultimate accuracy (to machine precision), avoids divergence, and is numerically stable even when fitting circles get arbitrary large. Lastly, our algorithm takes less than 10 iterations to converge, on average.Comment: 16 page

Experimental Measurements and Numerical Finite Element Models of Radial Indentation

Incremental Profile Forming (IPF) is a flexible manufacturing process that allows for the forming of complex design profiles on tubular structures. Since its invention at the Technical University of Dortmund (TUD) in 2013, IPF has been the focus of numerous research projects aimed at improving the accuracy of formed part geometry. These projects have shown that open-loop control of the IPF process is inadequate to ensure part geometric tolerances suitable for industrial production. To achieve the required accuracy of formed part geometry, improvements are needed in the sensing of profile geometry, as well as a deeper understanding of the process mechanics to enable the development of control-oriented models. This thesis accordingly presents novel strategies for assessing the accuracy of laser line sensors and aligning them to measure cross-sectional and longitudinal profiles during forming on the IPF machine at TUD. In addition, numerical Finite Element (FE) models for the elementary process of radial indentation were developed in Abaqus and corroborated with experimental measurements. The dynamic response of servo motors controlling indenter motion were also experimentally measured to determine their significance for model-based control schemes. The results showed that the laser line sensors record accurate data within 0.05 mm for use in the IPF process. Additionally, it was found that the laser line sensors can be quantitively aligned in-plane and with a global origin, allowing for coordinate transformations from each sensor with an accuracy of less than 0.2 mm. Stress resultants from the FE process model also showed that circumferential forces are dominant near the indentation region, with dominance relationships being more involved in other regions. Finally, results demonstrated that the indenter velocity was accurate to within 1.16% of the commanded velocity, indicating the indenting servos have a strong ability to reject forming loads during IPF. This work supports the development of both improved sensing and an enhanced understanding of the process mechanics during IPF, paving the way for future model-based control to enhance the capabilities of IPF and reduce the part geometric tolerances to within values suitable for industrial production.The National Science FoundationNo embargoAcademic Major: Mechanical Engineerin