Kanika Rajain will defend her thesis on Thursday, January 23rd

• The defence will take place at Salón de Grados of the School of Engineering (Bilbao) and online at 11:00 am

Kanika Rajain (Mathematical Design, Modelling and Simulations) will defend her thesis on the 23rd of January, at Salón de Grados of the School of Engineering (Bilbao) and online at 11:00 am.  
She is currently pursuing a PhD in Computational Mathematics at UPV/EHU and BCAM in Spain, where she is focusing on innovative 5-axis flank CNC machining and its applications. She holds a Master of Science in Mathematics from the National Institute of Technology, Odisha (Rourkela), India, and an undergraduate degree in Mathematics from Delhi University, India. Her research has included projects on evaluating eigenvalues, optimization methods, and dynamic slip inversion for earthquakes, which has led to her role as a Junior Research Fellow at IIT Hyderabad. She has presented her research at various international conferences and has been published in respected academic journals.

Her PhD thesis, 5-Axis Computer Numerically Controlled (CNC) Flank Milling of Free-Form Surfaces Using Straight and Custom-Shaped Tools,  is under the supervision Michael Barton (Group Leader.Ikerbasque Research Associate Professor Mathematical Design, Modelling and Simulations)

On behalf of all BCAM members, we would like to wish her the best of luck in his upcoming thesis defense. 

Abstract:

We introduce a new method for 5-axis flank milling of free-form surfaces. Current methods for planning flank milling paths typically use standard cylindrical or conical milling tools, which are not ideal for achieving fine tolerances required in manufacturing complex free-form surfaces like turbine blades, gears, or blisks. Our optimization-based approach, however, incorporates the shape of the tool into the optimization process, seeking to optimize both the milling paths and the tool shape. Given a free-form reference surface and a guiding path that roughly suggests the motion of the tool, the tangential movement of four spheres aligned in a straight line is analyzed to determine possible tool shapes and their motions. This produces G1 Hermite data in the space of rigid body motions, which are then interpolated and further optimized for both motion and tool shape (Chapter 5). We showcase our algorithm on synthetic free-form surfaces and industrial benchmark datasets, demonstrating that custom-shaped tools can meet acceptable industrial tolerances and outperform traditional, market-available tools.

When dealing with highly complex free-form surfaces, more than a single path of a straight tool is of- ten required to cover it within high machining tolerances. To address this issue, multi-strip path-planning strategies were introduced in the nineties. However, these methods typically resulted in small gaps or over- laps between neighboring paths, leading to artifacts and imperfections in the workpiece. To overcome these issues, we propose a new multi-strip path-planning method for the 5-axis flank milling of free-form surfaces (Chapter 6). This method aims to achieve G1 (tangent-plane) continuity of the neighboring strips along its shared boundaries. Although it may not be possible to achieve both G1 continuity and high approximation quality simultaneously for some geometries, our optimization framework provides a good balance between machining accuracy in terms of distance error and the G1 connection of neighboring strips. We have tested our algorithm on synthetic free-form surfaces as well as industrial benchmark datasets, and the results show that we can meet fine industrial tolerances while significantly reducing the kink angle of adjacent strips, thereby improving the surface finish in terms of smoothness.

Our results on the blisk blade confirm the modeling postulate that G1 continuity can be achieved for sufficiently flat surfaces. The proposed approach is compared with the state-of-the-art commercial software, Siemens NX, both in the simulation and in the physical experiment stage (Chapter 7). The comparisons show that our approach outperforms NX by an order of magnitude in terms of the maximum approximation error as well as smoothness across the neighboring paths.