In our competitive global society, successful and economical design of automotive and industrial structures is crucial. Optimizing the geometry of individual pieces of complex machines improves performance and efficiency of the entire device.
Langer, along with Peter Gangl, Antoine Laurain, Houcine Meftahi, and Kevin Sturm, co-authored a paper publishing tomorrow in the SIAM Journal on Scientific Computing that utilizes shape optimization techniques to enhance the performance of an electric motor. "By means of shape optimization methods, optimal motor geometries which could not be imagined beforehand can now be determined," says Langer.
Langer and his coauthors apply optimization techniques to an interior permanent magnet (IPM) brushless electric motor, the kind sometimes used in washing machines, computer cooling fans, and assembly tools. The motor's inner rotor contains an iron core and permanent magnets. Because not all parts of the rotor's geometry are able to be altered, the authors identify a modifiable design subregion in the rotor's iron core on which to apply shape optimization. Their objective is to improve the workings of the rotor, thus resulting in a smoother, more desirable rotation pattern.
The authors' optimization procedures stem from Lagrangian methods for approaching nonlinear problems, and demonstrate an efficient, exact means of calculating the shape derivative of the cost function. This simple and comprehensive method allows for the treatment of nonlinear partial differential equations (PDEs) and general cost functions, rather than only linear PDEs. Ultimately, their optimization procedures are able to achieve a 27 percent decrease in the cost functional of an IPM brushless electric motor, the particular example explored in the paper.
For now, their application of mathematics in the form of a shape-Lagrangian method adapted for nonlinear PDEs results in a shape that improves the electric rotor's rotation pattern and the motor's overall performance.
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About the authors: Peter Gangl is a PhD Student in the computational mathematics doctoral program and Ulrich Langer is a professor at the Institute of Computational Mathematics at Johannes Kepler University in Linz, Austria. Antoine Laurain and Houcine Meftahi are researchers at the Institut für Mathematik at Technische Universität Berlin. Kevin Sturm is a researcher at the University of Duisburg-Essen, Essen.
SIAM Journal on Scientific Computing