In our competitive global society, successful and economical design of automotive and industrial structures is crucial and optimising the geometry of individual pieces of complex machines improves performance and efficiency of the entire device.
The automotive and aeronautic industries often rely on shape optimisation, an approach that uses modeling to create a framework for making devices as smooth and efficient as possible. “A smoother rotation of the rotor can increase the energy efficiency of the motor, and at the same time reduce unwanted side effects like noise and vibrations,” says mathematician Ulrich Langer.
Langer, along with Peter Gangl, Antoine Laurain, Houcine Meftahi, and Kevin Sturm, co-authored a paper publishing in the SIAM Journal on Scientific Computing that utilises shape optimisation techniques to enhance the performance of an electric motor. “By means of shape optimisation methods, optimal motor geometries which could not be imagined beforehand can now be determined,” says Langer.
Shape optimisation problems are typically solved by minimising the cost function, a mathematical formula that predicts the losses (or ‘cost’) corresponding with a process; the end goal is the creation of an optimal shape, one that minimises the cost function while meeting certain constraints.
Langer and his co-authors apply optimisation 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 optimisation. Their objective is to improve the workings of the rotor, thus resulting in a smoother, more desirable rotation pattern.