Improving electric motor efficiency via shape optimization

December 22, 2015
Real world motor. Credit: Linz Center of Mechatronics (LCM), motor was produced by Hanning Elektro-Werke GmbH & Co KG

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.

To achieve this, the automotive and aeronautic industries often rely on shape , 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 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.

Shape optimization problems are typically solved by minimizing 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 minimizes the cost function while meeting certain constraints.

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.

Final result of optimization. Credit: Peter Gangl, Ulrich Langer, Antoine Laurain, Houcine Meftahi, and Kevin Sturm

"Differentiating with respect to the shape is more complicated than differentiating a function," says Antoine Laurain. "In fact, there are many ways to define shape perturbations and differentiation with respect to shapes. The so-called 'shape derivative' is one incarnation of these possibilities. It allows us to explore a wide range of possible geometries for the optimization." Unlike the topological derivative, which generates a shape with uneven contours, the shape derivative employs a smooth alteration of the boundary. Implementing the obtained shape derivative in a numerical algorithm provides a shape that allows the authors to improve the 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.

Now that they have effectively utilized a shape derivative in optimization, the authors hope to experiment further in the future. "We are currently working on the derivation of the so-called 'topological derivative' for the same nonlinear optimization problem," says Peter Gangl. "This quantity indicates regions where a local change of the material would lead to a decrease of the objective function."

For now, their application of mathematics in the form of a shape-Lagrangian method adapted for nonlinear PDEs results in a that improves the electric rotor's rotation pattern and the motor's overall performance.

Explore further: Improving radiation therapies for cancer mathematically

More information: Shape Optimization of an Electric Motor subject to Nonlinear Magnetostatics, SIAM Journal on Scientific Computing (to be published online on December 22, 2015).

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not rated yet Dec 22, 2015
I wonder what the net result in increased efficiency was. Electric motors are already fairly efficient so it would seem this work would be self limiting, you can't do better than 100% :)
5 / 5 (4) Dec 22, 2015
I wonder what the net result in increased efficiency was. Electric motors are already fairly efficient so it would seem this work would be self limiting, you can't do better than 100%

Every bit is a huge immprovement. Consider that an efficiency increase of 0.1% would mean you now can build 999 powerplants instead of 1000 (what makes motors more efficient makes generators more efficient as well) - and a single powerplant is an expensive piece of hardware.

(Not to mention that you'd suddenly be pumping out 0.1% less CO2 into the atmosphere without adding any filters or upgrading a fossil fuel plant in any other way except for swapping out the generators).
5 / 5 (1) Dec 26, 2015
Please note that motors are usually part of larger systems. One must consider the System design goals, not just the motor. As a result, the motor itself may have different primary design goals.. Some are designed for variable frequency service, some are designed for durability, some are designed for high torque applications, some for light weight, and so on and so forth.

Efficiency isn't always the primary goal, nor would it always be appropriate for the rest of the system.
not rated yet Dec 27, 2015
"(Not to mention that you'd suddenly be pumping out 0.1% less CO2 into the atmosphere without adding any filters or upgrading a fossil fuel plant in any other way except for swapping out the generators)."
I really doubt that a mere .1% improvement in efficiency could ever be used as justification for the replacement of a working generator. Yes, any little bit helps when designing a new plant or device.
not rated yet Dec 27, 2015
Efficient designs mostly lead to a longer useful life, reduced weight and reduced manufacturing costs. That is where the real savings are to a society.

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