Actuator goes non linear

The actuator that was deliberately badly designed in order to find improvements. Tom Shelley makes sense of the project

Two researchers in the US recently completed a study of a Lorentz Force linear actuator, that was made to be as non linear as possible in order to challenge computer aided design techniques.

Professor Ian Hunter and Dr Serge Lafontaine, based at The Massachusetts Institute of Technology (MIT) in the US, conducted the project. They made a device that used a moving coil with a static magnetic field generated by 18 square section bar magnets around the coil, magnetised radially, so that the magnetic field was at right angles to the current. The magnetic field passed through cylinders of 1018 steel both inside and outside the coil and bar magnets.

The simple linear formula normally used to predict the relationship between current and force in such devices: force = current x number of turns x length x magnetic flux density, is valid at current densities less than one million amps per square metre. But current densities in leading edge devices, such as the linear actuator developed for use in a needle free drug delivery system developed in the BioInstrumentation Laboratory at the site can be 200 times as great as this.

At such high current densities, the effect of the magnetic filed generated by the coil becomes significant and must be considered. In particular, in the presence of any ferromagnetic material in the return path, the coil generates a force which is different from that predicted by the simple equation, and will still exist even if no magnets are present. For modelling software to be any use, it has to be able to predict this effect, and also the effects of deliberate attempts to make the actuator as non linear as possible. Additionally, the effect of spacing the magnets well apart from each other further adds complication to the geometry.

The software used was ElectroMagneticWorks, which was revealed to us, along with details of the tests undertaken by the MIT scientists. In the experimental set up, the coil was 100mm long, as was the magnetic field zone. Current was supplied via an insulated gate bipolar transistor based power amplifier connected to a large battery bank.

The coil was cooled by pressurised air flowing over it and its temperature monitored. Forces were measured using strain gauges and magnetic flux density by a Hall effect sensor between the coil and magnets. Current pulses were applied to the coil in both directions, so that it could be made to push and pull.
In order to reduce computational requirements, modelling was limited to a representative slab, 25mm thick. This was made by slicing off the front and the back of the actuator, which was modelled in SolidWorks Premium 2009. The air spaces were modelled by creating extra SolidWorks parts to fill spaces, plus an additional 25% of the model X, Y and Z dimensions around it, since the analysis required that at the boundaries of outer air, the magnetic field density should be near to zero. Even in the simplified model, there were 667981 mesh elements and 119393 nodes.

However, it did closely predict the currents, magnetic fluxes and mechanical forces of the real world actuator, in all its non-linearity, and so it is concluded that this methodology can now be relied on to model novel actuator designs, working under fairly extreme conditions.


* An experimental actuator was constructed, that was devised so that it would be particularly non linear, and have large air gaps, complicating its modelling in software

* Nonetheless, the software modelling was able to closely predict the electrical, magnetic and mechanical behaviour of the real world actuator

* The modelling techniques can now be confidently applied to novel, high performance actuators, working under fairly extreme conditions

Tom Shelley

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