The Story

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The beginnings

The site is intended to tell the story of ‘Vibe,’ which is the name given to the interesting effect discovered by Ivan Garshelis and myself, Ryan Kari. The ‘Vibe’ project came about as a side project carried out at MagCanica – http://www.magcanica.com. Vibe came about as around 2015, when Ivan Garshelis and Ryan Kari were pondering what was the inverse of a magnetoelastic force transducer invented by Ivan several years before and published in the Journal of Applied Physics: https://aip.scitation.org/doi/10.1063/1.3360581 .

Our motivation was to find something new and interesting to explore outside of the standard world of magnetoelastic torque sensing that I was immersed in. We had a number of areas we discussed, but I think it is fair to say that Ivan was bothered for years at the idea there should be an inverse to the bending sensor. The idea was if bending stresses could influence a remanent circumferential magnetization in a member (the stress has an influence on the magnetization) the opposite should be true. Circumferential magnetization (such as from an applied current) should alter the strain in the member (could magnetization cause deflection)? We talked for weeks and carried out numerous literature and internet searches looking for the answer – the closest we found was the Guillemin effect: https://en.wikipedia.org/wiki/Guillemin_effect

As can be noted by the two sentence description in Wikipedia, there isn’t much information available on this effect. A further description is presented in the background section: https://magnetovibe.com/background/

The idea of a current through a wire producing a deflection is so fundamental, surely if it was real, it would have been explored? We were shocked to discover it really hasn’t been, leading us to where we are today.

In the coming posts, I’ll continue jotting down the history of this, and as it continues into the future, look forward to the progress being tracked and available for anyone to follow along. As this is devoted to the story of Vibe, the blog posts will be in chronological order, with the newest at the bottom. Our most recent work will soon find a home in Applications:

Applications

Other pages will be added as required.

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Initial experimental setup

If there was going to be any response, it was presumed that it would be small. The typical saturation magnetostrictive of iron is ~14ppm, and we expected any response to be a fraction of that. I’ll save our hypotheses as to why the effect would not be equivalent to the full magnitude of the saturated value for another section, but could start by assuming the magnetization is not at its fully saturated value. In order to detect such small motions without a full laser interferometer, it made sense to increase the amplitude by using the effect to induce a vibration at the beams resonance frequency. Ivan came up with the setup in which current would be conducted through two beams supporting a weight, allowing current to be conducted through a closed path. The parts were machined, current was conducted as driven by a high power amplifier driven by a frequency generator, and motion was seen to be self sustaining.

Our findings were submitted as an abstract to the 2016 MMM / Intermag Joint Conference held in San Diego.

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2017 Transactions on Magnetics publication

While we attended the MMM conference, we withdrew our paper associated with the conference as we felt that our work and understanding wasn’t complete enough, but also that we couldn’t explain the work within the page limitations. Instead, we decided to take additional time, and submit the final paper to the IEEE Transactions on Magnetics about a year later. The process of writing the paper was not easy – after each long day of working on it and feeling it was well done, rereading it the next day would be humbling. Every single word, sentence, and paragraph was reviewed, reconsidered, and refined again and again and again. As part of the process of writing the paper, our understanding was also constantly challenged as were any assumptions that were made. Ultimately, the process led to a better paper as well as a significantly better understanding of the phenomenon we were observing.

At this point of the research, the biggest assumptions that needed to be challenged were those that we based our understanding. For example, could our observations not have been magnetoelastic in nature but simply have been explained by force being created by current being acted upon by an external field such as that from the Earth’s magnetic field? Was the effect dependent upon the material being magnetostrictive and having a sufficient crystal anisotropy? Our list of questions seemed endless, but we continued to challenge by testing materials and devising experiments. Examples of the materials we tested included:

(i) copper such that we could conduct currents in the Earth’s field that were not magnetostrictive

(ii) materials with both positive and negative magnetostriction (steel versus Nickel)

(iii) magnetic materials that did not have sufficient anisotropy to allow the magnetization to be ‘pulled’ by current.

All our testing continued to support our hypotheses and understanding, which we did our best to elegantly describe within the published IEEE paper.

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Rectangular stock and field per unit current

Following the IEEE paper, we turned our interest to other attributes, with the first being rectangular stock. We were able to obtain sample strips of Alfenol and Galfenol, and turned to other materials that are more readily available in rectangular cross sections. From an analysis perspective, while it is relatively trivial to compute the magnetic field produced by conducted current within a circular wire (at DC), it is another matter on a rectangular member. As easy to use equations weren’t available, I had to turn to vector potential, which can be expressed for various geometries and then differentiated by taking the partial derivative to find the magnetic field. The vector potential for a rectangle can be expressed as:

Expanding this was not a trivial task. The field appeared as might be predicted, in which the largest axial field was at the center of the rectangular beam and would fall towards the ends as the flux reorients into the orthogonal direction.

The field at several specific locations on the conductor could be computed, in which the expansion was greatly simplified, ultimately resulting in:

Although an aside, these equations made it much easier to calculate how much field could be produced as a function of applied current for a given rectangular cross section.

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Energy balance equations

One approach to explain Vibe I wanted to use within our papers from the beginning, was describing the effect as per the magnetoelastic energy balance. However, we agreed that it was just an approximation such that we axed it from our poster and publication. Magnetoelastic effects are often described by using a minimization of energy, in which the applied directions of each component of energy are expressed as angles. Introduction to Magnetic Materials by Cullity is a great source of information to teach these methods.

Elastic energy is often presented as elastic terms dependent on stress, σ , magnetostriction, γ. Magnetic energy is presented as applied field H, and saturation magnetization Ms. Anisotropy is effectively the ‘spring force’ acting to return the magnetization to its initial state, and is expressed as Ku.

As shown in the image, the stress direction for compressive or tensile forces from bending is indicated by the ‘X’ direction, applied circumferential field as induced by current in the ‘Y’ direction, crystal anisotropy will vary depending upon the orientation of any particular crystal, and the resulting magnetization is represented by Ms. In order to solve for a result, the distribution of each crystal dependent upon the structure of the material needs to be considered. To carry this out, Ku will be discretized and solved for independently over the full expected distribution. For the material we were using, we will solve for the distribution of Ku from 0 to π.

An example is shown in the figure below. In A), there is no applied field or stress, in which the magnetization is represented by a uniform distribution from 0 to π . In B), a stress is applied, which the magnetostriction causes the magnetization to rotate toward the direction of applied stress. In C), only a field H is applied, causing the magnetization to rotate toward the direction of applied field. In D), a field and stress are applied. It can be noted the applied field causes the magnetization to rotate away from direction of applied stress by comparing this figure to B). Figure E) is indicating compressive rather than tensile stress, in which F) is compressive stress combined with applied field H.

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Continuation of testing

With an understanding of the fields applied to rectangular cross sections as well as new material samples, we created a second testing platform and started testing simultaneously in San Diego and Pittsfield. Rather than using open-loop or interesting and fun analog feedback circuit to maintain continuous motion, we put together an interface with a dsPIC33F that could provide conditioning for an optical emitter-detector pair used to measure the position of the suspended mass as well as enable closed loop control as a function of position to allow current pulses to be conducted through the beams at a controlled rate. The dsPIC was also connected to the LCD screen shown to provide some immediate feedback to the operator.

I initially started testing non-oriented and grain-oriented 0.25mm thick electrical steel. Much of the work was focused on exploring the setup, duty cycle, and different control loops, and was intended to be exploratory work for another paper. In truth it was very easy to become lost in the details and miss the forest for the trees. While significant numbers of experiments were conducted and we observed differences in the peak stroke obtained as a function of: (i) material, (ii) material composition, (iii) driving current, (iv) pulse width etc., it was difficult to really control each variable independently. It would really be better to return to this work with a better measurement of position and use laboratory control electronics to take control of the experimental setup. That said, the interface we came up with does function as a great showpiece for how simple an apparatus might be to implement the concept in practice (and still sits on my desk ready to be used) – a few dollar emitter / optical detector, low cost microcontroller, and some basic electronics.

Sample data is shown below, in which the shaft length of 63.5mm had 3A current pulses applied at an ~duty cycle of 20%, in which the pulse was ideally applied after the stroke passed through its lowest point and was beginning to rise. After approximately 33 seconds, the feedback was turned off such that the slow decay in oscillation magnitude indicated just how little damping was present in the system. The frequency of the oscillation can be see in the 3rd figure as around 12Hz, which was the expected resonance frequency. The scatter on the FFT was associated with the noise of the position measurement and as it would taken over the full duration of the data being recorded, such that there was likely some change due to the factors such as temperature variation resulting in changes in the shaft length through thermal expansion.

What we learned and demonstrated as part of this is both how simple of an interface can be used to generate the effect, but also how careful one must be when taking data to really characterize one variable at a time. Following this, still in exploratory mode, the effect was turned to a setup that fixed a cantilever at two ends, such that the resonance mode was significantly greater.

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Cantilever fixed at both ends

As shown in the video on the applications page, a cantilever is fixed at both ends, in which one end is on a linear stage that can be displaced in the vertical direction. The video was taken before the electronics were moved into the more aesthetically pleasing circuit board and 3D printed enclosure. By displacing the beam in the vertical direction, strain being placed into the cantilever and the deflection curve changes. An optical emitter / detector pair is configured to detect the position of the cantilever at one location. Amplification and filtering electronics amplify this signal and send it to a microcontroller (dsPIC), which carries out a control loop and is configured to send a pulse of current in phase with the oscillation of the beam, allowing it to sustain its oscillation. If there is more deflection (stress) for the magnetic field induced by current to act on, there is more ‘kick’ creating a greater oscillatory magnitude.

It’s this setup that really shows the potential. The magnitude of the oscillation is proportional to the deflection (or strain) of the beam, such that what is being demonstrated is an ‘active’ strain element measuring deflections of less than 1mm on a beam that was 55mm long, in which the magnitude is changing close to 100mV for 0.1mm of deflection in the regions the slope is the greatest, all with minimal resources applied to optimize the signal. In regards to the plot of AC RMS Versus Deflection, this is a figure indicating the amplitude of oscillation versus deflection, in which the RMS is 0 where the oscillation ceased. The measurement of ‘0’ being the neutral axis wasn’t exact as the measurements taken were relative. It seems that with a pre-load applied and environment controlled, the effect could be harnessed to produce a very good measurement of strain or force.