2016 Hackaday Prize entry video:

There are two functioning models right now:

The linear sensor (hereinafter referred to as Linear FCDT) that has the proper geometry (Length/Radius) ratio can measure tilt in a 40 degrees interval and has a relatively good resolution.

The circle-like sensor (hereinafter to as Toroid FCDT) that has the proper geometry can measure tilt in a 360 degrees interval.

There is a little demonstration video of the circle-like sensor in working:

(In this video, the sensors' signal conditioners' (Analog Devices AD598) output is measured with a multimeter, and the measured values are sent to a laptop via RS-232 serial port. Then a LabVIEW program calculates the tilt based on the sensors' characteristic, and indicates it.)

The idea

First, let's imagine three coils placed next to each other. The middle coil is called the primary coil, and the two on the sides are called the secondary coils. Let's place an iron core into the coils' air gap, and excite the primary coil with an AC signal (normally with a sine wave). Now, what will happen? Well, it's basically functioning like a transformer, so depending on the iron cores' position different voltages are being induced in the secondary coils. Then, if I move the iron core, the induced voltages in the secondary coils are changing. With the proper signal conditioning circuit, I made a linear displacement sensor! (By the way, these machines are called LVDTs - Linear Variable Differential Transformers, and are widely used in industry.) There's an awesome website where there is a more awesome simulation about the working of an LVDT: http://www.rdpe.com/ex/hiw-lvdt.htm

Cool. Now, you'd probably heard about what ferrofluid is (if don't: https://www.youtube.com/watch?v=5APHa7vscoI). Ferrofluid is a ferromagnetic fluid which contains nanoparticles of metal, that's why it's being attracted by magnets, and basically functioning like "liquid metal".

The basic idea is that what would happen if you'd remove the LVDT's iron core and replace it with a ferrofluid filled glass tube. Somehow like this:

Well, the ferrofluid would act like the replaced iron core, and as you tilt the sensor, the induced voltages in the secondary coils would change depending on the tilt, so you'd make a tilt sensor!

Linear FCDT

And that's it. That's the basic concept behind the sensor. I call this arrangement the Linear FCDT

(Linear - the coils placed "linearly next to each other; FCDT - Ferrofluid Core Differential Transformer)

Our next task is to make experiments with it. First, we'd like to know what is the maximum value of tilt it can measure. Based on experiments I made - as I mentioned earlier - it's a +/- 20 degrees interval. Why? Well, if you reach a specific state of tilt, the ferrofluid runs out from the air gap of one of the secondary coils, like this:

Thus, there won't be generated any voltage in that secondary coil (or the generated voltage would be insignificant), so the sensor's output voltage will deteriorate.

Our next thing to do is to make a sensor which can measure in a larger range, but first, let's measure the accuracy of this arrangement! After hours and hours of making an extremely precise measurement, I came up with this diagram:

(How the precise resolution measurements were made: https://hackaday.io/project/11225-a-new-high-accuracy-tilt-sensor/log/46066-how-the-precise-resolution-measurements-were-made)

Theoretical background of the Linear FCDT: https://hackaday.io/project/11225-a-new-high-accuracy-tilt-sensor/log/46957-theoretical-background-of-the-linear-fcdt

Toroid FCDT

So, if we would like to have a greater measuring range than 40 degrees, we'd have to redesign the whole sensor. The problem with the Linear FCDT was that the ferrofluid ran out from one of it's secondary coils after reaching + or - 20 degrees of tilt. What if we bend a glass tube like a circle, fill it half with ferrofluid, and turn the coils around it toroid-like (hence Toroid FCDT) with the secondaries...

Our article has been published!
Aron Molnar • 12/24/2016 at 21:51 • 0 comments

Our article about the project has just been published in the Journal of Magnetism and Magnetic Materials!
Thank you for your support!
http://www.sciencedirect.com/science/article/pii/S0304885316322703
Detecting the Moon!
Aron Molnar • 10/09/2016 at 01:36 • 1 comment

Peter Walsh was the one who came up with the idea that if the sensor is truly can reach that high resolution and sensitivity, it's theoretically capable of detecting the gravitational effect of the Moon.
To test the theorem I made a Linear FCDT especially for this experiment. This sensor should have a big L/R ratio (L: length of one coil, R: radius of the cell) (whys explained in this log: https://hackaday.io/project/11225-a-new-high-accuracy-tilt-sensor/log/46957-theoretical-background-of-the-linear-fcdt), and extremely symmetrically winded secondary coils. I made a sensor that has an L/R ratio of 20 or so: it's 196 mm long, the cell's inner diameter is 6 mm, has 5 layers of 0.25 mm coil wire in each coil, and looks something like this:To get reliable data from the sensor, we have to take it to a very massive and vibration-free place and make measurements with it for at least 3 days in a row. We found the proper place at the University of Pannonia on top of a high-tech CNC machine. To make it convenient, I made a little program in LabVIEW that sends the measured data to my email address at every 12th hour for 3 days (the program's VI can be found in 'Files' section).

The measurement was started on 7th of Oct at 11:47 a.m. (GMT+2:00) and we're planning to continue it for 1,5 week.
We got some anomalies in the data, but there is one encouraging fact: we detected a little sine wave signal that got a periode of 24 hours.
This means that we almost detected the gravitational effect of our Moon!
Project is about to be published in a scientific journal!
Aron Molnar • 10/08/2016 at 17:10 • 0 comments

That's right! We wrote an article about the sensor and we are about to publish it in a scientific article - it's under review!
Here is a little section of the article:
Deduction of the Linear FCDT volume formula
Aron Molnar • 10/08/2016 at 13:29 • 0 comments

In a previous log (https://hackaday.io/project/11225-a-new-high-accuracy-tilt-sensor/log/46957-theoretical-background-of-the-linear-fcdt) I showed that in case of $\color{White} \large \alpha < tan ^{-1} \frac{2R}{3L}$ tilt degrees, the volume of ferrofluid found in the (left) secondary coil is: $\color{White} \large V_{sec1}= \int_0^L \frac{R^{2}}{2} [2∙cos^{-1} ( \frac{(L+2x)tan \alpha}{2R} ) -sin (2∙cos^{-1 }(\frac{(L+2x)tan \alpha }{ 2R} ) ) ] dx$ And in case of $\color{White} \large \alpha \geq tan ^ {-1} \frac{2R}{3L}$ tilt degrees, the volume of ferrofluid found in the (left) secondary coil is: $\color{White} \large V_{sec1} =\int_0^ {Rcot \alpha - \frac{L}{2}} \frac{R^{2}}{2} [2∙cos^{-1} ( \frac{(L+2x)tan \alpha}{2R} ) -sin (2∙cos^{-1 } ( \frac{(L+2x)tan \alpha}{2R})) ] dx$ In this log I'm going to show you where this formula comes from.
First, we need to slice the sensor at a point, and calculate the area of the ferrofluid at that point. This area should only depend on values we already know, such as the alfa tilt degree, the L coil length, the R radius, and the x variable. If got the area at that point, we can integrate it along x, and we get the volume of the ferrofluid.

According to the picture above, the area of the fluid is: $\color{White} \large T=\frac{R^2\theta}{2}-\frac{R^2sin\theta}{2}=\frac{R^2 }{2}(\theta-sin⁡\theta )$
Next, we have to express theta with respect to R and h, since we only know the value of R (and we will know the value of h after the next step). We can do it using the simple angle-dependent cosine: With this, the formula of the area looks like this: $\color{White} \large T= \frac{R^2}{2} [2∙cos^{-1}⁡(\frac{R-h}{R})-sin⁡(2∙cos^{-1}⁡(\frac{R-h}{R})) ]$ Now there is only one variable we don't know: h. Let's determine it!

At a chosen x, h equals to:
$\color{White} \large tan \alpha = \frac{ h_{0}-h}{x} \Rightarrow h = h_{0}-x tan \alpha$
And from the picture above, h0 is: $\color{White} \large h_{0} = R - \frac{Ltan \alpha}{2}$ Substituting h0 to h's equation: $\color{White} \large h = R - tan \alpha( \frac{L}{2}+x)$
And that's it! The area of a slice looks like this: $\color{White} \large T = \frac{R^2}{2}[2∙cos^{-1}\big( \frac{(L+2x)tan \alpha}{2R}\big)⁡-2∙cos^{-1}\big( \frac{(L+2x)tan \alpha}{2R}\big)]$ In the formula, the area depend on the R radius, the L coil length, the alfa tilt degree, and the x variable. Our last thing to do is to integrate it along x, and we get the volume of ferrofluid in a coil. But note that in cases of $\color{White} \large \alpha < tan ^{-1} \frac{2R}{3L}$
we integrate from 0 to L, and in cases of $\color{White} \large \alpha \geq tan ^ {-1} \frac{2R}{3L}$ we integrate from 0 to $\color{White} \large Rcot \alpha - \frac{L}{2}$
Experimental and theoretical curves of the Linear FCDT
Aron Molnar • 10/04/2016 at 22:00 • 0 comments

Previous post: Theoretical background of the Linear FCDT (https://hackaday.io/project/11225-a-new-high-accuracy-tilt-sensor/log/46957-theoretical-background-of-the-linear-fcdt)
In the previous post I showed how we can calculate Vsec1, and Vsec2 with respect to the tilt of the sensor. I also pointed to that the measuring range and the sensitivity of the Linear FCDT is strongly depend on the L/R ratio. (Where L and R are shown in the previous post"s first picture.)
In this post I'm going to compare the theoretical and experimental curves of our Linear FCDT.
Our Linear FCDT was tested with the AD598 signal conditioner IC, which is used with LVDTs. The coil length of the sensor was L = 18 mm; the radius of the inner cell was R = 3 mm; the amplitude of the excitation voltage was A = 6 V; the frequency was f = 11 kHz; the M cell constant was determined using the already known dimensions of the cell, and the extreme values of Uout: $\color{White} \large M = 10.847 \frac{mV}{mm^{3}}$ The theoretical curve was determined with the knowledge of the L/R = 6 rate, and the M cell constant:
Theoretical background of the Linear FCDT
Aron Molnar • 10/04/2016 at 21:54 • 0 comments
The Linear FCDT has three coils, which take place next to each other. The primary coil is usually excited with a frequency of 1 to 20 kHz and an excitation voltage range of 1 to 24 V rms.
The cell surrounded by the three coils is exactly half-filled with ferrofluid, so there is a volume of
$\color{White} \large V_{pri} + V_{sec} = \frac{3 L R ^ {2} \pi}{2}$
ferrofluid in the cell. At any tilt of the sensor, there is always a volume of
$\color{White} \large V_{pri}= \frac{ L R ^ {2} \pi}{2}$
in the primary coil. The spare volume of
$\color{White} \large V_{sec} = V_{sec1} + V_{sec2} =L R ^ {2} \pi$
is divided amongst the secondary coils depending on the tilt of the Linear FCDT.
Let's check out the left secondary coil on the picture above. Starting from α = 0 °, in cases of positive α tilt, the Vsec1 amount of ferrofluid will decrease.
- In the case of $\color{White} \large \alpha < tan ^{-1} \frac{2R}{3L}$ tilt degrees, the liquid level can reach the outer wall, so the amount of ferrofluid in the left coil is: $\color{White} \large V_{sec1}= \int_0^L \frac{R^{2}}{2} [2∙cos^{-1} ( \frac{(L+2x)tan \alpha}{2R} ) -sin (2∙cos^{-1 }(\frac{(L+2x)tan \alpha }{ 2R} ) ) ] dx$
- In the case of $\color{White} \large \alpha \geq tan ^ {-1} \frac{2R}{3L}$ tilt degrees, the liquid level can’t reach the outer wall, so the amount of ferrofluid in the left coil is: $\color{White} \large V_{sec1} =\int_0^ {Rcot \alpha - \frac{L}{2}} \frac{R^{2}}{2} [2∙cos^{-1} ( \frac{(L+2x)tan \alpha}{2R} ) -sin (2∙cos^{-1 } ( \frac{(L+2x)tan \alpha}{2R})) ] dx$
Deduction of the formula can be found here: https://hackaday.io/project/11225-a-new-high-accuracy-tilt-sensor/log/47221-deduction-of-the-linear-fcdt-volume-formula
If we plot the values of Uout normalized to 1 in cases of disparate L and R rates between -90 ° and +90 ° it is noticable that the measuring range, and the sensitivity inside that, strongly depends on the L/R rate. In cases of low rate we get a relatively great measuring range, in cases of high rate we get a smaller measuring range, but higher sensitivity.

Next log: Experimental and theoretical curves of the Linear FCDT (https://hackaday.io/project/11225-a-new-high-accuracy-tilt-sensor/log/46959-experimental-and-theoretical-curves-of-the-linear-fcdt)
Experimental and theoretical curves of the Toroid FCDT
Aron Molnar • 10/04/2016 at 21:47 • 0 comments

Previous post: Theoretical background of the Toroid FCDT (https://hackaday.io/project/11225-a-new-high-accuracy-tilt-sensor/log/46947-theoretical-background-of-the-toroid-fcdt)
Now that we know from the previous post that how to calculate Vsec1, and Vsec2, we can move on to calculate Uout of the sensor with respect to the tilt, and compare our results with the experimental data.
In this post I'm going to compare the theoretical and experimental curves of our Toroid FCDT.
The output voltage of the toroidal sensor is given in a form of $\color{White} \large U_{out} = M \times (V{sec1} - V_{sec2})$ The M cell constant was determined using the known dimensions of the cell, and the extreme values of Uout,
$\color{White} \large M = 0.76 mV / mm^{3}$ The theoretical and the experimental curves of the sensor can be seen on the graph below:
Theoretical background of the Toroid FCDT
Aron Molnar • 10/04/2016 at 19:07 • 0 comments

The Toroidal FCDT is consist of three coils just as the Linear FCDT, but the coils were winded toroidal around a glass tube bent in an O-form. Each secondary coil overlays the half of the torus, and they has around 800-800 turns. The primary coil overlays the the whole torus:
The external radius of the Toroidal FCDT is R = 80 mm, the internal radius is r = 3 mm. The inner cell is precisely half-filled with ferrofluid, thus the volume of the fluid in the cell is $\color{White} \large V_{pri} = V_{sec} = R \times r^{2}\times \pi^{2}$ And the volume of $\color{White} \large V_{sec} = V_{sec1} + V_{sec2} = R\times r^{2}\times \pi^{2}$ ferrofluid is divided amongst the two secondary coils depending on the tilt of the sensor. It is obvious that when rotating the sensor, the amount of ferrofluid in the secondary coils is changing linearly with the tilt. In cases of α = 0 ° and α = 180 ° there is an equal volume of $\color{White} \large V_{sec1} = V_{sec2} = \frac{R \times r^{2} \times \pi^{2} }{2}$ ferrofluid in the secondary coils. In cases of α = 90 ° and α = 270 ° the ferrofluid is always in just one secondary coil. It can be seen on the diagram below:
Next post: Experimental and theoretical curves of the Toroid FCDT (https://hackaday.io/project/11225-a-new-high-accuracy-tilt-sensor/log/46956-experimental-and-theoretical-curves-of-the-toroid-fcdt)
3D models
Aron Molnar • 09/24/2016 at 16:10 • 0 comments

We made some 3D models about the sensors and the resolution measurement test bench just to visualize them better. Here they are:
Linear FCDT:
Toroid FCDT:
Resolution measurement test bench:
How the precise resolution measurements were made
Aron Molnar • 09/24/2016 at 13:22 • 0 comments

I've been saying that the Linear FCDT is capable of measuring tilt with a really high resolution, but I didn't say a word about from where do I know that. I just only said that „After hours and hours of making an extremely precise measurements...”. It’s time to say a few words about those extremely precise measurements.
The main idea is that get a laser pointer, attach it to the test bench (picture below), adjust the bench a little bit, see how many millimeters the laser point went from the relative horizontal level on the wall (the wall-test bench distance is about 10 meters), write down the output voltage of the signal conditioner IC, compute the tilt, and do it again at least 50 times.
This is the test bench with the Linear FCDT (sadly, I didn’t take photos with the laser attached to it when we made the measurements):

The schematic of the measurement looks something like this:

So after we tilt the sensor a little bit, the position of the laser point on the wall will change significantly, since L is great. Then we measure x, and compute the tilt with this single equation: $\color{White} \large \alpha = tan^{-1} \frac{x}{L}$
Next, we inspect how the output voltage of the signal conditioning circuit changed, and write down these two number next to each other: ouput of sig conditioner IC - tilt.
With this method, we can do extremely precise measurements, because L is great, so if we tilt the senor just a little bit, the chage of x will be great enough to measure that conveniently.

View all 11 project logs

LinearFCDT_Moon_MeasuringProgram.vi The LabVIEW program for measuring the output voltage of a Linear FCDT, and sending it to an email address in every 12th hour. vi - 38.57 kB - 10/09/2016 at 11:10		Download
SignalConditionerBoardEagle.zip Eagle CAD files for the first sensor signal conditioner circuit. Zip Archive - 70.76 kB - 09/24/2016 at 16:41		Download
PresentationalBoxBoardEagle.zip Eagle CAD files for the presentation box. The board consist of a 230V to +/-15V power supply and a carrier circuit for the AD598 signal conditioner. Zip Archive - 66.02 kB - 09/24/2016 at 16:41		Download
3D_ToroidFCDT-3.123dx Autodesk 123D Design files for the Toroid FCDT. 123dx - 1.44 MB - 09/24/2016 at 16:28		Download
3D_ToroidFCDT-2.123dx Autodesk 123D Design files for the Toroid FCDT. 123dx - 1.72 MB - 09/24/2016 at 16:28		Download

A new high accuracy tilt sensor

Description

Details

The idea

Linear FCDT

Toroid FCDT

Files

LinearFCDT_Moon_MeasuringProgram.vi

SignalConditionerBoardEagle.zip

PresentationalBoxBoardEagle.zip

3D_ToroidFCDT-3.123dx

3D_ToroidFCDT-2.123dx

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Our article has been published!

Detecting the Moon!

Project is about to be published in a scientific journal!

Deduction of the Linear FCDT volume formula

Experimental and theoretical curves of the Linear FCDT

Theoretical background of the Linear FCDT

Experimental and theoretical curves of the Toroid FCDT

Theoretical background of the Toroid FCDT

3D models

Linear FCDT:

Toroid FCDT:

Resolution measurement test bench:

How the precise resolution measurements were made

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A new high accuracy tilt sensor

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Linear FCDT

Toroid FCDT

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Linear FCDT:

Toroid FCDT:

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