Finding accelerometer location inside a phone

[Haversin]

I hope this experiment has not already been discussed. It's finding the location of the accelerometer inside a phone by placing the phone on a turntable and recording the accelerometer readings while the turntable is rotating. Combined with the phones position relative to the spindle (rotation center) and the turntable rotation speed, the location of the accelerometer can be calculated. To simply the calculations the middle right side of the phone was placed adjacent to the spindle with the z axis pointing up.
The first plot shows a run with accelerometer and gyro Wz data recorded. 

   

It's noted that the accelerometer Ax and Ay show bias terms of -0.27 and 0.085 m/s^2 respectively.

The second plot shows a different run with linear acceleration and gyro Wz data recorded.

   

 The linear acceleration Ax and Ay do not show bias terms but overshoot zero as the turntable is slowing down.


  Both runs start with the turntable stationary then the turntable is turned on and speeds up to 45 RPM. The turntable is then turned off and slows down to a stop.

[Haversin]

Here are some accelerometer position results from the data shown previously. First the geometry and calculation of accelerometer position is shown below. 
   
Photo of the actual setup.
   
Alignment of the phone x axis and turntable x axis is done by placing the center of the phone's right side against the spindle. 
   The position calculated using accelerometer, accelerometer minus bias and linear acceleration data did not agree so an alternative method of measuring accelerometer position was used for comparison. This other method I'm calling the “null method” and involves varying the phones position on the turntable until the Ax and Ay readings go to zero while the turntable rotates. Because the spindle is in the way for free positioning of the phone, the phone is placed on a small platform above the spindle. The null method setup is shown here.
   
The remote control feature of Phyphox came in very handy for this because I could start recording data after the turntable got up to full speed. With no startup transients on the graphs the scale of the plots remained small and I could clearly see the mean of Ax and Ay getting close to null. Once null was established a felt marking pen was used to trace circles on the glass cover of the phone. These marked circles allow the center of rotation and hence the accelerometer position to be measured.
Here is the accelerometer minus bias null position.
   
A table of the results.
   
The largest difference between the calculated position and the null position was seen in the linear acceleration with 1.6 cm, accelerometer was 3 mm and accelerometer minus bias was about 2 mm. Of course these results will probably vary with the type of phone.

[Physikator]

This should be included in the "sensor database experiment" :-)
My approach would have been to measure the distance of the sensor to the axis using the "centripetal force" experiment several times at different orientations relative to the spindle and then finding the intersection of the resulting circles. Unfortunately I don't have a turntable.

[Haversin]

My approach would have been to measure the distance of the sensor to the axis using the "centripetal force" experiment several times at different orientations relative to the spindle and then finding the intersection of the resulting circles. 

I like this idea, it's sounds like a 2 D version of how GPS works. For the first position/orientation I'd use middle right side of phone against the spindle (same as above). For the second I tried the middle top of the phone against the spindle and when I turned on the turntable the end of the phone hit the tone arm support  no damage done  I will need to use a platform to rise the phone above the tone arm support.

[Sebastian Staacks]

This should be included in the "sensor database experiment" :-)

If only we could give our users detailed instructions to characterize all the sensors and expect them to follow them properly...

[Physikator]

Not owning a turntable I used my salad spinner. I placed a circular piece of paper in there, placed my phone and measured the radius of the rotary motion. The better way would be to move around paper and phone and always mark the new center of rotation, then you can do it with compasses. I did it the other way round: I placed my phone in different positions and marked the outline of the phone (or part of it), overlaid them in a graphics software and then did the above. And it worked surprisingly well. However, I do not recommend the salad spinner (too clumsy), the old turntable is probably better.


  Ortung_Beschleunigungssensor_2.pdf (Size: 1.5 MB / Downloads: 866)
(now containing "theroretical" position of the chip)

Last of the measurements:
   

Anyway, using two components of the accelerometer is a lot more elegant since you only need one run.

[Haversin]

 I placed my phone in different positions and marked the outline of the phone (or part of it), overlaid them in a graphics software

Very nice. It's interesting how different the accelerometer positions are! The natural question is how accurate are all these different methods for determining the accelerometer position? Short of taking apart the phone, the only way I can think of is by using an accelerometer/gyro breakout board were the true position is known and then a applying the different methods to see how close there position estimates are. Is there any other way?

[Sebastian Staacks]

Short of taking apart the phone [...]

Luckily, quite often you do not have to, because others already did so. For many of the more popular phone models, you can find teardowns with photos on http://ifixit.com, which often even identifiy some of the chips on the main board.

[Haversin]

you can find teardowns with photos on http://ifixit.com, which often even identifiy some of the chips on the main board.

Thanks Sebastian, great idea ! if I can get photos of the front and rear sides of the motherboard for my phone (Galaxy J7 Crown) then I can transform the accelerometer position estimate from the experiment into image coordinates and see if there is a chip there.

[Physikator]

Opening an iPhone (6) is not that difficult, I recently had to exchange my gps module (kaputt.de has spare parts, tools and excellent videos!). From iFixit I located the sensor and inserted it into the pdf of my above post. I'm off by 7mm in my measurement. Meaning I would have soldered out the wrong chip