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-- ThomasHair - 01 May 2007
## Elevation Axis Runout

In preparation for installing the elevation axis front encoder readheads, a runout measurement was made of the encoder tapes and c-rings. Two of the RDP LVDT's were used to measure the runout. Matlab was used to measure the runout in 'live' time.
### LVDT placement

The LVDT's were held in place by mag bases with extension arms at the near the telescope front elevation readheads. The mag bases were mounted to the encoder mounting arm that is attached to the azimuth platform.
The roller tip of the LVDT was then placed perpendicular to the tape surface, and as close to the inside edge as possible. The purpose of this is to keep the LVDT roller tip on the tape as much as possible, and to keep it away frome the 'snake' feature on the encoder tape as possible. However, the space to mount the LVDT's was quite restrictive and avoiding the 'snake' feature was not possible. The 'noise' is seen in the figures where the telescope is moving quite noticeably.
**Notes:** I 'calibrated' the LVDT's on site with a dial indicator, two mag bases, and the National Instruments 'Measurement & Automation' program. I used a conversion factor of 385.014 mV/mm for channel 1 (DX side), and 385.581 mV/mm for channel 2 (SX side).
### Runout Results

On April 30, 2007, three measurements were taken. The first was just a 'static' run of the LVDT's in their mounted positions without the telescope moving. The second was measuring while moving the telescope from horizon to zenith, and the third was from zenith to horizon.
**Notes:** The negative direction of the figures is 'outbound' of the c-ring (for instance, the diameter would be increasing), and positive is 'inbound'.
The samplerate was taken at 8000 samples per second at 2 second intervals (triggers). So, 16,000 samples per interval.
#### Static Elevation Runout:

The figures below are the smoothed data (green plot is Lowess linear fit) versions with a cubic polynomial fit in the middle (indigo and red line). The DX figure is on the left and SX is on the right.

#### Horizon to Zenith Runout:

The figures below are the smoothed data (green plot is Lowess linear fit) versions with a fourier transform fit (red line) and cubic polynomial fit (indigo line). The DX figure is on the left and SX is on the right.

#### Zenith to Horizon Runout:

The figures below are the smoothed data (green plot is Lowess linear fit) versions with a fourier transform fit (red line) and cubic polynomial fit (indigo line). The DX figure is on the left and SX is on the right.

It is notable that these measurements are very similar to measurements taken for previous readhead installations. Previous runout measurements were done by 'eye' with digital dial indicators mounted tangentially to the encoder tape in a similar fashion as the LVDT's. A data program like Matlab was not used, instead, only a maximum and minimum were sighted visually on the dial indicators while the telescope was moving. Also, Jonathan Kern observed that these measurements also appear very simialr to measurements he took a few weeks ago of the HBS.#### MatLab FFT Results:

With Robert Meeks (very much appreciated) guidance and assistance in MatLab, I was able to get good fourier transforms of the raw data. The following figures are the fft's taken of the original data in Matlab. Most noticeable is the slight runout differences between the SX and DX sides. The SX side shows a delta runout of 30-34 microns, and the DX side shows a delta runout of 10-30 microns. ( An example of \the MatLab code used is at the end of this page.)

## Front Readheads Installation

A typical gap for the readheads is approximately .006 inches (152.4 microns). Taking account for the static measurement as 'noise' in comparison to the figures measuring runout with the telescope moving, it appears that the amount of runout does not go outbound more than approximately 40 to 60 microns. This is similar to what has been previously measured. I decided to 'gap' the readheads at .008 inches to compensate for the runout.
I checked the rear readheads gapping and found them to be at about .010 inches. The extra .002 inches in gap compared to what I set the front readheads can be seen in the figures above. As the telscope is moving from horizon to zenith it appears to 'jump' inbound. That would account for the .002 inches in gap difference.
## Rear Readheads Examination

I took the opportunity while comparing gap thickness of the rear and front readheads to check for any debris or 'buildup' between the rear readheads and the encoder tape. I didn't observe anything indicating damage due to particulate buildup, as has been seen with the azimuth readheads.
## MatLab Code

The example below is the code used for the raw data from the SX side moving from Horizon to Zenith. The data vectors used are the two labeled 'HtoZSXx' (time vector) and 'HtoZSXy' (LVDT displacement vector).
% Create time points (in milliseconds)

tmax=1151000;

t = HtoZSXx(1:tmax);

% Set the sampling frequency (Hertz)

fs = 8000;

% Set carrier signal array/vector

a = HtoZSXy(1:tmax);

% 'Filter' through the data and replace any NaN's with the average

% between the two points on either side of the NaN

for i = 1:tmax

if isnan(a(i)) == 1

a(i) = (a(i-1)+a(i+1))/2;

else

end

end

% Fourier transform the signal

A=fftshift(fft(a));

% Create frequency points for the FT

F=[-tmax/2:tmax/2-1]/tmax(1)*fs;

% Create a low pass filter (the number to the right of the "<"

% is the cutoff frequency in Hertz

L=abs(F) < .05;

% Apply the filter to the FT of the signal

AL=L.*A';

% Inverse FT to recover signal and filtered signal

ar=ifft(fftshift(A)); % This is the recovered original signal

al=ifft(fftshift(AL')); % This is the low-pass filtered signal

plot(t,ar,'r')

hold all

title('Horizon to Zenith - SX Side')

xlabel('seconds')

ylabel('mm')

plot(t,al)

The figures below are the smoothed data (green plot is Lowess linear fit) versions with a cubic polynomial fit in the middle (indigo and red line). The DX figure is on the left and SX is on the right.

The figures below are the smoothed data (green plot is Lowess linear fit) versions with a fourier transform fit (red line) and cubic polynomial fit (indigo line). The DX figure is on the left and SX is on the right.

The figures below are the smoothed data (green plot is Lowess linear fit) versions with a fourier transform fit (red line) and cubic polynomial fit (indigo line). The DX figure is on the left and SX is on the right.

It is notable that these measurements are very similar to measurements taken for previous readhead installations. Previous runout measurements were done by 'eye' with digital dial indicators mounted tangentially to the encoder tape in a similar fashion as the LVDT's. A data program like Matlab was not used, instead, only a maximum and minimum were sighted visually on the dial indicators while the telescope was moving. Also, Jonathan Kern observed that these measurements also appear very simialr to measurements he took a few weeks ago of the HBS.

With Robert Meeks (very much appreciated) guidance and assistance in MatLab, I was able to get good fourier transforms of the raw data. The following figures are the fft's taken of the original data in Matlab. Most noticeable is the slight runout differences between the SX and DX sides. The SX side shows a delta runout of 30-34 microns, and the DX side shows a delta runout of 10-30 microns. ( An example of \the MatLab code used is at the end of this page.)

tmax=1151000;

t = HtoZSXx(1:tmax);

% Set the sampling frequency (Hertz)

fs = 8000;

% Set carrier signal array/vector

a = HtoZSXy(1:tmax);

% 'Filter' through the data and replace any NaN's with the average

% between the two points on either side of the NaN

for i = 1:tmax

if isnan(a(i)) == 1

a(i) = (a(i-1)+a(i+1))/2;

else

end

end

% Fourier transform the signal

A=fftshift(fft(a));

% Create frequency points for the FT

F=[-tmax/2:tmax/2-1]/tmax(1)*fs;

% Create a low pass filter (the number to the right of the "<"

% is the cutoff frequency in Hertz

L=abs(F) < .05;

% Apply the filter to the FT of the signal

AL=L.*A';

% Inverse FT to recover signal and filtered signal

ar=ifft(fftshift(A)); % This is the recovered original signal

al=ifft(fftshift(AL')); % This is the low-pass filtered signal

plot(t,ar,'r')

hold all

title('Horizon to Zenith - SX Side')

xlabel('seconds')

ylabel('mm')

plot(t,al)

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Topic revision: r6 - 30 Jun 2008, ThomasHair

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