Analogue Signal Filtering & Conditioning

[fergusson]

Hi,

I am looking for some feedback on a project I am undertaking at the moment and some possible methods that could be used to arrive at a solution - all feedback and ideas are welcome.

Project:

The general idea is that I have a piece of copper wire that is being run between two sets of wheels that are rotating. These wheels are used to profile the copper wire (squash the copper) so if you were looking at it end on it would no longer be a circle but have a flat top and bottom. This wire then has an LVDT resting on top of it to measure displacement of the wire. In reality there is something running below the wire that changes the displacement but for arguments sake lets just say we are trying to measure the wire only as this is also relevant.

We will refer to the two sets of wheels as "Roll 1" and "Roll2" as can be seen in the diagram above. Both Roll 1 and Roll 2 have a flag on them that is being measured and occurs once every rotation so the frequency can be calculated continuously of these rollers and it can vary from system to system. The rollers have a different diameter although there is no specific rule for which is bigger than the other as it can vary from one setup to another.

Theory:

In theory these rollers are perfectly round and have a perfectly finished surface that profiles the copper uniformly as it rotates leaving you with zero displacement change measured by the LVDT and it all works perfectly, but of course this is only theory ...

Problems:

In reality there is a couple of problems that occur:

• Eccentricity - unfortunately due to the minute size of the things we are trying to measure, any eccentricity in Roll 1 and Roll 2 will be picked up by the LVDT, this only gets worse with time as the rollers wear.
• Surface - the surface of the rollers is not always perfectly finished so small deflections in the surface will also be seen by the LVDT as they will be imprinted on the wire.

Requirements:

It is required:

• Remove the Eccentricity and any small deflections that are seen by the LVDT due to the problems above using software
• Visualize the profile that each roller is leaving on the copper wire - once we have done the removal above we need to show the user this eccentricity/deflection profile so that deformation of the roller over time can be seen and replaced if required.

Assumptions:

1. Frequency of the roller can be calculated and should be considered known
2. We have full access to all Raw signals
3. All roller sizes can change
4. All frequencies can change
5. Wire is a defined thickness
6. Rollers are spinning in the region of 5 times per second or below (a lot slower than any introduced noise)

Current Ideas:

• Synchronous Averaging
• FFT
• Low/High/Bandpass Filtering

Filtering I believe is difficult due to the low frequency of the roller combined with the deflections on the surface.However, I am not a signal conditioning guru.

Attached:

Attached is a library that has a filtering test I was doing but I was struggling to get out the filtered profiles and it also doesnt account for surface deflections. There is some Raw data in a tdms file that can be used to do testing.

Any ideas and thoughts would be much appreciated - I have all hardware available including an FPGA although sampling rate is 1KHz at present but could go up if required.

[Henrik_Volkers]

The sound and vibration vis have vis for order analyses

They can be used to 'unfold' the signal sampled in even time to signals sampled to even angle (of the roller 1 and 2) (and mean them)

both rollers have there own periode , so I would start with the dominating one , remove these signals (and use it for this roller defects detektion) and apply the residuum for the second roller (convert to even angle, mean, analyse).

In short:

even angle resampling, averaging, polar plot and boundary check 🙂

Finally: Very good documented question. I wisch I had more time to dig into..

If the roller frequencies change to fast, an angle decoder migth be needed ..

[fergusson]

Hi Henrik,

Thank you for the reply.

I assume you are talking about Order Analysis using the Sound and Vibration Toolkit that is explained in this white paper?

It sounds from that white paper:

"The Order Analysis VIs included in the Sound and Vibration Measurement Suite present the capability to calculate and examine rotational speed and extract the order components from the original noise or vibration signal. Power distribution can be measured as a function of either time or rotational speed and measuring the phase and magnitude of any order component as a function of rotational speed is made easy."

Issues:

• That is what I am trying to do exactly however I still fail to see how this addresses the introduced defects?
• I do not have the Sound and Vibration toolkit?

Thoughts:

• on the most part the frequency of each rotating roller will be constant - there is certain speed up and slow down at the end but they are not relevant
• as they are different periods, by averaging a certain amount of the raw signal and then removing the DC component you can then remove the signal at that frequency for each one of those components - this will then also take into account the defects that you have on the rollers themselves?

I am unsure whether this is similar to what you were describing?

Thanks,

Matt

[Henrik_Volkers]

had a short look into the data..

you should use two timers to capture the rolls index markers, however since the wire get longer at the second roll the first roll periode will not fit 🙂  The second roll add factor 1.0388?? And main periodes seems to come from the first roll

the 3 order of the first roll and the 5th of the second match, so no way to seperate them

[Henrik_Volkers]

I used tone detection to find the main frequencies (loop and the residuals in a shift register for the next detection)

after that i will try a sort to roll periode.. .maybe more tomorrow

[Henrik_Volkers]

More things

- the frequency shift is due to slip ..  there are not 2 rolls, there are 4. Are the pairs mechanically coupled? Otherwise you each of the four rolls will have an individual slip, and your measure the sum of all.

- due to nonlinearities you will find mix frequency content..

- Since there are frequencies 'slipped' and non slipped: If the wire diameter gauge just hold a sample of not moving wire: How does the noise look like? I would bet that due to vibrations you will find some maschine and roll frequencies..

[Henrik_Volkers]

So here is my pause play (Q&D ) up to you to play now 😄 

Took the LDVT signal and applied sine fits (tone detections)

picket n=4 frequencies (manually tweaked a little, to match orders at higher freq )  and sorted all found sines to nearest order or residual (>Freq tolerance)

If a sine match I coerced the freq to the order and map it to XY chart ...

One frequency at 149.xx Hz I assume is due to a motor 😉

[fergusson]

Hi Henrik,

Thank you for taking the time to go through this, I had a couple of questions regarding the work you have done:

1. What are you stating to be the final signal?

2. How are you removing higher frequency components that recur for each roller?

3. How are you selecting the "freq to order unsorted"? What decisions are you making?

4. Where are you visualizing the removed frequencies?

I realise you have put alot of time into this already but would greatly appreciate some comments so I can better understand the decisions you have made or assumptions?

I look forward to your reply.

Thanks,

Matt

[Henrik_Volkers]

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@fergusson wrote:

Hi Henrik,

Thank you for taking the time to go through this, I had a couple of questions regarding the work you have done:

1. What are you stating to be the final signal?

2. How are you removing higher frequency components that recur for each roller?

3. How are you selecting the "freq to order unsorted"? What decisions are you making?

4. Where are you visualizing the removed frequencies?

I realise you have put alot of time into this already but would greatly appreciate some comments so I can better understand the decisions you have made or assumptions?

I look forward to your reply.

Thanks,

Matt

---

Matt,

your picture and task description is based on a lot of simplifications ..

Based on my experience and data you provided, here are some points:

Your sensor is (at least) a mass (small roll, sensor tip) spring (pushing to roll to the wire, and the wire itself) system , measuring the mass distance... hey, you have an accelerometer 🙂  so surrounding floor and maschine vibrations will be picked up, and you have a resonance and more effects ...

If I look at the spikes in the sensor signal I already can imagine the sensor roll jumping and 'ringing'...

As I already asked: You have 2 pairs of rolls.. how are the pairs coupled?

How sensitive to floor vibrations are the wire forming rolls? Are there other vibration sources nearby? 

I bet these vibrations will be seen in LVDT signal, wether by real inprint by the rolls or by the 'accelerometer'.

So I took the LVDT signal and looked for the major n (20-200) sine frequencies in that signal. (This could be done with a single FFT, but the tone detection already have a 'inbetween bins' correction).

So we have an array S_n of  frequencies, now we have to sort this array. If we find frequencies that are harmonic to another,we can assume that these belong together to one 'roll'  or source aka base frequency.

So I started to sort the elements of S_n to groups of harmonics or residual (noise) based on a threshold. I bet there exist already a nice algorythm to find these frequencies ... (linear fit??) .

I simply hand picked four base frequencies, two have quite big amplitude, but no or nearly no harmonics. (only low frequency contend) I assume that these are due to vibrations that couldn't  be filtered by simple mechanical (rubber/air pring based) dampers (that's hard for frequencies below ~5 Hz .. one would use tuned mass dampers)

the other two could be seeen as due to the rollers ..

1. What are you stating to be the final signal?

two of the four xy-chart plots.. , maybe the sign has to be changed..

2. How are you removing higher frequency components that recur for each roller?

I don't remove higher content, I just look for the major signal parts 😉

One could argue that, as long as the residual signal is in a acceptable noise band (RMS value?) the number of selected and removed frequencies is fine 🙂

3. How are you selecting the "freq to order unsorted"? What decisions are you making?

Match as many harmonics as possible?

I plot the 'diff' to nearest harmonic, and hand matched the frequency...

Is the frequency within a threshold limit to a multiple of one of the choosen base frequencies? If yes, choose the base freq. with the lowest diff. or put it to residual. See diagram

4. Where are you visualizing the removed frequencies?

in the graphs, have look at the diagram ...

For every (major) frequency found there is a physical cause, it's up to you to find it.

Harmonics are simple , but since metal forming is a nonlinear process there are some mixed frequencies (sum or differences) of (harmonic) base frequencies.  

And remember to analyse external causes (vibrations)

Still some work to do 😄