Experimental Vibration Analysis of a WM280 Lathe

Warning: run away if maths & computing aren't for you!

Got a book describing machine tool installation c1930. After levelling the floor, and maybe digging a deep 6" wide trench around the machine to isolate it from nearby machines, the first test is for vibration. Not levelling the bed or runout - they're for later. Vibration gets top priority because it's the main cause of poor finish. To detect it, a mechanical device consisting of several suspended pendulums was plonked on the ways. Any swinging indicated vibration frequencies to aid diagnosis. Much testing at various speeds and cuts. Here I attempt to replace the pendulum device with a computer, and investigate my WM280.

Running machines make noise due to bearings and gear settings. The noise is a rich mix of frequencies. Not a problem unless there's a match to one of the machine's natural resonances causing shaking at the cutting point.

I put a laptop on the bed of my WM280 and used its built-in mic to record the noise idling at 1260rpm. (Ubuntu command arecord -d 180 -D plughw foo.wav records 180s of audio from device plughw (the microphone), and saves it in a unsigned 8-bit mono wav file, sampled at 8000Hz )

Next is identifying frequency spikes in the sound. A wav file is a list of numbers representing frequencies changing over time. The image below is a simple test wave made from 3 clean sine waves and its already hard to see what they are. A Fast Fourier Transform converts the wave from the time domain into the frequency domain producing a sort of histogram showing how frequencies are spread across a spectrum.

Wunderbar, FFT found 3 inputs!

Applying FFT to the WM280 recording:

Complicated result, but big spike at 400Hz, which seems nicely related to the chuck at 21rps (19*21). Also related spikes at about 200, 600, 800, 1000, and 1200Hz.

No conclusions yet! Next, I'll look for lathe settings producing poor finish and repeat to see if it occurs at particular frequencies.

Python program doing the work:

Don't understand why I had to multiply frequencies by 44 to get the graph X scale right. Hate fudge & I'm baffled! A promising start though. My brain is cooked...

Dave

Edited By SillyOldDuffer on 23/05/2020 16:25:25

Good stuff, Dave ... Keep it coming

MichaelG.

That's an interesting experiment.

I expect the odd multiple to get the frequency axis correct is due to incorrect scaling in the time domain to start with. Caveat, see next paragraph.

If the chuck is rotating at 21Hz why is 400Hz (and the times 19) important? I'd expect a fundamental at 21Hz and multiples thereof depending upon the number of teeth on gears.

It might be a bit more difficult to implement but I expect that measurements from a vibration sensor will tell you a lot more than a microphone. Looks like cheap accelerometers are available for the popular single board computers. Quite small vibration levels may well affect surface finish, but won't produce much sound. You definitely don't need resonance to spoil a finish. Machine tool makers will design to avoid obvious resonances. If something is creating a regular impulse the item being impulsed will vibrate, resonant or not.

Andrew

Pulling up a chair and will be following with interest.

I agree a vibration sensor would be better than an audio microphone, but you have a good start.

Thanks Andrew,

I've ordered an Arduino KS037 Vibration Sensor Module (which does analog level and digital level detection) and an accelerometer. The first is simple to program, the accelerometer more tricky. Delivery expected next week.

Tried to justify my 400Hz and times 19 spindle speed claim by relating it to the lathe's change gear set-up and FAILED. On the assumption the noise is change gear whine, I reckon I should be seeing 126Hz, 504Hz and 840Hz. Calculations:

I had the fixed gearbox engaged on the half speed setting and turning the Feed Shaft, but not driving anything. I doubt it explains the discrepancy.

I assumed 19:1 would be the change gear ratio. Not so, if I've done the sums right, fine feed on a metric WM280 banjo is 14:1.

Back to the Drawing Board...

Dave

I did some work on vibration analysis at work, we were interested in the condition monitoring of the bearings on hoists. This proved to be rather difficult due to the short cycle time. On continuously running machines it quite easy to establish the healthy condition and see the deterioration and a traffic light monitoring system can be implemented. After installing accelerometers on the bearing blocks the data could be analyzed by an experienced eye and they did pick up some failing units early. The holy grail of the traffic light was not really workable with the short cycle and variable speed during the short cycle. My exposure to the subject taught me it is a useful tool but the analysis can be complex. It’s very useful for monitoring trends but absolutes are difficult to determine. The company we contracted motor maintenance to did regular patrols of all the important motors and these were fitted with monitoring points for the sensor of the handheld test unit. This is an interesting project SOD making sense of the data will be the hard part I feel.

Mike

Dave - do you have a tone generator to test your microphone response characteristics?

Might help eliminate false positives

Hi Dave,

Could the "44" be the 44 Khz audio sample rate ?

To Andy - yes I have a tone generator, and thanks for reminding me about the need for calibration. Thanks to Andrew I've added a vibration sensor and accelerometer to the microphone as input devices. I don't know what the response characteristics of any of them are - yet.

To John - good idea! Full of optimism I checked the file:

dave@hawk:~/grc$ ffmpeg -hide_banner -i foo.wav
Guessed Channel Layout for Input Stream #0.0 : mono
Input #0, wav, from 'foo.wav':
Duration: 00:03:00.00, bitrate: 64 kb/s
Stream #0:0: Audio: pcm_u8 ([1][0][0][0] / 0x0001), 8000 Hz, mono, u8, 64 kb/s

Blast, it's 64kb/s, not 44!

Have to agree strongly with Mike: 'making sense of the data will be the hard part I feel.' Bitten off more than I can chew and am currently gagging on it. Serves me right for being a smart-ass!

Dave

Edited By SillyOldDuffer on 25/05/2020 11:48:51

It would be useful to have all the data of the mechanical parts like number of balls in races, number of teeth on gears and so on, it surprised me that the vibration analysis guys could identify a cage failing on a ball race, clever stuff.

Mike

This is an interesting insight into the complexity of the subject. **LINK**. Ref Mike's comment above, it seems that there are libraries of bearing signatures available to the pro analysis tools.

many many years ago, when the BBC computer came out I became an asssistant to a noise engineer from Lucas Acton to see if we could design and build a system to detect bearing failures in our UVA internal bore grinders which were grinding the 6mm dia bores of the fuel injector bodies, the current method was a visual check of the bores as finish deteriated as the spindle started to fail and when you had thirty machines grinding the bores a lot of work could be lost before it was detected, sensors were fitted to the spindles and the information was fed back to the BBC computer for analysis, the software was written by the engineer I assisted, we spent months running tests on brand new spindles to determine a base line and then monitoring the actual machines to give us information to say that a spindle needed to be changed, it proved a very interesting and successful exercise, when I moved onto another job it was being looked at to fit to other types of machines.

Martin P

Oops double posting

Edited By martin perman on 25/05/2020 13:24:19

Interesting topic SOD!

May I suggest you have a look at the Noise & Vibration Handbook available to download from the ProSig website:-

<Prosig.com>

I have used their equipment extensively in investigating Internal Combustion Engine NVH problems, from camshaft breakages, crank breakages and probably the most difficult was a recurring geartooth failure in a propeller reduction gearbox on a 4 cylinder diesel engine (which flew a55 backwards!) in a UAV.

Non contact laser 'vibrometers are the way to go these days for their ease of use and adaptability - point and record on any part of the engine! No need to mount accelerometers and in so doing change the mass of a part. They are expensive but can be hired at reasonable cost.

The multiple frequencies you are seeing as harmonics (200, 400, 600, etc) could also be created by 'aliasing' if the sample rate is not correct.

Just a thought re your 44 fudge factor 8000/180 = 44.44444. Your scaling factor in the fftfreq is 8000/size and size is 8000*180

I recently downloaded a FFT app for my android phone, I think I will go lay it on my lathe bed.

Adrian

Edited By AdrianR on 25/05/2020 13:46:02

Thanks for responses and pointers chaps. Even more for me to think about.

The 44 fudge factor mystery is solved. My mistake - I plugged in the wrong sum instead of 1/sampleRate.  See AdrianR's post!

Latest version of the Python program that does the analysis:

Probably ought to mention in connection with the maths that 'data', 'normalData', 'fftResult' and 'xfreqs' are arrays of numbers, not individual values. An audio sample lasting 15 seconds consists of over 100,000 numbers, so - despite the programs' apparent simplicity - it's doing millions of floating point calculations. Not a job for a slide-rule or calculator!

Anyway, next analysis is of something bad! I rubbed a carbide insert on the shoulder of ⌀38mm steel at 1260rpm, which produces an awful 'stop now you idiot' screech. The frequency spectrum is:

There's a fundamental at about 864Hz, second harmonic at 1728Hz, third at 2592Hz, and maybe 4th at 3456Hz. Rubbing vibration completely dominates whatever other noises the lathe is making. So what's vibrating at 864Hz? It can only be the tool.

Applying the tuning fork formula to the size and material of my insert holder gets close:

The formula suggests a 12x10x106mm steel tool would vibrate at 864Hz, which is delightfully close to its actual size, 12x10x100. However, I don't believe it! Unfortunately the tool is clamped to the tool-post with three bolts, and its overhang is only 17mm. I think I'm measuring the vibration of the tool, tool-post, compound slide and saddle. Also, because the tool is rubbing, the vibration may be more forced than free. Not sure what part is played by the tool rubbing on a 33mm diameter shoulder rotating at 21 revolutions per second. Is my insert-holder & tool-post vibrating in tune like a violin string, or is it just responding to a frequency generated by the spindle and tool rubbing at a surface speed of 2.5m/s? I've no idea!

Dave

Edited By SillyOldDuffer on 27/05/2020 14:57:31

That's good; it's saved me writing out the mathematics of the Discrete Fourier Transform to demonstrate the relationship between the x-axis in time and frequency domains. The original FFT algorithm by Cooley and Tukey reduced the number of operations for an N length transform from ~N^2 to ~Nlog2(N), where N is a power of 2. Note that these operations are complex as the Fourier transform uses complex numbers. So each complex multiply is four real multiplies and two additions.

Andrew

Digitising data and the FFT opens the door on applying mathematical filters to data. In this next example I took two samples. The first is of my lathe running at 1260rpm without doing anything useful. The second is the same settings but with the saddle engaged to take a 0.2mm deep cut out of a 38mm diameter steel pipe.

The idea is to extract vibration due to just spinning from vibration due to spinning AND cutting. The subtraction should highlight vibration due to cutting while hiding vibration due to normal running.

So two samples are taken, trimmed to equal length, normalised, and both are analysed by FFT to produce a pair of frequency spectra. Then the difference of the two is taken, and the random noise filtered out by ignoring any frequency counts below a convenient level. What remains is vibration due to cutting.

Three graphs:

The Difference graph shows 7 frequency spikes appear whilst cutting. The good news is they are all small compared with ordinary running : it suggests my lathe doesn't have a vibration problem at 1260 rpm whilst cutting steel at feed-rate 0.28mm per revolution. I've no idea why my test combination of gears, belts and cutting conditions produces these 7 frequencies.

Dave

Edited By SillyOldDuffer on 27/05/2020 16:30:35

I had a go with my phone and a FFT app. Had to put sticky tape over the microphone so it only picked up vibrations.

My lathe vibrates at 100, 200, 300, 600Hz. I am sure is all from the induction motor as it does not change when I stop the chuck.

Quite surprised by the the energy in the higher harmonics, just occurred to me it could be the back chip guard ringing. Will have to check that.

This check did make me take notice of the lathe noises, I realised my motor belt was too loose and slapping against the casing. Ho hum

Adrian

Some interesting results, and as you're discovering the biggest problem is interpreting said results.

As for filtering it's a case of what they didn't say in Star Trek:

It's filtering Jim, but not as we know it.

Filtering in the mathematical sense is a convolution in the time domain, which conveniently transforms to a multiplication in the frequency domain. The Fourier transform exhibits linearity, so for two time series x(t) and y(t) we can say:

x(t) + y(t) <=> X(f) + Y(f)

So the subtraction in the frequency domain is the same as subraction in the time domain, if a bit more convenient in the frequency domain. In a sense it's a filter in that one is saying I don't want that frequency and removing it by subtraction. But of course the 'filter' characteristic would change with each FFT unless the unwanted frequency stayed exactly the same.

Feel free to have a beer after that!

Andrew