Torsional Vibration Analysis

[Vishy007]

Hi,

I have speed Vs Time data from one end of shaft and also from other end of shaft. I want to do torsional vibration analysis in Diadem. Could anyone help with the step by step procedure?

In the results, I would need the angular displacements (°) vs the shaft speed at various orders. Also there should be campbell plot showing critical frequency (having highest angular displacement at particular order of vibration)

Thanks,

Vishnu

[Artemis125]

Vishnu,

I'm not sure exactly what you're looking for but here are some helpful commands for calculation.

There are many functions in DIAdem that can help you with calculations. The following commands can also be found in the analysis area of DIAdem as well.

Call ChnAdd("ChannelGroup/Channel","ChannelGroup/Channel","/Added")
Call ChnSub("ChannelGroup/Channel","ChannelGroup/Channel,"/Subtracted")
Call ChnMul("ChannelGroup/Channel","ChannelGroup/Channel","/Multiplied")
Call ChnDiv("ChannelGroup/Channel","ChannelGroup/Channel","/Divided")

Call ChnOffset("ChannelGroup/Channel","/Offset",0,"free offset")
Call ChnLinScale("ChannelGroup/Channel","/LinearScaled",-1,0)

The first four functions will manupulate two channels (ie time + speed or * or whichever).

The last two (offset and linscale),  will add a constant quantity or multiply by a constant respectively.

There are also functions availble for integration, summation, and differentiation. All of these functions are in the basic mathematics portion in DIAdem analysis.

Hope that helps,

Sadie

[Marcel_ · Accepted solution]

Hi Vishnu,

Assuming speed data is phase correct for both ends of the shaft the difference will be momentary speed difference. You're actually looking for 'displacement' data or twist, so start by integrating both signals in time domain. This should provide a gradually increasing signal. Subtract one from the other and you should be left with a straight line with momentary variations around zero. If it's not straight around zero, then you will have a broken shaft (different speeds) or numerical issues due to long files and limitations during integration. Best option then is to evaluate shorter sections of data as high pass filtering of original or calculated data may introduce errors.

Assuming you start with velocity in °/s, the reading will be in °.

Frequency spectra and order plots will then have to be made for which you can search "Joint Time Frequency and Order Analysis Tool for DIAdem". Don't ask me about that, since I know it exists, but have found easier options using our dynamic frequency analysers.

Plotting order amplitude versus speed should normally show resonances, which you could convert to frequency again to show critical frequencies.

HTH,

Marcel

[Vishy007]

Hello Sadie,

                          Thanks for your reply. I needed little bit more information.

The next answer to my post looks in detail.

Best Regards,

Vishnu

[Vishy007]

Hello Marcel,

                          Thank you very much for the detailed answer. This is informative. I will do this for torsional analysis.

Coming to accelerations, actually I have high resolution data- 10kHz. This has too much oscillations. When differentiated, this results in very high accelerations.

I guess if data points are reduced, the accelerations will be lower.

What should I do reduce the data?

Also one speed data has a missing tooth signal which is shown as deep valley in speed point in each cycle.

Could you please help me to find a method to cut out this valley and join the adjacent points?

Looking forwards,

Vishnu A

[Marcel_]

Hello Vishnu,

Thank you for the explanation.

Firstly you will have to integrate and not differentiate:

°/s -> integrate -> °

°/s -> differentiate -> °/s2

Integration will act as a low pass filter as well so I would not do anything to the 10 kHz sample rate just yet.

If required you can reduce data during opening of the file taking mean value of 10, 20, 50 samples or whatever you require.

There is also a re-sample command in the analysis options to do just that.

Cutting out the valley is probably best done on the high resolution data set. Standard commands like smooth / filter may provide some effect, but often they still leave a ripple and once the ripple is gone, the signal you're interested in is also gone, because you reduced bandwidth too much.

If you calculate the difference between both speed signals you will get a 'flat' line with spikes (either peak of valley). You can build a script using the find command to find the spike. Once you find the spike you can replace the values around that spike (in the original speed signal) with NoValues. Repeat this to end of file and then you're left with a signal in which your valleys have been replaced with NoValues. Note that the following find command can start at the previous location plus an estimated time for 360 degrees to speed up the process. Then use the command to fill gaps replacing NoValues with interpolated values. It will still be a distortion of your signal since it is just a linear approximation which then lacks torsional vibration information, but that is probably the best it will get.

Another option is to use differentiated data to find the valleys since differentiated data which will also result in a 'flat' line (with noise) with sharp spikes showing the locations of the valley.

Having said this, it must also be said that this isn't an easy task. As far as I know there is no Diadem command to do this for you so it will need to be solved using scripts.

b/r

Marcel

[Vishy007]

Hello Marcel,

                        I will try this.

Just to give you added information, I'm analyzing both torsional vibration (°) and accelerations.

So I'm integrating and differentiating the signals to get this data. 🙂

The problem of sampling rate was found during the analysis of acceleration data.

I used "calculate peaks" options to reduce the data as shown in attachment.

The red curve is 10kHz speed signal (rpm)  and green one is from "Calculate peaks" option with a interval width of 100.

Acceleration from red curve is in range of 10000 rad/s2 but at low frequencies - 40 Hz, but for green curve the it ranges from 200 to 300 rad/s2 in frequencies from 200 to 1000 Hz.

So i mentioned this difference in results in last post.

Thanks,

Vishnu

[Marcel_]

Vishnu,

Feel free to send me the data. Even at 10 kHz it's probably within mail limits.

No promises, but it may be worthwile to play around with the data a bit.

I will forward my mail address via private message.

B/r

Marcel

[IanDeaville(ZF)]

Vishnu,

You may have a digital encoder as your angle / speed sensor.  Sampling from encoders at high rates does give a lot of jitter or noise in the signal.  An encoder is counting the steps taken while it is rotating.  When you sample this very quickly the number of steps becomes quite small. 

For example, an encoder with 4096 lines rotating on a shaft at 3000 deg/s will generate 34133 lines per second.  If this is a quadrature encoder, and we have x4 encoding, then we will get 136.5k lines per second.  Sampling from this at 10kHz the average would be 13.653 lines per sample.  Remember that encoders only count whole integer line values - no fractions of a line - so each sampling will really be either 13 or 14 lines, maybe 12 or 15 depending on the actual stability of the speed. 

So your trace of speed will show the speed equivalent to 13 and 14 lines as adjacent samples, interchanging with almost every sample.  Linear averaging the signal will be an effective way to recreate a more realistic speed signal. 

It is better to sample encoders relatively slowly, so the difference in line count from one sample to the next becomes small.  Alternatively use a much higher resolution encoder - higher number of lines per revolution.  10kHz is not high resolution - it is high sample rate.

Regards,

Ian