Shaft Rotation Analysis

The total number of rotations of the shaft (I think).

What was the resolution of your encoder, Grasshopper?

I don't quite understand what you will be plotting or what the data you have is telling you. If this is just a two dimensional plot with one axis being the shaft position and the other angular velocity (as your initial posting says) then this implies that the angular position will have a unique angular velocity or vice-versa to be able to calculate the area under a curve. This only makes sense if one only takes one revolution for data.

Your graph has as abscissa φ (the angle) and as ordinate ω (the angular velocity).

If you integrate the result is ∫ω*dφ which has no meaning from the mechanical point of view. If you consider that dφ= ω*dt the integral becomes ∫ω^2*dt which can be performed since ω=f(t). But again I do not see what this could bring you as information.

If in stead of integration you would differentiate you could obtain the angular acceleration which has for the machine dynamics a meaning and even an important one. Of course this is possible without big big errors only if your encoder has a fine resolution.

In this case you have the relation ε=dω/dt and from above equation you have dt=dφ/ω so you can write ε = dω/(dφ/ω) →ω*dω/dφ or going to finite differences with Δω=ω2-ω1; ω=0.5*(ω2+ω1) and Δφ=φ2-φ1→

ε ≈ 0.5*(ω2^2-ω1^2)/( φ2 - φ1 ).

This has to be computed between two successive measures 1 before 2 in time.

If the resolution is fine the values for ε are near to the real ones. For your information there are also new devices to measure accelerations in a continuous way. The above approach of differentiation is related with the generation of a lot of "noise" which pollutes the results.

Hope it will help since with this procedure you have ALL values: angle and velocity measured, acceleration computed. You may go also further and compute the jerk if you expect some thing from it with same procedure but the errors will grow up.

My encoder has a resolution of 2000 pulses per Rev. What each revolution of the shaft corresponds to a certain measure of fluid flowing though this machine. What I want to get is a calibration between the angular position and velocity or even possibly acceleration to the flow rate. I am measure the flow rate at the entrance, and i am collecting this shaft rotation at different flow rates. This is important because in the normal operation of the machine, the rotation of the shaft is the only source of information I can get to measure and control the flow rate though the system. I will post an image of my result, so you can see what it looks like. It seems impossible to curve fit the plot of this graph. I think the result may be the noise you are referring to.

1- Your resolution is too low it should be at least 2x the actual 2- My comment was for dynamic analysis 3- The answers are always function of the clarity of the request and of the given information. Now if you want to have a GOOD information you should give more details if not we still are blind. If you are afraid to give too much in the thread then use the private channel it has a protective scope. Questions you should bring an answer: - what kind of system ? - which flow ? - what generates the flow ? - How is the shaft rotation related to the flow ? Is it a ratio between the shaft rotation and the element generating the flow so that for the considered shaft the cycle covers more than 1 rotation ? Other question could appear when you bring answers to those at least. Could you indicate how you compute the acceleration and what results you got ? Could you show the initial plot speed versus angle ? How did you take the values are they at same time ? Do you have also the time as recorded value ?

An added fly in the ointment, if the OP's icon is any hint, this might be a very compressible fluid.

As far as resolution of the encoder, if the 2000 pulses per revolution is the lines of the rotary encoder and therefore also the number of pulses per revolution of the A and B signals then quadrature decoding will place the resolution at 8000 increments per revolution.

IF this is done, the problem is how its logic is programmed before the counter. Some have only a trigger on the flank of one channel. Thus my comment.

The impossibility to fit a curve seams to me quite curious since one always can fit a curve, the problem being only its "goodness" (a subject discussed not long ago).

An important noise can only occur when the original curve has very important steps which means that it already has an important noise. The question is how the velocity signal was filtered before record and processing. we do not know what kind of sensor was used.

The procedure I suggested is quite robust as long as the basic curve is not too fast changing its slope. I used it for some middle range speed data records where the values were acquired by use of the angle signal trigger and I had no time information.

The question is also what kind of fit is wished! May be reality is more complex than model and the behaviour is not what is thought!

A comment to previous remarks of Y: in fact in a rotating machine there is no constant velocity since ALL machines present a vibration more or less important. The procedure I suggested allows the determination of the accelerations thus of the load changes in quantitative form.

"I plotted angular velocity of shaft with its angular position."

When the load on the shaft varies, the shaft would experience 'tensional load'.

Regarding the angular velocity there could be only three possibilities: Constant velocity, increased velocity (accelerate) and reduced velocity (decelerate).

Constant velocity could represent constant load (could be flow, pressure and like parameters).

Increased velocity (accelerate) could represent increased load.

Reduced velocity (decelerate) could represent reduced load.

I don't think the integral tells you anything. The derivative gives you angular acceleration which could indicate friction, for example.

Have you considered adding a Mass Flow Meter to your tool? Sounds to me like you need one.