Acceleration phase shift with changing RPM.

[dynaman]

Hi guys,

I've been developing a simple dynamic balancer using a MEMS accelerometer and a tacho sensor. I have attached the setup to a rotating disc which is unbalanced by adding a small piece of tape. When I run it up I can see the vibration induced onto the accelerometer which appears as a sine wave. The tacho signal appears as a spike trace and indicates the relative position of the peak acceleration relative to the tacho marker.

My question is; Why does the relative phase shift between the tacho signal and the sine wave occur when the RPM changes? I would have thought the peak acceleration (or imbalance) would occur in the same location regardless of RPM?

cheers

M.

 

[electricpete]

In steady state, for simple static unbalance of machine modeled as single degree of freedom system:

Far below resonance:
displacement is in-phase with unbalance
velocity leads unbalance by 90
acceleration leads unbalance by 180 / lags by 180

At resonance resonance:
displacement lags unbalance by 90 degrees
velocity is in-phase with unbalance
acceleration leads unbalance by 90

Above resonance:
displacement lags unbalance by 180 degrees
velocity lags unbalance by 90
acceleration is in-phase with unbalance

The more damping included in the system, the more gradual the change in steady-state phase as a function of speed.


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(2B)+(2B)' ?

 

[electricpete]

I guess I should have mentioned that as you increase from zero speed you will pass from far below resonance to near resonance to far above resonance (if applicable).

The above conclusions apply to steady state, not transient.

Some machines may have more than one resonance and behavior may be more complicatd than above.

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(2B)+(2B)' ?

 

[Tmoose]

http://users.tpg.com.au/users/ldbutler/Fig1NoiseCancel.jpg

this one shows a curious (too me) phase shift at the low end for a piezo device. I have no knowledge of the importance/significance of the shunt device added.

http://rsta.royalsocietypublishing.org/content/366/1866/785/F25.medium.gif

Is this just a balancing instrument, or does it include a support or base ?

 

[dynaman]

Wow, didn't think about the natural frequency effect. The way I tried to find the heavey spot was like this;

1) Add a large piece of blu-tack or modelling clay at the tacho mark on the disc.

2) Bring the disc up to speed/RPM so that I got a clean sine wave with little noise.

3) Normally the speed I chose allows the peak of the sine wave to match the peak of the tacho trace.

4)Remove the the blu-tack and run up again at the same RPM.

5)Measure the phase shift between the tacho trace and the sine wave peak. (Note the peak is max acceleration).

6) Add a trial weight on the opposite side and try again until the vibration amplitude has reduced.

Sometimes this method works and sometimes it doesn't. Maybe the resonant frequency is giving me trouble here.

How can I get around this problem?

thanks

M.

 

[electricpete]

I think all you are trying to do is a single plane balance? And you have available magnitude and phase and ability to add trial weight. That is a problem that has been solved and re-told many times.

Choose two runs, both at the SAME SPEED, one with “trial weight” (blu-tack) added and one without.

That should be all you need for a single plane vector balance solution using graph paper.

Attached is a spreadsheet that shows the graphic solution.

Vibration without trial weight = O (for original vibration vector)
Vibration without trial weight = O + T (for original vibration vector plus trial vector)
(O+T) – O = T.

T is the vector response that you got from adding your trial weight. Think about how you would rotate and scale T in order to make it equal to –O (equal/opposite of original vibration0. That is how much you need to rotate and scale your trial weight in order to cancel the original unbalance.


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(2B)+(2B)' ?

 

[GregLocock]

I agree, only run at one speed. While you are developing your system do a 4 run method, with a trial weight at 120 degree increments. You can then construct the influence diagram and see what is going on exactly.



Cheers

Greg Locock


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[dynaman]

Great thanks guys and yes this is a single plane balance. I'm assuming that the units for magnitude in your spreadsheet are not critical here? For instance, I have attached my accelerometer to an opamp to magnify the signal and set the gain so I can see the sine wave. The output is a multiple of the accelerometers orginal voltage. (FYI.... I don't change the gain settings between runs).

Another thing I've had to do is add an RC low pass filter to remove any unwanted noise. I know that this produces a slight phase shift but hope that running at the same speed will not make any difference.

thanks again for your help,

M.

 

[GregLocock]

Yes, that sounds fine.

Cheers

Greg Locock


New here? Try reading these, they might help FAQ731-376

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[dynaman]

Guys, I have a question regarding your spreadsheet. The parameter "Ut" has units "inch-ounce" which is a torque. What is the unit for the magnitude value in the green input box (cell C8 under tab "Main")?

 

[Tmoose]

mass x radius

 

[electricpete]

Yup. Units of unbalance don’t matter as long as they represent mass times radius.
(you could use inch*ounce or gram*mm or many other similar items). If you work through the equations to compute correction weight, the vibration units cancel each other out and the unbalance variables cancel each other out (correction weight answer is in the same units as you specified trial weight units).

Vibration Variables: (displacement or veloctity or acceleration)
O = Original Vib (meausred)
O+T = Vib measured after adding trial weight (measured)
T = (O+T) – O = Computed vibration effect of trial weight

Unbalance Variables: (mass time radius)
UO = Original unbalance (unknown)
UT = Trial Weight unbalance (known)
UCW = Correction Weight unbalance (desired final answer)

(All of the above vibration and unbalance variables are 2-D vectors)

We want the correction weight unbalance to cancel out the original unbalance. Therefore we want:
UCW = -UO [Eq 1]

We assume vibration is proportional to unbalance. Therefore:
UO/UT = [O / T] = [O / (<O+T>-O) ]
UO = UT * [O / (<O+T>-O) ] [Eq 2]

Combine Eq1 and Eq2:
UCW = -U0 = - UT * [O / (<O+T>-O) ]
UCW = - UT * [O / (<O+T>-O) ] [Eq 3]

Reformat as ratio:
UCW/(-UT) = [O / (<O+T>-O) ] [Eq 4]

Equation 4 was only to demonstrate that the units of unbalance appear in a ratio and will cancel each other... same for units of vib.

Equation 3 shows how the spreadsheet calculates the required correction weight UCW.


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(2B)+(2B)' ?

 

[dynaman]

Hi guys,

Just want to clarify something. I've been running single plane balancing of my small fan units and all is good. Only thing I'm uncertain is the allowable tolerance of the imbalance. I would like to use ISO 1940 as a guide. If I choose G2.5 as my standard, how can I use the "UCW" variable in the spreadsheet to determine if meet the allowable imbalance?

thanks

Mark.