Trim weight calculation for two plane balancing

[smart2021]

Hi all

I have a 2 plane balancing software which calculates correction weights using the influence coefficient method. But it does not calculate trim weights.

I would like to calculate the amount of trim weight I need to install after trim run. Some of the commercial analysers does this eg: CSI 2130. How can I do this?

I'm more interested in formulas behind this trim weight calculation.

Thanks for your patience.

 

[electricpete]

all symbols below (entries within vectors and matrices) represent complex quantities (magnitude and phase)
[ul]
[li]Vibration vector V = [V1,V2]’[/li]
[li]Unbalance vector U = [U1,U2]’[/li]
[li]4x4 Influence coefficient matrix A satisfies V = A U[/li]
[li]You can calculate U as[/li]
[li]U = - inv(A) * V[/li]
[/ul]

Now the (obvious?) question is how to determine influence coefficient matrix A. The only systematic / general approach I know of (for 2-plane balance) would be to use the same influence coefficients that were used in calculating the correction weight, i.e. determine A based on original vibration and the trial run information. A11 = (V1-O1)/UB1 etc for all 4 elements based on 2 trial runs, one for UB1 and one for UB2.

Why not use results of correction run to recalculate influence coefficients? You don't have enough information to recalculate full influence coefficient matrix from the correction run because (presumably) both both weights were added at the same time.

In specific cases there may be some insight by examining the plots. For example if all vibrations changed roughly along the line to the origin then you could calculate some scalar multiple/ratio of the combined weight add (same proportions at bearing 1 and 2 and same angle difference between the weights) based on the effects of the correction run. Or a bit more sophisticated if both vibrations traveled an angle from the intended trajectoru toward the origin then rotate the weights with same angle between them (combined with scalar change as applicable). In this respect it resembles a static balance in that you scale and rotate the weights based on the results of addition at two planes simultaneously, the only difference being that those weight additions at each end can be different magnitudes and angles (same magnitude ratio and angle difference in the calculated weight).

But absent any insight from looking at the plots, I’m not aware of any systematic/general way to incorporate results of the correction to improve the influence coefficient matrix. But I don’t leave out that there are lots of things I don’t know. Maybe someone else has a better answer.


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(2B)+(2B)' ?

 

[GregLocock]

I've balanced dozens of engines and driveshafts. I don't understand the OP's terminology. What's the difference between a correction weight and a trim weight?

To calculate the influence matrix you need three runs and two accelerometers, unbalanced, trial weight on 1 rotor and then either leave that one or take it off, and a trial weight on the other rotor.


Cheers

Greg Locock


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[GregLocock]

ep- typically i'd just rinse and repeat. The IM shouldn't have changed, but I like to check. My runs are 'cheap', the extra time taken is irrelevant compared with the setup time.

Cheers

Greg Locock


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[smart2021]

Hello All,

Thanks for your replies.

@GregLocock

Correction weights are nothing but balance weights which are obtained after the initial,trail 1 and trial 2 runs.
The trimming of these balance weights are trim weights.

As stated by electricpete I'm confused in calculation of trimming balance weights and its position (angle) because both balance weights were added at the same time.

 

[electricpete]

So you went through a full 2-plane balance, added a correction weight, and don't like where you landed. The options are now:
[ul]
[li]Option 1 - Rinse and repeat as suggested by Greg. That means the post-correction weight run becomes your new original. And you need to do two more trial runs.[/li]
[li]Option 2 - Use the same influence coefficients as you used in calculating the correction weight in order to calculate a trim weight. It doesn't take any advantage of any new information obtained by the post-correction weight run to tweak the influence coefficients. The only thing it learns from the post-correction weight run is the vibration which will become the new "original" vibration which is combined with old influence coefficients to obtain a trim weight. [/li]
[/ul]
For Greg's benefit, the reason option 1 is often not attractive in an industrial plant environment is the difficulty involved in each trial run. If there is a lockout / clearance process involved there can be a lot of time required in between putting your hands in the machine and running the machine. Also for large motors there can be required cooling period between starts or we minimize the number of starts to prolong the motor lifetime. In a few cases there are fluid system lineup changes required every time you start and stop the machine.

Option 2 is vaguely unsatisfying to me. It feels like we should be able to incorporate results of the post-correction run to enhance our influence coefficient estimate somehow. It occurs to me that you might be able to use a fitting process... find the new influence coefficients A1 which satisfy (V[sub]postcorrection[/sub]-V[sub]original[/sub]) = A1 * U[sub]correction[/sub] which are closest to the old coefficients A0 in a least squares sense (note that A1 is underspecified by the equation listed since it is 2 complex equations with 4 complex unknowns). Or maybe there is a Bayesian logic approach. I'm going to ponder that for a bit. I suspect that looking at the plots and using experience/intuition could be a lot more effective than complicated math, but it's still an interesting question.

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(2B)+(2B)' ?

 

[smart2021]

Hi electricpet,


I tried this option2 to calculate trim weight, Just let me know if I understood wrongly

I took Vibration amplitude of Plane I & Plane II after adding balance weight at both locations at the same time as Voriginal and replaced this value with Initial vibration value in the IC matrix.

But the trim weight magnitude and phase is still not matching with values of CSI 2130.

 

[electricpete]

ok then, someone at CSI has figured out something clever there that I don't understand (that's not surprising)

I just asked your question on another forum that has a lot of knowledgeable rotating equipment vibration monitoring professionals. Let's see what they say...

https://www.machineryanalysis.org/p...-calculated-in-general-andor-for-csi-11782316

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(2B)+(2B)' ?

 

[electricpete]

Just thinking out loud, here are some theoretical ways you could proceed that are a lot simpler than what I mused about previously (least squares, Bayesian).

Pick two of the four original complex coefficients and ASSUME they are correct. Then you have two complex equations to solve the remaining two unknown complex coefficients.

Approach 1: If I had to pick two to assume correct, I’d pick the self coefficients A0(1,1) and A0(2,2) coefficients (the ones that relate unbalance at a given plane to vibration near that plane). That would allow you to compute the remaining two influence cross coefficients, i.e
solve A1(1,2) and A1(2,1) from
(Vpostcorrection-Voriginal) = A * Ucorrection
where A = [A0(1,1) A1(1,2); A1(2,1) A0(2,2)]
You could stop there if you’re more confident in your initial self coefficients A0(1,1) and A0(2,2) coefficients than you are in those the cross coefficients.

Approach 2: In theory you could repeat the same exercize assuming instead that the initial cross coefficients A0(1,2) and A0(2,1) were correct and solving for the new self coefficients A1(1,1) and A1(2,2).

You could combine the results from the two approaches by averaging the two resulting matrices from approach 1 and approach 2. Or weighted average if you trust one more than the other. Or you could add in some weighting toward the original unmodified coefficient matrix A0 if you don't trust the process that I outlined very much.

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(2B)+(2B)' ?

 

[electricpete]

CONCLUSION: I can report the most relevant result from the other thread: the CSI calculation for trim weight does indeed use the original influence coefficients from trim balance weight calculation (option 2 from the post 22 Jun 21 16:38).

Discussion: Stepping back it makes sense that would be the way to proceed with the original coefficients if the response was close to what you expected.
[ul]
[li]1 - maybe you scaled back the initial correction weight for some reason. As long as the result was close to predicted, there's no reason to suspect you were using bad coefficients[/li]
[li]2 - maybe the final vibration was much lower than initial vibration and you just want to get it closer to zero. Let's say you final vib is 10% of your initial, then that suggests (assuming linearity) that your correction weight calculation calculation was close but a little off (perhaps due to measurent errors) and would suggest another trim weight calculated using the same coefficients would reduce the vibration by another factor of 10% (again assuming linearity... which of course is not guaranteed especially getting close to 0).[/li]
[/ul]

If the vibration after correction weight doesn't match what you expected, then it's probably time to step back and re-assess the specific situation. I can imagine there might possibly arise a situation where I would be inclined to try the approach mentioned in my preceding post, but it would only be after careful consideration of the details and constraints surrounding the specific balance job.


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(2B)+(2B)' ?