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Dynamic Balancing in 1 and 2 planes. [ by Eugenio Úbeda ]
From the author’s Engineering Collection, included in the ETSII4 module.

These programs can be used to characterize the vibrations of a rotating system with trial tests (vector coefficients in g/s), and to calculate the corrective weights to compensate for torsional vibrations in stationary regimes. The programs allow for single or two-plane corrections, where typically the single plane is restricted to systems with shafts not longer than their diameters.

For Single-plane balancing the required data are the initial vibration, the trial weight and the resulting trial vibration.

For 2-plane balancing, the required data are the initial vibrations on each plane, but the trial tests are only needed if the system coefficients are not already known. The results obtained from the trial tests can be saved in an X-Memory file and reused in successive iterations of the corrective weight calculations (magnitude and position). These iterations can be repeated as often as required until the final vibration is within the accepted limits. The program also offers the possibility to enter the characteristic coefficients matrix manually – should their values are known but not currently in the X-Mem file.

Data entry is expected with the magnitude first, and then the position - separated by ENTER^. The angles are referred to the chosen origin and must follow a consistent convention as per their orientation. This applies equally to the vibrations (initial and actual) and weights (total and correcting).


Using the 1-plane balancing method, calculate the corrective weight and its position to compensate for an initial vibration measured like 155 mic. at 30 degrees. The trial test was made using a weight of 200 mic. at 0 deg position, which caused the trial vibration to be 35 mic. and 120 deg.

The results are shown below:

Vector coeff : S1 = 1.258634 g/s <) 342.724356 deg
Correcting weight: W' = 44 g <) 103 deg

If the new measured residual vibration is still V = 12 <)130.
Running a second iteration results in the additional results below:

Vector coeff : S2 = 1.892619 g/s <) 347.860674 deg
Correcting weight: W" = 23 g <) 118 deg
Total weight: Wt = 190 g <) 19 deg


Using the 2-plane balancing technique calculate the corrective weights and their positions to compensate for initial vibrations measured on each plane as: 7 mic at 80 degrees and 5 mic at 130 deg. The trial tests were made using weights of 375 mic at 1800 deg position on each plane, which caused the trial vibrations to be as shown below:

Trial weights            Plane-1 vibration   Plane-2 vibration
375 <) 180 in Plane 1    10.2 <) 25          8.5 <) 15
275 <) 180 in Plane 2    13.0 <) 50          9.5 <) 10

Results. The program calculates the system vector coefficients, which get stored in an X-memory file named “COEFFS”. This file can be used later instead of the trial tests, as it characterizes the unbalance behavior of the system.

    |  W1                             |  W2
P1  |  S11 = 64.768616 <) 73.384289   |  S12 =39.451436  <) 286.455879
P2  |  S21 = 58.588379 <) 255.104623  |  S22 = 42.819398 <) 65.392443

And the correcting weights are shown below:

W1' = 472 g <) 129 deg
W2' = 283 g <) 306 deg

If the new measured residual vibrations are still V1 = 1 <)85 and: V2 = 2.5 <) 110
Running a second iteration results in the additional results below:

W1" = 85 g <) 77 deg
W2" = 53 g <) 192 deg

For an equivalent total corrective weight of:

Wt1 = 529 g <) 122 deg
Wt2 = 266 g <) 295 deg

Note: The program includes 4 functions to perform arithmetic operations in polar mode, with the complex numbers entered in the stack registers as two pairs of {argument, ENTER^, module}; like in the standard P-R convention of the calculator. Their names are “W+”, “W-“ :W*”, and “W/”.
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