Dynamic Balancing in 1 and 2planes

11222016, 07:58 AM
(This post was last modified: 11222016 10:34 AM by Ángel Martin.)
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Dynamic Balancing in 1 and 2planes
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 twoplane corrections, where typically the single plane is restricted to systems with shafts not longer than their diameters. For Singleplane balancing the required data are the initial vibration, the trial weight and the resulting trial vibration. For 2plane 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 XMemory 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 XMem 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). Example1. Using the 1plane 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 Example2. Using the 2plane 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: Code: Trial weights Plane1 vibration Plane2 vibration Results. The program calculates the system vector coefficients, which get stored in an Xmemory file named “COEFFS”. This file can be used later instead of the trial tests, as it characterizes the unbalance behavior of the system. Code:  W1  W2 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 PR convention of the calculator. Their names are “W+”, “W“ :W*”, and “W/”. 

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