Interactive tool. Determines the plane set for modal balancing: the unbalance proportion and relative angle in each correction plane, from the planes' axial positions, the target mode, and the mode shapes, with a check of the set's authority over the mode. Companion to the at-speed calculator.
This calculator determines the plane set for modal balancing. Enter the correction planes' axial positions, the target bending mode, the controlling plane, and the mode shapes, idealized or from the rotordynamic analysis; it returns the unbalance proportion and relative angle in every plane that move that mode while leaving the rigid balance and every lower mode undisturbed, and checks the set's authority over the mode, in SI or US units, with an explanation in prose of what each result means, save and reload, and a printable report. The result is the set definition the At-Speed Balancing Calculator takes, which then sizes the set's trial masses. Companion tool to At-Speed Balancing: Machines and Procedure. Part of the balancing series.
The calculator's results have been compared with those of a separately written program in 4,000 randomized jobs, and every result agreed with it to within one part in ten million. Further tests confirmed that every set it computes carries no net force or moment and leaves each lower mode undisturbed, and in an independently written rotor model, the sets left the rigid balance essentially undisturbed: at low speed, the bearing forces they produced were no more than 0.17 % of those from the same unbalance in the controlling plane alone.
Sample output
The calculator's output for its first example, the second-mode set of the Modal Balancing section of At-Speed Balancing: Machines and Procedure: four planes on a 1,000 mm bearing span, at 0, 250, 750 and 1,000 mm from the DE bearing, with the NDE quarter plane controlling and idealized mode shapes.
Plane
Position (mm)
Unbalance proportion
Relative angle
DE end
0
0.5
0°
DE quarter
250
1
180°
NDE quarter controlling
750
1
0°
NDE end
1,000
0.5
180°
The diagram of the planes and the printed record for the same example. Click either image to enlarge it.
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