Static balancing of blades around a rotor
This sheet attempts at calculating the optimum distribution of weights attached to a rotor in order to keep the unbalance as low as possible.
The weights, typically blades of turbine wheels, are all supposed of similar, though slightly varying masses, spaced at equal angles, placed at the same axial location on the rotor and with their individual centers of gravity all at the same radial location.
Note that the terms used here and the figure in the sheet refer to blades, but the same calculation applies to other situations: from bolts in a flange to ferry's wheel baskets, hammers on a hammer mill or wear plates on a fan.
The sheet is in adimensional form: use whatever units for the blade masses, and all the results will be in those units.
The unbalance, as intended in this sheet, is the point mass that, when placed at the radius where the CoG of blades is, would give the same unbalance as the group of blades.
You specify a starting ordering (at your choice) for the blade masses in the input (blue) box, and the sheet provides a new sorting with (hopefully) a better unbalance.
The calculation is based on a number of random tentatives, with the best result being returned. This means that by repeatedly calculating the sheet, different results are normally obtained: you might use as the input for a new calculation the result of the preceding one. This is easily done by copying the content of the dialog box that opens by clicking the output list (then close it with Cancel), and pasting it into the dialog box of the input list.
The number of attempts is limited only by the computer time available, and is quite restricted for net usage: you might want to ask for support if you have special requirements on this.
You may also specify a sought unbalance (this will normally be zero) in order to counterbalance a known unbalance of the rotor alone: you'll see in the sheet the angular position of the obtained unbalance that you'll normally locate opposite to the location of rotor unbalance.
You may also specify a quasi zero unbalance: any unbalance lower than this value will be considered as equal to zero. You will normally set this value to the maximum acceptable unbalance that does not require further balancing.
If the number of masses is high (more than 60), it may be difficult to read the output list due to the superposition with the input list: simply click on the output list and you will be able to read (and copy and paste) the output list in the dialog box.