The problem of balancing flexible rotors consists mainly of eliminating rotating bearing forces. Analytical expressions are derived for the deformation and the rotating bearing forces of a rotor, using orthogonal functions. With this kind of representation it is possible to set up simple conditions for the vanishing rotating bearing forces. They lead to a linear system of equations giving the compensating unbalances in each of a set number of balancing planes. Two methods used in practice are theoretically explained and compared. The “N” method employs N planes for balancing a speed range up to, and including, the Nth critical speed and can be characterized by the condition A = 0, see equation (13). The “(N + 2)” method requires two more planes for the same speed range and is characterized by A = 0 and B = 0. It is proved that  
so that in the limiting case of an infinite number of balancing planes (speed range from zero to infinity) both methods are of equal value. The two methods differ for finite N in their accuracy and the amount of calculation. Considering simple examples with known unbalance distribution it will be shown that the main error of the N method is the result of treating B as equal to 0, which it is not, thus accounting for the greater accuracy of the N + 2 method. The additional effort needed for the latter method is justified in those cases where greater accuracy is demanded.
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