Balancing of a linear elastic rotor-bearing system with arbitrarily distributed unbalance using the Numerical Assembly Technique

In this paper, a new application of the Numerical Assembly Technique is presented for the balancing of linear elastic rotor-bearing systems with a stepped shaft and arbitrarily distributed mass unbalance. The method improves existing balancing techniques by combining the advantages of modal balancing with the fast calculation of an efficient numerical method. The rotating stepped circular shaft is modelled according to the Rayleigh beam theory. The Numerical Assembly Technique is used to calculate the steady-state harmonic response, eigenvalues and the associated mode shapes of the rotor. The displacements of a simulation are compared to measured displacements of the rotor-bearing system to calculate the generalized unbalance for each eigenvalue. The generalized unbalances are modified according to modal theory to calculate orthogonal correction masses. In this manner, a rotor-bearing system is balanced using a single measurement of the displacement at one position on the rotor for every critical speed. Three numerical examples are used to show the accuracy and the balancing success of the proposed method.