Online algebraic identification–based trial-weight-free modal balancing of asymmetric rotor–bearing systems

Asymmetric rotor–bearing systems exhibit parametric excitation and complex vibration behavior due to unequal stiffness along their principal axes, which significantly complicates conventional balancing procedures. Most existing methodologies require trial weights and multiple rotor runs to achieve acceptable vibration levels. A modal balancing method for asymmetric rotors that eliminates the need for test masses is proposed and experimentally validated in this work. The approach is based on an online algebraic identification model that estimates modal unbalance directly from vibration measurements acquired at a single point and at constant rotational speed. A Finite Element model of a multiple-degree-of-freedom asymmetric rotor–bearing system was developed and transformed into a pseudo-modal representation to allow mode-by-mode unbalance identification. The proposed algebraic identifier operates independently of initial conditions and requires only a short time window of the fundamental (1×) vibration component as input. The identified modal unbalance is then used to compute a modal mass arrangement using classical modal balancing principles. The methodology was validated using an experimental test rig comprising an asymmetric shaft with three inertial disks and two supports. Modal unbalance was accurately identified near the first and second critical speeds with errors below 10%, using only 5 s of vibration data. A single balancing run achieved vibration amplitude reductions exceeding 80% in the first mode and between 50% and 80% in the second mode across the operating range of 0–6000 rpm. For comparison, a classical influence-coefficient-based balancing procedure combined with modal balancing required seven experimental runs, including trial-weight runs, to balance the two modes and produced comparable vibration-reduction levels, although with greater variability among measurement locations. These results demonstrate that the proposed method can achieve comparable balancing performance with substantially lower experimental effort, while eliminating trial weights and reducing the number of rotor runs required.