Rotor unbalance identification plays a critical role in balancing rotors. In this paper, concerned with multi-disc and multi-span rotor-bearing systems, two novel algorithms called the Single Direction Algorithm (SDA) and the Two Orthogonal Direction Algorithm (TODA) are proposed for identifying rotor unbalance from unbalance responses. A matrix method is proposed to solve the problem of the equations being non-linear transcendental, there being too many unknown variables in the equations, and rotor unbalances and bearing coefficients being coupled together. The unbalance responses at all the eccentric discs are necessary for identifying their unbalances. Numerical simulations are conducted to validate the proposed methods. Moreover, an adjustment point is found, and a proper sensor resolution is suggested to achieve high identification accuracy by means of numerical studies. In addition, the identification accuracy of SDA is better than TODA, and SDA is more practical and suitable for medium-speed and high-speed rotors. The proposed algorithms have the flexibility to incorporate any number of bearings and discs and provide a technique for monitoring rotor unbalance without test runs or external exciters.
Identification of bearings’ stiffness and damping coefficients, which strongly affects the dynamic characteristics of rotors, is another inverse problem of Rotor Dynamics. In this paper, aiming at multi-disc and multi-span rotors, two novel algorithms are proposed for identifying each bearing’s coefficients based on the continuous rotor dynamic analysis method. A linear functional relationship between the main complex coefficients and the cross-coupled complex coefficients is obtained, which eliminates the coupling between the coefficients and the rotor unbalance in the forward problem. Then, Algorithm I is proposed. However, it is only suitable for rolling-bearing. To solve the problem, changing the rotating speed slightly is proposed to solve the difficulty that another set of equations cannot be developed because the slope of the proposed linear function is constant when the rotating speed is maintained at a fixed speed. Then, Algorithm II, which can be applied to both rolling-bearing and oil-journal bearing, is provided. Numerical investigations are conducted to study the two methods. It is indicated that there should be a measuring point, called an adjustment point, near each bearing, whose coefficients should be identified, to obtain high identification accuracy. Moreover, the identification accuracy of the two algorithms is strongly related to sensor resolution. When the measuring errors of all the required unbalance responses are zero or the same, the identification errors are almost equal to zero. In conclusion, the proposed algorithms provide a method for monitoring the stiffness and damping coefficients of all bearings in a multi-disc and multi-span rotor under operation conditions to predict rotor dynamic behavior for the safe and steady running of rotating machines.
Continuous rotor dynamics remains stagnant. In this paper, aim at multi-span and multi-disc rotor-bearing system, the continuous rotor dynamic analysis method (CRDAM) is proposed. The force acting on the shaft by the rotating eccentric disc is simulated as a point force. The counterforce of bearing is also considered as a point force. The shaft is considered free-ended. A continuous rotor dynamic model is obtained and an analytical solution is proposed to express the unbalance response as function of the position, unbalance, support stiffness and damping. The proposed method is validated by numerical experiments in which unbalance responses obtained by it are compared with that obtained by the two classical methods the finite element method (FEM) and Ricatti method. The results indicate that the proposed method is applicable to calculating unbalance response of multi-disc and multi-span rotor. Moreover, it is closer to FEM than Ricatti and can be applied to actual high speed rotors. Among the three methods, the calculating speed of Ricatti is the fastest, CRDAM is the second fastest and FEM is the slowest. The proposed method, which solves the forward problems of the continuous rotor dynamics for the multi-disc and multi-span rotors, can provide theoretical basis for further studies on inverse problems such as identification of rotor unbalance and bearing stiffness and damping coefficients without test runs and external excitations.
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