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Theoretical and Numerical Studies on Simultaneous Identification of Rotor Unbalance and Sixteen Dynamic Coefficients of Two Bearings Considering Unbalance Responses

Aiming Wang* and Wei Yao
International Journal of Control, Automation, and Systems, vol. 20, no. 6, pp.1971-2007, 2022

Abstract : Identification of rotor unbalance and support dynamic coefficient plays a critical role in operation safety of large rotating machineries. In this paper, aiming at single-disc and single-span rotors, a novel algorithm called Fine-tuning Rotating Speed and Frequency Domain Fusion Identification (FRS-FDFI) is proposed to simultaneously identify the rotor unbalance and two bearings’ 16 stiffness and damping coefficients based on the Continuous Rotor Dynamic Analysis Method (CRDAM). A major difficulty in the derivation of FRS-FDFI is that it is difficult to obtain the 18 unknown variables (rotor unbalance and bearing coefficients) by directly solving the equations developed based on CRDAM using unbalance responses as input. To overcome it, it is proposed to build six equations in which the unbalance responses at the two bearings and disc are considered as unknown variables and unbalance responses in x and y directions of three measured points are used as input. Then, a linear functional relationship between the bearing’s main coefficient and cross-coupled coefficient is obtained. However, the slope of the proposed function is constant at a fixed speed, which means it is impossible to develop another set of equations just by using more measured unbalance responses. Therefore, changing the rotating speed slightly is proposed to solve the problem and FRS-FDFI is derived. The requirement is measuring the unbalance response at two bearing positions and any other two positions on the shaft. Unbalance responses at the disc are not needed. The effectiveness of the proposed solutions are evaluated by numerical experiments. Simulation results indicate that the estimation accuracy is associated with the repeatability precision of vibration displacement measurement systems. The proposed method provides an efficient and easy implemented approach for the field identification of support stiffness and damping and rotor unbalance without test runs and external excitations.

Keyword : Continuous rotor dynamic, damping coefficient, rotor unbalance, simultaneous identification algorithm, stiffness coefficient.

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