Effects of Stator Stiffness, Gap Size, Unbalance, and Shaft’s Asymmetry on the Steady‐State Response and Stability Range of an Asymmetric Rotor with Rub‐Impact

Abstract

The asymmetric rotor and the rub-impact behavior are important sources of instability and may cause severe vibrations. However, the dynamics of the rotor-bearing system simultaneously considering the two factors has not gained sufficient attention in available investigations. In this paper, the steady-state response and stability of an asymmetric rotor with rub-impact were evaluated. The asymmetric rotor was modeled by beam elements with asymmetric cross section, and the nonlinear equations of motion were established in the rotating frame. The multiharmonic balance (MHB) method was employed to obtain the linearized form of the nonlinear equations of motion. Either the asymmetry of rotor or rub-impact can result in instability and make the problem difficult to solve. Thus, the arc-length method was utilized to trace the branch of the solutions. In order to improve the calculation speed and accurately predict the solution, the alternating frequency/time domain (AFT) was adopted to calculate the iteration of the arc-length method. Based on the proposed method, the effects of stator stiffness, gap size, unbalance, and asymmetric in shaft on the steady-state response and stability were obtained.

Nonlinear vibration analysis of forced response for rubbing problems using the automatic differential frame

“…Firstly, to show the accuracy of the presented method, validation in frequency domain is carried out by comparing our results with those obtained by Zheng et al 34 Stator stiffness k , initial clearance g , and friction coefficient μ are 1 × 10 6 N/m, 0.15 mm, and 0.15, respectively, which the essential system parameters. The first five harmonics are retained in the validation model, and results are illustrated in Figure 6.…”

“…The equation of motion of the system rub-impact forces in the rotating frame is 34 where m , c s , and k s are the mass matrix, damping matrix, and stiffness matrix of the rotor; Ω c cor is the matrix taking the effect of the Coriolis force into consideration; Ω 2 k d is the matrix considering the influence of spin softening phenomenon; u is the displacement vector; f l ( t ) is the periodical linear excitation force induced by unbalanced bass, which is associated with the rotating speed; and f n ( x ) is the nonlinear time-variant force induced by the rub between rotor and stator. By defining c = c s + Ω c cor and k = k s -Ω 2 k d , equation (25) can be written in a simple form as equation (1) as follows The unbalance vector can be written as equation (28) considering that the direction of f l ( t ) is constant where f unb is the unit force vector.…”

“…This phenomenon was also observed and investigated in Zheng's work. 34 Like system 1, the harmonic spectrum is shown in Figure 5 and demonstrates the importance of retaining the enough number of harmonics since those high-order harmonics also take up the large portions of the entire vibration. With the increase of harmonic indexes, however, the coefficients of the corresponding harmonics decline gradually.…”

Simulation study on unbalance vibration characteristics of dual-rotor system

“…Vibration analysis, as one of the most important criteria, is always used to evaluate the quality of an engine. The fault analysis of aeroengine rotor system mainly focuses on misalignment [4][5][6][7][8], cracked rotor [9][10][11], rub-impact [12][13][14] and multiple faults [15][16][17][18][19], and fan blade off (FBO) is the hot topic in the field of unbalance fault [20][21][22] at present. However, the studies for dynamic characteristics and laws of the rotor-bearing system simultaneously only considering the single unbalance factor have not gained sufficient attention in available investigations, namely that the analysis of unbalance fault caused by system operation or assembly is relatively less, and the research on unbalanced vibration of rotor system mainly focuses on the influence of structural parameters on unbalanced vibration and the influence of unbalanced parameters on the inherent characteristics, for instance, Al-Solihat and Behdinan analyzed the influence of unbalance mass on the critical speed region [23], Wang presented that the response amplitudes decrease with increasing rotating damping coefficients and increase with increasing unbalance for fan rotor system [24], Yang et al [25] studied the sensitive frequency ranges and effect factors of unbalanced vibration for different sides of blade-disk rotor, etc.…”