Abstract
This paper focuses on a nonlinear frequency response of a rotor system with power of Hertz contact and piecewise nonlinearities of bearing clearance. A complex equation of motion for this rotor system was deduced using the Lagrange equation. The natural frequency and phase portraits of the unperturbed rotor system were obtained to demonstrate hardening stiffness characteristics. The amplitude frequency and attraction basins of multiple solutions for the perturbed rotatory system without clearance were investigated. The analytical forms of amplitude frequency of the perturbed system with clearance were analyzed. Through numerical simulation, the correctness of the theoretical formula is verified, and it is in good agreement with the numerical results.
Highlights
Rotor system is a kind of mechanical model describing rotating system, which has been applied used in rotating engineering areas [1, 2], for example power generation [3], aviation [4], wind turbines [5], turbofan [6], etc
Many researchers investigate the nonlinear vibration of the nonlinear rotor system with Hertz contact force
Xiao et al determined the inherent frequency of the undamped vibration of the mass with the Hertzian contact stiffnes by using three methods [13]
Summary
Rotor system is a kind of mechanical model describing rotating system, which has been applied used in rotating engineering areas [1, 2], for example power generation [3], aviation [4], wind turbines [5], turbofan [6], etc. The complexity behavior of nonlinear rotor system is a long-standing problem in the mechanical engineering and rotary machine. Many researchers investigate the nonlinear vibration of the nonlinear rotor system with Hertz contact force. Hess and Soom studied nonlinear vibration with the Hertz contact by using multi-scale perturbation method [11]. Du et al estimated the tread contact stiffness and given the theoretical support of the wheel face design by using an innovative method based on the Hertz theory [19]. To find the natural frequency theoretically for both the free and the forced vibration by the complex harmonic balance (CHBM) method; 4. The rotor model consists of a disc, the stator with Hertz contact and clearance. A b Fig. 1 Model of nonlinear rotor. a – physical model of rotor with the bearing clearance, b – the rotor model with Hertz contact and the clearance
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