Abstract
Stochastic bifurcation and chaos of a rub-impact rotor system with random stiffness under random excitation are studied in this article. Due to the irrational and fractional expressions existing in the denominator of rub-impact force, the integral process is very complicated. Taylor series expansion is used to expand the irrational and fractional expressions into a series of polynomials. Chebyshev polynomial approximation method is applied to reduce the system equations with random parameter to its equivalent deterministic one, and the responses of stochastic system can be obtained by numerical methods. Numerical simulations show that random parameters have a significant effect on the rub-impact rotor system. It may promote the nonlinear response when the rotational speed is near the 1/2 first-order critical speed and may suppress the nonlinear response when the rotational speed is over the first-order critical speed.
Highlights
Rotor bearing system is the core component of rotating machines, and its dynamic characteristics have important influence on the working performance and reliability of rotating machines
Stochastic bifurcation and chaos of a rub-impact rotor system with random stiffness under random excitation are studied by the Taylor series expansion method and the Chebyshev polynomial approximation method in this article
It aims to reveal the influence of random stiffness under random excitation on the nonlinear response of rub-impact rotor
Summary
Rotor bearing system is the core component of rotating machines, and its dynamic characteristics have important influence on the working performance and reliability of rotating machines. Fang and Leng[11] first applied Chebyshev polynomial approximation to solve the dynamical response of the random system This method was introduced to study the dynamical behavior and its control in classical nonlinear systems with random parameters.[2,12] Leng et al.[13] studied the bifurcation and chaos response of a cracked rotor with random disturbance. Disk mass Linear stiffness of the shaft Nonlinear stiffness of the shaft Stator’s surface stiffness Clearance between rotor and stator Friction coefficient between rotor and stator Mass eccentricity of the disk Rotating speed Acceleration of gravity studied the stochastic bifurcation and chaos of a rubimpact rotor system with random parameter and proposed Taylor series expansion method to fully transfer the random equations to its equivalent deterministic one. Chebyshev polynomial approximation method is a good idea to deal with the stochastic nonlinear characteristics in a rub-impact rotor system with random parameters under random excitation.
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