Nonlinear Vibration Mechanism Of Marine Rotating System With Airbag Vibration Isolation Under Heaving Motion

In this thesis,the nonlinear dynamic characteristics and vibration mechanism of marine rotating machinery air bag vibration isolation system under heave excitation are studied.Firstly,based on nonlinear dynamics theory,considering the effects of heave motion,rotor mass imbalance and nonlinear elasticity of air bag,the dynamic model of marine rotating machinery air bag vibration isolation system under heave excitation is established.Multi-scale method and numerical method are used to analyze the nonlinear vibration mechanism and dynamic characteristics of the system under heave excitation.Secondly,the random vibration characteristics of marine rotating machinery air bag vibration isolation system under heave excitation are studied by using the orthogonal polynomial approximation method,and its stability of system is discussed.The main work is summarized as follows:(1)The multi-scale method is used to analyze the nonlinear vibration mechanism of the system,and various resonances are obtained,including the primary resonance,the second order superharmonic resonance,the third order superharmonic resonance,the 1/2 order subharmonic resonance,the 1/3 order subharmonic resonance and the combined resonance.Secondly,the analytical solution of the non-resonance case obtained by the multi-scale method is compared with the numerical solution obtained by the fourth-order Runge Kutta method,and the time-domain responses are in good agreement.(2)In the case of primary resonance,the stability of marine rotating m achinery with air bag vibration isolation system under heave excitation is analyzed.Under the nonlinear elasticity of airbag and heave excitation,the steady-state motion amplitude of marine rotating machinery system has multi-value and jump nonlinear characteristics in a certain frequency range.The increase of frequency ratio will reduce the instability region of the system,the amplitude of heave excitation is a significant factor affecting the stability of the system,the small increase of excitation amplitude will increase the instability region of the system,and the increase of damping can effectively suppress the main resonance peak.(3)In the case of harmonic resonance,frequency ratio is no longer the key factor affecting the vibration of marine rotating machinery system.However,the heave amplitude will still affect the resonance state of marine rotating machinery system.With the increase of rotor speed,the detuning factor needed to produce the third subharmonic resonance decreases.Reasonable control of rotor speed can avoid the occurrence of superharmonic resonance.Similar to the linear system,damping has a certain inhibitory effect on the resonance of the system,but has little effect in the non-resonance region.(4)The influence of rotor speed and frequency ratio on the dynamic characteristics of the system is studied by numerical method.The system is in a chaotic state at low speed.Under certain conditions,the half frequency of the combined frequency and its odd multiple frequency will appear in the steady-state response of the system.With the continuous increase of the system speed,the system presents a quasi-periodic state when it reaches a high speed.When the frequency is low,the amplitude of vibration changes greatly,which makes the whole system chaotic.With the increase of frequency ratio,the influence of heave on the system decreases gradually,and the system motion tends to a stable periodic state.(5)The random vibration of marine rotating machinery air bag vibration isolation system under heave excitation is discussed by orthogonal polynomial approximation method,and the equivalent deterministic system is obtained.The stability of the system at zero solution is analyzed by Routh Hurwitz criterion.The results show that the system is asymptotically stable under given parameters.