Dynamic Analysis Of Elastic Component And Study On Vibration Characteristic Of Two-stage Planetary Transmission System

Planetary transmission is an important mechanical transmission type.With the strict requirement of the International Maritime Organization(IMO)for the reliability and vibration,the vibration control of high-power marine planetary transmission systems has been a hotspot in recent years.And the dynamic modeling and vibration prediction have become difficult to overcome.Different from traditional method,this paper mainly studies the dynamic modeling,response prediction and experimental verification of the two-stage planetary transmission system.The specific work can be arranged as follows:The in-plane vibration model of the curved beam with the case of considering the moment of inertia and shear effect is constructed.The dispersion relationship expression between frequency and wavenumber are obtained by submitting the wave solution into the in-plane vibration equation.For the radial wave and tangential wave,the propagation mode,dispersion relationship between frequency and wavenumber,amplitude ratio and phase are also investigated.By periodically combining two different materials,forming a kind of periodical curved beam like semicircle type structures.Based on the wave solution and parameter coordination at interface junction,transfer matrix of in-plane vibration is derived theoretically.Combining the Bloch theory,the radial wave and tangential wave energy band curves of periodic curved beam structure are calculated.Furthermore,by loading displacement excitation for the curved beam,transmissibility curves of radial and tangential wave are obtained.Transmission characteristics of multilayer composite circular structures are analyzed.A translational-torsional coupled two-stage planetary gear system with sliding friction and elastic continuum ring gear is constructed.For the gear pairs,the variation law of parameters such as radius of curvature,sliding velocity and friction coefficient during gear mesh rotation are analyzed,and the effect of sliding friction on the time varying mesh stiffness are also discussed.For this system,the natural characteristic with different planet number are analyzed,and the vibration modes are also given.Additionally,the natural frequencies calculated by this model are compared with the results obtained by lumped parameter model.The effect of ring bending stiffness and sliding friction coefficient on natural frequency are also investigated.The mechanism of amplitude modulation,frequency modulation and phase modulation for the planetary transmission system is analyzed.The effect of planets number,planet space and component teeth number on the amplitude modulation,are investigated.The effect of frequency modulation and phase modulation on the sideband is given.The mathematical model with amplitude modulation,frequency modulation and phase modulation are modeled by introducing the manufacturing errors into the transmission error,mesh stiffness and internal mesh force.The time domain response and frequency domain response of the two-stage planetary gear are compared with the case of considering installation error modulation and not installation error modulation.The effects of ring's elasticity,coupling stiffness,rotation speed condition,load torque fluctuation and friction coefficient on sideband modulation are discussed.The translational-torsional coupled two-stage planetary gear nonlinear system with time-varying mesh stiffness,clearance,ring elasticity,tooth surface sliding friction is modeled.The curves of time-varying mesh stiffness with no clearance and no friction,clearance and no friction,clearance and friction are analyzed.The transverse and torsional displacement bifurcation curves with friction and without friction are compared numerically.The effect of excitation frequency on the nonlinear chaotic characteristics for the planetary transmission system are discussed.The nonlinear responses of the time domain curve,phase diagram and Poincare section of each central component are also given.The experimental model of two-stage planetary transmission system is constructed.The working condition,constant load condition and fluctuating load condition are tested.Also,the vibration characteristics of two-stage planetary transmission system such as time domain response,frequency domain response and axis trajectory are obtained.Additionally,time domain response and frequency domain response obtained by numerical simulation for different working condition are compared with the experimental results.The source of typical characteristic frequency is investigated,and the sideband modulation phenomenon is also explained.The time and frequency domain response obtained by theoretical calculation are verified by the experimental test results.