| In recent years,herringbone gear planetary transmission systems have been widely used in high-speed and heavy-duty working conditions such as aviation power transmission systems and vehicles(especially heavy vehicles),but the complex structure of planetary systems,many meshing relationships,and working in complex and harsh environments such as high-speed and heavy-duty,lead to a very high failure rate of mechanical components.Among them,the gear root crack factor is one of the main factors leading to planetary system dynamics instability,so it is essential to study the dynamics of herringbone gear planetary transmission system containing gear cracks,and its influence mechanism has important engineering significance for the stability and reliability of the system,which lays the basis for the research of transmission system dynamics characteristics under the case of containing cracks.The research in this paper is as follows.(1)According to the dynamic cross-section cantilever beam model,the energy method is used to derive the formulae for calculating the Hertzian stiffness,bending stiffness,shear stiffness and axial compression stiffness in the gears of meshing,and at last,the meshing stiffness of every gear tooth is linked in series to a total time-varying meshing stiffness,thus calculating the internal and external time-varying meshing stiffness of the herringbone gear planetary transmission system.The effect rule of different crack factors(depth,length and angle)on the internal and external time-varying mesh stiffnesses is also analyzed.(2)A centralized parametric model of the bending-torsion-shaft-pendulum coupling dynamics of a 55-degree-of-freedom herringbone gear planetary transmission system was developed.In the model,the Timoshenko beam unit equivalent herringbone gear receding slot is used to derive the calculation equations for the main excitation of each component of the herringbone gear planetary transmission such as error and stiffness.The differentiated equation for the dynamics of the system under its conditions considering time-varying meshing stiffness,time-varying support stiffness,and error are derived.(3)Through the model of planetary transmission system with cracked herringbone gears,the dynamic load-sharing characteristics of the system with different cracks(depth,length and angle)are analytically calculated by the Runge-Kutta numerical integration method,and the dynamic load-sharing influence law of cracks on the system is analyzed by the dynamic load-sharing system diagram,and the sensitivity characteristics of the system with the change of cracks are also analyzed.(4)Based on the planetary transmission system with cracked herringbone gears,the vibration characteristics of the system under the influence of different cracks(depth,length and angle)are studied and resolved by the Runge-Kutta numerical integration method,and the time domain,frequency domain,phase diagrams and Poincare diagrams characterizing the dynamic load characteristics are obtained.Poincare diagrams are acquired to compare the time domain,frequency domain,phase diagrams and Poincare diagrams of normal and cracked gear systems to reveal the influence of different crack levels on the displacement and vibration characteristics of the system.(5)The gears with different crack lengths are machined by wire cutting,and the vibration test bench of the planetary transmission system with cracked herringbone gears is built to measure the vibration signals of the system under different crack lengths and obtain the frequency spectrum of the system under different crack lengths,and compare the measured experimental data with the simulation results to further check the model reliability and the precision of the simulation results.Through the above study,the impact law of tooth root crack on the system’s time-varying meshing stiffness is revealed,and the system’s variation law with crack is revealed by a series of vibration and dynamic mean load coefficient diagrams,which can provide a scientific references for the vibration and noise reduced of herringbone gear planetary transmission system. |
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