Gear System Dynamics Analysis And Parameter Matching Research

The gear mechanism has the advantages of compact structure and high efficiency,and is widely used in the field of mechanical equipment.Due to the complex and changeable working conditions of the gear transmission system,it is easy to generate large noise and vibration during operation.It is necessary to further understand the nonlinear dynamic phenomena and vibration reduction methods in the gear transmission system.The grazing impact between gear tooth surfaces is a special form of impact in the gear transmission system.In order to study the influence of the grazing impact on the motion state of the system during the gear meshing process,according to the different impact states of the gear,the time Poincaré mapping,the Poincarémapping of the tooth surface impact surface and the Poincaré mapping of the tooth back impact surface were established respectively.Use P to denote the number of cycles of the system;Q and R to denote the number of flank meshing and tooth back impacts,respectively.When the system parameters change,the law of mutual transition between the periodic excitation,tooth surface meshing,tooth back contact P-Q-R motion and the formation process of tooth surface impact and tooth back impact are obtained by calculation.The study found that the grazing impact has a great influence on the motion state of the system,and may cause the system motion state and impact state to change.These results can help us to have a deeper understanding of the dynamic characteristics and laws of gears,and provide a certain theoretical basis for the optimal design and dynamic design of gear system parameters.The specific research work of this thesis is as follows:Taking the gear-bearing system as the research object,considering the timevarying mesh stiffness,backlash and other factors,a nonlinear dynamic model of the gear is established.Under the change of the key parameters of the system,the law of the mutual transition of the P-Q-R motion of the gear is studied,and the formation process of the tooth surface impact and the tooth back impact is analyzed by combining the phase diagram and the maximum Lyapunov exponent diagram.Combined with the Continuous-Poincaré-Newton-Floquet(CPNF)algorithm and Floquet theory,the stable and unstable periodic solutions under the given system parameters are found and the stability is judged.The sensitivity of the parameters of the gear system is calculated using the direct derivation method,and the sensitivity curve of the system response to the parameters is obtained.The single-parameter bifurcation diagram is extended to a two-parameter stability diagram,and the system parameters with greater sensitivity are selected as the research object.By analyzing the two-parameter stability diagrams and the maximum Lyapunov exponent stability diagrams of three Poincaré maps,the evolution process and parameter matching law of the system stability region in the parameter plane are obtained,and the influence of system parameters on the disengagement duty ratio and tooth back meshing ratio is analyzed.The vibration characteristics of the gear transmission system are experimentally tested using the gear system experimental platform,and the spectral characteristics are extracted from the experimental data and compared with the theoretical analysis to verify the correctness of the model and analysis method.