Rigid-Elastic Coupling Dynamic Modeling And Vibration Mechanism Analysis Of Thin-Walled Compliant Gears

Gear transmission systems are core components of naval and shipborne aerospace powers,and also the “aorta” of power transmission and distribution.To improve power density,the main reduction and accessory gears used in naval gas turbine and aerospace engine are often thinwalled compliant type,such as thin-plate-shaped,thin-ring-shaped and thin-webbed.In addition,they often work in high-speed and heavy-torque conditions.All these make elastic deformation and elastic vibration of thin-walled compliant gears prominent.Accurate dynamic modeling and vibration mechanism analysis of these gears have become a thorny issue to overcome.Dynamic modeling and vibration mechanism analysis of thin-walled compliant gears are the focus of this dissertation,and experiments are conducted using a newly built test rig to verify the theoretical parts.The main work is as follows:The thin-plate-shaped spur gear with uniform thickness is regarded as an elastic annular plate.An elastic dynamic model is proposed for a single gear with elastically restrained edges.Then,an elastic dynamic model of thin-plate-shaped spur gear pair is established using Rayleigh-Ritz method.The elastic ring theory is further introduced to develop a unified rigidelastic coupling dynamic model of high-speed thin-walled compliant spur gear pair including thin-plate-shaped,thin-ring-shaped and thin-webbed gears.The Coriolis and centripetal effects are modeled,and both the large-scale rigid motion and small-scale elastic deformation can be analyzed.The proposed model can accurately predict natural frequencies of ring-shaped gear pair,and is more universal and accurate than the existing ring pair model.Both linear and nonlinear vibration phenomena of solid cylindrical gear pair reported in literature can be accurately predicted using the proposed model.The influence of inner radius and elastic support on the vibration characteristics of low-speed thin-plate-shaped spur gear is analyzed,as well as Coriolis and centripetal effects of high-speed thin-walled compliant spur gear.A rigid-elastic coupling dynamic model of single-stage thin-walled spur gear transmission system is established considering the driving and loading components.Considering complete rigid body motion,a modified model for time-varying mesh stiffness is proposed.The modulation mechanism of the external fluctuating torque on gears is numerically obtained with the modified mesh stiffness.Based on the modulation mechanism,an analytical modulation model of external fluctuating torque and long-periodic non-load transmission error on timevarying mesh stiffness is established,which can accurately obtain the spectrum and sideband information of both mesh stiffness and internal excitation.The correlation of sidebands between dynamic response and internal excitation under different mesh statuses is analyzed using the rigid-elastic coupling dynamic model.With no cumbersome response calculation,the feasibility and reliability of using modulation sidebands of the internal excitation to quickly locate gear fault are further addressed under different meshing statuses.Based on the nonlinear Von Karman strain displacement relationship,the membrane stress field generated by in-plane mesh is embedded into out-of-plane potential energy.The out-ofplane rigid-elastic coupling dynamic model of thin-webbed spur gear is then proposed with the influence of membrane stress field.Perturbation parameter is selected based on the dynamic mesh force.Accurate mapping relationship between unstable regions and key parameters of gear is determined using method of multiple scales.Mechanism of the abnormal out-of-plane parametric instability phenomenon of thin-webbed spur gear is explained.The influence of some key geometric parameters on the bandwidth of unstable regions is analyzed furtherly.It is found that increasing the axial width of rim or the axial thickness of web can greatly decrease unstable regions,so as to restrain the occurrence of out-of-plane parametric resonance.A test rig of thin-webbed gear transmission system is designed and built up.Nearby the driving gear,eddy current displacement sensors are embedded into the gearbox.Acceleration sensors are installed on the driven gear.These sensors provide a more accurate test method for the vibration characteristics of thin-walled gear pair.The accuracy of rigid-elastic coupling dynamic model of thin-walled gear pair is verified by experiments.The maximum prediction deviation of in-plane natural frequency is 8.4%.It is verified that the fluctuating torque modulates the vibration response of gears.Regarding the distributed fault and local fault as long-periodic non-load transmission error is correct.The abnormal out-of-plane parametric resonance of actual aviation thin-webbed spur gear is successfully inverted within a limited maximum test speed,and the rationality of theoretical modeling is verified.