Study On Vibration Characteristics Of The Speed Integrated Gear Based On Harmonic Balance Method

As a new type of gear mechanism,the integrated gear of reduction and speed change integrates the transmission characteristics of non-circular gear and face gear,which can realize the transmission of speed ratio between intersecting shafts.Compared with the series transmission mechanism of common non-circular gear and circular gear,it has the outstanding advantages of high efficiency and lightweight.Therefore,it has a broad application prospect in the fields of aerospace,weapon equipment,medical devices and robots.As a new type of spatial non-circular gear transmission mechanism,it is of great significance to clarify its dynamic characteristics for the design and application of the integrated gear.According to the meshing principle of the integrated gear,the pitch curve and tooth profile model of the mechanism are established,and the mathematical description of the transient center,meshing stiffness and tooth error of the gear is given.Considering the large load,the gear teeth do not take off,so regardless of the backlash,the torsional vibration model of the reduced speed integrated gear under the combined excitation of time-varying transient center and meshing stiffness is constructed.The approximate analytical solution is obtained by the multi-order harmonic balance method,and the dynamic response of the gear and the sensitivity of each parameter are analyzed.The research results show that the gear has complex under the combined parameter excitation.The response amplitude of the hybrid multi frequency response increases with the increase of speed,eccentricity,error amplitude,meshing stiffness amplitude ratio and load torque.Further,considering the light load condition,the backlash will cause the teeth to take off teeth and impact repeatedly,so the backlash is included in the backlash,and a nonlinear torsional vibration model of the integrated gear backlash is constructed.The approximate analytical solution of the nonlinear model is derived by using the harmonic balance method and the discrete Fourier transform.It is found that with the increase of eccentricity,input speed and error amplitude,The gear will go through non impact state,unilateral impact state and bilateral impact state in turn,while the amplitude coefficient of meshing stiffness has little effect on the state transition of the gear.Finally,an integrated gear vibration test platform is built to test the lateral and axial vibration of the gear system through three-way acceleration sensor.The experimental results show that the frequency component in the actual vibration of the integrated gear is consistent with the harmonic component assumed in the theoretical analysis,and the influence law of the speed and load on the vibration amplitude of the gear is basically consistent with the theoretical analysis results,thus verifying the correctness of the vibration model and analysis method of the integrated gear.