Vibration Sensitivity Analysis And Optimization Design Of Planetary Gear Train Based On Matrix Perturbation Theory

Power split planetary gear transmission system contains differential planetary gear train and encased planetary gear train. It is widely used due to the advantages such as compact-size, large transmission ratio, more power branchs, strong carrying capacity and so on. Meanwhile, the vibration and noise of the system get more and more attention in order to keep the dynamic property of the system.The dynamic model of the power split planetary gear transmission system was established based on the lumped mass method. The meshing stiffness of the gear pair and the torsional stiffness of the floating component were calculated. The relative displacements in the meshing line were derived, and the meshing force was calculated. The dynamic differential equations of the system were deduced. The natural frequency and vibration mode of the system were solved and analyzed.The sensitivity of the natural frequencies to stiffness parameters was analyzed by the method of matrix perturbation.The results were compared with those solved by the derivation method, which demonstrated the matrix perturbation method was more convenient and accurate than the derivation method. The sensitivity of natural frequencies to mass parameters was solved by this method.The structural natural frequency could be away from the excitation frequency by amending the basic parameters of the system according to the results of sensitivity analysis.The differential equations of the system were solved and the relative vibration acceleration in the meshing line was obtained. The mathematical model for dynamic optimization design was established, and the optimal design was conducted targeting the minimum average root mean square of the vibration acceleration in the line of action during a meshing circle.The dynamic analysis and dynamic optimization software of the planetary gear transmission system were developed by the MATLAB.