A New Mathematical Modeling Method for Four-Stage Helicopter Main Gearbox and Dynamic Response Optimization

A new mathematical modeling method, namely, the finite element method and the lumped mass method (LMM-FEM) mixed modeling, is applied to establish the overall multinode dynamic model of a four-stage helicopter main gearbox. The design of structural parameters of the shaft is the critical link in the four-stage gearbox; it affects the response of multiple input and output branches; however, only the meshing pairs were frequently shown in the dynamic model in previous research. Therefore, each shaft is also treated as a single node and the shaft parameters are coupled into the dynamic equations in this method, which is more accurate for the transmission chain. The differential equations of the system are solved by the Fourier series method, and the dynamic response of each meshing element is calculated. The sensitivity analysis method and parameter optimization method are applied to obtain the key shaft parameters corresponding to each meshing element. The results show that the magnitude of dynamic response in converging meshing pair and tail output pair is higher than that of other meshing pairs, and the wall thickness has great sensitivity to a rotor shaft. In addition, the sensitivity analysis method can be used to select the corresponding shaft node efficiently and choose parameters appropriately for reducing the system response.