Effect of transmission error on the dynamic behaviour of gearbox housing

The dynamic response of gearbox remains a paramount concern because of noise generation. This work is concerned with numerical simulation of the overall dynamic behaviour of a parallel helical gear transmission. A dynamic sub-structuring method using different types of substructure (carrying and slave) is made to determine the natural frequencies and the corresponding mode shapes. The structure to be investigated is subdivided into components or sub-structures, which are then analyzed independently for natural frequencies and mode shapes. A numerical model taking into account the elastic coupling between the various components of a gearbox was developed. It allows studying and analyzing the dynamic behaviour of elastic housing in the presence of gear process. The static transmission error is introduced as a vibratory excitation source and it is represented by time-varying mesh stiffness. The discretization of the housing deformation energy and the kinetic energy expressions using plate finite elements leads to constructions of the stiffness and the mass matrixes. In dynamic analyses, time-discretization based on the Newmark method is used. The different equations governing movement of gearbox are established in a truncated modal base deduced from the average characteristics of the structure. A gearbox example is presented, and analyzed. A presentation and discussion of the numerical results was emphasized. The numerical results allow us to conclude on the dominant phenomena of the overall dynamic behaviour of the gear transmission.