Analysis of Vibration Transmission for Helical Gear System by Spectrally Formulated Elements

This paper presents a study on the analytical prediction of vibration transmission from helical gears to the bearing. The proposed method is based on the application of the three dimensional helical gear behaviors and complete description of shaft by the spectral method. Helical gear system used in this paper consists of the driving element, helical gears, shafts, bearings, couplings and load element. In order to describe all translation and rotation motion of helical gears, twelve degree of freedom equations of motion by the transmission error excitation are derived. Using these equations, transfer matrix for the helical gear is derived. For the detail behavior of shaft motion, rod, beam, and twisting shaft element by the spectral method are employed. Using the elements, the 12x12 transfer matrix for the shaft is derived. Bearings are modeled as the stiffness and dashpot and driving element and load have the mass moment of inertia. Transfer matrix for the bearing, coupling, driving element, and load is also derived. Application of the boundary conditions in the assembled transfer matrix produces the forces and displacements in each element of the helical gear system. The effect of the proposed method is shown by numerical example. This method shows that high frequency of the shaft can be calculated without increasing the degree of freedom in the mass-spring model of the shaft and accuracy of the analysis can be obtained without using a lot of mesh as the finite element modeling. It can also apply to the various multiple-mesh gear trains.