Torsional vibration analysis of gear-branched systems by finite element method

The purpose of this paper is to present a simple approach for eliminating the "dependent" torsional angles existing in the reduction gears of a gear-branched system so that this system may be modelled as an equivalent straight-geared (or direct-transmitted) system. Then the overall mass matrix? damping matrix, stiffness matrix, and load vector of the direct-transmitted system are obtained with the conventional finite element method (FEM) by assembling the elemental property matrices of all the shaft elements contained in the torsional system. Based on the overall property matrices determined, the equations of motion of the whole vibrating system are defined. Solution of the equations of motion gives the dynamic responses and solution of the associated eigenvalue equation provides the natural frequencies and the mode shapes of the system. A simple technique is also presented to study the influence of the shaft mass on the natural frequencies of a torsional system. (C) 2001 Academic Press.