SENSITIVITY ANALYSIS OF GEARBOX TORSIONAL VIBRATIONS

The paper deals with the modelling of a real gearbox used in cement mill applications and with the sensitivity analysis of its eigenfrequencies with respect to design param- eters. The torsional model (including a motor and couplings) based on the finite element method implemented in an in-house MATLAB application is described. The sensitivity analysis of gearbox eigenfrequencies is performed in order to avoid possible dangerous resonance states of the gearbox. The parameters chosen with respect to the sensitivity analysis are used for tuning the gearbox eigenfrequencies outside reso- nance areas. Two approaches (analytical and numerical) to the sensitivity calculation are discussed. The computational investigation of gearbox dynamic properties is an important step in the gearbox design. Mainly the resonance analysis (the comparison of system eigenfrequen- cies with possible excitation frequencies) is performed in order to avoid dangerous resonance states. The successive activity in case of possible resonances should lead to the tuning of chosen eigenfrequencies out of the resonance areas. The sensitivity analysis of the gearbox eigenfrequencies and eigenmodes is the most suitable tool in this case. It can be used for the identification of design parameters which are proper to influence chosen eigenfrequencies. The first necessary step of the introduced methodology is the modelling method of the gearbox vibration. The most often used methods are based on the finite element analysis of various complexity. Solid finite elements can be used in order to describe three-dimensional flexible bodies. However, considering limited computer capacity, rotation of the components and its mutual connections, the most efficient method is based on the torsional modelling (16) of an interior rotating gearbox system. The dynamic model of the real Wikov Gear gearbox (Figure 1) with a motor and couplings (not shown in Figure 1) is investigated in this paper. The model (see Figure 2) is based on the finite element method combined with discrete mass and flexible elements and it is implemented in an in-house MATLAB application. The possible extension of the torsional modelling methodology for the nonlinear systems was shown e.g. in (4).