An efficient modeling method for coupled vibration analysis of double-helical gear reduction

A modeling method of double-helical gear reduction for analysis of bending-torsional-axial-swinging coupled vibration is introduced in this study. Using integrating theories of system dynamics and structural dynamics, the model proposed is of sufficient simulation accuracy as well as high computational efficiency according to the modal verification. Based on hybrid user-defined element method (HUELM) combining TCA and LTCA methods, the model consists of four special finite elements: double-helical engagement element, bearing element, 3Dflexible shaft element and housing element. Models for each element are developed in FORTRAN language with precise mathematical representation. Frequency extraction by Lanczos method is applied to the model to predict free vibrations of the example system. Simulation results show that the predictions by HUELM in terms of the same order frequency and mode shape match well with the ones by 3D FEM. However, the efficiency comparison reveals that CPU time of the latter is nearly eight times longer than the time of HUELM. An experimental study on modal analysis of support box is also exhibited. It is demonstrated that maximum error of frequency between measured data and housing element simulation is less than 8%