A general method to predict unbalance responses of geared rotor systems

•A general method to predict the maximum radii of unbalance responses is proposed.•A strict mathematical deduction of the analytical expressions is given.•A typical modal synthesis is compared with the proposed method.•The proposed method has advantages over the modal synthesis.•The proposed method can save plenty of computer processing time.

This paper concerns a general method to predict unbalance responses for a geared rotor system, which contains n shafts and at least n−1 spur and/or helical gear meshes. Finite element models of spur gear pairs and helical gear pairs are developed with arbitrary orientation angles, respectively. Then, a general method with a strict mathematical proof is proposed to calculate maximum axis radii of the unbalance response orbit for a geared rotor system. The proposed method is validated through three applications, i.e, a spur geared two-shaft rotor system, a spur geared multi-shaft rotor system and a helical geared multi-shaft rotor system. A classical modal synthesis is also employed as a comparison. Results show that proposed analytical solutions are consistent with the numerical results and have advantages over the modal synthesis. In addition, plenty of computer processing time can be saved with the proposed method. The method reported here may be of interest to engineers and educators attempting to handle the unbalance response analysis effectively and easily.