*Article* **Similitude for the Dynamic Characteristics of Dual-Rotor System with Bolted Joints**

**Lei Li 1,2, Zhong Luo 1,2,3,\*, Fengxia He 1,2, Zhaoye Qin <sup>4</sup> , Yuqi Li <sup>5</sup> and Xiaolu Yan 1,2**


**Abstract:** The dual-rotor system has been widely used in aero-engines and has the characteristics of large axial size, the interaction between the high-pressure rotor and low-pressure rotor, and stiffness nonlinearity of bolted joints. However, the testing of a full-scale dual-rotor system is expensive and time-consuming. In this paper, the scaling relationships for the dual-rotor system with bolted joints are proposed for predicting the responses of full-scale structure, which are developed by generalized and fundamental equations of substructures (shaft, disk, and bolted joints). Different materials between prototype and model are considered in the derived scaling relationships. Moreover, the effects of bolted joints on the dual-rotor system are analyzed to demonstrate the necessity for considering bolted joints in the similitude procedure. Furthermore, the dynamic characteristics for different working conditions (low-pressure rotor excitation, high-pressure rotor excitation, two frequency excitations, and counter-rotation) are predicted by the scaled model made of a relatively cheap material. The results show that the critical speeds, vibration responses, and frequency components can be predicted with good accuracy, even though the scaled model is made of different materials.

**Keywords:** similitude; scaling relationships; dual-rotor system; bolted joint; dynamic characteristics
