## 1 Introduction
Although the Monte Carlo method was easy to carry out, the demand of large samples to obtain convergent results limits its developments. The polynomial chaos expansion (PCE) was a method that can overcome the demand of large samples. When using PCE, the uncertain response was replaced by polynomial chaos, of which the unknowns were the coefficients of the assumed polynomial. [PERSON] et al. [PERSON] _et al._ (2010) proposed the stochastic finite element method based on PCE to analyze the uncertain response of a uncertain rotor system. The robustness and efficiency of the proposed method were validated by a comparison with the results of the Monte Carlo method. [PERSON] et al. [PERSON] _et al._ (2010) extended the previous PCE for uncertain linear problems to uncertain nonlinear problems. The method they proposed was called the Stochastic Multi-dimensional Harmonic Balance Method. In their study, a two-DOF vibration problem with different types of nonlinearities was investigated to validate the proposed method. Then, their method was employed by [PERSON] et al. [PERSON] _et al._ (2010) to study the uncertain nonlinear vibration of a flexible rotor with nonlinearities due to cubic stiffness or clearance. [PERSON] and [PERSON] [PERSON] and [PERSON] (2011) studied the effect of the PCE order on the responses of an asymmetric rotor system with uncertainties. Results showed that the increase of PCE order could only reduce the level of spurious peaks, but could not eliminate them. The above Monte Carlo method and PCE belong to the probabilistic method. Although the two methods were able to solve uncertain problems, the probability distribution functions of uncertain factors should be known or assumed in advance. However, the probability distribution functions were not easy to gain in reality. Therefore, the assumption in the probability distribution functions could lead to unexpected error. An interval method that could overcome the difficulty of knowing the probability distribution functions in advance was proposed. In this interval method, the uncertain factors are treated as interval variables with the lower bounds and upper bounds. [PERSON] and [PERSON] [PERSON] and [PERSON] (2005) studied the uncertain response of static problems by using this interval method. A truncation approach was proposed to limit the unexpected growth of interval response. The results showed that the truncation approach was effective and necessary. [PERSON] et al. [PERSON] _et al._ (2010); [PERSON] _et al._ (2010) studied the uncertain static and dynamic structure problem based on this interval method. The widths of the bounds predicted by the interval method were found to be larger than those of probabilistic method. To deal with the unexpected overestimation of uncertain response, the Chebyshev interval method (CIM) was proposed by [PERSON] et al. [17; 23]. In CIM, the interval response was expanded based on a Chebyshev series in which the calculation was independent from the calculation of response, i.e., in a non-intrusive way. [PERSON] et al. [24] studied the uncertain nonlinear response of a breathing cracked rotor system. A surrogate model based on Chebyshev polynomial expansion was used in their study. Then, [PERSON] et al. [25] proposed an effective method based on a polynomial surrogate model to reduce the computational efforts. [PERSON] et al. [26] used CIM to study an uncertain geared transmission system. The interval responses influenced by uncertainties were evaluated. Then, [PERSON] et al. [27] evaluated the uncertain nonlinear response of a single-mesh gear system. Besides, CIM was used to study uncertain thermodynamics [28; 29; 30]. The above analysis showed that few papers about uncertain asymmetric rotor systems have been published. In this paper, the gravity responses of a two-pole generator rotor system with interval uncertainties are evaluated. The fixed-interface CMS is employed to reduce the number of DOFs. The equations of motion of the ROM are solved in the rotating frame.