## 1 Introduction
[21] proposed a method for bearing prognostics with wavelet packet decomposition and probabilistic modelling to realize the online tracking of bearing wear. [PERSON] et al. [22] investigated the impact of wear induced clearances on diagnostic characteristics, which confirmed the general understanding of increased amplitudes with clearance for the inner and outer race defects. Note that these efforts still focus on improving the performance of diagnosing local defects and few studies have been found to analyze the continuous changes in bearing clearance without local defects. To monitor the bearing clearances, [PERSON] [23] assessed the influence of the bearing radial clearance on vibration level by experiments and pointed out that medium vibration frequency band (300-1800 Hz) has the biggest impact. [PERSON] et al. [24] utilized spectral kurtosis to predict bearing clearance changes. [PERSON] et al. [19] studied the effect of the internal radial clearance on the damping characteristics and natural modes of vibration through experimental tests. [PERSON] et al. [25] applied three different methods (kurtosis, recurrences and neural networks) for measuring the bearing clearance and found a correlation between the bearing clearance, level of bearing vibrations and output signal structure. Recently, [PERSON] et al. [26] proposed an online bearing clearance monitoring approach based on modulation signal bispectrum (MSB) and Gini-index to diagnose the change of bearing clearance without local defects. Although there are some indicators utilized to monitor the change of bearing clearance of certain levels through experiments, it should be noted that the mechanism behind bearing clearance is not revealed and remains ambiguous, whereas it is the basis of accounting for various vibration phenomena and bearing condition monitoring. Overall, although a few studies have begun to focus on bearing clearances and paved the foundations for this study, several problems existed in these studies, such as a lack of mechanism research, incomplete vibration characteristics and insufficient reasonable monitoring indicators. These deficiencies bring difficulties to bearing condition monitoring and maintenance of WT systems. On the other hand, accurate monitoring of the bearing clearance before obvious local defect could provide sufficient lead time to perform maintenance and hence reduce accidents and economic losses. Thus, it is a meaningful exploration to study bearing clearances. In this paper, to bridge the gap, a nonlinear bearing vibration model is proposed to investigate the vibration characteristics for bearing condition monitoring under different internal clearances, as well as external loads. Firstly, a six degree of freedom (DOF) bearing dynamic model, which includes nonlinearity of radial clearance, is established based on structural mechanism analysis and Hertz contact theory. Then, experimental tests are carried out to verify the rationality of the model based on the comparison between simulation and test data. Finally, dynamic force, vibration characteristics and monitoring indicators are expounded at a wider range of radial clearance, load and rotational speed. The main contribution of this paper lies in the non-linear vibration model and the influence of continuously changing clearances on dynamic force and vibration characteristics.