## 5 Conclusions  
As an important supporting component in the bearing-rotor systems, DACBB commonly runs with angular misalignment. Lots of previous studies demonstrated that misalignment of the inner ring has a great influence on the performance of rolling bearings and rotor systems. However, the misalignment phenomenon in DACBB has not yet been thoroughly studied. Therefore, to study the influence of angular misalignment on the DACBB in theory, this paper established a three degree-of freedom static model of DACBB for back-to-back, face-to-face, and tandem configurations. According to the geometrical relationship inside the bearing, the deformations of DACBB caused by external loads and angular misalignment are systematically analyzed for back-to-back, face-to-face, and tandem configurations. Subsequently, based on the presented model, the influences of angular misalignment, axial preload, and external load on the displacement, maximum contact load, contact load distribution, and actual contact angle of DACBB are studied and discussed. Finally, according to the life theory proposed by [PERSON] and [PERSON], the theoretical fatigue life of DACBB under different axial preload, external radial load, and angular misalignment is evaluated in detail. Based on the aforementioned analysis and discussion, the following conclusions can be drawn:  
(1) Angular misalignment can considerably increase the contact load between ball and raceway. Angular misalignment will cause the fluctuation of contact load distribution of each row of DACBB, and accordingly lead to the uneven load distribution. With the increase of angular misalignment, the fluctuation is more severe. Contact load increases with the increase of axial preload. (2) Angular misalignment and axial preload significantly affect the contact zone of DACBB. Under higher angular misalignment, some rolling balls will be no longer constrained by the inner ring. With the increase of axial preload, the contact zone of bearing tends to be increased. (3) Contact angle increases with the increase of axial preload. With the increase of radial load, contact angle of the left row of DACBB decreases, while it tends to be increased for the right row. Increasing the axial load, the contact angle of the left row increases and the contact angle of the right row decreases. Angular misalignment will cause uneven distribution of contact angle of each row of DACBB. With the increase of angular misalignment, the contact angle can be significantly increased. (4) With the increase of external radial load or axial preload, fatigue life of DACBB tends to be decreased. Higher angular misalignment considerably reduces the fatigue life of DACBB, so higher angular misalignment should be avoided in the application of DACBB. For the combined loaded DACBB, angular misalignment of certain size can improve the fatigue life of DACBB, and the corresponding size of angular misalignment slightly increases with the increase of radial load. This paper established a static model for DACBB. However, the rotating effect of the rolling ball is ignored in the analysis. Therefore, the model needs to be extended in the future studies. In addition, this paper only focuses on the characteristics of DACBB. However, DACBB is commonly used to support the bearing-rotor systems. Therefore, the experimental device of bearing-rotor system will be used to study the operating performance of DACBB and the bearing-rotor system under angular misalignment conditions. Conceptualization, T.X. and L.Y. ; Methodology, T.X. ; Validation, T.X. ; and K.W. ; Formal Analysis, T.X. and K.W. ; Writing--Original Draft Preparation, T.X. and L.Y. ; Writing--Review and Editing, T.X. and K.W. ; Supervision, T.X. and L.Y. All authors have read and agreed to the published version of the manuscript. This research was funded by the National Science Foundation of China under Grant No.11872288 and No. 51575425, the Shaanxi Provincial Natural Science Foundation under Grant No. 2019 JM-219.