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This paper presents a mathematical model to investigate the nonlinear dynamic behavior of cage in high-speed cylindrical bearing. Variations of cage behavior due to varying cage eccentricity and cage guidance gap are observed. Hydrodynamic behavior in cage contacts is taken into consideration for a more realistic calculation of acting forces owing to high working speed. Analysis of real-time cage dynamic behavior on radial plane is carried out using chaos theory based on the theoretical and mathematical model established in the paper. The analytical results of this paper provide a solid foundation for designing and manufacturing of high-speed cylindrical roller bearing.

In the motion control of AUVs, especially those driven by multiple thrusters, the thruster misalignment and thrust loss cause the actual force and moment applied to the AUV to deviate from that desired, making accurate and fast motion control difficult. This paper proposes a sliding mode control method with dual-observer estimation for the AUV 3D motion control problem in the presence of thruster misalignment uncertainty and thrust loss uncertainty. Firstly, this paper considers the force and moment deviation as disturbances that vary with the controller output, and proposes the TD disturbance observer to address the problem of deviation caused by uncertainty in thruster misalignment. Secondly, this paper introduces the dynamics equation of thrust loss and designs the gain disturbance observer to estimate the thrust loss uncertainty during AUV navigation. The designed controller, verified by simulation and field tests, ensures that the AUV maintains better motion control despite thruster misalignment and thrust loss.

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