The commonly known effects of both the rotating speeds and external loads on the bearing dynamics or life behaviors are mostly caused by its cage dynamics, because of the complicated contact and collision interactions between the cage and other parts such as the inner or outer rings and balls. In this paper, experimental investigation of dynamic motions of a cage is carried out under various rotating speeds and external loads in a ball bearing. On a bearing test rig, the cage motions in axial and radial directions are measured by use of eddy transducers installed inside the bearing house and the subpanel. Then the measured results are analyzed by fast Fourier transform and compared at different operating conditions including rotating speeds, axial and radial forces, or moments. The three-dimensional space motions of the cage are also constructed to illustrate its different modes. Results reveal that the cage motions are typically periodic in the three directions. The motion frequencies consist of the cage rotating frequency and its multi-frequency, the inner ring rotating frequency, and also some combination frequencies of the cage and inner ring. The obtained characteristic frequencies of the cage motion in axial are similar to that in radial, but different in the variety of amplitudes under the same operating conditions. The increment of rotating speeds and axial loads of the bearing gradually make the whirl trajectories of the cage mass center regular, and enlarge its whirl radii. Instead, the whirl trajectories change from well-defined patterns to complicated ones, and its whirl radii decrease on increasing the radial loads and moments of the bearing. All the obtained experimental results are useful references for dynamic design and life prediction of high-speed and low-load bearings commonly used in many machines.

Purpose The oil film thickness provides a key performance indicator of a ball bearing lubrication condition. This paper aims to propose an approach to calculate and measure the oil film thickness of the bearing. Design/methodology/approach On a specially designed test rig, measurement of the capacitance is used to monitor the oil film thickness of ball bearing. A corrected film thickness formula taking account of the influences of non-Newtonian shear thinning and thermal is introduced to predict the oil film thickness of ball bearing. And then the film thickness distribution and the corresponding capacitances are calculated. Findings Measurement and calculation of oil film thickness in a ball bearing are carried out under various rotating speeds and external loads. By comparing the calculated capacitances with measured results, it can be concluded that the calculated results obtained by the amended film thickness formula are much closer to the test findings than the classical computed values according to Hamrock–Dowson. Originality/value A new corrected film thickness formula is introduced in predicting oil film thickness of ball bearing and verified by the series of experiments according to capacitance method.

The motion of bearing cage in the rotor system displays very complicated behavior affected by rotor unbalance. In order to gain an insight into the complex cage motions due to rotor unbalance, a scaled rotor test rig is designed and developed that is made to be dynamically similar to the actual rotor system in aero-engines. Eddy transducers are used to measure the cage motions and monitor the rotor vibrations. Based on the test rig, a dynamic model of its rotor system with four degrees-of-freedom is developed to determine the reaction forces due to rotor unbalance, which are introduced as boundary conditions for the bearing dynamic analysis. And then, a three degrees-of-freedom dynamic model of bearing cage taking the obtained reaction forces into account is also proposed. Finally, the experiment and simulation of the cage motions are carried out and compared at different rotating speeds and rotor unbalances. The experimental results of the cage motions agree with the theoretical predictions and reveal that the cage motions generally contain the multiple harmonic components, such as the cage rotating frequency and its multi-frequency, the inner ring rotating frequency, and also some combination frequencies due to rotor unbalance. The amplitudes of the inner ring rotating frequency and combination frequencies of the cage motions increase with the increment of the rotor unbalance values. Besides, the trajectories of cage are affected by the rotor unbalances.

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Abstract：Integral gear assembly centrifugal compressor is critical in modern energy equipment field, which has advantages of high efficiency, lower cost and compact structure. The most important characteristic of its rotor system is its complicated dynamic characteristics due to the interaction of the multiple rotors in paralleled arrangement and coupled by different gears, which would make the performance of the equipment significantly influenced by the nonlinear characteristics of mesh force. In this paper, a dynamic model of the gear system in a five shaft integrally geared centrifugal compressor is proposed, where the time-varying stiffness, tooth backlash and the gear mesh errors are considered and the dimensionless method is applied. Then, the response characteristics and complex dynamics behaviors of the gear system are analyzed with different meshing frequencies and different loads with numerical analysis method. The result shows that the obvious nonlinear phenomena of the gear system are shown with the increasing meshing frequency. The impact between the gears could be reduced under controlled loading, which would ensure the gear system vibrate in a particular state. Key words：five