A nonlinear dynamic model is proposed to investigate the dynamic interactions between the rolling element and cage under rotational speed fluctuation conditions. Discontinuous Hertz contact between the rolling element and the cage and lubrication and interactions between rolling elements and raceways are considered. The dynamic model is verified by comparing simulation result with the published experimental data. Based on this model, the interaction forces and the contact positions between the rolling element and the cage with and without the rotational speed fluctuation are analyzed. The effects of fluctuation amplitude, fluctuation frequency, and cage pocket clearance on the interaction forces between the rolling element and the cage are also investigated. The results show that the fluctuation of the rotational speed and the cage pocket clearance significantly affects the interaction forces between the rolling element and the cage.

Rolling-element bearings play vital roles in the dynamic vibration performance of the whole machinery. Hence, accurate modeling and assessment of the rolling-element bearing are beneficial for the well understanding of the vibration response of rolling-element bearing. However, cage slip is usually ignored in the traditional rolling-element bearing modeling methods, which has a direct influence on the rotating speed and friction force of the rolling elements. To settle the modeling problem of rolling-element bearing with cage slip, in this study, a nonlinear dynamic model with multiple degrees of freedom of the roller bearing is established. The cage slip, the motion of each roller, nonlinear contact, damping, and friction are taken into consideration. With the proposed method, a nonlinear traction model is presented to describe the friction forces induced by cage slip. Furthermore, both the friction force acting on rolling elements and the effects of cage slip on the vibration response are investigated based on the established model. Some comparisons between the proposed modeling method with cage slip and the classical method without cage slip are made. The results show that the friction force applied to the balls increases with the cage slip, friction coefficient, rotational speed, and radial load. A slight cage slip could be beneficial for reducing the vibration energy of rolling-element bearing; however, it will result in more friction loss and impact components.

The vibration response of rolling element bearing has a close relation with its fault. An accurate evaluation of the bearing vibration response is essential to the bearing fault diagnosis. At present, most bearing dynamics models are built based on rigid assumptions, which may not faithfully reveal the dynamic characteristics of bearing in the presence of fault. Moreover, previous similar works mainly focus on the fault with a specified size without considering the varying contact characteristics as the fault evolves. This paper developed an explicit dynamics finite element model for the bearing with three types of raceway faults considering the flexibility of each bearing component in order to accurately study the contact characteristic and vibration mechanism of defective bearings in the process of fault evolution. The developed model is validated by comparing its simulation results with both analytical and experimental results. The dynamic contact patterns between the rolling elements and the fault, the additional displacement due to the fault and the faulty characteristics within the bearing vibration signal during the fault evolution process are investigated. The analysis results from this work can provide practitioners an in-depth understanding towards the internal contact characteristics with the existence of raceway fault and theoretical basis for rolling bearing fault diagnosis.

Skidding has a great influence on the reliability and the life of rolling element bearings. The previous research of bearing skidding mainly focussed on the gross skidding of bearings under severe conditions. However, the local skidding of rolling element also exists and cannot be ignored when bearing normally runs at steady state. In this paper, considering the discontinuous contact between the roller and the cage, the Hertz contact between the roller and races, lubrication, centrifugal effects and the cage pocket clearance, a nonlinear dynamic model is established to investigate the local skidding behaviour of a roller in cylindrical roller bearings. The equations of the dynamic model are solved by the fourth-order Runge–Kutta algorithm and verified by comparing simulation results with the published experimental data. The results show that the local skidding of the roller still noticeably exists in bearings even when the gross skidding can be ignored, especially on the inner raceway. The local skidding at the entry of the loaded zone may cause the smearing on the raceway surface. However, it can be found that the probability of the local skidding of the roller will be decreased by increasing radial load and reducing the bearing rotational speed. The cage pocket clearance would induce violent fluctuations on the roller rotational angular velocity as well as on the sliding velocity. Furthermore, it can generate extraordinary impact forces between the rollers and the cage. Thus, the cage pocket clearance should be carefully considered in the design of bearings.

An internal impact usually happens when there is a small defect in one part of rolling bearings. The Fault signal from this impact is always masked by different noises such as strong vibrations from other parts and the random noise of instrumentation, which makes it difficult to extract an accurate feature signal for early fault diagnosis. In this paper, a simulation study is conducted using the method of finite element analysis (FEA) to understand the vibration characteristics from the small impact. The vibration responses have been modelled based on a typical bearing assembly. Common faults including outer ring defect, inner ring defect and rolling ball defect are simulated and their vibration responses are compared between different faults and at different locations in the bearing housing. The results obtained have shown that under the same defect size, the vibration from the outer ring is the highest whereas that from the rolling ball is the smallest. In addition the vibration close to the mounting hole attenuates considerably compared to that close to outer ring. These findings provide fundamental information to place vibration sensors and to analyse vibration signals.

To illustrate the vibration characteristics of the defective bearing more precisely, a dynamic model considering the detailed motion of the roller and the impact between the roller and the cage when the roller passes through the defect has been proposed. It overcomes the shortcomings of the previous models in which the roller's and cage's rotational speeds are set as constant values. The proposed model considers the detailed motion of the roller and the impact between the roller and the cage when the roller passes through the bearing defect. The validity and accuracy of the proposed model were verified by an experimental study. The motion characteristics, force characteristics, and vibration characteristics, when the roller passes through the defect, are analyzed. In addition, the vibration signals of the roller passing through two different types of defects are studied. The results show that the roller's rotational speed suddenly increases and the fluctuation amplitude of the revolution speed increases when the roller exits from the large defect. The large defect leads to high-frequency unstable collisions between the roller and the defective raceway. In addition, the slip velocity and the friction force between the roller and the raceway intensify the collision amplitude and generate high-frequency components of the vibration signal. They will also lower the frequency of the roller passing through the outer raceway, especially under high speed and light load conditions. The slipping and the restress between the roller and the defected raceway lead to small variations and big shocks in the vibration acceleration signal, respectively. These phenomena demonstrate the necessity of considering the detailed motion of the roller and the impact between the roller and the cage in the dynamic model.