•This work reviews mechanical model development of rolling bearing-rotor systems.•Five kinds of rolling bearing models are summarized.•The coupled modeling between bearing models and rotor models are ...addressed.•Challenges and prospects of model development are discussed.
The rolling bearing rotor (RBR) system is the kernel of many rotating machines, which affects the performance of the whole machine. Over the past decades, extensive research work has been carried out to investigate the dynamic behavior of RBR systems. However, to the best of the authors' knowledge, no comprehensive review on RBR modelling has been reported yet. To address this gap in the literature, this paper reviews and critically discusses the current progress of mechanical model development of RBR systems, and identifies future trends for research. Firstly, five kinds of rolling bearing models, i.e., the lumped-parameter model, the quasi-static model, the quasi-dynamic model, the dynamic model, and the finite element (FE) model are summarized. Then, the coupled modelling between bearing models and various rotor models including De Laval/Jeffcott rotor, rigid rotor, transfer matrix method (TMM) models and FE models are presented. Finally, the paper discusses the key challenges of previous works and provides new insights into understanding of RBR systems for their advanced future engineering applications.
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•Temperature-related fit clearance is considered for the ceramic bearing dynamics.•The effect of fit clearance increases with the working temperature.•The orbit-spinning ratio ...reflects the rolling and sliding in the bore of pedestal.•Increase of the axial load helps with the offset of fit clearance.
Owing to the difference in thermal deformation of the ceramic outer ring and steel pedestal, the outer ring experiences orbital and spinning motions in the fit clearance in wide temperature ranges, which has significant impacts on the bearing performance. In this paper, a dynamic model considering the temperature-related clearance is proposed, and the interactions between bearing and pedestal are calculated with a loose outer ring boundary condition. The orbit and spinning speeds are obtained, and the parameters concerning the speed ratio are used to evaluate the dynamic behaviors of the outer ring. Parametric analyses of temperature, rotation speed, and external load are conducted, and the results are verified through an experiment. The results show that changes in orbit-spinning behaviors are produced by variations in contact forces and area, and increased axial preload improves the stability of the bearing system. The results provide insights on bearing dynamics, and are useful for the design of ceramic bearing systems.
•An overall gear transmission model which incorporates with gearbox casing is proposed.•Introduced a new way to model gear tooth pitting and spalling.•The proposed model in simulating tooth pitting ...and spalling is validated by experimental tests.•The vibration fault features of tooth pitting and spalling are discussed.
Dynamical modeling of a gear system with faults has been an important research topic for understanding fault features and their associated fault vibration mechanisms. Due to the complicated structures and intricate interactions between the components of the gear system, the fault vibration features and corresponding vibration mechanisms due to tooth pitting and spalling remain mostly unknown. This paper proposes a novel spur gear dynamical model, validated by various experimental tests, to analytically investigate the effects of tooth pitting and spalling on the vibration responses of a gear transmission. The proposed dynamical model considers the effects of tooth surface roughness changes and geometric deviations due to pitting and spalling, and also incorporates Time Varying Mesh Stiffness (TVMS), a time-varying load sharing ratio, as well as dynamic tooth contact friction forces, friction moments and dynamic mesh damping ratios. The proposed gear dynamical model is validated by comparison with responses obtained from experimental test rig under different conditions. Comparisons indicate that the responses of the proposed dynamical model are consistent with experimental results, in both time and frequency domains under different rotation speeds and fault severity conditions.
•A nonlinear tribo-dynamic model of a spur gear drive under run-dry condition is built.•Temperature rise and tooth wear are included in the proposed model.•Friction coefficient is predicted based on ...computational inverse technique.•The natural frequency is evidently affected by the flexibility of shaft but friction.•Tooth wear not only aggravates gear vibration but also changes the phase of DTE.
Gearbox is required to serve for ≥ 30 min in helicopter design to improve survivability, when the gear drive loses lubrication due to battle damage. Under such loss-of-lubrication condition, tooth friction, wear and temperature pose serious problems to dynamic performance of gears. Therefore, a nonlinear tribo-dynamic model of spur gear drives is established and experimentally validated in this work. The time-varying friction coefficient is predicted under loss-of-lubrication condition on the basis of computational inverse technique. The temperature rise and tooth wear caused by friction were included by using thermal network model and dynamic wear model. The flexibility of gear shafts and the gyroscopic effect of gear rotors are also considered. The results indicate the gyroscopic effect apparently affects the natural frequency of the gear drive, while friction has negligible effect on the natural frequency but has considerable effect on the nonlinear behavior. The influence of temperature and gyroscopic effect on nonlinear behavior are reflected in the region of middle and high speed, while tooth wear mainly affects the bifurcation at the middle speed. In addition, tooth wear not only aggravates gear vibration but also can change the phase of dynamic transmission error. The analysis and experiment results can be an important reference in reducing friction and wear, restraining nonlinear behavior, and reducing vibration and noise.
The effective remaining useful life (RUL) prediction of rolling bearings could guarantee mechanical equipment reliability and stability. The hybrid physical and data-driven prognosis model (HPDM) is ...recently receiving increasing attention. However, HPDM approaches suffer from two significant challenges that limit their applicability to complex prognosis scenarios: (1) the reality gap between the simulation and measurement data and (2) the limited model generality to accommodate different working conditions and machines. From the perspective of leveraging physical model inference as 'teachers' for the data-driven model, this article proposes a calibrated-based hybrid transfer learning framework to improve the data fidelity and model generality. Firstly, a 5-DOF dynamic model of rolling bearing is constructed. Comprehensively considering the crack and spall behaviors of degradation evolution, the physical model could provide various failure trajectories. Secondly, the particle filter-based calibration is proposed to retain the high fidelity of the physical simulation. Finally, a Physics-informed Bayes Deep Dual Network (PI-BDDN) is designed. The designed network fuses the physical calibrated simulation as augmented input space to learn representative prognosis features and makes the transfer learning process interpretable by combining the physical model parameters into adversarial learning to selectively identify the most informative knowledge for RUL prediction. The effectiveness of the proposed method is verified on two representative bearing datasets, and comparative results show the superiority of the proposed method on prediction accuracy and uncertainty quantification.
This paper is aimed on the analysis of monthly spot oil prices (WTI) between 1986 and 2015. The methodology is based on Dynamic Model Averaging (DMA) and Dynamic Model Selection (DMS) framework. The ...important feature of DMA method is an allowance for both time-varying coefficients and large state space model (i.e., the set of oil price determinants can change in time). Within this framework it was explicitly shown how the significance of oil price determinants vary in time. These determinants itself were chosen with respect to some previous studies. Contrary to the currently reported DMA applications in some other fields, no significant evidence was found that DMA is superior over, for example, ARIMA model. However, DMA could also not been rejected as a significantly worse model due to certain statistical tests. The performed DMA analysis was checked for robustness on various model parameters and for certain computational issues.
It was found, for example, that in the context of the 2008 oil price peak exchange rates and stock markets were important oil price drivers, whereas oil production or oil import were just minor determinants. Some role of the change in inventories was found, but not greater than the one in 1991. The role of China's economy as an oil price driver in 2008 was found to be relatively smaller than in other time periods. Also, the robustness of these findings was discussed.
•spot oil prices were analysed between 1986 and 2015 basing on Dynamic Model Averaging and Dynamic Model Selection framework,•stock markets, treasury bill rate, exchange rates, import, inventories, stock market volatility and consumption impact on spot oil price was analyzed,•the results are quite robust.
In the present works, a tribo-dynamic model considering the transient friction force is proposed to study the tribo-dynamic performances of the Water-Lubricated Microgroove Bearings (WLMB) during ...start-up under three acceleration modes. Based on the developed model, the tribo-dynamic performances of WLMB between three bottom shapes, i.e. triangle, left triangle, right triangle, are compared. In addition, the effects of the key factors, including the acceleration time, bearing shell thickness, surface parameters and dry friction coefficient, on the tribo-dynamic performances of WLMB are identified. Numerical results demonstrate that at the initial stage of start-up, the transient horizontal friction force drives the rotor along the opposite direction of rotation. The comparative analysis indicates that the sinusoidal acceleration mode and left triangle bottom shape may be recommended to yield the optimal tribo-dynamic performances of WLMB during start-up. The parametric studies reveal that during start-up, the acceleration time and the surface roughness significantly affect the tribo-dynamic performances, whereas the asperity curvature slightly affects the tribo-dynamic performances. Furthermore, the numerical results demonstrate that the dry friction coefficient plays an important role in tribo-dynamic analysis for WLMB during start-up.
•The transient friction force is considered in the tribo-dynamic model for water-lubricated microgroove bearing.•The optimal acceleration mode and bottom shape are determined by numerical analysis.•The effects of systematic parameters on the tribo-dynamic performance are identified.
•We present a simulation model of honey bee colony development.•The model effectively simulates patterns of colony population dynamics across several years.•The model helps to define situations ...likely to cause colony failure.
Rates of honey bee colony failure have increased significantly across much of North America and Europe, which has directed attention to the need to better understand the process of bee colony growth and development, and the factors that can cause colony failure. Here we present a simple model of honey bee colony dynamics as a tool to explore what factors may have the strongest influence on colony growth and survival. Our model focuses on how internal demographic processes within a colony interact with food availability and brood rearing to alter growth trajectories. The model is implemented as a series of difference equations operating at discrete time steps to model changes in bee population day by day. We base our rate equations on the analytic models of Khoury et al. (2013), and go further by simulating colony growth across three years to capture seasonal and annual growth cycles. Our resulting model successfully captures realistic seasonal variations in colony populations. Sensitivity analysis of the model suggests that colony survival is strongly influenced by rates of forager bee mortality, food availability and factors that influence the age at which worker bees transition from working inside the hive raising brood to working outside the hive as foragers. We discuss these findings with reference to known agents that can cause colony failure. The presented model is very simple, and makes minimal assumptions, but could easily be extended to more accurately simulate the performance of field honey bee colonies and/or specific environmental or pathogen pressures.
•Propose a hierarchical model for identifying resilience enhancement strategies.•Adopt a control-based framework to model the transient system behaviors under disruptions.•Propose a multi-objective ...optimization model to find the optimal RES combinations.•Provide a unified framework for analyzing the tradeoffs of different RES options.
Resilience is becoming a key concept for risk assessment and safety management of interdependent critical infrastructures (ICIs). This work proposes a resilience enhancement framework for ICIs. With reference to the accidental event, ex-ante and ex-post solutions for enhancing system resilience are analysed and included into a hierarchical model of resilience enhancement strategies (RES). To provide specific resilience enhancement solutions for ICIs, we integrate the hierarchical model with a model predictive control-based dynamic model of ICI system operation. The relationships between the solutions implemented and their impacts on the system parameters are discussed. A multi-objective optimization (MOO) problem is defined, with the objectives of simultaneously minimizing RES cost and maximizing ICIs resilience. The fast non-dominated sorting genetic algorithm NSGA-II is used to solve the MOO problem. For exemplification, a case study is considered, involving interdependent natural gas network and electric power grid. The results show that the resilience enhancement framework is effective in finding optimal RESs for given ICIs.
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