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In view of the issue that current gear dynamics model contains no parameters about tooth surface topography, this paper puts forward an improved nonlinear dynamic model of gear pair with tooth surface microscopic features through revision of the backlash equation by W–M function from fractal theory and combination with the tradition gear torsional model. The model sets up a mathematical relationship between gear dynamic characteristics and surface microscopic parameters such as surface roughness and fractal dimension. Results of the numerical simulations indicate that as surface roughness decreases, meshing stiffness increases and viscous damping rises, the gear dynamic performance tends to be better, which is consistent with the existing research reports. Furthermore, it is found that dropping of fractal dimension is good to improve gear dynamic performance, so gear dynamics can be enhanced by decreasing the fractal dimension if surface roughness is set or cannot be decreased anymore. Moreover, it is also shown that initial backlash has little impact on the rule of gear dynamics response but influences the size of start-up or stop shock. Finally, the model is validated by a series of simulations and comparison with experimental data and existing model. The theory here opens up a mathematical methodology to analyze gear dynamics with respect to tooth surface microscopic features, which lays a theoretical basis for design of tooth surface topography to obtain better performance of gear transmission in the future.

A dynamic model of an L-shaped multi-beam joint structure is presented to investigate the nonlinear dynamic behavior of the system. Firstly, the nonlinear partial differential equations (PDEs) of motion for the beams, the governing equations of the tip mass, and their matching conditions and boundary conditions are obtained. The natural frequencies and the global mode shapes of the linearized model of the system are determined, and the orthogonality relations of the global mode shapes are established. Then, the global mode shapes and their orthogonality relations are used to derive a set of nonlinear ordinary differential equations (ODEs) that govern the motion of the L-shaped multi-beam jointed structure. The accuracy of the model is verified by the comparison of the natural frequencies solved by the frequency equation and the ANSYS. Based on the nonlinear ODEs obtained in this model, the dynamic responses are worked out to investigate the effect of the tip mass and the joint on the nonlinear dynamic characteristic of the system. The results show that the inertia of the tip mass and the nonlinear stiffness of the joints have a great influence on the nonlinear response of the system.

A nonlinear analytical model for a spacecraft with flexible jointed appendages is presented and subsequently used to investigate the nonlinear vibration phenomenon of the system caused by the joints nonlinearities during the spacecraft maneuvering. In this model, the joint transmitted characteristics which included linear and nonlinear stiffness, damping and friction are introduced into the system by applying the equilibrium conditions between the beams and the joints. Consequently, an explicit set of reduced-order nonlinear ordinary differential equations (ODEs) of motion for the flexible spacecraft with nonlinear joints are obtained based on the global mode method. Through the nonlinear ODEs obtained in this model, the dynamic responses of the system with various joint parameters are worked out numerically for the cases of attitude maneuver and orbit maneuver, respectively. For the case of attitude maneuver, the simulation results show that the damping and friction in the joints have a great influence on the vibration response of the system, especially the residual vibration. For the case of orbit maneuver, some nonlinear behaviors caused by the nonlinear joints are observed such as hardening, jump, sub-harmonic and super-harmonic resonance. More importantly, due to the cubic stiffness of the joint, modal coupling is exhibited, which result in the interaction between translation and rotation of the central rigid body.

This paper proposes a finite-time decoupling control strategy for aircraft with thrust vector at high angle of attack maneuver. Firstly, the nonlinear mathematical model of the aircraft is presented. Taking into account the insufficiency of the aerodynamic control surface, a thrust vector model with double nozzles is added. Subsequently, a three-channel decoupling control scheme based on finite-time extended state observer is employed to realize the high angle of attack maneuver. Strong coupling among different channels, aerodynamic uncertainties and other unmodeled dynamics are regarded as total disturbance and estimated by a finite-time extended state observer. Super-twisting (SWT) sliding mode control is utilized to obtain expected performance and finite-time stability. The daisy chain method is adopted to realize the control allocation. Finally, the numerical simulations are provided to demonstrate the effectiveness and robustness of the proposed methodology.

The elastic hydraulic isolator is a novel liquid-gas mixture isolator applied to floating slab track structure. The dynamic parameters of isolators are the key to the attenuation effect of ground vibration. Therefore, a nonlinear dynamic model and parameter identification method for vibration isolation supports of floating slab track structure is proposed. The changes in stiffness and damping parameters of the elastic hydraulic isolator are studied by changing its damping components and comparing them with those of the steel spring isolator and rubber isolator. The results indicate that the accuracy of the nonlinear dynamic model is verified by comparing the experimental curve with the reconstructed curve. The dynamic parameters of the elastic hydraulic isolator are dependent on the excitation frequency and amplitude and are influenced by the liquid viscosity and the damping plate. The stiffness and damping parameters of the elastic hydraulic isolator are similar to those of the rubber isolator, but the variation law with excitation frequency is different.

The roll-bearing-bearing housing (RBBH) system is one of the most common kernel structures used to determine strip mill stability and product surface quality in modern metallurgical machinery. To better understand dynamic characteristics of the RBBH system, this paper provides a nonlinear dynamic model and designs an engineering test platform on the RBBH system in the whole rolling process. First, a nonlinear dynamic model of the RBBH system supported by four-row rolling bearings under high speed and heavy load is established. Then, the method of combining Riccati transfer matrix and Newmark-β numerical integration is employed to solve nonlinear dynamic equations. After that, the engineering test platform is designed and assembled to capture and analyze the vibration signals of weathering steel (SPA-H) with finished thicknesses of 1.6 and 3.2 mm. Finally, the dynamic characteristics of the RBBH system are studied with the method of the dynamic model and vibration data fusion. The results show that the SPA-H with a finished thickness of 1.6 mm is rolled, the RBBH system fluctuates violently in both horizontal and vertical directions, and numerical results are highly consistent with experimental results in acceleration response, velocity response, and displacement response. In addition, the dynamic performance parameters of the four-row rolling bearing will also fluctuate greatly. Finally, there is significant interest to gain the benefits for the RBBH system design and mill stable rolling purposes.

This study used Markov regime switching-cum-trend and the Fourier component models to explore tourism development in Taiwan and found that during the Severe Acute Respiratory Syndrome (SARS) outbreak, tourism policy adjustments and political environment based on political relations with China, risk-increasing timing or lag timing can create systemic shifts in tourism development. Among these shifts, policy adjustments have a positive effect on the development of tourism from a low- to high-level regime. This result is different from the previous literature's conclusion that the effect of policy adjustment is insufficient and that SARS and political risks had a negative effect on tourism development from a high- to low-level regime. However, the political environment effect is limited to visitors from mainland China, Hong Kong, and Macao. This study confirms the adverse effects on sustainable tourism development when the risks in the international political environment increase.

Vibrating flip-flow screens (VFFSs) provide an effective solution for deeply screening moist and fine-grained minerals, and an accurate dynamic model of VFFSs is critical for its dynamic analysis and optimization, thereby improving the vibration stability and symmetry of VFFSs. In this paper, uniaxial tension, uniaxial compression, plane tension, and shear stress relaxation experiments were conducted on screen panel samples to illustrate that the third-order Ogden model and the generalized Maxwell model can accurately describe the hyperelasticity and viscoelasticity of screen panels. Then, the coupling method of finite element and discrete element was adopted to establish the simulation model of the screen panel and material group coupling system, and the dynamics of the coupling system under different loading conditions were explored. Finally, the dynamic model of the coupling system of VFFSs mass, screen panel, and material group was proposed, and the non-dominated sorting genetic algorithm II was applied to optimize the system’s dynamic response. The results reveal that the use of optimized shear springs can reduce the relative amplitude change rate of the main and floating screen frame by 44.30% while maintaining the periodic motion of the VFFSs under operation conditions, greatly enhancing the stability of the VFFSs system.

A polymer electrolyte membrane is a core component of proton exchange membrane fuel cell. Since the ionic conductivity of polymer electrolyte membrane depends on water content, it is necessary to understand the water transport mechanism in the polymer electrolyte membrane. When the electric current demand is varied rapidly, the transient water transport results in the shortage or flooding in the polymer electrolyte membrane. The transient behavior of water transport in the polymer electrolyte membrane is nonlinear due to the water sorption/desorption mechanism. In this study, the nonlinear water transport mechanism of polymer electrolyte membrane is established to understand the transient behavior of water transport over the rapid change of electric current. Since the nonlinear dynamics delay the response of water transport under rapid change of electric current, system-level simulation is conducted to evaluate the system response by delayed water transport. Results show that the rapid change of electric current dramatically affects the water transport dynamics. As a result, this study confirms that water transport in the electrode is delayed depending on the polymer electrolyte membrane (PEM) thickness and that flooding occurs in the cathode depending on the relative humidity at the anode inlet.

Rolling element bearing is a vital component in rotating machinery, such as a wind turbine (WT) system. By accurately monitoring its health condition, the faults can be detected at an early stage, providing sufficient lead time to perform maintenance and hence reducing accidents and economic losses. Bearing usually suffers from various wears and tears, which result in a gradual increase in clearance through its lifetime. Insufficient understanding of vibration characteristics under different clearances brings difficulties for bearing condition monitoring. Thus, this paper presents a nonlinear bearing vibration model with six degrees of freedom (DOF) to investigate the vibration characteristics under different radial clearances and load conditions. Then, a dedicated bearing test is established to verify the reasonability and effectiveness of the vibration model. Furthermore, a comprehensive simulation analysis is conducted to study the vibration characteristics over an extended range of the internal radial clearance and external load. Results show that the dynamic force on each ball presents an impulse whose magnitudes increases whereas the pulse width reduces with clearance increases. Ball pass frequency of outer race (BPFO) is the dominant modulation component and the frequency is in accordance with the number of dynamic force impulses. Two indicators, i.e., root mean square (RMS) value and spectral centroid, are proposed to indicate clearance changes. In general, they show an uptrend with the increase in clearance, which is in line with the dynamic force increasing with clearance, especially the spectral centroid of the low frequency band. However, it should be noted that the RMS value and spectral centroid exhibit a fluctuating behavior due to nonlinear vibration responses. For the first time, this study shows the details of vibration characteristics with clearance variations and provides a foundation for monitoring the bearing conditions before any obvious local defects on raceways.