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Based on Nodal Coordinate Formulation (NCF) and Absolute Nodal Coordinate Formulation (ANCF), this paper establishes rigid-flexible coupling dynamic model of the spacecraft with large deployable solar arrays and multiple clearance joints to analyze and control the satellite attitude under deployment disturbance. Considering torque spring, close cable loop (CCL) configuration and latch mechanisms, a typical spacecraft composed of a rigid main-body described by NCF and two flexible panels described by ANCF is used as a demonstration case. Nonlinear contact force model and modified Coulomb friction model are selected to establish normal contact force and tangential friction model, respectively. Generalized elastic force are derived and all generalized forces are defined in the NCF-ANCF frame. The Newmark-β method is used to solve system equations of motion. The availability and superiority of the proposed model is verified through comparing with numerical co-simulations of Patran and ADAMS software. The numerical results reveal the effects of panel flexibility, joint clearance and their coupling on satellite attitude. The effects of clearance number, clearance size and clearance stiffness on satellite attitude are investigated. Furthermore, a proportional-differential (PD) attitude controller of spacecraft is designed to discuss the effect of attitude control on the dynamic responses of the whole system.

First, an improved local mean decomposition (LMD) method called differential rational spline-based LMD (DRS) is developed for signal decomposition. Differential and integral operations are introduced in LMD, which can weaken the mode mixing problem. Meanwhile, an optimized rational spline interpolation is proposed to calculate the envelope functions aiming to reduce the large errors caused by moving average in the traditional LMD. A series of product functions (PFs) is obtained after the application of the proposed DRS-LMD. Then, Kullback–Leibler (K–L) divergence is adopted to select main PF components that contain most fault information. The machine fault can be easily identified from the amplitude spectrum of the selected PF component. The effectiveness of the proposed DRS-LMD and K–L strategy is tested on simulated vibration signals and experimental vibration signals. Results show that the proposed method can increase the decomposition accuracy of the signals and can be used to detect early faults on the gears and rolling bearings.

Piezoelectric energy harvesting from the base excitation is usually accompanied with narrow bandwidth around the natural frequency of the harvester. To realize broadband energy harvesting, a hybrid energy harvester is designed by incorporating the galloping effect. For such a harvester, the approximate solutions of the distributed parameter model are derived using the electromechanical decoupled method and confirmed by the numerical solutions of the full coupled model. An equivalent harvested power is defined to compare the powers scavenged by the hybrid, base-excitation-alone and galloping-alone systems in an excitation-frequency band symmetric to the natural frequency of each harvester. Two optimal load resistances for the maximal equivalent power of the hybrid system are obtained. The first one coincides with the optimal resistance of the base-excitation-alone system corresponding to the maximal electrical damping. The second one approximates to the optimal resistance of the galloping-alone system with the optimal electrical damping. For the cases with relatively small excitation acceleration and large wind speed, the galloping dominates the hybrid system. The equivalent power of the hybrid system is maximized at the second optimal resistance. Otherwise, the base excitation dominates the hybrid system with the equivalent power of the hybrid system maximized at the first optimal resistance. For broadband energy harvesting, especially at the excitation frequency away from the natural frequency, the optimal load resistance is found to be the second one as long as the galloping initiates. The bandwidth can even be infinite when the minimal harvested power determined by the quenching boundaries is acceptable. The hybrid system advances the base-excitation-alone system with ultra-wide band introduced by the galloping effect.

This paper presents a dynamic modeling approach for flexible spacecraft with multiple solar panels and flexible joints. Firstly, the characteristic equation for the flexible spacecraft is derived in terms of the partial differential equations of motion for the solar panels, the ordinary differential equations of motion for the central rigid body, the matching conditions at the joints, and the boundary conditions. The natural frequencies and global mode shapes of the flexible spacecraft are determined, and orthogonality relations of the global mode shapes are established. Then, the global mode shapes and their orthogonality relations are used to truncate the dynamical equation of the flexible spacecraft to a set of ordinary differential equations with multiple-DOF. The validity of the derived model is verified by comparing the natural frequencies obtained from the characteristic equation with those obtained from FEM. For each global mode shape, a translation index and a set of rotation indexes are introduced to describe the interaction between the elastic deformation of the solar arrays and the displacements of the central rigid body. Based on the truncated dynamic model obtained in this paper, dynamical responses of the flexible spacecraft with flexible joints are worked out numerically for the cases of orbit control and attitude control, respectively. The corresponding results of the flexible spacecraft with rigid joints are given to illustrate the effects of flexible joints on the responses of the system. The results show that the joint flexibility has a significant effect on the dynamical responses of the flexible spacecraft, especially, in the case of very small stiffness of the joints.

Health condition identification of planetary gearboxes is crucial to reduce the downtime and maximize productivity. This paper aims to develop a novel fault diagnosis method based on modified multi-scale symbolic dynamic entropy (MMSDE) and minimum redundancy maximum relevance (mRMR) to identify the different health conditions of planetary gearbox. MMSDE is proposed to quantify the regularity of time series, which can assess the dynamical characteristics over a range of scales. MMSDE has obvious advantages in the detection of dynamical changes and computation efficiency. Then, the mRMR approach is introduced to refine the fault features. Lastly, the obtained new features are fed into the least square support vector machine (LSSVM) to complete the fault pattern identification. The proposed method is numerically and experimentally demonstrated to be able to recognize the different fault types of planetary gearboxes.

This paper numerically investigates the effects of torque spring, close cable loop (CCL) configuration and latch mechanism on the overall dynamic characteristics of a deployable solar arrays system considering joint clearance; and presents significant guidance for the key parameters design of these three mechanisms. A typical mechanism composed of a main-body with a yoke and two panels is used as a demonstration case to study the dynamic response of the deployable solar array system in the deployment process and post-latch phase. The normal contact force model and tangential friction model in clearance joint are established using nonlinear contact force model and modified Coulomb friction model, respectively. The numerical simulation results reveal that the joint clearances influence the dynamic characteristics of the deployable space solar arrays in different operation phases. Besides, parametric studies indicate some rules to design preload and stiffness coefficient of torque spring, equivalent stiffness coefficient of CCL mechanism and stiffness and damping coefficient of latch mechanism.

Early fault diagnosis is crucial to reduce the machine downtime. This paper presents a novel method based on symbolic dynamic filtering (SDF) for early fault detection and intrinsic characteristic-scale decomposition (ICD) for fault type recognition. SDF is first applied to extract the fault feature for depicting bearing performance degradation. Then, a fault alarm is triggered using cumulative sum. Finally, the extracted abnormal signal is decomposed by the ICD method, and the kurtosis method is used to select a principal product component that contains most fault information for fault detection. The real life experimental results validate the effectiveness of the proposed method in early detection of bearing fault and fault diagnosis in comparison with Fourier transform, Hilbert envelope spectrum, original local mean decomposition and spectral kurtosis.

This paper presents a new rolling bearing fault diagnosis method based on local mean decomposition (LMD), improved multiscale fuzzy entropy (IMFE), Laplacian score (LS) and improved support vector machine based binary tree (ISVM-BT). When the fault occurs in rolling bearings, the measured vibration signal is a multi-component amplitude-modulated and frequency-modulated (AM–FM) signal. LMD, a new self-adaptive time-frequency analysis method can decompose any complicated signal into a series of product functions (PFs), each of which is exactly a mono-component AM–FM signal. Hence, LMD is introduced to preprocess the vibration signal. Furthermore, IMFE that is designed to avoid the inaccurate estimation of fuzzy entropy can be utilized to quantify the complexity and self-similarity of time series for a range of scales based on fuzzy entropy. Besides, the LS approach is introduced to refine the fault features by sorting the scale factors. Subsequently, the obtained features are fed into the multi-fault classifier ISVM-BT to automatically fulfill the fault pattern identifications. The experimental results validate the effectiveness of the methodology and demonstrate that proposed algorithm can be applied to recognize the different categories and severities of rolling bearings.

A new method called intrinsic characteristic-scale decomposition (ICD) is proposed in this paper, which is particularly suitable for processing the nonlinear and non-stationary time series. When fault occurs in gearbox and rolling bearing, the measured vibration signals would exactly present non-stationary characteristics. ICD, a new self-adaptive time-frequency analysis method, can decompose the non-stationary signal into a series of product components (PCs). Therefore, it is possible to diagnose gearbox and rolling bearing fault. In this paper, the ICD method is introduced and the decomposition performance is compared with LMD method. The results demonstrate that ICD has the advantages at least in running time, alleviating the mode mixing problem and restraining the end effect. The ICD method is applied to the practical gear and rolling bearing fault diagnosis. The results demonstrate that the proposed method is effective in the fault signature analysis of the rotating machinery.

The active-passive hybrid piezoelectric network (APPN) is investigated to reduce the vibration of cantilever beam. Hamilton’s principle with the Rayleigh-Ritz method is used to derive the equations of motion of the beam with the APPN. Only one piezoelectric actuator is bonded on the cantilever beam, so in the segment of the beam where the piezoelectric actuator is attached, the neutral axis is not the geometric center of the beam. This change on the neutral axis is considered in the process of deriving equations. Selecting RL circuit as passive shunt circuit, open-loop analysis is performed to gain insight into the passive damping features. Velocity feedback control is then employed to analyze the characteristics of the closed-loop system. Numerical results show that the APPN has a significant effect on vibration suppression, especially at narrow frequency bands. On this basis, variable RL circuit is proposed and analyzed for broadband vibration attenuation. Numerical simulations illustrate that this scheme is effective and feasible.

Empirical mode decomposition (EMD) is powerful in analyzing the vibration signals of bearings. However, the accuracy of its decomposition result is heavily dependent on the choice of envelope interpolation algorithms. In this paper, we propose a bandwidth method to select the envelope in EMD called bandwidth based EMD (BEMD). Since there is an optimization process in envelope selection, the scale mixing problem caused by envelope interpolation can be significantly weakened. The proposed BEMD method is demonstrated to be effective in rolling bearing fault diagnosis by comparing with existing improved EMD.

This article numerically investigates the effects of revolute joint clearance and structural flexibility on the overall dynamic characteristics of a deployable solar array system. Considering torque spring, close cable loop configuration, and lock mechanism, a typical mechanism composed of a main body with a yoke and two panels is used as a demonstration case to study the effects of clearance and flexibility on the dynamic response of the deployable solar array system in the deployment and lock process. The normal contact force model and tangential friction model in clearance joint are established using Lankarani Nikravesh model and modified Coulomb friction model, respectively. The numerical simulation results reveal that the coupling of clearance and flexibility makes different effects on the dynamic characteristics of the deployable space solar arrays for different operation stages. Besides, the clearance and flexibility of a mechanical system play crucial roles in predicting accurately the dynamic response of the system, which is the foundation of mechanism design, precision analysis, and control system design.

PurposeThe purpose of this paper is to analyze a new, whole‐spacecraft isolator and its performance of vibration isolation, which has been designed to ensure spacecraft safety at the launching stage.Design/methodology/approachThe design is based on the analysis of fractional derivative stress‐strain constitutive relationship of viscoelastic materials. First, the authors study the constitutive relationships for viscoelastic solid of the damping materials, then the authors introduce the results obtained to the equations of motion for the damped isolator.FindingsBy performing a series of transformation, the authors obtain the analytical solution of the equations. It is shown that the results compare favourably to the numerical simulations and experiments. In addition, a saturation phenomenon for the first order damping ratio is also discussed.Practical implicationsIt is found that the constitutive relationships written in terms of the fractional calculus can be applied in the system function of the whole‐spacecraft vibration isolator. Such relationships, developed previously from a model analysis base, have been shown to be useful tools for engineering analyses.Originality/valueSome suggestions are given to improve the design of viscoelastic whole‐spacecraft isolators. The establishment of a theoretical basis for the new fractional differential dynamical system enhances their value, as they may now be used with increased reliability of satellite.

To study the nonlinear dynamic behavior of the bladed overhang rotor system with squeeze film damper (SFD), a blade-overhang rotor-SFD model is formulated using the lumped mass method and the Lagrange approach. The cavitated short bearing model is employed to describe the nonlinear oil force of the SFD. To reduce the scale of the nonlinear coupling system, a set of orthogonal transformations is employed to decouple the one nodal diameter equations of blades, which are coupled with the dynamical equations of the rotor, with other equations of blades. In this way, the original system with 16+4n (n≥3) degrees of freedom (DoF) is reduced to a system with 24 DoF only. Then the parametric excitation terms in the blade-overhang rotor-SFD model are simplified in terms of periodic transformations. The coupling equations are numerically solved and the solutions are used to analyze the dynamic behavior of the system in terms of the bifurcation diagram, whirl orbit, Poincare map and spectrum plot. A variety of motion types are found such as multi-periodic, quasi-periodic, and chaotic motions. Moreover, the typical nonlinear dynamic evolutions including the periodic-doubling bifurcation and reverse bifurcation are noted. It is noticed that there exist apparent differences in the dynamic behavior between the blade-overhang rotor-SFD models without and with considering the effect of blades.

PurposeAs the installation of the vibration isolation device to the spacecraft for the whole spacecraft vibration isolation, the interface structure is typically modeled as a rigid structure during the design phase. However, the flexibility of the interface structure does exist for a large‐sized adaptor. This is a source of uncertainty and could reduce the reliability of the system. It is necessary to investigate the influence of this type of flexibility on the vibration isolation performance in an engineering practice. This paper aims to address this situation.Design/methodology/approachThe vibratory transmissibility from the bottom of the isolator is generally used to evaluate the performance of the vibration isolation. By introducing the interface flexibility from both the adaptor and the vibration isolation device, a planar model which includes a flexible beam representing the interface structure is established to study the influence of this type of flexibility on the vibratory transmissibility.FindingsIt is found that, when this type of flexibility is included, an extra low‐frequency mode dominated locally by the interface structure is induced, and then a significant resonance appears in the vibratory transmissibility of the vibration isolation device at a low frequency.Originality/valueThe vibration isolation performance may be over‐estimated in the design by taking the interface as rigid. The inherent flexibility of the interface structure, on the other hand, may degrade the performance of the vibration isolation device and degrade the function of the rotation constraint device added into the vibration isolation device.

Stewart platform is widely used for vibration isolation and precise pointing. As it is a statically determinate structure, if any strut has fault, a disaster could be unavoidable. In the present paper, an octo-strut passive vibration isolation platform with redundancy is introduced and applied to whole-spacecraft vibration isolation. This platform is modeled with the Newton–Euler method. To avoid such possibility that the spacecraft may interact with the fairing, an approach of stiffness design is proposed to reinforce the rotation stiffness of the platform. With the mathematical model, design parameters of the isolator that will affect the nature frequencies of the isolator-spacecraft system are studied. The transmissibility of the isolator topped with rigid and flexible spacecraft is also studied. Results of analytical and numerical studies show that the octo-strut platform is a reliable and effective approach to improving the dynamic environment of a spacecraft.

Summary A 3D static mathematical model of a bottomhole assembly (BHA) including steerable downhole motor assembly under large deflection has been established. The forces and deflections of the drillstring have been accurately computed by making use of the method of weighted residuals, the weighted objective function, and the method of optimization to calculate the tangency point and to reduce the effect of the indistinct tangency point conditions. The effects of the weight on bit, the borehole geometry, the geometry and tool face rotation of the BHA on the bit building, and right walking force have been studied separately. There is a significant difference between the bit forces of large deflection analysis and small deflection analysis.

Satellites are subject to severe vibrations during flight. These vibrations are induced by multiple sources during liftoff and the instant of final separation. Severe vibrations may cause damage to satellites. For this reason a payload adaptor is needed. Magnetorheological (MR) damper can be utilized to keep the satellites safe. But the common MR damper can’t be used in cases of high-frequency vibrations because of stiffness hardening. For this reason, a new MR damper with decoupling mechanism has been designed by adding a decoupling sheet to the common MR damper. The decoupling mechanism makes the damper sensitive to vibration. This means that the damper has different stiffness and damping in case of different vibration amplitude. Based on the Bingham model, the model of the suggested MR damper has been built, and mathematical formulas has been deduced for dynamic stiffness, delay angle and transmissibility of the damper. Dynamic characteristics have been simulated. The results show that the decoupling sheet doesn’t work in case of low frequency and high amplitude vibration and the damper presents high damping. In case of high frequency and low amplitude vibration, the decoupling sheet works and the damper presents small damping and stiffness. Thus the stiffness hardening has been avoided. Influence of internal sub structure resonance can be reduced by choosing appropriate parameters. This damper can be used for semi-active control of broadband vibration.Copyright © 2007 by ASME

Genetic algorithms (GAs) are adaptive procedures that find solution to problems by an evolutionary process that mimics natural selection. In this paper, methods based on GAs have been developed and presented for design optimization of journal bearings in nonlinear rotor system. The GA uses a 30-bit chromosome to represent the bearing radial clearance, aspect ratio and lubricant viscosity, with 10-bit for each design variable. The instability onset speed of the system is taken as the fitness function in GA, in which the nonlinear effects of the bearing fluid forces are considered. The instability onset speed is defined in two different cases, that is, periodic and quasi-periodic or chaotic motions. To verify the effectiveness of the suggested method, a rigid rotor-bearing system is taken as an example to be optimized. The different crossover probabilities, mutation probabilities and population sizes are employed to analyze their influences on GA so that a set of appropriate parameters are chosen to be used in the final calculation. The results are compared with those obtained by numerical simulation. It is shown that the proposed algorithm is effective in the optimum design of rotor-bearing system.Copyright © 2005 by ASME

The traditional payload attaching fitting (PAF) does not provide any vibration isolation, because of its large stiffness. Whole-spacecraft vibration isolation is a direct and effective approach to assure the successful launching and orbit insertion of a spacecraft. In view of the problems of stiffness and vibration isolation design, for which the designers care most, the study of whole-spacecraft vibration isolator (WSVI) consists of two parts. In the first part, the stiffness feature of the WSVI is studied with reliability analysis and experimental data. In the second part, the problems induced by stiffness feature are discussed. The simulated and experimental data show that the transmissibility, which is coupled with stiffness, can be reduced by attaching the vibration isolator between the spacecraft and the launch vehicle.