Frequency analysis of a two-stage planetary gearbox using two different methodologies

This paper is focused on the characterization of the frequency content of vibration signals issued from a two-stage planetary gearbox. To achieve this goal, two different methodologies are adopted: the lumped-parameter modeling approach and the phenomenological modeling approach. The two methodologies aim to describe the complex vibrations generated by a two-stage planetary gearbox. The phenomenological model describes directly the vibrations as measured by a sensor fixed outside the fixed ring gear with respect to an inertial reference frame, while results from a lumped-parameter model are referenced with respect to a rotating frame and then transferred into an inertial reference frame. Two different case studies of the two-stage planetary gear are adopted to describe the vibration and the corresponding spectra using both models. Each case presents a specific geometry and a specific spectral structure.     

Gear fault diagnosis under non-stationary operating mode based on EMD,TKEO, and Shock Detector

Condition monitoring of gearboxes running under non-stationary operating conditions is a very difficult task. In this study, a signal processing technique is developed for damage detection of a bevel gearbox running under variable load and speed conditions. The proposed technique is applied on simulated vibration data computed through a dynamic model of bevel gearbox. The procedure used in this technique is based on the extraction of the shock related to the defect using the Shock Detector (SD) method. Firstly, vibration signals are decomposed into IMFs using Empirical Mode Decomposition (EMD). Then, the Teager–Kaiser Energy Operator (TKEO) is used to assess the instantaneous energy of the signal. Afterwards, SD is applied to examine and quantify the shock contents of the TKEO signal, which reflect the effect of the defect.     

青洲斜拉桥的基准动力有限元模型

讨论了斜拉桥有限元动力分析模型,给出了基于环境振动试验结果建立大跨度斜拉桥基准有限元模型的步骤;讨论了桥面初始平衡构型、几何非线性、桥面板、混凝土桥面板与钢梁的剪力连接和端部纵向约束对模型的影响。经通车前现场环境振动试验结果验证的青洲闽江斜拉桥三维有限元模型,反映了桥梁在运营前的真实动力行为,可作为该桥各种复杂响应分析和长期健康监测、使用状态评估的基准。     

Modelling of gearbox dynamics under time-varying nonstationary load for distributed fault detection and diagnosis

Fault detection and diagnosis in mechanical systems during their time-varying nonstationary operation is one of the most challenging issues. In the last two decades or so researches have noticed that machines work in nonstationary load/speed conditions during their normal operation. Diagnostic features for gearboxes were found to be load dependent. This was experimentally confirmed by a smearing effect in the spectrum.In order to better understand the involved phenomena and to ensure agreement between simulation and experimental results, two models of gearboxes (a fixed-axis two-stage gearbox and a planetary gearbox) operating under varying load conditions are proposed. The models are based on two mechanical systems used in the mining industry, i.e. the belt conveyor and the bucket wheel excavator. An original transmission error function expressing changes in technical condition and load variation is presented.Energy based parameters (the signal RMS value or the arithmetic sum of the amplitudes of spectral gearmesh components) are adopted as the diagnostic features. Simulation results show a strong correlation between load values, changes in condition and the diagnostic features. The findings are key to condition monitoring. Thanks to the use of the models one can better understand the phenomena identified through an analysis of vibration signals captured from real machines.     

Morphological covering based generalized dimension for gear fault diagnosis

This investigation presents a new generalized dimension estimation method based on morphological covering (MC) technique for characterizing the nonlinearity and complexity of vibration signals measured from gearbox. A synthetic fractal signal is employed to evaluate and compare the proposed MC technique with the traditional box-counting (BC) method and a similar approach developed in literature. Results revealed that the presented MC method is the one providing the most reliable generalized dimension estimation results. Furthermore, we applied this scheme to analyze the vibration signals from a gearbox with three operation states. The estimated general dimensions are used as the input feature vector for classifiers to the gear working states. Experimental results showed that our presented scheme achieves the best performance on discriminating the gear conditions. We also explore the calculational efficiency of the MC method. Results demonstrated that the MC method requires much less computational cost than BC method and seems to be more suitable for on-line condition monitoring of gearboxes.     

挠性航天器太阳翼全局模态动力学建模与实验研究

现代柔性航天器通常安装有大型太阳翼为其在轨运行提供所需动力. 航天器入轨后太阳翼展开并锁定成为铰链连接多板结构, 此类结构质量轻、跨度大、刚度低的特点使其低频振动和非线性振动问题越来越凸显. 分析和处理此类结构出现的复杂振动问题的关键在于建立系统精确的非线性动力学模型. 为此, 本文提出铰链连接多板结构解析全局模态的提取方法, 获取太阳翼的固有频率和解析函数表征的全局模态. 提出可变刚度的扭转弹簧等效模型, 考虑铰链非线性刚度及摩擦力矩等因素, 通过全局模态离散得到系统的低维高精度非线性动力学模型, 研究了太阳翼在周期激励作用下的非线性特性. 开展太阳翼地面振动实验研究, 采用锤击法获取系统模态, 利用振动台施加正弦扫频激励, 将物理实验结果与理论结果进行对比, 从而验证全局模态动力学建模方法的合理性与准确性. 结果表明, 铰链刚度等结构参数对系统固有特性的影响较大, 铰链的存在会使太阳翼的动态响应出现跳跃等非线性现象. 全局模态动力学建模方法能很好地解决多板结构在非经典边界下解析全局模态求解的困难, 系统全局模态反映的是系统各个部件弹性振动的真实模态, 所建立的动力学模型具有低维高精度的特点, 对于复杂组合结构非线性动力学建模具有重要的参考价值.      

Application of energy operators for detection of failures in gearboxes

The paper presents the possibility of detection of early stages of local faults in gears using energy operators. During operation of gearbox, the local faults, such as pitting or tooth base fracture, are causing disturbances in the teeth contacts resulting in creation of local and transient anomalies in a vibration signal. Analysis performed on the diagnostic signal are focused on, as early as possible, detection of such anomalies but also on assess localization of defects and remaining useful life of gears. Methods of signal analysis presented in the paper allow detection of local nonstationarities in the time-domain vibration signal. It is assumed that such transient events are linked to the fatigue tooth damages. Described methods use energetic operators for obtaining diagnostically useful information.     

Analytical study of the nonlinear behavior of a shape memory oscillator: Part II—resonance secondary

In this work, the response of a single-degree-of-freedom shape memory oscillator subjected to the excitation harmonic has been investigated. Equation of motion is formulated assuming a polynomial constitutive model to describe the restitution force of the oscillator. Here the method of multiple scales is used to obtain an approximate solution to the equations of the motion describing the modulation equations of amplitude and phase, and to investigate theoretically its stability. This work is presented in two parts. In Part I of this study we showed the modeling of the problem where the free vibration of the oscillator at low temperature is analyzed, where martensitic phase is stable. Part I also presents the investigation dynamics of the primary resonance of the pseudoelastic oscillator. Part II of the work is focused on the study in the secondary resonance of a pseudoelastic oscillator using the model developed in Part I. The analysis of the system in Part I as well as in Part II is accomplished numerically by means of phase portraits, Lyapunov exponents, power spectrum and Poincare maps. Frequency-response curves are constructed for shape memory oscillators for various excitation levels and detuning parameter. A rich class of solutions and bifurcations, including jump phenomena and saddle-node bifurcations, is found.     

Analytical study of the nonlinear behavior of a shape memory oscillator: Part I—primary resonance and free response at low temperatures

In this work, the response of a single-degree-of-freedom shape memory oscillator subjected to the excitation harmonic has been investigated. Equation of motion is formulated assuming a polynomial constitutive model to describe the restitution force of the oscillator. Here the method of multiple scales is used to obtain an approximate solution to the equations of the motion describing the modulation equations of amplitude and phase, and to investigate theoretically its stability. This work is presented in two parts. In Part I of this study we showed the modeling of the problem where the free vibration of the oscillator at low temperature is analyzed, where martensitic phase is stable. Part I also presents the investigation dynamics of the primary resonance of the pseudoelastic oscillator. Part II of the work is focused on the study in the secondary resonance of a pseudoelastic oscillator using the model developed in Part I. The analysis of the system in Part I as well as in Part II is accomplished numerically by means of phase portraits, Lyapunov exponents, power spectrum and Poincare maps. Frequency-response curves are constructed for shape memory oscillators for various excitation levels and detuning parameter. A rich class of solutions and bifurcations, including jump phenomena and saddle-node bifurcations, is found.     

Free transverse vibration analysis of a toothed gear

Analysis of transverse vibration of the gear found in a high-speed gearbox considered as an annular plate reflecting gear geometry is the subject of this paper. How gear angular velocity affects the deformation of normal modes of transverse vibration of the system under consideration is analysed. Models considered were discretized by the finite elements method. Numerical computations have been performed in the ANSYS environment. The algorithm to identify the proper distorted mode shapes is presented. The Campbell diagram for the system under consideration is elaborated. The problems discussed here can be useful for engineers dealing with dynamics of rotating machine systems.     

改进的小损伤结构动力学有限元建模方法

在遗传算法或神经网络方法识别结构损伤位置和程度时,都是基于少量的在线测量的损伤结构振动响应数据和大量的模型仿真数据来实现的,因而建立高效和精确的损伤结构动力学有限元模型,以便仿真获得损伤结构的大量动力学响应数据是十分重要的基础前提工作。本文针对ANSYS结构分析软件在建立结构小损伤有限元动力学模型存在两个关键问题,结构损伤处直接网格划分的计算结果误差和网格节省问题,以结构损伤振动检测的实际需要为出发点,提出了建立含小损伤结构的ANSYS动力学建模技术,研究了结构局部小损伤及其位置与所在处单元刚度矩阵变化的数量关系。     

挠性根部梁的动力学建模

挠性根部梁具有整体平动和转动自由度，其传统模型只适宜根部挠性很小的梁．采用柔性多体系统的建模方法建立了挠性根部Euler—Bernoulli梁的非线性动力学模型及线性耦合模型，所建模型不受根部挠性大小的限制；既可描述挠性根部梁的耦合振动，也可分别退化为固支梁或刚性梁的动力学模型；且线性耦合模型可线性变换为挠性根部梁传统模型．作为算例，采用假设模态法分析了两类线性模型的振动特性，表明线性耦合模型优于挠性根部梁传统模型．     

大型柔性航天器动力学与振动控制研究进展

随着航天重大工程的逐步实施,航天器正朝着超高速、超大尺度、多功能的方向发展,其面临的发射和运行环境也更加恶劣.航天器发射过程中的振动及其主/被动控制、在轨运行中大型柔性航天器动力学建模与动态响应分析、结构振动与飞行器姿态的混合控制等问题越来越复杂且难于处理;航天器结构的大型化和柔性化(如大阵面天线和太阳翼等)也对其地面试验和半实物仿真提出了挑战.本文着重介绍大型柔性航天器涉及到的动力学与振动控制问题,包括航天器发射过程中的整星隔振,大型柔性结构动力学建模与振动响应分析,大型柔性航天器的结构振动与姿轨控耦合动力学及其混合控制等.提炼出航天动力学与控制领域中亟待解决的若干基础科学问题,包括:多刚柔体系统动力学建模与模型降阶(涉及大变形柔性体动力学建模、多求解器合作仿真、模型降阶、组合结构动力学建模的解析方法等);复杂结构状态空间模型构建方法与能控性(涉及状态空间模型构建的理论与实验方法、复杂结构振动控制系统的能观性与能控性等);航天器姿态运动与大型柔性结构振动的混合控制律设计(涉及姿态机动与结构振动的鲁棒混合控制、执行机构与压电控制器的协同控制等).      

压电与摩擦电复合型旋转能量采集动力学协同调控机制研究

低转速激励下能量采集性能差是目前制约旋转能量采集技术应用的瓶颈问题. 本文提出了动力学协同调控机制, 并用于调控系统的动力学行为, 可以使器件在低转速激励下有效工作, 提高了旋转能量采集系统的电学性能. 旋转刚度软化、非线性磁力、几何边界的协同调控既可以增加系统在低速下的振动位移以及压电材料的形变, 也可调控系统的最大位移, 使其振动可控并限制位移过大提高可靠性. 此外, 几何边界可以方便地集成摩擦纳米发电机, 实现压电与摩擦两种机电转换机制在振动和碰撞过程中协同发电, 有效利用空间和提高输出电能. 基于哈密顿原理建立了系统的机电耦合动力学模型并进行了实验验证. 实验结果表明系统能够在0~250 r/min的低转速范围内有效工作, 在转速为250 r/min时, 压电单元和摩擦纳米发电机的最大峰峰值电压分别为132 V和1128 V, 总平均功率为1426 μW. 本文提出的动力学协同调控机制为能量采集系统动力学和电学性能改进提供新的途径, 有益于促进自供能物联网技术的发展与应用.      

关于弹性梁的数学模型

叙述和比较一维弹性体的两种不同建模方法, 即弹性梁的传统建模方法和基于 Kirchhoff-Cosserat模型的建模方法. 应用精确Cosserat模型分析梁的三维运动. 考虑中 心线的拉伸压缩变形、截面的剪切变形、截面转动的惯性和端部载荷影响等因素, 建立精确 的弹性梁动力学方程. 讨论梁的静态和动态平衡稳定性. Kirchhoff杆、铁摩辛柯 梁和欧拉--伯努利梁等为Cosserat模型在各种简化条件下的特例.     

独塔斜拉桥的环境振动试验与分析

桥梁环境振动试验具有简单方便和花费少等优点.本文以吉林市临江门大桥为工程背景,通过动力试验,研究了该桥在天然脉动荷载作用下的固有特性.采用结构分析软件ANSYS建立全桥的空间模型,计算该桥的固有特性.有限元计算结果与动力试验结果比较吻合.结果表明,环境振动响应足以识别出该桥所感兴趣的模态,可作为该桥的有限元模型修正、损伤检测、使用状态评估和健康监测的基础.     

Non-smooth predictive control for mechanical transmission systems with backlash-like hysteresis

This paper proposes a non-smooth predictive control approach for mechanical transmission systems described by dynamic models with preceded backlash-like hysteresis. In this type of system, the work platform is driven by a DC motor through a gearbox. The work platform is represented by a linear dynamic sub-model connected in series with a backlash-like hysteresis inherent in gearbox. Here, backlash-like hysteresis is modeled as a non-smooth function with multi-valued mapping. In this case, the conventional model predictive control for such system cannot be implemented directly since the gradients of the control objective function with respect to control variables do not exist at non-smooth points. In order to solve this problem, a non-smooth receding horizon strategy is proposed. Moreover, the stability of predictive control of such non-smooth dynamic systems is analyzed. Finally, a numerical example and a simulation study on a mechanical transmission system are presented for validating the proposed method.     

机床非线性颤振的分段线性化及其数学模型

通过引入非线性调制环节N(S),本文实现了非线性颤振的分段线性化,建立了统一的切削动力学系统模型。这一模型使线性颤振理论、非线性颤振理论趋于统一,并使超声振动切削抑制颤振的机理从理论上得到解释。     

A modified wake oscillator model for vortex-induced vibration of circular cylinders for a wide range of mass-damping ratio

In this paper, the behavior of an elastically mounted cylinder, subjected to vortex-induced vibrations (VIV), is investigated by a low-dimensional model. The classical wake oscillator model, as a standard model, predicts the behavior of the system at high mass-damping ratios but fails in modeling the system at low mass-damping ratios. A modified wake oscillator model is introduced in order to describe the response of the system over a wide range of mass-damping ratios. The results of this new model are compared to experimental results from the literature and shown to be in good agreement. The new model can describe most of the features of vortex-induced vibration phenomenology, such as the Griffin plot and lock-in domains.     

Validation of CFD-DEM simulation of a liquid–solid fluidized bed by dynamic analysis of time series

Liquid–solid fluidized beds (LSFB) modeling validation is crucial for establishing design rules and monitoring tools. However, it generally relies on comparing global variables, which overlook dynamic features that influence reaction outputs. This work aims to implement time series analysis tools to compare Radioactive Particle Tracking data with a simulation consisting of Computational Fluid Dynamics coupled with Discrete-Element Method. Experiments have been performed in a pilot-scale LSFB of calcium alginate spheres fluidized with a calcium chloride solution. The Diks’ test indicates that the simulation can capture the LSFB behavior. It also allows diagnosing flow regime transitions from the simulation. Trends of solid dispersion coefficients and mixing times predicted by the simulation are in good agreement with the experiments.