Analytical modelling of spur gear tooth crack and influence on gearmesh stiffness

Due to excessive service load, inappropriate operating conditions or simply end of life fatigue, damage can occur in gears. When a fault, either distributed or localised, is incurred by gears, the stiffness and consequently vibration characteristics of the damaged tooth will change. In this work an analytical formulation of the time varying gearmesh stiffness was derived. An original analytical modelling of tooth cracks is presented and the gearmesh stiffness reduction due to this fault is quantified. A comparison with finite element model is presented in order to validate the analytical formulation.     

小波变换理论在损伤探测中的应用

本文采用小波变换技术，对含边裂纹的悬臂梁受冲击载荷作用的情况进行分析。根据电测法得到的动态应变的实验结果，用Morlet小波变换处理，能够很好地确定边缘缺陷的特性。这为结构损伤检测提供了一个很有效的方法，具有广阔的工程应用前景。     

Calculation of conformal mapping function of the tooth profile on evolvent gear by computer

The exact solution of the stress and the displacement on spur gear can be gained by the method of conformal mapping of complex variables in plane elasticity. But it is difficult to get the comformal mapping function for the tooth profile with different parameters. They used to be obtained through trial method. This is time-consuming and expensive. In this paper a computer program is drawn up for the conformal mapping function. A large amount of calculation has given proof of its success and of the precision of the mapping function: thereby the main obstacle has been removed for the practical application of the conformal mapping method to the stress and displacement of tooth on evolvent gear.     

Nonlinear vibration of the spiral bevel gear with a novel tooth surface modification method

Meccanica - The issue of gear noise is fairly common in power transmission systems. This noise largely stems from the gear pairs vibration triggered by transmission error excitation. This is mainly...     

小波分析用于陀螺仪漂移测试信号分析的研究

为建立陀螺仪漂移特性模型，需对其进行测试。由测试得到的数据是含有噪声的，且一般是非平稳的，用小波分析测试数据是一种很有效的方法。在简述小波分析中的多分辨分析理论的基础上，用其对某型陀螺仪的实测数据进行了分析－预处理，其结果证实了所研究方法的有效性。     

Dynamic modeling and analysis of a spur planetary gear involving tooth wedging and bearing clearance nonlinearity

Tooth wedging, also known as tight mesh, occurs when a gear tooth comes into contact on the drive-side and back-side simultaneously. Tooth wedging risks bearing failures from elevated forces. This work studies the nonlinear tooth wedging behavior and its correlation with planet bearing forces by analyzing the dynamic response of an example planetary gear. This planetary gear is representative of a wind turbine geartrain. A two-dimensional lumped-parameter model is extended to include tooth separation, back-side contact, tooth wedging, and bearing clearances. The results show significant impact of tooth wedging on planet bearing forces for a wide range of operating speeds. To develop a physical understanding of the tooth wedging mechanism, connections between planet bearing forces and tooth forces are studied by investigating physical forces and displacements acting throughout the planetary gear. A method to predict tooth wedging based on geometric interactions is developed and verified. The major causes of tooth wedging relate directly to translational vibrations caused by gravity forces and the presence of clearance-type nonlinearities in the form of backlash and bearing clearance.     

小波分析在捷联惯导陀螺信号滤波中的应用

介绍了小波变换和多分辨率分析理论。针对捷联惯导系统中光纤陀螺输出信号的特点，对其进行小波变换，去除信号中高频部分的噪声，从而抑制了陀螺的随机漂移。通过仿真实验，肯定了使用小波分析算法对陀螺输出信号进行滤波消噪处理的可行性。在实际用于捷联惯导系统中的实验结果表明，有效地提高了系统的精度。     

Comparison of spur,helical and curvilinear gear drives by means of stress and tooth contact analyses

Involute tooth surfaces are a successful technical solution for both spur and helical gear drives since they provide linear contact and a low-level function of transmission errors under good conditions of meshing. Tip relief is usually required to improve contact conditions during the transfer of meshing between adjacent pairs of teeth. Yet, unfavorable conditions of contact appear when shaft deflections and misalignments are present. Localization of contact through lead crowning is a solution that increases the cost of machining in both spur and helical gear drives. In this sense, the generation process of curvilinear gear drives provides localization of contact with no additional cost. Comparison of stresses and transmission error functions in spur, helical and curvilinear gear drives is investigated to show if the application of curvilinear gear drives yields some advantages respect to spur and helical gear drives. The three mentioned types of cylindrical parallel-axis gear drives are provided, firstly, with linear contact, and, secondly, with localized contact, for the purpose of comparison. Different misalignments conditions are taken into account by means of several numerical examples.     

Application of Wavelet Analysis to Identification of Structurally Inhomogeneous Deformable Materials

A wavelet–based experimental technique for studying the structure of material surfaces is proposed. The basic theoretical concepts of the local–frequency and wavelet analyses are given. Examples of the wavelet analysis of model images are considered. The structure of briquettes obtained by compaction of titanium sponge is determined with the use of wavelet analysis.     

小波加权残值法在斜板后屈曲上的应用

将斜板在大挠度理论下的平衡方程和变形协调方程转化为斜坐标系下的表达式,并无量纲化,对于四边固支斜板,选用尺度小于1的二维bior3.1重构尺度函数与小波作试函数,满足板在平面外的几何与自然边界条件,利用小波-Galerkin法将板的无量纲平衡控制方程与变形协调方程转化为两个非线性方程组,从而将后屈曲路径的求解转化为两非线性方程组的求解问题.以载荷作为迭代步长,采用Newton-Raphson迭代算法求得承受单向压缩四边固支斜板在不同边长比、不同斜角下的后屈曲平衡路径及四级渐近解.     

Effect of spalling or tooth breakage on gearmesh stiffness and dynamic response of a one-stage spur gear transmission

Tooth faults affecting gear transmission are always accompanied by a stiffness reduction. In this article an analytical method is proposed to quantify the reduction of gearmesh stiffness due to two common tooth faults: spalling and breakage. Bending, fillet-foundation and contact deflection are taken into account. The dynamic response of a single stage spur gear transmission is computed by using analytical gearmesh issued from analytical modelling and the vibration signatures of each tooth fault is identified.     

Dynamic behaviour modelling of a flexible gear system by the elastic foundation theory in presence of defects

In this paper a novel approach for modelling a spur gear system using finite element method combined with elastic foundation theory is developed. The pinion is modelled by shaft finite element and the wheel by a three-dimensional finite element. Elastic foundation is utilized to model the gearmesh. The modal analysis showed the presence of lower natural frequency for thin rimmed gear cases susceptible to be excited by the operating running condition. The transmission error is affected by the wheel shape and by the presence of lower natural frequencies. Eccentricity error and tooth crack are also modelled to observe their influence on the dynamics behaviour of the system. It was found that they are responsible of the apparition of an amplitude modulation.     

Application of the Fourier transform in electronic speckle photography

In speckle photograph technology, to determine the displacement of the points on the surface of the measured body, the conventional method is to put the film which has recorded the speckle patterns before and after displacement into a system of optical Fourier transforms. After filtering on the spectrum plane, the experimentalist can obtain the displacement information from the interference pattern on the image plane. Instead of setting up a complex optical Fourier transform system, we consider the speckle field as a light intensity function of 2 dimensions, which will change with different positioning of the points. After working on the function's discrete Fourier transform (DFT), according to one of the properties of Fourier transformation, the displacement of the measured point is involved in the phase of its spectrum. Having extracted the displacement information from the phase, we obtain the distribution of the displacement field. In this paper, we deduce the expression for the displacement field by using Fourier transformation under conditions of both equal and unequal displacement and show their applications.     

Application of the wavelet transform for a channel flow in a mixed convection phenomenon

The aim of this paper is to investigate laminar-turbulent transition in a mixed convection phenomenon occurring in a horizontal rectangular duct. Indeed, laminar-turbulent transition is well known in the case of forced convection but the presence of secondary flow induced by natural convection on this transition is not well highlighted. In this study, we will not be concerned by determining a critical threshold value of a Reynolds number of transition but only to estimate the degree of turbulence in the transition regime, i.e. weak turbulence in the case of a mixed convection phenomenon. This is possible thanks to the application of the wavelet transform. The calculation of the Hölder exponent, associated with the maximum value of the singularity spectrum for various experimental conditions allows the degree of turbulence to be measured. The variation of the Hölder exponent versus heat flux and Reynolds number enables us to show that there are two ways to go towards turbulence: thermal by increasing heat flux and hydrodynamic by increasing fluid velocity.     

Application of wavelet transform to bifuraation and chaos study

The response of a nonlinear vibration system may be of three types, namely, periodic, quasiperiodic or chaotic, when the parameters of the system are changed. The periodic motions can be identified by Poincare map, and harmonic wavelet transform (HWT) can distinguish quasiperiod from chaos, so the existing domains of different types of motions of the system can be revealed in the parametric space with the method of HWT joining with Poincar'e map. Communicated Zhang Ruqing Project supported by the National Natural Science Foundation of China     

非结构混合网格在气动热标模模拟中的应用

非结构混合网格消除了结构网格节点的结构性限制,可以较好地处理边界,同时兼顾了粘性边界层模拟的需求,具有灵活性大、对复杂外形适应能力强和生成耗时短等优点,在飞行器气动特性模拟中得到广泛应用.本文针对非结构混合网格的特点,把前期针对非结构混合网格气动力高精度模拟发展改进的梯度计算方法和Roe格式熵修正方法推广应用到气动热流的数值模拟.以典型钝锥标模外形的高超声速绕流为研究对象,开展了不同网格形式和第一层网格不同间距的影响研究.结果 表明,热流计算时,头部物面网格最好采用四边形或四边形交叉剖分得到的三角形网格,物面法向的网格雷诺数取20左右,为热流计算时非结构混合网格的生成提供了指导,同时验证了计算方法的有效性和可靠性.     

Analysis of Wind Fluctuations Using the Orthogonal Wavelet Transform

This paper presents a study of velocity fluctuations occurring in the stably stratified atmospheric boundary layer over an Antarctic ice shelf. The approach is based on wavelet analysis which has advantages over conventional Fourier analysis. Two case studies are presented, comprising: pure turbulent flow and a large amplitude solitary wave.