Localised tooth contact analysis of single envelope worm gears with assembly errors

This paper presents the basis of loaded tooth contact analysis and predicts the influence of assembly errors on localised contact stress distribution in single enveloping (cylindrical) worm gearing during a meshing cycle. A method for loaded tooth contact analysis, geometry and kinematics of such gear pairs is developed. The method accounts for the effects of tooth composite deflection caused by bending, shearing, foundation, tooth contact deformation and initial profile separation due to assembly errors. The method includes the determination of contact lines, load and stress distribution due to assembly errors. Because of the complex geometry of worm gear teeth, the tooth bending stiffness is calculated using the slicing technique developed earlier by the authors. Classical Hertz theory is used for calculating contact stress and deformation. A computer program based on the presented method has been developed and used to study the influence of errors on mating teeth contact. It is shown that the governing factors in loaded gears with assembly error are the mesh stiffness and the amount of error which is linked to load sharing between adjacent tooth pairs. A numerical example is presented to further clarify the outlined method.     

Multisensor monitoring of gear tooth fatigue for predictive diagnostics

Successful machinery diagnostics depends on the collection and processing of prognostic features that relate back to failure precursors. Since gear teeth are a critical element in drive-train systems, single gear tooth failure has been examined, and the identification of new prognostic features explored. A special jig was employed to orient and constrain gear samples while Hertzian loading was applied along a single contact line on the gear tooth face. This set-up simulates the loading conditions experienced by a single tooth during gear train operation. Optical, ultrasonic, and mechanical sensors measured a variety of observables while the gear fatigue testing was under way. After monitoring the fatigue test with these three non-commensurate sensors, data features were related to crack growth phenomena. Data collection, analysis, and interpretation are discussed for spur gear samples that show both the absence and presence of cracks and support the validity of the identified features as failure precursors. The results demonstrate the potential for using non-traditional sensors and techniques for an in situ monitoring system.     

Spur Gear Tooth Pitting Propagation Assessment Using Model-based Analysis

Tooth pitting is a common failure mode of a gearbox. Many researchers investigated dynamic properties of a gearbox with localized pitting damage on a single gear tooth. The dynamic properties of a gearbox with pitting distributed over multiple teeth have rarely been investigated. In this paper, gear tooth pitting propagation to neighboring teeth is modeled and investigated for a pair of spur gears. Tooth pitting propagation effect on time-varying mesh stiffness, gearbox dynamics and vibration characteristics is studied and then fault symptoms are revealed. In addition, the influence of gear mesh damping and environmental noise on gearbox vibration properties is investigated. In the end, 114 statistical features are tested to estimate tooth pitting growth. Statistical features that are insensitive to gear mesh damping and environmental noise are recommended.     

渐开线圆柱齿轮参数化建模思路研究

主要阐述了通过曲线、曲面、实体的流程进行圆柱齿轮参数化建模的方法。首先进行了球面坐标系下两个端面齿形的渐开线、齿根圆弧、齿顶圆弧以及螺旋母线的方程推导,讨论了齿根圆大于和小于基圆两种情况,并给出了相应的处理方法,完成了单齿的线框模型。然后通过边界混合、曲面合并、实体化方法生成单齿实体模型。最后通过齿根圆拉伸、单齿阵列、相应关系参数添加,完成了圆柱渐开线齿轮的参数化实体模型的建立。该齿轮可以随意改变变位系数等参数,而不用担心再生失败的问题,为后续的齿轮原型系统研究提供了基础模型。     

Performance improvement method for Nylon 6 spur gears

Plastic gears made of Nylon 6 are especially susceptible to failure due to extreme heat accumulation in the single tooth mesh area, which results in damage that consequently shortens gear teeth life and causes transmission errors. In this experimental study, the teeth width of plastic spur gears made of Nylon 6 were modified and investigated. The values of load sharing, F/b, in single and double tooth meshing areas were leveled by widening the single tooth zone along the meshing area, and the performances of both modified and unmodified gears were studied experimentally under three different loadings. It was observed that modified Nylon 6 gears exhibit lower tooth temperatures, which results in a decrease in wear rate as compared to unmodified gears. Consequently, teeth width modification helps to increase Nylon 6 gear performance.     

温变工况下螺栓松动检测的独立成分分析方法

导波损伤检测技术的关键在于检测出结构损伤引起的导波信号变化,但环境温度变化也会影响导波传播过程,引起信号改变,导致损伤检测的失败。为了消除温度变化的影响,笔者采用独立成分分析(independent component analysis,简称ICA)方法处理导波响应信号。作为一种盲源分离的算法,ICA能够从混合信号中提取得到独立的未知源信号分量。因此利用ICA方法能将导波的响应源信号从被温度变化干扰的混合信号中分离出来,实现消除温度变化干扰的目的。为验证该方法的可行性,以螺栓连接铝板为对象进行实验,采集不同温度下螺栓全紧及松动状态的导波响应信号,将其经过ICA方法处理后应用到损伤定位算法中。结果表明,应用ICA处理后的导波信号能够成功定位松动螺栓,证实了ICA方法排除温度变化对导波传播影响的有效性。     

渐开线斜齿圆柱齿轮的三维造型

渐开线斜齿圆柱齿轮的三维造型存在两大难点:端面齿廓的绘制和轮齿的生成。利用渐开线的参数方程式并通过AutoLISP编程绘制出端面齿廓一侧的渐开线;在对轮齿端面齿廓进行几何分析与计算的基础上,确定并绘制出其对称线及齿顶圆弧,并利用该对称线获得轮齿端面齿廓另一侧的渐开线;绘制出齿轮轮齿两端的齿廓曲线及通过齿廓曲线两端点的齿根螺旋线后,用AutoCAD的“边界曲面”命令,构造斜齿圆柱齿轮的轮齿表面模型。     

含双裂纹齿轮副轮齿裂纹扩展寿命分析

裂纹扩展是齿轮传动的主要故障,而且裂纹所处位置对裂纹扩展行为作用明显。为探讨齿轮副轮齿裂纹位置与裂纹扩展寿命的关系,提出几种相邻轮齿含分度圆裂纹和齿根裂纹的双裂纹齿轮副模型,基于ABAQUS建立齿轮副的三齿啮合有限元分析模型,分析不同载荷作用下分度圆裂纹和齿根裂纹尖端的主应力值和应力强度因子值;结合Pairs方程探讨分度圆裂纹扩展和齿根裂纹扩展寿命之间的关系。结果表明:齿轮副单齿啮合时的裂纹尖端应力比齿轮副双齿啮合时的裂纹尖端应力大,而且裂纹尖端的弯曲应力明显大于剪切应力;同一载荷同一裂纹深度时,齿根裂纹尖端的应力强度因子值大于分度圆裂纹尖端的应力强度因子值;相同加载时,含齿根裂纹齿轮的裂纹扩展寿命小于含分度圆裂纹齿轮的裂纹扩展寿命;裂纹扩展过程中,齿根裂纹深度和分度圆裂纹深度之比非定值,而且深度之比与载荷无关。     

Modelling, Implementation, and Manufacturing of Spiral Bevel Gears with Crown

The operational performance of gears in terms of smoothness, quietness, wear and life span is largely affected by how gear and pinion teeth make contact. To enhance the operational performance, a crown is often applied to a standard (nominal) gear tooth surface. Regardless of the presence of a crown, all the gears are machined by special types of machine tools, such as gear hobbers and shapers. This paper develops a tooth surface for a spiral bevel gear with a crown so that it can be machined by numerically controlled machine tools. Specifically, we derived: 1. A bi-parametric tooth surface model for a standard spiral bevel gear. 2. A crown model along the spiral curve direction. 3. A crown model along the involute curve direction. The developed algorithm was tested and implemented in a prototype software system called GearCAM. With the GearCAM system, a set of spiral bevel gear and pinion was machined using a 4-axis CNC milling machine to check the validity and effectiveness of the crowning method. Through various verifications, it is shown that the models developed for the standard and crown gears can be used as a means for design and verification of spiral bevel gears.     

汽车门锁闭锁器小模数齿轮副接触有限元分析

汽车门锁闭锁器中的塑料齿轮在节线附近容易发生断裂,设计时需校核其强度。首先在CAXA中建立齿轮副模型,之后运用接触有限元方法,借助Ansys12.0有限元分析软件研究了齿轮副在一个啮合周期内的接触应力及结点位移的分布。得出了以下结论:齿轮副最大接触应力和结点位移都发生在节点啮合时;最大接触应力小于大小齿轮接触强度的极限值;相邻两啮合位置的接触应力相差较大时说明在此两位置之间发生了单对轮齿与双对轮齿接触的变换;对于塑料齿轮来说,当啮合位置是从齿顶向节点方向变化的单齿啮合时,齿轮副的最大接触应力总体呈减少趋势。为汽车门锁闭锁器中齿轮的设计提供理论参考。     

含侧隙齿轮副的动载荷分析

以振动理论为基础，提出一种考虑齿轮拍击振动的齿轮动载荷的数值计算方法。建立计算动载荷的齿轮冲击模型，在模型中考虑了齿轮正、反冲击时实际的啮合刚度，并给出啮合柔度的计算方法。分析在考虑静态传递误差、啮合刚度、侧隙、摩擦力及外部扭矩变化等多种激励时，作用在轮齿上的动态载荷以及整个齿轮上的综合动态载荷的计算公式。最后通过实例分析作用在轮齿上的动态载荷、综合动态载荷变化规律以及相关激励参数对动态载荷的影响。     

基于Ansys起重机用鼓形齿联轴器有限元分析

为解决传统的齿式联轴器理论计算公式不适用于重载起重机用鼓形齿联轴器这一问题,基于Ansys对某起重机用卷筒鼓形齿联轴器展开有限元分析,得到其应力应变分布特点,并基于此对此类联轴器常见故障展开分析,结果表明:起重机用鼓形齿联轴器最大应力位于齿轮副的外齿处,达到556.74 MPa,在法兰盘单个连接螺栓上也存在较大内应力,为49.748 MPa,有限元计算结果与理论计算值相差<5%;起重机用鼓形齿联轴器的主要失效形式为连接螺栓断裂和齿面磨损破坏,可通过定期检验和添加润滑油脂等形式改善。     

Blind source separation for classification and detection of flaws in impact-echo testing

This paper presents a technique for defect detection and material classification based on blind source separation by independent component analysis (ICA) for application in impact-echo testing. The transfer functions between the impact point and the defects in the material are modelled as “sources” for blind source separation. The sensors located on the material surface measure a convolutive mixture of the contribution of each of the defects. From spectral analysis the dominant resonance frequencies, varying from homogeneous to defective material, are selected. These frequencies are processed by instantaneous ICA in order to obtain more information about the defects using bootstrap resampling to analyse the stability of the solution. Results show that source estimates fit well with the theoretical response of the material. In addition, it has been found that the number of defects can be estimated by ICA in simulations and experiments with various defective parallelepiped-shape materials of aluminium alloy series 2000.     

大跨径桥梁实时动态挠度信号的分离

由于经验模式分解(empirical mode decomposition,简称EMD)将非线性非平稳信号分解成为一系列线性、平稳的本征模函数(intrinsic mode function,简称IMF)信号,针对单通道大跨径桥梁挠度信号分离问题,结合盲源分离和经验模式分解各自优点,提出基于经验模式分解的盲源分离方法。利用奇异值分解(singular value decomposition,简称SVD)估计信号源数目,根据源信号数目将单通道挠度信号和其本征模函数重组为多通道输入信号,应用独立分量分析（independent component analysis,简称ICA）理论中的快速独立分量分析（fast independent component analysis,简称FastICA）算法对输入信号进行分解,实现桥梁挠度信号各分量的分离。仿真研究表明,该方法能较好地解决ICA模型源数估计和单通道挠度信号盲源分离难题。     

Study on development of polyamide gears for improvement of load-carrying capacity

In polyamide based gears, thermal damage of the gear tooth surfaces occurs during gear meshing due to accumulated heat in the tooth body. In the experimental study reported in this paper, polyamide gear teeth have been modified in order to distribute the generated heat on the tooth surface by means of drilled cooling holes at different locations on the gear tooth body. The main aims of this paper were to study the effect of cooling holes on the accumulated heat on the tooth surface and on the measured wear. It was shown that the drilled cooling holes on the tooth body decreased the tooth surface temperature and led to an increase in the load carry capacity and improved wear resistance. Geometrically modified gears have showed an improved service life and a decreased surface temperature.     

中低速齿轮副效率与齿数及中心距有限增量的关系

对中低速渐开线直齿齿轮机构稳定运行时齿轮副传递的有效功与齿间摩擦系数，齿数及中心距有限增量等有关参数的关系进行了分析和研究，导出一组可直接确定中低速齿轮副效率的方程组，由该方程组所显示的关系可知，齿轮副效率不仅直接与齿间摩擦系数有关，而且还随齿数、传动比及中心距有有限增量等参数变化而变化。     

Detecting gear tooth fatigue cracks in advance of complete fracture

Some results from using vibration-based methods to detect gear tooth fatigue cracks are presented. An experimental test rig was used to fail a number of spur-gear specimens through bending fatigue. The gear tooth fatigue crack in each test was initiated through a small notch in the fillet area of a tooth on the gear. The primary purpose of these tests was to verify analytical predictions of fatigue crack propagation direction and rate as a function of gear rim thickness. The vibration signal from a total of three tests was monitored and recorded for gear fault detection research. The damage consisted of complete rim fracture on the two thin rim gears and single tooth fracture on the standard full rim test gear. Vibration-based fault detection methods were applied to the vibration signal both on-line and after the tests were completed. The objectives of this were to identify methods capable of detecting the fatigue crack, and determine how far in advance of total failure positive detection was given. Results showed that the fault detection methods failed to respond to the fatigue crack prior to complete rim fracture in the thin rim gear tests. In the standard full rim gear test all of the methods responded to the fatigue crack in advance of tooth fracture; however, only three of the methods responded to the fatigue crack in the early stages of crack propagation.     

Assessing the role of plastic deformation in gear-health monitoring by precision measurement of failed gears

For constant loading and speed conditions, the principal sources of vibration excitation arising from meshing gears, characterised by the “static transmission error” (STE) excitation, are geometric deviations of the working surfaces of the teeth from equi-spaced perfect involute surfaces, and tooth/gear body elastic deformations. Changes in these two sources caused by tooth-bending-fatigue damage on one or a few teeth are manifested primarily in the rotational-harmonic content of the STE of each individual damaged gear of the meshing pair, and are most effectively detected in the time domain. The optimum number of gear rotations to be used in synchronous averaging is specified, along with how such synchronous averaging can be used to eliminate the effects of the mating gear in the case of “hunting tooth” gear pairs, and to minimise these effects otherwise. Precision measurements made on the teeth of a gear failed in a tooth-bending-fatigue test strongly suggest that whole-tooth plastic deformation—i.e. yielding, rather than changes in tooth stiffness caused by tooth-root cracks, is the principal source of detectable damage in the case of tooth bending fatigue. Such plastic deformations are geometric deviation STE contributions. Differences in gear materials, materials processing, and gear operating properties may significantly affect the amounts of such plastic deformations before tooth breakage and the operating duration between initial damage detection and tooth breakage, thereby suggesting the need for testing to determine such dependencies.     

齿轮箱复合故障信号的非线性盲源分离算法研究

针对齿轮箱复合故障分析问题,文中提出一种新型非线性盲源分离（Nonlinear Blind Source Separation, NBSS）算法。该算法先利用反向传播（Back Propagation, BP）神经网络逼近非线性混合模型的逆,并对经过BP 神经网络处理后的信号进行独立成分分析（Independent Component Analysis, ICA）;然后以独立成分分析后的信号的负熵作为适应度函数,采用遗传算法对BP神经网络的参数进行寻优;最后利用优化的BP神经网络参数,对观测到的混合信号进行分解,分离出纯净的振源信号。与采用粒子群优化（Particle Swarm Optimization, PSO）算法的核独立成分分析（Kernel ICA, KICA）相比,该方法提取的分离信号具有更高的精度,为齿轮箱复合故障诊断提供了关键技术与有效方法。     

新型两齿差外啮合行星传动的等磨损参数的优化模型

基于两齿差外啮合行星传动的结构特点及失效形式,提出一种防止结构失效的齿轮参数优化设计方法,通过优化算法得到了各齿轮副间的变位系数合理分配,使得主、从动齿轮与行星轮啮合时的滑动系数趋于相等,减少各齿轮副啮合时的相对滑动,从而大大提高了这种新型结构的寿命。