A comparative experimental study on the diagnostic and prognostic capabilities of acoustics emission,vibration and spectrometric oil analysis for spur gears

Prognosis of gear life using the acoustic emission (AE) technique is relatively new in condition monitoring of rotating machinery. This paper describes an experimental investigation on spur gears in which natural pitting was allowed to occur. Throughout the test period, AE, vibration and spectrometric oil samples were monitored continuously in order to correlate and compare these techniques to natural life degradation of the gears. It was observed that based on the analysis of root mean square (rms) levels only the AE technique was more sensitive in detecting and monitoring pitting than either the vibration or spectrometric oil analysis (SOA) techniques. It is concluded that as AE exhibited a direct relationship with pitting progression, it offers the opportunity for prognosis.     

Investigation of the Thermal Behaviour of Non‐metallic Curved‐Face‐Width Spur Gears

This paper describes a curved‐face‐width spur gear, specially designed for manufacture from non‐metallic materials. The benefits of this gear are the higher contact ratio, bending and Hertzian contact resistance, and greater tooth stiffness compared to standard spur gears. A modified geometry is proposed for the gear tooth, the height of which varies along the gear face width. Due to the reduction in tooth height, in sections away from the gear centre, lower sliding friction is expected, with consequences for the gear's thermal behaviour. The complex gear geometry makes the design of a die difficult; therefore the gears were cut on a milling machine, using a special kinematic generation process and related equipment. The tooth flank profile, an involute or near involute in sections away from the gear half‐width plane, as well as the flank surface quality determined by the single‐cutter tool used for gear manufacture, influence the meshing condition, and can be detrimental to the thermal behaviour of the gear. Experimental tests were carried out to examine the influence of load and speed on the temperature of the curved‐face‐width spur gears with modified geometry. The measured temperature of the non‐standard gear is further compared with the predicted temperature of plastic standard spur gears of the same specification.     

基于ABAQUS的滤波减速器的齿轮本体温度场分析

对设计的一种新型滤波传动件进行受力分析,采用C语言编程计算的方法,对滤波减速器齿轮啮合齿对的相对滑动速度及啮合齿面的单位面积的摩擦热流量进行分析计算,确定滤波减速器齿轮本体温度场热分析的边值问题、加载参系数后,应用有限元分析软件ABAQUS进行分析计算,分析齿轮的本体温度场分布情况.结果表明:在载荷一定的条件下,随着转速的增加,单位面积的摩擦热流量也随之增加,但温度场的分布不会因转速的变化而改变;齿轮上温度场分布不均匀,最高温度点出现在齿轮接触面靠近节线处,最低温度出现在轮齿端部,这会造成齿轮的热应力变形,导致减速器承载能力下降、传动精度降低、使用寿命缩短.     

A new fault diagnosis algorithm for helical gears rotating at low speed using an optical encoder

Helical gears are widely used in gearboxes due to its low noise and high load carrying capacity, but it is difficult to diagnose their early faults based on the signals produced by condition monitoring systems, particularly when the gears rotate at low speed. In this paper, a new concept of Root Mean Square (RMS) value calculation using angle domain signals within small angular ranges is proposed. With this concept, a new diagnosis algorithm based on the time pulses of an encoder is developed to overcome the difficulty of fault diagnosis for helical gears at low rotational speeds. In this proposed algorithm, both acceleration signals and encoder impulse signal are acquired at the same time. The sampling rate and data length in angular domain are determined based on the rotational speed and size of the gear. The vibration signals in angular domain are obtained by re-sampling the vibration signal of the gear in the time domain according to the encoder pulse signal. The fault features of the helical gear at low rotational speed are then obtained with reference to the RMS values in small angular ranges and the order tracking spectrum following the Angular Domain Synchronous Average processing (ADSA). The new algorithm is not only able to reduce the noise and improves the signal to noise ratio by the ADSA method, but also extracts the features of helical gear fault from the meshing position of the faulty gear teeth, hence overcoming the difficulty of fault diagnosis of helical gears rotating at low speed. The experimental results have shown that the new algorithm is more effective than traditional diagnosis methods. The paper concludes that the proposed helical gear fault diagnosis method based on time pulses of encoder algorithm provides a new means of helical gear fault detection and diagnosis.     

精确载荷分布下斜齿轮三维建模及弯曲应力分析

从范成法加工齿轮的原理出发,利用三维建模软件建立了渐开线斜齿圆柱齿轮的精确模型。根据齿轮啮合变形协调方程,利用线性规划法求解了齿轮副在各啮合节点的载荷分布情况,并计算了轮齿间的载荷分配率。利用有限元软件ANSYS计算了完整齿轮模型在啮合过程中的最大齿根弯曲应力,为齿轮弯曲强度校核提供了依据。研究结果发现,斜齿轮的最大弯曲应力有可能出现在多齿啮合的区域,这种现象与直齿轮有所不同。     

轮胎起重机行走部分变速箱的设计

根据轮胎起重机的使用要求,设计了一台起重机行走时使用的变速箱。汽缸通过拨叉控制,齿套分别与双联齿轮联接完成高速挡和低速挡两种输出形式。该变速箱是采用斜齿圆柱齿轮和双联斜齿带内花键的齿数不同螺旋角方向相反的圆柱齿轮输入轴高度变位的形式完成设计的。通过实践,该设计能很好地完成以往使用2台减速器才能完成的任务,并解决了噪音大的难题。     

Modeling of helical gear contact with tooth deflection

The majority of gear tribological studies are made on spur gears. However, helical gears are generally used in industry, and their contact behavior deserves more attention to establish a realistic base for detailed friction, wear and life studies. This study focuses on the modeling of helical gear contact with tooth deflection. A calculation model for helical gear contact analysis is introduced. Helical gear surface profiles are constructed from gear tool geometry by simulating the hobbing process. The model uses three-dimensional finite elements for the calculation of tooth deflection including tooth bending, shearing and tooth foundation flexibility. The model combines contact analysis with structural analysis to avoid large meshes. Tooth foundation flexibility was found to have an essential role in contact load sharing between the meshing teeth, whereas contact flexibility plays only a minor role. The capability of different local contact calculation methods was also studied.     

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.     

交错轴斜齿轮传动变齿厚技术现状与发展趋势

变厚齿轮技术是交错轴斜齿轮传动系统发展的主要方向。介绍了变厚齿轮传动的原理及其在交错轴传动中的应用,在分析国内外交错轴斜齿轮传动研究现状的基础上,探讨了开展交错轴变厚齿轮研究的发展趋势及要解决的关键技术问题,对研究新型交错轴传动形式及非渐开线空间变厚齿轮传动情况下提高系统承载能力、优化系统动态特性具有重要的理论意义和学术价值。     

Experimental studies on the effects of reduction in gear tooth stiffness and lubricant film thickness in a spur geared system

Gears are one of the most common mechanisms for transmitting power and motion and their usage can be found in numerous applications. Studies on gear teeth contacts have been considered as one of the most complicated applications in tribology. Depending on the application, the speed and load conditions of teeth may change triggering several types of failures on teeth surface such as wear, scuffing, micro-pitting and pitting. The above-mentioned faults influence changes in vibration and acoustic signals, due to changes in operating conditions such as increase in temperature and decrease in lubricant film thickness and specific film thickness. These abnormal changes result in cumulative effects on localised or distributed faults on load bearing surfaces of gears. Such damages cause reduction in tooth stiffness and severity of damage can be assessed by evaluating the same using vibration-based signals.This paper presents the results of experimental investigations carried out to assess wear in spur gears of back-to-back gearbox under accelerated test conditions. The studies considered the estimation of operating conditions such as film thickness and their effects on the fault growth on teeth surface. Modal testing experiments have been carried out on the same gear starting from healthy to worn out conditions to quantify wear damage. The results provide a good understanding of dependent roles of gearbox operating conditions and vibration parameters as measures for effective assessment of wear in spur gears.     

A Study on the Extrusion by a two-step process for manufacturing helical gear

Much research has been carried out in the manufacturing of helical gears by cold forging or by extrusion. Although cold forging is applied to some bevel, spur, and helical gears, problems in connection with the reduction forming load and tool life still make it difficult for these methods to be commercialized. In this study, focusing on reducing a load in forming helical gears, the extrusion of helical gears by two-step process is proposed. This process is composed primarily of extruding a billet to a spur gear and then twisting the previous spur gear extruded to a helical gear. Cylindrical billets of Cr-Mo steel(SCM 415) and aluminium alloy(Al60 series) were used as specimen materials for the experiments. The maximum loads obtained by upper-bound analysis and FEM are compared with the results of experiments. The loads of the analysis have good agreements with those of the experiment. The newly proposed method can be used as an advanced technique that remarkably reduces the forming load and replaces the conventional forming.     

Influences of friction and mesh misalignment on time-varying mesh stiffness of helical gears

As one of the most important excitation sources of vibration, time-varying mesh stiffness of helical gear pairs need accurately calculated. Compared with spur gears, friction in helical gears is significant. This work for the first time presents an improved calculation method for the mesh stiffness of helical gears with effect of friction incorporated. Firstly, helical gear is sliced into number of pieces along its axis direction and each piece could be regarded as spur gear. Then forces applied to each piece including friction force are analyzed. Potential energy method is employed to develop time-varying mesh stiffness of each piece pair of both kinds of helical gears with different transverse and axial contact ratios. Furthermore, influences of various working conditions and misalignment on mesh stiffness are also investigated. Results indicate that effect brought by friction on total mesh stiffness should be not neglected. The reduction amount of stiffness increases with lower speed, heavier load and rougher surface. The stiffness difference between cases with and without friction is affected by gear geometry and mounting parameters like module, helix angle and mounting misalignment. This work provides an essential tool for comprehensive dynamics analysis with consideration of the relationship between stiffness and working conditions.     

直齿轮齿廓修形的实验研究

对3种不同齿廓修形参数的渐开线直齿轮进行了振动和噪声的传动实验研究。实验结果表明，按下述原则设计的修形直齿轮具有较好的减振降噪效果：不计误差的理论设计修形齿轮的最大综合修形量应能消除含误差齿廓轮齿在啮入和啮出位置产生的几何干涉，理论设计修形齿轮的静态传动误差应保持最小的幅值变化。     

插值法构建渐开线圆柱齿轮模型

对插值法生成渐开线圆柱齿轮的渐开线方法进行了分析,分别讨论了Matlab生成差值和Excel生成差值以及软件生成渐开线的方法,分析研究了直齿圆柱齿轮和斜齿圆柱齿轮的造型。对渐开线圆柱齿轮的精确快速造型和齿轮分析及加工有着重要的意义。     

Acetal gear wear and performance prediction under unlubricated running condition

Tests have shown that the acetal gear wear rate will be increased dramatically when the load reaches a critical value for a specific geometry. The gear surface will wear slowly with a low specific wear rate if the gear is loaded below the critical condition. The sudden increase in wear rate may be due to the gear operating temperature reaching the material melting point under the critical load condition. Gear surface temperature has been investigated in detail by studying three components: ambient, bulk and flash temperatures. Through extensive experimental investigations and modelling on gear surface temperature variations, a general relation has been built up between gear surface temperature and gear load capacity. A new design method for acetal gear has been proposed based on the link between polymer gear wear rate and its surface temperature. The method has been related to test results under different operating ambient temperature and gear geometries. Good agreements have been achieved between the proposed method predictions and experimental test results. The maximum torque the acetal gears can transmit is 9 Nm for both the driver and driven with a 2 mm module, 30 teeth and 17 mm face width. Copyright © 2006 John Wiley & Sons, Ltd.     

减变速一体化齿轮啮合原理的研究

突破常规非圆齿轮副的节曲线都是非圆形的限制,提出由普通直齿圆柱齿轮和非圆面齿轮组成的传动机构,可实现任意的减变速一体化传动,从而最大限度地简化传统减变速装置的传动结构,节省传动空间,提高传动效率。提出用非圆曲线代替普通面齿轮节圆的设想,根据传动过程中两齿轮节曲线之间进行纯滚动的原理,建立圆柱齿轮的空间节曲线方程,从而揭示正交轴圆柱齿轮与非圆面齿轮的传动机理;将圆柱齿轮与非圆面齿轮的传动比分解成减速比和变速比两部分,建立几何参数与两部分传动比的对应关系,可方便地设计任意减变速传动规律。根据齿轮空间啮合原理,建立由标准齿轮插刀包络非圆面齿轮的齿面模型,可为进一步轮齿几何特性分析及强度计算提供理论基础。计算出不同设计参数下非圆面齿轮副的传动比,分析了其独特的传动性能,并利用数字化制造仿真技术模拟标准齿轮插刀加工非圆面齿轮的过程,得到与齿廓数学模型完全吻合的齿面数据,从而验证了新型齿轮的传动机理及齿面模型的正确性。     

高速重载齿轮传动的多目标优化设计

讨论了重载齿轮设计中的各种影响因素；分析了斜齿轮和人字齿轮的优缺点，在此基础上将重载齿轮确定为弧齿线圆柱齿轮，并对其建立了以重合度最大、体积和相对滑动率最小为目标的多目标优化数学模型；给出了重载齿轮传动优化设计约束条件，运用多目标优化的乘除法获得了最优解。采用MATLAB软件实现了实例的优化设计目的，提高了机械设计效率和精度。     

动力传动圆锥渐开线齿轮的设计、制造和应用Ⅱ

圆锥渐开线齿轮（斜面体齿轮）被用于交叉或倾斜轴变速器和平行轴自由侧隙变速器中。圆锥齿轮是在齿宽横断面上具有不同齿项高修正（齿厚）的直齿或斜齿圆柱齿轮。这类齿轮的几何形状是已知的,但应用在动力传动上则多少是个例外。ZF公司已将该斜面体齿轮装置应用于各种场合：4WD轿车传动装置、船用变速器（主要用于快艇）、机器人齿轮箱和工业传动等领域。斜面体齿轮的模数在0．7mm-8mm之间,交叉传动角在0°-25°之间。这些边界条件需要对斜面体齿轮的设计、制造和质量有一个深入的理解。在锥齿轮传动中为获得高承载能力和低噪声所必须进行的齿侧修形可采用范成法磨削工艺制造。为降低制造成本,机床设定和由于磨削加工造成的齿侧偏差可在设计阶段利用仿真制造进行计算。本文从总体上介绍了动力传动变速器斜面体齿轮的研发,包括：基本几何形状、宏观及微观几何形状的设计、仿真、制造、齿轮测量和试验。     

齿轮传动中啮合冲击的计算分析

在文献[1]所建立的齿轮传动啮合冲击动力学模型的基础上,通过理论分析并编制相应的分析程序,计算了渐开线直齿轮传动中啮入冲击力、冲击速度的变化情况,分析了传动比、模数、载荷等对齿轮传动中冲击力的影响情况。结果表明：(1)随着传动比的增大,齿轮传动中的冲击力随之降低;(2)模数增大,使得轮齿之间的冲击力增大;(3)在其他条件不变时,载荷增大将导致冲击力增大;(4)载荷和速度相比,速度对冲击力的影响较大。     

高速斜齿轮传动稳态温度场仿真分析

结合摩擦学、传热学和齿轮啮合原理,给出稳态条件下轮齿本体的热平衡方程及摩擦热流量、对流换热计算方法,分析了啮合面压力及摩擦热流量的分布情况;利用ANSYS参数化编程语言,建立三维斜齿轮温度场分析有限元模型,并给出加载热流密度的方法;在不同节线速度下,对斜齿轮本体温度场进行数值仿真,分析了斜齿轮本体温度场分布规律;对比高速齿轮测温实验结果,表明温度仿真结果与测试结果吻合良好;在此基础上,计算了修形斜齿轮本体温度场。