基于PSO算法的斜齿轮NURBS齿面重构研究

斜齿轮被广泛应用于高速重载的传动系统中,需要通过齿轮接触分析(TCA)以及齿轮承载接触分析(LTCA)进行强度校核。针对传统的齿轮接触分析所采用的有限元几何模型精度差的问题,提出了一种四阶斜齿轮齿面非均匀有理B样条(NURBS)拟合方法,并对齿轮渐开线曲面控制点权重进行粒子群优化(PSO)。通过参数化方程生成斜齿轮齿面型值点以进行节点矢量以及齿面控制点的计算,并利用粒子群优化算法,将拟合点到理论曲面的法向投影距离的最大差值作为拟合误差,对构成齿轮的渐开线曲面控制点权重进行调整,实现更为精确的斜齿轮齿面重构拟合。在10×6的网格控制点下,所生成的斜齿轮NURBS渐开线齿面拟合误差为2.059μm,优化后可以达到1.657μm,满足齿廓总偏差2级精度要求,可以为齿轮接触分析以及齿轮承载接触分析提供精确的几何模型。     

斜齿内齿轮齿向及螺旋角误差测量

在制造斜齿内齿轮过程中,如能测出齿向及螺旋角误差,就能通过修磨斜齿插齿刀分度圆螺旋角来消除误差,从而提高齿轮的精度。本文介绍在3301型导程仪上测量斜齿内齿轮齿向及螺旋角误差的方法,供参考。     

同时测量左右齿面齿距误差

本文提出利用齿条形测头和齿轮左右齿面同时接触测量两面齿距误差的新方法，文中详细分析了原理及影响精度的几个要素，该法测量效率高，并能获得径向跳动误差。     

齿轮全齿宽整体误差的计算机处理

本首次应用计算机处理在光栅式单啮仪上测得的齿轮全齿宽整体误差，介绍了斜齿轮的齿向误差，接触线误差及轴向齿中是的处理问题，并给出测量和处理实例。     

基于负载与啮合特征的WN齿轮传动接触强度分析

为了探求WN齿轮传动的强度机理和失效原因, 依据WN齿轮负载传动时齿面的三维几何接触特征和弹性变形理论建立了接触强度分析模型,提出了基于WN 齿轮啮合特征的接触强度分析方法．根据啮合过程中齿面接触载荷、啮合齿轮副和接触点数的变化,利用有限元分析进行了各种状况下的齿面接触应力计算,明确了WN齿轮接触强度设计中的螺旋角、中心距误差、齿宽及重合度对最大接触应力的影响结果．研究发现,当中心距和重合度及螺旋角等变化时,WN齿轮与渐开线齿轮呈现出了完全不同的载荷特征和强度机理．     

硬齿面渐开线齿轮强度的优化设计

本文对目前日益广泛应用的硬齿面齿的弯曲强度与接触强度进行了分析，提出了加权因子的方法来统一齿轮的弯曲强度与接触强度，使之符合等强度设计原则，进而构造优化设计的目标函数，进行硬齿面齿轮的参数设计，对硬齿面齿轮的强度设计具有一定的实际意义。     

直齿圆锥齿轮齿向误差的测量

本文介绍一种采用测量棒沿齿面节锥母线接触测量直齿圆锥齿轮齿向误差的方法。     

面齿轮副齿面磨损动态响应及其典型特征分析EI北大核心CSCD

为了揭示齿面磨损对面齿轮传动的影响,提出了一种结合黏着磨损公式的面齿轮副齿面接触分析方法。通过齿面接触分析得到面齿轮副接触椭圆离散点上的相对位移及接触应力,再根据黏着磨损公式可以定量得到齿轮的磨损深度;编写了含磨损的面齿轮副齿面坐标,并在ABAQUS软件中计算了不同磨损下系统的啮合刚度;将齿面磨损等效为齿面偏差,讨论了不同磨损对静态传递误差的影响;对比了面齿轮副在正常和磨损时的动态响应,分析了转矩对磨损的影响。结果表明:齿面磨损主要影响啮合刚度和静态传递误差的幅值,并且会导致加速度与啮合力幅值的快速增长;转矩的增大会引起磨损加重;相比于无量纲统计指标,加速度均方根对于磨损故障更敏感。     

一种确定斜齿轮传递误差和啮合刚度的快速有效方法

基于Smith切片法理论,提出了一种快速计算斜齿轮副传递误差和啮合刚度的改进方法。该模型将斜齿轮沿齿宽方向划分为一系列相互独立的薄直齿轮,考虑单个切片的弯曲-剪切变形、局部接触变形及轮体结构变形,通过各切片间的变形协调关系建立斜齿轮非线性承载接触模型,进而得到齿面载荷分布、传递误差和啮合刚度等信息。该方法较Smith切片法增加了时变单齿刚度、接触变形非线性效应以及轮体结构参数的影响,提高了模型的计算精度和适用性。该模型的计算精度与有限元方法相当,但具有更高的计算效率,更适合于齿轮传动系统振动和噪声的快速预测。     

大型斜齿轮齿向误差在位测量的新方法研究

本文提出了一种用空间直线作为测量基淮对被测大型斜齿轮齿向误差进行在线测量的新方法，给出了该方法的测量原理和数学模型，并讨论了通过误差分解得到相邻两齿面齿向误差的方法．     

Process Performance Comparison of ECH and PECH for Quality Enhancement of Bevel Gears

This paper presents a comparative analysis of constant-current electrochemical honing (ECH) and pulsed electrochemical honing (PECH) for quality enhancement of straight bevel gears. The quality of straight bevel gears after finishing by ECH and PECH is compared focusing on tooth flank finish and microgeometry. Tooth flank finish was evaluated in terms of percentage enhancement in average roughness value, maximum roughness value, and 5-point roughness value. Percentage enhancements in pitch error, pitch variation error, accumulated pitch error, and total runout were used to evaluate the microgeometry of the bevel gears. It was found that the PECH process is capable of simultaneously enhancing the tooth flank finish and microgeometry of bevel gears by more than 50% as compared with ECH-finished bevel gears. The PECH-finished gears also exhibited superior microstructure as compared with ECH-finished gears. These improvements will enhance the service life and working performance of gears.     

Laser Heat Treatment on Gear Surface and Its Practical Application

Making gears with hardened tooth flank is one of the important developments in gear manufacturing. However, the conventional heat treating methods have a common shortcoming--producing big deformation. In this work, we demonstrate, by study, experiment and practical use, that not only has the laser heat treatment solved the difficult problems in conventional technique, but also it has great superiority. The use cases proved that the laser-treated gears are able to substitute for all the gears including gears with complicated shape, high precision and high performance imported gears and all those gears that cannot be manufactured by conventional methods. Moreover, our laser-treated gears have won quite good economic benefit.Obviously, the laser heat treatment for gears is a highly competitive technique having good prospects.     

Effect of applied voltage and electrolyte parameters on pitch,runout, flank topology,and finishing productivity of the straight bevel gears in PECH process

This paper describes improvements in the considered parameters of micro-geometry: flank surface topology and finishing productivity of 20MnCr5 alloy steel straight bevel gears through their finishing by pulsed electrochemical honing (PECH) process. Effects of three most important parameters of PECH process, namely applied voltage, electrolyte composition, and electrolyte concentration were investigated to identify their optimum values. Pre-identified values of other PECH parameters and an aqueous mixture of NaCl and NaNO₃ as an electrolyte were used in the present work. Errors in pitch (i.e., single pitch error, adjacent pitch error, and cumulative pitch error) and runout were used to evaluate micro-geometry of the straight bevel gears while volumetric material removal rate was used to judge the finishing productivity of the PECH process. Topology of the gear tooth flank surface and microstructure of the best-finished bevel gears were also studied. The results revealed considerable improvements in the micro-geometry, flank surface topology, and microstructure of the bevel gears finished by PECH. Applied voltage of 8?V, electrolyte composition of 75?wt.% NaCl?+?25?wt.% NaNO_3, and electrolyte concentration of 7.5?wt.% were identified as the optimum values to achieve simultaneous improvement in all the considered responses.     

Experimental studies and simulation of hypoid gear lapping

Gear lapping is a highly productive method of hard finishing hypoid gears for appliances with high demands regarding transmission noise. However, there is a major disadvantage compared to competing processes. The flank topology after lapping is not completely predictable, making the definition of process variables a matter of personal experience and empirical efforts.This paper presents a method to simulate the local surface wear produced by lapping bevel and hypoid gears, based on a widely used wear approach and a fast and accurate tooth contact simulation. High-resolution experimental investigations of lapped tooth flanks are used to evaluate the accuracy of the current simulation method and deduce possible improvements.     

圆弧齿锥齿轮接触动力学分析

运用三角网格方法重构了三维离散的圆弧齿啮合齿面模型。基于多体动力学理论和迟滞接触动力学方法,提出了考虑全齿面动态接触关系的螺旋锥齿轮三维接触动力学模型和动力学分析方法。运用三角网格单元接触的包围盒搜索技术和微分代数方程求解方法,仿真分析了单侧齿面接触、双侧齿面接触、负载扭矩和齿侧侧隙等因素对齿轮啮合传动特性的影响,获得了圆弧齿啮合全齿面接触冲击力,力矩和角速度等齿轮啮合传动的动态响应特性。研究表明：新方法和动力学模型较好地模拟了圆弧齿锥齿轮的承载特性和啮合接触动力学特性,对以动力学特性为目标的圆弧齿锥齿轮设计和齿轮系统动力学研究提供了理论参考。     

Differential diagnosis of spall versus cracks in the gear tooth fillet region

This paper presents a technique to differentially diagnose two localized gear tooth faults: a spall and a crack in the gear tooth fillet region. These faults could have very different prognoses, but existing diagnostic techniques only indicate the presence of local tooth faults without being able to differentiate between a spall and a crack. The effects of spalls and cracks on the behavior/response of gear assemblies were studied using static and dynamic simulation models. Changes in the kinematics of a pair of meshing gears due to a gear tooth root crack and a tooth flank spall were compared using a static analysis model. The difference in the variation of the transmission error caused by the two faults reveals their characteristics. The effect of a tooth crack depends on the change in stiffness of the tooth, while the effect of a spall is predominantly determined by the geometry of the fault. The effect of the faults on the gear dynamics was studied by simulating the transmission error in a lumped parameter dynamic model. A technique had previously been proposed to detect spalls, using the cepstrum to detect a negative echo in the signal (from entry into and exit from the spall). In the authors’ simulations, echoes were detected with both types of fault, but their different characteristics should allow differential diagnosis. These concepts are presented prior to experimental validation in hopes that the diagnostic techniques will be useful in the failure analysis community prior to the validation by ongoing experimental testing of the concepts and the evaluation of how metallurgical defects may influence fault development and detection.     

弧齿锥齿轮基本参数优化设计

为改善因传统机械式机床加工运动受限而采用局部共轭接触造成的齿面接触区域小的现状,同时为提升齿面接触性能,提出了一种弧齿锥齿轮基本参数优化设计方法。基于齿轮副全齿面接触的实现方法,以齿轮基本参数为优化变量、排除啮合界限线和根切界限线（以下简称为“2类界限线”）及防止齿顶变尖为约束条件,建立了以传动润滑性能综合参数和齿面瞬时接触线总长度最大为目标的齿面接触性能多目标优化数学模型。引入更加适合模型本身的现代多目标骨干粒子群算法求解最优基本参数。以一个具体的弧齿锥齿轮为研究对象,对比基本参数优化设计前后齿面的接触性能指标。数值仿真结果表明,优化后2类界限线分布于工作齿面区域外,表征润滑性能的综合参数的最小值和表征承载能力的齿面瞬时接触线总长度的最小值都有明显提升。有限元模型仿真结果表明,优化后工作齿面无干涉且呈全齿面接触。该研究提供了一种快速可行的弧齿锥齿轮基本参数最优设计方法,为弧齿锥齿轮的优化设计提供了参考。     

Contact Pattern Analysis: Simulation of a Laser-Assisted Thermographic Approach

The contact pattern, defined as the area where gear teeth come into contact during their meshing, is a crucial quality feature of gears. If the size and location of the contact pattern are wrong, the gear meshing properties can be significantly affected (e.g., lifetime, noise). Despite several disadvantages, the so-called “paste method” is established as a method to analyse contact patterns. Here, a new measuring approach is examined using the Finite Elements Method (FEM). It is based on the heating-up of one tooth flank with a powerful laser, a subsequent partial transfer of the heat to a meshing tooth of the second gear wheel and finally capturing the heat distribution on that flank as an infrared image shortly afterwards. The thermal image should correspond to the contact pattern of that individual combination of teeth. A numerical analysis shows that at medium- and large-sized gears the achievable temperature increase will be high enough to be detected with modern infrared cameras.     

Fiber Reinforcement in Injection Molded Nylon 6/6 Spur Gears

Injection molded polymer composite gears are being used in many power and or motion transmission applications. In order to widen the utilization of reinforced polymers for precision motion transmission and noise less applications, the accuracy of molded gears should be increased. Since the injection molded gear accuracy is significantly influenced by the material shrinkage behaviour, there is a need to understand the influence of fiber orientation and gate location on part shrinkage behaviour and hence the gear accuracy. Unreinforced and 20% short glass fiber reinforced Nylon 6/6 spur gears were injection molded in the laboratory and computer aided simulations of gear manufacturing was also carried out. Results of the mold flow simulation of gear manufacturing were correlated with the actual fiber orientation and measured major geometrical parameters of the molded gears. Actual orientation of the fibers near the tooth profile, weld line region and injection points of molded gears were observed using optical microscope and correlated with predicted fiber orientation.