Investigations on surface quality of WEDM-manufactured meso bevel and helical gears

This article presents investigations on and analysis of surface finish of meso bevel and helical gears made of stainless steel (SS 304) manufactured by wire electric discharge machining (WEDM) process using thin soft plain brass wire of 0.25?mm diameter. Effects of eight WEDM process parameters, namely, peak current, pulse-on time, pulse-off time, wire feed rate, wire tension, servo-gap voltage, dielectric pressure, and cutting speed on average and maximum surface roughness of the meso bevel and helical gears have been studied by conducting 31 experiments using one-factor-at-a-time approach to identify their optimum ranges/values for further experiments. Tooth profile, microstructure, microhardness, and topography of tooth flank surface have been studied for the best quality meso gears. Average and maximum surface roughness of tooth flank surfaces of meso bevel and helical gears increase with increase in peak current, servo-gap voltage, pulse-on time, wire feed rate, wire tension and cutting speed, and decrease with increase in pulse-off time while dielectric pressure does not significantly influence surface roughness. This work establishes that WEDM process can be an economic and sustainable manufacturing alternative for net-shaped meso-sized bevel and helical gears having better surface finish which will eliminate need of any subsequent finishing processes.     

Three‐dimensional fatigue crack growth modelling in a helical gear using extended finite element method

In this paper, the fatigue crack growth in helical gear tooth root has been simulated using linear elastic fracture mechanics. The extended finite element method has been used to simulate 3D fatigue crack growth and obtain growth path. Paris equation has been used to calculate the fatigue life of the gear. The modelling time has reduced considerably compared to previous works carried out on 3D crack growth in gears. Some verifications have been carried out to ensure the reliability of the results.     

Critical stress and load conditions for bending calculations of involute spur and helical gears

In this paper, a non-uniform model of load distribution along the line of contact of spur and helical gears, obtained from the minimum elastic potential criterion, has been used, combined with the equations of the linear elasticity, to evaluate the fatigue tooth-root stress. The critical value of the stress and the critical load conditions have been obtained and a complete analysis of the tooth bending strength has been carried out. As the load per unit of length at any point of the line of contact and any position of the meshing cycle has been described by a very simple analytic equation, a complete study of the location and the value of the tooth-root bending stress has been carried out. From this study, a recommendation for the calculation of the bending load capacity of spur and helical gears is proposed.     

同功重比修形斜齿和直齿面齿轮性能对比研究

为深入了解同功重比修形斜齿与直齿面齿轮的性能差异,选择更适合于高速重载工况下的面齿轮传动.基于啮合原理推导了修形斜齿与直齿面齿轮齿面方程,基于CATIA建立了修形斜齿与直齿面齿轮三维模型,采用有限元接触分析方法,以接触应力、弯曲应力和重合度为面齿轮传动性能指标展开研究.研究结果表明:修形斜齿面齿轮相比修形直齿面齿轮接触应力大幅降低,算例最大接触应力降低16.3%;修形斜齿面齿轮相比修形直齿面齿轮弯曲应力大幅降低,算例最大弯曲应力降低32.4%;修形斜齿面齿轮相比修形直齿面齿轮重合度大幅提高,算例重合度提高10.3%.所以同功重比情况下,修形斜齿面齿轮传动性能优于修形直齿面齿轮,前者更适合于高速重载工况下的轻量化设计.     

人字齿轮减振修形优化设计

通过理论齿面与修形曲面叠加设计人字齿轮修形齿面,结合TCA、LTCA技术,综合考虑轮齿刚度、轴向窜动及啮合冲击激励,建立人字齿轮啮合型弯-扭-轴-摆10自由度动力学模型。以LTE幅值、轴向力及振动加速度最小为目标,通过优化确定最佳修形齿面。研究表明,轴向窜动与修形可共同改善齿面载荷分布;转速增加啮合冲击激励较刚度激励、轴向窜动激励振动更明显,刚度激励与冲击激励为引起啮合线方向振动的主要原因,而轴向位移激励对啮合线方向振动无影响;轴向位移激励为引起轴向、扭摆方向振动的主要原因;修形可降低啮合冲击、轴向窜动量、轮齿刚度及刚度波动,能有效降低系统振动。     

圆柱斜齿轮齿面接触动应力计算与分析研究

为了有效计算动态工况下斜齿圆柱齿轮副的齿面接触应力,建立了考虑时变啮合刚度激励和啮入冲击激励的滚动轴承支撑的斜齿圆柱齿轮副啮合型弯-扭-轴耦合六自由度振动模型,通过其计算了齿面啮合动载荷。提出了综合考虑轮齿动载荷、齿间载荷分配系数以及齿面赫兹接触的斜齿圆柱齿轮齿面接触动应力计算方法,同时也利用Abaqus有限元软件动力学模块分析了齿面接触动应力。分别计算了800 N·m、1 200 N·m、1 600 N·m三种负载扭矩下的齿面接触动应力变化过程,基于承载接触分析法的最大接触应力与AGMA标准计算值最大相差为11.6%,基于Abaqus有限元法的最大接触应力与AGMA标准计算值最大相差13.8%,而两种方法的齿面接触动应力变化曲线最大偏差11.3%,从而证实了本文提出的斜齿圆柱齿轮齿面接触动应力计算方法合理有效。     

Use of a measurement technique for reproducing the surfaces of circular teeth of conical wheels

Problems are considered for determining settings for an ideal machine tool for reproducing a prescribed side surface of a circular tooth of a conical wheel that may be represented by a table obtained analytically or by measuring the tooth surface, and resetting the gear-grinding machine to compensate for production errors determined by a coordinate measuring machine. __________ Translated from Izmeritel’naya Tekhnika, No. 8, pp. 33–37, August, 2006.     

Method for the evaluation of wear and durability of involute conical straight-bevel gears

A new computational model is proposed for the investigation of the kinetics of wear of teeth of straight-bevel gears. The model is used to assess wear and establish the regularities of its behavior along the length of the gear.     

Influence analysis of system parameters on characteristics of the nutation drive with double circular arc spiral bevel gears

Gear transmission systems are one of the most frequently used systems for power transmission. The characteristics of a gear transmission system have important guiding significance in the design, manufacture and application of transmissions. This paper focuses on the influence of system parameters on the characteristics of a specific type of gear transmission, the nutation drive with double circular arc spiral bevel gears. Based on the transmission ratio analysis of single-stage and two-stage nutation drive systems, the system parameters, including nutation angle, gear spiral angle, pitch angle and cone distance, were defined. An analysis of the influence of system parameters on transmission efficiency was performed. Furthermore, the influence of system parameters on axial misalignment and cone displacement error was investigated. Finally, by changing the input frequency, input load, nutation angle, and spiral angle, variation regularity of the dynamic meshing force was obtained. A transmission performance analysis based on the influence of system parameters was achieved and provides the theoretical basis for better design of the nutation drive with double circular arc spiral bevel gear.     

基于双谱分布区域的齿轮聚类分析与故障诊断

齿轮(尤其是故障齿轮)振动信号具有明显的非高斯性,双谱是分析非高斯信号的有效方法.齿轮不同故障模式振动信号双谱分析表明齿轮双谱分布区域与故障模式间存在映射关系,可作为分类特征.采用阈值化的双谱二值图作为特征向量,基于目标函数的聚类法实现分类与故障诊断.聚类过程以训练样本双谱二值图的逻辑与运算表征类间分布共性,逻辑或运算表征类间分布范围,构成类模板,测试样本与类模板距离最小值构造最近邻模板分类器,实现聚类,整个过程只是计算1的个数,简单、实用.齿轮故障诊断实例验证了该方法的有效性.     

Continuous generating grinding method for beveloid gears and analysis of grinding characteristics

Continuous generating grinding has become an important gear processing method owing to its high efficiency and precision. In this study, an adaptive design model is proposed for the continuous generation of beveloid gears in common gear grinding machines. Based on this model, a method for determining the installation position and grinding kinematics is developed alongside an analytical meshing model for grinding contact trace and derivation of key grinding parameters. By combining these aspects, a general mathematical model for the continuous generation of beveloid gears is presented, comprising the entire grinding process from worm wheel dressing to the evaluation of grinding deviation. The effects of the worm and dressing wheel parameters on the grinding deviation were analysed, facilitating the development of an approach to improve the grinding accuracy. The presented procedure represents a novel design method for the continuous generation of beveloid gears in common gear grinding machines, facilitating the appropriate selection of worm and dressing wheel parameters.The full text can be downloaded at https://link.springer.com/article/10.1007/s40436-022-00388-z     

Characteristics of flow and heat transfer of shell-and-tube heat exchangers with overlapped helical baffles

The characteristics of flow and heat transfer of shell-and-tube heat exchangers with overlapped helical baffles (STHXsHB) were illustrated through a theoretical analysis and numerical simulation. The ideal helical flow model was constructed to demonstrate parts of the flow characteristics of the STHXsHB, providing theoretical evidence of short-circuit and back flows in a triangular zone. The numerical simulation was adopted to describe the characteristics of helical, leakage, and bypass streams. In a fully developed section, the distribution of velocity and wall heat transfer coefficient has a similar trend, which presents the effect of leakage and bypass streams. The short-circuit flow accelerates the axial velocity of the flow through the triangular zone. Moreover, the back flow enhances the local heat transfer and causes the ascent of flow resistance. This study shows the detailed features of helical flow in STHXsHB, which can inspire a reasonable optimization on the shell-side structure.     

考虑动载荷和表面粗糙度的渐开线齿轮摩擦因数的研究

 进行齿面摩擦因数的研究,对于减少摩擦损失、改善系统传动性能等具有重要的意义．建立渐开线圆柱齿轮的非线性时变单自由度动力学模型,求解得到动态啮合力和单对轮齿的受力．结合载荷分担概念和弹流润滑理论,得到考虑表面粗糙度和动态载荷的不同啮合位置处的齿面摩擦因数,并与静态载荷条件的结果进行对比．同时分析转速、表面粗糙度和润滑剂黏度等工作条件对摩擦因数的影响．研究结果表明：动态载荷对油膜厚度、油膜承载比例和摩擦因数均有一定程度的影响．进入啮合段,油膜较薄,油膜承载比例较低.退出啮合段,油膜增厚,油膜承载比例增高.转速对摩擦因数的影响并非单调的,摩擦因数先是随着转速的增大显著减小,而后随着转速的增大而增大．随着表面粗糙度的增大,摩擦因数随之明显增大．在一定的黏度范围内,随着润滑剂黏度的增大,摩擦因数随之明显减小．     

Study on transmission error of double circular arc spiral bevel gears for nutation drive based on assembly errors and different loads

Forschung im Ingenieurwesen - As a new type of gear transmission, nutation gear drive is extensively applied in aviation, ship, medical equipment and other fields. In this paper,...     

Multiaxial fatigue life calculation model for components in rolling‐sliding line contact with application to gears

Important components such as gears, rollers, or bearings operate in rolling‐sliding contact loading conditions. Determination of their fatigue lives remains a challenging task due to complex states of stress and strain in the contact region, as well as complex contact conditions such as variable loading amplitude and complex geometry of contact. A mathematical model of rolling‐sliding line contact combined with a multiaxial fatigue life calculation model based on the Fatemi‐Socie critical plane crack initiation criterion is proposed. The developed model was applied to gears' teeth in mesh and compared with fatigue lives of gears reported in the literature. Good agreement was determined confirming the validity of the proposed model. A further advantage is obtaining locations of initiated cracks and the orientation of critical plane(s), which can subsequently be used for the estimation of crack shapes in initial phases of their growth and the damage type that they can be expected to develop into.     

A generalized method for the evaluation of the influence of teeth correction on the service life,wear, and contact strength of cylindrical involute gears

A generalized method is developed for the computational evaluation of the wear and service life of cylindrical gears with meshing correction. Gears with angular and height displacement were considered. Using the power gears of a VL-10 locomotive as an example, we established the influence of both kinds of displacement on the gear durability, the wear of wheel teeth for 1 h of operation, the maximal contact pressures, and the sliding velocity. It is shown that, in the case of angular correction, there exist optimal shift coefficients for which the service life is maximal as compared with the case of uncorrected meshing. However, for this gearing, the height correction is inappropriate because it decreases the gear service life.     

支承刚度及齿面涂层对斜齿轮副啮合特性的影响研究

支承刚度对自动变速器齿轮副的啮合质量有着重要影响,研究支承刚度及齿面涂层对斜齿轮副啮合特性的影响具有重要意义。以某七挡双离合自动变速器的一挡斜齿轮副为研究对象,建立了2种不同支承刚度的齿轴系统刚柔耦合模型,分析了不同工况下支承刚度对斜齿轮副啮合特性的影响规律;通过FCL-250H齿轮精测试验台得到有/无磷酸锰转化涂层齿轮的齿形齿向参数,并将其代入有限元模型进行仿真分析;进行齿轮接触疲劳点蚀实验,对比齿面涂层处理前后齿轮的接触疲劳寿命,并从齿轮表面形貌、动力性能及跑合性能等角度进一步揭示了涂层的强化机理。研究结果表明：齿轴跨度增大,支承刚度减小,则齿轮单位长度所受最大载荷和啮合错位量对输入扭矩的变化更为敏感;有涂层齿轮跑合后更有利于啮合,其疲劳寿命得到提高。研究结果为汽车自动变速器齿轮传动系统的结构优化和齿轮疲劳寿命的提高提供了参考。     

基于C和gnuplot的渐线齿轮辅助几何设计程序发简

 以渐开线齿廓几何模型为基础,结合开源程序和类库,在Windows平台上开发了齿轮辅助几何设计程序．简要介绍了国内外学者针对齿轮几何模型的建立和基于gnuplot的数据可视化模块设计的研究概况．针对计算模块的程序实现,推导并给出全齿廓的曲线参数方程．用C编写计算模块,在gnuplot的基础上编写数据可视化模块．两模块以纯文本方式传递数据,通过管道传递指令．以Windows API的方式建立窗口程序过程,并为程序设计了图形用户界面．用CxImage库替代picture控件,解决png格式设计结果图片的显示问题．这里将计算机程序设计技术融入传统机械设计理论,并借鉴众多开源软件和函数库,开发的辅助机械设计软件提升了机械设计效率和水平．     

Dynamical problem for an incompressible laminated cylinder with helical anisotropy. Part 1. Theory

Exact analytical solutions have been obtained of a one-dimensional dynamical problem for an incompressible elastic radially inhomogeneous helically orthotropic thick-walled cylinder under plane strain conditions, loaded with nonsteady internal or external pressure. Necessary and sufficient conditions for the existence, uniqueness and physical adequacy of the solutions have been established. Convergence of wave solutions for slightly compressible cylinders to the analytical dependences obtained for incompressible cylinders has been analytically proved. __________ Translated from Problemy Prochnosti, No. 2, pp. 114–123, March–April, 2006.     

Dynamical problem for an incompressible laminated cylinder with helical anisotropy. Part 2. Numerical analysis

For weakly compressible elastic helically orthotropic laminated cylinders loaded by internal impulsive pressure under conditions of plane deformation, we perform the numerical investigation of the character of convergence of one-dimensional wave solutions to the analytic relations for incompressible thick-walled shells obtained earlier by the author. An approximate engineering analytic procedure is proposed for the evaluation of the dynamic stress-strain state of inhomogeneous helically reinforced thick-walled cylindrical shells. __________ Translated from Problemy Prochnosti, No. 1, pp. 114–120, January–February, 2007. Notation is taken from Part 1 of the present work [1]. Here, we continue the numeration of formulas started in Part 1 and the reader is frequently referred to the formulas presented there.