斜齿轮啮合显式动态模拟及结构参数对齿轮性能的影响研究

运用显式动力学分析方法,对斜齿轮副进行了啮合的动态模拟,对某啮合齿轮副结构参数中的变位系数和螺旋角的改变对齿轮啮合瞬态性能的影响进行了研究,通过动态模拟计算和分析,结果显示了结构参数的改变引起的齿轮啮合瞬态性能的变化趋势,在斜齿轮设计时,可为齿轮变位系数和螺旋角的选取提供一定的参考。     

基于Matlab的渐开线变位直齿轮时变啮合刚度计算分析

考虑齿轮真实的渐开线及过渡曲线方程,对齿轮进行精确建模,推导并利用Weber能量法计算了变位齿轮变形量,推导了刚度计算中涉及的载荷角β_j、压力角αk、旋转角tanαk同载荷点坐标XMj的映射关系,根据齿轮重合度,计算了齿轮啮合周期中单、双对齿轮交替啮合的区段边界;在此基础上,考虑齿轮副综合啮合效应,求解出齿轮副综合时变刚度。通过Matlab GUI编程,实现了齿轮参数化建模设计与齿轮时变刚度计算的有机结合。研究结果为进一步进行变位齿轮动力学研究提供了重要支撑。     

变位系数与螺旋角变化对齿轮性能影响的研究

运用显式动力学分析法,研究对啮合齿轮副结构参数中的变位系数和螺旋角的改变对啮合瞬态性能的影响,并通过动态模拟计算,结果可清楚地显示结构参数的变化引起的齿轮啮合瞬态性能的变化趋势。对齿轮设计中,齿轮变位系数和螺旋角的选取有一定的参考价值。     

齿轮内啮合传动的重合度及载荷修正系数的计算(Ⅱ)--载荷修正系数数据表

在获得齿轮内啮合传动的齿侧间隙计算公式以后，结合齿对刚度的计算公式，推导出齿轮内啮合传动的加载重合度及载荷修正系数。通过对具有不同模数、齿数、齿数差、变位系数及载荷的齿轮内啮合传动模型的计算，发现载荷及齿数(传动比)的变化对载荷修正系数的影响较大，齿数差及变位系数的变化对载荷修正系数的影响较小，齿轮的精度对载荷修正系数的影响最大。载荷修正系数在0．30至1．00之间变化。     

齿轮变位对啮合刚度影响的数值仿真

为探究齿轮变位对啮合刚度的影响,采用两种不同方法计算齿轮啮合刚度:一是运用Pro/E二次开发对齿轮进行参数化建模,并将齿轮模型导入Abaqus软件进行有限元仿真计算,根据计算结果得出不同变位系数齿轮的时变啮合刚度曲线;二是基于能量法的解析法计算得出时变啮合刚度曲线。结果表明,在一定范围内,齿轮啮合的重合度随齿轮变位系数的增大而减小,齿轮的平均啮合刚度随齿轮变位系数的增大而减小。     

变齿厚渐开线齿轮副啮合效率研究

由于变齿厚渐开线啮合副变位系数沿轴向变化的特点,其啮合角、锥角、重合度、不同端截面齿顶圆上的压力角、滑动率等参数与普通渐开线啮合副不同,其啮合效率计算也与普通渐开线啮合副有所区别.分析了变齿厚齿轮啮合副效率的计算特点和影响因素,如变位系数对变齿厚齿轮副重合度和啮合效率的影响;在此基础上,提出了一种新型效率计算方法;通过...     

点线啮合齿轮变位系数的研究

为了避免根切,根据点线啮合齿轮、特点及啮合的基本定律,研究了点线啮合齿轮通用无侧隙啮合方程、直齿点线啮合齿轮和斜齿点线啮合齿轮最小变位系数计算公式。以一实例来阐述点线啮合齿轮中大齿轮变位系数的计算过程,整个计算过程通过软件完成。得出点线啮合齿轮无侧隙啮合方程,及最小变位系数计算同渐开线圆柱齿轮类似、点线啮合齿轮应计算最小变位系数、只能在封闭图中才能准确地确定大齿轮变位系数和螺旋角等3个结论。     

少齿数齿轮变位系数的精确选择

为了提高少齿数齿轮副的抗胶合能力和耐磨损的能力,结合少齿数齿轮传动的特点和各参数之间的关系,考虑了螺旋角和侧隙对变位系数的影响,推导了齿轮有侧隙啮合方程,确定变位系数总和;以等滑动率作为分配条件,以变位系数基本限制条件作为约束条件,利用MATLAB软件编写程序实现了少齿数齿轮副变位系数的数值选取。程序选取普通齿轮的变位系数与经典变位系数图谱对比结果表明:该程序不仅可以实现少齿数齿轮副变位系数的精确数值选择,而且可实现普通正变位齿轮副的变位系数的选取,为少齿数齿轮的深入研究和推广提供了参考依据。     

斜齿轮及断齿故障下时变啮合刚度计算与齿间载荷分配研究

斜齿轮副啮合刚度计算和齿间载荷分配是其动力学分析和强度计算的基础。针对斜齿轮啮合刚度近似代替法的准确性问题，结合斜齿轮线长度接触变化规律、单齿单位长度啮合刚度抛物线模型和ISO6336-1标准，建立了斜齿轮啮合刚度计算准静态弹性模型，并与基于准静态刚性模型的近似代替法、ISO6336-1标准进行了对比研究。结果表明，单对齿最小刚度与最大刚度比值α_k=0.55时的准静态弹性模型计算结果与ISO标准结果一致性较好，准静态刚性模型计算结果与ISO标准结果误差较大。分析了几何参数对斜齿轮综合啮合刚度和载荷分配系数的影响规律，针对斜齿轮典型断齿故障，讨论了不同断齿形式和断齿尺寸对啮合刚度和载荷分配系数的影响变化，为其故障动力学研究提供基础。     

基于时变啮合刚度与齿侧间隙的斜齿轮副动力学研究

为研究斜齿轮副啮合过程中螺旋角与驱动扭矩对斜齿轮副动力学特性的影响,建立了基于时变啮合刚度与齿侧间隙的斜齿轮副6自由度弯扭轴耦合动力学模型.利用斜齿轮副瞬时接触线,计算理论时变啮合刚度;结合齿侧间隙函数,通过4阶龙格库塔数值积分法,求解斜齿轮副的振动响应,分析螺旋角与工况对斜齿轮副振动响应的具体影响.研究发现,随着螺旋...     

内啮合斜齿轮高精度三维有限元自动建模方法

为提高内啮合斜齿轮有限元接触分析的建模速度和模型精度,提出了一种齿轮高精度三维有限元模型的自动建模方法。基于齿轮插刀齿廓方程,利用齿廓法线法,得到包括齿根过渡曲线的内、外斜齿轮端面齿廓,建立了内、外齿轮参数化粗网格有限元模型。开发了表层六面体网格剖分方法,自动识别齿面接触带单元,进行分级剖分细化,保证了有限元模型的建模精度和网格密度。进行了齿面接触分析,得到了内啮合斜齿轮的弯曲应力、接触应力、接触印痕、传动误差、时变啮合刚度和载荷分配率。粗细网格有限元模型计算结果对比分析表明,该方法提高了内啮合斜齿轮有限元建模效率和计算精度,缩短了计算时间,为快速准确的齿轮接触分析奠定了基础。     

Geometry design and tooth contact analysis of crossed beveloid gears for marine transmissions

Beveloid gears,also known as conical gears,gain more and more importance in industry practice due to their abilities for power transmission between parallel,intersected and crossed axis.However,this ty...     

Calculation of time dependent mesh stiffness of helical planetary gear system using analytical approach

Time-dependent mesh stiffness is a most important reason of vibration and dynamic excitation in gear sets. In this research, analytical formulas of the helical gear set and the planetary gear system are combined to calculate the time-dependent mesh stiffness of the helical planetary gear system. For this purpose, at the first step, the analytical equations are derived for the spur gear pair. Then by dividing a helical tooth into the several independent thin spur tooth slices, the helical gear pair mesh stiffness is extracted. Finally, these equations are extended to the helical planetary gear system. The suggested analytical results and those which obtained by the finite element method (FEM) are compared and are in good agreement when the helix angle is less than 15 degrees. Also, the helical planetary gear system mesh stiffness in different cases such as fixed carrier, fixed sun gear and fixed ring gears is calculated. These results show that the value of mesh frequency ratio in each case scales the mesh stiffness shapes in the rotation angle direction. In other words, mesh frequency ratio parameter determines the number of meshing period in each rotation of planets.     

Comparison of localised spalling and crack damage from dynamic modelling of spur gear vibrations

This paper presents a 26 degree of freedom gear dynamic model of three shafts and two pairs of spur gears in mesh for comparison of localised tooth spalling and damage. This paper details how tooth spalling and cracks can be included in the model by using the combined torsional mesh stiffness of the gears. The FEA models developed for calculation of the torsional stiffness and tooth load sharing ratio of the gears in mesh with the spalling and crack damage are also described. The dynamic simulation results of vibration from the gearbox were obtained by using Matlab and Simulink models, which were developed from the equations of motion. The simulation results were found to be consistent with results from previously published mathematical analysis and experimental investigations. The difference and comparison between the vibration signals with the tooth crack and spalling damage are discussed by investigating some of the common diagnostic functions and changes to the frequency spectra results. The result of this paper indicates that the amplitude and phase modulation of the coherent time synchronous vibration signal average can be effective in indicating the difference between localised tooth spalling and crack damage.     

人字齿轮直线型对角修形设计及成形磨原理

为了降低承载传动误差波动产生的振动激励，提出了成形磨人字齿轮直线型对角修形优化设计。根据ISO对角修形定义，计算齿顶、齿根修形起始线在旋转投影面上的螺旋角，将修形曲线设计为直线型，给定最大修形量，确定对角修形的齿面方程。利用齿面接触分析和轮齿承载接触分析，以工作载荷下人字齿轮承载传动误差波动量最小为优化目标，采用遗传算法优化对角修形参数。确定以目标修形齿面法向偏差的平方和最小的目标函数，以螺旋角、模数、压力角为设计变量，采用遗传算法分别对齿顶和齿根修形区域进行逼近，从而实现对角修形的成形磨加工。结果表明，人字齿轮直线型对角修形可以将承载传动误差波动量降低到36.65%；采用三截面砂轮成形磨的理论误差控制在1μm以内，获得较高的齿面精度；试验人字齿小轮齿的检测结果控制在4级精度以内，并进行了齿轮副的滚检试验，从而验证该方法的有效性。     

齿轮纯滚动啮合的原理与实现

渐开线,摆线和圆弧等常用齿轮机构在传动中都存在的相啮齿面间的相对滑动,导致一系列不良后果。本文简要回顾了滚动接触齿轮传动的研究史。详细阐述了齿轮纯滚动啮合的实现方法,工作原理及传动特点,纯滚动齿轮及切削刀具的齿廓设计和轮齿设计;给出了多种简单实用的纯滚齿廓曲线。通过计算机仿真和实物对本文理论和方案作出了验证。     

基于齿背接触刚度的高速斜齿轮瞬态振动特性

为了分析基于齿背接触刚度的高速斜齿轮瞬态振动放大特性,针对高转速瞬态工况下斜齿轮齿面啮合-脱啮-齿背接触的齿面实际承载接触状态,建立了同时考虑啮合时间与齿面振动位移耦合机理的斜齿轮动态啮合刚度。在细化考虑齿背啮合机理、基于齿背实际啮合刚度的模型基础上,进一步建立斜齿轮啮合型瞬态振动模型,并在此基础上展开不同齿侧间隙以及齿背接触对系统瞬态振动特性影响分析研究。搭建封闭功率流式斜齿轮瞬态扭转振动测试试验台,对基于齿背接触刚度的斜齿轮瞬态振动特性进行了验证。该研究具有较好的理论研究意义,有利于斜齿轮传动系统在航空传动、新能源传动系统上的应用推广,进一步提升高转速齿轮系统的瞬态振动噪声品质。     

The forging of helical gears (I): Experiments and upper-bound analysis

In this paper, the forging of helical gears has been investigated. A punch and a die are tooth-shaped for the guiding type forging of helical gears. The punch compresses a cylindrical billet placed in a die insert. As a consequence the material of a billet flows into the tooth region. The forging has been analysed by using the upper-bound method. Kinematically admissible velocity fields have been developed, where an involute curve has been introduced to represent tooth profile of the gear. Numerical calculations have been carried out to investigate the effects of various parameters, such as modules, numbers of teeth, helix angles and friction factors on the forging of helical gears. Some forging experiments were carried out with commercial aluminium alloy to show the validity of the analysis. Good agreements were found between the predicted values of the forging load and those obtained from the experimental results.     

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.     

混合标架下宽斜齿轮三维接触有限元前处理技术

本文针对宽斜齿轮，采用混合标架，建立了轮齿在各个不同位置的啮合时的有限元网格自动生成的算法；并开发了模块化；结构化，参数化的前处理程序，只需输入齿轮基本参数，即可得到完整的轮齿三维接触有限元分析数据文件，本文程序使用方便，适于在工程设计推广使用。