基于时变啮合力的非圆齿轮传动动态磨损研究

由非圆齿轮变速比传动特性引起的时变啮合力对轮齿传动磨损具有重要影响,以精梳机中关键核心部件的椭圆齿轮副为研究对象,应用Hertz基础理论和Archard磨损公式,建立了基于时变啮合力的齿轮磨损计算模型,采用当量齿数法对非圆齿轮的啮合刚度进行求解,分析了单个齿廓的时变啮合力和磨损量的变化规律;在此基础上,研究了阶数和偏心率对椭圆齿轮时变啮合力及磨损量的影响。结果表明,齿轮时变啮合力和齿面磨损量随着偏心率和椭圆齿轮阶数的增加呈现不同程度的增加;时变啮合力在单双齿啮合区交界处发生突变;齿廓磨损量在节圆附近接近零,在齿根和齿顶处的磨损量较大。在对非圆齿轮不同节曲线向径处的磨损量进行研究时发现,在最小节曲线向径处的齿根磨损量显著大于最大节曲线向径处。该研究结果为使用修形方法降低时变啮合力与磨损量,从而延长齿轮寿命提供了一定的理论依据。     

增速齿轮副非均匀磨损时变啮合刚度研究

以某渐开线直齿圆柱增速齿轮副为研究对象,基于Hertz接触理论与Archard磨损公式,推导齿轮副齿面接触应力与相对滑动速度,建立齿轮副非均匀磨损模型,计算了不同循环次数下齿面磨损深度;基于势能法推导基圆与齿根圆不同位置下轮齿非均匀磨损时变啮合刚度解析公式,研究了非均匀磨损对时变啮合刚度的影响规律。研究结果表明,磨损深度在渐开线齿廓上分布不均匀,节圆附近的磨损最小,齿顶齿根处磨损深度较大,且齿顶处累积磨损深度最大;齿面磨损深度随循环次数增加而增大,齿轮时变啮合刚度随磨损深度增加而减小,且双齿啮合区刚度减小量大于单齿啮合区。     

渐开线直齿圆柱齿轮磨损的数值计算与分析

以标准渐开线直齿圆柱齿轮为研究对象,以Archard磨损计算模型为载体,将齿轮啮合区域的齿廓进行离散化处理,建立齿轮齿廓磨损计算模型。运用数值计算方法模拟齿廓各点的磨损情况,编写相关的计算程序,分析齿廓各啮合点处压力角与滑动系数、磨损率、摩擦距离、磨损量之间的关系,并进行曲线拟合。结果表明:在啮合区域内,齿廓的相对滑动系数、摩擦距离、磨损率、磨损量从齿根到齿顶的变化规律都是先减小后增大,在节点处理论值为0。提出的数值计算方法可实现对不同尺寸、不同材料、不同工况条件下的齿轮副的磨损量的定量计算,从而实现对齿轮使用寿命的预测。     

齿轮磨损故障动态响应特征与诊断指标研究

齿轮磨损属于典型的早期故障,为监测齿轮磨损状态,开展齿轮磨损故障机理与诊断指标研究.采用解析建模的方法,定量研究了齿轮磨损对时变啮合刚度和无负载静态传递误差动力学参数的影响规律:采用Archard磨损模型计算齿轮齿面磨损深度,获得沿齿廓方向的非均匀磨损分布;采用势能法计算齿轮啮合刚度,揭示了齿轮磨损对啮合刚度幅值影响的定量规律;将齿轮磨损等效为轮齿齿廓偏差,揭示了齿轮磨损对无负载静态传递误差影响的定量规律.采用集中参数法建立齿轮传动的动力学模型,通过两级直齿轮疲劳寿命试验对比验证了齿轮磨损动态响应特征.结果 表明,齿轮磨损主要影响齿轮啮合频率及其谐波成分,同时啮合频率及其谐波的边频带以转频为主,且随磨损增加出现明显变化.基于获得的磨损动态响应特征,构造了四个基于振动信号啮合频率边带的诊断指标,该指标对磨损状态变化敏感,通过仿真和试验验证了指标的有效性和鲁棒性.     

准静态工况下渐开线直齿轮齿面磨损建模与分析

根据Hertz理论和Archard磨损公式,建立面向真实工况的直齿圆柱齿轮准静态磨损模型,并对其齿面磨损特性进行了数值仿真。计算表明,理想工况下直齿轮副齿面沿齿宽方向均匀磨损,其在节圆附近的磨损量最小,而在小齿轮靠近齿根部位的磨损量最大;当存在啮合偏差时,齿面磨损深度沿齿向不再均布。在此基础上,进一步分析了负载工况和磨损循环次数对齿面磨损量的影响。分析表明,负载转矩和循环次数对齿面磨损量影响显著,近似呈指数映射关系。当以减磨延寿为齿轮设计目标时,必须计入负载工况和齿轮役期的影响。最后,分析了齿轮啮合偏差和微观修形对齿面磨损量的影响。研究表明,从改善齿面载荷分布和减缓齿面磨损角度考量,应严控齿轮啮合偏差量,并可通过制定合适的齿面修形策略来减缓齿面磨损失效。     

直齿轮齿面非均匀磨损对模态特性的影响

研究准静态工况下齿面非均匀磨损对齿轮模态特性的影响。根据Hertz接触理论和Archard公式建立准静态磨损模型,对齿轮齿面磨损情况进行数值仿真。计算结果表明,主、从动轮的齿顶处和齿根处磨损较大,其中,齿顶处磨损量小于齿根处,主动轮的齿根位置磨损量最大,节点处齿轮做纯滚动,不产生磨损,在单齿、双齿啮合区交替处磨损量有突变。在此基础上,按数值分析结果施加齿面磨损故障,导入到Abaqus中进行仿真,进一步分析了磨损前后齿轮的模态特性。仿真结果表明,齿轮具有丰富的振动形态,磨损对振型影响不明显,但固有频率出现明显升高,其中,7～10阶的高阶固有频率增大幅度要高于低阶固有频率增大的幅度。     

Ease-off修形准双曲面齿轮齿面动态抗磨设计与分析

为了改善准双曲面齿轮动态性能、减小齿面磨损提出齿面动态抗磨修形设计与分析方法。小轮修形齿面表示为共轭齿面与法向Ease-off曲面两个矢量的和,Ease-off曲面通过预置抛物线修形参数及几何传动误差参数表达。提出考虑磨损深度影响的齿面承载接触分析（Tooth contact analysis with wear,WLTCA）数值方法,该方法通过承载接触分析（Tooth contactanalysis,LTCA）方法获得啮合刚度及齿面静载荷,在此基础上根据动力学分析获得齿面动载荷,结合Archard磨损公式进一步获得齿面磨损量,将齿形更新时的同时啮合齿对的磨损量叠加到齿对的初始间隙,为磨损后的LTCA计算提供准确的参数,重复以上循环可得到齿形更新后齿面上任一点的磨损深度及次数。以无磨损时法向相对振动加速度均方根最小、齿面磨损量最小进行修形优化获得最优Ease-off曲面;分析齿面磨损与系统动态响应之间的耦合作用。结果表明最优Ease-off齿面主要通过齿廓修形减少了磨损量,有效改善了系统动态响应。该方法充分考虑了齿面修形、磨损、动态响应的耦合性且计算效率较高,为高性能准双曲面齿轮齿面抗磨、减振设计与分析提供理论参考。     

齿面磨损对齿轮系统动态特性的影响

为研究齿面磨损对齿轮系统动态特性的影响,综合考虑齿轮齿侧间隙、传输误差、齿面磨损,采用集中参数法建立齿轮平移-扭转非线性动力学模型,分析齿轮的转速、运行次数对含有齿面磨损的齿轮传动系统动态特性的影响。结果表明:在啮合区域内,齿根处的齿面磨损量呈减小趋势,在节点处理论磨损量为零,齿顶处的齿面磨损呈增加趋势,齿面磨损量减小趋势大于增加趋势,整个过程中齿面磨损会造成啮合刚度的减小;存在齿面磨损时,过大或过小的转速都会使齿轮系统的振幅波动变大,幅值减小;当转速一定时,含有齿面磨损的系统随着运行次数的增加,振幅幅值会逐渐减小,传动的波动会加剧。     

某机械手回转机构的轮齿磨损特征分析

为获得某机械手回转机构的轮齿动态磨损特征,将渐开线齿形离散成一系列点。引入弹簧阻尼元件描述啮合过程中接触表面的弹性变形和阻尼,采用石川法计算时变啮合刚度并考虑磨损间隙,建立了齿轮啮合动力学模型。提取啮合力结合Archard磨损方程推导了离散齿面的磨损深度计算公式,并给出齿形重构方法。算例分析表明:节点之上的齿面比节点之下的齿面磨损速度慢,节点处磨损速度最慢理想情况下为零;一定范围内,啮合力随着磨损增加而趋于平稳,对啮合力傅里叶变换发现除1倍和2倍啮合频率振幅增大外,其它频率振幅均降低,高频部分尤其明显。     

直齿锥齿轮啮合刚度计算方法研究

针对直齿锥齿轮啮合刚度的计算问题,将其齿形转换成齿宽中点处的当量直齿圆柱齿形,再把当量齿轮的轮齿简化为齿根圆上的悬臂梁,通过能量法计算分析了单齿啮合刚度;基于位移容差的原理,进一步提出了齿轮时变啮合刚度计算模型;将其与有限元计算结果对比,并分析误差来源,完成了计算方法的验证.文中提出的计算方法不仅进一步丰富和发展了齿轮刚度的计算理论,对齿轮动力学的研究也具有重要意义.     

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.     

RV减速器摆线轮磨损量的数值计算与分析

基于Archard磨损模型和Hertz接触理论为理论基础,将摆线轮齿廓啮合区域离散化,建立了摆线轮磨损的计算模型;根据该计算模型分析了各啮合点处滑动系数、磨损率、磨损量与啮合相位角之间的关系,并进行曲线拟合。结果表明,建立的数值计算方法可以实现对不同修形方法、不同尺寸、不同工况条件下摆线针轮齿廓磨损量的定量计算。     

齿轮故障对直齿轮副时变啮合刚度的影响研究

提出了一种基于计算机仿真的解析法,用于量化齿轮副在不同齿轮故障情况下的时变啮合刚度.齿轮故障在影响齿轮副传动的同时往往也伴随着刚度的降低,时变啮合刚度是状态监测和啮合齿轮副动态特性描述的一项重要参数,势能法是计算时变啮合刚度最常用的分析方法之一.采用势能法研究了含裂纹齿轮、断齿和齿面剥落等3种故障情况对于齿轮啮合刚度的...     

Mesh relationship modeling and dynamic characteristic analysis of external spur gears with gear wear

Gear wear is one of the most common gear failures, which changes the mesh relationship of normal gear. A new mesh relationship caused by gear wear affects meshing excitations, such as mesh stiffness and transmission error, and further increases vibration and noise level. This paper aims to establish the model of mesh relationship and reveal the vibration characteristics of external spur gears with gear wear. A geometric model for a new mesh relationship with gear wear is proposed, which is utilized to evaluate the influence of gear wear on mesh stiffness and unloaded static transmission error (USTE). Based on the mesh stiffness and USTE considering gear wear, a gear dynamic model is established, and the vibration characteristics of gear wear are numerically studied. Comparison with the experimental results verifies the proposed dynamic model based on the new mesh relationship. The numerical and experimental results indicate that gear wear does not change the structure of the spectrum, but it alters the amplitude of the meshing frequencies and their sidebands. Several condition indicators, such as root-mean-square, kurtosis, and first-order meshing frequency amplitude, can be regarded as important bases for judging gear wear state.     

Experimental measurement of gear mesh stiffness of cracked spur gear by strain gauge technique

In this paper, an experimental technique based on strain gauge has been proposed to measure the gear mesh stiffness of healthy spur gear as well as of cracked spur gear pair system. Calculation of mesh stiffness of healthy and cracked spur gear tooth are based on strain energy and strain energy release rate respectively. The location of strain gauge plays an important role in calculation of strain energy stored in gear tooth. The locations of strain gauge on gear tooth are illustrated for healthy and cracked gear. Stress intensity factor (SIF) has been calculated by strain gauge technique for calculating the stiffness of cracked pinion tooth. The effect of crack length on mesh stiffness has been investigated by strain gauge technique and results are compared with the established analytical method.     

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。     

An investigation on the influence of modification parameters on transmission characteristics of planetary gear system

A new gear tooth modification model of planetary gear system was established by considering the characteristics of tooth longitudinal crowning modification and tooth profile modification. Using this model, the influences of modification parameters on the time-varying mesh stiffness, transmission error, contact spots and dynamic response of the planetary gear system were analyzed through numerical analysis. The results show that tooth profile modification can effectively restrain the mesh stiffness sudden variation in the single and double tooth alternation of both the internal and external mesh pairs, and significantly decrease the transmission error fluctuation. However, longitudinal crowning modification has no marked influence on mesh stiffness sudden variation or transmission error fluctuation. The tooth profile modification can significantly reduce the sudden variation of tooth surface load during gear mesh course. Longitudinal crowning modification can make the tooth surface load evenly distributed in tooth width direction. When the external meshing pairs are modified at the tooth profile individually, the magnitude values of main response resonance peaks of internal meshing pairs have a great reduction, but those values of external meshing pairs change slightly. In the case of tooth profile modification of the internal meshing pairs, the phenomenon is reversed. By contrast with tooth profile modification, longitudinal crowning modification has little influence on the resonance peaks of internal and external meshing pairs.

     

Thermo-elastohydrodynamic lubrication of an involute gear

This paper analyses the thermo-elastohydrodynamic lubrication on an involute spur gear tooth surface and the influence of the inlet temperature of the lubricant. The oil film temperature distribution shows a minimum near the point where the pressure distribution is a maximum and the energy loss a minimum. Then the temperature increases slightly in the outlet region. Calculated results show a decrease of a few percent in the maximum pressure distribution compared with an oil film on a rigid surface. Based on oil film thickness and gear tooth deflection, the load sharing coefficient and the relative transmitting errors are calculated. The behaviour of the oil film due to the variation of the normal tooth load at the transition point of the meshing is investigated also