纯电动汽车高速斜齿轮传动振动特性分析

为研究高转速情况下时变啮合刚度和啮合冲击对斜齿轮传动振动特性的影响,以某纯电动汽车高速斜齿轮传动为研究对象,建立了弯-扭-轴动力学模型;采用改进的基于承载接触分析的计算方法获得时变啮合刚度曲线,并计算了啮合冲击时间及啮合冲击力幅值;分析了时变啮合刚度、啮合冲击以及两者综合3种激励条件下高速斜齿轮传动系统的振动特性。结果表明：时变啮合刚度激励下,在过共振区,转速变化对系统振动的影响不显著;啮合冲击激励以及综合激励条件下,系统振动随转速的升高而增大,与啮合冲击激励相比,综合激励下振动加速度增幅较缓。研究结果可为纯电动汽车高速斜齿轮传动的设计和工程应用提供参考依据。     

基于有限元法的疲劳点蚀斜齿轮时变啮合刚度分析与试验研究

疲劳点蚀斜齿轮啮合刚度计算是齿轮故障动力学分析的重要基础.基于有限元的斜齿轮啮合刚度计算方法,建立了正常齿轮和疲劳点蚀齿轮的有限元模型.通过有限元模型计算,得到了齿面法向接触力和综合弹性变形量;并根据啮合刚度计算方法,得到了齿轮的单齿啮合刚度和多齿综合啮合刚度.分析不同点蚀剥落长度和宽度对齿轮啮合刚度的影响得知,剥落长度和宽度对齿轮啮合刚度影响较大;而且剥落长度会影响齿轮啮合刚度的变化区域.通过疲劳点蚀试验证明,齿轮啮合刚度的减小使得齿轮振动冲击响应增大.     

齿轮传动系统的动态模拟

针对齿轮副非线性振动问题展开研究,综合分析了啮合冲击激励、时变啮合刚度和误差激励对齿轮系统振动的影响。根据扭转啮合刚度定义,分别建立了无齿面缺陷和有齿面缺陷的齿轮三维接触仿真分析模型。计算了两种运行状态下,不同接触位置上的扭转啮合刚度。在进行齿轮副非线性振动的分析时,综合考虑了啮合冲击激励、时变啮合刚度和误差激励等非线性因素,建立了齿轮副非线性动力学模型,采用变步长四阶Runge-Kutta数值积分方法求解了系统的动态响应。     

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。     

齿轮啮合内部动态激励数值根据

把具有内部激励和时变刚度齿轮系统非线性微分方程变换为近似的线性微分方程,把时变刚度激励、误差激励、啮合冲击激励作为右端顶。时变刚度曲线用轮齿三维接触有限元方法求得,啮合冲击激励力用轮齿三维 冲击－动力接触有限元混合法求得。误差激励按精度等级确定的齿轮偏差进行模拟。把激励力作用在整个齿轮系统的三维有限元模型上,以便求得其振动响应。     

斜齿轮啮合传动内部激励研究

齿轮啮合传动的内部激励是引起齿轮振动和噪声的关键因素,以某8挡自动变速器中一对常啮合斜齿轮为研究对象,对其啮合传动过程的内部激励开展全面深入研究,包括齿面接触状态、时变啮合刚度、误差激励和啮合冲击。采用有限元法分析斜齿轮的静态和动态接触过程,得到齿面接触应力的大小及分布;采用接触线长度变化表示时变啮合刚度的理论方法和采用有限元仿真的方法得到斜齿轮传动的时变啮合刚度曲线;采用理论计算和有限元法分析斜齿轮误差激励,包含啮合误差、静态传递误差和动态传递误差;采用有限元法分析啮合冲击,得到齿轮传动过程的齿根应力;采用有限元法计算齿面接触线上应力分布。研究为斜齿轮传动状态的改善提供了基础。     

齿轮传动振动噪声计算的Kato方法

建立了齿轮传动的时变动力学模型，分析了啮合刚度，传动误差对振动响应的影响，在此基础上，将齿轮传动啮合分成单齿啮合区，采用Kato方法对振动产生的噪声进行了定量计算，得出了双齿啮合区内辐射噪声大于单齿啮合区，并给出了每一啮合时刻辐射噪声大小，研究表明该方法可以较好地对齿轮振动所产生的噪声进行定量计算，为齿轮系统的降噪设计奠定了基础。     

渐开线齿轮传动的扭转刚度研究

齿轮传动刚度的计算对于动力传动系统的振动噪声研究具有重要意义,基于Abaqus软件的有限元计算研究了渐开线齿形的直齿轮啮合扭转刚度。研究中,采用了接触模型处理了齿与齿之间的啮合关系,得出单齿模型整个啮合周期内多个状态下的扭转刚度结果,分析了齿轮刚度计算的石川公式,并与有限元计算结果进行了比较,分析了精度和误差来源。还采用接触有限元模型计算了全齿轮模型啮合刚度,得出直齿轮啮合刚度的变化规律。根据直齿轮有限元计算结果,给出了斜齿轮啮合扭转刚度的快速计算方法。     

基于指数窗截取递推最小二乘法的齿轮啮合刚度辨识算法研究

齿轮在机械传动系统中有着广泛应用,由于齿轮啮合过程中参与啮合的轮齿对数周期变化,因此,齿轮啮合刚度为时变参数,在啮合时会产生啮合振动。当齿轮副出现齿根裂纹时,啮合刚度会减小,齿轮啮合产生的系统振动响应也发生改变,通过振动响应辨识齿轮啮合刚度能够监测齿轮副的健康状态。针对齿轮啮合刚度的时变特征,提出了基于指数窗截取递推最小二乘(Exponential window recursive least square,EWRLS)算法和振动信号瞬时频率的齿轮啮合刚度辨识方法。进行啮合刚度辨识时,EWRLS算法将输入、输出齿轮的转速曲线分别作为辨识输入信号和观测信号,使用指数窗函数进行数据截断,使用递推最小二乘算法估计系统参数。为了计算输入、输出齿轮的转速曲线,使用经验模态分解(Empirical mode decomposition,EMD)方法将振动信号分解为具有不同变化频率的本征模态函数(Intrinsic mode function,IMF),并根据IMF的平均频率重构输入、输出齿轮的特征信号。通过Hilbert变换计算特征信号的瞬时频率曲线,从而获得各齿轮的转速曲线。使用仿真和实测信号对算法进行验证,结果表明,EWRLS算法能够辨识齿轮副的时变啮合刚度。     

车辆行星齿轮啮合刚度的建模及分析研究

齿轮副啮合刚度的周期性变化是行星齿轮传动系统产生振动的主要内部激励,深入研究齿轮的啮合刚度对解明齿轮系统的振动特征具有重要意义。采用能量法、有限元法和矩形波法分别建立了行星齿轮啮合刚度激励模型,并采用这3种模型分别求解了太阳轮、行星轮以及行星轮齿圈综合啮合刚度,对比了这3种模型求解啮合刚度的优劣。结果表明,3种刚度激励下的复合行星排各个构件的振动加速度幅值相差很小,且有限元法计算得到的振动加速度幅值稍大于解析法计算得到的振动加速度幅值,矩形波法计算得到的加速度幅值最小。     

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.     

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.     

3K-Ⅱ型直齿行星齿轮传动的固有特性

为揭示3K-Ⅱ型直齿行星齿轮传动的固有特性,建立该类传动系统在系杆随动参考坐标系下的平移-扭转耦合动力学模型.模型设定系统中每个构件均拥有3自由度,并计入各构件的支承刚度、轮齿时变啮合刚度和陀螺效应等影响因素.通过分析各构件间的相对位移关系,推导出系统的运动微分方程,进而求解其特征值问题即可获知系统的固有频率和相应振型.固有特性分析表明,3K-Ⅱ型行星齿轮传动具有与2K-H行星齿轮传动类似的三种典型振动模式,即扭转振动模式、平移振动模式和行星轮振动模式.列出三种典型振动模式下传动系统的运动特征.     

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.     

Dynamic behavior of the spur gear system with time varying stiffness by gear positions in the backlash

Gear backlash is a nonlinear effect of the gear system. In a spur gear system with the backlash, the initial position of gears with the backlash affects the impact force. This work conducted a dynamic analysis of the spur gear system with time-varying mesh stiffness and bearing stiffness with a focus on the initial gear position within the backlash. For this purpose, the time-varying stiffness of the gears and rolling bearings were calculated. Mesh force with the time-varying stiffness and the gear backlash was applied to four DOF equations of motion. The equations of motion were solved using the Newmark beta method and Newton-Raphson method. The dynamic characteristics of the spur gear system by the initial position of gears within the backlash were investigated along with the magnitude of the backlash. The results showed that as the backlash increased, the mesh and bearing forces increased as well. The mesh and bearing forces were highly dependent on the initial gear position within the backlash. Significant initial mesh and bearing forces by the initial gear position within the backlash can lead to cumulative damages to the gear system.     

Effects of different coupling models of a helical gear system on vibration characteristics

Time-varying mesh stiffness (TVMS) and the dynamic coupling between the helical gears have a great influence on the vibration characteristics of a helical gear rotor system. Considering the effects of TVMS and adopting two coupling models (lateral-torsional coupling model and lateral-torsional-axial-swing coupling model), the dynamic behavior of a helical gear system was studied. First, an analytical model was used to analyze TVMS of a helical gear pair where the helical tooth is simulated by many spur tooth slices along the direction of the tooth width and the mesh stiffness of each slice is calculated using the energy method. Then, considering the effects of the TVMS excitation, the finite element model of a helical gear rotor system was established. Gear mesh was simulated by the above-mentioned two coupling models to investigate the effects of coupling forms on the system vibration characteristics. The strain energy was used to distinguish the dominant mode and dominant shaft of a gear system in natural characteristics analysis. The results show that the full coupling model can analyze accurately the vibration characteristics of the system and the axial and swing motions cannot be ignored in vibration analysis. Finally, the effects of helix angle on TVMS and vibration responses of a helical gear system were also studied.     

计入齿圈柔性的直齿行星传动动力学建模

为揭示齿圈柔性对传动系统动态性能的影响,在系杆随动坐标系下建立计入齿圈柔性的直齿行星传动精细化动力学模型,建模中计入时变啮合刚度、支承刚度、陀螺效应和齿圈柔性等诸多影响因素。采用有限段单元的离散化建模方法,将连续体的柔性齿圈离散成由等效虚拟弹簧连接的刚性齿圈段,并推导齿圈段与行星轮的啮合判据。通过分析各构件间的相对位移关系及其受力,最终建立系统的运动微分方程。以三行星轮的NGW型直齿行星传动为例对其进行固有特性分析,得出系统的低阶固有频率分布及相应的振动模式,并进一步分析齿圈柔性和安装方式对系统固有特性的影响。研究结果表明,直齿行星传动的振型可归结为中心构件(太阳轮、系杆)扭转振动和中心构件平移振动两种模式,两种模式下齿圈和行星轮均做复杂平面振动;齿圈的柔性会降低系统的低阶固有频率,且其影响程度与齿圈安装方式有关,齿圈完全固定时其影响最小,径向浮动或周向转动时影响较明显。     

混合动力两级行星机构动力耦合系统动力学建模及分析

以基于双转子电机的混合动力传动系统的两级行星齿轮机构动力耦合系统为研究对象,考虑前后两级行星齿轮机构的齿轮副啮合刚度、中心构件的扭转支撑刚度、连接部分的扭转耦合刚度、各构件惯性等基本因素,详细推导并建立两级行星齿轮耦合系统的纯扭转动力学模型。利用两级行星齿轮机构的有关参数进行特征值问题求解,得到系统整体模型的固有特性,按照振型特点把系统的振动形式划分为三种模式:整体扭转振动模式、前排行星轮振动模式和后排行星轮振动模式。在整体模式下固有频率为单根,系统各构件均以一定幅度做扭转振动;前、后排行星轮模式下固有频率均为二重根,且除了其自身外,其他构件均无振动。归纳分析得到的各振动模式特征与前人有关结论相吻合。同时指出连接部分的耦合刚度对系统振动特性的影响,并作了初步分析。