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.     

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.     

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.     

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。     

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...     

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。     

考虑磨损的直齿轮啮合刚度计算与分析

基于能量法和Archard磨损模型,提出了一种考虑磨损的齿轮啮合刚度数值计算方法.根据展成法原理,建立了精确的齿廓曲线方程.利用能量法计算齿轮单齿啮合刚度,并通过分段1阶傅里叶级数拟合获得齿轮总啮合刚度.以Archard磨损模型为基础,计算得到齿面法向磨损量与啮合点处压力角的关系.计算分析了不同磨损量对齿轮啮合刚度的影...     

Dynamic characteristics of a planetary gear system based on contact status of the tooth surface

Studies on the planetary gear have attracted considerable attention because of its advantages, such as compactness, large torque-to-weight ratio, vibrations, and high efficiency, which have resulted in its wide applications in industry, wind turbine, national defense, and aerospace fields. We have established a novel dynamic model of the planetary gear transmission by using Newton’s theory, in which some key factors such as time-variant meshing stiffness, phase relationships, and tooth contact characteristics are considered. The influences of gear axial tipping, operating conditions, and the meshing phase on the contact characteristics and the dynamic characteristics were researched systematically. It was found that the contact area of the tooth surface was moved due to the axial gear tipping, which obviously affected the meshing stiffness. With the increase in the inclination angle of the sun gear, the meshing stiffness decreases, which produces an evident influence on the high natural frequency in the planetary transmission system. In terms of the dynamic characteristics of the system, the component of rotating frequency appeared in the dynamic meshing force of the sun gear and the planetary gear. Moreover, the floating track of the center wheel varied significantly and exhibited an oval distribution as the inclination angle of the sun gear changed. When the inclination angle of the sun gear increased, the rotating frequency component increased significantly, but the other meshing frequency components remained unchanged; meanwhile, the deformation of the floating track also increased. If the inclination angle of the sun gear changes, the vibration state of the system and the collision impact could become more serious, and the lifetime of the planetary transmission system will reduce. Furthermore, when the load was increased, we found that the gear-tooth contact zone transformed from line contact to surface contact, the meshing stiffness increased, the effect of high natural frequency on the planetary transmission system became more evident, but its low-order natural frequency remained stable. With regard to the dynamic characteristics of the system, the components of the major frequency at the external gearing remained unchanged, but the rotation frequency of the sun gear and the meshing frequency amplitude increased linearly with the increase in load. In conclusion, the variation in the meshing stiffness of the planetary gear system had minor impact on the low-order natural frequency, but had a significant impact on the high natural frequency of the planetary transmission system due to the phase variation of the gear.     

齿面接触应力计算中曲率系数的商榷

分析了ISO6336与AGMA2001标准齿面接触应力计算中曲率系数的一些问题，认为无论对大小、直斜或内外齿轮，均宜采用通一的实际啮合线中点或小齿轮单齿啮合区内界点的综合曲率半径作为计算依据。     

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。     

系统刚度对行星齿轮传动振动特性影响研究

为了分析齿轮啮合刚度、支承刚度对行星传动系统振动特性的影响,建立了基于人字齿行星传动的平移一扭转耦合的动力学模型.在动力学模型中,每个运动构件假定有3个自由度,同时考虑各构件的支承刚度、轮齿时变啮合刚度等影响因素.根据各构件的运动方程建立传动系统的动力学微分方程,并对其进行特征值问题求解,获取行星传动系统振动特性.     

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.     

Dynamic interaction between contact loads and tooth wear of engaged plastic gear pairs

This study investigates the interaction between the dynamic contact load and the tooth profile wear of POM and Nylon 66 plastic gear pairs. A dynamic model of a plastic gear pair is presented. This model incorporates the effects of position-varying tooth mesh stiffness, damping ratio, load sharing, tooth profile wear and temperature on the dynamic contact load. The tooth wear equation developed by Flodin and Andersson [Simulation of mild wear in spur gears. Wear 1997;207:16–23] is utilized to simulate tooth wear and tooth profile variation. The variation of the contact load generated by the cumulative tooth profile wear is simulated and examined. A computational algorithm is developed to simulate the interaction between a dynamic contact load and tooth profile wear. Numerical results demonstrate that the dynamic load histogram of an engaged plastic gear pair can change markedly due to tooth wear.     

多平行轴齿轮耦合转子系统的振动响应

以一个两对斜齿轮耦合的三平行轴转子系统膨胀机子系统为研究对象,建立了斜齿轮啮合副动力学模型和转子系统有限元模型,考虑了齿轮啮合刚度、方位角、啮合角、螺旋角以及主动轴转动方向的影响,推导出齿轮啮合刚度矩阵。基于模态叠加法,对弯-扭耦合转子系统膨胀机子系统进行了固有特性分析和瞬态方式的不平衡响应分析,得到齿轮啮合前、后系统加载处的不平衡响应变化曲线。研究表明,齿轮间的耦合使系统之间的振动强烈,系统可能会在某个非固有频率处不平衡响应进行积累叠加,出现最大振动的现象,同时识别出共振峰的产生机理。齿轮耦合对转子系统动力学特性产生了很大的影响,使系统振型表现为耦合振型,必须以耦合的方式分析系统的振动特性,为防止系统发生大的振动提供依据,对齿轮系统的设计和故障分析具有指导意义。     

Investigation on Mesh and Sideband Vibrations of Helical Planetary Ring Gear Using Structure,Excitation and Deformation Symmetries

Time?variant excitations in planetary gear trains can cause excessive noise and vibration and even damage the system on a permanent basis. This paper focuses on the elastic vibrations of a helical planetary ring gear subjected to mesh and planet?pass excitations. Motivated by the structure, excitation and deformation symmetries, this paper proposes dual?frequency superposition and modulation methods to capture the mesh and sideband vibrations. The transi?tion between ring gear tooth and planet is introduced to address the excitations and vibrations. The phasing e ect of ring gear tooth and planet on various deformations is formulated. The inherent connections between the two types of vibrations are identified. The vibrations share identical exciting rules and the wavenumber and modulating signal order both equal the linear combination of tooth and planet counts. The results cover in?plane bending and extensional, out?of?plane bending and torsional deformations. Main findings are verified by numerical calculation and comparisons with the open literature. The analytical expressions can be used to determine whether the sideband is caused by component fault or only by elastic vibration. The methods can be extended to other power?transmission systems because little restriction is imposed during the analysis.     

Spur Gear Tooth Pitting Propagation Assessment Using Model-based Analysis

Tooth pitting is a common failure mode of a gearbox. Many researchers investigated dynamic properties of a gearbox with localized pitting damage on a single gear tooth. The dynamic properties of a gearbox with pitting distributed over multiple teeth have rarely been investigated. In this paper, gear tooth pitting propagation to neighboring teeth is modeled and investigated for a pair of spur gears. Tooth pitting propagation effect on time-varying mesh stiffness, gearbox dynamics and vibration characteristics is studied and then fault symptoms are revealed. In addition, the influence of gear mesh damping and environmental noise on gearbox vibration properties is investigated. In the end, 114 statistical features are tested to estimate tooth pitting growth. Statistical features that are insensitive to gear mesh damping and environmental noise are recommended.     

基于流体动力学的斜齿轮副搅油功率损失分析

在高速工况下,搅油损失在总功率损失中占很大比重,研究齿轮搅油功率损失对于提高传动效率具有重要意义。提出一种基于流体动力学的能够计算斜齿轮副搅油功率损失的计算模型,该模型采用将斜齿轮沿接触线划分为若干个薄直齿轮的方法计算斜齿轮副的搅油损失;将齿轮副搅油功率损失分为周面搅油功率损失、端面搅油功率损失以及啮合区挤压功率损失三部分,分析浸油深度、转速、螺旋角、齿宽、模数对搅油损失的影响以及各部分搅油损失占总搅油损失的比重。结果表明：搅油损失随着浸油深度、转速、螺旋角、齿宽、模数的增大而增大,其中转速、齿宽和模数对搅油损失的影响较大,浸油深度和螺旋角对搅油损失的影响较小;啮合区挤压功率损失在整个搅油功率损失中占最大比重。     

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.

     

A semi-analytical method of time-varying mesh stiffness in concentric face gear split-torque transmission system

Concentric face gear split-torque transmission system (CFGSTTS) has great applied value in the field of aeronautical transmission due to the characteristic of high integration. Mesh stiffness, as one of the most primary sources of vibration, is vitally important for the dynamic performances of gear transmission system. The existing finite element method (FEM) and analytical method (AM) are not suitable for tackling the mesh stiffness calculation of closed-loop multi-branch system such as CFGSTTS. Thus, a semi-analytical method (SAM) is presented and verified, which combines the high precision of FEM with the high efficiency of AM. Additionally, the differences between the mesh stiffness of independent face gear drive and that of the same gear pair in CFGSTTS under accordant load is researched by applying SAM. The influence rules of distribution angle and load condition on the mesh stiffness of gear pairs considering system structure are also studied. Results demonstrate that the mesh stiffness of gear pairs in CFGSTTS is time-varying and tends to be consistent with each other by adjusting load parameters.     

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.