齿轮-转子-轴承系统复合故障振动特性研究

针对齿轮-转子-轴承系统发生复合故障时齿轮副振动响应,结合齿轮副模型和滚子轴承模型,基于拉格朗日方程建立了36自由度的齿轮-转子-轴承系统耦合振型,设定齿轮副主动轮剥落和轴承表面损伤复合故障,研究了复合故障下齿轮副的振动响应。结果表明,在健康的齿轮-转子-轴承系统振动响应下,系统振动时域幅值较为均匀,振动频谱主要为轴承外圈特征频率和齿轮副啮合频率;当齿轮副发生剥落单故障时,系统振动频谱上出现啮合频率与转轴频率调制生成的边频带;当齿轮-转子-轴承系统发生复合故障时,系统振动时域上的振动幅值增大,振动愈加复杂,频域信号调制现象严重,而且调制生成的信号幅值增大,但在其振动频域上可以找到其故障频率以及调制生成的谐波频率,以此可以判断系统的故障类型。     

考虑齿距偏差的直齿轮转子系统振动特性分析

针对工程实际中的齿轮存在齿距偏差,主要研究齿距偏差对齿轮系统振动特性的影响。考虑齿距偏差,建立了齿轮啮合刚度和传递误差模型,在此基础上,建立了通用齿轮啮合动力学模型,将该模型与转子系统有限元模型进行耦合,得到了齿轮转子系统有限元模型,分析了齿距偏差对系统振动响应的影响。研究结果表明:由于齿距偏差的存在,齿轮双齿啮合区刚度降低,无载荷传递误差增大,齿轮系统振动增大,频谱图中出现啮合频率及其高次谐波的边频带成分,这些边频带主要由主动和从动齿轮的转频及其倍频组成。减小齿距偏差和增大作用扭矩均能降低齿距偏差引起的边频带幅值。研究结果可为含齿距偏差的齿轮振动分析提供理论依据。     

复杂齿轮耦合转子-轴承系统动力学的规范建模方法

由于齿轮的耦合作用,齿轮-转子-轴承系统中各个转子的振动是相互耦合、相互影响的,研究齿轮-转子-轴承系统动力学,必须基于系统的、整体的观念进行分析。因此,齿轮-转子-轴承耦合系统动力学建模和模型降阶一直是人们普遍关注的问题。基于齿廓啮合基本定理,给出了直齿轮、斜齿轮、直齿锥齿轮、弧齿锥齿轮共4种齿轮的几何耦合模型（或称运动耦合模型）;利用耦合模型矩阵,给出了含以上4种齿轮副的复杂齿轮转子-轴承系统纵-弯-扭耦合动力学研究的统一、方便、规范的建模方法。为复杂齿轮-转子-轴承耦合系统动力学分析研究提供了方便。     

含柔性转子的齿轮-轴承系统动态特性分析

为了分析齿轮系统动力学中的全耦合振动,提出采用虚拟样机建模的方法,将柔性转子引入到啮合耦合系统中,考虑齿轮时变啮合刚度、齿侧间隙和轴承间隙的影响,建立齿轮-柔性转子-轴承系统虚拟样机模型,通过求解模型的动力学方程得到系统的非线性动力学响应。仿真结果表明:考虑柔性转子的耦合系统,啮合冲击峰值下降明显;转子柔性增加,齿轮低频扭转振动出现"拍"现象;高速轻载时啮合振动非线性特性增强;轴承间隙增大使啮合力振动幅值显著增大。     

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.     

细高齿齿轮啮合刚度及动态特性研究

为了研究细高齿齿轮的振动特性,以一对标准齿齿轮和细高齿齿轮为对比研究对象,建立直齿轮传动系统平移-扭转动力学模型;采用有限元方法求解细高齿齿轮的时变啮合刚度,分析了负载对刚度的影响规律;通过Newmark-β时间积分法计算齿轮的振动响应,对比标准齿齿轮和细高齿齿轮传动系统的轴承动载荷及齿轮啮合激励,求解了不同转速下两对齿轮系统的输入、输出轴承动载荷。结果表明,细高齿齿轮啮合为两齿-三齿交替接触,刚度变化减弱;轴承动载荷波动幅值较标准齿大幅降低,啮合频率及其倍频幅值明显下降,轮齿间啮合力减小。     

含故障传动系统齿轮-轴承耦合动力学特性研究

针对齿轮传动系统工作环境复杂,故障率高的问题,对传动系统进行动力学分析并探究其故障机理。根据Hertz接触理论考虑轴承钢球离心力的作用,建立深沟球轴承时变刚度模型。利用能量法得到正常与含裂纹故障齿轮的时变啮合刚度。利用集中参数法建立齿轮传动系统齿轮-轴承耦合动力学模型。考虑齿轮传动系统传递误差、时变刚度等参数激励因素,对齿轮传动系统的动力学特性进行仿真分析,得到了传动系统的振动加速度,分析了裂纹故障对齿轮动态响应的影响;通过台架试验验证了模型的正确性。研究结果表明:建立的动力学模型能够很好地描述含故障齿轮传动系统的动力学特性,在时域波形图中,由于裂纹故障的存在会产生周期性的冲击信号,同时频谱图中在啮合频率的周围会产生边频带。     

齿轮轴承转子系统支撑刚度特性研究

建立考虑齿轮-轴承转子系统多刚体、多柔体及刚柔耦合的动力学模型,并采用不同轴承刚度计算方法获得支撑刚度。在此基础上,研究系统支撑刚度对齿轮动态啮合力及振动位移等响应的影响规律,并与理论值对比分析。研究结果表明:刚性体模型仿真结果与理论值相比数值普遍偏大,而柔性体仿真结果与理论值基本一致;齿轮-轴承转子系统支撑刚度对齿轮动态响应产生较大影响,支撑刚度取3倍齿轮啮合刚度时,齿轮振动角速度等值与理论值基本相符。因此,利用柔性体模型并选择合理的支撑刚度对齿轮-轴承转子系统的动力学仿真分析具有实际意义。     

多轴齿轮耦合转子系统的振动分析

以膨胀机子系统为研究对象,考虑静态传递误差,建立了斜齿轮啮合副动力学模型,同时考虑转子系统的影响,建立了三平行轴系齿轮转子系统有限元模型;对齿轮弯-扭耦合膨胀机子系统进行了不平衡响应分析,同时考虑轴承刚度、齿轮螺旋角对齿轮动态啮合力的影响。研究表明,膨胀机子系统因为齿轮的耦合振动而明显加剧,齿轮耦合使系统振型表现为耦合振型,因此必须以耦合的方式分析系统的振动特性;轴承处刚度及螺旋角对相对应的齿轮啮合处的动态啮合力影响很大,甚至使动态啮合力峰值发生了偏移,为转子系统轴承刚度的确定以及齿轮的设计都提供了较好的理论基础。     

支承轴承作用下齿轮系统动力学分析

基于牛顿动力学原理,建立了非线性直齿齿轮副系统数学模型,在Matlab软件环境中采用四阶Runge-Kutta方法求解数值解,分析了齿轮系统启动时支承轴承的支承刚度,支承阻尼对直齿齿轮系统中齿轮位移振动,齿轮相对位置变化以及齿轮动态传递误差的动力学影响。结果表明,主动轮与从动轮的相对位移在中、高频区的位移振动随齿轮轴承支承刚度增加而增强,且振动频率从低频向中高频偏移。增大支承阻尼能减缓齿轮啮合时沿啮合线方向的相对位移振动,改善低频区的传动效果。轴承支承刚度的增加使齿轮动态传递误差振动加剧,影响齿轮转动精度;支承阻尼变化不影响齿轮动态传递误差的振动频率,只改变振动幅值。     

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 analysis of gear-rotor system with viscoelastic supports under residual shaft bow effect

This paper investigates the dynamic behaviors of a gear-rotor system with viscoelastic supports under effects of the gear eccentricity, the transmission error of gear mesh and the residual shaft bow. The investigated dynamic characteristics include system natural frequencies and steady-state response. The finite element method is used to model the system and Lagrangian approach is applied to derive the system equations of motion. The results show that the mass, the stiffness and the loss factor of the viscoelastic support will significantly affect system critical speeds and steady-state response. It needs larger loss factor and more rigid stiffness of the viscoelastic supports to suppress the systematic amplitude of resonance. As the results shown, the magnitude and phase angle of the residual bow have tremendous influence on first critical speed when the geared system mounted on stiff viscoelastic supports. The transmission error of the gear mesh is assumed to be sinusoidal with tooth passing frequency and it will induce multiple low resonant frequencies in the system response. It is observed that the excited critical speed equals to the original critical speed divided by gear tooth number.     

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.     

一种舰船用齿轮传动的动态优化设计方法

舰船用宽斜齿轮副的动态特性直接关系到舰船轮机系统的整体性能。本文考虑单自由度齿轮传动动态特性，以接触线长度的变化代替啮合刚度的变化，求解一对啮合齿轮副的综合啮合刚度及轮齿啮合刚度，以啮合线方向上加速度最小为优化目标函数，给出了基于动力学研究的舰船用齿轮副动态优化设计方法。     

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.     

Effects of dynamic transmission errors and vibration stability in helical gears

Transmission error is an important reason for instability in helical gears. A six-degree-of-freedom dynamic model coupled flexional, torsional and axial motion of a helical gear transmission system, which includes time varying mesh stiffness, bearing supporting stiffness, mesh damping and backlash, is developed, after taking into account the dynamic characteristics and vibration responses of helical gear in three dimensions. Influences of involute contact ratio, bearing supporting stiffness, mesh damping and backlash on the dynamic transmission errors and vibration stability of the helical gear system are investigated using numerical simulation technique. The effects on dynamic transmission errors and stabilities by contact ratio, supporting stiffness and mesh damping as well as gear backlash are analyzed. The intrinsic relationship between above parameters and dynamic transmission errors and stabilities for helical gear system are presented. The stable and unstable regions under different parameters are given. The results in this paper can be helpful to the dynamic and stable design of a helical gear transmission 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.     

变风速运行控制下风电传动系统的动态特性

基于齿轮系统动力学的方法对风电传动系统进行研究。运用基于自回归模型的线性滤波法(Auto-regressive,AR)建立的风速模型对实际风场的随机风速进行模拟;根据风力发电机在实际情况中的运行控制策略获得风力发电机齿轮传动系统的时变输入转矩激励;综合考虑风力发电机齿轮传动系统中各个齿轮副的时变啮合刚度、各个滚动轴承的刚度、各个轮齿综合啮合误差等内部激励,采用集中参数质量法建立风力发电机齿轮传动系统的耦合动力学模型;在此基础上建立风力发电机齿轮传动系统的动力学微分方程并进行仿真计算,分别求解风力发电机齿轮传动系统的固有频率、振动响应、动态啮合力和滚动轴承动态轴承力。研究结果为风力发电机传动系统的动态性能优化设计和可靠性设计奠定了基础。     

Comparisons of gear dynamic responses with rectangular mesh stiffness and its approximate form

The mesh stiffness is close to rectangular stiffness, and the first harmonic approximate term of rectangular stiffness is generally adopted in the nonlinear gear dynamic analysis. The differences between the rectangular stiffness and its approximate form are analyzed in detail. The frequency response and dynamic factor are calculated by a numerical method, to illustrate the dynamic characteristics of the gear nonlinear system with different mesh stiffness forms. The results show that: The trends of frequency response of gear dynamic system with rectangular stiffness and its approximate form are identical. The jump phenomena are detected in both cases. Without the effect of static transmission error, the dynamic factor with rectangular mesh stiffness is larger than that with approximate mesh stiffness. Under design power and speed condition, the result with approximate mesh stiffness function may deduce reasonless suggestions for a designer. The static transmission error will enlarge the vibration amplitude and dynamic factor when the approximate mesh stiffness is adopted, but the effects on the response of gear system with rectangular mesh stiffness are fractional. The mesh stiffness may excite the odd subharmonic resonance, and the static transmission error may excite the even sub-harmonic resonance respectively.