张力拉矫机的二自由度行星齿轮减速箱故障诊断研究

张力拉矫机是生产带钢非常重要的关键性设备,某钢厂冷轧酸洗线的张力拉矫机主减速箱是二自由度差动轮系结构,行星包中的太阳轮、行星轮和大齿圈、行星架都同时运转,其运行轨迹复杂。为研究1#锥齿减速箱和主减速箱振动大的原因,对其进行振动信号测试和频谱分析,分析结论得出,引起主减速箱和1#锥齿减速箱振动大的主要原因是主减速箱中行星包中齿轮啮合不良,并且推测出行星轮有严重损伤。实际检测结果表明,基于传统的频谱分析能够识别出行星齿轮箱的故障。     

An improved time-varying mesh stiffness algorithm and dynamic modeling of gear-rotor system with tooth root crack

When a tooth crack failure occurs, the vibration response characteristics caused by the change of time-varying mesh stiffness play an important role in crack fault diagnosis. In this paper, an improved time-varying mesh stiffness algorithm is presented. A coupled lateral and torsional vibration dynamic model is used to simulate the vibration response of gear-rotor system with tooth crack. The effects of geometric transmission error (GTE), bearing stiffness, and gear mesh stiffness on the dynamic model are analyzed. The simulation results show that the gear dynamic response is periodic impulses due to the periodic sudden change of time varying mesh stiffness. When the cracked tooth comes in contact, the impulse amplitude will increase as a result of reductions of mesh stiffness. Amplitude modulation phenomenon caused by GTE can be found in the simulation signal. The lateral–torsional coupling frequency increases greatly within certain limits and thereafter reaches a constant while the lateral natural frequency nearly remains constant as the gear mesh stiffness increases. Finally, an experiment was conducted on a test bench with 2 mm root crack fault. The results of experiment agree well with those obtained by simulation. The proposed method improves the accuracy of using potential energy method to calculate the time-varying mesh stiffness and expounds the vibration mechanism of gear-rotor system with tooth crack failure.     

裂纹对弧齿锥齿轮扭转啮合刚度的影响分析

运用Pro/E软件建立了无裂纹和含裂纹弧齿锥齿轮完整的三维接触模型,并基于有限元分析软件ANSYS对模型进行了仿真模拟与数值计算,分析了两种运行状态下,不同接触位置上的扭转啮合刚度。仿真结果表明：裂纹使弧齿锥齿轮的扭转啮合刚度变化更加剧烈。     

Manufacture of elastic composite ring for planetary traction drive with silicon rubber and carbon fiber

Advantages of planetary gear speed reducer are the high degree of efficiency, various reduction ratio, stress distribution by the planet gear and compaction in designing driving system. However there is noise in running at high r.p.m, so the use of planetary gear system is restricted in quiet place such as indoors, etc.

If following problems are solved such as low transmission torque that resulted from the slip and the deformation by the heat generated between ring and planet roller, planet roller and sun roller, the planetary traction drive will have not only the advantage of planetary gear speed reducer, but also silence in running. Thus it can be used at the high r.p.m in noise control area.

In this paper, speed reducer, which uses the elastic displacement of ring as preload, was developed. This system uses composite, which has superior elastic absorption and heat transfer property between ring and housing to exclude the effect of heat from the periodic and continuous elastic deformation of ring. This composite consists of silicon rubber and carbon fiber in a ratio of 7:3.     

行星齿轮箱齿轮组合故障振动频谱特征

行星齿轮箱的局部故障容易发展成为组合故障,复合故障频谱特征与局部故障有明显区别。研究太阳轮与齿圈、太阳轮与行星轮、行星轮与齿圈等组合故障频谱结构对行星齿轮箱故障诊断具有重要意义。考虑组合故障对振动信号的调幅-调频作用,以及时变振动传递路径的调幅作用,建立了组合故障振动信号模型,推导了Fourier频谱公式,总结了组合故障的频谱特征规律。推导了太阳轮与齿圈、太阳轮与行星轮、齿圈与行星轮两两组合故障以及太阳轮、行星轮与齿圈三种齿轮同时故障的特征频率计算公式。通过行星齿轮箱实验信号分析验证了理论推导结果,基于Fourier频谱分析诊断了太阳轮与齿圈、太阳轮与行星轮、齿圈与行星轮组合故障。     

Review on dynamics of cracked gear systems

Dynamic characteristics of cracked gear systems, also known as cracked-gear rotor systems, have received increasing interests among industry and academy in the past two decades. This paper reviews published papers on the dynamics of cracked gear systems. These studies mainly focused on three topics: crack propagation prediction, time-varying mesh stiffness (TVMS) calculation and vibration response calculation; Study objects involve the spur gear, helical gear and planetary gear; Different modeling methods including analytical method, finite element (FE) method, combined analytical-FE approach were adopted. More specifically, this review is composed of three related parts according to the above three topics. The first part involves the prediction of the crack propagation path based on two-dimensional (2D) or three-dimensional (3D) gear models, which provides a basis for the hypothesis of crack path in the process of TVMS calculation of cracked gear pairs. The second part summarizes the TVMS calculation methods including analytical methods, FE methods, combined analytical-FE approaches and experimental methods. The final part reviews the dynamic models for vibration analysis of cracked gear systems including lumped mass models and FE models, where the crack effects are characterized by introducing TVMS of cracked gear pairs into the system dynamic models. The well known open problems about cracked gear dynamics are finally stated, and some new research interests are also pointed out. The review will provide valuable references for future studies on dynamics of cracked gears.     

斜齿行星传动多体动力学建模与分析

建立了斜齿行星传动的多体动力学模型,对其进行了动态特性仿真,获知了该类系统的自由振动特性、稳态动力响应以及部分设计参数对系统动态特性的影响规律。根据系统特征值的重根数、中心构件的振型坐标及各行星轮间振型坐标的比例,将斜齿行星轮系的自由振动归结为3类典型振动模式,即：轴向平移—扭转振动模式、径向平移—扭摆振动模式和行星轮振动模式,并进一步给出了各类模式的特点。当不考虑构件自身柔性时,基于多体动力学模型的自由振动特性与前人的集中参数模型的仿真结果完全一致,表明了本文所建模型的正确性。斜齿行星轮系的稳态动力学响应表明,内、外啮合力在一个啮合周期内围绕静态均值作较大幅度的波动,而啮频激励是引起该类系统振动的主要原因。参数影响分析表明,构件支承刚度和行星轮周向安装误差对系统动态特性的影响明显,浮动太阳轮、严控行星轮周向安装误差可有效抑制系统的振动。     

Simulation of crack propagation in spur gear tooth for different gear parameter and its influence on mesh stiffness

Most of the gear dynamic model relies on the analytical measurement of time varying gear mesh stiffness in the presence of a tooth fault. The variation in gear mesh stiffness reflects the severity of tooth damage. This paper proposes a cumulative reduction index (CRI) which uses a variable crack intersection angle to study the effect of different gear parameters on total time varying mesh stiffness. A linear elastic fracture mechanics based two dimensional FRANC (FRacture ANalysis Code) finite element computer program is used to simulate the crack propagation in a single tooth of spur gear at root level. A total potential energy model and variable crack intersection angle approach is adopted to calculate the percentage change in total mesh stiffness using simulated straight line and predicted crack trajectory information. A low contact ratio spur gear pair has been simulated and the effect of crack path on mesh stiffness has been studied under different gear parameters like pressure angle, fillet radius and backup ratio. The percentage reduction of total mesh stiffness for the simulated straight line and predicted crack path is quantified by CRI. The CRI helps in comparing the percentage variation in mesh stiffness for consecutive crack. From the result obtained, it is observed that the proposed method is able to reflect the effect of different gear parameters with increased deterioration level on total gear mesh stiffness values.     

基于增量谐波平衡法的复合行星齿轮传动系统非线性动力学

建立了包含时变啮合刚度、齿侧间隙与综合啮合误差的Ravigneaux式复合行星齿轮传动系统纯扭转动力学模型。运用增量谐波平衡法对系统运动微分方程组进行求解,得到系统的基频稳态响应。研究了时变啮合刚度、外部激励、齿侧间隙等参数的变化对系统动力学特性的影响。研究结果表明,间隙的存在使得复合行星齿轮系统的频响曲线出现了幅值跳跃与多值解等典型非线性特征,系统参数的共同作用使得复合行星齿轮系统出现了丰富的非线性动力学行为。利用本文的方法可以获得系统任意精度的近似解,为控制系统的振动与噪声,实现复合行星齿轮传动系统动态设计奠定基础。     

行星齿轮箱太阳轮故障动态啮合周期特性

与定轴齿轮箱相比,行星齿轮箱内部齿轮副复杂的相对运动所引发的振动响应更加复杂多样,因而对其关键部件进行故障诊断颇具挑战。当内部轮齿发生故障时,由于故障啮合位置的动态性引起传递路径的时变性,固定在系统箱体上的单个传感器观测到的故障信息强度亦将呈现不规则变化的独特性。若想恰如其分的利用这些故障信息实现简单而有效的诊断,需重点关注故障啮合位置的周期特性,而后基于该周期所观测的信号进行“统筹兼顾”的分析,便可突显出各类故障的差异性。该研究在深入研究行星齿轮系统内部齿轮副的运行规律的基础上,创新性的提出了确定太阳轮故障动态啮合位置周期的方法,并考虑了以下两种情况:行星轮各不相同;行星轮完全相同。基于上述两种情况分别推导出太阳轮和行星架所需的最小旋转圈数的一般性表达式,该表达式可用于计算齿圈固定型的行星齿轮箱中的太阳轮故障啮合位置的运动周期。最后通过实验提出并验证了基于上述周期的故障诊断最小数据长度。     

行星传动系统的固有特性及模态跃迁研究

建立了单级2K-H直齿行星传动的纯扭转集中参数动力学模型。研究了行星传动的固有特性,归纳出两种振动模式:行星轮振动模式和扭转振动模式,并研究了两种振动模式下行星传动的振动特征。通过求解子特征值问题得到了解析形式的固有频率表达式,并推导了固有频率对构件的支承刚度、质量、转动惯量以及齿轮啮合刚度等参数的敏感度解析式。从模态能量角度深入分析了模态跃迁现象对传动特性的影响,并给出了此现象发生的判别准则。仿真算例证明了所得结论的正确性。     

Experimental investigation of spur gear tooth mesh stiffness in the presence of crack using photoelasticity technique

Gear mesh stiffness plays a very important role in gear dynamics and it varies in the presence of gear fault such as crack. The measurement of stress intensity factor can lead to the determination of gear tooth mesh stiffness variation in the presence of crack in a spur gear system. In this paper, the technique of conventional photoelasticity has been revisited to explore the possibility of using it as a supplementary technique to experimentally measure the variation of gear mesh stiffness. An attempt has been made to calculate the variation of mesh stiffness for a pinion having a cracked tooth and a gear tooth with no crack of a spur gear pair. An analytical methodology based on elastic strain energy method in conjunction with total potential energy model has been adopted and implemented within the mesh stiffness calculations. To visualize the state of stress in a structure using finite element and other currently available methods, photoelasticity is considered to be one of the oldest and most developed experimental technique. An experimental methodology based on conventional photo-elasticity technique for computing stress intensity factor (SIF) for cracked spur gear tooth is presented for different single tooth contact position and crack length. The relation between contact position, crack length, crack configuration, SIF and the variation of total effective mesh stiffness have been quantified. Finally, a comparison has been made and the results obtained from finite element method (FEM) based on linear elastic fracture mechanics (LEFM), analytical method and proposed experimental method has been outlined.     

Analytical model for mesh stiffness calculation of spur gear pair with non-uniformly distributed tooth root crack

Gear tooth crack is likely to happen when a gear transmission train is working under excessive and/or long-term dynamic loads. Its appearance will reduce the effective tooth thickness for load carrying, and thus cause a reduction in mesh stiffness and influence the dynamic responses of the gear transmission system, which enables the possibility for gear fault detection from variations of the dynamic features. Accurate mesh stiffness calculation is required for improving the prediction accuracy of the dynamic features with respect to the tooth crack fault. In this paper, an analytical mesh stiffness calculation model for non-uniformly distributed tooth root crack along tooth width is proposed based on previous studies. It enables a good prediction on the mesh stiffness for a spur gear pair with both incipient and larger tooth cracks. This method is verified by comparisons with other analytical models and finite element model (FEM) in previous papers. Finally, a dynamic model of a gear transmission train is developed to simulate the dynamic responses when cracks with different dimensions are seeded in a gear tooth, which could reveal the effect of the tooth root crack on the dynamic responses of the gear transmission system. The results indicate that both the mesh stiffness and the dynamic response results show that the proposed analytical model is an alternative method for mesh stiffness calculation of cracked spur gear pairs with a good accuracy for both small and large cracks.     

Crack behavior in a high contact ratio spur gear tooth and its effect on mesh stiffness

The efficiency of high contact ratio (HCR) gearing can be achieved by proper selection of gear geometry for increased load capacity and smoother operation despite of their high sliding velocities. The prediction of variation in mesh stiffness of HCR gearing is critical as the average number of teeth being in contact is high at a given time as compared to conventional low contact ratio (LCR) gearing. In this paper, linear elastic fracture mechanics (LEFM) based finite element method is used to perform the crack propagation path studies of HCR spur gear having tooth root crack for two gear parameters viz. backup ratio and pressure angle. A total potential energy model has been adopted to analytically estimate the mesh stiffness variation. The results depict the mesh stiffness reduction in the presence of the crack. The percentage change in mesh stiffness with increasing crack length is an important parameter in fault diagnosis of geared transmission. Higher the percentage change in mesh stiffness, easier to detect the fault. Two gear parameters viz. back-up ratio and pressure angle has been studied and the effect of crack length on mesh stiffness have been outlined. With the increase of deterioration level gears having lower back-up ratio fault can be detected at an early stage, similarly, chances for early fault detection is more for gears having higher pressure angle.     

含裂纹故障的齿轮系统动力学特性研究及其故障特征分析

考虑齿轮的时变啮合刚度、传动误差和轴承支撑刚度的影响,建立含齿根裂纹故障的齿轮系统多自由度力学模型,基于动力学方法对其故障机理进行研究。通过材料力学的方法计算齿轮在正常和含裂纹两种情况下的啮合刚度,对比两种刚度曲线的变化趋势,便于进行精确的动力学特性分析;对建立的模型求解系统的动态响应,结果表明当齿根存在裂纹时,其时域波形中会出现周期性的冲击现象,频谱中在啮合频率的基频及其倍频等地方形成一系列等间隔的边频谱线,其间隔大小等于故障齿轮的转频;这些边频成分幅值较低,能量分散且分布不均匀,在不同频带的幅值大小存在差异。针对上述特点,通过正交小波包方法对信号的频带进行分解,应用倒频谱分析各子频带信号的边频成分;结果表明,该方法能够有效的提高信号的信噪比,有助于识别和提取信号中由裂纹故障引起的边频成分。     

基于变分模式分解的行星齿轮箱齿轮组合故障频率解调分析

行星齿轮箱组合故障振动信号具有多源调制特点,在频域内边带结构复杂,通过常规Fourier频谱分析难以有效提取故障特征;组合故障振动信号的调频部分包含故障信息,且不受传递路径影响。为了准确提取行星齿轮箱组合故障特征,提出基于变分模式分解的频率解调分析方法。根据采样频率和载波频率确定单分量个数,通过变分模式分解将多分量信号自适应地分解为一系列本质模式函数;计算本质模式函数的瞬时频率,根据中心频率和啮合频率的匹配关系选取敏感单分量;通过分析敏感单分量瞬时频率频谱诊断组合故障。通过仿真信号和实验信号分析验证了方法的有效性,诊断了太阳轮与行星轮、太阳轮与齿圈、行星轮与齿圈的组合故障。     

斜齿轮动力学建模中啮合刚度处理与对比验证

为准确建立斜齿轮动力学模型,更好分析斜齿轮系统振动特性,提出基于轮齿承载接触分析、考虑齿轮轴扭转变形的轮齿啮合刚度计算方法。分析国内文献普遍采用的基于啮合刚度分解建立斜齿轮动力学模型,指出其与理论力学相悖之处,提出基于力、振动位移分解法建立综合考虑时变啮合刚度激励、啮入冲击激励的斜齿轮啮合型弯-扭-轴耦合振动模型。以某斜齿轮副为例进行的仿真计算结果表明,基于承载接触分析的轮齿啮合刚度计算方法能准确、方便求得轮齿啮合刚度,文献[8]动力学响应结果与理论实际存在明显差别,而基于力、振动位移分解法的响应则能与理论实际较好吻合。     

Reducing mass while improving the operational behavior: form optimization of planetary gearbox housings

The optimization of load sharing between planets is one of the most important goals in planetary gearbox design. Unevenly distributed load will cause locally higher flank pressures and therefore, less durability of gears and bearings. Furthermore, unevenly distributed or fluctuating loads can cause excitations in the gear mesh and structural vibrations. The load sharing in planetary gear stages depends on the individual stiffness conditions in each mesh position. The stiffness is not only influenced by the gear geometry but also by the surrounding structural elements like shafts, housings and torque arms. In wind industry these components are often designed very stiff in order to reduce their effect on the operational behavior.

Within this paper, a method is presented, which allows combining the structural optimization process with a tooth contact analysis for planetary gearboxes. By means of this combined approach, it is possible to optimize the housing structure of the ring gear in terms of mass reduction while keeping the operational behavior in focus. With a weighted design objective function, it is possible to decide whether the main objective should be load distribution, excitation behavior, low mass or a balanced design.

     

Dynamic simulation of spur gear with tooth root crack propagating along tooth width and crack depth

Gear tooth crack will cause changes in vibration characteristics of gear system, based on which, operating condition of the gear system is always monitored to prevent a presence of serious damage. However, it is also a unsolved puzzle to establish the relationship between tooth crack propagation and vibration features during gear operating process. In this study, an analytical model is proposed to investigate the effect of gear tooth crack on the gear mesh stiffness. Both the tooth crack propagations along tooth width and crack depth are incorporated in this model to simulate gear tooth root crack, especially when it is at very early stage. With this analytical formulation, the mesh stiffness of a spur gear pair with different crack length and depth can be obtained. Afterwards, the effects of gear tooth root crack size on the gear dynamics are simulated and the corresponding changes in statistical indicators – RMS and kurtosis are investigated. The results show that both RMS and kurtosis increase with the growth of tooth crack size for propagation whatever along tooth width and crack length. Frequency spectrum analysis is also carried out to examine the effects of tooth crack. The results show that sidebands caused by the tooth crack are more sensitive than the mesh frequency and its harmonics. The developed analytical model can predict the change of gear mesh stiffness with presence of a gear tooth crack and the corresponding dynamic responses could supply some guidance to the gear condition monitoring and fault diagnosis, especially for the gear tooth crack at early stage.