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.     

Performance improvement method for Nylon 6 spur gears

Plastic gears made of Nylon 6 are especially susceptible to failure due to extreme heat accumulation in the single tooth mesh area, which results in damage that consequently shortens gear teeth life and causes transmission errors. In this experimental study, the teeth width of plastic spur gears made of Nylon 6 were modified and investigated. The values of load sharing, F/b, in single and double tooth meshing areas were leveled by widening the single tooth zone along the meshing area, and the performances of both modified and unmodified gears were studied experimentally under three different loadings. It was observed that modified Nylon 6 gears exhibit lower tooth temperatures, which results in a decrease in wear rate as compared to unmodified gears. Consequently, teeth width modification helps to increase Nylon 6 gear performance.     

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.     

Analysis of the effects of surface pitting and wear on the vibration of a gear transmission system

A comprehensive procedure to simulate and analyse the vibrations in a gear transmission system with surface pitting, wear, and partial tooth fracture of the gear teeth is presented. An analytical model was developed where the effects of surface pitting and wear of the gear tooth were simulated by phase and magnitude changes in the gear mesh stiffness. Changes in the gear mesh stiffness were incorporated into each gear-shaft model during the global dynamic simulation of the system. The overall dynamics of the system were evaluated by solving for the transient dynamics of each shaft system simultaneously with the vibration of the gearbox structure. In order to reduce the number of degrees-of-freedom in the system, a modal synthesis procedure was used in the global transient dynamic analysis of the overall transmission ststem. An FFT procedure was used to transform the averaged time signal into the frequency domain for signature analysis. In addition, the Wigner-Ville distribution was also introduced to examine the gear vibration in the joint time-frequency domain for vibration pattern recognition. Experimental results obtained from a gear fatigue test rig at NASA Lewis Research Center were used to evaluate the analytical model.     

Model-based analysis and fault diagnosis of a compound planetary gear set with damaged sun gear

The vibration properties of compound planetary gears are more complicated than that of simple ones. This paper aims to investigate the fault properties of a compound planetary gear set in chipped sun gear conditions using model-based method. A three-dimensional lumped-parameter nonlinear dynamic model for the compound planetary gear set is established. This model considers the time-varying mesh stiffness (TVMS), the mesh phase relations, and gear chipping defects. The analytical equations are derived to quantify the TVMS reduction induced by the chipped gear based on the improved potential energy method. Further, the simulations are performed to demonstrate the fault features of sun gears with single or multiple chipped teeth in different gear stages. Moreover, the theoretical derivations are validated through the experimental signals analysis.     

齿轮失效及激光熔覆修复技术的研究

齿轮传动是通过轮齿的啮合来传递运动和动力,运转过程中因承受一定的交变载荷,轮齿容易发生损伤,常见的失效形式有折断、齿面点蚀和磨损等。通过搭建合适的实验系统,采用侧向送粉单向扫描和轴向分齿跳齿法对齿面进行激光熔覆实验,得到了不同工艺参数对齿面熔覆层宏观质量和稀释率影响的关系,确定了大面积熔覆修复时的搭接系数,成功地对失效齿面进行了修复。     

Dynamic characteristics analysis and experimental research on a new type planetary gear apparatus with small tooth number difference

Aimed at an internal mesh planetary gear with small tooth number difference (PGSTD) reducer, this paper proposes dynamic characteristics analysis. First, static finite element (FE) analysis is performed to check the structural strength with the stress distribution in the gear teeth. Second, by means of the dynamic contact FE method, the internal dynamic excitations of teeth mesh are obtained, including mesh stiffness excitation, transmission error excitation and mesh impact excitation. According to the established model for dynamic FE modal analysis, the natural frequencies and mode shapes of the planetary gear apparatus (PGA) are calculated, and its structural dynamic response and acceleration noise are researched with the comprehensive consideration of internal and external excitations. Finally, the noise and vibration testing on the PGA is carried out by utilizing the vibration test equipment. The results confirm that the predicted values are consistent with the experimental results.     

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。     

Experimental studies on the effects of reduction in gear tooth stiffness and lubricant film thickness in a spur geared system

Gears are one of the most common mechanisms for transmitting power and motion and their usage can be found in numerous applications. Studies on gear teeth contacts have been considered as one of the most complicated applications in tribology. Depending on the application, the speed and load conditions of teeth may change triggering several types of failures on teeth surface such as wear, scuffing, micro-pitting and pitting. The above-mentioned faults influence changes in vibration and acoustic signals, due to changes in operating conditions such as increase in temperature and decrease in lubricant film thickness and specific film thickness. These abnormal changes result in cumulative effects on localised or distributed faults on load bearing surfaces of gears. Such damages cause reduction in tooth stiffness and severity of damage can be assessed by evaluating the same using vibration-based signals.This paper presents the results of experimental investigations carried out to assess wear in spur gears of back-to-back gearbox under accelerated test conditions. The studies considered the estimation of operating conditions such as film thickness and their effects on the fault growth on teeth surface. Modal testing experiments have been carried out on the same gear starting from healthy to worn out conditions to quantify wear damage. The results provide a good understanding of dependent roles of gearbox operating conditions and vibration parameters as measures for effective assessment of wear in spur gears.     

斜齿轮渐进性磨损对齿轮振动特性的影响分析

目前,研究磨损对齿轮动力学特性的影响大多采用传统的Archard磨损模型,并未考虑齿轮的润滑特性,且主要研究对象多为直齿轮。为了弥补斜齿轮研究方面的不足,数值模拟了混合弹流润滑状态下斜齿轮的磨损过程,建立了一个8自由度斜齿轮动力学模型,研究齿面磨损对斜齿轮动态特性的影响。在斜齿轮试验台上进行了齿轮疲劳试验,对数值仿真结果进行验证。结果表明,齿面磨损主要发生在靠近齿根和齿顶部分,且由于齿根处较高的滑滚比导致其磨损更加严重。根据齿轮啮合频率及其谐波幅值的变化可知,磨损导致齿轮的振动增加。试验分析与数值仿真有较好的一致性,说明该研究可以为斜齿轮磨损的预测和故障诊断提供可靠的理论依据。     

Study on development of polyamide gears for improvement of load-carrying capacity

In polyamide based gears, thermal damage of the gear tooth surfaces occurs during gear meshing due to accumulated heat in the tooth body. In the experimental study reported in this paper, polyamide gear teeth have been modified in order to distribute the generated heat on the tooth surface by means of drilled cooling holes at different locations on the gear tooth body. The main aims of this paper were to study the effect of cooling holes on the accumulated heat on the tooth surface and on the measured wear. It was shown that the drilled cooling holes on the tooth body decreased the tooth surface temperature and led to an increase in the load carry capacity and improved wear resistance. Geometrically modified gears have showed an improved service life and a decreased surface temperature.     

时变刚度渐开线直齿轮啮合冲击响应的研究

由于渐开线齿轮啮合刚度的时变性,传动齿轮的振动具有非线性振动的性质。文章将啮合冲击区分成若干微区段,视各微区段啮合刚度为定值,采用时域方法辨识出相应模态参数,用直线拟合固有频率分布曲线,从而提出一种新的计算啮合冲击响应的方法,其计算结果与实验值相符,并给出了用固有频率作敏感因子诊断轮齿裂纹故障的例子。     

Relation between wear and tooth width modification in spur gears

In this experimental study, width modification of a spur gear was investigated to fix instantaneous pressure changes along single meshing area on the gear profile. In this gear, variable pressure distribution caused by the single and double teeth meshing and the radius of curvature along the active gear profile was approximately kept constant by maintaining a constant ratio of applied load to the tooth width (F/b) on every point. Hence, Hertz pressure distribution along the gear profile was approximately equally achieved. Other factors affecting wear were kept constant during the experiment. The specimen used was made from AISI 4140 steel. Finally, the amount of wear in the teeth profiles between the modified and unmodified gears was compared. And wear depth of modified gear along the meshing area was almost uniform.     

Simulation of wear in gears with flank interference—a mixed FE and analytical approach

Gears in precision mechanisms, such as industrial robots, are often designed to have no backlash. Deviations from the ideal gear geometries and unfavourable deformations during operation may cause interference between interacting tooth flanks, resulting in high and strongly varying friction. Mild wear of the tooth flanks may improve such conditions. Therefore, this theoretical study has been conducted of wear in spur gears with interference. A mixed finite element (FE) and analytical approach is used. The FE method is used to determine contact loads between the interacting gear teeth. The main drawback with FE analyses of this type of problem is normally the computation time needed. Therefore, a novel FE meshing method is used, giving a dense FE mesh in the contact regions and a coarse mesh in the rest of the teeth. Based on the FE determined loads between the interacting teeth, the contact pressures and the contact widths are then easily determined using analytical expressions based on Hertz theory. The wear of a point on a tooth flank is determined by integrating the product of sliding distance and contact pressure during the time it is in contact with its mating flank.The results show that the wear of the gear tooth flanks may eliminate the interference and consequently the high and strongly varying friction will decrease dramatically. However, the transmission error will change, since the gears will not preserve their accurate involute profiles.     

Sliding friction effect on dynamics of crossed beveloid gears with small shaft angle

We propose a new method of incorporating the gear sliding friction model and loaded mesh model into an analytical nonlinear crossed beveloid geared vibration model to evaluate the mesh and dynamic characteristics. A 3-dimensional quasi-static loaded tooth contact analysis is employed and the derivation of distributed sliding friction forces and synthesis of frictions to the effective form is applied in the nonlinear dynamic analysis. Using the proposed method, the excitation effects of frictions on tooth mesh and dynamic responses at different load levels are found and investigated. The analysis results show that the existence of sliding frictions between the engaged teeth indeed tends to affect the contact pattern, normal load distribution and maximum contact pressure, but it is unsubstantial. The torque load effect of friction is found with greater degressive influence on mesh stiffness and transmission error at heavier load case. The magnitude and directionality of sliding friction on effective total engaged teeth exhibit less obvious variations than on each tooth due to the contributions from multiple teeth effect. Also, friction excitations tend to decrease the dynamic mesh force slightly for both light and heavy load cases.     

Assessing the role of plastic deformation in gear-health monitoring by precision measurement of failed gears

For constant loading and speed conditions, the principal sources of vibration excitation arising from meshing gears, characterised by the “static transmission error” (STE) excitation, are geometric deviations of the working surfaces of the teeth from equi-spaced perfect involute surfaces, and tooth/gear body elastic deformations. Changes in these two sources caused by tooth-bending-fatigue damage on one or a few teeth are manifested primarily in the rotational-harmonic content of the STE of each individual damaged gear of the meshing pair, and are most effectively detected in the time domain. The optimum number of gear rotations to be used in synchronous averaging is specified, along with how such synchronous averaging can be used to eliminate the effects of the mating gear in the case of “hunting tooth” gear pairs, and to minimise these effects otherwise. Precision measurements made on the teeth of a gear failed in a tooth-bending-fatigue test strongly suggest that whole-tooth plastic deformation—i.e. yielding, rather than changes in tooth stiffness caused by tooth-root cracks, is the principal source of detectable damage in the case of tooth bending fatigue. Such plastic deformations are geometric deviation STE contributions. Differences in gear materials, materials processing, and gear operating properties may significantly affect the amounts of such plastic deformations before tooth breakage and the operating duration between initial damage detection and tooth breakage, thereby suggesting the need for testing to determine such dependencies.     

渐开线直齿轮修形的有限元分析与研究

针对不同修形曲线对齿轮修形产生不同效果的问题,首先推导出了渐开线参数方程和修形曲线的齿廓参数方程,然后应用Pro/E建立了标准渐开线直齿轮与修形齿轮的三维模型,最后利用ANSYS Workbench的瞬态动力学模块对其进行了有限元分析;通过仿真得出了渐开线直齿轮和修形齿轮在啮合过程中的齿面接触应力的变化曲线.研究结果表明,在齿轮传动时的单双齿啮合交替时及啮入/啮出时,Walker修形曲线较直线修形曲线具有更好的修形效果,但同时两种修形曲线都导致了齿轮重合度的降低,增加了单齿啮合区,为修形齿轮的设计提供了数值实验依据.     

振动分析技术在齿轮减速器故障诊断中的应用

利用CSI2130振动分析仪对浆液循环泵齿轮减速器进行振动监测与故障诊断,并使用PeakVue技术进行频谱和时域分析,认为较大的振动是因为齿轮啮合不良而导致输入端齿轮轴断齿造成,停机检修发现输入端齿轮轴有3个齿沿齿轮根部断裂,更换新齿轮轴后,设备运行恢复正常。     

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。     

双压力角非对称齿廓渐开线齿轮的振动分析

基于非对称渐开线圆柱齿轮传动时的啮合机理和齿轮系统动力学。同时考虑到齿轮系统时变啮合刚度和静态传递误差的影响，建立了齿轮动力学模型，利用数值积分和数值仿真方法对其进行了非线性振动研究。比较了标准齿轮与非对称齿轮的振动特性，分析了齿轮系统各参数对系统动态特性的影响。仿真结果对考虑动载荷情况下的油膜厚度计算提供了基础数据，为进一步研究非对称渐开线的各种特性提供了理论依据。