A study on load-sharing structure of multi-stage planetary transmission system

Unequal load distribution is a crucial factor in decreasing bearing capacity and stability of the planetary transmission system. In this paper, a dynamical model of two-stage helical planetary gear transmission system is established based on lumped-parameter method and Lagrange general function. Nonlinearity of gear tooth backlash and error is taken into account. Four load-sharing structures are proposed to study the load-sharing performance. A method to calculate dynamic sensitivity of load-sharing coefficient to errors is presented that can provide a reference to component precision determination in order to make planetary system have a better load distribution. Finally, a numerical method of load-sharing performance is validated by a test. These results provide fundamental basis for multi-stage planetary gear transmission system design.     

基于层级有限元法的大型航空行星机构可靠性优化设计

大型航空行星机构作为多种重型航空器传动系统的基础与核心,它的可靠性水平在很大程度上制约着航空器的经济可承受性与服役安全性。将某型号重型直升机行星机构作为研究对象,以保证和提高该系统的疲劳可靠性水平为目标,利用层级有限元法计算系统全局弹性行为耦合作用下的轮齿疲劳载荷历程,并基于齿轮低周疲劳试验与最小次序统计量转化方法拟合出轮齿概率疲劳强度,为系统可靠性预测模型提供经济有效的载荷与强度输入变量。据此,建立从大型航空行星机构关键结构要素到系统可靠性指标的映射路径,提出可靠性驱动的行星机构结构尺寸多目标优化设计新方法。最后,分析了内齿圈轮缘厚度与行星架基板厚度对行星轮系疲劳可靠性的影响规律,并得到了指定型号的大型航空行星机构的轮缘与基板尺寸最佳刚度匹配结果,最大限度地发挥了核心结构要素的刚度潜力,以此平衡大型航空行星装备在可靠性与轻量化要求之间的矛盾。     

风电齿轮箱行星齿轮用连铸坯的试验研究

为了验证合金钢连铸坯作为兆瓦级风电齿轮箱行星齿轮原材料是否能满足设计要求,在控制合金钢连铸坯冶金质量的前提下,进行试验研究.具体试验包括旋转弯曲疲劳试验、齿根弯曲疲劳试验、齿面接触疲劳试验等.最终得到的试验数据表明,对于内孔不小于300 mm的行星齿轮而言,使用合金钢连铸坯作为原材料,能够满足设计要求.     

基于虚拟样机技术的行星齿轮传动系统分析

利用实体建模软件UG建立了减速器行星齿轮传动系统的虚拟样机,并利用UG与动力学仿真分析软件ADAMS,将虚拟样机导入到ADAMS中建立仿真模型。齿轮啮合中轮齿间除了滚动接触外还存在相应的滑动接触,使轮齿间具有较大的摩擦了,针对传统赫兹理论形成的齿面接触力计算没有考虑齿间摩擦,将摩擦系数引入计算,得到了齿轮之间的接触力曲线变化。应用UG NX的"高级仿真"模块,建立行星轮有限元模型,通过解算器NX NASTRAN对有限元模型进行分析求解,得到行星轮在接触力作用下应变和应力分布情况,再根据设计要求对零件参数进行优化,使行星轮的结构既满足设计要求,又达到体积小和成本低。     

考虑残余应力的螺旋锥齿轮接触疲劳裂纹萌生-扩展寿命计算方法研究

考虑渗碳、磨齿、喷丸等工艺产生的齿面残余应力,建立齿面接触应力与残余应力的复合应力场,提出一种螺旋锥齿轮接触疲劳裂纹萌生-扩展寿命计算方法。构建齿轮有限元接触分析模型,计算多轴交变接触应力场。考虑空间螺旋曲面残余应力分布的复杂性,将变曲率齿面离散为网状节点;测量各节点表面与次表面的残余应力,建立齿面残余应力场。基于Dang Van多轴疲劳准则,构建齿面裂纹萌生模型;计及残余应力与裂纹闭合效应,构建齿面裂纹扩展模型。计算复合应力场下齿轮接触疲劳寿命,研究残余应力对齿面裂纹萌生-扩展寿命的影响规律。结果发现：复杂齿面空间变曲率会影响喷丸等工艺产生的残余应力分布,中心区域的残余压应力高出齿面边缘区域约20%;复合应力场下齿面裂纹萌生位置与寿命主要取决于接触应力,残余应力会改变齿面节点平均应力进而影响疲劳寿命;齿面裂纹扩展寿命约占全寿命的10%,表征齿轮接触疲劳快速失效至迅速断裂。上述研究对于高性能齿轮传动的长寿命、高可靠性设计具有一定的参考价值。     

18CrNiMo7-6和20CrMnTi材料齿根弯曲疲劳寿命对比

对比了齿轮钢材料18CrNiMo7-6与20CrMnTi的齿根弯曲疲劳寿命。基于这两种材料的疲劳特性,采用SolidWorks中的GearTrax插件建立齿轮模型,并通过Workbench对齿轮的轮齿进行静力学分析;将静力学分析结果导入疲劳分析软件FE-SAFE中,结合载荷谱信息对两种材料齿轮进行疲劳寿命计算,得到齿轮的寿命云图并进行了仿真分析比较;通过试验验证了该仿真方法的可行性。结果表明,在相同的载荷条件下,18CrNiMo7-6齿轮的疲劳寿命大于20CrMnTi齿轮的疲劳寿命,与试验结果较为接近。该分析结果对工程实践具有一定的指导作用。     

非对称齿廓齿轮弯曲疲劳强度理论分析与试验

为提高齿轮承载能力设计齿轮两侧压力角不等的非对称渐开线新齿形,推导双压力角非对称齿廓齿轮工作齿侧与非工作齿侧的渐开线齿廓方程和齿根过渡曲线方程,通过迭代计算和优化策略提出非对称齿廓齿轮疲劳强度解析法计算公式。编制生成非对称齿轮齿廓的参数化程序,在此基础上建立非对称齿廓齿轮有限元分析模型。通过解析法对不同压力角组合的非对称齿廓齿轮弯曲应力和危险截面位置计算得出,随着工作齿侧压力角的增大齿根最大弯曲应力逐渐降低,单齿啮合区向齿顶偏移;通过对有限元模型进行计算得出的结果与解析法一致,应用最小二乘法拟合出非对称齿廓齿轮齿根弯曲应力随工作齿侧压力角变化的计算公式。采用数控电火花线切割方法加工制造非对称与标准齿廓齿轮,在高频疲劳试验机上采用双齿脉动加载方法对其进行疲劳强度试验。试验结果表明,非对称齿廓齿轮在相同寿命下比对称齿轮极限载荷提高了50%,非对称齿廓齿轮的应力值变化趋势与前两种方法是一致的。     

基于行星减速器的多目标可靠性优化设计方法研究

将优化技术与可靠性设计理论相结合,以齿轮疲劳强度可靠度和行星轮系配齿条件等为约束,以行星齿轮减速器传动效率高、重量轻、体积小为优化目标,根据工程实践和统一目标函数法建立其优化数学模型,应用混合惩罚函数法、Powell法等多种优化算法对其进行优化设计[1].通过实例说明,应用这种理论方法可在保证减速器使用寿命的前提下,得到满意的优化结果.     

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.     

K—H—V型渐开线少齿差行星传动的建模设计与CAD技术

本文对Ｋ－Ｈ－Ｖ渐开线少齿差行星齿轮减速器,建立了优化设计数学模型,研制了它的自动设计系统软件。为了提高产品的合格率,综合考虑了国工内齿轮的插齿刀为新刀和旧刀两种情况下的约束条件。此外,还对Ｋ－Ｈ－Ｖ少齿差行星减速器主要传动零件的强度及寿命采用计算机辅助设计,通过检验薄环节来调整某些参数,从而快速、准确地确定标准件的规格型号和其它传动零件的主要尺寸。本文还建立了Ｋ－Ｈ－Ｖ渐开线少齿差行星减速器系列     

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.

     

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.     

Statistical modification analysis of helical planetary gears based on response surface method and Monte Carlo simulation

Tooth modification technique is widely used in gear industry to improve the meshing performance of gearings. However, few of the present studies on tooth modification considers the influence of inevitable random errors on gear modification effects. In order to investigate the uncertainties of tooth modification amount variations on system's dynamic behaviors of a helical planetary gears, an analytical dynamic model including tooth modification parameters is proposed to carry out a deterministic analysis on the dynamics of a helical planetary gear. The dynamic meshing forces as well as the dynamic transmission errors of the sun-planet 1 gear pair with and without tooth modifications are computed and compared to show the effectiveness of tooth modifications on gear dynamics enhancement. By using response surface method, a fitted regression model for the dynamic transmission error(DTE) fluctuations is established to quantify the relationship between modification amounts and DTE fluctuations. By shifting the inevitable random errors arousing from manufacturing and installing process to tooth modification amount variations, a statistical tooth modification model is developed and a methodology combining Monte Carlo simulation and response surface method is presented for uncertainty analysis of tooth modifications. The uncertainly analysis reveals that the system's dynamic behaviors do not obey the normal distribution rule even though the design variables are normally distributed. In addition, a deterministic modification amount will not definitely achieve an optimal result for both static and dynamic transmission error fluctuation reduction simultaneously.     

Detecting gear tooth fatigue cracks in advance of complete fracture

Some results from using vibration-based methods to detect gear tooth fatigue cracks are presented. An experimental test rig was used to fail a number of spur-gear specimens through bending fatigue. The gear tooth fatigue crack in each test was initiated through a small notch in the fillet area of a tooth on the gear. The primary purpose of these tests was to verify analytical predictions of fatigue crack propagation direction and rate as a function of gear rim thickness. The vibration signal from a total of three tests was monitored and recorded for gear fault detection research. The damage consisted of complete rim fracture on the two thin rim gears and single tooth fracture on the standard full rim test gear. Vibration-based fault detection methods were applied to the vibration signal both on-line and after the tests were completed. The objectives of this were to identify methods capable of detecting the fatigue crack, and determine how far in advance of total failure positive detection was given. Results showed that the fault detection methods failed to respond to the fatigue crack prior to complete rim fracture in the thin rim gear tests. In the standard full rim gear test all of the methods responded to the fatigue crack in advance of tooth fracture; however, only three of the methods responded to the fatigue crack in the early stages of crack propagation.     

基于动力学仿真的行星轮系损伤检测方法

为了解决行星轮系的损伤检测问题,提出了基于动力学仿真的损伤检测方法。针对2K-H行星轮系,首先建立了健康与损伤状态的动力学模型,在分析模型仿真信号的基础上,提取了基于残差信号频谱边带的特征,然后采用仿真信号和试验数据对该特征进行了验证。验证结果表明,对于太阳轮缺齿损伤,该特征不仅具有理想的检测效果,而且具有较强的抗干扰能力。     

灰色GM(1,1)模型在齿轮疲劳寿命预测中的应用

在齿轮疲劳寿命预测中,需要大量的齿轮疲劳试验数据.运用灰色GM(1,1)模型预测疲劳试验数据,可以大幅度缩短试验时间,节约试验费用,快速获得齿轮可靠性指标.文中简要介绍了灰色GM(1,1)模型的原理,通过具体实例建立了齿轮疲劳寿命GM(1,1)模型.预测结果表明,将灰色系统理论用于齿轮的疲劳寿命试验数据预测是可行的,理论上为有效缩短齿轮疲劳寿命试验时间提供了一个快速有效的方法.     

差速器锥齿轮参数化建模及模态分析

运用CATIAV5知识工程模块,结合齿轮齿廓渐开线方程,针对圆锥和内花键的齿形实体特点,建立了汽车差速器行星齿轮和半轴齿轮的参数化模型。运用ANSYS软件对行星齿轮建立有限元模型并进行模态分析,计算出了其低阶固有振动频率和模态振型。提高开发效率,为圆锥齿轮设计和差速器振动分析提供了一定的参考。     

Multisensor monitoring of gear tooth fatigue for predictive diagnostics

Successful machinery diagnostics depends on the collection and processing of prognostic features that relate back to failure precursors. Since gear teeth are a critical element in drive-train systems, single gear tooth failure has been examined, and the identification of new prognostic features explored. A special jig was employed to orient and constrain gear samples while Hertzian loading was applied along a single contact line on the gear tooth face. This set-up simulates the loading conditions experienced by a single tooth during gear train operation. Optical, ultrasonic, and mechanical sensors measured a variety of observables while the gear fatigue testing was under way. After monitoring the fatigue test with these three non-commensurate sensors, data features were related to crack growth phenomena. Data collection, analysis, and interpretation are discussed for spur gear samples that show both the absence and presence of cracks and support the validity of the identified features as failure precursors. The results demonstrate the potential for using non-traditional sensors and techniques for an in situ monitoring system.     

高速动车组斜齿轮的齿根裂纹萌生寿命数值计算

为分析高速动车组斜齿轮的齿根裂纹萌生寿命,采用UG建模软件建立了斜齿轮副的三维模型,并通过ABAQUS软件确定了裂纹萌生位置。基于疲劳损伤累积理论,对试验齿轮分别采用名义应力法和局部应力应变法模拟计算出裂纹萌生寿命;进行了高频疲劳试验,得到了裂纹萌生寿命,通过对比模拟结果与试验结果,确定了最佳损伤模型,计算得出了斜齿轮齿根的裂纹萌生寿命。分析了载荷、表面粗糙度、残余应力、齿顶修缘等因素对裂纹萌生寿命的影响规律。研究结果表明,载荷及表面粗糙度对裂纹萌生寿命的影响比较显著;裂纹萌生寿命随着残余压应力的增大而延长;适当的修形可延长斜齿轮裂纹萌生寿命。     

时变位姿下行星齿轮传动系统动应力计算模型及其参数影响研究

考虑行星轮系内部非惯性和机体时变位姿外部非惯性的综合影响,推导了任意时变位姿下带有机匣的行星轮系构件运动方程,计入时变啮合刚度、啮合误差、侧隙和啮入冲击,建立了时变位姿下行星齿轮传动系统级动力学模型,并采用精细积分时程法（Precision integration method,PIM）求解得到了动态啮合力序列。根据齿间载荷分配关系进一步得到单齿啮合力序列。最后结合修正Heywood公式与Hertz公式构建了时变位姿下行星齿轮传动系统齿根弯曲动应力和接触动应力计算模型,并研究了机体平飞、滚转和筋斗位姿参数对接触动应力、弯曲动应力的影响规律。结果表明：不同时变位姿参数对弯曲、接触动应力影响显著,且对不同齿轮副影响不同,即加剧了齿轮副间承载不均;筋斗运动角速度对动应力影响比平飞加速度、滚转角速度以及筋斗回转半径对其影响复杂;机匣对动应力影响随加速度增大而增加。研究成果为时变位姿下行星齿轮传动动应力计算与高可靠性设计提供了理论依据。