Influence of support stiffness on vibrations of a planet gear system considering ring with flexible support

Planet gear systems(PGSs)are key components of transmission mechanisms.Structural and material characteristics of gearbox and shaft can affect the support stiffness and vibrations of PGSs.The ring gear flexibility should affect the vibrations of PGSs too.However,most previous work did not completely consider the effects of the ring gear flexibility on the vibrations of PGSs and flexible supports of ring and sun gears.Thus,this paper presents a flexible-rigid coupling multi-body dynamic(FMBD)model for a PGS with the flexible supports and ring gear flexibility.A finite element model of ring gear is established to formulate the ring gear flexibility.The influences of clearance and damping of planet bearings on the vibrations of PGS are considered.The effects of flexible supports and ring gear flexibility on the vibrations of PGS under different moment and speed conditions are studied.The statistical parameters and peak frequencies of PGS from the proposed FMBD and previous rigid multi-body dynamic(RMBD)models are compared.The results denote that the flexible support has a great effect on the vibrations of PGS.This paper can provide some guidance for the support structure design and vibration control for PGSs.

Developments and perspectives on the precision forming processes for ultra-large size integrated components

In order to meet the requirements of high reliability,long-lifetime and lightweight in a new generation of aerospace,aviation,high-speed train,and energy power equipment,integrated components are urgently needed to replace traditional multi-piece,welded components.The applications of integrated components involve in a series of large-size,complex-shaped,highperformance components made of difficult-to-deform materials,which present a huge challenge for forming ultra-large size integrated components.In this paper,the developments and perspectives of several extreme forming technologies are reviewed,including the sheet hydroforming of ultra-large curved components,dieless hydroforming of ellipsoidal shells,radial-axial ring rolling of rings,in situ manufacturing process of flanges,and local isothermal forging of titanium alloy components.The principle and processes for controlling deformation are briefly illustrated.The forming of typical ultra-large size integrated components and industrial applications are introduced,such as the high strength aluminum alloy,3m in diameter,integrated tank dome first formed by using a sheet blank with a thickness the same as the final component,and a 16m diameter,integrated steel ring rolled by using a single billet.The trends for extreme forming of ultra-large size integrated components are discussed with a goal of providing ideas and fundamental guidance for the further development of new forming processes for extreme-size integrated components in the future.

Effects of Prestressing of the Ring Gear in Interference Fit on Flexural Fatigue Strength of Tooth Root

When the gearbox body interference is connected to the ring gear, prestressing occurs in the ring gear, which has a significant impact on the strength and life of the gear. Research on the prestressing of the inner ring gear is in the preliminary stage, and the distribution rule of the prestressing and the influence of each parameter on the interference prestressing have not been derived. In this paper, based on the method of calculating the prestressing of the thick cylinder in interference fit, the ring gear is found to be equivalent to a thick cylinder, and the distribution rule of prestressing of the ring gear in the interference fit is inferred. Then, by modeling and analyzing the gearbox body and ring gear in the interference fit using ABAQUS, the distribution rule of prestressing the ring gear in the interference fit is obtained through a numerical simulation. Finally, the prestressing of the ring gear in the interference fit is measured using X-ray di raction, and the distribution rule of prestressing of the ring gear in the interference fit is obtained through analysis. Compared with the distribution rule of prestressing in theory, numerical simulation, and experiment, the theoretical distribution rule of prestressing is amended through a statistical method, and a more accurate formula of prestressing is obtained. Through the calculation of the stress and bending moment in the dangerous section of the ring gear through prestressing, the formula for checking the tooth root flexural fatigue strength in the interference fit prestressing is inferred. This research proposes a tooth root bending strength conditional formula for the inner ring gear of the interference fit, which serves as a guide for the design and production of the actual interference joint inner ring gear.

Backlash analysis of a new planetary gearing with internal gear ring

Due to low carrying capacity and short life of current ring reducer,we proposed a new planetary gearing with internal gear ring,which consisted of two stages.One was an involute planetary drive and the other was an N-type planetary drive with small teeth difference.The kinematic calculation was conducted based on the analysis of structural composition and working principle.Formulas of backlash calculation for the new planetary gearing were derived by using probabilistic theory and the analytical model was created at the same time.Then,main factors that affect the systematic backlash were introduced and the effects of manufacture error,misaligments and roller bearing parameters on the distribution of backlash were presented.The influence of gear backlash on systematic return difference was performed based on the backlash mathematic model proposed.The results show that the backlash is a little large,of which the backlash of bearing takes a greater part than two gearing stages.So we presented some practical methods to reduce the systematic backlash.

Theoretical Explanation for Lower Order Harmonic Resonance Phenomenon of Three-Ring Gear Transmissions

Dynamic investigations revealed that lower order harmonic resonance phenomenon exists in the three ring gear transmission. That is, when the input speed is close to 1/3, 1/6, 1/9,…, 1/3 n of the primary natural frequency of the transmission, the loads on the bearings and gears are especially high. This paper explained this phenomenon from the viewpoint of parametric resonance in terms of perturbation technique. A conclusion was drawn that the basic reason for this phenomenon is the primary resonance caused by forcing excitation and parametric resonance caused by parametric change.

EFFICIENCY ANALYSIS OF DOUBLE CRANK RING-PLATE-TYPE PIN-CYCLOIDAL GEAR PLANETARY DRIVE

From the general formula for calculating the efficiency of planetary geartrains, the efficiency of the double crank ring-plate-type pin-cycloidal gear planetary drive isderived. To prove the theory, an experimental study has been conducted. The tested value of theefficiency of a sample set of the new-type drive in the experiment agrees with the calculated one.It shows that the new-type drive is of not merely high bearing capacity, but also quite highefficiency.

Experimental Study on Load Equilibration and Vibration Reduction in 3-Ring-Gear Reducer

Following the principle of elastic floating compensation, this paper presents a new metal elastic ring for load equilibration and vibration reduction in 3-ring-gear reducer, and design and fabrivcation of a metal elastic ring for SCH 3-ring-gear reducer. Comparison tests run with 3-ring-gear reducers without or with the metal elastic ring show satisfactory load equilibration and vibration reduction can be achieved with the metal elastic ring, and the metal elastic ring is a good solution for the problem of unequilibrated load and excessive vibration from which 3-ring-gear reducers suffered long.- This will further the improvement of design and application of 3-ring-gear reducers in both theory and practice.

Natural Frequency of Planetary Transmission with Thin-Walled Ring Gear on Elastic Supports

A lumped parameter-rigid elastic coupled dynamic model of two-stage planetary gears for a hybrid car is established through the inter-stage coupled method,in which the supports of the ring gear of planet set Ⅱ are represented as an elastic foundation with radial and tangential uniform distributed stiffness,and the ring gear of planet set Ⅱ is modeled as an elastic continuum body. The natural frequencies based on the eigenvalue problem of dynamic model of planetary transmission are solved and the associated vibration modes are discussed. The rules are revealed which are the influences of the ring gear elastic supports stiffness and rim thickness on natural frequencies of planetary transmission. The theoretical analysis indicates that the vibration modes of planetary transmission with thin-walled ring gear on elastic supports are classified into seven types: Ⅰ/Ⅱ stage coupled rotational mode,Ⅰ stage translational mode,Ⅰ stage planet mode,Ⅱ stage translational mode,Ⅱ stage degenerate planet mode,Ⅱ stage distinct planet mode and purely ring gear mode. For each vibration mode, its properties are summarized. The numerical solutions show that the elastic supports stiffness and rim thickness of the ring gear of planet set Ⅱ have different influences on natural frequencies.

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.

基于磁网络法的正弦调磁环磁齿轮研究

提出的一种适合高速运行的磁齿轮,其调磁环具有正弦轮廓。为了研究这类磁齿轮性能,引入磁网络法,该方法将计算区域离散化,便于描述不规则边界条件,并建立等效磁网络模型。对比研究了矩形调磁块磁齿轮和正弦调磁环磁齿轮的气隙磁密、峰值转矩、稳态转矩和涡流损耗。结果表明,磁网络法和有限元结果整体吻合,局部存在偏差,正弦调磁环内、外转子峰值转矩的相对误差为12.95%和14.9%,相较于传统结构,正弦调磁环磁齿轮的峰值转矩减小了15%,涡流损耗降低了29%,验证了所提出结构在高速下的潜在应用前景。

考虑齿圈柔性的采煤机截割部行星传动动态特性研究

为研究均质煤层及夹矸煤层2种煤体工况下的采煤机截割部行星传动系统响应特点,综合考虑各构件的支撑刚度、轮齿啮合刚度及齿圈柔性等因素,建立了截割部行星传动平移-扭转耦合动力学模型。分别分析了刚性/柔性齿圈行星传动系统在2种煤体工况下的太阳轮与行星轮啮合力波动变化特点、行星架输出转速变化规律以及太阳轮中心浮动轨迹曲线。研究发现柔性齿圈状态下,太阳轮与行星轮啮合力幅值呈长周期波动变化,均质煤层工况下的齿圈柔性改善了两轮的啮合力状态且对行星架输出转速波动具有一定的稳定作用,研究成果可为传动系统的设计提供一定的理论指导作用。

内齿圈柔性对航空行星齿轮系统偏载行为的影响机制研究

行星齿轮系统因其体积小、质量轻、承载能力大等优点被广泛应用于航空器传动设备中,但由于各种误差造成的偏载问题无法避免,严重的偏载状态将会导致行星系统的优点无法充分发挥。以某型号航空行星齿轮系统为研究对象,探究了内齿圈柔性变化对系统偏载行为的影响机制。通过试验测量了不同的行星数以及不同轮缘厚度下内齿圈挠度、应力及应变,分析了偏载的影响机制并评估了行星数及轮缘厚度对系统偏载行为的影响程度;利用层级有限元模型完成了大型航空行星系统的高级仿真计算和分析任务,量化了内齿圈柔性变化对系统载荷分布以及齿圈偏移的影响机制。将试验与仿真计算结果在相同的参数范围内进行拟合对比,评估了仿真计算结果的准确性。研究结果为大型航空行星齿轮系统内齿圈的开发和设计提供了有针对性的结构优化指导,能够极大降低该类大型航空设备在设计和迭代过程中的成本。

Finite Element Analysis of Internal Gear in High-Speed Planetary Gear Units

The stress and the elastic deflection of internal ring gear in high-speed spur planetary gear units are investigated. A rim thickness parameter is defined as the flexibility of internal ring gear. Six evenly spaced linear springs are used to describe the fitting status between internal ring gear and the gearcase. The finite element model of the whole internal ring gear is established by means of Pro/E and ANSYS. The loads on meshing teeth of internal ring gear are applied according to the contact ratio and the load-sharing coefficient. With the finite element analysis (FEA), the influences of flexibility and fitting status on the stress and elastic deflection of internal ring gear are predicted. The simulation reveals that the principal stress and deflection increase with the decrease of rim thickness of internal ring gear. Moreover, larger spring stiffness helps to reduce the stress and deflection of internal ring gear. Therefore, the flexibility of internal ring gear must be considered during the design of high-speed planetary gear transmissions.

Numerical Simulation of Deforming Manufacture Process for Automobile Bevel Gear Blank

Aiming at solving the difficulties of deforming manufacture of the automobile rear axle bevel gear blank,the paper presented to adopt the numerical simulation method to study the rolling process of the bevel gear blank instead of the traditional expensive trail-and-error method. A three-dimensional simulation model of the Φ500 bevel gear blank radial ring rolling machine was firstly created based on the general dynamic explicit finite element code ANSYS/LS-DYNA,and then realized the virtual simulation of the entire rolling process of the bevel gear blank within a producing cycle. The simulation results displayed the real-time blank enlarging and fleck generating as well as the stress,strain and displacement contours,which are in good agreements with the real ring rolling process. It is concluded that this numerical simulation method is feasible and can be used to guide the practical rolling process of the bevel gear blank as well as other profile-shaped annular blanks.

喷油润滑内齿圈外圆面红外测温及误差分析

高速重载人字齿轮箱的摩擦功率损失会转换成为温升,齿面温度测量是评价齿轮箱润滑和冷却设计的重要手段。针对某人字齿轮箱中内齿圈外圆面温度的在线实时准确测量需求,提出了一种基于红外测温仪的旋转齿轮表面温度测量方法,并分别设计搭建了相关测试试验装置。首先,分析了基于红外测温仪的旋转齿轮表面温度测量误差的影响因素;其次,通过试验对待测齿面的发射率进行标定;最后,开展了不同转速工况下的喷油润滑齿轮表面温度测量试验,并分析了吹气压力和吹气温度对红外测温误差的影响。研究结果表明:待测齿面喷涂黑色哑光漆后的标定发射率为0.96,而红外测温光路上的光学镜片会使红外测温值低2℃左右;带有空气吹扫管的红外测温仪可以在线实时测量旋转内齿圈外圆面的温度,且红外与热电偶测温值的最大相对误差不超过7%;选择合适的空气吹扫压力和吹扫温度,可以进一步减小红外测温误差。

柔性齿圈下的行星齿轮传动系统动力特性研究

建立了计入内圈齿轮柔性的行星齿轮传动系统刚柔耦合动力学模型,考虑了时变啮合刚度和静态传输误差激励,采用龙格-库塔数值算法计算了行星齿轮传动系统的动态响应特性,研究了齿轮节线和齿根上的动态应力和变形分布。结果表明柔性内齿圈的降低了内齿圈与行星轮之间的动态负载分配系数,传动系统的负载特性得到了明显的改善。对于固定内齿圈,最大应力位于沿轴向的中点上,沿齿宽方向的动态变形最大值出现在齿面末端,动态变形从齿顶边缘到齿根边缘呈递减趋势。由于支承刚度较小,负载分配系数随厚度的增加迅速减小,且行星销的错位和静态传输误差对系统的负载分配系数产生负面影响。

附加阻尼环的航空齿轮强迫响应分析方法

为了避免航空齿轮振动过大导致齿轮辐板破裂,在齿轮外缘安装阻尼环是一种有效减振方法。针对工程中阻尼环设计时缺乏有效便捷的设计方法问题,基于能量法建立了航空齿轮节径型振动下阻尼环的等效参数模型。在给定模态振型下,将阻尼环的影响效果简化为依赖于齿轮振幅(振动应力)的等效阻尼、等效刚度和等效质量,实现了齿轮-阻尼环系统幅频响应快速求解。以某航空齿轮为例,分析了激励载荷、摩擦系数、转速以及结构固有阻尼对强迫响应的影响,结合许用振动应力进行了阻尼环优化设计。结果表明:阻尼环减振效果与振动应力具有强非线性,在本文给定的激励载荷及100 MPa许用振动应力下,阻尼环质量比不应大于5%,最佳摩擦系数为0.1,设计得当的阻尼环能够降低50%以上的振动应力。

柔性齿轮运动特性及其振动抑制性能的实验研究

在三缸发动机平衡轴齿轮传动系统的传动过程中,存在着较大的振动和噪声问题,为此,提出了一种附加阻尼环的齿轮传动系统刚柔耦合模型,对柔性齿轮结构的运动特性及其振动抑制性能进行了实验研究。首先,采用集中质量法,建立了考虑齿轮间隙和时变啮合刚度的附加阻尼环6自由度齿轮传动系统的弯曲-扭转模型,利用石川公式计算出了柔性齿轮的时变啮合刚度,对比了有无阻尼环的齿轮系统的振动响应;然后,搭建了专门的齿轮传动系统测试设备,测试了不同转速下钢齿轮和柔性齿轮的加速度和噪声峰值;最后,设计了激光位移试验台,对比分析了不同转速下齿轮的微抖动,对柔性齿轮的减振效果进行了测试,并验证了理论模型的正确性。研究结果表明:当转速为1000 r/min时,钢齿轮和柔性齿轮的最大加速度信号分别为35.58 m/s^(2)和20.37 m/s^(2);当齿轮转速为4000 r/min时,柔性齿轮的阻尼效果最佳,加速度峰值降低了45.23%,噪声峰值降低了39.06%;钢齿轮的微抖动幅值明显高于柔性齿轮,两者的变化趋势相似。柔性齿轮能有效抑制轮齿微抖动振幅曲线的不平滑、毛刺现象,从而增强了三缸发动机平衡轴系的稳定性。

三轴环板式永磁齿轮气隙磁场及转矩计算

利用标量磁位法获得了三轴环板式永磁齿轮(Triple-shaft Ring-plate Magnet Gear,TRMG)的气隙磁场数理模型,根据磁场叠加原理建立了内、外永磁圈间气隙磁场及其相应的电磁转矩模型;由于所有计算均基于TRMG的平面磁场建立,因此,所建模型与二维有限元结果间具有较高的准确度(误差≤5%);其计算速度远快于三维有限元法,且与二维及三维有限元分析具有较好的吻合度与趋势性,验证了所建模型的准确性,可适用于三轴以上的多轴环板式永磁齿轮的磁场分析与结构动力学计算。

考虑齿圈柔性的内啮合齿轮时变啮合刚度计算分析

当前大多数内齿轮啮合刚度都是基于忽略齿圈基体变形的假设计算的,文中应用Weber能量法基于精确的齿廓曲线方程建立内齿轮悬臂梁等效模型,同时基于铁木辛柯(Timoshenko)曲梁理论计算齿圈基体的变形量,并将齿圈变形耦合到齿轮啮合刚度计算中。通过MATLAB GUI编程进行内啮合齿轮时变啮合刚度数值计算,分析了齿圈柔性对啮合变形的影响,研究了齿圈厚度、支撑数量及啮合力位置对啮合刚度的影响。结果表明:齿圈厚度和支撑数量的增加均有利于齿轮副啮合刚度的增大;啮合齿中线位于固定支撑点时,齿圈啮合刚度最大,在靠近支撑中间位置时,啮合刚度最小,齿圈啮合刚度对应于螺栓支撑呈周期性波动。