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.

Sheet Bulk Forming of Thin-Walled Components with External Gearing through Upsetting Using Controllable Deformation Zone Method

Sheet-bulk metal forming(SBMF)is a promising process for manufacturing complex sheet components with functional elements.In this study,the entire forming process for a typical thin-walled component with external gearing is investigated,including sheet forming and bulk forming processes.Deep drawn cups are prepared during sheet forming;subsequently,upsetting is performed on the sidewall to form external gearing.The upsetting method performed is known as upsetting with a controllable deformation zone(U-CDZ).Compared with the conventional upsetting method,a floating counter punch with a counter force is used in the U-CDZ method such that the forming mechanism is changed into the accumulation of the deformation zone instead of deformation throughout the entire sidewall.The effects of the counter force and material flow are investigated to understand the mechanism.The forming quality,i.e.,the formfilling and effective strain distribution,improved,whereas a high forming load is avoided.In addition,a punch with a lock bead is used to prevent folding at the inner corner during the experiment.

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.

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

From the general formula for calculating the efficiency of planetary gear trains, the efficiency of the double crank ring-plate-type pin-cycloidal gear planetary drive is derived. To prove the theory, an experimental study has been conducted. The tested value of the efficiency 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 high efficiency.

Design and Dynamics Simulation of a Novel Double-Ring-Plate Gear Reducer

A patented double-ring-plate gear reducer was designed and its dynamic performance was simulated. One unique characteristic of this novel drive is that the phase angle difference between two parallelogram mechanisms is a little less than 180 degree and four counterweights on two crankshafts are designed to balance inertia forces and inertia moments of the mechanisms. Its operating principle, advantages, and design issues were discussed. An elasto-dynamics model was presented to acquire its dynamic response by considering the elastic deformations of ring-plates, gears, bearings, etc. The simulation results reveal that compared with housing bearings, planetary bearings work in more severe conditions. The fluctuation of loads on gears and bearings indicates that the main reason for reducer vibration is elastic deformations of the system rather than inertia forces and inertia moments of the mechanisms.

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.

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

Following the principle of elastic floating compensation,this paper presentS a new metalelastic ring for load equilibration and vibration reduction in 3-ring-gear reducer,and design andfabrivcation 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 loadequilibration and vibration reduction can be achieved with the metal clastic ring,and themetal elastic ring is a good solution for the problem of unequilibrated load and excessivevibration from which 3-ring-gear reducers suffered long.This will further the improve-ment of design and application of 3-ring-gear reducers in both theory and practice.

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.

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.

Theoretical calculation and experimental study on the load distribution coefficient (LDC) of three-ring gear reducer

In this paper, primary manufacturing and assembling errors of three-ring gear reducer (TRGR) are analyzed. TRGR is a new transmission type whose eccentric phase difference between middle ring plate and side ring plates is 120°. Its mass of middle ring plate is equal to that of side ring plate or 180°, and its mass of middle ring plate is twice of that of side ring plate, which affects load distribution between ring plates. The primary manufacturing and assembling errors include eccentric error of eccentric sheath E_m, internal gear plate E_r and output external gear E_w. A new theoretical method is presented in this paper, which converts load on ring plates into the dedendum bending stress of ring plate to calculate load distribution coefficient (LDC), by means of gap element method(GEM), one of finite element method (FEM). The theoretical calculation and experimental study, which measures ring plate dedendum bending stress by means of sticking strain gauges on the dedendum of middle ring plate internal gear and side ring plate internal gears, are presented. The theoretical calculation and comparison with experiment result of LDC are implemented on two kinds of three-ring gear reducers whose eccentric phase difference between eccentric sheaths is 120° and 180° respectively. The research indicates that the result of theoretical calculation is consistent with that of experimental study. That is to say, the theoretical calculation method is feasible.

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。

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。

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。

大型轴/齿圈类钢制件喷丸强化工艺的探讨

本文根据大型轴/齿圈类钢制件外形特点,对不同尺寸和形状的轴类和齿圈类零件的喷丸工艺进行研究,首先根据所研究的零件类型,确定了运用测定抛喷丸强度,覆盖率等参数来间接特性来表现内应力及疲劳使用寿命的强化指标,通过控制弹丸类型、喷枪口径、喷射压力、喷射距离、弹丸流量、强化时间、喷枪移动速度、工件旋转速度等强化参数对上述零件进行喷丸强化,对实验数据与理论数据进行对比后,优化测试参数,经实际生产检验,此工艺方法完全满足工件的强化要求。

挖掘机回转支承内齿加工工艺研究

针对某外资12 t挖掘机配套内齿回转支承断齿问题,分析断齿原因,研究相应改进方案,为避免断齿事故的发生提供技术参考。

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.

The Additive Manufacturing Process of Electric Power Fittings Fabricated by Metal Droplet Deposition

Metal droplet deposition is a kind of additive manufacturing(3D Printing)technique that fabricates near-net part through droplets deposition with lower cost and higher efficiency.This paper proposed a solution to problems of electric power fittings that large inventories,high procurement costs,low manufacturing efficiency and transportation cost.Using additive Manufacturing technique-metal droplet deposition,electric power fittings fabricated on power construction site.This paper describes the manufacturing process of typical thin-walled samples(the structure optimized based on additive manufacturing principle)and ball head rings of electric power fittings.Aiming at the integral AM forming for ball and ball socket electric power fitting workpiece,a novel easy removal forming support material(ceramics and gypsum mixed with UV cured resin)have been developed.Here this support material was used to fabricate nested integral workpieces.Dimensional accuracy and microstructure of the test pieces were analyzed.The error of the height and width of the forming workpiece is within 5%.No obvious overlap trace(such as overlap line and cracks)observed,and the internal microstructure is equiaxial crystal.The average density of the component is 99.51%,which measured by drainage method and 13.39%higher than the cast raw material.

重载工况下行星齿轮传动啮合偏载分析

为了深入研究重载行星齿轮传动多柔体变形下齿面载荷分布规律,提出一种计入结构柔性与齿轮副动态接触的行星齿轮传动耦合动力学建模方法。以某型兆瓦级风电齿轮箱行星轮系为研究对象,根据内齿圈、行星架结构及其边界特征,采用有限元缩聚理论建立内齿圈轮齿、行星架耦合点与弹性支撑之间的关联关系,利用齿轮副动态承载接触作为界面协调条件将各构件进行耦合,建立行星齿轮传动耦合动力学模型,分析了啮合偏载现象以及结构参数对啮合特性的影响。研究结果表明,作用在行星轮上的合弯矩以及行星架销轴非对称结构变形是造成啮合偏载的主要原因,系统共振会加剧啮合偏载程度;在共振区附近,齿轮动态啮合刚度与静态啮合刚度存在较大差异;增加销轴刚性、增大螺旋角可以改善啮合偏载程度,减小共振区系统振动,但在低转速区不利于系统减振,而增大行星架连接板刚性可以保持低转速区系统振动状态,同时减小共振区系统振动。

计入结构柔性的风电齿轮箱行星轮系动力学特性研究

针对常规梁/壳单元无法考虑复杂构件几何特征、计算精度低和大规模有限元计算量大、系统级建模与动态分析困难的问题,提出一种计入结构柔性的行星轮系变速动力学建模方法。以某型5 MW级风电齿轮箱低速级行星轮系为研究对象,根据内齿圈结构及边界特征,采用有限元缩聚理论建立内齿圈轮齿与弹性支撑的耦合关系,通过引入啮合副变速表征变量和内齿圈虚拟振动线位移,将驱动轮转角与行星轮系多轮齿啮合状态进行关联,并计入行星架和太阳轮轴柔性,利用界面位移协调条件将各构件耦合,建立行星轮系变速动力学模型。研究结果表明,当5个行星轮受力平衡时,内齿圈轮齿节点瞬态变形整体呈“五角星”形状,并随着行星架旋转;行星轮系轮齿动载荷先增大后减小,变化趋势与单对齿啮合刚度相似;稳态工况下的内齿圈轮齿节点振动位移呈现大幅低频波动和高频振动的叠加特征;输入扭矩突变会破坏多个行星轮之间的动载荷平衡,而柔性内齿圈可在一定程度上吸收部分因冲击载荷引起的构件振动,提高了均载性能。