Investigation of assembly,power direction and load sharing in concentric face gear split-torque transmission system

Meccanica - As a special transmission mechanism used in aeronautical transmission field, a concentric face gear split-torque transmission system (CFGSTTS) is investigated in this study, with the...     

Energy dissipation mechanism and experiment of particle dampers for gear transmission under centrifugal loads

As a passive means of vibration reduction, particle damping is mainly applied to the horizontal or vertical steady field. However, it is seldom applied to centrifugal fields. Under high speed and heavy loading, the vibration of tooth surfaces of gear transmissions becomes more severe shortening gear service life and augmenting noise. Under centrifugal loading, the particle system exhibits different characteristics, for example, particles are extruded at the end farthest from the center. We investigated gears with drilled via holes filled with damping particles. Using the discrete-element method, we developed an energy dissipation model for the particle system accounting for friction and inelastic collisions. Energy dissipation and damping characteristics of this system were analyzed. Experiments were also conducted with the gear system having different particle filling rates. The results show that this filling rate is an important parameter associated with particle damping in a centrifugal field. An unsuitable filling rate would significantly reduce damping effectiveness. With changes in rotation speed and load, the gear transmission system has different optimal filling rates. The results provide guidelines for the application of particle damping in centrifugal fields of gear transmissions.     

Nonlinear dynamic characteristic of a face gear drive with effect of modification

Face gear drive is one of the main directions of research for aeronautical transmission for its advantages, but the vibration induced gear noise and dynamic load are rarely involved by researchers. The present work examines the complex, nonlinear dynamic behavior of a 6DOF face gear drive system combining with time varying stiffness, backlash, time varying arm of meshing force and supporting stiffness. The mesh pattern of the face gear drive system is analyzed when the modification strategy is applied and the effect of modification on the dynamics response, the time varying arm of meshing force based on the TCA is deduced. The dynamic responses of the face gear drive system show rich nonlinear phenomena. Nonlinear jumps, chaotic motions, period doubling bifurcation and multiple coexisting stable solutions are detected but different from the spur and bevel gear dynamics, which don’t occur near primary and higher harmonic resonance.     

Nomographs for synthesis of epicyclic-type automatic transmissions

This paper presents a MATLAB optimization technique for the determination of the gear ratios of epicyclic-type transmission mechanisms for a given set of velocity ratios. First, all of the feasible clutching sequences are enumerated directly without using complicated techniques. Then, for the transmission mechanism with the associated clutching sequence graph, the overall velocity ratios are derived and expressed in terms of the gear ratios of all the mating gears. Next, following the general trend of increased shift stages and a wider range of velocity ratios, the numbers of teeth of all gears are estimated by MATLAB optimization technique in a single run. Ravigneaux gear mechanisms are used as design examples. The methodology can be applied to any transmission mechanism depending on its kinematic and geometric constraints. New five- and six-velocity automatic transmissions are enumerated from the Ravigneaux gear mechanism. It is a major breakthrough to design a completely satisfactory six-speed automatic transmission from the Ravigneaux gear mechanism since it has only eight links. The new design makes use of the benefits of the Ravigneaux gear train and overcomes the previous art difficulties. This structural design has realized a six-speed automatic transmission, while having minimal number of clutches, and brakes. It is also low cost due to adoption of the conventional available Ravigneaux gear train.     

基于承载接触特性的直齿面齿轮滑动摩擦啮合效率研究

为了解决直齿面齿轮滑动摩擦啮合效率的问题,基于弹性流体动力润滑理论,提出了一种计算直齿面齿轮啮合效率的方法.首先,运用轮齿接触分析(TCA)和轮齿承载接触分析技术(LTCA)对直齿面齿轮承载啮合过程进行数值仿真;其次,运用非牛顿准稳态热弹流理论建立滑动摩擦系数的计算模型,从而建立直齿面齿轮啮合效率的计算模型,最后分析了输入扭矩、转速等对啮合效率的影响.结果表明:滑动摩擦系数是影响齿轮啮合效率的重要因素;齿面不同位置滑动摩擦系数也不相同;滑动摩擦系数受输入转速、输入扭矩的影响.该方法为直齿面齿轮的进一步优化计算提供一定的理论依据.     

评价半流体润滑剂性能的齿轮台架

作者对全尺寸功率流封闭式齿轮试验台架成功地进行了改进和完善,发展了一种测试方法齐全、测量精度高的齿轮试验台架与测试系统,并以其进行了00~#半流体润滑脂、50~#机械油等润滑时啮合齿面间的油膜电压、齿轮传动效率、减速器的振动和噪声、润滑剂的温升和抗磨性能等多方面的对比分析和评价。结果表明,这种全尺寸齿轮试验台架与测试系统对半流体润滑剂性能的评价分析是可靠的,适合作为各种半流体润滑剂性能的全尺寸试验台架推广应用。     

Three-dimensional photoelastic study of the load-carrying capacity/face width ratio of Wildhaber-Novikov gears for automotive applications

Wildhaber-Novikov gears are becoming more and more popular for heavy load applications. They have been tried as speed-reducing gears, in spite of heavy noise generation, in aircraft jet engines, marine engines and agricultural machinery. These circular-arc gears, though stronger than involute geras, have the disadvantage of needing larger face width. Axial face width required can be minimized only at the expense of load-carrying capacity. This is not a serious disadvantage with stationary engines. But in the case of automotive applications, this fact limits the load-carrying capacity of Wildhaber-Novikov gears, since space problem is very critical in these applications and large face widths, therefore, cannot be used for such gear-reduction units. The face width is determined by the helix angle and, therefore, a thorough investigation of the dependence of the load-carrying capacity on helix angle is necessary, if these special types of gears have to make headway into the automotive field. In this experimental investigation, three-dimensional photoelastic technique has been employed to study the load-carrying capacity/face width ratio. Three-dimensional gear models made of epoxy castings (Araldite B) were loaded in a specially built gear-loading fixture and were stress frozen. Gear cutters of Wildhaber-Novikov gears developed at the laboratory were used for the preparation of these three-dimensional gear models. The stress-frozen models were analyzed using the conventional slicing technique to study the contact and bending-stress distribution along the face width. The load-carrying capacity in terms of contact stress and bending stress has been studied for different face widths and helix angles. Twenty-deg pressure angle, 14-mm module gears of alladdendum type of Wildhaber-Novikov gears with different helix angles up to 40 deg were tested. The helical-overlap ratio used was 1.0. The conventional profile parameters were employed for the manufacture of gear cutters of end-mill type. The decrease in contact and bending strength with increase in the helix angle or decrease in the face width, as obtained from this photoelastic method of stress analysis has been compared with existing theoretical results.     

Comparison of spur,helical and curvilinear gear drives by means of stress and tooth contact analyses

Involute tooth surfaces are a successful technical solution for both spur and helical gear drives since they provide linear contact and a low-level function of transmission errors under good conditions of meshing. Tip relief is usually required to improve contact conditions during the transfer of meshing between adjacent pairs of teeth. Yet, unfavorable conditions of contact appear when shaft deflections and misalignments are present. Localization of contact through lead crowning is a solution that increases the cost of machining in both spur and helical gear drives. In this sense, the generation process of curvilinear gear drives provides localization of contact with no additional cost. Comparison of stresses and transmission error functions in spur, helical and curvilinear gear drives is investigated to show if the application of curvilinear gear drives yields some advantages respect to spur and helical gear drives. The three mentioned types of cylindrical parallel-axis gear drives are provided, firstly, with linear contact, and, secondly, with localized contact, for the purpose of comparison. Different misalignments conditions are taken into account by means of several numerical examples.     

Design parameters for continuously variable power-split transmissions using planetaries with 3 active shafts

Since 1996, when the first agricultural tractor with CVT transmission was shown, the presence of this type of transmissions has been increasing. All companies offer them in their products range. Nevertheless, there is little technical documentation that explains the basics of its operation. This report shows all types of CVT transmissions: non-power-split type and power-split ones, as well as the three types used in agricultural tractors, hydro-mechanical power-split transmissions (3 active shafts, input coupled planetary; 3 active shafts, output coupled planetary and 4 active shafts). The report also describes the design parameters of a type of CVT transmission, which use a power-split system with 3 active shafts as well as the fundamental relations among them.     

The analysis of power circulation and the simplified expression of the transmission efficiency of 2K-H closed epicyclic gear trains

Transmission efficiency is a principal index for estimating the performance of 2K-H closed epicyclical gear trains. To calculate transmission efficiency, it must confirm the power flow direction in transformation gear train and verify if there is power circulation in closed epicyclical gear train firstly. In this paper, a simple algorithm is proposed to confirm the power flow direction and estimate if there exist the power circulation based on transmission ratio of basic links in differential gear train and transformation gear train. The simplified equations are deduced to calculate the transmission efficiency and some examples are given finally.     

磨损与动力学耦合的行星传动齿轮动力学研究

行星齿轮磨损会导致齿轮齿侧间隙非线性增大、传动精度下降、齿面冲击力增大, 进而会导致齿轮传动系统振动加剧, 因此需要对行星齿轮的齿面磨损与动力学耦合特性进行研究. 本文构建了齿轮非线性磨损与考虑齿轮齿侧间隙的非线性动力学耦合计算模型, 对行星传动齿轮磨损动力学特性进行了研究. 首先建立齿轮啮合非线性动力学模型, 获得齿轮运行过程中的非线性啮合力; 进一步将非线性啮合力与齿轮齿面磨损模型相结合, 研究齿轮齿面磨损分布规律; 并根据齿轮磨损后的齿侧间隙对齿面重构, 同时对齿轮动力学模型进行更新; 进而得到行星齿轮传动中动态啮合力和磨损特性的变化趋势, 并获得齿轮传动系统齿轮齿向振动响应. 数值计算结果表明, 行星齿轮磨损导致齿轮在单?双齿交替啮合时产生的冲击增大, 同时太阳轮?行星轮啮合齿对对磨损较为敏感, 齿面啮合条件剧烈恶化, 是造成行星齿轮传动性能退化的主要原因, 本文研究结果为行星齿轮传动系统运行状态评估与可靠性预测提供了理论基础.      

Improvements on noise reduction and efficiency of gears

The main requirements for transmissions are a high load carrying capacity, a low sound excitation behaviour and high efficiency, which becomes more and more important with the increasing environmental awareness.     

换向持续时间和换向点位置对往复运动齿轮齿条弹流润滑的影响

往复运动齿轮齿条的润滑失效通常发生在换向死点位置附近,因此研究齿轮齿条换向点位置和换向持续时间对换向过程中润滑油膜的影响具有重要的实际意义。根据齿轮齿条换向瞬间的运动几何关系,建立了换向过程齿轮齿条弹流润滑的瞬态数值模型。采用Ree-Eyring润滑流体,应用多重网格法和多重网格积分法等数值方法,计算得到了齿轮齿条往复运动过程中换向点位置附近一对啮合轮齿间的压力、膜厚和温度,并与前人的实验结果进行了对比验证。分析了不同换向持续时间和换向点位置对一对啮合轮齿间压力、膜厚和温度的影响。齿轮齿条换向过程中油膜厚度明显降低,缩短换向持续时间虽然可以增大齿轮齿条的润滑膜厚,但会导致瞬间油温升高,因此换向持续时间存在最优值。通过比较不同换向死点位置的膜厚发现,当换向死点在单齿啮合后的双齿啮合区时,啮合轮齿间具有较理想的润滑膜厚。无论换向持续时间长短,润滑膜厚的最小值都在换向死点位置,换向死点位置是往复运动齿轮齿条润滑失效的危险点。研究结果为往复运动齿轮齿条的润滑设计提供了理论依据。     

Periodic decentralized event-triggered control for nonlinear systems with asynchronous update and dynamic quantization

Nonlinear Dynamics - Periodic event-triggered control (PETC) is an aperiodic sampling technique aiming at reducing the working time of the sensors and the transmissions in the feedback control...     

A review of space tether in new applications

Gear eccentricities are one of the practical types of the manufacturing errors that affect the dynamic performance of a planetary gear train (PGT). Previous research about the effects of the gear eccentricities is abundant, and many of them focus on the parallel shaft gear set. However, almost none of them have considered the influence of the gear eccentricities on the mesh stiffness. In fact, the existence of the gear eccentricities can change the center distance and the mesh positions of a meshing gear pair, which will directly affect the mesh stiffness. Situation can be even more complex for the PGT with either sun gear eccentricities or planet gear eccentricities or both of them. Based on that, a new dynamic model of a PGT with gear eccentricities is established. The planar motions of the PGT and the mesh stiffness are integrated and solved simultaneously where the mesh stiffness is determined by the actual mesh positions of the meshing gear pair. The mesh stiffness is calculated by the energy potential method. The time-varying center distance caused by the gear eccentricities is also considered, which can result in the change of line of action, pressure angle, contact ratio and mesh positions. The influence of gear eccentricities on the dynamic performance of a 4-planet PGT is studied. Some useful results are derived at last.     

A general and systematic framework for the kinematic analysis of complex gear systems

It is presented an integral approach for the velocity analysis of complex gear systems. Due to the intrinsic nature of the method, it can be systematically applied for gear trains with arbitrary architecture, including bevel gears with non-parallel motion axes. As a result, not only velocity ratios can be computed, but also angular velocities of any body composing the gear system. Several application examples are presented to prove the feasibility and the validity of the proposed method.     

Modeling and analyzing of torsional dynamics for helical gear pair considered double and three teeth drive-side meshing

Helical gears are generally considered to be more stable than spur gears. But rattling of the helical gear transmission is found in the engineering practice. The torsional dynamics equations of helical gear pair in high-speed railway gearbox are established in order to reveal the rattling mechanism of helical gear transmission. Double and three teeth pair drive-side meshing are considered. The multi-state meshing zone, load distribution rate and time-varying stiffness determined by contact ratio are analyzed and calculated. The dynamic characteristic transition process of the system is analyzed according to the bifurcation diagrams and the corresponding top Lyapunov exponent (TLE) diagrams, phase portraits, Poincaré maps and time history spectrums of dynamic meshing force based on the calculation of these parameters. The tooth disengagement, tooth back-side contact and their parameter range are found. This study can provide theoretical basis for rattling suppression and transmission stability improvement of helical gear pair.

     

Dynamic response of a single-mesh gear system with periodic mesh stiffness and backlash nonlinearity under uncertainty

Parametric uncertainties play a critical role in the response predictions of a gear system. However, accurately determining the effects of the uncertainty propagation in nonlinear time-varying models of gear systems is awkward and difficult. This paper improves the interval harmonic balance method (IHBM) to solve the dynamic problems of gear systems with backlash nonlinearity and time-varying mesh stiffness under uncertainties. To deal with the nonlinear problem including the fold points and uncertainties, the IHBM is improved by introducing the pseudo-arc length method in combination with the Chebyshev inclusion function. The proposed approach is demonstrated using a single-mesh gear system model, including the parametrically varying mesh stiffness and the gear backlash nonlinearity, excited by the transmission error. The results of the improved IHBM are compared with those obtained from the scanning method. Effects of parameter uncertainties on its dynamic behavior are also discussed in detail. From various numerical examples, it is shown that the results are consistent meanwhile the computational cost is significantly reduced. Furthermore, the proposed approach could be effectively applied for sensitivity analysis of the system response to parameter variations.     

Computerized Developments in Design,Generation, Simulation of Meshing,and Stress Analysis of Gear Drives

The paper represents new computerized developments in design, generation, simulation of meshing, and stress analysis of gear drives. The main contents of the paper are: (i) application of a predesigned parabolic function of transmission errors for reduction of noise, (ii) computerized simulation of noise caused by transmission errors, (iii) modification of the basic algorithm of tooth contact analysis, and (iv) application of approaches developed for enhanced design and simulation of meshing of the following gear drives: (a) spiral bevel gear drives, (b) face-gear drives (including an approach for grinding), and (c) modified helical gear drives. The developed theory is illustrated with numerical examples.     

Dynamic modeling and analysis of a spur planetary gear involving tooth wedging and bearing clearance nonlinearity

Tooth wedging, also known as tight mesh, occurs when a gear tooth comes into contact on the drive-side and back-side simultaneously. Tooth wedging risks bearing failures from elevated forces. This work studies the nonlinear tooth wedging behavior and its correlation with planet bearing forces by analyzing the dynamic response of an example planetary gear. This planetary gear is representative of a wind turbine geartrain. A two-dimensional lumped-parameter model is extended to include tooth separation, back-side contact, tooth wedging, and bearing clearances. The results show significant impact of tooth wedging on planet bearing forces for a wide range of operating speeds. To develop a physical understanding of the tooth wedging mechanism, connections between planet bearing forces and tooth forces are studied by investigating physical forces and displacements acting throughout the planetary gear. A method to predict tooth wedging based on geometric interactions is developed and verified. The major causes of tooth wedging relate directly to translational vibrations caused by gravity forces and the presence of clearance-type nonlinearities in the form of backlash and bearing clearance.