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.     

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。     

Stochastic Vibration Model of Gear Transmission Systems Considering Speed-Dependent Random Errors

A dynamic and stochastic simulation model is developed for analyzing the vibration of gear transmission systems with consideration of the influence of the time-variant stiffness, loads, and gear transmission errors. The gear transmission system is viewed as a non-linear, time-correlated and stationary stochastic system. The transmission errors of gears are decomposed into harmonic and random components based on the spectral analysis. To simulate the random component, a second order Markov process with time-variant parameters considering influence of rotational speed is proposed and the method to determine the model parameters based on the random error of measured gear transmission error is developed. A simulation system is developed. The input to the simulation system is a white Gaussian noise process and harmonic errors, and the output is the rotational vibration acceleration of gears. Experiments are carried out to verify the proposed model. The influences of the random error on vibration acceleration are examined using the developed simulation system.     

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.     

Dynamic behavior of an agricultural power take-off driveline for rattle noise reduction: Part 1. Effect of spline tolerance on the power take-off rattle noise

An agricultural tractor has a power take-off (PTO) driveline that is directly connected to the engine to improve its power transmission efficiency. The PTO driveline comprises various mechanical components coupled by a spline joint. The spline coupling tolerance causes collisions between various mechanical parts of the PTO driveline and affects gear collision, thereby causing rattle noise. Therefore, the aim of this study is to conduct a dynamic behavior analysis to predict the gear rattle noise level of a PTO driveline. The dynamic behavior of the PTO driveline was analyzed through 1D simulations, and the results confirmed that the dynamic behavior changes according to rotation speed. Experimental verification of the dynamic behavior analysis results confirmed that the dynamic behavior changes as the main engine excitation-component amplification changes and then decreases at a relatively high rotation speed. Additionally, the dynamic behavior changes of the PTO driveline resulted in a jumping phenomenon that occurs rapidly at a specific rotation speed. The amplification of the engine’s main components was reduced from 3 to 4 times to 1.2 times owing to the jumping phenomenon; the noise level of the gear rattle was also reduced by approximately 10.9 dB(A).     

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.     

Experimental research for robust design of power transmission components

In the future progress of technical systems it is impossible to avoid the power transmission (PT) components. Mechatronical technical systems will include the innovated PT components with high-level quality indicators. The article proposes the application of the new approaches to those components design in order to challenge innovation and inventions. The main objective is to define the design parameters in terms of reliability, vibration and noise as design constraints in the stage of the Embodiment design of PT components. Robust design is provided by using the axiomatic method in this way. Reliability as the design constraint of PT components is defined and modeled in a specific way suitable for this purpose and application. Also, the model of gear vibrations and gear units noise generation is presented in a new way suitable for applying as the design constraint. Those design constraints provide design parameters definition in an efficient way, with high-level service quality indicators. The presented models are based on a great volume of experimental data about service conditions probability, gear and bearing failure probability, gear units vibration and modal behavior etc. Theoretical knowledge and models are insufficient yet to provide the necessary data. The article contains presentation of testing methods and data processing oriented to provide data necessary for the application in the suggested approach to PT components design.     

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.      

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 dynamics of a spur gear pair with force-dependent mesh stiffness

Time-varying mesh stiffness is one of the main excitation sources of a gear system, and it is also considered as an important factor for the vibration and noise of gears. Thus, this excitation is usually taken as an input into the gear dynamic model to obtain the system dynamic responses. However, the mesh stiffness of a gear pair is actually nonlinear with respect to the dynamic mesh force (DMF) that fluctuates during the operation of gears. Therefore, the dynamic model of gears with the quasi-static mesh stiffness calculated under a constant load is not accurate sufficiently. In this paper, a dynamic model of spur gear is established with considering the effect of the force-dependent time-varying mesh stiffness, backlash and profile deviation. Due to the nonlinear relationship between the mesh stiffness and the load for each tooth pair, it needs first to determine the load sharing among tooth pairs and then calculate the overall mesh stiffness of the gear pair. As the mesh stiffness and DMF are related, the mesh stiffness is no longer directly taken into the gear dynamic model as an input, but is jointly solved with the numerical integration process using the gear dynamic model. Finally, the dynamic responses predicted from the established gear dynamic model are compared with the experimental results for validation and compared with the traditional models to reveal their differences. The results indicate that the established dynamic model of spur gear transmission has a wider application range than the traditional models.     

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.     

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.

     

Computational approach to design face-milled spiral bevel gear drives with favorable conditions of meshing and contact

The micro-geometry of the tooth surfaces of spiral bevel and hypoid pinions has to be fine-adjusted to obtain enhanced meshing and contact characteristics during the meshing process with their corresponding mating gears. In this paper, a new methodology is proposed to design face-milled spiral bevel gear drives to, firstly, derive favorable orientation and dimensions of the contact pattern between the mating surfaces of the gears and, secondly, obtain a predesigned parabolic function of negative transmission errors with limited magnitude of maximum transmission errors. The proposed approach is based on the definition of the desired topography for the active surfaces of the pinion followed by a numerical derivation of their finishing machine-tool settings through a bound-constrained optimization algorithm. Increasing mechanical strength and reducing the levels of noise and vibration of face-milled spiral bevel gear drives constitute the main objectives of the proposed design process. A numerical example is provided to illustrate the applicability of the developed theory .     

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.     

Dynamic characteristics and load-sharing performance of concentric face gear split-torque transmission systems with time-varying mesh stiffness,flexible supports and deformable shafts

Meccanica - The concentric face gear split-torque transmission system is a new gear mechanism which integrates the advantages of face gears, split-torque transmissions and concentric transmissions....     

On Gear Modelling in Multistage Rotary Vane Engines

A discussion of the dynamics of a multistage rotary vane engine is given in terms of a simplified model for combustion driving torques, power dissipation, and torque transmission. Torque transmission is effected by conjugate gear pairs attached to each unit of the engine. An argument for the design of such pairs is presented so that unwanted torque fluctuations in a flywheel attached to a member of the pair can be significantly attenuated. It is suggested that a variant of simple Cosserat dynamics offers a useful modelling tool for discussing the complex interaction between interacting gear teeth. A quasi-stationary analysis is used to place bounds of a particular choice of conjugate gear coupling in the presence of such interactions. It is concluded that a multistage rotary vane engine with at least two units can be usefully coupled to a single flywheel via a well-defined conjugate gear system that attenuates unwanted torque fluctuations over a broad range of rotary speeds.     

Dynamic behavior of gear pumps: effect of variations in operational and design parameters

This work presents a wide number of results about the influence that variations in terms of operational and design parameters play on the dynamic behavior of external gear pumps. These results are obtained by using a non-linear lumped-parameter kineto-elastodynamic model developed and experimentally assessed with the aim of including all the important dynamic effects. On the one hand, the effects of variations in the operational parameters—namely output pressure, rotational speed and oil viscosity—are analysed; on the other hand, the effects of modifications of some design parameters are shown: clearances and relief groove dimension. The results in terms of gear eccentricity, pressure evolution, pressure forces, gear accelerations and variable forces exciting the pump casing enlighten the dynamic behavior of gear pumps and give useful indications for design improvements and vibration and noise reduction. As regards specifically gear accelerations as well as forces exciting the casing, they strongly increase with both output pressure and rotational speed, but variations in rotational speed in the operational range give lower effects. Conversely, the modifications of the clearances give negligible effects, while the relief groove dimension is very important: the larger the relief grooves are, the higher the gear accelerations and forces exciting the casing become.     

Effect of spalling or tooth breakage on gearmesh stiffness and dynamic response of a one-stage spur gear transmission

Tooth faults affecting gear transmission are always accompanied by a stiffness reduction. In this article an analytical method is proposed to quantify the reduction of gearmesh stiffness due to two common tooth faults: spalling and breakage. Bending, fillet-foundation and contact deflection are taken into account. The dynamic response of a single stage spur gear transmission is computed by using analytical gearmesh issued from analytical modelling and the vibration signatures of each tooth fault is identified.     

Non-Newtonian mixed elastohydrodynamics of differential hypoid gears at high loads

Prediction of friction and transmission efficiency are design objectives in transmission engineering. Unlike spur and helical involute gears, there is a dearth of numerical analysis in the case of hypoid gear pairs. In particular, it is important to take into account the side leakage of the lubricant from the contact as the result of the lubricant entrainment at an angle to the elliptical contact footprint. In the automobile differential hypoid gears, high loads result in non-Newtonian behaviour of the lubricant, which may exceed its limiting shear stress, a fact which has not been taken into account in the open literature. This results in conditions which deviate from observed experimental tractive behaviour. The paper takes into account these salient practical features of hypoid gear pair analysis under high load. It highlights a non-Newtonian shear model, which limits the lubricant shear behaviour. Prediction of friction and transmission efficiency is in line with those reported in the literature.     

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...