含侧隙齿轮副的动载荷分析

以振动理论为基础，提出一种考虑齿轮拍击振动的齿轮动载荷的数值计算方法。建立计算动载荷的齿轮冲击模型，在模型中考虑了齿轮正、反冲击时实际的啮合刚度，并给出啮合柔度的计算方法。分析在考虑静态传递误差、啮合刚度、侧隙、摩擦力及外部扭矩变化等多种激励时，作用在轮齿上的动态载荷以及整个齿轮上的综合动态载荷的计算公式。最后通过实例分析作用在轮齿上的动态载荷、综合动态载荷变化规律以及相关激励参数对动态载荷的影响。     

基于MATLAB与SolidWorks联合建模的渐开线圆柱直齿轮接触特性仿真分析

通过渐开线直齿轮齿廓方程在MATLAB中构建出渐开线直齿轮的点云模型生成精确地齿廓,将点云数据导入到SolidWorks中构建出齿廓精确的渐开线直齿轮副的三维模型;然后对渐开线直齿轮副进行理论接触应力计算,并对联合建模的齿轮副与参数化建模的齿轮副进行接触应力的有限元仿真分析和动力学仿真分析结果进行对比.结果表明:联合建...     

Producing gear teeth with high form accuracy and fine surface finish using water-lubricated chemical reactions

A new method was investigated for high-accuracy fine finishing of gear teeth surfaces using a water-lubricated tribo-chemical technique. A pair of shaved gears with rather low surface roughness was rotated in water lubricant for 30 min so that the gear tooth surface contacting the mating tooth was ‘worn’ to a mirror surface and ideal tooth profile, due to the mechano-chemical mild erosion of the contact area. The wear rate was 2.0 μm per 20,000 meshings, corresponding to a wear of one atomic radius thickness per meshing. Oxidation of the steel surface by water molecules is proposed as the dominant wear process. Operation noise from the gear pair rotation was drastically reduced to lower than about 10–15 dB compared to conventionally machined gear surfaces (30 dB in average), as a result of the wear of the tooth surface to form a best-fit profile. The noise increased with further processing of the gear pair. Thus, there is an appropriate number of rotations for suitable surface wear treatment. This new and simple procedure for surface treatment assures saving in energy, and does not require expensive honing techniques or high-accuracy grinding tools.The wear mechanisms used in this process are discussed along with the application of the technique to other processes for precision finishing.     

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.

     

Characteristics of transmission error and vibration of broken tooth contact

One of the most important research topics relating to the development of a vibration-based condition monitoring system for a gearbox is that of quantitative analysis and testing of the effect of gear tooth damage on gearbox vibration. This paper presents a finite element model of the Transmission error (TE) and its associated characteristics, together with experimental results of vibration of broken tooth contact in a spur gear. The two-dimensional finite element model is developed to analyze the TE of the spur gear, and the TE for both the normal contact and broken tooth contact state of the spur gear pair are analyzed. As a result, the developed FE model well represents the difference in the static TE for a single-tooth and double-tooth contact of the undamaged and damaged gear pair. The Peak-to-peak magnitude of the static TE of the full-tooth fractured gear pair is significantly higher than that of undamaged gear pair. While the Peak-to-peak TE (PPTE) of the damaged gear tooth increases with increasing load, the ratio of PPTE of the undamaged gear pair and the full-tooth fractured gear pair decreases exponentially with increasing load. This shows that, to determine the fault level of gearbox, it is necessary to carefully apply the condition indicator when analyzing the impulse character of a vibration signal.

     

一种摆线针轮传动多齿啮合接触特性分析方法

为有效地揭示齿廓修形、弹性接触及负载变化对摆线针轮传动多齿啮合接触动态特性的影响规律,基于多体动力学和弹性接触理论提出了一种可精确预估摆线针齿动态啮合对数、确定接触点位置并获取接触载荷的动力学分析方法。首先,建立了摆线针轮系统刚体多体动力学模型;其次,在数值计算的任一时刻,循环判断摆线齿廓的离散点与各个针齿之间是否满足接触条件,确定最大接触深度并计算法向接触载荷;最后,将摆线针齿接触载荷等效为系统广义力,建立了含多齿啮合接触关系的摆线针轮传动系统动力学方程。在此基础上,以某一针摆传动系统为算例,分析齿廓修形、弹性接触及负载变化对摆线针轮传动多齿啮合接触动态特性的影响。研究结果表明,摆线针轮传动的实际传力针齿数由齿廓修形和负载特性决定。该方法对于具有不同传动比的摆线针轮传动系统,均能高效准确地完成齿廓修形和负载变化条件下的传力针齿数预估和接触载荷计算。     

基于ADAMS多体动力学的轮齿动态载荷仿真分析

齿轮啮合过程中的轮齿动态载荷是齿轮研究领域的一个重要问题。文中介绍了直齿圆柱齿轮啮合传动特性以及ADAMS多体动力学分析中的接触碰撞模型;建立了基于ADAMS的直齿圆柱齿轮副多体动力学分析模型;通过动态仿真分析,获得齿轮啮合过程中的轮齿动态载荷历程,以及不同转速时轮齿的动载系数变化规律,为进一步研究直齿圆柱齿轮齿顶修形设计提供理论依据。     

汽车门锁闭锁器小模数齿轮副接触有限元分析

汽车门锁闭锁器中的塑料齿轮在节线附近容易发生断裂,设计时需校核其强度。首先在CAXA中建立齿轮副模型,之后运用接触有限元方法,借助Ansys12.0有限元分析软件研究了齿轮副在一个啮合周期内的接触应力及结点位移的分布。得出了以下结论:齿轮副最大接触应力和结点位移都发生在节点啮合时;最大接触应力小于大小齿轮接触强度的极限值;相邻两啮合位置的接触应力相差较大时说明在此两位置之间发生了单对轮齿与双对轮齿接触的变换;对于塑料齿轮来说,当啮合位置是从齿顶向节点方向变化的单齿啮合时,齿轮副的最大接触应力总体呈减少趋势。为汽车门锁闭锁器中齿轮的设计提供理论参考。     

圆弧齿轮齿面沿接触线是滚动与滑动并存的证明

经严格的数学与运动学论证,否定了圆弧齿轮经典著作中的一个基本观点：凸齿廓与凹齿廓之间沿接触线是纯滚动.并得出了正确结论：两齿面之间沿接触线的运动形式是滚动与滑动并存.通过对凸凹齿廓上两螺旋接触线的分析可知,齿轮副的两条接触线长度不相等,进而得到啮合点在接触线上的速度大小亦不相等,因而得出上述结论.依此定量之结论,便可合理解释圆弧齿轮传动中的一些物理现象：如油膜厚度大,齿面磨损均匀,跑合性良好等.     

点线啮合齿轮动态接触应力仿真分析与齿廓修形

针对DZLY180型硬齿面点线啮合齿轮减速器,利用SolidWorks建立其高速级齿轮副三维模型,采用Ansys Workbench对模型进行动态接触应力仿真分析,然后对其进行修形并重新建模、仿真,结果显示修形后点线啮合齿轮接触应力减小,啮入冲击得到明显改善。     

润滑和载荷状态对聚甲醛齿轮服役性能的影响

基于齿轮耐久性能试验台开展了一系列干接触/油润滑下POM(聚甲醛)-POM齿轮副承载能力试验,并测量了服役过程中的轮齿温度、磨损量、齿廓精度和齿面形貌。试验发现,POM齿轮失效形式与载荷和润滑方式有关。通过对齿面微观形貌和磨屑表征,确认干接触下POM齿轮主要磨损模式为黏着磨损与磨粒磨损,而油润滑下POM齿轮失效形式为接触疲劳失效。由于润滑油减少了齿面摩擦,降低了运行温度,延缓了齿面劣化程度,因此POM齿轮在油润滑下的承载能力明显提高。     

高重合度摆线内齿轮副时变啮合刚度计算与齿间载荷分配研究

高重合度摆线内齿轮副时变啮合刚度计算和齿间载荷分配是其动力学分析和强度设计的基础,由于是多齿啮合,齿间载荷分配非常复杂,属于静不定问题。结合现有文献,考虑了真实的过渡曲线和精确的轮齿建模,采用更为准确的齿面赫兹接触刚度计算方法,基于势能法建立了与摆线齿形相适应的单轮齿对啮合综合刚度模型,针对该齿轮副的传动特点,构建了其变形协调方程,提出了多齿啮合齿间载荷分配模型。为验证所建模型的正确性并提高仿真分析效率,在ABAQUS中利用Python脚本编程进行二次开发,实现了精确化建模、参数化分析和自动化操作,根据齿轮加载接触分析结果和基于有限元法的轮齿对受载啮合刚度计算方法,得到了不同负载转矩作用下单轮齿对、多轮齿对的啮合综合刚度和轮齿啮合力。对比表明,计算结果趋势吻合、数值接近,验证了建模分析的正确性,可为动力学分析和强度计算提供基础。     

Mathematical model and meshing analysis of internal meshing gear transmission with curve element

A new internal meshing gear transmission with curve element is put forward in this paper. The mathematical principle of tooth profile generation is described based on conjugate curves theory. For a given spatial curve, the meshing equation and its conjugated spatial curve under the motion law were derived. Considering the equidistant kinematic method, general internal tooth profiles models were established by the conjugate-curve pair. Numerical example of the internal gear pair was developed according to gear parameters and gear solid models were established by MATLAB and UG software. Motion simulation result shows that the gear pair satisfies point contact condition and design requirements. Meshing analysis of tooth profiles using FEA method was carried out. Stress analysis results of tooth profiles with single point contact and two points contact were, respectively, obtained. The conclusions lay the foundation for multi-point contact generation and tooth profile design. Also, further studies on transmission characteristics and manufacturing technology of the new gear drive will be carried out.

     

Modeling of helical gear contact with tooth deflection

The majority of gear tribological studies are made on spur gears. However, helical gears are generally used in industry, and their contact behavior deserves more attention to establish a realistic base for detailed friction, wear and life studies. This study focuses on the modeling of helical gear contact with tooth deflection. A calculation model for helical gear contact analysis is introduced. Helical gear surface profiles are constructed from gear tool geometry by simulating the hobbing process. The model uses three-dimensional finite elements for the calculation of tooth deflection including tooth bending, shearing and tooth foundation flexibility. The model combines contact analysis with structural analysis to avoid large meshes. Tooth foundation flexibility was found to have an essential role in contact load sharing between the meshing teeth, whereas contact flexibility plays only a minor role. The capability of different local contact calculation methods was also studied.     

矿用减速器斜齿轮副动态啮合仿真分析

利用大型有限元分析软件ANSYS建立了某矿用减速器变位斜齿轮副多齿对啮合的有限元非缌性接触分析模型.基于该模型,对齿轮副进行了在一定工况下的动态啮合仿真分析,得出瞬态啮合时轮齿的接触状态、接触应力、齿根弯曲应力以及主从动齿轮的转矩、转速随啮合位置变化的规律符合实际啮合规律,同时得到最恶接触位置,并在此位置进行了静态接触强度分析.分析结果表明,动态啮合仿真能够真实反映轮齿的接触状态、接触应力以及齿根弯曲应力的动态变化,静态接触分析进一步验证动态啮合分析的可靠性,也为疲劳寿命分析提供了依据.     

Tribological Study of Grease Lubricated Plastic Wormgear for Automotive Applications

Plastic wormgear has many application opportunities in automotive industry because of its low noise and lightweight properties. Three major concerns about plastic wormgear are bending strength, efficiency or friction, and wear. Since standard worm and wormgear designs are developed mainly for metal gears, they are not applicable for the design of plastic wormgear. This paper presented a non-standard design to increase the bending strength of plastic wormgear. By increasing gear contact ratio, the maximum contact stress on the plastic gear tooth was reduced to prevent wear of the plastic wormgear flank. The load, speed, and grease effects on gearbox efficiency and friction coefficient were experimentally studied. While load had a major effect on friction coefficient of grease lubricated plastic wormgear, the speed had much less influence on the friction coefficient of the plastic wormgear. Misalignment of the worm shaft had significant impact on the efficiency of the worm gearbox.     

Ease-off修形准双曲面齿轮齿面动态抗磨设计与分析

为了改善准双曲面齿轮动态性能、减小齿面磨损提出齿面动态抗磨修形设计与分析方法。小轮修形齿面表示为共轭齿面与法向Ease-off曲面两个矢量的和,Ease-off曲面通过预置抛物线修形参数及几何传动误差参数表达。提出考虑磨损深度影响的齿面承载接触分析（Tooth contact analysis with wear,WLTCA）数值方法,该方法通过承载接触分析（Tooth contactanalysis,LTCA）方法获得啮合刚度及齿面静载荷,在此基础上根据动力学分析获得齿面动载荷,结合Archard磨损公式进一步获得齿面磨损量,将齿形更新时的同时啮合齿对的磨损量叠加到齿对的初始间隙,为磨损后的LTCA计算提供准确的参数,重复以上循环可得到齿形更新后齿面上任一点的磨损深度及次数。以无磨损时法向相对振动加速度均方根最小、齿面磨损量最小进行修形优化获得最优Ease-off曲面;分析齿面磨损与系统动态响应之间的耦合作用。结果表明最优Ease-off齿面主要通过齿廓修形减少了磨损量,有效改善了系统动态响应。该方法充分考虑了齿面修形、磨损、动态响应的耦合性且计算效率较高,为高性能准双曲面齿轮齿面抗磨、减振设计与分析提供理论参考。     

Coefficient of friction of a starved lubricated spur gear pair

The frictional power loss issue of gear pairs becomes an important concern in both industry and academia due to the requirement of the energy saving and the improvement of power density of gear drives. A thermal starved elastohydrodynamic lubrication model is developed to study the tribological performance of a spur gear pair under starved lubrication conditions. The contact pressure, the film thickness, the temperature rise, the frictional power loss, as well as the coefficient of friction are evaluated by considering the variation of the curvature radius, the sliding/rolling motion, and the load distribution of gear tooth within the meshing period. Effects of lubrication starvation condition, load and speed on the coefficient of friction are studied.

     

Effect of variation of angular velocity in gear rolling process on profile error

In the gear generating method, such as the hobbing method; the variation of angular velocity becomes a cause of involute profile error. This study deals with the effect of the variation of angular velocity in gear rolling on the tooth profile error. The fluctuation of center distance is one of the phenomena in rolling. This phenomenon has not been clarified in relationship with the profile error. It is assumed that the fluctuation of center distance induces the variation of angular velocity. In this experiment, the steel belt was set between the tool and work gear, and the variation of angular velocity in rolling was detected as a change of the tension on the belt. The angular velocity between the tool and work gear varies slightly by the period of the normal pitch between contact teeth. In the next step, the effect of this variation of the tooth profile error was theoretically revealed.

The following results were obtained.

The variation of angular velocity is based on the rolled profile error. The amplitude of the variation corresponds to the difference of the amount of plastic deformation between the driven side and the follower side of the rolled tooth.     

Parametric modeling and contact analysis of helical gears with modifications

An approach for a mathematical model and contact analysis of helical gears including tip relief, root relief, end relief and longitudinal crowning modification was developed. First, tooth profile equations of non-modified involutes, tip reliefs, root reliefs and fillets were derived after applying gear principles and coordinate transformation to transverse cross section profiles of a rack cutter. Then the intersecting lines between different profiles were solved through by Gauss-Newton numerical method. Parametric modeling program of modified helical gears was obtained to automatically generate exact gear surfaces of tip reliefs, root reliefs, end reliefs and longitudinal crowning modifications via Matlab code. Subsequently, an example of helical gear pair in practical engineering was presented, and the solid model and finite element model with modification were established. Finally, the dynamic contact characteristic of helical gear pair was calculated by three-dimensional dynamic contact finite element method. It is expected that the proposed approach can be applied in analyzing the effect of modification on radiation noise prediction of gear system in further study.