EFFECT OF INVOLUTE CONTACT RATIO ON THE DYNAMIC PERFORMANCE OF SPUR GEAR WITH NOTOOTH PROFILE MODIFICATION

The effect of involute contact ratio on the torsional vibration behavior ofspur gear-pair is studied analytically through a mass-spring model. The tooth stiffness in model notonly has a relation with time, as many prior studies presented, but, more important, with involutecontact ratio (ICR) as well. The ICR embodies its impact on the spur gear's dynamic performancethrough changing the proportion of tooth stiffness when there are n+1 teeth in contact to toothstiffness when there are n teeth in contact. A couple of curves about impact of ICR on the gear'sdynamic performance are presented, and they clearly demonstrate that the model can accuratelydescribe the effects of ICR on dynamic transmission error. Finally, some conclusions useful toreduce vibration and noise of gear-pair are proposed.

STUDY ON THE LUBRICATION FACTOR OF INVOLUTE SPUR GEARS

Based on a lot of numerical solutions to the problems of the thermalnon-Newtonian elastohydrodynamic lubrication and some fatigue tests with rollers, the lubricationfactor of involute spur gears (called gear for short) is investigated. The results suggest that gearlubrication effects bear close relations to a dimensionless parameter D which is syntheticallydetermined by gearing rotational speed, load, material, dimension and lubricant viscosity. When D<=8, the gear fatigue life increases as the lubricant viscosity is increased; When D>8, however, thelife decreases with the viscosity addition, which is in marked contrast to the lubrication factorZ_L recommended by the International Standard for Computing Cylindrical Gear Strength. At the end, aset of formulae for calculating gear lubrication factors suitable for different working conditionsare advanced.

Effect of integral squeeze film damper on vibration and noise of spur gear with center-distance error

When the actual installation center distance between a pair of spur gears is greater than the theoretical center distance,backlash increases,leading to increased vibration and noise.The structural parameters of an integral squeeze film damper(ISFD)were designed with the stiffness of rigid support as reference to investigate the effect of an ISFD on the dynamic characteristics of a spur gear transmission system with center-distance installation error.A spur gear test bench with center distance-error was built to investigate the vibration and noise reduction characteristics of ISFD.The experimental results indicate that,compared with a rigid support,the ISFD can reduce vibration by approximately 40%and noise by approximately 5 d B.ISFD can effectively absorb the impact energy caused by an increase of in backlash,which is conducive to the stable operation of the spur gear transmission system.

Topological Modeling of a One Stage Spur Gear Transmission

Finding a basis of unification for the modeling of mechatronic systems is the search subject of several works.This paper is a part of a general research designed to the application of topology as a new approach for the modeling of mechatronic systems.Particularly,the modeling of a one stage spur gear transmission using a topological approach is tackled.This approach is based on the concepts of topological collections and transformations and implemented using the MGS（modeling of general systems）language.The topological collections are used to specify the interconnection laws of the one stage spur gear transmission and the transformations are used to specify the local behavior laws of its different components.In order to validate this approach,simulation results are presented and compared with those obtained with MODELICA language using Dymola solver.Since good results are achieved,this approach might be used as a basis of unification for the modeling of mechatronic systems.

Numerical and experimental study on new cold precision forging technique of spur gears

A new cold precision forging technique is proposed to form a spur gear from a hollow billet, that is blocking the divided flow region and then final forging by the relief hole. 3D FEM simulation of the whole process of a pure aluminium spur gear is performed using DEFORM 3D TM . The load stroke curve, effective stress distribution, effective strain distribution, velocity distribution, and so on, are achieved. These results are compared with those achieved using the conventional closed die forging in the same conditions. The results show that this new technique has many advantages over the conventional one. The deformation load is reduced by near 30% and the filling ability of the tooth profile is also improved. Precision forging experiments of spur gears with the new process were performed using material Pb. The experimental results show a good agreement with the numerical results.

Application of response surface method for contact fatigue reliability analysis of spur gear with consideration of EHL

In order to consider the effects of elastohydrodynamic lubrication(EHL) on contact fatigue reliability of spur gear, an accurate and efficient method that combines with response surface method(RSM) and first order second moment method(FOSM) was developed for estimating the contact fatigue reliability of spur gear under EHL. The mechanical model of contact stress analysis of spur gear under EHL was established, in which the oil film pressure was mapped into hertz contact zone. Considering the randomness of EHL, material properties and fatigue strength correction factors, the proposed method was used to analyze the contact fatigue reliability of spur gear under EHL. Compared with the results of 1.5×105 by traditional Monte-Carlo, the difference between the two failure probability results calculated by the above mentioned methods is 2.2×10-4, the relative error of the failure probability results is 26.8%, and time-consuming only accounts for 0.14% of the traditional Monte-Carlo method(MCM). Sensitivity analysis results are in very good agreement with practical cognition. Analysis results show that the proposed method is precise and efficient, and could correctly reflect the influence of EHL on contact fatigue reliability of spur gear.

An intelligent method for contact fatigue reliability analysis of spur gear under EHL

To complete the contact fatigue reliability analysis of spur gear under elastohydrodynamic lubrication(EHL) efficiently and accurately, an intelligent method is proposed. Oil film pressure is approximated using quadratic polynomial with intercrossing term and then mapped into the Hertz contact zone. Considering the randomness of the EHL, material properties and fatigue strength correction factors, the probabilistic reliability analysis model is established using artificial neural network(ANN). Genetic algorithm(GA) is employed to search the minimum reliability index and the design point by introducing an adjusting factor in penalty function. Reliability sensitivity analysis is completed based on the advanced first order second moment(AFOSM). Numerical example shows that the established probabilistic reliability analysis model could correctly reflect the effect of EHL on contact fatigue of spur gear, and the proposed intelligent method has an excellent global search capability as well as a highly efficient computing performance compared with the traditional Monte Carlo method(MCM).

Profile Modification for Increasing the Tooth Strength in Spur Gear Using CAD

This paper examines the tooth failure in spur gears. Corrective measures are taken to avoid tooth damage by introducing profile modification in root fillet. In general, spur gear with less than 17 numbers of teeth had the problem of undercutting during gear manufacturing process which minimizes the strength of gear at root. In this study, a novel design method, namely circular root fillet instead of the standard trochoidal root fillet is introduced in spur gear and analyzed using ANSYS version 11.0 software. The strength of these modified teeth is studied in comparison with the standard design. The analysis demonstrates that the novel design exhibit higher bending strength over the standard trochoidal root fillet gear. The result reveals that the circular root fillet design is particularly suitable for lesser number of teeth in pinion and where as the trochoidal root fillet gear is more opt for higher number of teeth.

Controlling Flow Instability in Straight Spur Gear Forging Using Numerical Simulation and Response Surface Method

Workability domain without the onset of flow instability was developed by numerical simulation and response surface method （RSM） for complex-shaped straight spur gear forging. The processing map of AZ31B alloys was calculated from flow stress curves and then integrated with the finite element model to simulate the distribution of flow instability in the straight spur gear undergoing isothermal forging process. Occurrence of flow instability depends on forging temperature, punch velocity and billet reduction. Taking forging temperature and punch velocity as design variables, while billet reduction as response variable, RSM of workability domain was established. Analysis of variance indicates that forging temperature is the most significant factor determining the appearance of flow instability in the forged gear. Flow instability is easier to take place at lower temperatures of 250 and 300 ℃ in the early stage of forging but at higher temperatures of 350 and 400 ℃ in the later stage of forging, which is attributed to different deformation mechanisms and dynamic recrystallization behaviors at different temperatures or deformation levels. Meanwhile, increasing punch velocity further reduces the workability of the forged gear. Four different processing paths were chosen to carry out the gear forging trials. Visual observations and metallographic examinations demonstrate that the developed workability domain contributes to optimization of forging parameters.

Two Step Forging Process of Spur Gear Based on Rigid Parallel Motion

To improve the forging process of spur gear,the metal flow rule is investigated in detail,and a hypothesis of radial rigid-parallel-motive (RPM) flow mode is given. Based on the RPM mode a novel specific gear forging technology is put forward by introduced upend forging process and constrained divided-flow technique. Firstly,finite element method is used to simulate the upend forging pre-forming and RPM finish forging,and equivalent stress field and load-stroke curve are investigated. Secondly,a corresponding experiment is carried out with pure lead to validate the numerical simulation. Thirdly,the peak value of conventional forging process is also simulated and is used to compare with the novel forging process,and the result shows that the forming force decreases significantly,about 35%. Finally,the effect on forming load of two key process parameters (the height of gear tooth after pre-forming and friction factor) is analyzed,and the superiority of the novel forging process is further proved.

Investigation on meshing and dynamic characteristics of spur gears with tip relief under wear fault

Combining the loaded tooth contact analysis(LTCA)method and the gear dynamic model,a wear prediction model for spur gears with tip relief is established.The simulated wear depth is verified by the experimental results in a published reference.Based on the wear profile,the mesh stiffness and the tooth root stress obtained from the proposed model are compared with those obtained from the finite element model.Relative to the finite element method,the proposed method can greatly reduce the computation time.The effects of the tip relief and surface wear on the meshing and the dynamic characteristics are discussed.The tip relief can greatly decelerate the surface wear.Appropriate tip relief and slight wear can decrease the tooth interference and reduce the system vibration.Furthermore,the effects of the rotational speed on the wear depth are also studied and it is found that the quasi-static model is applicable to wear prediction when the rotational speed is away from the harmonic resonance peak.

Effect of key factors on cold orbital forging of a spur bevel gear

Cold orbital forging is an advanced spur bevel gear forming technology. Generally, the spur bevel gear in the cold orbital forging process is formed by two steps: the preforming step and the final step. Due to the great importance of the final step to gear forming and its complication with interactive factors, this work aims at examining the influence of key factors on the final step in cold orbital forging of a spur bevel gear. Using the finite element(FE) method and control variate method, the influence rules of four key factors, rotation velocity of the upper tool, n, feeding velocity of the lower tool, v, tilted angle of the upper tool, γ, friction factor between the tools and the billet, m, on the geometry and the deformation inhomogeneity of the cold orbital forged gear are thoroughly clarified. The research results show that the flash becomes more homogeneous with increasing v, increasing m, decreasing n or decreasing γ. And the deformation of the gear becomes more homogeneous with increasing v, decreasing n or decreasing γ. Finally, a corresponding experiment is conducted, which verifies the accuracy of FE simulation conclusions.

高重合度直齿圆柱齿轮温度场分析及试验验证

直升机传动系统中的高重合度直齿圆柱齿轮多采用喷油方式进行润滑冷却,其温度特性关系到齿轮的使用寿命。基于计算流体力学(Computational Fluid Dynamics,CFD),建立了高重合度直齿圆柱齿轮喷油润滑温度场数值计算模型;采用气液两相流(Volume of Fluid,VOF)、多重参考系(Multiple Reference Frame,MRF)法获得了齿轮表面的温度和对流换热系数大小及分布;使用控制变量法分析了润滑油参数、工况参数、齿轮参数对齿面温度及对流换热的影响规律;在CL-100型齿轮试验机上开展了齿轮温度试验。结果表明,齿轮温度随载荷增加而升高的趋势与CFD仿真计算结果一致,高重合度齿轮温度高于普通重合度齿轮,而且随着载荷的增大,这种现象越明显。

正交面齿轮传动的两类界线

为了建立系统的正交面齿轮传动啮合界线与曲率干涉界线理论,本文通过求解非线方程组获得了两类界线的数值解。证明了啮合界线在小轮齿面上是渐开线;其共轭线也是渐开线。发现干涉界线一般有2条,近齿面干涉界线存在于面齿轮内端附近,大致沿齿高走向。近齿面干涉界点存在平凡解,是干涉界线和啮合界线共轭线的交点,位于传动副瞬时相对转动轴上。基于近齿面干涉界线,建立了面齿轮无根切内径公式,通过数值迭代可以获得内径准确值;还导出了无根切内径估算公式,便于设计中应用。

小模数直齿轮免参数并行快速测量

小模数齿轮在实际制造中,单条产线多台设备通常同时生产多种不同参数的齿轮,迄今无法用单台齿轮测量仪器在生产线上同时实时全检这些不同参数的齿轮。开发了基于Facet的齿轮亚像素边缘定位算法、基于迭代重加权最小二乘的齿轮中心定位法、圆与齿廓交点快速定位法、正弦函数拟合齿数法和齿廓近似测压力角法等;若结合适当的送料与定位机构,本文方法能够在未知参数时,实现多种不同型号齿轮的混合测量,无需装夹,测量效率高。可以实现齿数、模数、压力角、齿顶圆直径、齿根圆直径、全齿高、齿宽、公法线变动量、变位系数、齿廓偏差和形位误差的测量。实验结果表明:该方法测量0.5~1.0 mm模数的直齿轮的重复性精度为4μm。该方法在小模数齿轮柔性化生产线具有重要应用前景。

一种直齿锥齿轮啮合检测工装设计以及啮合分析

设计这个工装的起因源于对于锥齿轮装配间隙的测量。直齿锥齿轮加工件单件检测有许多的检测项目,例如,齿形检测、公法线长度、齿厚、齿高、等等,但是对于另一些描述齿轮啮合的检测项目,没有办法通过单件检测进行测量,必须对锥齿轮进行配对后才能进行检查。所以,为了满足直齿锥齿轮在正式装配前的配对检测需要,我们需要设计一种简单易操作的齿轮啮合的检测工装,再配合一定的检测方法就可以对齿面啮合情况做出判断,例如齿面啮合的侧隙、齿顶间隙、接触斑点等等。

正交直齿面齿轮车齿刀具精确设计方法

为提高正交直齿面齿轮的加工精度,提出了一种针对正交直齿面齿轮的车齿刀具精确设计方法。基于齿轮交错轴啮合原理,对面齿轮的车齿加工过程进行解析;通过与面齿轮啮合的圆柱齿轮渐开线齿廓,包络出车齿刀齿面方程;基于法向平面,设计了刀具结构并推导了刀具切削刃表达式;求解切削刃与面齿轮的啮合条件式,推导数控加工规律并对面齿轮齿面进行了理论计算与仿真加工;将结果与面齿轮理论齿面进行了数值对比。结果表明,当刀具不存在误差时,可以得到面齿轮理论齿面;通过Vericut仿真,齿面误差保持在10 μm以内。

Nonlinear Dynamic Analysis of Coupled Gear-Rotor-Bearing System with the Effect of Internal and External Excitations

Extensive studies on nonlinear dynamics of gear systems with internal excitation or external excitation respectively have been carried out. However, the nonlinear characteristics of gear systems under combined internal and external excitations are scarcely investigated. An eight-degree-of-freedom（8-DOF） nonlinear spur gear-rotor-bearing model, which contains backlash, transmission error, eccentricity, gravity and input/output torque, is established, and the coupled lateral-torsional vibration characteristics are studied. Based on the equations of motion, the coupled spur gear-rotor-bearing system（SGRBS） is investigated using the Runge-Kutta numerical method, and the effects of rotational speed, error fluctuation and load fluctuation on the dynamic responses are explored. The results show that a diverse range of nonlinear dynamic characteristics such as periodic motion, quasi-periodic motion, chaotic behaviors and impacts exhibited in the system are strongly attributed to the interaction between internal and external excitations. Significantly, the changing rotational speed could effectively control the vibration of the system. Vibration level increases with the increasing error fluctuation. Whereas the load fluctuation has an influence on the nonlinear dynamic characteristics and the increasing excitation force amplitude makes the vibration amplitude increase, the chaotic motion may be restricted. The proposed model and numerical results can be used for diagnosis of faults and vibration control of practical SGRBS.

基于改进分形方法的齿面磨损故障直齿轮啮合特性分析

考虑实际的轮齿表面微观形貌,建立了轮齿间相互作用的三维分形接触模型。结合轮齿承载接触分析方法,考虑轮齿间摩擦力的影响,建立了直齿轮副的时变啮合刚度模型,并通过有限元方法进行了验证。结合Archard磨损模型,考虑齿面粗糙度和摩擦力的影响,分析了齿面磨损故障状态下直齿轮副的啮合特性和磨损深度,同时分析了摩擦力和分形参数对时变啮合刚度和磨损深度的影响。摩擦力导致节线处的时变啮合刚度发生突变。当直齿轮副处于双齿啮合时,摩擦因数的增加和分形维数的降低导致磨损深度的增加和时变啮合刚度的降低。时变啮合刚度随分形维数的变化呈线性变化。分形维数对时变啮合刚度和磨损深度的影响随着磨损周期的增加更为明显,超过了摩擦因数对其的影响。

低滑动率摆线正齿轮啮合特性与疲劳寿命研究

为提高齿轮的传动性能,基于啮合线原理提出了一种低滑动率摆线正齿轮。首先通过齿轮啮合原理推导出摆线正齿轮齿廓与过渡曲线方程;然后基于齿廓参数与重合度公式计算得出其最大重合度为3.0134;最后分析了摆线正齿轮啮合过程中的稳定性、接触应力和疲劳寿命。结果表明,高重合度摆线齿轮齿间切向啮合力为1238.2 N,与相同工况下的渐开线标准齿轮相比,减小了5.24%;通过疲劳寿命分析可知,最小疲劳寿命为4.534×10^(6)次,齿面接触应力主要集中在齿轮啮合位置以及齿根部位,因此疲劳破坏易发生于主动轮与从动轮啮合处以及齿根部位。