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 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.

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.

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).

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.

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.

Effects of forging parameters on uniformity in deformation and microstructure of AZ31B straight spur gear

The effects of forging parameters on the deformation and microstructure distributions of as-forged straight spur gears wereinvestigated by finite element(FE)simulation and statistical analysis method.Spur gear forging using the movable cavity die designwas investigated by integrating the FE method with the microstructure evolution models for AZ31B magnesium alloys.The requiredinputs such as flow stress curves and microstructure evolution models,were obtained through the Gleeble thermal mechanical testingand quantitative metallography analysis method.Numerical simulation and experimental examination confirm that both thedeformation and microstructure are non-uniformly distributed in the as-forged gears.Decreasing deformation temperature orincreasing strain rate is beneficial to obtaining fine-grained microstructure but is harmful to the uniformity in deformation ormicrostructure.The level of the non-uniformity results from the complex shape of gear and the friction between the billet and dies,which is closely associated with the characteristics of flow stress curve.

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.

航空圆柱直齿轮热摆辗成形工艺分析

为研究航空圆柱直齿轮热摆辗成形过程中金属变形规律和齿形充填特点,利用DEFORM-3D软件建立了圆柱直齿轮热摆辗成形三维刚塑性有限元模型,模拟了其热摆辗成形过程。结果表明,圆柱直齿轮热摆辗成形过程中,坯料变形区分为主动变形区和被动变形区,并随着摆头的运动而呈周期性变化;随着变形的进行,主动变形区金属流动方向从径向转变为轴向充填模具型腔,齿形从上端到下端逐渐成形,坯料呈蘑菇状;齿根区域等效应变与等效应力值最大,齿顶温度高于齿根温度;轴向载荷随塑性变形的进行逐渐增大,最大值约为2500 kN,径向载荷呈周期性变化,径向载荷远小于轴向载荷。开展了圆柱直齿轮热摆辗工艺实验,实验结果与模拟结果吻合。

大重合度直齿轮动载特性分析

针对大重合度直齿轮啮合齿数与普通直齿轮间的差异性变化,以一对大重合度直齿轮和普通直齿轮为研究对象,通过有限元法求解齿轮时变啮合刚度,建立大重合度直齿轮啮合耦合型动力学模型,利用Newmark-β时域积分求解齿轮系统动态响应,对其进行时频域分析并与普通直齿轮进行对比,获得了大重合度直齿轮在不同转速、误差影响下的动载系数变化规律。结果表明,大重合度直齿轮啮合刚度与普通齿轮有较大差异,其动态响应结果波动幅值较普通直齿轮有明显降低,提升了系统稳定性;大重合度直齿轮动载系数与普通直齿轮相比有明显下降,并且随着转速的升高和误差的增大出现不同程度的增加,其中在共振转速区域范围内增幅明显。

裂纹故障下细高齿齿轮齿根动应变研究

为探究裂纹故障对细高齿齿轮齿根动应变的影响规律,采用集中质量法建立齿轮系统动力学模型,将故障下的时变啮合刚度作为输入,对系统动力学方程进行求解得到不同裂纹深度下的齿轮副动态啮合力。利用有限元法建立含裂纹故障齿轮结构动力学分析模型,结合轮齿承载接触分析确定裂纹故障下的齿间载荷分配关系,采用瞬态分析得到齿根应变时域历程,并对不同裂纹深度下的齿根动应变进行分析。仿真结果表明,当从动轮发生裂纹故障后,其齿根动应变故障特征主要表现为啮合区内齿根应变数值的变化,主动轮齿根动应变故障特征主要表现为齿根应变时域历程中出现周期性冲击及幅值衰减,在1.5 mm裂纹深度下主动轮齿根应变峰值因子相对变化量达到12.72%。

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。

齿面点蚀对直齿轮副时变啮合刚度及振动响应的影响分析

齿面点蚀作为齿轮传动中最常见的故障之一,它的存在直接影响齿轮副的时变啮合刚度(time-varying meshing stiffness, TVMS),进而导致系统动态特性的改变。鉴于此,将每个点蚀形状近似地视为椭圆柱的一部分,根据点蚀的分布位置和数量定义了三种损伤级别:轻度点蚀、中度点蚀和重度点蚀。基于势能法计算并比较了无故障齿轮和含有不同程度点蚀齿轮的TVMS,讨论了点蚀位置和点蚀尺寸对TVMS的影响。研究了单级直齿圆柱齿轮传动系统的故障动态特性,并利用动力传动故障诊断综合试验台对理论结果进行了定性验证。结果表明,该研究中的齿面点蚀模型与实际点蚀形貌更接近。随着点蚀位置参数的增大,点蚀区域由基圆逐渐向齿顶圆方向移动;点蚀长轴长越长,点蚀区域内TVMS的减小量越明显;在相同的主动轮角位移变化范围内,随着短轴长的变化,不同程度的点蚀故障引起的啮合刚度的减小量是相同的。所建模型能够预测齿轮系统的啮合刚度及振动行为,相应的振动分析结果为齿面点蚀故障的检测和诊断提供了理论参考。

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。

基于ADAMS GearAT直齿轮接触特性研究

为了获得传动特性优良、疲劳寿命长的齿轮传动系统,以某直齿轮为研究对象,建立其三维模型,导入ADAMS GearAT建立直齿轮接触特性有限元仿真模型,对等效应力、等效弹性应变及接触应力等接触特性进行仿真分析。仿真结果表明:等效应力及弹等效性应变主要分布在主、从动齿轮接触部分及其附近,且最大等效应力满足齿轮传动静动态工况需求;动齿轮接触面等效应力及等效弹性应变大小及其分布存在差异;接触面接触应力在齿宽方向呈现先减小后增加的趋势;在接触线宽度方向上呈现先增加后减小的趋势,整体接触面接触应力在不同齿宽及接触线宽度方向上存在一定的波动。该研究为齿轮传动系统综合传动性能的提高、接触及疲劳寿命的提升提供理论依据。